%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW100+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:36:33 AM UTC 2025
% Result : Theorem 163.48s 163.74s
% Output : Proof 163.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW100+1 : TPTP v9.0.0. Released v5.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 11:14:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 163.48/163.74 % SZS status Theorem
% 163.48/163.74 % SZS output start Proof
% 163.48/163.74 tff(d_type, type, (
% 163.48/163.74 d: $i > $o)).
% 163.48/163.74 tff(impl_type, type, (
% 163.48/163.74 impl: ( $i * $i ) > $i)).
% 163.48/163.74 tff(lazy_impl_type, type, (
% 163.48/163.74 lazy_impl: ( $i * $i ) > $i)).
% 163.48/163.74 tff(phi_type, type, (
% 163.48/163.74 phi: $i > $i)).
% 163.48/163.74 tff(f6_type, type, (
% 163.48/163.74 f6: ( $i * $i ) > $i)).
% 163.48/163.74 tff(tptp_fun_R_5_type, type, (
% 163.48/163.74 tptp_fun_R_5: $i > $i)).
% 163.48/163.74 tff(tptp_fun_P_7_type, type, (
% 163.48/163.74 tptp_fun_P_7: $i)).
% 163.48/163.74 tff(prop_type, type, (
% 163.48/163.74 prop: $i > $i)).
% 163.48/163.74 tff(apply_type, type, (
% 163.48/163.74 apply: ( $i * $i ) > $i)).
% 163.48/163.74 tff(tptp_fun_X_4_type, type, (
% 163.48/163.74 tptp_fun_X_4: ( $i * $i ) > $i)).
% 163.48/163.74 tff(f4_type, type, (
% 163.48/163.74 f4: ( $i * $i * $i ) > $i)).
% 163.48/163.74 tff(false_type, type, (
% 163.48/163.74 false: $i)).
% 163.48/163.74 tff(f5_type, type, (
% 163.48/163.74 f5: ( $i * $i ) > $i)).
% 163.48/163.74 tff(true_type, type, (
% 163.48/163.74 true: $i)).
% 163.48/163.74 tff(bool_type, type, (
% 163.48/163.74 bool: $i > $o)).
% 163.48/163.74 tff(not1_type, type, (
% 163.48/163.74 not1: $i > $i)).
% 163.48/163.74 tff(err_type, type, (
% 163.48/163.74 err: $i)).
% 163.48/163.74 tff(forallprefers_type, type, (
% 163.48/163.74 forallprefers: ( $i * $i ) > $o)).
% 163.48/163.74 tff(false2_type, type, (
% 163.48/163.74 false2: $i)).
% 163.48/163.74 tff(f7_type, type, (
% 163.48/163.74 f7: $i > $i)).
% 163.48/163.74 tff(tptp_fun_P_6_type, type, (
% 163.48/163.74 tptp_fun_P_6: $i)).
% 163.48/163.74 tff(f1_type, type, (
% 163.48/163.74 f1: ( $i * $i * $i ) > $i)).
% 163.48/163.74 tff(tptp_fun_R_0_type, type, (
% 163.48/163.74 tptp_fun_R_0: ( $i * $i ) > $i)).
% 163.48/163.74 tff(and2_type, type, (
% 163.48/163.74 and2: ( $i * $i ) > $i)).
% 163.48/163.74 tff(tptp_fun_X_3_type, type, (
% 163.48/163.74 tptp_fun_X_3: $i > $i)).
% 163.48/163.74 tff(exists2_type, type, (
% 163.48/163.74 exists2: $i > $i)).
% 163.48/163.74 tff(exists1_type, type, (
% 163.48/163.74 exists1: $i > $i)).
% 163.48/163.74 tff(existsprefers_type, type, (
% 163.48/163.74 existsprefers: ( $i * $i ) > $o)).
% 163.48/163.74 tff(f2_type, type, (
% 163.48/163.74 f2: ( $i * $i * $i ) > $i)).
% 163.48/163.74 tff(1,plain,
% 163.48/163.74 (^[P: $i, X: $i, R: $i] : refl((f4(P, X, R) = impl(apply(P, X), R)) <=> (f4(P, X, R) = impl(apply(P, X), R)))),
% 163.48/163.74 inference(bind,[status(th)],[])).
% 163.48/163.74 tff(2,plain,
% 163.48/163.74 (![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R)) <=> ![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))),
% 163.48/163.74 inference(quant_intro,[status(thm)],[1])).
% 163.48/163.74 tff(3,plain,
% 163.48/163.74 (![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R)) <=> ![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))),
% 163.48/163.74 inference(rewrite,[status(thm)],[])).
% 163.48/163.74 tff(4,axiom,(![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','def_f4')).
% 163.48/163.74 tff(5,plain,
% 163.48/163.74 (![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[4, 3])).
% 163.48/163.74 tff(6,plain,(
% 163.48/163.74 ![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))),
% 163.48/163.74 inference(skolemize,[status(sab)],[5])).
% 163.48/163.74 tff(7,plain,
% 163.48/163.74 (![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[6, 2])).
% 163.48/163.74 tff(8,plain,
% 163.48/163.74 ((~![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))) | (f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.48/163.74 inference(quant_inst,[status(thm)],[])).
% 163.48/163.74 tff(9,plain,
% 163.48/163.74 (f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.48/163.74 inference(unit_resolution,[status(thm)],[8, 7])).
% 163.48/163.74 tff(10,plain,
% 163.48/163.74 (impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.48/163.74 inference(symmetry,[status(thm)],[9])).
% 163.48/163.74 tff(11,plain,
% 163.48/163.74 (d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> d(f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.48/163.74 inference(monotonicity,[status(thm)],[10])).
% 163.48/163.74 tff(12,plain,
% 163.48/163.74 (d(f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.48/163.74 inference(symmetry,[status(thm)],[11])).
% 163.48/163.74 tff(13,plain,
% 163.48/163.74 (^[X: $i] : refl(((prop(X) = true) <=> bool(X)) <=> ((prop(X) = true) <=> bool(X)))),
% 163.48/163.74 inference(bind,[status(th)],[])).
% 163.48/163.74 tff(14,plain,
% 163.48/163.74 (![X: $i] : ((prop(X) = true) <=> bool(X)) <=> ![X: $i] : ((prop(X) = true) <=> bool(X))),
% 163.48/163.74 inference(quant_intro,[status(thm)],[13])).
% 163.48/163.74 tff(15,plain,
% 163.48/163.74 (![X: $i] : ((prop(X) = true) <=> bool(X)) <=> ![X: $i] : ((prop(X) = true) <=> bool(X))),
% 163.48/163.74 inference(rewrite,[status(thm)],[])).
% 163.48/163.74 tff(16,axiom,(![X: $i] : ((prop(X) = true) <=> bool(X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','prop_true')).
% 163.48/163.74 tff(17,plain,
% 163.48/163.74 (![X: $i] : ((prop(X) = true) <=> bool(X))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[16, 15])).
% 163.48/163.74 tff(18,plain,(
% 163.48/163.74 ![X: $i] : ((prop(X) = true) <=> bool(X))),
% 163.48/163.74 inference(skolemize,[status(sab)],[17])).
% 163.48/163.74 tff(19,plain,
% 163.48/163.74 (![X: $i] : ((prop(X) = true) <=> bool(X))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[18, 14])).
% 163.48/163.74 tff(20,plain,
% 163.48/163.74 ((~![X: $i] : ((prop(X) = true) <=> bool(X))) | ((prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true) <=> bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.48/163.74 inference(quant_inst,[status(thm)],[])).
% 163.48/163.74 tff(21,plain,
% 163.48/163.74 ((prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true) <=> bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.48/163.74 inference(unit_resolution,[status(thm)],[20, 19])).
% 163.48/163.74 tff(22,assumption,(lazy_impl(prop(false), impl(f5(P!7, false), false)) = true), introduced(assumption)).
% 163.48/163.74 tff(23,plain,
% 163.48/163.74 (d(false) <=> d(false)),
% 163.48/163.74 inference(rewrite,[status(thm)],[])).
% 163.48/163.74 tff(24,axiom,((d(true) & d(false)) & d(err)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','false_true_err_in_d')).
% 163.48/163.74 tff(25,plain,
% 163.48/163.74 (d(true) & d(false)),
% 163.48/163.74 inference(and_elim,[status(thm)],[24])).
% 163.48/163.74 tff(26,plain,
% 163.48/163.74 (d(false)),
% 163.48/163.74 inference(and_elim,[status(thm)],[25])).
% 163.48/163.74 tff(27,plain,
% 163.48/163.74 (d(false)),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[26, 23])).
% 163.48/163.74 tff(28,plain,
% 163.48/163.74 ((d(false) | (~(phi(false) = err))) | (~d(false))),
% 163.48/163.74 inference(tautology,[status(thm)],[])).
% 163.48/163.74 tff(29,plain,
% 163.48/163.74 (d(false) | (~(phi(false) = err))),
% 163.48/163.74 inference(unit_resolution,[status(thm)],[28, 27])).
% 163.48/163.74 tff(30,plain,
% 163.48/163.74 (^[X: $i] : refl(((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))) <=> ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))))),
% 163.48/163.74 inference(bind,[status(th)],[])).
% 163.48/163.74 tff(31,plain,
% 163.48/163.74 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))) <=> ![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 163.48/163.74 inference(quant_intro,[status(thm)],[30])).
% 163.48/163.74 tff(32,plain,
% 163.48/163.74 (^[X: $i] : trans(monotonicity(rewrite((d(X) & (phi(X) = X)) <=> (~((~d(X)) | (~(phi(X) = X))))), rewrite(((~d(X)) & (phi(X) = err)) <=> (~(d(X) | (~(phi(X) = err))))), (((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))))), rewrite(((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))) <=> ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))), (((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))))),
% 163.48/163.74 inference(bind,[status(th)],[])).
% 163.48/163.74 tff(33,plain,
% 163.48/163.74 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 163.48/163.74 inference(quant_intro,[status(thm)],[32])).
% 163.48/163.74 tff(34,plain,
% 163.48/163.74 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 163.48/163.74 inference(rewrite,[status(thm)],[])).
% 163.48/163.74 tff(35,axiom,(![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','def_phi')).
% 163.48/163.74 tff(36,plain,
% 163.48/163.74 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[35, 34])).
% 163.48/163.74 tff(37,plain,(
% 163.48/163.74 ![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 163.48/163.74 inference(skolemize,[status(sab)],[36])).
% 163.48/163.74 tff(38,plain,
% 163.48/163.74 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[37, 33])).
% 163.48/163.74 tff(39,plain,
% 163.48/163.74 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[38, 31])).
% 163.48/163.74 tff(40,plain,
% 163.48/163.74 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(false)) | (~(phi(false) = false)))) | (~(d(false) | (~(phi(false) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(false)) | (~(phi(false) = false)))) | (~(d(false) | (~(phi(false) = err)))))),
% 163.48/163.74 inference(rewrite,[status(thm)],[])).
% 163.48/163.74 tff(41,plain,
% 163.48/163.74 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(false)) | (~(phi(false) = false)))) | (~(d(false) | (~(phi(false) = err)))))),
% 163.48/163.74 inference(quant_inst,[status(thm)],[])).
% 163.48/163.74 tff(42,plain,
% 163.48/163.74 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(false)) | (~(phi(false) = false)))) | (~(d(false) | (~(phi(false) = err))))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[41, 40])).
% 163.48/163.74 tff(43,plain,
% 163.48/163.74 (~((~d(false)) | (~(phi(false) = false)))),
% 163.48/163.74 inference(unit_resolution,[status(thm)],[42, 39, 29])).
% 163.48/163.74 tff(44,plain,
% 163.48/163.74 (((~d(false)) | (~(phi(false) = false))) | (phi(false) = false)),
% 163.48/163.74 inference(tautology,[status(thm)],[])).
% 163.48/163.74 tff(45,plain,
% 163.48/163.74 (phi(false) = false),
% 163.48/163.74 inference(unit_resolution,[status(thm)],[44, 43])).
% 163.48/163.74 tff(46,plain,
% 163.48/163.74 ((not1(false) = true) <=> (not1(false) = true)),
% 163.48/163.74 inference(rewrite,[status(thm)],[])).
% 163.48/163.74 tff(47,axiom,(not1(false) = true), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','not1_axiom2')).
% 163.48/163.74 tff(48,plain,
% 163.48/163.74 (not1(false) = true),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[47, 46])).
% 163.48/163.74 tff(49,plain,
% 163.48/163.74 ((not1(false) = phi(false)) <=> (true = false)),
% 163.48/163.74 inference(monotonicity,[status(thm)],[48, 45])).
% 163.48/163.74 tff(50,plain,
% 163.48/163.74 ((true = false) <=> (not1(false) = phi(false))),
% 163.48/163.74 inference(symmetry,[status(thm)],[49])).
% 163.48/163.74 tff(51,plain,
% 163.48/163.74 ((~(true = false)) <=> (~(not1(false) = phi(false)))),
% 163.48/163.74 inference(monotonicity,[status(thm)],[50])).
% 163.48/163.74 tff(52,plain,
% 163.48/163.74 ((~(true = false)) <=> (~(true = false))),
% 163.48/163.74 inference(rewrite,[status(thm)],[])).
% 163.48/163.74 tff(53,axiom,(((~(true = false)) & (~(true = err))) & (~(false = err))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','distinct_false_true_err')).
% 163.48/163.74 tff(54,plain,
% 163.48/163.74 ((~(true = false)) & (~(true = err))),
% 163.48/163.74 inference(and_elim,[status(thm)],[53])).
% 163.48/163.74 tff(55,plain,
% 163.48/163.74 (~(true = false)),
% 163.48/163.74 inference(and_elim,[status(thm)],[54])).
% 163.48/163.74 tff(56,plain,
% 163.48/163.74 (~(true = false)),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[55, 52])).
% 163.48/163.74 tff(57,plain,
% 163.48/163.74 (~(not1(false) = phi(false))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[56, 51])).
% 163.48/163.74 tff(58,plain,
% 163.48/163.74 (^[A: $i] : refl((bool(A) | (not1(A) = phi(A))) <=> (bool(A) | (not1(A) = phi(A))))),
% 163.48/163.74 inference(bind,[status(th)],[])).
% 163.48/163.74 tff(59,plain,
% 163.48/163.74 (![A: $i] : (bool(A) | (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 163.48/163.74 inference(quant_intro,[status(thm)],[58])).
% 163.48/163.74 tff(60,plain,
% 163.48/163.74 (![A: $i] : (bool(A) | (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 163.48/163.74 inference(rewrite,[status(thm)],[])).
% 163.48/163.74 tff(61,plain,
% 163.48/163.74 (^[A: $i] : rewrite(((~bool(A)) => (not1(A) = phi(A))) <=> (bool(A) | (not1(A) = phi(A))))),
% 163.48/163.74 inference(bind,[status(th)],[])).
% 163.48/163.74 tff(62,plain,
% 163.48/163.74 (![A: $i] : ((~bool(A)) => (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 163.48/163.74 inference(quant_intro,[status(thm)],[61])).
% 163.48/163.74 tff(63,axiom,(![A: $i] : ((~bool(A)) => (not1(A) = phi(A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','not1_axiom1')).
% 163.48/163.74 tff(64,plain,
% 163.48/163.74 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[63, 62])).
% 163.48/163.74 tff(65,plain,
% 163.48/163.74 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[64, 60])).
% 163.48/163.74 tff(66,plain,(
% 163.48/163.74 ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 163.48/163.74 inference(skolemize,[status(sab)],[65])).
% 163.48/163.74 tff(67,plain,
% 163.48/163.74 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[66, 59])).
% 163.48/163.74 tff(68,plain,
% 163.48/163.74 (((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(false) | (not1(false) = phi(false)))) <=> ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(false) | (not1(false) = phi(false)))),
% 163.48/163.74 inference(rewrite,[status(thm)],[])).
% 163.48/163.74 tff(69,plain,
% 163.48/163.74 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(false) | (not1(false) = phi(false)))),
% 163.48/163.74 inference(quant_inst,[status(thm)],[])).
% 163.48/163.74 tff(70,plain,
% 163.48/163.74 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(false) | (not1(false) = phi(false))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[69, 68])).
% 163.48/163.74 tff(71,plain,
% 163.48/163.74 (bool(false) | (not1(false) = phi(false))),
% 163.48/163.74 inference(unit_resolution,[status(thm)],[70, 67])).
% 163.48/163.74 tff(72,plain,
% 163.48/163.74 (bool(false)),
% 163.48/163.74 inference(unit_resolution,[status(thm)],[71, 57])).
% 163.48/163.74 tff(73,plain,
% 163.48/163.74 (^[B: $i] : refl(((~bool(B)) | (impl(true, B) = B)) <=> ((~bool(B)) | (impl(true, B) = B)))),
% 163.48/163.74 inference(bind,[status(th)],[])).
% 163.48/163.74 tff(74,plain,
% 163.48/163.74 (![B: $i] : ((~bool(B)) | (impl(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 163.48/163.74 inference(quant_intro,[status(thm)],[73])).
% 163.48/163.74 tff(75,plain,
% 163.48/163.74 (![B: $i] : ((~bool(B)) | (impl(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 163.48/163.74 inference(rewrite,[status(thm)],[])).
% 163.48/163.74 tff(76,plain,
% 163.48/163.74 (^[B: $i] : rewrite((bool(B) => (impl(true, B) = B)) <=> ((~bool(B)) | (impl(true, B) = B)))),
% 163.48/163.74 inference(bind,[status(th)],[])).
% 163.48/163.74 tff(77,plain,
% 163.48/163.74 (![B: $i] : (bool(B) => (impl(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 163.48/163.74 inference(quant_intro,[status(thm)],[76])).
% 163.48/163.74 tff(78,axiom,(![B: $i] : (bool(B) => (impl(true, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','impl_axiom4')).
% 163.48/163.74 tff(79,plain,
% 163.48/163.74 (![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[78, 77])).
% 163.48/163.74 tff(80,plain,
% 163.48/163.74 (![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[79, 75])).
% 163.48/163.74 tff(81,plain,(
% 163.48/163.74 ![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 163.48/163.74 inference(skolemize,[status(sab)],[80])).
% 163.48/163.74 tff(82,plain,
% 163.48/163.74 (![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[81, 74])).
% 163.48/163.74 tff(83,plain,
% 163.48/163.74 (((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | ((~bool(false)) | (impl(true, false) = false))) <=> ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | (~bool(false)) | (impl(true, false) = false))),
% 163.48/163.74 inference(rewrite,[status(thm)],[])).
% 163.48/163.74 tff(84,plain,
% 163.48/163.74 ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | ((~bool(false)) | (impl(true, false) = false))),
% 163.48/163.74 inference(quant_inst,[status(thm)],[])).
% 163.48/163.74 tff(85,plain,
% 163.48/163.74 ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | (~bool(false)) | (impl(true, false) = false)),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[84, 83])).
% 163.48/163.74 tff(86,plain,
% 163.48/163.74 (impl(true, false) = false),
% 163.48/163.74 inference(unit_resolution,[status(thm)],[85, 82, 72])).
% 163.48/163.74 tff(87,plain,
% 163.48/163.74 (^[P: $i, R: $i] : refl((~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R)))))) <=> (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R)))))))),
% 163.48/163.74 inference(bind,[status(th)],[])).
% 163.48/163.74 tff(88,plain,
% 163.48/163.74 (![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R)))))) <=> ![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R))))))),
% 163.48/163.74 inference(quant_intro,[status(thm)],[87])).
% 163.48/163.74 tff(89,plain,
% 163.48/163.74 (^[P: $i, R: $i] : rewrite((~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R)))))) <=> (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R)))))))),
% 163.48/163.74 inference(bind,[status(th)],[])).
% 163.48/163.74 tff(90,plain,
% 163.48/163.74 (![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R)))))) <=> ![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R))))))),
% 163.48/163.74 inference(quant_intro,[status(thm)],[89])).
% 163.48/163.74 tff(91,plain,
% 163.48/163.74 (![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R)))))) <=> ![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R))))))),
% 163.48/163.74 inference(transitivity,[status(thm)],[90, 88])).
% 163.48/163.74 tff(92,plain,
% 163.48/163.74 (^[P: $i, R: $i] : rewrite(((f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R))) & ![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R)))) <=> (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R)))))))),
% 163.48/163.74 inference(bind,[status(th)],[])).
% 163.48/163.74 tff(93,plain,
% 163.48/163.74 (![P: $i, R: $i] : ((f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R))) & ![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R)))) <=> ![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R))))))),
% 163.48/163.74 inference(quant_intro,[status(thm)],[92])).
% 163.48/163.74 tff(94,plain,
% 163.48/163.74 (![P: $i, R: $i] : ?[X: $i] : ((f5(P, R) = phi(f4(P, X, R))) & (~?[X1: $i] : forallprefers(f4(P, X1, R), f4(P, X, R)))) <=> ![P: $i, R: $i] : ?[X: $i] : ((f5(P, R) = phi(f4(P, X, R))) & (~?[X1: $i] : forallprefers(f4(P, X1, R), f4(P, X, R))))),
% 163.48/163.74 inference(rewrite,[status(thm)],[])).
% 163.48/163.74 tff(95,axiom,(![P: $i, R: $i] : ?[X: $i] : ((f5(P, R) = phi(f4(P, X, R))) & (~?[X1: $i] : forallprefers(f4(P, X1, R), f4(P, X, R))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','def_f5')).
% 163.48/163.74 tff(96,plain,
% 163.48/163.74 (![P: $i, R: $i] : ?[X: $i] : ((f5(P, R) = phi(f4(P, X, R))) & (~?[X1: $i] : forallprefers(f4(P, X1, R), f4(P, X, R))))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[95, 94])).
% 163.48/163.74 tff(97,plain,(
% 163.48/163.74 ![P: $i, R: $i] : ((f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R))) & ![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R))))),
% 163.48/163.74 inference(skolemize,[status(sab)],[96])).
% 163.48/163.74 tff(98,plain,
% 163.48/163.74 (![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R))))))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[97, 93])).
% 163.48/163.74 tff(99,plain,
% 163.48/163.74 (![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R))))))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[98, 91])).
% 163.48/163.74 tff(100,plain,
% 163.48/163.74 ((~![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R))))))) | (~((~(f5(P!7, false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~![X1: $i] : (~forallprefers(f4(P!7, X1, false), f4(P!7, tptp_fun_X_4(false, P!7), false))))))),
% 163.48/163.74 inference(quant_inst,[status(thm)],[])).
% 163.48/163.74 tff(101,plain,
% 163.48/163.74 (~((~(f5(P!7, false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~![X1: $i] : (~forallprefers(f4(P!7, X1, false), f4(P!7, tptp_fun_X_4(false, P!7), false)))))),
% 163.48/163.74 inference(unit_resolution,[status(thm)],[100, 99])).
% 163.48/163.74 tff(102,plain,
% 163.48/163.74 (((~(f5(P!7, false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~![X1: $i] : (~forallprefers(f4(P!7, X1, false), f4(P!7, tptp_fun_X_4(false, P!7), false))))) | (f5(P!7, false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.48/163.74 inference(tautology,[status(thm)],[])).
% 163.48/163.74 tff(103,plain,
% 163.48/163.74 (f5(P!7, false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 163.48/163.74 inference(unit_resolution,[status(thm)],[102, 101])).
% 163.48/163.74 tff(104,plain,
% 163.48/163.74 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f5(P!7, false)),
% 163.48/163.74 inference(symmetry,[status(thm)],[103])).
% 163.48/163.74 tff(105,plain,
% 163.48/163.74 ((~![X: $i] : ((prop(X) = true) <=> bool(X))) | ((prop(false) = true) <=> bool(false))),
% 163.48/163.74 inference(quant_inst,[status(thm)],[])).
% 163.48/163.74 tff(106,plain,
% 163.48/163.74 ((prop(false) = true) <=> bool(false)),
% 163.48/163.74 inference(unit_resolution,[status(thm)],[105, 19])).
% 163.48/163.74 tff(107,plain,
% 163.48/163.74 ((~((prop(false) = true) <=> bool(false))) | (prop(false) = true) | (~bool(false))),
% 163.48/163.74 inference(tautology,[status(thm)],[])).
% 163.48/163.74 tff(108,plain,
% 163.48/163.74 ((~((prop(false) = true) <=> bool(false))) | (prop(false) = true)),
% 163.48/163.74 inference(unit_resolution,[status(thm)],[107, 72])).
% 163.48/163.74 tff(109,plain,
% 163.48/163.74 (prop(false) = true),
% 163.48/163.74 inference(unit_resolution,[status(thm)],[108, 106])).
% 163.48/163.74 tff(110,plain,
% 163.48/163.74 (true = prop(false)),
% 163.48/163.74 inference(symmetry,[status(thm)],[109])).
% 163.48/163.74 tff(111,plain,
% 163.48/163.74 (lazy_impl(true, impl(f5(P!7, false), false)) = lazy_impl(prop(false), impl(f5(P!7, false), false))),
% 163.48/163.74 inference(monotonicity,[status(thm)],[110])).
% 163.48/163.74 tff(112,plain,
% 163.48/163.74 (^[B: $i] : refl((lazy_impl(true, B) = phi(B)) <=> (lazy_impl(true, B) = phi(B)))),
% 163.48/163.74 inference(bind,[status(th)],[])).
% 163.48/163.74 tff(113,plain,
% 163.48/163.74 (![B: $i] : (lazy_impl(true, B) = phi(B)) <=> ![B: $i] : (lazy_impl(true, B) = phi(B))),
% 163.48/163.74 inference(quant_intro,[status(thm)],[112])).
% 163.48/163.74 tff(114,plain,
% 163.48/163.74 (![B: $i] : (lazy_impl(true, B) = phi(B)) <=> ![B: $i] : (lazy_impl(true, B) = phi(B))),
% 163.48/163.74 inference(rewrite,[status(thm)],[])).
% 163.48/163.74 tff(115,axiom,(![B: $i] : (lazy_impl(true, B) = phi(B))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','lazy_impl_axiom3')).
% 163.48/163.74 tff(116,plain,
% 163.48/163.74 (![B: $i] : (lazy_impl(true, B) = phi(B))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[115, 114])).
% 163.48/163.74 tff(117,plain,(
% 163.48/163.74 ![B: $i] : (lazy_impl(true, B) = phi(B))),
% 163.48/163.74 inference(skolemize,[status(sab)],[116])).
% 163.48/163.74 tff(118,plain,
% 163.48/163.74 (![B: $i] : (lazy_impl(true, B) = phi(B))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[117, 113])).
% 163.48/163.74 tff(119,plain,
% 163.48/163.74 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, impl(f5(P!7, false), false)) = phi(impl(f5(P!7, false), false)))),
% 163.48/163.74 inference(quant_inst,[status(thm)],[])).
% 163.48/163.74 tff(120,plain,
% 163.48/163.74 (lazy_impl(true, impl(f5(P!7, false), false)) = phi(impl(f5(P!7, false), false))),
% 163.48/163.74 inference(unit_resolution,[status(thm)],[119, 118])).
% 163.48/163.74 tff(121,plain,
% 163.48/163.74 (phi(impl(f5(P!7, false), false)) = lazy_impl(true, impl(f5(P!7, false), false))),
% 163.48/163.74 inference(symmetry,[status(thm)],[120])).
% 163.48/163.74 tff(122,plain,
% 163.48/163.74 (((false2 = phi(f7(P!6))) & ![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) <=> ((false2 = phi(f7(P!6))) & ![P1: $i] : (~forallprefers(f7(P1), f7(P!6))))),
% 163.48/163.74 inference(rewrite,[status(thm)],[])).
% 163.48/163.74 tff(123,plain,
% 163.48/163.74 (?[P: $i] : ((false2 = phi(f7(P))) & (~?[P1: $i] : forallprefers(f7(P1), f7(P)))) <=> ?[P: $i] : ((false2 = phi(f7(P))) & (~?[P1: $i] : forallprefers(f7(P1), f7(P))))),
% 163.48/163.74 inference(rewrite,[status(thm)],[])).
% 163.48/163.74 tff(124,axiom,(?[P: $i] : ((false2 = phi(f7(P))) & (~?[P1: $i] : forallprefers(f7(P1), f7(P))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','def_false2')).
% 163.48/163.74 tff(125,plain,
% 163.48/163.74 (?[P: $i] : ((false2 = phi(f7(P))) & (~?[P1: $i] : forallprefers(f7(P1), f7(P))))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[124, 123])).
% 163.48/163.74 tff(126,plain,
% 163.48/163.74 ((false2 = phi(f7(P!6))) & ![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[125, 122])).
% 163.48/163.74 tff(127,plain,
% 163.48/163.74 (false2 = phi(f7(P!6))),
% 163.48/163.74 inference(and_elim,[status(thm)],[126])).
% 163.48/163.74 tff(128,plain,
% 163.48/163.74 (phi(f7(P!6)) = false2),
% 163.48/163.74 inference(symmetry,[status(thm)],[127])).
% 163.48/163.74 tff(129,plain,
% 163.48/163.74 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, false) = phi(false))),
% 163.48/163.74 inference(quant_inst,[status(thm)],[])).
% 163.48/163.74 tff(130,plain,
% 163.48/163.74 (lazy_impl(true, false) = phi(false)),
% 163.48/163.74 inference(unit_resolution,[status(thm)],[129, 118])).
% 163.48/163.74 tff(131,plain,
% 163.48/163.74 (lazy_impl(prop(false), false) = lazy_impl(true, false)),
% 163.48/163.74 inference(monotonicity,[status(thm)],[109])).
% 163.48/163.74 tff(132,plain,
% 163.48/163.74 (^[P: $i] : refl((f7(P) = lazy_impl(prop(P), P)) <=> (f7(P) = lazy_impl(prop(P), P)))),
% 163.48/163.74 inference(bind,[status(th)],[])).
% 163.48/163.74 tff(133,plain,
% 163.48/163.74 (![P: $i] : (f7(P) = lazy_impl(prop(P), P)) <=> ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 163.48/163.74 inference(quant_intro,[status(thm)],[132])).
% 163.48/163.74 tff(134,plain,
% 163.48/163.74 (![P: $i] : (f7(P) = lazy_impl(prop(P), P)) <=> ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 163.48/163.74 inference(rewrite,[status(thm)],[])).
% 163.48/163.74 tff(135,axiom,(![P: $i] : (f7(P) = lazy_impl(prop(P), P))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','def_f7')).
% 163.48/163.74 tff(136,plain,
% 163.48/163.74 (![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[135, 134])).
% 163.48/163.74 tff(137,plain,(
% 163.48/163.74 ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 163.48/163.74 inference(skolemize,[status(sab)],[136])).
% 163.48/163.74 tff(138,plain,
% 163.48/163.74 (![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[137, 133])).
% 163.48/163.74 tff(139,plain,
% 163.48/163.74 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(false) = lazy_impl(prop(false), false))),
% 163.48/163.74 inference(quant_inst,[status(thm)],[])).
% 163.48/163.74 tff(140,plain,
% 163.48/163.74 (f7(false) = lazy_impl(prop(false), false)),
% 163.48/163.74 inference(unit_resolution,[status(thm)],[139, 138])).
% 163.48/163.74 tff(141,plain,
% 163.48/163.74 (^[B: $i] : refl((lazy_impl(false, B) = true) <=> (lazy_impl(false, B) = true))),
% 163.48/163.74 inference(bind,[status(th)],[])).
% 163.48/163.74 tff(142,plain,
% 163.48/163.74 (![B: $i] : (lazy_impl(false, B) = true) <=> ![B: $i] : (lazy_impl(false, B) = true)),
% 163.48/163.74 inference(quant_intro,[status(thm)],[141])).
% 163.48/163.74 tff(143,plain,
% 163.48/163.74 (![B: $i] : (lazy_impl(false, B) = true) <=> ![B: $i] : (lazy_impl(false, B) = true)),
% 163.48/163.74 inference(rewrite,[status(thm)],[])).
% 163.48/163.74 tff(144,axiom,(![B: $i] : (lazy_impl(false, B) = true)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','lazy_impl_axiom2')).
% 163.48/163.74 tff(145,plain,
% 163.48/163.74 (![B: $i] : (lazy_impl(false, B) = true)),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[144, 143])).
% 163.48/163.74 tff(146,plain,(
% 163.48/163.74 ![B: $i] : (lazy_impl(false, B) = true)),
% 163.48/163.74 inference(skolemize,[status(sab)],[145])).
% 163.48/163.74 tff(147,plain,
% 163.48/163.74 (![B: $i] : (lazy_impl(false, B) = true)),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[146, 142])).
% 163.48/163.74 tff(148,plain,
% 163.48/163.74 ((~![B: $i] : (lazy_impl(false, B) = true)) | (lazy_impl(false, P!6) = true)),
% 163.48/163.74 inference(quant_inst,[status(thm)],[])).
% 163.48/163.74 tff(149,plain,
% 163.48/163.74 (lazy_impl(false, P!6) = true),
% 163.48/163.74 inference(unit_resolution,[status(thm)],[148, 147])).
% 163.48/163.74 tff(150,assumption,(prop(P!6) = false), introduced(assumption)).
% 163.48/163.74 tff(151,plain,
% 163.48/163.74 (lazy_impl(prop(P!6), P!6) = lazy_impl(false, P!6)),
% 163.48/163.74 inference(monotonicity,[status(thm)],[150])).
% 163.48/163.74 tff(152,plain,
% 163.48/163.74 (lazy_impl(prop(P!6), P!6) = true),
% 163.48/163.74 inference(transitivity,[status(thm)],[151, 149])).
% 163.48/163.74 tff(153,plain,
% 163.48/163.74 (^[X: $i, Y: $i] : refl((forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))))) <=> (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))))))),
% 163.48/163.74 inference(bind,[status(th)],[])).
% 163.48/163.74 tff(154,plain,
% 163.48/163.74 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))))) <=> ![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))),
% 163.48/163.74 inference(quant_intro,[status(thm)],[153])).
% 163.48/163.74 tff(155,plain,
% 163.48/163.74 (^[X: $i, Y: $i] : rewrite((forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)))) <=> (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))))))),
% 163.48/163.74 inference(bind,[status(th)],[])).
% 163.48/163.74 tff(156,plain,
% 163.48/163.74 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)))) <=> ![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))),
% 163.48/163.74 inference(quant_intro,[status(thm)],[155])).
% 163.48/163.74 tff(157,plain,
% 163.48/163.74 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)))) <=> ![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 163.48/163.74 inference(rewrite,[status(thm)],[])).
% 163.48/163.74 tff(158,plain,
% 163.48/163.74 (^[X: $i, Y: $i] : rewrite((forallprefers(X, Y) <=> ((((~d(X)) & d(Y)) | (((d(X) & d(Y)) & (~bool(X))) & bool(Y))) | ((X = false) & (Y = true)))) <=> (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)))))),
% 163.48/163.74 inference(bind,[status(th)],[])).
% 163.48/163.74 tff(159,plain,
% 163.48/163.74 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((((~d(X)) & d(Y)) | (((d(X) & d(Y)) & (~bool(X))) & bool(Y))) | ((X = false) & (Y = true)))) <=> ![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 163.48/163.74 inference(quant_intro,[status(thm)],[158])).
% 163.48/163.74 tff(160,axiom,(![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((((~d(X)) & d(Y)) | (((d(X) & d(Y)) & (~bool(X))) & bool(Y))) | ((X = false) & (Y = true))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','def_forallprefers')).
% 163.48/163.74 tff(161,plain,
% 163.48/163.74 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[160, 159])).
% 163.48/163.74 tff(162,plain,
% 163.48/163.74 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[161, 157])).
% 163.48/163.74 tff(163,plain,(
% 163.48/163.74 ![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 163.48/163.74 inference(skolemize,[status(sab)],[162])).
% 163.48/163.74 tff(164,plain,
% 163.48/163.74 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[163, 156])).
% 163.48/163.74 tff(165,plain,
% 163.48/163.74 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))),
% 163.48/163.74 inference(modus_ponens,[status(thm)],[164, 154])).
% 163.48/163.74 tff(166,plain,
% 163.48/163.74 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))))))),
% 163.48/163.74 inference(rewrite,[status(thm)],[])).
% 163.48/163.74 tff(167,plain,
% 163.48/163.74 ((forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~((~(false = false)) | (~(lazy_impl(prop(P!6), P!6) = true)))) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(false) | (~d(false)))))) <=> (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6)))))))),
% 163.48/163.75 inference(rewrite,[status(thm)],[])).
% 163.48/163.75 tff(168,plain,
% 163.48/163.75 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~((~(false = false)) | (~(lazy_impl(prop(P!6), P!6) = true)))) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(false) | (~d(false))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))))))),
% 163.48/163.75 inference(monotonicity,[status(thm)],[167])).
% 163.48/163.75 tff(169,plain,
% 163.48/163.75 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~((~(false = false)) | (~(lazy_impl(prop(P!6), P!6) = true)))) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(false) | (~d(false))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))))))),
% 163.48/163.75 inference(transitivity,[status(thm)],[168, 166])).
% 163.48/163.75 tff(170,plain,
% 163.48/163.75 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((~((~(false = false)) | (~(lazy_impl(prop(P!6), P!6) = true)))) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(false) | (~d(false))))))),
% 163.48/163.75 inference(quant_inst,[status(thm)],[])).
% 163.48/163.75 tff(171,plain,
% 163.48/163.75 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6)))))))),
% 163.48/163.75 inference(modus_ponens,[status(thm)],[170, 169])).
% 163.48/163.75 tff(172,plain,
% 163.48/163.75 (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))))),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[171, 165])).
% 163.48/163.75 tff(173,plain,
% 163.48/163.75 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(P!6) = lazy_impl(prop(P!6), P!6))),
% 163.48/163.75 inference(quant_inst,[status(thm)],[])).
% 163.48/163.75 tff(174,plain,
% 163.48/163.75 (f7(P!6) = lazy_impl(prop(P!6), P!6)),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[173, 138])).
% 163.48/163.75 tff(175,plain,
% 163.48/163.75 (lazy_impl(prop(P!6), P!6) = f7(P!6)),
% 163.48/163.75 inference(symmetry,[status(thm)],[174])).
% 163.48/163.75 tff(176,plain,
% 163.48/163.75 (lazy_impl(prop(false), false) = f7(false)),
% 163.48/163.75 inference(symmetry,[status(thm)],[140])).
% 163.48/163.75 tff(177,plain,
% 163.48/163.75 (lazy_impl(true, false) = lazy_impl(prop(false), false)),
% 163.48/163.75 inference(symmetry,[status(thm)],[131])).
% 163.48/163.75 tff(178,plain,
% 163.48/163.75 (phi(false) = lazy_impl(true, false)),
% 163.48/163.75 inference(symmetry,[status(thm)],[130])).
% 163.48/163.75 tff(179,plain,
% 163.48/163.75 (false = phi(false)),
% 163.48/163.75 inference(symmetry,[status(thm)],[45])).
% 163.48/163.75 tff(180,plain,
% 163.48/163.75 (false = f7(false)),
% 163.48/163.75 inference(transitivity,[status(thm)],[179, 178, 177, 176])).
% 163.48/163.75 tff(181,plain,
% 163.48/163.75 (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> forallprefers(f7(false), f7(P!6))),
% 163.48/163.75 inference(monotonicity,[status(thm)],[180, 175])).
% 163.48/163.75 tff(182,plain,
% 163.48/163.75 (forallprefers(f7(false), f7(P!6)) <=> forallprefers(false, lazy_impl(prop(P!6), P!6))),
% 163.48/163.75 inference(symmetry,[status(thm)],[181])).
% 163.48/163.75 tff(183,plain,
% 163.48/163.75 ((~forallprefers(f7(false), f7(P!6))) <=> (~forallprefers(false, lazy_impl(prop(P!6), P!6)))),
% 163.48/163.75 inference(monotonicity,[status(thm)],[182])).
% 163.48/163.75 tff(184,plain,
% 163.48/163.75 (^[P1: $i] : refl((~forallprefers(f7(P1), f7(P!6))) <=> (~forallprefers(f7(P1), f7(P!6))))),
% 163.48/163.75 inference(bind,[status(th)],[])).
% 163.48/163.75 tff(185,plain,
% 163.48/163.75 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6))) <=> ![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 163.48/163.75 inference(quant_intro,[status(thm)],[184])).
% 163.48/163.75 tff(186,plain,
% 163.48/163.75 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 163.48/163.75 inference(and_elim,[status(thm)],[126])).
% 163.48/163.75 tff(187,plain,
% 163.48/163.75 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 163.48/163.75 inference(modus_ponens,[status(thm)],[186, 185])).
% 163.48/163.75 tff(188,plain,
% 163.48/163.75 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(false), f7(P!6)))),
% 163.48/163.75 inference(quant_inst,[status(thm)],[])).
% 163.48/163.75 tff(189,plain,
% 163.48/163.75 (~forallprefers(f7(false), f7(P!6))),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[188, 187])).
% 163.48/163.75 tff(190,plain,
% 163.48/163.75 (~forallprefers(false, lazy_impl(prop(P!6), P!6))),
% 163.48/163.75 inference(modus_ponens,[status(thm)],[189, 183])).
% 163.48/163.75 tff(191,plain,
% 163.48/163.75 ((~(forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6)))))))) | forallprefers(false, lazy_impl(prop(P!6), P!6)) | (~((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6)))))))),
% 163.48/163.75 inference(tautology,[status(thm)],[])).
% 163.48/163.75 tff(192,plain,
% 163.48/163.75 (~((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))))),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[191, 190, 172])).
% 163.48/163.75 tff(193,plain,
% 163.48/163.75 (((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6)))))) | (~(lazy_impl(prop(P!6), P!6) = true))),
% 163.48/163.75 inference(tautology,[status(thm)],[])).
% 163.48/163.75 tff(194,plain,
% 163.48/163.75 (~(lazy_impl(prop(P!6), P!6) = true)),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[193, 192])).
% 163.48/163.75 tff(195,plain,
% 163.48/163.75 ($false),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[194, 152])).
% 163.48/163.75 tff(196,plain,(~(prop(P!6) = false)), inference(lemma,lemma(discharge,[]))).
% 163.48/163.75 tff(197,plain,
% 163.48/163.75 (^[X: $i] : refl((~(bool(X) <=> (prop(X) = false))) <=> (~(bool(X) <=> (prop(X) = false))))),
% 163.48/163.75 inference(bind,[status(th)],[])).
% 163.48/163.75 tff(198,plain,
% 163.48/163.75 (![X: $i] : (~(bool(X) <=> (prop(X) = false))) <=> ![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 163.48/163.75 inference(quant_intro,[status(thm)],[197])).
% 163.48/163.75 tff(199,plain,
% 163.48/163.75 (![X: $i] : (~(bool(X) <=> (prop(X) = false))) <=> ![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 163.48/163.75 inference(rewrite,[status(thm)],[])).
% 163.48/163.75 tff(200,plain,
% 163.48/163.75 (^[X: $i] : trans(rewrite(((prop(X) = false) <=> (~bool(X))) <=> (~(bool(X) <=> (prop(X) = false)))), rewrite((~(bool(X) <=> (prop(X) = false))) <=> (~(bool(X) <=> (prop(X) = false)))), (((prop(X) = false) <=> (~bool(X))) <=> (~(bool(X) <=> (prop(X) = false)))))),
% 163.48/163.75 inference(bind,[status(th)],[])).
% 163.48/163.75 tff(201,plain,
% 163.48/163.75 (![X: $i] : ((prop(X) = false) <=> (~bool(X))) <=> ![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 163.48/163.75 inference(quant_intro,[status(thm)],[200])).
% 163.48/163.75 tff(202,axiom,(![X: $i] : ((prop(X) = false) <=> (~bool(X)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','prop_false')).
% 163.48/163.75 tff(203,plain,
% 163.48/163.75 (![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 163.48/163.75 inference(modus_ponens,[status(thm)],[202, 201])).
% 163.48/163.75 tff(204,plain,
% 163.48/163.75 (![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 163.48/163.75 inference(modus_ponens,[status(thm)],[203, 199])).
% 163.48/163.75 tff(205,plain,(
% 163.48/163.75 ![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 163.48/163.75 inference(skolemize,[status(sab)],[204])).
% 163.48/163.75 tff(206,plain,
% 163.48/163.75 (![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 163.48/163.75 inference(modus_ponens,[status(thm)],[205, 198])).
% 163.48/163.75 tff(207,plain,
% 163.48/163.75 ((~![X: $i] : (~(bool(X) <=> (prop(X) = false)))) | (~(bool(P!6) <=> (prop(P!6) = false)))),
% 163.48/163.75 inference(quant_inst,[status(thm)],[])).
% 163.48/163.75 tff(208,plain,
% 163.48/163.75 (~(bool(P!6) <=> (prop(P!6) = false))),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[207, 206])).
% 163.48/163.75 tff(209,plain,
% 163.48/163.75 ((bool(P!6) <=> (prop(P!6) = false)) | bool(P!6) | (prop(P!6) = false)),
% 163.48/163.75 inference(tautology,[status(thm)],[])).
% 163.48/163.75 tff(210,plain,
% 163.48/163.75 (bool(P!6) | (prop(P!6) = false)),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[209, 208])).
% 163.48/163.75 tff(211,plain,
% 163.48/163.75 (bool(P!6)),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[210, 196])).
% 163.48/163.75 tff(212,plain,
% 163.48/163.75 (^[X: $i] : refl((bool(X) <=> ((X = false) | (X = true))) <=> (bool(X) <=> ((X = false) | (X = true))))),
% 163.48/163.75 inference(bind,[status(th)],[])).
% 163.48/163.75 tff(213,plain,
% 163.48/163.75 (![X: $i] : (bool(X) <=> ((X = false) | (X = true))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 163.48/163.75 inference(quant_intro,[status(thm)],[212])).
% 163.48/163.75 tff(214,plain,
% 163.48/163.75 (![X: $i] : (bool(X) <=> ((X = false) | (X = true))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 163.48/163.75 inference(rewrite,[status(thm)],[])).
% 163.48/163.75 tff(215,axiom,(![X: $i] : (bool(X) <=> ((X = false) | (X = true)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','def_bool')).
% 163.48/163.75 tff(216,plain,
% 163.48/163.75 (![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 163.48/163.75 inference(modus_ponens,[status(thm)],[215, 214])).
% 163.48/163.75 tff(217,plain,(
% 163.48/163.75 ![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 163.48/163.75 inference(skolemize,[status(sab)],[216])).
% 163.48/163.75 tff(218,plain,
% 163.48/163.75 (![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 163.48/163.75 inference(modus_ponens,[status(thm)],[217, 213])).
% 163.48/163.75 tff(219,plain,
% 163.48/163.75 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(P!6) <=> ((P!6 = false) | (P!6 = true)))),
% 163.48/163.75 inference(quant_inst,[status(thm)],[])).
% 163.48/163.75 tff(220,plain,
% 163.48/163.75 (bool(P!6) <=> ((P!6 = false) | (P!6 = true))),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[219, 218])).
% 163.48/163.75 tff(221,plain,
% 163.48/163.75 ((~(bool(P!6) <=> ((P!6 = false) | (P!6 = true)))) | (~bool(P!6)) | ((P!6 = false) | (P!6 = true))),
% 163.48/163.75 inference(tautology,[status(thm)],[])).
% 163.48/163.75 tff(222,plain,
% 163.48/163.75 ((~bool(P!6)) | ((P!6 = false) | (P!6 = true))),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[221, 220])).
% 163.48/163.75 tff(223,plain,
% 163.48/163.75 ((P!6 = false) | (P!6 = true)),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[222, 211])).
% 163.48/163.75 tff(224,plain,
% 163.48/163.75 (d(true) <=> d(true)),
% 163.48/163.75 inference(rewrite,[status(thm)],[])).
% 163.48/163.75 tff(225,plain,
% 163.48/163.75 (d(true)),
% 163.48/163.75 inference(and_elim,[status(thm)],[25])).
% 163.48/163.75 tff(226,plain,
% 163.48/163.75 (d(true)),
% 163.48/163.75 inference(modus_ponens,[status(thm)],[225, 224])).
% 163.48/163.75 tff(227,plain,
% 163.48/163.75 ((d(true) | (~(phi(true) = err))) | (~d(true))),
% 163.48/163.75 inference(tautology,[status(thm)],[])).
% 163.48/163.75 tff(228,plain,
% 163.48/163.75 (d(true) | (~(phi(true) = err))),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[227, 226])).
% 163.48/163.75 tff(229,plain,
% 163.48/163.75 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(true)) | (~(phi(true) = true)))) | (~(d(true) | (~(phi(true) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(true)) | (~(phi(true) = true)))) | (~(d(true) | (~(phi(true) = err)))))),
% 163.48/163.75 inference(rewrite,[status(thm)],[])).
% 163.48/163.75 tff(230,plain,
% 163.48/163.75 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(true)) | (~(phi(true) = true)))) | (~(d(true) | (~(phi(true) = err)))))),
% 163.48/163.75 inference(quant_inst,[status(thm)],[])).
% 163.48/163.75 tff(231,plain,
% 163.48/163.75 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(true)) | (~(phi(true) = true)))) | (~(d(true) | (~(phi(true) = err))))),
% 163.48/163.75 inference(modus_ponens,[status(thm)],[230, 229])).
% 163.48/163.75 tff(232,plain,
% 163.48/163.75 (~((~d(true)) | (~(phi(true) = true)))),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[231, 39, 228])).
% 163.48/163.75 tff(233,plain,
% 163.48/163.75 (((~d(true)) | (~(phi(true) = true))) | (phi(true) = true)),
% 163.48/163.75 inference(tautology,[status(thm)],[])).
% 163.48/163.75 tff(234,plain,
% 163.48/163.75 (phi(true) = true),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[233, 232])).
% 163.48/163.75 tff(235,plain,
% 163.48/163.75 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, true) = phi(true))),
% 163.48/163.75 inference(quant_inst,[status(thm)],[])).
% 163.48/163.75 tff(236,plain,
% 163.48/163.75 (lazy_impl(true, true) = phi(true)),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[235, 118])).
% 163.48/163.75 tff(237,plain,
% 163.48/163.75 ((~![X: $i] : ((prop(X) = true) <=> bool(X))) | ((prop(true) = true) <=> bool(true))),
% 163.48/163.75 inference(quant_inst,[status(thm)],[])).
% 163.48/163.75 tff(238,plain,
% 163.48/163.75 ((prop(true) = true) <=> bool(true)),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[237, 19])).
% 163.48/163.75 tff(239,plain,
% 163.48/163.75 ((false = true) <=> (true = false)),
% 163.48/163.75 inference(commutativity,[status(thm)],[])).
% 163.48/163.75 tff(240,plain,
% 163.48/163.75 ((not1(true) = false) <=> (not1(true) = false)),
% 163.48/163.75 inference(rewrite,[status(thm)],[])).
% 163.48/163.75 tff(241,axiom,(not1(true) = false), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','not1_axiom3')).
% 163.48/163.75 tff(242,plain,
% 163.48/163.75 (not1(true) = false),
% 163.48/163.75 inference(modus_ponens,[status(thm)],[241, 240])).
% 163.48/163.75 tff(243,plain,
% 163.48/163.75 ((not1(true) = phi(true)) <=> (false = true)),
% 163.48/163.75 inference(monotonicity,[status(thm)],[242, 234])).
% 163.48/163.75 tff(244,plain,
% 163.48/163.75 ((not1(true) = phi(true)) <=> (true = false)),
% 163.48/163.75 inference(transitivity,[status(thm)],[243, 239])).
% 163.48/163.75 tff(245,plain,
% 163.48/163.75 ((true = false) <=> (not1(true) = phi(true))),
% 163.48/163.75 inference(symmetry,[status(thm)],[244])).
% 163.48/163.75 tff(246,plain,
% 163.48/163.75 ((~(true = false)) <=> (~(not1(true) = phi(true)))),
% 163.48/163.75 inference(monotonicity,[status(thm)],[245])).
% 163.48/163.75 tff(247,plain,
% 163.48/163.75 (~(not1(true) = phi(true))),
% 163.48/163.75 inference(modus_ponens,[status(thm)],[56, 246])).
% 163.48/163.75 tff(248,plain,
% 163.48/163.75 (((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(true) | (not1(true) = phi(true)))) <=> ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(true) | (not1(true) = phi(true)))),
% 163.48/163.75 inference(rewrite,[status(thm)],[])).
% 163.48/163.75 tff(249,plain,
% 163.48/163.75 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(true) | (not1(true) = phi(true)))),
% 163.48/163.75 inference(quant_inst,[status(thm)],[])).
% 163.48/163.75 tff(250,plain,
% 163.48/163.75 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(true) | (not1(true) = phi(true))),
% 163.48/163.75 inference(modus_ponens,[status(thm)],[249, 248])).
% 163.48/163.75 tff(251,plain,
% 163.48/163.75 (bool(true) | (not1(true) = phi(true))),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[250, 67])).
% 163.48/163.75 tff(252,plain,
% 163.48/163.75 (bool(true)),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[251, 247])).
% 163.48/163.75 tff(253,plain,
% 163.48/163.75 ((~((prop(true) = true) <=> bool(true))) | (prop(true) = true) | (~bool(true))),
% 163.48/163.75 inference(tautology,[status(thm)],[])).
% 163.48/163.75 tff(254,plain,
% 163.48/163.75 ((~((prop(true) = true) <=> bool(true))) | (prop(true) = true)),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[253, 252])).
% 163.48/163.75 tff(255,plain,
% 163.48/163.75 (prop(true) = true),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[254, 238])).
% 163.48/163.75 tff(256,plain,
% 163.48/163.75 (lazy_impl(prop(true), true) = lazy_impl(true, true)),
% 163.48/163.75 inference(monotonicity,[status(thm)],[255])).
% 163.48/163.75 tff(257,plain,
% 163.48/163.75 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(true) = lazy_impl(prop(true), true))),
% 163.48/163.75 inference(quant_inst,[status(thm)],[])).
% 163.48/163.75 tff(258,plain,
% 163.48/163.75 (f7(true) = lazy_impl(prop(true), true)),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[257, 138])).
% 163.48/163.75 tff(259,assumption,(P!6 = true), introduced(assumption)).
% 163.48/163.75 tff(260,plain,
% 163.48/163.75 (f7(P!6) = f7(true)),
% 163.48/163.75 inference(monotonicity,[status(thm)],[259])).
% 163.48/163.75 tff(261,plain,
% 163.48/163.75 (lazy_impl(prop(P!6), P!6) = true),
% 163.48/163.75 inference(transitivity,[status(thm)],[175, 260, 258, 256, 236, 234])).
% 163.48/163.75 tff(262,plain,
% 163.48/163.75 ($false),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[194, 261])).
% 163.48/163.75 tff(263,plain,(~(P!6 = true)), inference(lemma,lemma(discharge,[]))).
% 163.48/163.75 tff(264,plain,
% 163.48/163.75 ((~((P!6 = false) | (P!6 = true))) | (P!6 = false) | (P!6 = true)),
% 163.48/163.75 inference(tautology,[status(thm)],[])).
% 163.48/163.75 tff(265,plain,
% 163.48/163.75 (P!6 = false),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[264, 263, 223])).
% 163.48/163.75 tff(266,plain,
% 163.48/163.75 (f7(P!6) = f7(false)),
% 163.48/163.75 inference(monotonicity,[status(thm)],[265])).
% 163.48/163.75 tff(267,plain,
% 163.48/163.75 (f7(P!6) = false),
% 163.48/163.75 inference(transitivity,[status(thm)],[266, 140, 131, 130, 45])).
% 163.48/163.75 tff(268,plain,
% 163.48/163.75 (phi(f7(P!6)) = phi(false)),
% 163.48/163.75 inference(monotonicity,[status(thm)],[267])).
% 163.48/163.75 tff(269,plain,
% 163.48/163.75 (phi(false) = phi(f7(P!6))),
% 163.48/163.75 inference(symmetry,[status(thm)],[268])).
% 163.48/163.75 tff(270,plain,
% 163.48/163.75 (false = false2),
% 163.48/163.75 inference(transitivity,[status(thm)],[179, 269, 128])).
% 163.48/163.75 tff(271,plain,
% 163.48/163.75 (impl(f5(P!7, false), false) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)),
% 163.48/163.75 inference(monotonicity,[status(thm)],[103, 270])).
% 163.48/163.75 tff(272,plain,
% 163.48/163.75 (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2) = impl(f5(P!7, false), false)),
% 163.48/163.75 inference(symmetry,[status(thm)],[271])).
% 163.48/163.75 tff(273,plain,
% 163.48/163.75 (phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = phi(impl(f5(P!7, false), false))),
% 163.48/163.75 inference(monotonicity,[status(thm)],[272])).
% 163.48/163.75 tff(274,plain,
% 163.48/163.75 (phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = true),
% 163.48/163.75 inference(transitivity,[status(thm)],[273, 121, 111, 22])).
% 163.48/163.75 tff(275,plain,
% 163.48/163.75 ((phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err) <=> (true = err)),
% 163.48/163.75 inference(monotonicity,[status(thm)],[274])).
% 163.48/163.75 tff(276,plain,
% 163.48/163.75 ((true = err) <=> (phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)),
% 163.48/163.75 inference(symmetry,[status(thm)],[275])).
% 163.48/163.75 tff(277,plain,
% 163.48/163.75 ((~(true = err)) <=> (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err))),
% 163.48/163.75 inference(monotonicity,[status(thm)],[276])).
% 163.48/163.75 tff(278,plain,
% 163.48/163.75 ((~(true = err)) <=> (~(true = err))),
% 163.48/163.75 inference(rewrite,[status(thm)],[])).
% 163.48/163.75 tff(279,plain,
% 163.48/163.75 (~(true = err)),
% 163.48/163.75 inference(and_elim,[status(thm)],[54])).
% 163.48/163.75 tff(280,plain,
% 163.48/163.75 (~(true = err)),
% 163.48/163.75 inference(modus_ponens,[status(thm)],[279, 278])).
% 163.48/163.75 tff(281,plain,
% 163.48/163.75 (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)),
% 163.48/163.75 inference(modus_ponens,[status(thm)],[280, 277])).
% 163.48/163.75 tff(282,plain,
% 163.48/163.75 ((d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err))) | (phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)),
% 163.48/163.75 inference(tautology,[status(thm)],[])).
% 163.48/163.75 tff(283,plain,
% 163.48/163.75 (d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err))),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[282, 281])).
% 163.48/163.75 tff(284,plain,
% 163.48/163.75 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~(d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)))) | (~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~(d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)))) | (~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))))))),
% 163.48/163.75 inference(rewrite,[status(thm)],[])).
% 163.48/163.75 tff(285,plain,
% 163.48/163.75 (((~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))))) | (~(d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err))))) <=> ((~(d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)))) | (~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))))))),
% 163.48/163.75 inference(rewrite,[status(thm)],[])).
% 163.48/163.75 tff(286,plain,
% 163.48/163.75 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))))) | (~(d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~(d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)))) | (~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)))))))),
% 163.48/163.75 inference(monotonicity,[status(thm)],[285])).
% 163.48/163.75 tff(287,plain,
% 163.48/163.75 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))))) | (~(d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~(d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)))) | (~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))))))),
% 163.48/163.75 inference(transitivity,[status(thm)],[286, 284])).
% 163.48/163.75 tff(288,plain,
% 163.48/163.75 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))))) | (~(d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)))))),
% 163.48/163.75 inference(quant_inst,[status(thm)],[])).
% 163.48/163.75 tff(289,plain,
% 163.48/163.75 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~(d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)))) | (~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)))))),
% 163.48/163.75 inference(modus_ponens,[status(thm)],[288, 287])).
% 163.48/163.75 tff(290,plain,
% 163.48/163.75 ((~(d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)))) | (~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)))))),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[289, 39])).
% 163.48/163.75 tff(291,plain,
% 163.48/163.75 (~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))))),
% 163.48/163.75 inference(unit_resolution,[status(thm)],[290, 283])).
% 163.48/163.75 tff(292,plain,
% 163.48/163.75 (((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)))) | (phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))),
% 163.48/163.76 inference(tautology,[status(thm)],[])).
% 163.48/163.76 tff(293,plain,
% 163.48/163.76 (phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)),
% 163.48/163.76 inference(unit_resolution,[status(thm)],[292, 291])).
% 163.48/163.76 tff(294,plain,
% 163.48/163.76 (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2) = phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))),
% 163.48/163.76 inference(symmetry,[status(thm)],[293])).
% 163.48/163.76 tff(295,plain,
% 163.48/163.76 (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = impl(f5(P!7, false), false)),
% 163.48/163.76 inference(monotonicity,[status(thm)],[104])).
% 163.48/163.76 tff(296,assumption,(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))), introduced(assumption)).
% 163.48/163.76 tff(297,plain,
% 163.48/163.76 (phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false)),
% 163.48/163.76 inference(symmetry,[status(thm)],[296])).
% 163.48/163.76 tff(298,plain,
% 163.48/163.76 (phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true),
% 163.48/163.76 inference(transitivity,[status(thm)],[297, 295, 271, 294, 273, 121, 111, 22])).
% 163.48/163.76 tff(299,plain,
% 163.48/163.76 ((phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err) <=> (true = err)),
% 163.48/163.76 inference(monotonicity,[status(thm)],[298])).
% 163.48/163.76 tff(300,plain,
% 163.48/163.76 ((true = err) <=> (phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err)),
% 163.48/163.76 inference(symmetry,[status(thm)],[299])).
% 163.48/163.76 tff(301,plain,
% 163.48/163.76 ((~(true = err)) <=> (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err))),
% 163.48/163.76 inference(monotonicity,[status(thm)],[300])).
% 163.48/163.76 tff(302,plain,
% 163.48/163.76 (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err)),
% 163.48/163.76 inference(modus_ponens,[status(thm)],[280, 301])).
% 163.48/163.76 tff(303,plain,
% 163.48/163.76 ((d(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err))) | (phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err)),
% 163.48/163.76 inference(tautology,[status(thm)],[])).
% 163.48/163.76 tff(304,plain,
% 163.48/163.76 (d(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err))),
% 163.48/163.76 inference(unit_resolution,[status(thm)],[303, 302])).
% 163.48/163.76 tff(305,plain,
% 163.48/163.76 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))) | (~(d(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))) | (~(d(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err)))))),
% 163.48/163.76 inference(rewrite,[status(thm)],[])).
% 163.48/163.76 tff(306,plain,
% 163.48/163.76 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))) | (~(d(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err)))))),
% 163.48/163.76 inference(quant_inst,[status(thm)],[])).
% 163.48/163.76 tff(307,plain,
% 163.48/163.76 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))) | (~(d(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err))))),
% 163.48/163.76 inference(modus_ponens,[status(thm)],[306, 305])).
% 163.48/163.76 tff(308,plain,
% 163.48/163.76 ((~((~d(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))) | (~(d(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err))))),
% 163.48/163.76 inference(unit_resolution,[status(thm)],[307, 39])).
% 163.48/163.76 tff(309,plain,
% 163.48/163.76 (~((~d(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))),
% 163.48/163.76 inference(unit_resolution,[status(thm)],[308, 304])).
% 163.48/163.76 tff(310,plain,
% 163.48/163.76 (((~d(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))) | (phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.48/163.76 inference(tautology,[status(thm)],[])).
% 163.48/163.76 tff(311,plain,
% 163.48/163.76 (phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 163.48/163.76 inference(unit_resolution,[status(thm)],[310, 309])).
% 163.48/163.76 tff(312,plain,
% 163.48/163.76 (impl(f5(P!7, false), false) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false)),
% 163.48/163.76 inference(symmetry,[status(thm)],[295])).
% 163.48/163.76 tff(313,plain,
% 163.48/163.76 (phi(impl(f5(P!7, false), false)) = phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))),
% 163.48/163.76 inference(symmetry,[status(thm)],[273])).
% 163.48/163.76 tff(314,plain,
% 163.48/163.76 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = lazy_impl(true, impl(f5(P!7, false), false))),
% 163.48/163.76 inference(symmetry,[status(thm)],[111])).
% 163.48/163.76 tff(315,plain,
% 163.48/163.76 (true = lazy_impl(prop(false), impl(f5(P!7, false), false))),
% 163.48/163.76 inference(symmetry,[status(thm)],[22])).
% 163.48/163.76 tff(316,plain,
% 163.48/163.76 (true = f5(P!7, false)),
% 163.48/163.76 inference(transitivity,[status(thm)],[315, 314, 120, 313, 293, 272, 312, 296, 311, 104])).
% 163.48/163.76 tff(317,plain,
% 163.48/163.76 (impl(true, false) = impl(f5(P!7, false), false)),
% 163.48/163.76 inference(monotonicity,[status(thm)],[316])).
% 163.48/163.76 tff(318,plain,
% 163.48/163.76 (impl(f5(P!7, false), false) = impl(true, false)),
% 163.48/163.76 inference(symmetry,[status(thm)],[317])).
% 163.48/163.76 tff(319,plain,
% 163.48/163.76 (true = false),
% 163.48/163.76 inference(transitivity,[status(thm)],[315, 314, 120, 313, 293, 272, 318, 86])).
% 163.48/163.76 tff(320,plain,
% 163.48/163.76 ($false),
% 163.48/163.76 inference(unit_resolution,[status(thm)],[56, 319])).
% 163.48/163.76 tff(321,plain,((~(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))) | (~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = true))), inference(lemma,lemma(discharge,[]))).
% 163.48/163.76 tff(322,plain,
% 163.48/163.76 (~(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.48/163.76 inference(unit_resolution,[status(thm)],[321, 22])).
% 163.48/163.76 tff(323,plain,
% 163.48/163.76 (^[A: $i, B: $i] : refl((bool(A) | (impl(A, B) = phi(A))) <=> (bool(A) | (impl(A, B) = phi(A))))),
% 163.48/163.76 inference(bind,[status(th)],[])).
% 163.48/163.76 tff(324,plain,
% 163.48/163.76 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 163.48/163.76 inference(quant_intro,[status(thm)],[323])).
% 163.48/163.76 tff(325,plain,
% 163.48/163.76 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 163.48/163.76 inference(rewrite,[status(thm)],[])).
% 163.48/163.76 tff(326,plain,
% 163.48/163.76 (^[A: $i, B: $i] : rewrite(((~bool(A)) => (impl(A, B) = phi(A))) <=> (bool(A) | (impl(A, B) = phi(A))))),
% 163.48/163.76 inference(bind,[status(th)],[])).
% 163.48/163.76 tff(327,plain,
% 163.48/163.76 (![A: $i, B: $i] : ((~bool(A)) => (impl(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 163.48/163.76 inference(quant_intro,[status(thm)],[326])).
% 163.48/163.76 tff(328,axiom,(![A: $i, B: $i] : ((~bool(A)) => (impl(A, B) = phi(A)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','impl_axiom1')).
% 163.48/163.76 tff(329,plain,
% 163.48/163.76 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 163.48/163.76 inference(modus_ponens,[status(thm)],[328, 327])).
% 163.48/163.76 tff(330,plain,
% 163.48/163.76 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 163.48/163.76 inference(modus_ponens,[status(thm)],[329, 325])).
% 163.48/163.76 tff(331,plain,(
% 163.48/163.76 ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 163.48/163.76 inference(skolemize,[status(sab)],[330])).
% 163.48/163.76 tff(332,plain,
% 163.48/163.76 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 163.48/163.76 inference(modus_ponens,[status(thm)],[331, 324])).
% 163.48/163.76 tff(333,plain,
% 163.48/163.76 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))),
% 163.48/163.76 inference(rewrite,[status(thm)],[])).
% 163.48/163.76 tff(334,plain,
% 163.48/163.76 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))),
% 163.48/163.76 inference(quant_inst,[status(thm)],[])).
% 163.48/163.76 tff(335,plain,
% 163.48/163.76 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.48/163.76 inference(modus_ponens,[status(thm)],[334, 333])).
% 163.48/163.76 tff(336,plain,
% 163.48/163.76 (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.48/163.76 inference(unit_resolution,[status(thm)],[335, 332])).
% 163.48/163.76 tff(337,plain,
% 163.48/163.76 (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.48/163.76 inference(unit_resolution,[status(thm)],[336, 322])).
% 163.48/163.76 tff(338,plain,
% 163.48/163.76 ((~((prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true) <=> bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))) | (prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true) | (~bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.48/163.76 inference(tautology,[status(thm)],[])).
% 163.48/163.76 tff(339,plain,
% 163.48/163.76 ((~((prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true) <=> bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))) | (prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true)),
% 163.48/163.76 inference(unit_resolution,[status(thm)],[338, 337])).
% 163.48/163.76 tff(340,plain,
% 163.48/163.76 (prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true),
% 163.48/163.76 inference(unit_resolution,[status(thm)],[339, 21])).
% 163.48/163.76 tff(341,plain,
% 163.48/163.76 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) <=> ((lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false) | (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true)))),
% 163.48/163.76 inference(quant_inst,[status(thm)],[])).
% 163.48/163.76 tff(342,plain,
% 163.48/163.76 (bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) <=> ((lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false) | (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true))),
% 163.48/163.76 inference(unit_resolution,[status(thm)],[341, 218])).
% 163.48/163.76 tff(343,plain,
% 163.48/163.76 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))) | (~((~(false = true)) | (~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false)))) | (~((~d(false)) | d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))) | (~((~(false = true)) | (~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false)))) | (~((~d(false)) | d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))))))),
% 163.48/163.76 inference(rewrite,[status(thm)],[])).
% 163.48/163.76 tff(344,plain,
% 163.48/163.76 ((forallprefers(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), false) <=> ((~((~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false)) | (~(false = true)))) | (~(d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))))) <=> (forallprefers(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))) | (~((~(false = true)) | (~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false)))) | (~((~d(false)) | d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))))),
% 163.48/163.76 inference(rewrite,[status(thm)],[])).
% 163.48/163.76 tff(345,plain,
% 163.48/163.76 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), false) <=> ((~((~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false)) | (~(false = true)))) | (~(d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))) | (~((~(false = true)) | (~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false)))) | (~((~d(false)) | d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))))))),
% 163.48/163.76 inference(monotonicity,[status(thm)],[344])).
% 163.48/163.76 tff(346,plain,
% 163.48/163.76 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), false) <=> ((~((~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false)) | (~(false = true)))) | (~(d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))) | (~((~(false = true)) | (~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false)))) | (~((~d(false)) | d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))))))),
% 163.48/163.76 inference(transitivity,[status(thm)],[345, 343])).
% 163.48/163.76 tff(347,plain,
% 163.48/163.76 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), false) <=> ((~((~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false)) | (~(false = true)))) | (~(d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))))))),
% 163.48/163.76 inference(quant_inst,[status(thm)],[])).
% 163.48/163.76 tff(348,plain,
% 163.48/163.76 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))) | (~((~(false = true)) | (~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false)))) | (~((~d(false)) | d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))))),
% 163.48/163.76 inference(modus_ponens,[status(thm)],[347, 346])).
% 163.48/163.76 tff(349,plain,
% 163.48/163.76 (forallprefers(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))) | (~((~(false = true)) | (~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false)))) | (~((~d(false)) | d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))))),
% 163.48/163.76 inference(unit_resolution,[status(thm)],[348, 165])).
% 163.48/163.76 tff(350,plain,
% 163.48/163.76 (^[P: $i, Q: $i, R: $i] : refl((f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R))) <=> (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R))))),
% 163.48/163.76 inference(bind,[status(th)],[])).
% 163.48/163.76 tff(351,plain,
% 163.48/163.76 (![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R))) <=> ![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))),
% 163.48/163.76 inference(quant_intro,[status(thm)],[350])).
% 163.48/163.76 tff(352,plain,
% 163.48/163.76 (![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R))) <=> ![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))),
% 163.48/163.76 inference(rewrite,[status(thm)],[])).
% 163.48/163.76 tff(353,axiom,(![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','def_f1')).
% 163.48/163.76 tff(354,plain,
% 163.48/163.76 (![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))),
% 163.48/163.76 inference(modus_ponens,[status(thm)],[353, 352])).
% 163.48/163.76 tff(355,plain,(
% 163.48/163.76 ![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))),
% 163.48/163.76 inference(skolemize,[status(sab)],[354])).
% 163.48/163.76 tff(356,plain,
% 163.48/163.76 (![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))),
% 163.48/163.76 inference(modus_ponens,[status(thm)],[355, 351])).
% 163.48/163.76 tff(357,plain,
% 163.48/163.76 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(true, false, tptp_fun_R_0(false, true)) = lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))),
% 163.48/163.76 inference(quant_inst,[status(thm)],[])).
% 163.48/163.76 tff(358,plain,
% 163.48/163.76 (f1(true, false, tptp_fun_R_0(false, true)) = lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))),
% 163.48/163.76 inference(unit_resolution,[status(thm)],[357, 356])).
% 163.48/163.76 tff(359,plain,
% 163.48/163.76 (lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = f1(true, false, tptp_fun_R_0(false, true))),
% 163.48/163.76 inference(symmetry,[status(thm)],[358])).
% 163.48/163.76 tff(360,plain,
% 163.48/163.76 ((~![B: $i] : (lazy_impl(false, B) = true)) | (lazy_impl(false, impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = true)),
% 163.48/163.76 inference(quant_inst,[status(thm)],[])).
% 163.48/163.76 tff(361,plain,
% 163.48/163.76 (lazy_impl(false, impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = true),
% 163.48/163.76 inference(unit_resolution,[status(thm)],[360, 147])).
% 163.48/163.76 tff(362,assumption,(prop(tptp_fun_R_0(false, true)) = false), introduced(assumption)).
% 163.48/163.76 tff(363,plain,
% 163.48/163.76 (lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = lazy_impl(false, impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))),
% 163.48/163.76 inference(monotonicity,[status(thm)],[362])).
% 163.48/163.76 tff(364,plain,
% 163.48/163.76 (lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = true),
% 163.48/163.76 inference(transitivity,[status(thm)],[363, 361])).
% 163.48/163.76 tff(365,plain,
% 163.48/163.76 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))) <=> ((lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = true) | (~((~d(false)) | bool(false) | (~bool(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))) <=> ((lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = true) | (~((~d(false)) | bool(false) | (~bool(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))))))))),
% 163.48/163.77 inference(rewrite,[status(thm)],[])).
% 163.48/163.77 tff(366,plain,
% 163.48/163.77 ((forallprefers(false, lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))) <=> ((~((~(false = false)) | (~(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = true)))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))) | bool(false) | (~d(false)))))) <=> (forallprefers(false, lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))) <=> ((lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = true) | (~((~d(false)) | bool(false) | (~bool(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))))))))),
% 163.48/163.77 inference(rewrite,[status(thm)],[])).
% 163.48/163.77 tff(367,plain,
% 163.48/163.77 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))) <=> ((~((~(false = false)) | (~(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = true)))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))) | bool(false) | (~d(false))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))) <=> ((lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = true) | (~((~d(false)) | bool(false) | (~bool(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))))))))),
% 163.48/163.77 inference(monotonicity,[status(thm)],[366])).
% 163.48/163.77 tff(368,plain,
% 163.48/163.77 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))) <=> ((~((~(false = false)) | (~(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = true)))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))) | bool(false) | (~d(false))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))) <=> ((lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = true) | (~((~d(false)) | bool(false) | (~bool(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))))))))),
% 163.48/163.77 inference(transitivity,[status(thm)],[367, 365])).
% 163.48/163.77 tff(369,plain,
% 163.48/163.77 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))) <=> ((~((~(false = false)) | (~(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = true)))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))) | (~bool(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))) | bool(false) | (~d(false))))))),
% 163.48/163.77 inference(quant_inst,[status(thm)],[])).
% 163.48/163.77 tff(370,plain,
% 163.48/163.77 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(false, lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))) <=> ((lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = true) | (~((~d(false)) | bool(false) | (~bool(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))))))))),
% 163.48/163.77 inference(modus_ponens,[status(thm)],[369, 368])).
% 163.48/163.77 tff(371,plain,
% 163.48/163.77 (forallprefers(false, lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))) <=> ((lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = true) | (~((~d(false)) | bool(false) | (~bool(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))))))),
% 163.48/163.77 inference(unit_resolution,[status(thm)],[370, 165])).
% 163.48/163.77 tff(372,plain,
% 163.48/163.77 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(true, false, false) = lazy_impl(prop(false), impl(impl(true, impl(false, false)), false)))),
% 163.48/163.77 inference(quant_inst,[status(thm)],[])).
% 163.48/163.77 tff(373,plain,
% 163.48/163.77 (f1(true, false, false) = lazy_impl(prop(false), impl(impl(true, impl(false, false)), false))),
% 163.48/163.77 inference(unit_resolution,[status(thm)],[372, 356])).
% 163.48/163.77 tff(374,plain,
% 163.48/163.77 (lazy_impl(prop(false), impl(impl(true, impl(false, false)), false)) = f1(true, false, false)),
% 163.48/163.77 inference(symmetry,[status(thm)],[373])).
% 163.48/163.77 tff(375,plain,
% 163.48/163.77 (((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | ((~bool(true)) | (impl(true, true) = true))) <=> ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | (~bool(true)) | (impl(true, true) = true))),
% 163.48/163.77 inference(rewrite,[status(thm)],[])).
% 163.48/163.77 tff(376,plain,
% 163.48/163.77 ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | ((~bool(true)) | (impl(true, true) = true))),
% 163.48/163.77 inference(quant_inst,[status(thm)],[])).
% 163.48/163.77 tff(377,plain,
% 163.48/163.77 ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | (~bool(true)) | (impl(true, true) = true)),
% 163.48/163.77 inference(modus_ponens,[status(thm)],[376, 375])).
% 163.48/163.77 tff(378,plain,
% 163.48/163.77 (impl(true, true) = true),
% 163.48/163.77 inference(unit_resolution,[status(thm)],[377, 82, 252])).
% 163.48/163.77 tff(379,plain,
% 163.48/163.77 (^[B: $i] : refl(((~bool(B)) | (impl(false, B) = true)) <=> ((~bool(B)) | (impl(false, B) = true)))),
% 163.48/163.77 inference(bind,[status(th)],[])).
% 163.48/163.77 tff(380,plain,
% 163.48/163.77 (![B: $i] : ((~bool(B)) | (impl(false, B) = true)) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 163.48/163.77 inference(quant_intro,[status(thm)],[379])).
% 163.48/163.77 tff(381,plain,
% 163.48/163.77 (![B: $i] : ((~bool(B)) | (impl(false, B) = true)) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 163.48/163.77 inference(rewrite,[status(thm)],[])).
% 163.48/163.77 tff(382,plain,
% 163.48/163.77 (^[B: $i] : rewrite((bool(B) => (impl(false, B) = true)) <=> ((~bool(B)) | (impl(false, B) = true)))),
% 163.48/163.77 inference(bind,[status(th)],[])).
% 163.48/163.77 tff(383,plain,
% 163.48/163.77 (![B: $i] : (bool(B) => (impl(false, B) = true)) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 163.48/163.77 inference(quant_intro,[status(thm)],[382])).
% 163.48/163.77 tff(384,axiom,(![B: $i] : (bool(B) => (impl(false, B) = true))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','impl_axiom3')).
% 163.48/163.77 tff(385,plain,
% 163.48/163.77 (![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 163.48/163.77 inference(modus_ponens,[status(thm)],[384, 383])).
% 163.48/163.77 tff(386,plain,
% 163.48/163.77 (![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 163.48/163.77 inference(modus_ponens,[status(thm)],[385, 381])).
% 163.48/163.77 tff(387,plain,(
% 163.48/163.77 ![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 163.48/163.77 inference(skolemize,[status(sab)],[386])).
% 163.48/163.77 tff(388,plain,
% 163.48/163.77 (![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 163.48/163.77 inference(modus_ponens,[status(thm)],[387, 380])).
% 163.48/163.77 tff(389,plain,
% 163.48/163.77 (((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | ((~bool(false)) | (impl(false, false) = true))) <=> ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | (~bool(false)) | (impl(false, false) = true))),
% 163.48/163.77 inference(rewrite,[status(thm)],[])).
% 163.48/163.77 tff(390,plain,
% 163.48/163.77 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | ((~bool(false)) | (impl(false, false) = true))),
% 163.48/163.77 inference(quant_inst,[status(thm)],[])).
% 163.48/163.77 tff(391,plain,
% 163.48/163.77 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | (~bool(false)) | (impl(false, false) = true)),
% 163.48/163.77 inference(modus_ponens,[status(thm)],[390, 389])).
% 163.48/163.77 tff(392,plain,
% 163.48/163.77 (impl(false, false) = true),
% 163.48/163.77 inference(unit_resolution,[status(thm)],[391, 388, 72])).
% 163.48/163.77 tff(393,plain,
% 163.48/163.77 (impl(true, impl(false, false)) = impl(true, true)),
% 163.48/163.77 inference(monotonicity,[status(thm)],[392])).
% 163.48/163.77 tff(394,plain,
% 163.48/163.77 (impl(true, impl(false, false)) = true),
% 163.48/163.77 inference(transitivity,[status(thm)],[393, 378])).
% 163.48/163.77 tff(395,plain,
% 163.48/163.77 (impl(impl(true, impl(false, false)), false) = impl(true, false)),
% 163.48/163.77 inference(monotonicity,[status(thm)],[394])).
% 163.48/163.77 tff(396,plain,
% 163.48/163.77 (impl(impl(true, impl(false, false)), false) = false),
% 163.48/163.77 inference(transitivity,[status(thm)],[395, 86])).
% 163.48/163.77 tff(397,plain,
% 163.48/163.77 (lazy_impl(prop(false), impl(impl(true, impl(false, false)), false)) = lazy_impl(true, false)),
% 163.48/163.77 inference(monotonicity,[status(thm)],[109, 396])).
% 163.48/163.77 tff(398,plain,
% 163.48/163.77 (lazy_impl(true, false) = lazy_impl(prop(false), impl(impl(true, impl(false, false)), false))),
% 163.48/163.77 inference(symmetry,[status(thm)],[397])).
% 163.48/163.77 tff(399,plain,
% 163.48/163.77 (false = f1(true, false, false)),
% 163.48/163.77 inference(transitivity,[status(thm)],[179, 178, 398, 374])).
% 163.48/163.77 tff(400,plain,
% 163.48/163.77 (forallprefers(false, lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))) <=> forallprefers(f1(true, false, false), f1(true, false, tptp_fun_R_0(false, true)))),
% 163.48/163.77 inference(monotonicity,[status(thm)],[399, 359])).
% 163.48/163.77 tff(401,plain,
% 163.48/163.77 (forallprefers(f1(true, false, false), f1(true, false, tptp_fun_R_0(false, true))) <=> forallprefers(false, lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))),
% 163.48/163.77 inference(symmetry,[status(thm)],[400])).
% 163.48/163.77 tff(402,plain,
% 163.48/163.77 ((~forallprefers(f1(true, false, false), f1(true, false, tptp_fun_R_0(false, true)))) <=> (~forallprefers(false, lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))))),
% 163.48/163.77 inference(monotonicity,[status(thm)],[401])).
% 163.48/163.77 tff(403,plain,
% 163.48/163.77 (^[P: $i, Q: $i] : refl((~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P))))))) <=> (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P))))))))),
% 163.48/163.77 inference(bind,[status(th)],[])).
% 163.48/163.77 tff(404,plain,
% 163.48/163.77 (![P: $i, Q: $i] : (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P))))))) <=> ![P: $i, Q: $i] : (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P)))))))),
% 163.48/163.77 inference(quant_intro,[status(thm)],[403])).
% 163.48/163.77 tff(405,plain,
% 163.48/163.77 (^[P: $i, Q: $i] : rewrite((~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P))))))) <=> (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P))))))))),
% 163.48/163.77 inference(bind,[status(th)],[])).
% 163.48/163.77 tff(406,plain,
% 163.48/163.77 (![P: $i, Q: $i] : (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P))))))) <=> ![P: $i, Q: $i] : (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P)))))))),
% 163.48/163.77 inference(quant_intro,[status(thm)],[405])).
% 163.48/163.77 tff(407,plain,
% 163.48/163.77 (![P: $i, Q: $i] : (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P))))))) <=> ![P: $i, Q: $i] : (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P)))))))),
% 163.48/163.77 inference(transitivity,[status(thm)],[406, 404])).
% 163.48/163.77 tff(408,plain,
% 163.48/163.77 (^[P: $i, Q: $i] : rewrite(((and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P)))) & ![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P))))) <=> (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P))))))))),
% 163.48/163.77 inference(bind,[status(th)],[])).
% 163.48/163.77 tff(409,plain,
% 163.48/163.77 (![P: $i, Q: $i] : ((and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P)))) & ![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P))))) <=> ![P: $i, Q: $i] : (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P)))))))),
% 163.48/163.77 inference(quant_intro,[status(thm)],[408])).
% 163.48/163.77 tff(410,plain,
% 163.48/163.77 (![P: $i, Q: $i] : ?[R: $i] : ((and2(P, Q) = phi(f1(P, Q, R))) & (~?[R1: $i] : forallprefers(f1(P, Q, R1), f1(P, Q, R)))) <=> ![P: $i, Q: $i] : ?[R: $i] : ((and2(P, Q) = phi(f1(P, Q, R))) & (~?[R1: $i] : forallprefers(f1(P, Q, R1), f1(P, Q, R))))),
% 163.48/163.77 inference(rewrite,[status(thm)],[])).
% 163.48/163.77 tff(411,axiom,(![P: $i, Q: $i] : ?[R: $i] : ((and2(P, Q) = phi(f1(P, Q, R))) & (~?[R1: $i] : forallprefers(f1(P, Q, R1), f1(P, Q, R))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','def_and2')).
% 163.48/163.77 tff(412,plain,
% 163.48/163.77 (![P: $i, Q: $i] : ?[R: $i] : ((and2(P, Q) = phi(f1(P, Q, R))) & (~?[R1: $i] : forallprefers(f1(P, Q, R1), f1(P, Q, R))))),
% 163.48/163.77 inference(modus_ponens,[status(thm)],[411, 410])).
% 163.48/163.77 tff(413,plain,(
% 163.48/163.77 ![P: $i, Q: $i] : ((and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P)))) & ![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P)))))),
% 163.48/163.77 inference(skolemize,[status(sab)],[412])).
% 163.48/163.77 tff(414,plain,
% 163.48/163.77 (![P: $i, Q: $i] : (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P)))))))),
% 163.48/163.77 inference(modus_ponens,[status(thm)],[413, 409])).
% 163.48/163.77 tff(415,plain,
% 163.48/163.77 (![P: $i, Q: $i] : (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P)))))))),
% 163.48/163.77 inference(modus_ponens,[status(thm)],[414, 407])).
% 163.48/163.77 tff(416,plain,
% 163.48/163.77 ((~![P: $i, Q: $i] : (~((~(and2(P, Q) = phi(f1(P, Q, tptp_fun_R_0(Q, P))))) | (~![R1: $i] : (~forallprefers(f1(P, Q, R1), f1(P, Q, tptp_fun_R_0(Q, P)))))))) | (~((~(and2(true, false) = phi(f1(true, false, tptp_fun_R_0(false, true))))) | (~![R1: $i] : (~forallprefers(f1(true, false, R1), f1(true, false, tptp_fun_R_0(false, true)))))))),
% 163.48/163.77 inference(quant_inst,[status(thm)],[])).
% 163.48/163.77 tff(417,plain,
% 163.48/163.77 (~((~(and2(true, false) = phi(f1(true, false, tptp_fun_R_0(false, true))))) | (~![R1: $i] : (~forallprefers(f1(true, false, R1), f1(true, false, tptp_fun_R_0(false, true))))))),
% 163.48/163.77 inference(unit_resolution,[status(thm)],[416, 415])).
% 163.48/163.77 tff(418,plain,
% 163.48/163.77 (((~(and2(true, false) = phi(f1(true, false, tptp_fun_R_0(false, true))))) | (~![R1: $i] : (~forallprefers(f1(true, false, R1), f1(true, false, tptp_fun_R_0(false, true)))))) | ![R1: $i] : (~forallprefers(f1(true, false, R1), f1(true, false, tptp_fun_R_0(false, true))))),
% 163.48/163.77 inference(tautology,[status(thm)],[])).
% 163.48/163.77 tff(419,plain,
% 163.48/163.77 (![R1: $i] : (~forallprefers(f1(true, false, R1), f1(true, false, tptp_fun_R_0(false, true))))),
% 163.48/163.77 inference(unit_resolution,[status(thm)],[418, 417])).
% 163.48/163.77 tff(420,plain,
% 163.48/163.77 ((~![R1: $i] : (~forallprefers(f1(true, false, R1), f1(true, false, tptp_fun_R_0(false, true))))) | (~forallprefers(f1(true, false, false), f1(true, false, tptp_fun_R_0(false, true))))),
% 163.48/163.77 inference(quant_inst,[status(thm)],[])).
% 163.48/163.77 tff(421,plain,
% 163.48/163.77 (~forallprefers(f1(true, false, false), f1(true, false, tptp_fun_R_0(false, true)))),
% 163.48/163.77 inference(unit_resolution,[status(thm)],[420, 419])).
% 163.48/163.77 tff(422,plain,
% 163.48/163.77 (~forallprefers(false, lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))),
% 163.48/163.77 inference(modus_ponens,[status(thm)],[421, 402])).
% 163.48/163.77 tff(423,plain,
% 163.48/163.77 ((~(forallprefers(false, lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))) <=> ((lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = true) | (~((~d(false)) | bool(false) | (~bool(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))))))))) | forallprefers(false, lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))) | (~((lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = true) | (~((~d(false)) | bool(false) | (~bool(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))))))))),
% 163.48/163.77 inference(tautology,[status(thm)],[])).
% 163.48/163.77 tff(424,plain,
% 163.48/163.77 (~((lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = true) | (~((~d(false)) | bool(false) | (~bool(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))))))),
% 163.48/163.77 inference(unit_resolution,[status(thm)],[423, 422, 371])).
% 163.48/163.77 tff(425,plain,
% 163.48/163.77 (((lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = true) | (~((~d(false)) | bool(false) | (~bool(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))))))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))))))) | (~(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = true))),
% 163.48/163.77 inference(tautology,[status(thm)],[])).
% 163.48/163.77 tff(426,plain,
% 163.48/163.77 (~(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = true)),
% 163.48/163.77 inference(unit_resolution,[status(thm)],[425, 424])).
% 163.48/163.77 tff(427,plain,
% 163.48/163.77 ($false),
% 163.48/163.77 inference(unit_resolution,[status(thm)],[426, 364])).
% 163.48/163.77 tff(428,plain,(~(prop(tptp_fun_R_0(false, true)) = false)), inference(lemma,lemma(discharge,[]))).
% 163.48/163.77 tff(429,plain,
% 163.48/163.77 ((~![X: $i] : (~(bool(X) <=> (prop(X) = false)))) | (~(bool(tptp_fun_R_0(false, true)) <=> (prop(tptp_fun_R_0(false, true)) = false)))),
% 163.48/163.77 inference(quant_inst,[status(thm)],[])).
% 163.48/163.77 tff(430,plain,
% 163.48/163.77 (~(bool(tptp_fun_R_0(false, true)) <=> (prop(tptp_fun_R_0(false, true)) = false))),
% 163.48/163.77 inference(unit_resolution,[status(thm)],[429, 206])).
% 163.48/163.77 tff(431,plain,
% 163.48/163.77 ((bool(tptp_fun_R_0(false, true)) <=> (prop(tptp_fun_R_0(false, true)) = false)) | bool(tptp_fun_R_0(false, true)) | (prop(tptp_fun_R_0(false, true)) = false)),
% 163.48/163.77 inference(tautology,[status(thm)],[])).
% 163.48/163.77 tff(432,plain,
% 163.48/163.77 (bool(tptp_fun_R_0(false, true)) | (prop(tptp_fun_R_0(false, true)) = false)),
% 163.48/163.77 inference(unit_resolution,[status(thm)],[431, 430])).
% 163.48/163.77 tff(433,plain,
% 163.48/163.77 (bool(tptp_fun_R_0(false, true))),
% 163.48/163.77 inference(unit_resolution,[status(thm)],[432, 428])).
% 163.48/163.77 tff(434,plain,
% 163.48/163.77 (((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | ((~bool(tptp_fun_R_0(false, true))) | (impl(true, tptp_fun_R_0(false, true)) = tptp_fun_R_0(false, true)))) <=> ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | (~bool(tptp_fun_R_0(false, true))) | (impl(true, tptp_fun_R_0(false, true)) = tptp_fun_R_0(false, true)))),
% 163.48/163.77 inference(rewrite,[status(thm)],[])).
% 163.48/163.77 tff(435,plain,
% 163.48/163.77 ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | ((~bool(tptp_fun_R_0(false, true))) | (impl(true, tptp_fun_R_0(false, true)) = tptp_fun_R_0(false, true)))),
% 163.48/163.77 inference(quant_inst,[status(thm)],[])).
% 163.48/163.77 tff(436,plain,
% 163.48/163.77 ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | (~bool(tptp_fun_R_0(false, true))) | (impl(true, tptp_fun_R_0(false, true)) = tptp_fun_R_0(false, true))),
% 163.48/163.77 inference(modus_ponens,[status(thm)],[435, 434])).
% 163.48/163.77 tff(437,plain,
% 163.48/163.77 ((~bool(tptp_fun_R_0(false, true))) | (impl(true, tptp_fun_R_0(false, true)) = tptp_fun_R_0(false, true))),
% 163.48/163.77 inference(unit_resolution,[status(thm)],[436, 82])).
% 163.48/163.77 tff(438,plain,
% 163.48/163.77 (impl(true, tptp_fun_R_0(false, true)) = tptp_fun_R_0(false, true)),
% 163.48/163.77 inference(unit_resolution,[status(thm)],[437, 433])).
% 163.48/163.77 tff(439,plain,
% 163.48/163.77 (((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | ((~bool(tptp_fun_R_0(false, true))) | (impl(false, tptp_fun_R_0(false, true)) = true))) <=> ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | (~bool(tptp_fun_R_0(false, true))) | (impl(false, tptp_fun_R_0(false, true)) = true))),
% 163.48/163.77 inference(rewrite,[status(thm)],[])).
% 163.48/163.77 tff(440,plain,
% 163.48/163.77 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | ((~bool(tptp_fun_R_0(false, true))) | (impl(false, tptp_fun_R_0(false, true)) = true))),
% 163.48/163.77 inference(quant_inst,[status(thm)],[])).
% 163.48/163.77 tff(441,plain,
% 163.48/163.77 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | (~bool(tptp_fun_R_0(false, true))) | (impl(false, tptp_fun_R_0(false, true)) = true)),
% 163.48/163.77 inference(modus_ponens,[status(thm)],[440, 439])).
% 163.48/163.77 tff(442,plain,
% 163.48/163.77 ((~bool(tptp_fun_R_0(false, true))) | (impl(false, tptp_fun_R_0(false, true)) = true)),
% 163.48/163.77 inference(unit_resolution,[status(thm)],[441, 388])).
% 163.48/163.77 tff(443,plain,
% 163.48/163.77 (impl(false, tptp_fun_R_0(false, true)) = true),
% 163.48/163.77 inference(unit_resolution,[status(thm)],[442, 433])).
% 163.48/163.77 tff(444,plain,
% 163.48/163.77 (impl(true, impl(false, tptp_fun_R_0(false, true))) = impl(true, true)),
% 163.48/163.77 inference(monotonicity,[status(thm)],[443])).
% 163.48/163.77 tff(445,plain,
% 163.48/163.77 (impl(true, impl(false, tptp_fun_R_0(false, true))) = true),
% 163.48/163.77 inference(transitivity,[status(thm)],[444, 378])).
% 163.48/163.77 tff(446,plain,
% 163.48/163.77 (impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)) = impl(true, tptp_fun_R_0(false, true))),
% 163.48/163.77 inference(monotonicity,[status(thm)],[445])).
% 163.48/163.77 tff(447,plain,
% 163.48/163.77 (impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)) = tptp_fun_R_0(false, true)),
% 163.48/163.77 inference(transitivity,[status(thm)],[446, 438])).
% 163.48/163.77 tff(448,plain,
% 163.48/163.77 (lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))),
% 163.48/163.77 inference(monotonicity,[status(thm)],[447])).
% 163.48/163.77 tff(449,plain,
% 163.48/163.77 (lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true)))),
% 163.48/163.77 inference(symmetry,[status(thm)],[448])).
% 163.48/163.77 tff(450,plain,
% 163.48/163.77 ((lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = true) <=> (lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = true)),
% 163.48/163.78 inference(monotonicity,[status(thm)],[448])).
% 163.48/163.78 tff(451,plain,
% 163.48/163.78 ((~(lazy_impl(prop(tptp_fun_R_0(false, true)), impl(impl(true, impl(false, tptp_fun_R_0(false, true))), tptp_fun_R_0(false, true))) = true)) <=> (~(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = true))),
% 163.48/163.78 inference(monotonicity,[status(thm)],[450])).
% 163.48/163.78 tff(452,plain,
% 163.48/163.78 (~(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = true)),
% 163.48/163.78 inference(modus_ponens,[status(thm)],[426, 451])).
% 163.48/163.78 tff(453,plain,
% 163.48/163.78 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) <=> ((lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false) | (lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = true)))),
% 163.48/163.78 inference(quant_inst,[status(thm)],[])).
% 163.48/163.78 tff(454,plain,
% 163.48/163.78 (bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) <=> ((lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false) | (lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = true))),
% 163.48/163.78 inference(unit_resolution,[status(thm)],[453, 218])).
% 163.48/163.78 tff(455,plain,
% 163.48/163.78 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))))))))),
% 163.48/163.78 inference(rewrite,[status(thm)],[])).
% 163.48/163.78 tff(456,plain,
% 163.48/163.78 ((forallprefers(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)), false) <=> ((~((~(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false)) | (~(false = true)))) | (~(d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))))) <=> (forallprefers(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))))),
% 163.48/163.78 inference(rewrite,[status(thm)],[])).
% 163.48/163.78 tff(457,plain,
% 163.48/163.78 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)), false) <=> ((~((~(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false)) | (~(false = true)))) | (~(d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))))))))),
% 163.48/163.78 inference(monotonicity,[status(thm)],[456])).
% 163.48/163.78 tff(458,plain,
% 163.48/163.78 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)), false) <=> ((~((~(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false)) | (~(false = true)))) | (~(d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))))))))),
% 163.48/163.78 inference(transitivity,[status(thm)],[457, 455])).
% 163.48/163.78 tff(459,plain,
% 163.48/163.78 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)), false) <=> ((~((~(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false)) | (~(false = true)))) | (~(d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))))))))),
% 163.48/163.78 inference(quant_inst,[status(thm)],[])).
% 163.48/163.78 tff(460,plain,
% 163.48/163.78 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))))),
% 163.48/163.78 inference(modus_ponens,[status(thm)],[459, 458])).
% 163.48/163.78 tff(461,plain,
% 163.48/163.78 (forallprefers(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))))))),
% 163.48/163.78 inference(unit_resolution,[status(thm)],[460, 165])).
% 163.48/163.78 tff(462,plain,
% 163.48/163.78 (f7(false) = f7(P!6)),
% 163.48/163.78 inference(symmetry,[status(thm)],[266])).
% 163.48/163.78 tff(463,plain,
% 163.48/163.78 (false = f7(P!6)),
% 163.48/163.78 inference(transitivity,[status(thm)],[179, 178, 177, 176, 462])).
% 163.48/163.78 tff(464,plain,
% 163.48/163.78 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(tptp_fun_R_0(false, true)) = lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))),
% 163.48/163.78 inference(quant_inst,[status(thm)],[])).
% 163.48/163.78 tff(465,plain,
% 163.48/163.78 (f7(tptp_fun_R_0(false, true)) = lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))),
% 163.48/163.78 inference(unit_resolution,[status(thm)],[464, 138])).
% 163.48/163.78 tff(466,plain,
% 163.48/163.78 (lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = f7(tptp_fun_R_0(false, true))),
% 163.48/163.78 inference(symmetry,[status(thm)],[465])).
% 163.48/163.78 tff(467,plain,
% 163.48/163.78 (forallprefers(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)), false) <=> forallprefers(f7(tptp_fun_R_0(false, true)), f7(P!6))),
% 163.48/163.78 inference(monotonicity,[status(thm)],[466, 463])).
% 163.48/163.78 tff(468,plain,
% 163.48/163.78 (forallprefers(f7(tptp_fun_R_0(false, true)), f7(P!6)) <=> forallprefers(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)), false)),
% 163.48/163.78 inference(symmetry,[status(thm)],[467])).
% 163.48/163.78 tff(469,plain,
% 163.48/163.78 ((~forallprefers(f7(tptp_fun_R_0(false, true)), f7(P!6))) <=> (~forallprefers(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)), false))),
% 163.48/163.78 inference(monotonicity,[status(thm)],[468])).
% 163.48/163.78 tff(470,plain,
% 163.48/163.78 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(tptp_fun_R_0(false, true)), f7(P!6)))),
% 163.48/163.78 inference(quant_inst,[status(thm)],[])).
% 163.48/163.78 tff(471,plain,
% 163.48/163.78 (~forallprefers(f7(tptp_fun_R_0(false, true)), f7(P!6))),
% 163.48/163.78 inference(unit_resolution,[status(thm)],[470, 187])).
% 163.48/163.78 tff(472,plain,
% 163.48/163.78 (~forallprefers(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)), false)),
% 163.48/163.78 inference(modus_ponens,[status(thm)],[471, 469])).
% 163.48/163.78 tff(473,plain,
% 163.48/163.78 ((~(forallprefers(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))))) | forallprefers(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)), false) | (~((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))))),
% 163.48/163.78 inference(tautology,[status(thm)],[])).
% 163.48/163.78 tff(474,plain,
% 163.48/163.78 (~((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))))))),
% 163.48/163.78 inference(unit_resolution,[status(thm)],[473, 472, 461])).
% 163.48/163.78 tff(475,plain,
% 163.48/163.78 (((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))) | ((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))),
% 163.48/163.78 inference(tautology,[status(thm)],[])).
% 163.48/163.78 tff(476,plain,
% 163.48/163.78 ((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))))),
% 163.48/163.78 inference(unit_resolution,[status(thm)],[475, 474])).
% 163.48/163.78 tff(477,plain,
% 163.48/163.78 (((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))) | ((~d(false)) | d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))))),
% 163.48/163.78 inference(tautology,[status(thm)],[])).
% 163.48/163.78 tff(478,plain,
% 163.48/163.78 ((~d(false)) | d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))),
% 163.48/163.78 inference(unit_resolution,[status(thm)],[477, 474])).
% 163.48/163.78 tff(479,plain,
% 163.48/163.78 ((~((~d(false)) | d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))))) | (~d(false)) | d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))),
% 163.48/163.78 inference(tautology,[status(thm)],[])).
% 163.48/163.78 tff(480,plain,
% 163.48/163.78 ((~((~d(false)) | d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))))) | d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))),
% 163.48/163.78 inference(unit_resolution,[status(thm)],[479, 27])).
% 163.48/163.78 tff(481,plain,
% 163.48/163.78 (d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))),
% 163.48/163.78 inference(unit_resolution,[status(thm)],[480, 478])).
% 163.48/163.78 tff(482,plain,
% 163.48/163.78 ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))) | (~d(false)) | (~bool(false)) | bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))))),
% 163.48/163.78 inference(tautology,[status(thm)],[])).
% 163.48/163.78 tff(483,plain,
% 163.48/163.78 ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))))) | bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) | (~d(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))))),
% 163.48/163.78 inference(unit_resolution,[status(thm)],[482, 27, 72])).
% 163.48/163.78 tff(484,plain,
% 163.48/163.78 (bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))),
% 163.48/163.78 inference(unit_resolution,[status(thm)],[483, 481, 476])).
% 163.48/163.78 tff(485,plain,
% 163.48/163.78 ((~(bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) <=> ((lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false) | (lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = true)))) | (~bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)))) | ((lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false) | (lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = true))),
% 163.48/163.78 inference(tautology,[status(thm)],[])).
% 163.48/163.78 tff(486,plain,
% 163.48/163.78 ((~(bool(lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))) <=> ((lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false) | (lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = true)))) | ((lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false) | (lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = true))),
% 163.48/163.78 inference(unit_resolution,[status(thm)],[485, 484])).
% 163.48/163.78 tff(487,plain,
% 163.48/163.78 ((lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false) | (lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = true)),
% 163.48/163.78 inference(unit_resolution,[status(thm)],[486, 454])).
% 163.48/163.78 tff(488,plain,
% 163.48/163.78 ((~((lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false) | (lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = true))) | (lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false) | (lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = true)),
% 163.48/163.78 inference(tautology,[status(thm)],[])).
% 163.48/163.78 tff(489,plain,
% 163.48/163.78 ((lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false) | (lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = true)),
% 163.48/163.78 inference(unit_resolution,[status(thm)],[488, 487])).
% 163.48/163.78 tff(490,plain,
% 163.48/163.78 (lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true)) = false),
% 163.48/163.78 inference(unit_resolution,[status(thm)],[489, 452])).
% 163.48/163.78 tff(491,plain,
% 163.48/163.78 (false = lazy_impl(prop(tptp_fun_R_0(false, true)), tptp_fun_R_0(false, true))),
% 163.48/163.78 inference(symmetry,[status(thm)],[490])).
% 163.48/163.78 tff(492,plain,
% 163.48/163.78 (false = f1(true, false, tptp_fun_R_0(false, true))),
% 163.48/163.78 inference(transitivity,[status(thm)],[491, 449, 359])).
% 163.48/163.78 tff(493,plain,
% 163.48/163.78 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(true, false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), impl(impl(true, impl(false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))),
% 163.48/163.78 inference(quant_inst,[status(thm)],[])).
% 163.48/163.78 tff(494,plain,
% 163.48/163.78 (f1(true, false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), impl(impl(true, impl(false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.48/163.78 inference(unit_resolution,[status(thm)],[493, 356])).
% 163.48/163.78 tff(495,plain,
% 163.48/163.78 (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), impl(impl(true, impl(false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) = f1(true, false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.48/163.78 inference(symmetry,[status(thm)],[494])).
% 163.48/163.78 tff(496,plain,
% 163.48/163.78 (((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | ((~bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (impl(true, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))) <=> ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | (~bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (impl(true, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.48/163.78 inference(rewrite,[status(thm)],[])).
% 163.48/163.78 tff(497,plain,
% 163.48/163.78 ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | ((~bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (impl(true, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.48/163.78 inference(quant_inst,[status(thm)],[])).
% 163.48/163.78 tff(498,plain,
% 163.48/163.78 ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | (~bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (impl(true, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.48/163.78 inference(modus_ponens,[status(thm)],[497, 496])).
% 163.48/163.78 tff(499,plain,
% 163.48/163.78 (impl(true, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 163.48/163.78 inference(unit_resolution,[status(thm)],[498, 82, 337])).
% 163.48/163.78 tff(500,plain,
% 163.48/163.78 (((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | ((~bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (impl(false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true))) <=> ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | (~bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (impl(false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true))),
% 163.48/163.78 inference(rewrite,[status(thm)],[])).
% 163.48/163.78 tff(501,plain,
% 163.48/163.78 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | ((~bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (impl(false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true))),
% 163.48/163.78 inference(quant_inst,[status(thm)],[])).
% 163.48/163.78 tff(502,plain,
% 163.48/163.78 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | (~bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (impl(false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true)),
% 163.48/163.78 inference(modus_ponens,[status(thm)],[501, 500])).
% 163.48/163.78 tff(503,plain,
% 163.48/163.78 (impl(false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true),
% 163.48/163.78 inference(unit_resolution,[status(thm)],[502, 388, 337])).
% 163.48/163.78 tff(504,plain,
% 163.48/163.78 (impl(true, impl(false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) = impl(true, true)),
% 163.48/163.78 inference(monotonicity,[status(thm)],[503])).
% 163.48/163.78 tff(505,plain,
% 163.48/163.78 (impl(true, impl(false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) = true),
% 163.48/163.78 inference(transitivity,[status(thm)],[504, 378])).
% 163.48/163.78 tff(506,plain,
% 163.48/163.78 (impl(impl(true, impl(false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = impl(true, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.48/163.78 inference(monotonicity,[status(thm)],[505])).
% 163.48/163.78 tff(507,plain,
% 163.48/163.78 (impl(impl(true, impl(false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 163.48/163.78 inference(transitivity,[status(thm)],[506, 499])).
% 163.48/163.78 tff(508,plain,
% 163.48/163.78 (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), impl(impl(true, impl(false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) = lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.48/163.78 inference(monotonicity,[status(thm)],[507])).
% 163.48/163.78 tff(509,plain,
% 163.48/163.78 (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), impl(impl(true, impl(false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.48/163.78 inference(symmetry,[status(thm)],[508])).
% 163.48/163.78 tff(510,plain,
% 163.48/163.78 (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = f1(true, false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.48/163.78 inference(transitivity,[status(thm)],[509, 495])).
% 163.48/163.78 tff(511,plain,
% 163.48/163.78 (forallprefers(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), false) <=> forallprefers(f1(true, false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), f1(true, false, tptp_fun_R_0(false, true)))),
% 163.48/163.78 inference(monotonicity,[status(thm)],[510, 492])).
% 163.48/163.78 tff(512,plain,
% 163.48/163.78 (forallprefers(f1(true, false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), f1(true, false, tptp_fun_R_0(false, true))) <=> forallprefers(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), false)),
% 163.48/163.79 inference(symmetry,[status(thm)],[511])).
% 163.48/163.79 tff(513,plain,
% 163.48/163.79 ((~forallprefers(f1(true, false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), f1(true, false, tptp_fun_R_0(false, true)))) <=> (~forallprefers(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), false))),
% 163.48/163.79 inference(monotonicity,[status(thm)],[512])).
% 163.48/163.79 tff(514,plain,
% 163.48/163.79 ((~![R1: $i] : (~forallprefers(f1(true, false, R1), f1(true, false, tptp_fun_R_0(false, true))))) | (~forallprefers(f1(true, false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), f1(true, false, tptp_fun_R_0(false, true))))),
% 163.48/163.79 inference(quant_inst,[status(thm)],[])).
% 163.48/163.79 tff(515,plain,
% 163.48/163.79 (~forallprefers(f1(true, false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), f1(true, false, tptp_fun_R_0(false, true)))),
% 163.48/163.79 inference(unit_resolution,[status(thm)],[514, 419])).
% 163.48/163.79 tff(516,plain,
% 163.48/163.79 (~forallprefers(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), false)),
% 163.48/163.79 inference(modus_ponens,[status(thm)],[515, 513])).
% 163.48/163.79 tff(517,plain,
% 163.48/163.79 ((~(forallprefers(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))) | (~((~(false = true)) | (~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false)))) | (~((~d(false)) | d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))))) | forallprefers(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), false) | (~((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))) | (~((~(false = true)) | (~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false)))) | (~((~d(false)) | d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))))),
% 163.48/163.79 inference(tautology,[status(thm)],[])).
% 163.48/163.79 tff(518,plain,
% 163.48/163.79 (~((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))) | (~((~(false = true)) | (~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false)))) | (~((~d(false)) | d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))))),
% 163.48/163.79 inference(unit_resolution,[status(thm)],[517, 516, 349])).
% 163.48/163.79 tff(519,plain,
% 163.48/163.79 (((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))) | (~((~(false = true)) | (~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false)))) | (~((~d(false)) | d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))) | ((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))),
% 163.48/163.79 inference(tautology,[status(thm)],[])).
% 163.48/163.79 tff(520,plain,
% 163.48/163.79 ((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))),
% 163.48/163.79 inference(unit_resolution,[status(thm)],[519, 518])).
% 163.48/163.79 tff(521,plain,
% 163.48/163.79 (((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))) | (~((~(false = true)) | (~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false)))) | (~((~d(false)) | d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))) | ((~d(false)) | d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))),
% 163.48/163.79 inference(tautology,[status(thm)],[])).
% 163.48/163.79 tff(522,plain,
% 163.48/163.79 ((~d(false)) | d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.48/163.79 inference(unit_resolution,[status(thm)],[521, 518])).
% 163.48/163.79 tff(523,plain,
% 163.48/163.79 ((~((~d(false)) | d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))) | (~d(false)) | d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.48/163.79 inference(tautology,[status(thm)],[])).
% 163.48/163.79 tff(524,plain,
% 163.48/163.79 ((~((~d(false)) | d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))) | d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.48/163.79 inference(unit_resolution,[status(thm)],[523, 27])).
% 163.48/163.79 tff(525,plain,
% 163.48/163.79 (d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.48/163.79 inference(unit_resolution,[status(thm)],[524, 522])).
% 163.48/163.79 tff(526,plain,
% 163.48/163.79 ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))) | (~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))),
% 163.48/163.79 inference(tautology,[status(thm)],[])).
% 163.48/163.79 tff(527,plain,
% 163.48/163.79 ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))),
% 163.48/163.79 inference(unit_resolution,[status(thm)],[526, 27, 72])).
% 163.48/163.79 tff(528,plain,
% 163.48/163.79 (bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.48/163.79 inference(unit_resolution,[status(thm)],[527, 525, 520])).
% 163.48/163.79 tff(529,plain,
% 163.48/163.79 ((~(bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) <=> ((lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false) | (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true)))) | (~bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))) | ((lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false) | (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true))),
% 163.48/163.79 inference(tautology,[status(thm)],[])).
% 163.48/163.79 tff(530,plain,
% 163.48/163.79 ((~(bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) <=> ((lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false) | (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true)))) | ((lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false) | (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true))),
% 163.48/163.79 inference(unit_resolution,[status(thm)],[529, 528])).
% 163.48/163.79 tff(531,plain,
% 163.48/163.79 ((lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false) | (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true)),
% 163.48/163.79 inference(unit_resolution,[status(thm)],[530, 342])).
% 163.48/163.79 tff(532,plain,
% 163.48/163.79 ((phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false)) <=> (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.48/163.79 inference(commutativity,[status(thm)],[])).
% 163.48/163.79 tff(533,plain,
% 163.48/163.79 (true = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false)),
% 163.48/163.79 inference(transitivity,[status(thm)],[315, 314, 120, 313, 293, 272, 312])).
% 163.48/163.79 tff(534,plain,
% 163.48/163.79 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.48/163.79 inference(quant_inst,[status(thm)],[])).
% 163.48/163.79 tff(535,plain,
% 163.48/163.79 (lazy_impl(true, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.48/163.79 inference(unit_resolution,[status(thm)],[534, 118])).
% 163.48/163.79 tff(536,plain,
% 163.48/163.79 (true = prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.48/163.79 inference(symmetry,[status(thm)],[340])).
% 163.48/163.79 tff(537,plain,
% 163.48/163.79 (lazy_impl(true, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.48/163.79 inference(monotonicity,[status(thm)],[536])).
% 163.48/163.79 tff(538,plain,
% 163.48/163.79 (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = lazy_impl(true, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.48/163.79 inference(symmetry,[status(thm)],[537])).
% 163.48/163.79 tff(539,plain,
% 163.48/163.79 (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.48/163.79 inference(transitivity,[status(thm)],[538, 535])).
% 163.48/163.79 tff(540,plain,
% 163.48/163.79 ((lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true) <=> (phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false))),
% 163.48/163.79 inference(monotonicity,[status(thm)],[539, 533])).
% 163.48/163.79 tff(541,plain,
% 163.48/163.79 ((lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true) <=> (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.48/163.79 inference(transitivity,[status(thm)],[540, 532])).
% 163.48/163.79 tff(542,plain,
% 163.48/163.79 ((impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) <=> (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true)),
% 163.48/163.79 inference(symmetry,[status(thm)],[541])).
% 163.48/163.79 tff(543,plain,
% 163.48/163.79 ((~(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))) <=> (~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true))),
% 163.48/163.79 inference(monotonicity,[status(thm)],[542])).
% 163.48/163.79 tff(544,plain,
% 163.48/163.79 (~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true)),
% 163.48/163.79 inference(modus_ponens,[status(thm)],[322, 543])).
% 163.48/163.79 tff(545,plain,
% 163.48/163.79 ((~((lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false) | (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true))) | (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false) | (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true)),
% 163.48/163.79 inference(tautology,[status(thm)],[])).
% 163.48/163.79 tff(546,plain,
% 163.48/163.79 (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false),
% 163.48/163.79 inference(unit_resolution,[status(thm)],[545, 544, 531])).
% 163.48/163.79 tff(547,assumption,(~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))))), introduced(assumption)).
% 163.48/163.79 tff(548,plain,
% 163.48/163.79 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false) <=> ((~((~d(false)) | d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))) | (~((~(false = true)) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = false)))) | (~((~d(false)) | (~bool(false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false) <=> ((~((~d(false)) | d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))) | (~((~(false = true)) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = false)))) | (~((~d(false)) | (~bool(false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), true))))))))),
% 163.48/163.79 inference(rewrite,[status(thm)],[])).
% 163.48/163.79 tff(549,plain,
% 163.48/163.79 ((forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false) <=> ((~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = false)) | (~(false = true)))) | (~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), true))))))) <=> (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false) <=> ((~((~d(false)) | d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))) | (~((~(false = true)) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = false)))) | (~((~d(false)) | (~bool(false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))))))),
% 163.48/163.79 inference(rewrite,[status(thm)],[])).
% 163.48/163.79 tff(550,plain,
% 163.48/163.79 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false) <=> ((~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = false)) | (~(false = true)))) | (~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false) <=> ((~((~d(false)) | d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))) | (~((~(false = true)) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = false)))) | (~((~d(false)) | (~bool(false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), true))))))))),
% 163.48/163.79 inference(monotonicity,[status(thm)],[549])).
% 163.48/163.79 tff(551,plain,
% 163.48/163.79 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false) <=> ((~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = false)) | (~(false = true)))) | (~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false) <=> ((~((~d(false)) | d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))) | (~((~(false = true)) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = false)))) | (~((~d(false)) | (~bool(false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), true))))))))),
% 163.48/163.79 inference(transitivity,[status(thm)],[550, 548])).
% 163.48/163.79 tff(552,plain,
% 163.48/163.79 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false) <=> ((~((~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = false)) | (~(false = true)))) | (~(d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))))))),
% 163.48/163.79 inference(quant_inst,[status(thm)],[])).
% 163.48/163.79 tff(553,plain,
% 163.48/163.79 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false) <=> ((~((~d(false)) | d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))) | (~((~(false = true)) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = false)))) | (~((~d(false)) | (~bool(false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))))))),
% 163.48/163.79 inference(modus_ponens,[status(thm)],[552, 551])).
% 163.48/163.79 tff(554,plain,
% 163.48/163.79 (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false) <=> ((~((~d(false)) | d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))) | (~((~(false = true)) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = false)))) | (~((~d(false)) | (~bool(false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), true))))))),
% 163.48/163.79 inference(unit_resolution,[status(thm)],[553, 165])).
% 163.48/163.79 tff(555,plain,
% 163.48/163.79 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) <=> ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = true)))),
% 163.48/163.79 inference(quant_inst,[status(thm)],[])).
% 163.48/163.79 tff(556,plain,
% 163.48/163.79 (bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) <=> ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = true))),
% 163.48/163.79 inference(unit_resolution,[status(thm)],[555, 218])).
% 163.48/163.79 tff(557,plain,
% 163.48/163.79 (^[P: $i, R: $i] : refl((f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R))) <=> (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R))))),
% 163.48/163.79 inference(bind,[status(th)],[])).
% 163.48/163.79 tff(558,plain,
% 163.48/163.79 (![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R))) <=> ![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R)))),
% 163.48/163.79 inference(quant_intro,[status(thm)],[557])).
% 163.48/163.79 tff(559,plain,
% 163.48/163.79 (![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R))) <=> ![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R)))),
% 163.48/163.79 inference(rewrite,[status(thm)],[])).
% 163.48/163.79 tff(560,axiom,(![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','def_f6')).
% 163.48/163.79 tff(561,plain,
% 163.48/163.79 (![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R)))),
% 163.48/163.79 inference(modus_ponens,[status(thm)],[560, 559])).
% 163.48/163.79 tff(562,plain,(
% 163.48/163.79 ![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R)))),
% 163.48/163.79 inference(skolemize,[status(sab)],[561])).
% 163.48/163.79 tff(563,plain,
% 163.48/163.79 (![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R)))),
% 163.48/163.79 inference(modus_ponens,[status(thm)],[562, 558])).
% 163.48/163.79 tff(564,plain,
% 163.48/163.79 ((~![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R)))) | (f6(P!7, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.48/163.79 inference(quant_inst,[status(thm)],[])).
% 163.48/163.79 tff(565,plain,
% 163.48/163.79 (f6(P!7, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.48/163.79 inference(unit_resolution,[status(thm)],[564, 563])).
% 163.48/163.80 tff(566,plain,
% 163.48/163.80 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7))),
% 163.48/163.80 inference(symmetry,[status(thm)],[565])).
% 163.48/163.80 tff(567,plain,
% 163.48/163.80 (d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> d(f6(P!7, tptp_fun_R_5(P!7)))),
% 163.48/163.80 inference(monotonicity,[status(thm)],[566])).
% 163.48/163.80 tff(568,plain,
% 163.48/163.80 (d(f6(P!7, tptp_fun_R_5(P!7))) <=> d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.48/163.80 inference(symmetry,[status(thm)],[567])).
% 163.48/163.80 tff(569,plain,
% 163.48/163.80 ((~![B: $i] : (lazy_impl(false, B) = true)) | (lazy_impl(false, impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)),
% 163.48/163.80 inference(quant_inst,[status(thm)],[])).
% 163.48/163.80 tff(570,plain,
% 163.48/163.80 (lazy_impl(false, impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true),
% 163.48/163.80 inference(unit_resolution,[status(thm)],[569, 147])).
% 163.48/163.80 tff(571,assumption,(prop(tptp_fun_R_5(P!7)) = false), introduced(assumption)).
% 163.48/163.80 tff(572,plain,
% 163.48/163.80 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(false, impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.48/163.80 inference(monotonicity,[status(thm)],[571])).
% 163.48/163.80 tff(573,plain,
% 163.48/163.80 (f6(P!7, tptp_fun_R_5(P!7)) = true),
% 163.48/163.80 inference(transitivity,[status(thm)],[565, 572, 570])).
% 163.48/163.80 tff(574,plain,
% 163.48/163.80 (d(f6(P!7, tptp_fun_R_5(P!7))) <=> d(true)),
% 163.48/163.80 inference(monotonicity,[status(thm)],[573])).
% 163.48/163.80 tff(575,plain,
% 163.48/163.80 (d(true) <=> d(f6(P!7, tptp_fun_R_5(P!7)))),
% 163.48/163.80 inference(symmetry,[status(thm)],[574])).
% 163.48/163.80 tff(576,plain,
% 163.48/163.80 (d(true) <=> d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.48/163.80 inference(transitivity,[status(thm)],[575, 568])).
% 163.48/163.80 tff(577,plain,
% 163.48/163.80 (d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.48/163.80 inference(modus_ponens,[status(thm)],[226, 576])).
% 163.48/163.80 tff(578,plain,
% 163.48/163.80 (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> bool(f6(P!7, tptp_fun_R_5(P!7)))),
% 163.58/163.80 inference(monotonicity,[status(thm)],[566])).
% 163.58/163.80 tff(579,plain,
% 163.58/163.80 (bool(f6(P!7, tptp_fun_R_5(P!7))) <=> bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.58/163.80 inference(symmetry,[status(thm)],[578])).
% 163.58/163.80 tff(580,plain,
% 163.58/163.80 (bool(f6(P!7, tptp_fun_R_5(P!7))) <=> bool(true)),
% 163.58/163.80 inference(monotonicity,[status(thm)],[573])).
% 163.58/163.80 tff(581,plain,
% 163.58/163.80 (bool(true) <=> bool(f6(P!7, tptp_fun_R_5(P!7)))),
% 163.58/163.80 inference(symmetry,[status(thm)],[580])).
% 163.58/163.80 tff(582,plain,
% 163.58/163.80 (bool(true) <=> bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.58/163.80 inference(transitivity,[status(thm)],[581, 579])).
% 163.58/163.80 tff(583,plain,
% 163.58/163.80 (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.58/163.80 inference(modus_ponens,[status(thm)],[252, 582])).
% 163.58/163.80 tff(584,plain,
% 163.58/163.80 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)))))))),
% 163.58/163.80 inference(rewrite,[status(thm)],[])).
% 163.58/163.80 tff(585,plain,
% 163.58/163.80 ((forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)))) | (~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))))))) <=> (forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true))))))),
% 163.58/163.80 inference(rewrite,[status(thm)],[])).
% 163.58/163.80 tff(586,plain,
% 163.58/163.80 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)))) | (~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false))))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)))))))),
% 163.58/163.80 inference(monotonicity,[status(thm)],[585])).
% 163.58/163.80 tff(587,plain,
% 163.58/163.80 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)))) | (~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false))))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)))))))),
% 163.58/163.80 inference(transitivity,[status(thm)],[586, 584])).
% 163.58/163.80 tff(588,plain,
% 163.58/163.80 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)))) | (~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false))))))))),
% 163.58/163.80 inference(quant_inst,[status(thm)],[])).
% 163.58/163.80 tff(589,plain,
% 163.58/163.80 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true))))))),
% 163.58/163.80 inference(modus_ponens,[status(thm)],[588, 587])).
% 163.58/163.80 tff(590,plain,
% 163.58/163.80 (forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)))))),
% 163.58/163.80 inference(unit_resolution,[status(thm)],[589, 165])).
% 163.58/163.80 tff(591,plain,
% 163.58/163.80 ((~![P: $i, R: $i] : (f6(P, R) = lazy_impl(prop(R), impl(f5(P, R), R)))) | (f6(P!7, false) = lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 163.58/163.80 inference(quant_inst,[status(thm)],[])).
% 163.58/163.80 tff(592,plain,
% 163.58/163.80 (f6(P!7, false) = lazy_impl(prop(false), impl(f5(P!7, false), false))),
% 163.58/163.80 inference(unit_resolution,[status(thm)],[591, 563])).
% 163.58/163.80 tff(593,plain,
% 163.58/163.80 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = f6(P!7, false)),
% 163.58/163.80 inference(symmetry,[status(thm)],[592])).
% 163.58/163.80 tff(594,plain,
% 163.58/163.80 (forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> forallprefers(f6(P!7, false), f6(P!7, tptp_fun_R_5(P!7)))),
% 163.58/163.80 inference(monotonicity,[status(thm)],[593, 566])).
% 163.58/163.80 tff(595,plain,
% 163.58/163.80 (forallprefers(f6(P!7, false), f6(P!7, tptp_fun_R_5(P!7))) <=> forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.58/163.80 inference(symmetry,[status(thm)],[594])).
% 163.58/163.80 tff(596,plain,
% 163.58/163.80 ((~forallprefers(f6(P!7, false), f6(P!7, tptp_fun_R_5(P!7)))) <=> (~forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 163.58/163.80 inference(monotonicity,[status(thm)],[595])).
% 163.58/163.80 tff(597,plain,
% 163.58/163.80 (^[P: $i] : refl((~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P))))))) <=> (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P))))))))),
% 163.58/163.80 inference(bind,[status(th)],[])).
% 163.58/163.80 tff(598,plain,
% 163.58/163.80 (![P: $i] : (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P))))))) <=> ![P: $i] : (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P)))))))),
% 163.58/163.80 inference(quant_intro,[status(thm)],[597])).
% 163.58/163.80 tff(599,plain,
% 163.58/163.80 (^[P: $i] : rewrite((~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P))))))) <=> (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P))))))))),
% 163.58/163.80 inference(bind,[status(th)],[])).
% 163.58/163.80 tff(600,plain,
% 163.58/163.80 (![P: $i] : (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P))))))) <=> ![P: $i] : (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P)))))))),
% 163.58/163.80 inference(quant_intro,[status(thm)],[599])).
% 163.58/163.80 tff(601,plain,
% 163.58/163.80 (![P: $i] : (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P))))))) <=> ![P: $i] : (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P)))))))),
% 163.58/163.80 inference(transitivity,[status(thm)],[600, 598])).
% 163.58/163.80 tff(602,plain,
% 163.58/163.80 (^[P: $i] : rewrite(((exists2(P) = phi(f6(P, tptp_fun_R_5(P)))) & ![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P))))) <=> (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P))))))))),
% 163.58/163.80 inference(bind,[status(th)],[])).
% 163.58/163.80 tff(603,plain,
% 163.58/163.80 (![P: $i] : ((exists2(P) = phi(f6(P, tptp_fun_R_5(P)))) & ![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P))))) <=> ![P: $i] : (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P)))))))),
% 163.58/163.80 inference(quant_intro,[status(thm)],[602])).
% 163.58/163.80 tff(604,plain,
% 163.58/163.80 (![P: $i] : ?[R: $i] : ((exists2(P) = phi(f6(P, R))) & (~?[R1: $i] : forallprefers(f6(P, R1), f6(P, R)))) <=> ![P: $i] : ?[R: $i] : ((exists2(P) = phi(f6(P, R))) & (~?[R1: $i] : forallprefers(f6(P, R1), f6(P, R))))),
% 163.58/163.80 inference(rewrite,[status(thm)],[])).
% 163.58/163.80 tff(605,axiom,(![P: $i] : ?[R: $i] : ((exists2(P) = phi(f6(P, R))) & (~?[R1: $i] : forallprefers(f6(P, R1), f6(P, R))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','def_exists2')).
% 163.58/163.80 tff(606,plain,
% 163.58/163.80 (![P: $i] : ?[R: $i] : ((exists2(P) = phi(f6(P, R))) & (~?[R1: $i] : forallprefers(f6(P, R1), f6(P, R))))),
% 163.58/163.80 inference(modus_ponens,[status(thm)],[605, 604])).
% 163.58/163.80 tff(607,plain,(
% 163.58/163.80 ![P: $i] : ((exists2(P) = phi(f6(P, tptp_fun_R_5(P)))) & ![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P)))))),
% 163.58/163.80 inference(skolemize,[status(sab)],[606])).
% 163.58/163.80 tff(608,plain,
% 163.58/163.80 (![P: $i] : (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P)))))))),
% 163.58/163.80 inference(modus_ponens,[status(thm)],[607, 603])).
% 163.58/163.80 tff(609,plain,
% 163.58/163.80 (![P: $i] : (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P)))))))),
% 163.58/163.80 inference(modus_ponens,[status(thm)],[608, 601])).
% 163.58/163.80 tff(610,plain,
% 163.58/163.80 ((~![P: $i] : (~((~(exists2(P) = phi(f6(P, tptp_fun_R_5(P))))) | (~![R1: $i] : (~forallprefers(f6(P, R1), f6(P, tptp_fun_R_5(P)))))))) | (~((~(exists2(P!7) = phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~![R1: $i] : (~forallprefers(f6(P!7, R1), f6(P!7, tptp_fun_R_5(P!7)))))))),
% 163.58/163.80 inference(quant_inst,[status(thm)],[])).
% 163.58/163.80 tff(611,plain,
% 163.58/163.80 (~((~(exists2(P!7) = phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~![R1: $i] : (~forallprefers(f6(P!7, R1), f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.58/163.80 inference(unit_resolution,[status(thm)],[610, 609])).
% 163.58/163.80 tff(612,plain,
% 163.58/163.80 (((~(exists2(P!7) = phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~![R1: $i] : (~forallprefers(f6(P!7, R1), f6(P!7, tptp_fun_R_5(P!7)))))) | ![R1: $i] : (~forallprefers(f6(P!7, R1), f6(P!7, tptp_fun_R_5(P!7))))),
% 163.58/163.80 inference(tautology,[status(thm)],[])).
% 163.58/163.80 tff(613,plain,
% 163.58/163.80 (![R1: $i] : (~forallprefers(f6(P!7, R1), f6(P!7, tptp_fun_R_5(P!7))))),
% 163.58/163.80 inference(unit_resolution,[status(thm)],[612, 611])).
% 163.58/163.80 tff(614,plain,
% 163.58/163.80 ((~![R1: $i] : (~forallprefers(f6(P!7, R1), f6(P!7, tptp_fun_R_5(P!7))))) | (~forallprefers(f6(P!7, false), f6(P!7, tptp_fun_R_5(P!7))))),
% 163.58/163.80 inference(quant_inst,[status(thm)],[])).
% 163.58/163.80 tff(615,plain,
% 163.58/163.80 (~forallprefers(f6(P!7, false), f6(P!7, tptp_fun_R_5(P!7)))),
% 163.58/163.80 inference(unit_resolution,[status(thm)],[614, 613])).
% 163.58/163.80 tff(616,plain,
% 163.58/163.80 (~forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.58/163.80 inference(modus_ponens,[status(thm)],[615, 596])).
% 163.58/163.80 tff(617,plain,
% 163.58/163.80 ((~(forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true))))))) | forallprefers(lazy_impl(prop(false), impl(f5(P!7, false), false)), lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~((~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true))))))),
% 163.58/163.80 inference(tautology,[status(thm)],[])).
% 163.58/163.80 tff(618,plain,
% 163.58/163.80 (~((~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)))))),
% 163.58/163.80 inference(unit_resolution,[status(thm)],[617, 616, 590])).
% 163.58/163.80 tff(619,plain,
% 163.58/163.80 (((~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true))))) | (d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))),
% 163.58/163.80 inference(tautology,[status(thm)],[])).
% 163.58/163.80 tff(620,plain,
% 163.58/163.80 (d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 163.58/163.80 inference(unit_resolution,[status(thm)],[619, 618])).
% 163.58/163.80 tff(621,plain,
% 163.58/163.80 ((~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 163.58/163.80 inference(tautology,[status(thm)],[])).
% 163.58/163.80 tff(622,plain,
% 163.58/163.80 (d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 163.58/163.80 inference(unit_resolution,[status(thm)],[621, 620])).
% 163.58/163.80 tff(623,plain,
% 163.58/163.80 (d(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 163.58/163.80 inference(unit_resolution,[status(thm)],[622, 577])).
% 163.58/163.80 tff(624,plain,
% 163.58/163.80 (((~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true))))) | ((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))),
% 163.58/163.81 inference(tautology,[status(thm)],[])).
% 163.58/163.81 tff(625,plain,
% 163.58/163.81 ((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[624, 618])).
% 163.58/163.81 tff(626,plain,
% 163.58/163.81 ((~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 163.58/163.81 inference(tautology,[status(thm)],[])).
% 163.58/163.81 tff(627,plain,
% 163.58/163.81 ((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[626, 625])).
% 163.58/163.81 tff(628,plain,
% 163.58/163.81 (bool(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[627, 623, 583, 577])).
% 163.58/163.81 tff(629,plain,
% 163.58/163.81 ((~(bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) <=> ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = true)))) | (~bool(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = true))),
% 163.58/163.81 inference(tautology,[status(thm)],[])).
% 163.58/163.81 tff(630,plain,
% 163.58/163.81 ((~(bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) <=> ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = true)))) | ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = true))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[629, 628])).
% 163.58/163.81 tff(631,plain,
% 163.58/163.81 ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = true)),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[630, 556])).
% 163.58/163.81 tff(632,plain,
% 163.58/163.81 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true),
% 163.58/163.81 inference(transitivity,[status(thm)],[572, 570])).
% 163.58/163.81 tff(633,plain,
% 163.58/163.81 (((~(d(lazy_impl(prop(false), impl(f5(P!7, false), false))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (~d(lazy_impl(prop(false), impl(f5(P!7, false), false)))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false))))) | (~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true))))) | ((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)))),
% 163.58/163.81 inference(tautology,[status(thm)],[])).
% 163.58/163.81 tff(634,plain,
% 163.58/163.81 ((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[633, 618])).
% 163.58/163.81 tff(635,plain,
% 163.58/163.81 ((~((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)))) | (~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true))),
% 163.58/163.81 inference(tautology,[status(thm)],[])).
% 163.58/163.81 tff(636,plain,
% 163.58/163.81 ((~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[635, 634])).
% 163.58/163.81 tff(637,plain,
% 163.58/163.81 (~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = false)),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[636, 632])).
% 163.58/163.81 tff(638,plain,
% 163.58/163.81 ((~((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = true))) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = true)),
% 163.58/163.81 inference(tautology,[status(thm)],[])).
% 163.58/163.81 tff(639,plain,
% 163.58/163.81 ((~((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = true))) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = true)),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[638, 637])).
% 163.58/163.81 tff(640,plain,
% 163.58/163.81 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = true),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[639, 631])).
% 163.58/163.81 tff(641,plain,
% 163.58/163.81 (~(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[321, 640])).
% 163.58/163.81 tff(642,plain,
% 163.58/163.81 (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[336, 641])).
% 163.58/163.81 tff(643,plain,
% 163.58/163.81 (impl(true, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[498, 82, 642])).
% 163.58/163.81 tff(644,plain,
% 163.58/163.81 (impl(false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[502, 388, 642])).
% 163.58/163.81 tff(645,plain,
% 163.58/163.81 (impl(true, impl(false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) = impl(true, true)),
% 163.58/163.81 inference(monotonicity,[status(thm)],[644])).
% 163.58/163.81 tff(646,plain,
% 163.58/163.81 (impl(true, impl(false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) = true),
% 163.58/163.81 inference(transitivity,[status(thm)],[645, 378])).
% 163.58/163.81 tff(647,plain,
% 163.58/163.81 (impl(impl(true, impl(false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = impl(true, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.58/163.81 inference(monotonicity,[status(thm)],[646])).
% 163.58/163.81 tff(648,plain,
% 163.58/163.81 (impl(impl(true, impl(false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 163.58/163.81 inference(transitivity,[status(thm)],[647, 643])).
% 163.58/163.81 tff(649,plain,
% 163.58/163.81 (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), impl(impl(true, impl(false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) = lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.58/163.81 inference(monotonicity,[status(thm)],[648])).
% 163.58/163.81 tff(650,plain,
% 163.58/163.81 (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), impl(impl(true, impl(false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.58/163.81 inference(symmetry,[status(thm)],[649])).
% 163.58/163.81 tff(651,plain,
% 163.58/163.81 (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = f1(true, false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.58/163.81 inference(transitivity,[status(thm)],[650, 495])).
% 163.58/163.81 tff(652,plain,
% 163.58/163.81 (forallprefers(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), false) <=> forallprefers(f1(true, false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), f1(true, false, tptp_fun_R_0(false, true)))),
% 163.58/163.81 inference(monotonicity,[status(thm)],[651, 492])).
% 163.58/163.81 tff(653,plain,
% 163.58/163.81 (forallprefers(f1(true, false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), f1(true, false, tptp_fun_R_0(false, true))) <=> forallprefers(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), false)),
% 163.58/163.81 inference(symmetry,[status(thm)],[652])).
% 163.58/163.81 tff(654,plain,
% 163.58/163.81 ((~forallprefers(f1(true, false, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), f1(true, false, tptp_fun_R_0(false, true)))) <=> (~forallprefers(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), false))),
% 163.58/163.81 inference(monotonicity,[status(thm)],[653])).
% 163.58/163.81 tff(655,plain,
% 163.58/163.81 (~forallprefers(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), false)),
% 163.58/163.81 inference(modus_ponens,[status(thm)],[515, 654])).
% 163.58/163.81 tff(656,plain,
% 163.58/163.81 (~((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))))) | (~((~(false = true)) | (~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false)))) | (~((~d(false)) | d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[517, 655, 349])).
% 163.58/163.81 tff(657,plain,
% 163.58/163.81 ((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[519, 656])).
% 163.58/163.81 tff(658,plain,
% 163.58/163.81 ((~d(false)) | d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[521, 656])).
% 163.58/163.81 tff(659,plain,
% 163.58/163.81 (d(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[524, 658])).
% 163.58/163.81 tff(660,plain,
% 163.58/163.81 (bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[527, 659, 657])).
% 163.58/163.81 tff(661,plain,
% 163.58/163.81 ((~(bool(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) <=> ((lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false) | (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true)))) | ((lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false) | (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[529, 660])).
% 163.58/163.81 tff(662,plain,
% 163.58/163.81 ((lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false) | (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true)),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[661, 342])).
% 163.58/163.81 tff(663,plain,
% 163.58/163.81 (phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = true),
% 163.58/163.81 inference(transitivity,[status(thm)],[273, 121, 111, 640])).
% 163.58/163.81 tff(664,plain,
% 163.58/163.81 ((phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err) <=> (true = err)),
% 163.58/163.81 inference(monotonicity,[status(thm)],[663])).
% 163.58/163.81 tff(665,plain,
% 163.58/163.81 ((true = err) <=> (phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)),
% 163.58/163.81 inference(symmetry,[status(thm)],[664])).
% 163.58/163.81 tff(666,plain,
% 163.58/163.81 ((~(true = err)) <=> (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err))),
% 163.58/163.81 inference(monotonicity,[status(thm)],[665])).
% 163.58/163.81 tff(667,plain,
% 163.58/163.81 (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err)),
% 163.58/163.81 inference(modus_ponens,[status(thm)],[280, 666])).
% 163.58/163.81 tff(668,plain,
% 163.58/163.81 (d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = err))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[282, 667])).
% 163.58/163.81 tff(669,plain,
% 163.58/163.81 (~((~d(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))) | (~(phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2))))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[290, 668])).
% 163.58/163.81 tff(670,plain,
% 163.58/163.81 (phi(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false2)),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[292, 669])).
% 163.58/163.81 tff(671,plain,
% 163.58/163.81 (true = lazy_impl(prop(false), impl(f5(P!7, false), false))),
% 163.58/163.81 inference(symmetry,[status(thm)],[640])).
% 163.58/163.81 tff(672,plain,
% 163.58/163.81 (true = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false)),
% 163.58/163.81 inference(transitivity,[status(thm)],[671, 314, 120, 313, 670, 272, 312])).
% 163.58/163.81 tff(673,plain,
% 163.58/163.81 ((~((prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true) <=> bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))) | (prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true)),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[338, 642])).
% 163.58/163.81 tff(674,plain,
% 163.58/163.81 (prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[673, 21])).
% 163.58/163.81 tff(675,plain,
% 163.58/163.81 (true = prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.58/163.81 inference(symmetry,[status(thm)],[674])).
% 163.58/163.81 tff(676,plain,
% 163.58/163.81 (lazy_impl(true, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.58/163.81 inference(monotonicity,[status(thm)],[675])).
% 163.58/163.81 tff(677,plain,
% 163.58/163.81 (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = lazy_impl(true, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.58/163.81 inference(symmetry,[status(thm)],[676])).
% 163.58/163.81 tff(678,plain,
% 163.58/163.81 (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.58/163.81 inference(transitivity,[status(thm)],[677, 535])).
% 163.58/163.81 tff(679,plain,
% 163.58/163.81 ((lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true) <=> (phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false))),
% 163.58/163.81 inference(monotonicity,[status(thm)],[678, 672])).
% 163.58/163.81 tff(680,plain,
% 163.58/163.81 ((lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true) <=> (impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.58/163.81 inference(transitivity,[status(thm)],[679, 532])).
% 163.58/163.81 tff(681,plain,
% 163.58/163.81 ((impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) <=> (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true)),
% 163.58/163.81 inference(symmetry,[status(thm)],[680])).
% 163.58/163.81 tff(682,plain,
% 163.58/163.81 ((~(impl(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)), false) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))))) <=> (~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true))),
% 163.58/163.81 inference(monotonicity,[status(thm)],[681])).
% 163.58/163.81 tff(683,plain,
% 163.58/163.81 (~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true)),
% 163.58/163.81 inference(modus_ponens,[status(thm)],[641, 682])).
% 163.58/163.81 tff(684,plain,
% 163.58/163.81 (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[545, 683, 662])).
% 163.58/163.81 tff(685,plain,
% 163.58/163.81 (phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = lazy_impl(true, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.58/163.81 inference(symmetry,[status(thm)],[535])).
% 163.58/163.81 tff(686,plain,
% 163.58/163.81 (phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false),
% 163.58/163.81 inference(transitivity,[status(thm)],[685, 676, 684])).
% 163.58/163.81 tff(687,plain,
% 163.58/163.81 ((phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err) <=> (false = err)),
% 163.58/163.81 inference(monotonicity,[status(thm)],[686])).
% 163.58/163.81 tff(688,plain,
% 163.58/163.81 ((false = err) <=> (phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err)),
% 163.58/163.81 inference(symmetry,[status(thm)],[687])).
% 163.58/163.81 tff(689,plain,
% 163.58/163.81 ((~(false = err)) <=> (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err))),
% 163.58/163.81 inference(monotonicity,[status(thm)],[688])).
% 163.58/163.81 tff(690,plain,
% 163.58/163.81 ((~(false = err)) <=> (~(false = err))),
% 163.58/163.81 inference(rewrite,[status(thm)],[])).
% 163.58/163.81 tff(691,plain,
% 163.58/163.81 (~(false = err)),
% 163.58/163.81 inference(and_elim,[status(thm)],[53])).
% 163.58/163.81 tff(692,plain,
% 163.58/163.81 (~(false = err)),
% 163.58/163.81 inference(modus_ponens,[status(thm)],[691, 690])).
% 163.58/163.81 tff(693,plain,
% 163.58/163.81 (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err)),
% 163.58/163.81 inference(modus_ponens,[status(thm)],[692, 689])).
% 163.58/163.81 tff(694,plain,
% 163.58/163.81 (d(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[303, 693])).
% 163.58/163.81 tff(695,plain,
% 163.58/163.81 (~((~d(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[308, 694])).
% 163.58/163.81 tff(696,plain,
% 163.58/163.81 (phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[310, 695])).
% 163.58/163.81 tff(697,plain,
% 163.58/163.81 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.58/163.81 inference(symmetry,[status(thm)],[696])).
% 163.58/163.81 tff(698,plain,
% 163.58/163.81 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false),
% 163.58/163.81 inference(transitivity,[status(thm)],[697, 685, 676, 684])).
% 163.58/163.81 tff(699,plain,
% 163.58/163.81 ((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err) <=> (false = err)),
% 163.58/163.81 inference(monotonicity,[status(thm)],[698])).
% 163.58/163.81 tff(700,plain,
% 163.58/163.81 ((false = err) <=> (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err)),
% 163.58/163.81 inference(symmetry,[status(thm)],[699])).
% 163.58/163.81 tff(701,plain,
% 163.58/163.81 ((~(false = err)) <=> (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err))),
% 163.58/163.81 inference(monotonicity,[status(thm)],[700])).
% 163.58/163.81 tff(702,plain,
% 163.58/163.81 (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err)),
% 163.58/163.81 inference(modus_ponens,[status(thm)],[692, 701])).
% 163.58/163.81 tff(703,plain,
% 163.58/163.81 ((d(f4(P!7, tptp_fun_X_4(false, P!7), false)) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err))) | (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err)),
% 163.58/163.81 inference(tautology,[status(thm)],[])).
% 163.58/163.81 tff(704,plain,
% 163.58/163.81 (d(f4(P!7, tptp_fun_X_4(false, P!7), false)) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[703, 702])).
% 163.58/163.81 tff(705,plain,
% 163.58/163.81 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false))))) | (~(d(f4(P!7, tptp_fun_X_4(false, P!7), false)) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false))))) | (~(d(f4(P!7, tptp_fun_X_4(false, P!7), false)) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err)))))),
% 163.58/163.81 inference(rewrite,[status(thm)],[])).
% 163.58/163.81 tff(706,plain,
% 163.58/163.81 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false))))) | (~(d(f4(P!7, tptp_fun_X_4(false, P!7), false)) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err)))))),
% 163.58/163.81 inference(quant_inst,[status(thm)],[])).
% 163.58/163.81 tff(707,plain,
% 163.58/163.81 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false))))) | (~(d(f4(P!7, tptp_fun_X_4(false, P!7), false)) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err))))),
% 163.58/163.81 inference(modus_ponens,[status(thm)],[706, 705])).
% 163.58/163.81 tff(708,plain,
% 163.58/163.81 ((~((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false))))) | (~(d(f4(P!7, tptp_fun_X_4(false, P!7), false)) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err))))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[707, 39])).
% 163.58/163.81 tff(709,plain,
% 163.58/163.81 (~((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[708, 704])).
% 163.58/163.81 tff(710,plain,
% 163.58/163.81 (((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 163.58/163.81 inference(tautology,[status(thm)],[])).
% 163.58/163.81 tff(711,plain,
% 163.58/163.81 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false)),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[710, 709])).
% 163.58/163.81 tff(712,plain,
% 163.58/163.81 (false = lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.58/163.81 inference(symmetry,[status(thm)],[684])).
% 163.58/163.81 tff(713,plain,
% 163.58/163.81 (false = f4(P!7, tptp_fun_X_4(false, P!7), false)),
% 163.58/163.81 inference(transitivity,[status(thm)],[712, 677, 535, 696, 711])).
% 163.58/163.81 tff(714,plain,
% 163.58/163.81 ((~![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))) | (f4(P!7, tptp_fun_X_3(P!7), false) = impl(apply(P!7, tptp_fun_X_3(P!7)), false))),
% 163.58/163.81 inference(quant_inst,[status(thm)],[])).
% 163.58/163.81 tff(715,plain,
% 163.58/163.81 (f4(P!7, tptp_fun_X_3(P!7), false) = impl(apply(P!7, tptp_fun_X_3(P!7)), false)),
% 163.58/163.81 inference(unit_resolution,[status(thm)],[714, 7])).
% 163.58/163.81 tff(716,plain,
% 163.58/163.81 (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = f4(P!7, tptp_fun_X_3(P!7), false)),
% 163.58/163.81 inference(symmetry,[status(thm)],[715])).
% 163.58/163.81 tff(717,plain,
% 163.58/163.81 (impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, false)) = impl(apply(P!7, tptp_fun_X_3(P!7)), true)),
% 163.58/163.81 inference(monotonicity,[status(thm)],[392])).
% 163.58/163.81 tff(718,plain,
% 163.58/163.81 (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, false))),
% 163.58/163.81 inference(symmetry,[status(thm)],[717])).
% 163.58/163.81 tff(719,plain,
% 163.58/163.81 (((~(exists2(P!7) = phi(f6(P!7, tptp_fun_R_5(P!7))))) | (~![R1: $i] : (~forallprefers(f6(P!7, R1), f6(P!7, tptp_fun_R_5(P!7)))))) | (exists2(P!7) = phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 163.58/163.81 inference(tautology,[status(thm)],[])).
% 163.58/163.81 tff(720,plain,
% 163.58/163.82 (exists2(P!7) = phi(f6(P!7, tptp_fun_R_5(P!7)))),
% 163.58/163.82 inference(unit_resolution,[status(thm)],[719, 611])).
% 163.58/163.82 tff(721,plain,
% 163.58/163.82 (phi(f6(P!7, tptp_fun_R_5(P!7))) = exists2(P!7)),
% 163.58/163.82 inference(symmetry,[status(thm)],[720])).
% 163.58/163.82 tff(722,plain,
% 163.58/163.82 (phi(f6(P!7, tptp_fun_R_5(P!7))) = phi(true)),
% 163.58/163.82 inference(monotonicity,[status(thm)],[573])).
% 163.58/163.82 tff(723,plain,
% 163.58/163.82 (phi(true) = phi(f6(P!7, tptp_fun_R_5(P!7)))),
% 163.58/163.82 inference(symmetry,[status(thm)],[722])).
% 163.58/163.82 tff(724,plain,
% 163.58/163.82 (true = phi(true)),
% 163.58/163.82 inference(symmetry,[status(thm)],[234])).
% 163.58/163.82 tff(725,plain,
% 163.58/163.82 (true = exists2(P!7)),
% 163.58/163.82 inference(transitivity,[status(thm)],[724, 723, 721])).
% 163.58/163.82 tff(726,plain,
% 163.58/163.82 (^[P: $i] : refl((~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P))))))) <=> (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P))))))))),
% 163.58/163.82 inference(bind,[status(th)],[])).
% 163.58/163.82 tff(727,plain,
% 163.58/163.82 (![P: $i] : (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P))))))) <=> ![P: $i] : (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P)))))))),
% 163.58/163.82 inference(quant_intro,[status(thm)],[726])).
% 163.58/163.82 tff(728,plain,
% 163.58/163.82 (^[P: $i] : rewrite((~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P))))))) <=> (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P))))))))),
% 163.58/163.82 inference(bind,[status(th)],[])).
% 163.58/163.82 tff(729,plain,
% 163.58/163.82 (![P: $i] : (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P))))))) <=> ![P: $i] : (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P)))))))),
% 163.58/163.82 inference(quant_intro,[status(thm)],[728])).
% 163.58/163.82 tff(730,plain,
% 163.58/163.82 (![P: $i] : (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P))))))) <=> ![P: $i] : (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P)))))))),
% 163.58/163.82 inference(transitivity,[status(thm)],[729, 727])).
% 163.58/163.82 tff(731,plain,
% 163.58/163.82 (^[P: $i] : rewrite(((exists1(P) = phi(apply(P, tptp_fun_X_3(P)))) & ![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P))))) <=> (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P))))))))),
% 163.58/163.82 inference(bind,[status(th)],[])).
% 163.58/163.82 tff(732,plain,
% 163.58/163.82 (![P: $i] : ((exists1(P) = phi(apply(P, tptp_fun_X_3(P)))) & ![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P))))) <=> ![P: $i] : (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P)))))))),
% 163.58/163.82 inference(quant_intro,[status(thm)],[731])).
% 163.58/163.82 tff(733,plain,
% 163.58/163.82 (![P: $i] : ?[X: $i] : ((exists1(P) = phi(apply(P, X))) & (~?[X1: $i] : existsprefers(apply(P, X1), apply(P, X)))) <=> ![P: $i] : ?[X: $i] : ((exists1(P) = phi(apply(P, X))) & (~?[X1: $i] : existsprefers(apply(P, X1), apply(P, X))))),
% 163.58/163.82 inference(rewrite,[status(thm)],[])).
% 163.58/163.82 tff(734,axiom,(![P: $i] : ?[X: $i] : ((exists1(P) = phi(apply(P, X))) & (~?[X1: $i] : existsprefers(apply(P, X1), apply(P, X))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','exists1_axiom1')).
% 163.58/163.82 tff(735,plain,
% 163.58/163.82 (![P: $i] : ?[X: $i] : ((exists1(P) = phi(apply(P, X))) & (~?[X1: $i] : existsprefers(apply(P, X1), apply(P, X))))),
% 163.58/163.82 inference(modus_ponens,[status(thm)],[734, 733])).
% 163.58/163.82 tff(736,plain,(
% 163.58/163.82 ![P: $i] : ((exists1(P) = phi(apply(P, tptp_fun_X_3(P)))) & ![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P)))))),
% 163.58/163.82 inference(skolemize,[status(sab)],[735])).
% 163.58/163.82 tff(737,plain,
% 163.58/163.82 (![P: $i] : (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P)))))))),
% 163.60/163.82 inference(modus_ponens,[status(thm)],[736, 732])).
% 163.60/163.82 tff(738,plain,
% 163.60/163.82 (![P: $i] : (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P)))))))),
% 163.60/163.82 inference(modus_ponens,[status(thm)],[737, 730])).
% 163.60/163.82 tff(739,plain,
% 163.60/163.82 ((~![P: $i] : (~((~(exists1(P) = phi(apply(P, tptp_fun_X_3(P))))) | (~![X1: $i] : (~existsprefers(apply(P, X1), apply(P, tptp_fun_X_3(P)))))))) | (~((~(exists1(P!7) = phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~![X1: $i] : (~existsprefers(apply(P!7, X1), apply(P!7, tptp_fun_X_3(P!7)))))))),
% 163.60/163.82 inference(quant_inst,[status(thm)],[])).
% 163.60/163.82 tff(740,plain,
% 163.60/163.82 (~((~(exists1(P!7) = phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~![X1: $i] : (~existsprefers(apply(P!7, X1), apply(P!7, tptp_fun_X_3(P!7))))))),
% 163.60/163.82 inference(unit_resolution,[status(thm)],[739, 738])).
% 163.60/163.82 tff(741,plain,
% 163.60/163.82 (((~(exists1(P!7) = phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~![X1: $i] : (~existsprefers(apply(P!7, X1), apply(P!7, tptp_fun_X_3(P!7)))))) | (exists1(P!7) = phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.82 inference(tautology,[status(thm)],[])).
% 163.60/163.82 tff(742,plain,
% 163.60/163.82 (exists1(P!7) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.82 inference(unit_resolution,[status(thm)],[741, 740])).
% 163.60/163.82 tff(743,plain,
% 163.60/163.82 (phi(apply(P!7, tptp_fun_X_3(P!7))) = exists1(P!7)),
% 163.60/163.82 inference(symmetry,[status(thm)],[742])).
% 163.60/163.82 tff(744,plain,
% 163.60/163.82 (((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))))) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.82 inference(tautology,[status(thm)],[])).
% 163.60/163.82 tff(745,plain,
% 163.60/163.82 (phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))),
% 163.60/163.82 inference(unit_resolution,[status(thm)],[744, 547])).
% 163.60/163.82 tff(746,plain,
% 163.60/163.82 (apply(P!7, tptp_fun_X_3(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.82 inference(symmetry,[status(thm)],[745])).
% 163.60/163.82 tff(747,plain,
% 163.60/163.82 (apply(P!7, tptp_fun_X_3(P!7)) = exists1(P!7)),
% 163.60/163.82 inference(transitivity,[status(thm)],[746, 743])).
% 163.60/163.82 tff(748,plain,
% 163.60/163.82 ((apply(P!7, tptp_fun_X_3(P!7)) = true) <=> (exists1(P!7) = exists2(P!7))),
% 163.60/163.82 inference(monotonicity,[status(thm)],[747, 725])).
% 163.60/163.82 tff(749,plain,
% 163.60/163.82 ((exists1(P!7) = exists2(P!7)) <=> (apply(P!7, tptp_fun_X_3(P!7)) = true)),
% 163.60/163.82 inference(symmetry,[status(thm)],[748])).
% 163.60/163.82 tff(750,plain,
% 163.60/163.82 ((~(exists1(P!7) = exists2(P!7))) <=> (~(apply(P!7, tptp_fun_X_3(P!7)) = true))),
% 163.60/163.82 inference(monotonicity,[status(thm)],[749])).
% 163.60/163.82 tff(751,plain,
% 163.60/163.82 ((![X1: $i, X2: $i] : ((~((~bool(apply(P!7, X1))) & (~bool(apply(P!7, X2))))) | (apply(P!7, X1) = apply(P!7, X2))) & (~(exists1(P!7) = exists2(P!7)))) <=> (![X1: $i, X2: $i] : ((~((~bool(apply(P!7, X1))) & (~bool(apply(P!7, X2))))) | (apply(P!7, X1) = apply(P!7, X2))) & (~(exists1(P!7) = exists2(P!7))))),
% 163.60/163.82 inference(rewrite,[status(thm)],[])).
% 163.60/163.82 tff(752,plain,
% 163.60/163.82 ((~![P: $i] : ((~![X1: $i, X2: $i] : ((~((~bool(apply(P, X1))) & (~bool(apply(P, X2))))) | (apply(P, X1) = apply(P, X2)))) | (exists1(P) = exists2(P)))) <=> (~![P: $i] : ((~![X1: $i, X2: $i] : ((~((~bool(apply(P, X1))) & (~bool(apply(P, X2))))) | (apply(P, X1) = apply(P, X2)))) | (exists1(P) = exists2(P))))),
% 163.60/163.82 inference(rewrite,[status(thm)],[])).
% 163.60/163.82 tff(753,plain,
% 163.60/163.82 ((~![P: $i] : (![X1: $i, X2: $i] : (((~bool(apply(P, X1))) & (~bool(apply(P, X2)))) => (apply(P, X1) = apply(P, X2))) => (exists1(P) = exists2(P)))) <=> (~![P: $i] : ((~![X1: $i, X2: $i] : ((~((~bool(apply(P, X1))) & (~bool(apply(P, X2))))) | (apply(P, X1) = apply(P, X2)))) | (exists1(P) = exists2(P))))),
% 163.60/163.82 inference(rewrite,[status(thm)],[])).
% 163.60/163.82 tff(754,axiom,(~![P: $i] : (![X1: $i, X2: $i] : (((~bool(apply(P, X1))) & (~bool(apply(P, X2)))) => (apply(P, X1) = apply(P, X2))) => (exists1(P) = exists2(P)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','exists1_exists2')).
% 163.60/163.82 tff(755,plain,
% 163.60/163.82 (~![P: $i] : ((~![X1: $i, X2: $i] : ((~((~bool(apply(P, X1))) & (~bool(apply(P, X2))))) | (apply(P, X1) = apply(P, X2)))) | (exists1(P) = exists2(P)))),
% 163.60/163.82 inference(modus_ponens,[status(thm)],[754, 753])).
% 163.60/163.82 tff(756,plain,
% 163.60/163.82 (~![P: $i] : ((~![X1: $i, X2: $i] : ((~((~bool(apply(P, X1))) & (~bool(apply(P, X2))))) | (apply(P, X1) = apply(P, X2)))) | (exists1(P) = exists2(P)))),
% 163.60/163.82 inference(modus_ponens,[status(thm)],[755, 752])).
% 163.60/163.82 tff(757,plain,
% 163.60/163.82 (~![P: $i] : ((~![X1: $i, X2: $i] : ((~((~bool(apply(P, X1))) & (~bool(apply(P, X2))))) | (apply(P, X1) = apply(P, X2)))) | (exists1(P) = exists2(P)))),
% 163.60/163.82 inference(modus_ponens,[status(thm)],[756, 752])).
% 163.60/163.82 tff(758,plain,
% 163.60/163.82 (~![P: $i] : ((~![X1: $i, X2: $i] : ((~((~bool(apply(P, X1))) & (~bool(apply(P, X2))))) | (apply(P, X1) = apply(P, X2)))) | (exists1(P) = exists2(P)))),
% 163.60/163.82 inference(modus_ponens,[status(thm)],[757, 752])).
% 163.60/163.82 tff(759,plain,
% 163.60/163.82 (![X1: $i, X2: $i] : ((~((~bool(apply(P!7, X1))) & (~bool(apply(P!7, X2))))) | (apply(P!7, X1) = apply(P!7, X2))) & (~(exists1(P!7) = exists2(P!7)))),
% 163.60/163.82 inference(modus_ponens,[status(thm)],[758, 751])).
% 163.60/163.82 tff(760,plain,
% 163.60/163.82 (~(exists1(P!7) = exists2(P!7))),
% 163.60/163.82 inference(and_elim,[status(thm)],[759])).
% 163.60/163.82 tff(761,plain,
% 163.60/163.82 (~(apply(P!7, tptp_fun_X_3(P!7)) = true)),
% 163.60/163.82 inference(modus_ponens,[status(thm)],[760, 750])).
% 163.60/163.82 tff(762,plain,
% 163.60/163.82 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(apply(P!7, tptp_fun_X_4(false, P!7))) <=> ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = true)))),
% 163.60/163.82 inference(quant_inst,[status(thm)],[])).
% 163.60/163.82 tff(763,plain,
% 163.60/163.82 (bool(apply(P!7, tptp_fun_X_4(false, P!7))) <=> ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = true))),
% 163.60/163.82 inference(unit_resolution,[status(thm)],[762, 218])).
% 163.60/163.82 tff(764,plain,
% 163.60/163.82 ((false = apply(P!7, tptp_fun_X_4(false, P!7))) <=> (apply(P!7, tptp_fun_X_4(false, P!7)) = false)),
% 163.60/163.82 inference(commutativity,[status(thm)],[])).
% 163.60/163.82 tff(765,plain,
% 163.60/163.82 (((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))))) | d(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.82 inference(tautology,[status(thm)],[])).
% 163.60/163.82 tff(766,plain,
% 163.60/163.82 (d(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.82 inference(unit_resolution,[status(thm)],[765, 547])).
% 163.60/163.82 tff(767,plain,
% 163.60/163.82 (^[X: $i, Y: $i] : refl((existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))))) <=> (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))))))),
% 163.60/163.82 inference(bind,[status(th)],[])).
% 163.60/163.82 tff(768,plain,
% 163.60/163.82 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))))) <=> ![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))),
% 163.60/163.82 inference(quant_intro,[status(thm)],[767])).
% 163.60/163.82 tff(769,plain,
% 163.60/163.82 (^[X: $i, Y: $i] : rewrite((existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = true) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)))) <=> (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X)))))))),
% 163.60/163.82 inference(bind,[status(th)],[])).
% 163.60/163.82 tff(770,plain,
% 163.60/163.82 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = true) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)))) <=> ![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))),
% 163.60/163.82 inference(quant_intro,[status(thm)],[769])).
% 163.60/163.82 tff(771,plain,
% 163.60/163.82 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = true) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)))) <=> ![X: $i, Y: $i] : (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = true) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 163.60/163.82 inference(rewrite,[status(thm)],[])).
% 163.60/163.82 tff(772,plain,
% 163.60/163.82 (^[X: $i, Y: $i] : rewrite((existsprefers(X, Y) <=> ((((~d(X)) & d(Y)) | (((d(X) & d(Y)) & (~bool(X))) & bool(Y))) | ((X = true) & (Y = false)))) <=> (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = true) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y)))))),
% 163.60/163.82 inference(bind,[status(th)],[])).
% 163.60/163.82 tff(773,plain,
% 163.60/163.82 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((((~d(X)) & d(Y)) | (((d(X) & d(Y)) & (~bool(X))) & bool(Y))) | ((X = true) & (Y = false)))) <=> ![X: $i, Y: $i] : (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = true) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 163.60/163.82 inference(quant_intro,[status(thm)],[772])).
% 163.60/163.82 tff(774,axiom,(![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((((~d(X)) & d(Y)) | (((d(X) & d(Y)) & (~bool(X))) & bool(Y))) | ((X = true) & (Y = false))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','def_existsprefers')).
% 163.60/163.82 tff(775,plain,
% 163.60/163.82 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = true) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 163.60/163.82 inference(modus_ponens,[status(thm)],[774, 773])).
% 163.60/163.82 tff(776,plain,
% 163.60/163.82 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = true) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 163.60/163.82 inference(modus_ponens,[status(thm)],[775, 771])).
% 163.60/163.82 tff(777,plain,(
% 163.60/163.82 ![X: $i, Y: $i] : (existsprefers(X, Y) <=> (((~d(X)) & d(Y)) | ((X = true) & (Y = false)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 163.60/163.82 inference(skolemize,[status(sab)],[776])).
% 163.60/163.82 tff(778,plain,
% 163.60/163.82 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))),
% 163.60/163.82 inference(modus_ponens,[status(thm)],[777, 770])).
% 163.60/163.82 tff(779,plain,
% 163.60/163.82 (![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))),
% 163.60/163.82 inference(modus_ponens,[status(thm)],[778, 768])).
% 163.60/163.82 tff(780,plain,
% 163.60/163.82 (((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))))) <=> ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))))))))),
% 163.60/163.82 inference(rewrite,[status(thm)],[])).
% 163.60/163.82 tff(781,plain,
% 163.60/163.82 ((existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))))))) <=> (existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))))),
% 163.60/163.82 inference(rewrite,[status(thm)],[])).
% 163.60/163.82 tff(782,plain,
% 163.60/163.82 (((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))))) <=> ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))))))))),
% 163.60/163.82 inference(monotonicity,[status(thm)],[781])).
% 163.60/163.82 tff(783,plain,
% 163.60/163.82 (((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))))) <=> ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))))))))),
% 163.60/163.82 inference(transitivity,[status(thm)],[782, 780])).
% 163.60/163.82 tff(784,plain,
% 163.60/163.82 ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))))),
% 163.60/163.82 inference(quant_inst,[status(thm)],[])).
% 163.60/163.82 tff(785,plain,
% 163.60/163.82 ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))))),
% 163.60/163.82 inference(modus_ponens,[status(thm)],[784, 783])).
% 163.60/163.82 tff(786,plain,
% 163.60/163.82 (existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))))))),
% 163.60/163.82 inference(unit_resolution,[status(thm)],[785, 779])).
% 163.60/163.82 tff(787,plain,
% 163.60/163.82 (((~(exists1(P!7) = phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~![X1: $i] : (~existsprefers(apply(P!7, X1), apply(P!7, tptp_fun_X_3(P!7)))))) | ![X1: $i] : (~existsprefers(apply(P!7, X1), apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.82 inference(tautology,[status(thm)],[])).
% 163.60/163.82 tff(788,plain,
% 163.60/163.82 (![X1: $i] : (~existsprefers(apply(P!7, X1), apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.82 inference(unit_resolution,[status(thm)],[787, 740])).
% 163.60/163.82 tff(789,plain,
% 163.60/163.82 ((~![X1: $i] : (~existsprefers(apply(P!7, X1), apply(P!7, tptp_fun_X_3(P!7))))) | (~existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.82 inference(quant_inst,[status(thm)],[])).
% 163.60/163.82 tff(790,plain,
% 163.60/163.82 (~existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.82 inference(unit_resolution,[status(thm)],[789, 788])).
% 163.60/163.82 tff(791,plain,
% 163.60/163.82 ((~(existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))))) | existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) | (~((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))))),
% 163.60/163.82 inference(tautology,[status(thm)],[])).
% 163.60/163.82 tff(792,plain,
% 163.60/163.82 ((~(existsprefers(apply(P!7, tptp_fun_X_4(false, P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))))) | (~((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))))),
% 163.60/163.82 inference(unit_resolution,[status(thm)],[791, 790])).
% 163.60/163.82 tff(793,plain,
% 163.60/163.82 (~((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))))))),
% 163.60/163.82 inference(unit_resolution,[status(thm)],[792, 786])).
% 163.60/163.82 tff(794,plain,
% 163.60/163.82 (((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))) | (d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))),
% 163.60/163.82 inference(tautology,[status(thm)],[])).
% 163.60/163.82 tff(795,plain,
% 163.60/163.82 (d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.82 inference(unit_resolution,[status(thm)],[794, 793])).
% 163.60/163.82 tff(796,plain,
% 163.60/163.82 ((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.82 inference(tautology,[status(thm)],[])).
% 163.60/163.82 tff(797,plain,
% 163.60/163.82 (d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.82 inference(unit_resolution,[status(thm)],[796, 795])).
% 163.60/163.82 tff(798,plain,
% 163.60/163.82 (d(apply(P!7, tptp_fun_X_4(false, P!7)))),
% 163.60/163.82 inference(unit_resolution,[status(thm)],[797, 766])).
% 163.60/163.82 tff(799,plain,
% 163.60/163.82 ((d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(false, P!7))) = err))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))),
% 163.60/163.82 inference(tautology,[status(thm)],[])).
% 163.60/163.82 tff(800,plain,
% 163.60/163.82 (d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(false, P!7))) = err))),
% 163.60/163.82 inference(unit_resolution,[status(thm)],[799, 798])).
% 163.60/163.82 tff(801,plain,
% 163.60/163.82 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(false, P!7))) = apply(P!7, tptp_fun_X_4(false, P!7)))))) | (~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(false, P!7))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(false, P!7))) = apply(P!7, tptp_fun_X_4(false, P!7)))))) | (~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(false, P!7))) = err)))))),
% 163.60/163.82 inference(rewrite,[status(thm)],[])).
% 163.60/163.82 tff(802,plain,
% 163.60/163.82 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(false, P!7))) = apply(P!7, tptp_fun_X_4(false, P!7)))))) | (~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(false, P!7))) = err)))))),
% 163.60/163.82 inference(quant_inst,[status(thm)],[])).
% 163.60/163.82 tff(803,plain,
% 163.60/163.82 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(false, P!7))) = apply(P!7, tptp_fun_X_4(false, P!7)))))) | (~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(false, P!7))) = err))))),
% 163.60/163.82 inference(modus_ponens,[status(thm)],[802, 801])).
% 163.60/163.82 tff(804,plain,
% 163.60/163.82 (~((~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(false, P!7))) = apply(P!7, tptp_fun_X_4(false, P!7)))))),
% 163.60/163.82 inference(unit_resolution,[status(thm)],[803, 39, 800])).
% 163.60/163.82 tff(805,plain,
% 163.60/163.82 (((~d(apply(P!7, tptp_fun_X_4(false, P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(false, P!7))) = apply(P!7, tptp_fun_X_4(false, P!7))))) | (phi(apply(P!7, tptp_fun_X_4(false, P!7))) = apply(P!7, tptp_fun_X_4(false, P!7)))),
% 163.60/163.82 inference(tautology,[status(thm)],[])).
% 163.60/163.82 tff(806,plain,
% 163.60/163.82 (phi(apply(P!7, tptp_fun_X_4(false, P!7))) = apply(P!7, tptp_fun_X_4(false, P!7))),
% 163.60/163.82 inference(unit_resolution,[status(thm)],[805, 804])).
% 163.60/163.82 tff(807,plain,
% 163.60/163.82 (f4(P!7, tptp_fun_X_4(false, P!7), false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 163.60/163.82 inference(symmetry,[status(thm)],[711])).
% 163.60/163.82 tff(808,plain,
% 163.60/163.82 ((~![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))) | (f4(P!7, tptp_fun_X_4(false, P!7), false) = impl(apply(P!7, tptp_fun_X_4(false, P!7)), false))),
% 163.60/163.82 inference(quant_inst,[status(thm)],[])).
% 163.60/163.82 tff(809,plain,
% 163.60/163.82 (f4(P!7, tptp_fun_X_4(false, P!7), false) = impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)),
% 163.60/163.82 inference(unit_resolution,[status(thm)],[808, 7])).
% 163.60/163.82 tff(810,plain,
% 163.60/163.82 (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = f4(P!7, tptp_fun_X_4(false, P!7), false)),
% 163.60/163.82 inference(symmetry,[status(thm)],[809])).
% 163.60/163.82 tff(811,plain,
% 163.60/163.82 (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = false),
% 163.60/163.82 inference(transitivity,[status(thm)],[810, 807, 697, 685, 676, 684])).
% 163.60/163.82 tff(812,plain,
% 163.60/163.82 ((impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = phi(apply(P!7, tptp_fun_X_4(false, P!7)))) <=> (false = apply(P!7, tptp_fun_X_4(false, P!7)))),
% 163.60/163.82 inference(monotonicity,[status(thm)],[811, 806])).
% 163.60/163.83 tff(813,plain,
% 163.60/163.83 ((impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = phi(apply(P!7, tptp_fun_X_4(false, P!7)))) <=> (apply(P!7, tptp_fun_X_4(false, P!7)) = false)),
% 163.60/163.83 inference(transitivity,[status(thm)],[812, 764])).
% 163.60/163.83 tff(814,plain,
% 163.60/163.83 ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) <=> (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = phi(apply(P!7, tptp_fun_X_4(false, P!7))))),
% 163.60/163.83 inference(symmetry,[status(thm)],[813])).
% 163.60/163.83 tff(815,plain,
% 163.60/163.83 ((~(apply(P!7, tptp_fun_X_4(false, P!7)) = false)) <=> (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = phi(apply(P!7, tptp_fun_X_4(false, P!7)))))),
% 163.60/163.83 inference(monotonicity,[status(thm)],[814])).
% 163.60/163.83 tff(816,assumption,(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false), introduced(assumption)).
% 163.60/163.83 tff(817,assumption,(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true), introduced(assumption)).
% 163.60/163.83 tff(818,plain,
% 163.60/163.83 (lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = lazy_impl(true, phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.60/163.83 inference(monotonicity,[status(thm)],[817])).
% 163.60/163.83 tff(819,plain,
% 163.60/163.83 (lazy_impl(true, phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.60/163.83 inference(symmetry,[status(thm)],[818])).
% 163.60/163.83 tff(820,plain,
% 163.60/163.83 (phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false),
% 163.60/163.83 inference(transitivity,[status(thm)],[685, 819, 816])).
% 163.60/163.83 tff(821,plain,
% 163.60/163.83 ((phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err) <=> (false = err)),
% 163.60/163.83 inference(monotonicity,[status(thm)],[820])).
% 163.60/163.83 tff(822,plain,
% 163.60/163.83 ((false = err) <=> (phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err)),
% 163.60/163.83 inference(symmetry,[status(thm)],[821])).
% 163.60/163.83 tff(823,plain,
% 163.60/163.83 ((~(false = err)) <=> (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err))),
% 163.60/163.83 inference(monotonicity,[status(thm)],[822])).
% 163.60/163.83 tff(824,plain,
% 163.60/163.83 (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err)),
% 163.60/163.83 inference(modus_ponens,[status(thm)],[692, 823])).
% 163.60/163.83 tff(825,plain,
% 163.60/163.83 (d(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = err))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[303, 824])).
% 163.60/163.83 tff(826,plain,
% 163.60/163.83 (~((~d(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~(phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[308, 825])).
% 163.60/163.83 tff(827,plain,
% 163.60/163.83 (phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[310, 826])).
% 163.60/163.83 tff(828,plain,
% 163.60/163.83 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = phi(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.60/163.83 inference(symmetry,[status(thm)],[827])).
% 163.60/163.83 tff(829,plain,
% 163.60/163.83 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = false),
% 163.60/163.83 inference(transitivity,[status(thm)],[828, 685, 819, 816])).
% 163.60/163.83 tff(830,plain,
% 163.60/163.83 ((phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err) <=> (false = err)),
% 163.60/163.83 inference(monotonicity,[status(thm)],[829])).
% 163.60/163.83 tff(831,plain,
% 163.60/163.83 ((false = err) <=> (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err)),
% 163.60/163.83 inference(symmetry,[status(thm)],[830])).
% 163.60/163.83 tff(832,plain,
% 163.60/163.83 ((~(false = err)) <=> (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err))),
% 163.60/163.83 inference(monotonicity,[status(thm)],[831])).
% 163.60/163.83 tff(833,plain,
% 163.60/163.83 (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err)),
% 163.60/163.83 inference(modus_ponens,[status(thm)],[692, 832])).
% 163.60/163.83 tff(834,plain,
% 163.60/163.83 (d(f4(P!7, tptp_fun_X_4(false, P!7), false)) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = err))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[703, 833])).
% 163.60/163.83 tff(835,plain,
% 163.60/163.83 (~((~d(f4(P!7, tptp_fun_X_4(false, P!7), false))) | (~(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false))))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[708, 834])).
% 163.60/163.83 tff(836,plain,
% 163.60/163.83 (phi(f4(P!7, tptp_fun_X_4(false, P!7), false)) = f4(P!7, tptp_fun_X_4(false, P!7), false)),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[710, 835])).
% 163.60/163.83 tff(837,plain,
% 163.60/163.83 (f4(P!7, tptp_fun_X_4(false, P!7), false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 163.60/163.83 inference(symmetry,[status(thm)],[836])).
% 163.60/163.83 tff(838,assumption,(apply(P!7, tptp_fun_X_4(false, P!7)) = false), introduced(assumption)).
% 163.60/163.83 tff(839,plain,
% 163.60/163.83 (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = impl(false, false)),
% 163.60/163.83 inference(monotonicity,[status(thm)],[838])).
% 163.60/163.83 tff(840,plain,
% 163.60/163.83 (impl(false, false) = impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)),
% 163.60/163.83 inference(symmetry,[status(thm)],[839])).
% 163.60/163.83 tff(841,plain,
% 163.60/163.83 (true = impl(false, false)),
% 163.60/163.83 inference(symmetry,[status(thm)],[392])).
% 163.60/163.83 tff(842,plain,
% 163.60/163.83 (true = false),
% 163.60/163.83 inference(transitivity,[status(thm)],[841, 840, 810, 837, 828, 685, 819, 816])).
% 163.60/163.83 tff(843,plain,
% 163.60/163.83 ($false),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[56, 842])).
% 163.60/163.83 tff(844,plain,((~(apply(P!7, tptp_fun_X_4(false, P!7)) = false)) | (~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false)) | (~(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.83 tff(845,plain,
% 163.60/163.83 (~(apply(P!7, tptp_fun_X_4(false, P!7)) = false)),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[844, 684, 674])).
% 163.60/163.83 tff(846,plain,
% 163.60/163.83 (~(impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = phi(apply(P!7, tptp_fun_X_4(false, P!7))))),
% 163.60/163.83 inference(modus_ponens,[status(thm)],[845, 815])).
% 163.60/163.83 tff(847,plain,
% 163.60/163.83 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = phi(apply(P!7, tptp_fun_X_4(false, P!7)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = phi(apply(P!7, tptp_fun_X_4(false, P!7)))))),
% 163.60/163.83 inference(rewrite,[status(thm)],[])).
% 163.60/163.83 tff(848,plain,
% 163.60/163.83 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = phi(apply(P!7, tptp_fun_X_4(false, P!7)))))),
% 163.60/163.83 inference(quant_inst,[status(thm)],[])).
% 163.60/163.83 tff(849,plain,
% 163.60/163.83 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = phi(apply(P!7, tptp_fun_X_4(false, P!7))))),
% 163.60/163.83 inference(modus_ponens,[status(thm)],[848, 847])).
% 163.60/163.83 tff(850,plain,
% 163.60/163.83 (bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = phi(apply(P!7, tptp_fun_X_4(false, P!7))))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[849, 332])).
% 163.60/163.83 tff(851,plain,
% 163.60/163.83 (bool(apply(P!7, tptp_fun_X_4(false, P!7)))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[850, 846])).
% 163.60/163.83 tff(852,plain,
% 163.60/163.83 ((~(bool(apply(P!7, tptp_fun_X_4(false, P!7))) <=> ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = true)))) | (~bool(apply(P!7, tptp_fun_X_4(false, P!7)))) | ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = true))),
% 163.60/163.83 inference(tautology,[status(thm)],[])).
% 163.60/163.83 tff(853,plain,
% 163.60/163.83 ((~(bool(apply(P!7, tptp_fun_X_4(false, P!7))) <=> ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = true)))) | ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = true))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[852, 851])).
% 163.60/163.83 tff(854,plain,
% 163.60/163.83 ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = true)),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[853, 763])).
% 163.60/163.83 tff(855,plain,
% 163.60/163.83 ((~((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = true))) | (apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = true)),
% 163.60/163.83 inference(tautology,[status(thm)],[])).
% 163.60/163.83 tff(856,plain,
% 163.60/163.83 ((~((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = true))) | (apply(P!7, tptp_fun_X_4(false, P!7)) = true)),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[855, 845])).
% 163.60/163.83 tff(857,plain,
% 163.60/163.83 (apply(P!7, tptp_fun_X_4(false, P!7)) = true),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[856, 854])).
% 163.60/163.83 tff(858,plain,
% 163.60/163.83 (((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))) | ((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)))),
% 163.60/163.83 inference(tautology,[status(thm)],[])).
% 163.60/163.83 tff(859,plain,
% 163.60/163.83 ((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = true))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[858, 793])).
% 163.60/163.83 tff(860,plain,
% 163.60/163.83 ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)))) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = true))),
% 163.60/163.83 inference(tautology,[status(thm)],[])).
% 163.60/163.83 tff(861,plain,
% 163.60/163.83 ((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = true))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[860, 859])).
% 163.60/163.83 tff(862,plain,
% 163.60/163.83 (~(apply(P!7, tptp_fun_X_3(P!7)) = false)),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[861, 857])).
% 163.60/163.83 tff(863,plain,
% 163.60/163.83 ((~((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = true))) | (apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = true)),
% 163.60/163.83 inference(tautology,[status(thm)],[])).
% 163.60/163.83 tff(864,plain,
% 163.60/163.83 (~((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = true))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[863, 862, 761])).
% 163.60/163.83 tff(865,plain,
% 163.60/163.83 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) <=> ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = true)))),
% 163.60/163.83 inference(quant_inst,[status(thm)],[])).
% 163.60/163.83 tff(866,plain,
% 163.60/163.83 (bool(apply(P!7, tptp_fun_X_3(P!7))) <=> ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = true))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[865, 218])).
% 163.60/163.83 tff(867,plain,
% 163.60/163.83 ((~(bool(apply(P!7, tptp_fun_X_3(P!7))) <=> ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = true)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = true))),
% 163.60/163.83 inference(tautology,[status(thm)],[])).
% 163.60/163.83 tff(868,plain,
% 163.60/163.83 ((~bool(apply(P!7, tptp_fun_X_3(P!7)))) | ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = true))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[867, 866])).
% 163.60/163.83 tff(869,plain,
% 163.60/163.83 (~bool(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[868, 864])).
% 163.60/163.83 tff(870,plain,
% 163.60/163.83 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = phi(apply(P!7, tptp_fun_X_3(P!7)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 163.60/163.83 inference(rewrite,[status(thm)],[])).
% 163.60/163.83 tff(871,plain,
% 163.60/163.83 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 163.60/163.83 inference(quant_inst,[status(thm)],[])).
% 163.60/163.83 tff(872,plain,
% 163.60/163.83 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.83 inference(modus_ponens,[status(thm)],[871, 870])).
% 163.60/163.83 tff(873,plain,
% 163.60/163.83 (bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[872, 332])).
% 163.60/163.83 tff(874,plain,
% 163.60/163.83 (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[873, 869])).
% 163.60/163.83 tff(875,plain,
% 163.60/163.83 (phi(apply(P!7, tptp_fun_X_3(P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), true)),
% 163.60/163.83 inference(symmetry,[status(thm)],[874])).
% 163.60/163.83 tff(876,plain,
% 163.60/163.83 (apply(P!7, tptp_fun_X_3(P!7)) = impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, false))),
% 163.60/163.83 inference(transitivity,[status(thm)],[746, 875, 718])).
% 163.60/163.83 tff(877,plain,
% 163.60/163.83 (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, false)), false)),
% 163.60/163.83 inference(monotonicity,[status(thm)],[876])).
% 163.60/163.83 tff(878,plain,
% 163.60/163.83 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, false)), false) = impl(apply(P!7, tptp_fun_X_3(P!7)), false)),
% 163.60/163.83 inference(symmetry,[status(thm)],[877])).
% 163.60/163.83 tff(879,plain,
% 163.60/163.83 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, false)), false) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false)),
% 163.60/163.83 inference(monotonicity,[status(thm)],[717])).
% 163.60/163.83 tff(880,plain,
% 163.60/163.83 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, false)), false)),
% 163.60/163.83 inference(symmetry,[status(thm)],[879])).
% 163.60/163.83 tff(881,plain,
% 163.60/163.83 (apply(P!7, tptp_fun_X_3(P!7)) = impl(apply(P!7, tptp_fun_X_3(P!7)), true)),
% 163.60/163.83 inference(transitivity,[status(thm)],[746, 875])).
% 163.60/163.83 tff(882,plain,
% 163.60/163.83 (bool(apply(P!7, tptp_fun_X_3(P!7))) <=> bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true))),
% 163.60/163.83 inference(monotonicity,[status(thm)],[881])).
% 163.60/163.83 tff(883,plain,
% 163.60/163.83 ((~bool(apply(P!7, tptp_fun_X_3(P!7)))) <=> (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))),
% 163.60/163.83 inference(monotonicity,[status(thm)],[882])).
% 163.60/163.83 tff(884,plain,
% 163.60/163.83 (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true))),
% 163.60/163.83 inference(modus_ponens,[status(thm)],[869, 883])).
% 163.60/163.83 tff(885,plain,
% 163.60/163.83 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true))))),
% 163.60/163.83 inference(rewrite,[status(thm)],[])).
% 163.60/163.83 tff(886,plain,
% 163.60/163.83 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true))))),
% 163.60/163.83 inference(quant_inst,[status(thm)],[])).
% 163.60/163.83 tff(887,plain,
% 163.60/163.83 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))),
% 163.60/163.83 inference(modus_ponens,[status(thm)],[886, 885])).
% 163.60/163.83 tff(888,plain,
% 163.60/163.83 (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[887, 332])).
% 163.60/163.83 tff(889,plain,
% 163.60/163.83 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[888, 884])).
% 163.60/163.83 tff(890,plain,
% 163.60/163.83 (phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false)),
% 163.60/163.83 inference(symmetry,[status(thm)],[889])).
% 163.60/163.83 tff(891,plain,
% 163.60/163.83 (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = apply(P!7, tptp_fun_X_3(P!7))),
% 163.60/163.83 inference(transitivity,[status(thm)],[874, 745])).
% 163.60/163.83 tff(892,plain,
% 163.60/163.83 (phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.83 inference(monotonicity,[status(thm)],[891])).
% 163.60/163.83 tff(893,plain,
% 163.60/163.83 (phi(apply(P!7, tptp_fun_X_3(P!7))) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true))),
% 163.60/163.83 inference(symmetry,[status(thm)],[892])).
% 163.60/163.83 tff(894,plain,
% 163.60/163.83 (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = f4(P!7, tptp_fun_X_3(P!7), false)),
% 163.60/163.83 inference(transitivity,[status(thm)],[874, 893, 890, 880, 878, 716])).
% 163.60/163.83 tff(895,plain,
% 163.60/163.83 (forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false) <=> forallprefers(f4(P!7, tptp_fun_X_3(P!7), false), f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 163.60/163.83 inference(monotonicity,[status(thm)],[894, 713])).
% 163.60/163.83 tff(896,plain,
% 163.60/163.83 (forallprefers(f4(P!7, tptp_fun_X_3(P!7), false), f4(P!7, tptp_fun_X_4(false, P!7), false)) <=> forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false)),
% 163.60/163.83 inference(symmetry,[status(thm)],[895])).
% 163.60/163.83 tff(897,plain,
% 163.60/163.83 ((~forallprefers(f4(P!7, tptp_fun_X_3(P!7), false), f4(P!7, tptp_fun_X_4(false, P!7), false))) <=> (~forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false))),
% 163.60/163.83 inference(monotonicity,[status(thm)],[896])).
% 163.60/163.83 tff(898,plain,
% 163.60/163.83 (((~(f5(P!7, false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~![X1: $i] : (~forallprefers(f4(P!7, X1, false), f4(P!7, tptp_fun_X_4(false, P!7), false))))) | ![X1: $i] : (~forallprefers(f4(P!7, X1, false), f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.60/163.83 inference(tautology,[status(thm)],[])).
% 163.60/163.83 tff(899,plain,
% 163.60/163.83 (![X1: $i] : (~forallprefers(f4(P!7, X1, false), f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[898, 101])).
% 163.60/163.83 tff(900,plain,
% 163.60/163.83 ((~![X1: $i] : (~forallprefers(f4(P!7, X1, false), f4(P!7, tptp_fun_X_4(false, P!7), false)))) | (~forallprefers(f4(P!7, tptp_fun_X_3(P!7), false), f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.60/163.83 inference(quant_inst,[status(thm)],[])).
% 163.60/163.83 tff(901,plain,
% 163.60/163.83 (~forallprefers(f4(P!7, tptp_fun_X_3(P!7), false), f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[900, 899])).
% 163.60/163.83 tff(902,plain,
% 163.60/163.83 (~forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false)),
% 163.60/163.83 inference(modus_ponens,[status(thm)],[901, 897])).
% 163.60/163.83 tff(903,plain,
% 163.60/163.83 ((~(forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false) <=> ((~((~d(false)) | d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))) | (~((~(false = true)) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = false)))) | (~((~d(false)) | (~bool(false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))))))) | forallprefers(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false) | (~((~((~d(false)) | d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))) | (~((~(false = true)) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = false)))) | (~((~d(false)) | (~bool(false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))))))),
% 163.60/163.83 inference(tautology,[status(thm)],[])).
% 163.60/163.83 tff(904,plain,
% 163.60/163.83 (~((~((~d(false)) | d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))) | (~((~(false = true)) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = false)))) | (~((~d(false)) | (~bool(false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), true))))))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[903, 902, 554])).
% 163.60/163.83 tff(905,plain,
% 163.60/163.83 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) <=> d(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.83 inference(monotonicity,[status(thm)],[891])).
% 163.60/163.83 tff(906,plain,
% 163.60/163.83 (d(apply(P!7, tptp_fun_X_3(P!7))) <=> d(impl(apply(P!7, tptp_fun_X_3(P!7)), true))),
% 163.60/163.83 inference(symmetry,[status(thm)],[905])).
% 163.60/163.83 tff(907,plain,
% 163.60/163.83 (d(impl(apply(P!7, tptp_fun_X_3(P!7)), true))),
% 163.60/163.83 inference(modus_ponens,[status(thm)],[766, 906])).
% 163.60/163.83 tff(908,plain,
% 163.60/163.83 ((~((~d(false)) | (~bool(false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), true))))) | (~d(false)) | (~bool(false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))),
% 163.60/163.83 inference(tautology,[status(thm)],[])).
% 163.60/163.83 tff(909,plain,
% 163.60/163.83 ((~((~d(false)) | (~bool(false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), true))))) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[908, 27, 72, 884])).
% 163.60/163.83 tff(910,plain,
% 163.60/163.83 (~((~d(false)) | (~bool(false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), true))))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[909, 907])).
% 163.60/163.83 tff(911,plain,
% 163.60/163.83 (((~((~d(false)) | d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))) | (~((~(false = true)) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = false)))) | (~((~d(false)) | (~bool(false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))))) | ((~d(false)) | (~bool(false)) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (~d(impl(apply(P!7, tptp_fun_X_3(P!7)), true))))),
% 163.60/163.83 inference(tautology,[status(thm)],[])).
% 163.60/163.83 tff(912,plain,
% 163.60/163.83 ($false),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[911, 910, 904])).
% 163.60/163.83 tff(913,plain,(((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))))) | (~(prop(tptp_fun_R_5(P!7)) = false))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.83 tff(914,plain,
% 163.60/163.83 (~(prop(tptp_fun_R_5(P!7)) = false)),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[913, 547])).
% 163.60/163.83 tff(915,plain,
% 163.60/163.83 (impl(true, impl(true, true)) = impl(true, true)),
% 163.60/163.83 inference(monotonicity,[status(thm)],[378])).
% 163.60/163.83 tff(916,plain,
% 163.60/163.83 (impl(true, impl(true, true)) = true),
% 163.60/163.83 inference(transitivity,[status(thm)],[915, 378])).
% 163.60/163.83 tff(917,plain,
% 163.60/163.83 (impl(impl(true, impl(true, true)), true) = impl(true, true)),
% 163.60/163.83 inference(monotonicity,[status(thm)],[916])).
% 163.60/163.83 tff(918,plain,
% 163.60/163.83 (impl(impl(true, impl(true, true)), true) = true),
% 163.60/163.83 inference(transitivity,[status(thm)],[917, 378])).
% 163.60/163.83 tff(919,plain,
% 163.60/163.83 (lazy_impl(prop(true), impl(impl(true, impl(true, true)), true)) = lazy_impl(true, true)),
% 163.60/163.83 inference(monotonicity,[status(thm)],[255, 918])).
% 163.60/163.83 tff(920,plain,
% 163.60/163.83 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(true, true, true) = lazy_impl(prop(true), impl(impl(true, impl(true, true)), true)))),
% 163.60/163.83 inference(quant_inst,[status(thm)],[])).
% 163.60/163.83 tff(921,plain,
% 163.60/163.83 (f1(true, true, true) = lazy_impl(prop(true), impl(impl(true, impl(true, true)), true))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[920, 356])).
% 163.60/163.83 tff(922,assumption,(bool(tptp_fun_R_5(P!7))), introduced(assumption)).
% 163.60/163.83 tff(923,plain,
% 163.60/163.83 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(tptp_fun_R_5(P!7)) <=> ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = true)))),
% 163.60/163.83 inference(quant_inst,[status(thm)],[])).
% 163.60/163.83 tff(924,plain,
% 163.60/163.83 (bool(tptp_fun_R_5(P!7)) <=> ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = true))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[923, 218])).
% 163.60/163.83 tff(925,plain,
% 163.60/163.83 ((~(bool(tptp_fun_R_5(P!7)) <=> ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = true)))) | (~bool(tptp_fun_R_5(P!7))) | ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = true))),
% 163.60/163.83 inference(tautology,[status(thm)],[])).
% 163.60/163.83 tff(926,plain,
% 163.60/163.83 ((~bool(tptp_fun_R_5(P!7))) | ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = true))),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[925, 924])).
% 163.60/163.83 tff(927,plain,
% 163.60/163.83 ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = true)),
% 163.60/163.83 inference(unit_resolution,[status(thm)],[926, 922])).
% 163.60/163.83 tff(928,plain,
% 163.60/163.83 (((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))))))) <=> ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))))))),
% 163.60/163.84 inference(rewrite,[status(thm)],[])).
% 163.60/163.84 tff(929,plain,
% 163.60/163.84 ((existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))))) <=> (existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))))))),
% 163.60/163.84 inference(rewrite,[status(thm)],[])).
% 163.60/163.84 tff(930,plain,
% 163.60/163.84 (((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))))))) <=> ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))))))),
% 163.60/163.84 inference(monotonicity,[status(thm)],[929])).
% 163.60/163.84 tff(931,plain,
% 163.60/163.84 (((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))))))) <=> ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))))))),
% 163.60/163.84 inference(transitivity,[status(thm)],[930, 928])).
% 163.60/163.84 tff(932,plain,
% 163.60/163.84 ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))))))),
% 163.60/163.84 inference(quant_inst,[status(thm)],[])).
% 163.60/163.84 tff(933,plain,
% 163.60/163.84 ((~![X: $i, Y: $i] : (existsprefers(X, Y) <=> ((~(d(X) | (~d(Y)))) | (~((~(X = true)) | (~(Y = false)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))))))),
% 163.60/163.84 inference(modus_ponens,[status(thm)],[932, 931])).
% 163.60/163.84 tff(934,plain,
% 163.60/163.84 (existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))))),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[933, 779])).
% 163.60/163.84 tff(935,plain,
% 163.60/163.84 ((~![X1: $i] : (~existsprefers(apply(P!7, X1), apply(P!7, tptp_fun_X_3(P!7))))) | (~existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.84 inference(quant_inst,[status(thm)],[])).
% 163.60/163.84 tff(936,plain,
% 163.60/163.84 (~existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[935, 788])).
% 163.60/163.84 tff(937,plain,
% 163.60/163.84 ((~(existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))))))) | existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) | (~((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))))))),
% 163.60/163.84 inference(tautology,[status(thm)],[])).
% 163.60/163.84 tff(938,plain,
% 163.60/163.84 ((~(existsprefers(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), apply(P!7, tptp_fun_X_3(P!7))) <=> ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))))))) | (~((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))))))),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[937, 936])).
% 163.60/163.84 tff(939,plain,
% 163.60/163.84 (~((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))))),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[938, 934])).
% 163.60/163.84 tff(940,plain,
% 163.60/163.84 (((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))))) | (d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))),
% 163.60/163.84 inference(tautology,[status(thm)],[])).
% 163.60/163.84 tff(941,plain,
% 163.60/163.84 (d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[940, 939])).
% 163.60/163.84 tff(942,plain,
% 163.60/163.84 ((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.84 inference(tautology,[status(thm)],[])).
% 163.60/163.84 tff(943,plain,
% 163.60/163.84 (d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[942, 941])).
% 163.60/163.84 tff(944,plain,
% 163.60/163.84 (d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[943, 766])).
% 163.60/163.84 tff(945,plain,
% 163.60/163.84 (((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | ((~bool(tptp_fun_R_5(P!7))) | (impl(false, tptp_fun_R_5(P!7)) = true))) <=> ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | (~bool(tptp_fun_R_5(P!7))) | (impl(false, tptp_fun_R_5(P!7)) = true))),
% 163.60/163.84 inference(rewrite,[status(thm)],[])).
% 163.60/163.84 tff(946,plain,
% 163.60/163.84 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | ((~bool(tptp_fun_R_5(P!7))) | (impl(false, tptp_fun_R_5(P!7)) = true))),
% 163.60/163.84 inference(quant_inst,[status(thm)],[])).
% 163.60/163.84 tff(947,plain,
% 163.60/163.84 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | (~bool(tptp_fun_R_5(P!7))) | (impl(false, tptp_fun_R_5(P!7)) = true)),
% 163.60/163.84 inference(modus_ponens,[status(thm)],[946, 945])).
% 163.60/163.84 tff(948,plain,
% 163.60/163.84 ((~bool(tptp_fun_R_5(P!7))) | (impl(false, tptp_fun_R_5(P!7)) = true)),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[947, 388])).
% 163.60/163.84 tff(949,plain,
% 163.60/163.84 (impl(false, tptp_fun_R_5(P!7)) = true),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[948, 922])).
% 163.60/163.84 tff(950,plain,
% 163.60/163.84 (((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | ((~bool(tptp_fun_R_5(P!7))) | (impl(true, tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)))) <=> ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | (~bool(tptp_fun_R_5(P!7))) | (impl(true, tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)))),
% 163.60/163.84 inference(rewrite,[status(thm)],[])).
% 163.60/163.84 tff(951,plain,
% 163.60/163.84 ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | ((~bool(tptp_fun_R_5(P!7))) | (impl(true, tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)))),
% 163.60/163.84 inference(quant_inst,[status(thm)],[])).
% 163.60/163.84 tff(952,plain,
% 163.60/163.84 ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | (~bool(tptp_fun_R_5(P!7))) | (impl(true, tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))),
% 163.60/163.84 inference(modus_ponens,[status(thm)],[951, 950])).
% 163.60/163.84 tff(953,plain,
% 163.60/163.84 ((~bool(tptp_fun_R_5(P!7))) | (impl(true, tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[952, 82])).
% 163.60/163.84 tff(954,plain,
% 163.60/163.84 (impl(true, tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[953, 922])).
% 163.60/163.84 tff(955,plain,
% 163.60/163.84 ((~![X: $i] : ((prop(X) = true) <=> bool(X))) | ((prop(tptp_fun_R_5(P!7)) = true) <=> bool(tptp_fun_R_5(P!7)))),
% 163.60/163.84 inference(quant_inst,[status(thm)],[])).
% 163.60/163.84 tff(956,plain,
% 163.60/163.84 ((prop(tptp_fun_R_5(P!7)) = true) <=> bool(tptp_fun_R_5(P!7))),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[955, 19])).
% 163.60/163.84 tff(957,plain,
% 163.60/163.84 ((~((prop(tptp_fun_R_5(P!7)) = true) <=> bool(tptp_fun_R_5(P!7)))) | (prop(tptp_fun_R_5(P!7)) = true) | (~bool(tptp_fun_R_5(P!7)))),
% 163.60/163.84 inference(tautology,[status(thm)],[])).
% 163.60/163.84 tff(958,plain,
% 163.60/163.84 ((prop(tptp_fun_R_5(P!7)) = true) | (~bool(tptp_fun_R_5(P!7)))),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[957, 956])).
% 163.60/163.84 tff(959,plain,
% 163.60/163.84 (prop(tptp_fun_R_5(P!7)) = true),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[958, 922])).
% 163.60/163.84 tff(960,assumption,((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = true)), introduced(assumption)).
% 163.60/163.84 tff(961,assumption,(prop(tptp_fun_R_5(P!7)) = true), introduced(assumption)).
% 163.60/163.84 tff(962,assumption,(impl(true, tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)), introduced(assumption)).
% 163.60/163.84 tff(963,assumption,(impl(false, tptp_fun_R_5(P!7)) = true), introduced(assumption)).
% 163.60/163.84 tff(964,assumption,(~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))), introduced(assumption)).
% 163.60/163.84 tff(965,plain,
% 163.60/163.84 (((~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.84 inference(tautology,[status(thm)],[])).
% 163.60/163.84 tff(966,plain,
% 163.60/163.84 ((~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[965, 964])).
% 163.60/163.84 tff(967,plain,
% 163.60/163.84 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))))) | (~(d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))))) | (~(d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err)))))),
% 163.60/163.84 inference(rewrite,[status(thm)],[])).
% 163.60/163.84 tff(968,plain,
% 163.60/163.84 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))))) | (~(d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err)))))),
% 163.60/163.84 inference(quant_inst,[status(thm)],[])).
% 163.60/163.84 tff(969,plain,
% 163.60/163.84 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))))) | (~(d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err))))),
% 163.60/163.84 inference(modus_ponens,[status(thm)],[968, 967])).
% 163.60/163.84 tff(970,plain,
% 163.60/163.84 ((~((~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))))) | (~(d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err))))),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[969, 39])).
% 163.60/163.84 tff(971,plain,
% 163.60/163.84 (~(d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err)))),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[970, 966])).
% 163.60/163.84 tff(972,plain,
% 163.60/163.84 ((d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err))) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err)),
% 163.60/163.84 inference(tautology,[status(thm)],[])).
% 163.60/163.84 tff(973,plain,
% 163.60/163.84 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[972, 971])).
% 163.60/163.84 tff(974,plain,
% 163.60/163.84 ((~![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))) | (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.84 inference(quant_inst,[status(thm)],[])).
% 163.60/163.84 tff(975,plain,
% 163.60/163.84 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[974, 7])).
% 163.60/163.84 tff(976,plain,
% 163.60/163.84 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 163.60/163.84 inference(symmetry,[status(thm)],[975])).
% 163.60/163.84 tff(977,assumption,(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))), introduced(assumption)).
% 163.60/163.84 tff(978,plain,
% 163.60/163.84 (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.84 inference(symmetry,[status(thm)],[977])).
% 163.60/163.84 tff(979,plain,
% 163.60/163.84 ((f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.84 inference(commutativity,[status(thm)],[])).
% 163.60/163.84 tff(980,plain,
% 163.60/163.84 (err = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.84 inference(symmetry,[status(thm)],[973])).
% 163.60/163.84 tff(981,plain,
% 163.60/163.84 (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 163.60/163.84 inference(transitivity,[status(thm)],[978, 976])).
% 163.60/163.84 tff(982,plain,
% 163.60/163.84 ((phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err) <=> (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 163.60/163.84 inference(monotonicity,[status(thm)],[981, 980])).
% 163.60/163.84 tff(983,plain,
% 163.60/163.84 ((phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err) <=> (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.84 inference(transitivity,[status(thm)],[982, 979])).
% 163.60/163.84 tff(984,plain,
% 163.60/163.84 ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err)),
% 163.60/163.84 inference(symmetry,[status(thm)],[983])).
% 163.60/163.84 tff(985,plain,
% 163.60/163.84 ((~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err))),
% 163.60/163.84 inference(monotonicity,[status(thm)],[984])).
% 163.60/163.84 tff(986,plain,
% 163.60/163.84 (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err)),
% 163.60/163.84 inference(modus_ponens,[status(thm)],[964, 985])).
% 163.60/163.84 tff(987,plain,
% 163.60/163.84 ((d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err))) | (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err)),
% 163.60/163.84 inference(tautology,[status(thm)],[])).
% 163.60/163.84 tff(988,plain,
% 163.60/163.84 (d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err))),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[987, 986])).
% 163.60/163.84 tff(989,plain,
% 163.60/163.84 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err)))))),
% 163.60/163.84 inference(rewrite,[status(thm)],[])).
% 163.60/163.84 tff(990,plain,
% 163.60/163.84 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err)))))),
% 163.60/163.84 inference(quant_inst,[status(thm)],[])).
% 163.60/163.84 tff(991,plain,
% 163.60/163.84 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err))))),
% 163.60/163.84 inference(modus_ponens,[status(thm)],[990, 989])).
% 163.60/163.84 tff(992,plain,
% 163.60/163.84 ((~((~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err))))),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[991, 39])).
% 163.60/163.84 tff(993,plain,
% 163.60/163.84 (~((~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[992, 988])).
% 163.60/163.84 tff(994,plain,
% 163.60/163.84 (((~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))) | (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 163.60/163.84 inference(tautology,[status(thm)],[])).
% 163.60/163.84 tff(995,plain,
% 163.60/163.84 (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[994, 993])).
% 163.60/163.84 tff(996,plain,
% 163.60/163.84 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 163.60/163.84 inference(symmetry,[status(thm)],[995])).
% 163.60/163.84 tff(997,plain,
% 163.60/163.84 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 163.60/163.84 inference(transitivity,[status(thm)],[996, 978, 976])).
% 163.60/163.84 tff(998,plain,
% 163.60/163.84 (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.84 inference(monotonicity,[status(thm)],[997])).
% 163.60/163.84 tff(999,plain,
% 163.60/163.84 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 163.60/163.84 inference(symmetry,[status(thm)],[998])).
% 163.60/163.84 tff(1000,plain,
% 163.60/163.84 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 163.60/163.84 inference(transitivity,[status(thm)],[999, 978, 976])).
% 163.60/163.84 tff(1001,plain,
% 163.60/163.84 ($false),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[964, 1000])).
% 163.60/163.84 tff(1002,plain,((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.84 tff(1003,plain,
% 163.60/163.84 (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[1002, 964])).
% 163.60/163.84 tff(1004,plain,
% 163.60/163.84 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))),
% 163.60/163.84 inference(rewrite,[status(thm)],[])).
% 163.60/163.84 tff(1005,plain,
% 163.60/163.84 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))),
% 163.60/163.84 inference(quant_inst,[status(thm)],[])).
% 163.60/163.84 tff(1006,plain,
% 163.60/163.84 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))),
% 163.60/163.84 inference(modus_ponens,[status(thm)],[1005, 1004])).
% 163.60/163.84 tff(1007,plain,
% 163.60/163.84 (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[1006, 332])).
% 163.60/163.84 tff(1008,plain,
% 163.60/163.84 (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[1007, 1003])).
% 163.60/163.84 tff(1009,assumption,(~(bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) <=> ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)))), introduced(assumption)).
% 163.60/163.84 tff(1010,plain,
% 163.60/163.84 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) <=> ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)))),
% 163.60/163.84 inference(quant_inst,[status(thm)],[])).
% 163.60/163.84 tff(1011,plain,
% 163.60/163.84 ($false),
% 163.60/163.84 inference(unit_resolution,[status(thm)],[1010, 218, 1009])).
% 163.60/163.84 tff(1012,plain,(bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) <=> ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.84 tff(1013,plain,
% 163.60/163.84 ((~(bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) <=> ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)))) | (~bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true))),
% 163.60/163.85 inference(tautology,[status(thm)],[])).
% 163.60/163.85 tff(1014,plain,
% 163.60/163.85 ((~bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true))),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[1013, 1012])).
% 163.60/163.85 tff(1015,plain,
% 163.60/163.85 ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[1014, 1008])).
% 163.60/163.85 tff(1016,assumption,(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err), introduced(assumption)).
% 163.60/163.85 tff(1017,assumption,(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true), introduced(assumption)).
% 163.60/163.85 tff(1018,plain,
% 163.60/163.85 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = impl(true, tptp_fun_R_5(P!7))),
% 163.60/163.85 inference(monotonicity,[status(thm)],[1017])).
% 163.60/163.85 tff(1019,plain,
% 163.60/163.85 (impl(true, tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.85 inference(symmetry,[status(thm)],[1018])).
% 163.60/163.85 tff(1020,plain,
% 163.60/163.85 (tptp_fun_R_5(P!7) = impl(true, tptp_fun_R_5(P!7))),
% 163.60/163.85 inference(symmetry,[status(thm)],[962])).
% 163.60/163.85 tff(1021,plain,
% 163.60/163.85 (tptp_fun_R_5(P!7) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 163.60/163.85 inference(transitivity,[status(thm)],[1020, 1019, 976])).
% 163.60/163.85 tff(1022,plain,
% 163.60/163.85 (phi(tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.85 inference(monotonicity,[status(thm)],[1021])).
% 163.60/163.85 tff(1023,plain,
% 163.60/163.85 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 163.60/163.85 inference(quant_inst,[status(thm)],[])).
% 163.60/163.85 tff(1024,plain,
% 163.60/163.85 (lazy_impl(true, tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[1023, 118])).
% 163.60/163.85 tff(1025,plain,
% 163.60/163.85 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = lazy_impl(true, tptp_fun_R_5(P!7))),
% 163.60/163.85 inference(monotonicity,[status(thm)],[961])).
% 163.60/163.85 tff(1026,plain,
% 163.60/163.85 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = err),
% 163.60/163.85 inference(transitivity,[status(thm)],[1025, 1024, 1022, 1016])).
% 163.60/163.85 tff(1027,plain,
% 163.60/163.85 (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) <=> bool(err)),
% 163.60/163.85 inference(monotonicity,[status(thm)],[1026])).
% 163.60/163.85 tff(1028,plain,
% 163.60/163.85 (bool(err) <=> bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.85 inference(symmetry,[status(thm)],[1027])).
% 163.60/163.85 tff(1029,plain,
% 163.60/163.85 ((~bool(err)) <=> (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.60/163.85 inference(monotonicity,[status(thm)],[1028])).
% 163.60/163.85 tff(1030,plain,
% 163.60/163.85 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(err) <=> ((err = false) | (err = true)))),
% 163.60/163.85 inference(quant_inst,[status(thm)],[])).
% 163.60/163.85 tff(1031,plain,
% 163.60/163.85 (bool(err) <=> ((err = false) | (err = true))),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[1030, 218])).
% 163.60/163.85 tff(1032,plain,
% 163.60/163.85 ((err = false) <=> (false = err)),
% 163.60/163.85 inference(commutativity,[status(thm)],[])).
% 163.60/163.85 tff(1033,plain,
% 163.60/163.85 ((false = err) <=> (err = false)),
% 163.60/163.85 inference(symmetry,[status(thm)],[1032])).
% 163.60/163.85 tff(1034,plain,
% 163.60/163.85 ((~(false = err)) <=> (~(err = false))),
% 163.60/163.85 inference(monotonicity,[status(thm)],[1033])).
% 163.60/163.85 tff(1035,plain,
% 163.60/163.85 (~(err = false)),
% 163.60/163.85 inference(modus_ponens,[status(thm)],[692, 1034])).
% 163.60/163.85 tff(1036,plain,
% 163.60/163.85 ((err = true) <=> (true = err)),
% 163.60/163.85 inference(commutativity,[status(thm)],[])).
% 163.60/163.85 tff(1037,plain,
% 163.60/163.85 ((true = err) <=> (err = true)),
% 163.60/163.85 inference(symmetry,[status(thm)],[1036])).
% 163.60/163.85 tff(1038,plain,
% 163.60/163.85 ((~(true = err)) <=> (~(err = true))),
% 163.60/163.85 inference(monotonicity,[status(thm)],[1037])).
% 163.60/163.85 tff(1039,plain,
% 163.60/163.85 (~(err = true)),
% 163.60/163.85 inference(modus_ponens,[status(thm)],[280, 1038])).
% 163.60/163.85 tff(1040,plain,
% 163.60/163.85 ((~((err = false) | (err = true))) | (err = false) | (err = true)),
% 163.60/163.85 inference(tautology,[status(thm)],[])).
% 163.60/163.85 tff(1041,plain,
% 163.60/163.85 (~((err = false) | (err = true))),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[1040, 1039, 1035])).
% 163.60/163.85 tff(1042,plain,
% 163.60/163.85 ((~(bool(err) <=> ((err = false) | (err = true)))) | (~bool(err)) | ((err = false) | (err = true))),
% 163.60/163.85 inference(tautology,[status(thm)],[])).
% 163.60/163.85 tff(1043,plain,
% 163.60/163.85 (~bool(err)),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[1042, 1041, 1031])).
% 163.60/163.85 tff(1044,plain,
% 163.60/163.85 (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.85 inference(modus_ponens,[status(thm)],[1043, 1029])).
% 163.60/163.85 tff(1045,plain,
% 163.60/163.85 (d(lazy_impl(prop(P!6), P!6)) <=> d(f7(P!6))),
% 163.60/163.85 inference(monotonicity,[status(thm)],[175])).
% 163.60/163.85 tff(1046,plain,
% 163.60/163.85 (d(f7(P!6)) <=> d(lazy_impl(prop(P!6), P!6))),
% 163.60/163.85 inference(symmetry,[status(thm)],[1045])).
% 163.60/163.85 tff(1047,plain,
% 163.60/163.85 (d(f7(P!6)) <=> d(false)),
% 163.60/163.85 inference(monotonicity,[status(thm)],[267])).
% 163.60/163.85 tff(1048,plain,
% 163.60/163.85 (d(false) <=> d(f7(P!6))),
% 163.60/163.85 inference(symmetry,[status(thm)],[1047])).
% 163.60/163.85 tff(1049,plain,
% 163.60/163.85 (d(false) <=> d(lazy_impl(prop(P!6), P!6))),
% 163.60/163.85 inference(transitivity,[status(thm)],[1048, 1046])).
% 163.60/163.85 tff(1050,plain,
% 163.60/163.85 (d(lazy_impl(prop(P!6), P!6))),
% 163.60/163.85 inference(modus_ponens,[status(thm)],[27, 1049])).
% 163.60/163.85 tff(1051,plain,
% 163.60/163.85 (bool(lazy_impl(prop(P!6), P!6)) <=> bool(f7(P!6))),
% 163.60/163.85 inference(monotonicity,[status(thm)],[175])).
% 163.60/163.85 tff(1052,plain,
% 163.60/163.85 (bool(f7(P!6)) <=> bool(lazy_impl(prop(P!6), P!6))),
% 163.60/163.85 inference(symmetry,[status(thm)],[1051])).
% 163.60/163.85 tff(1053,plain,
% 163.60/163.85 (bool(f7(P!6)) <=> bool(false)),
% 163.60/163.85 inference(monotonicity,[status(thm)],[267])).
% 163.60/163.85 tff(1054,plain,
% 163.60/163.85 (bool(false) <=> bool(f7(P!6))),
% 163.60/163.85 inference(symmetry,[status(thm)],[1053])).
% 163.60/163.85 tff(1055,plain,
% 163.60/163.85 (bool(false) <=> bool(lazy_impl(prop(P!6), P!6))),
% 163.60/163.85 inference(transitivity,[status(thm)],[1054, 1052])).
% 163.60/163.85 tff(1056,plain,
% 163.60/163.85 (bool(lazy_impl(prop(P!6), P!6))),
% 163.60/163.85 inference(modus_ponens,[status(thm)],[72, 1055])).
% 163.60/163.85 tff(1057,plain,
% 163.60/163.85 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)))))))),
% 163.60/163.85 inference(rewrite,[status(thm)],[])).
% 163.60/163.85 tff(1058,plain,
% 163.60/163.85 ((forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~((~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(lazy_impl(prop(P!6), P!6) = true)))) | (~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))))) <=> (forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false))))))),
% 163.60/163.85 inference(rewrite,[status(thm)],[])).
% 163.60/163.85 tff(1059,plain,
% 163.60/163.85 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~((~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(lazy_impl(prop(P!6), P!6) = true)))) | (~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)))))))),
% 163.60/163.85 inference(monotonicity,[status(thm)],[1058])).
% 163.60/163.85 tff(1060,plain,
% 163.60/163.85 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~((~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(lazy_impl(prop(P!6), P!6) = true)))) | (~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)))))))),
% 163.60/163.85 inference(transitivity,[status(thm)],[1059, 1057])).
% 163.60/163.85 tff(1061,plain,
% 163.60/163.85 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~((~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)) | (~(lazy_impl(prop(P!6), P!6) = true)))) | (~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))))))),
% 163.60/163.85 inference(quant_inst,[status(thm)],[])).
% 163.60/163.85 tff(1062,plain,
% 163.60/163.85 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false))))))),
% 163.60/163.85 inference(modus_ponens,[status(thm)],[1061, 1060])).
% 163.60/163.85 tff(1063,plain,
% 163.60/163.85 (forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)))))),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[1062, 165])).
% 163.60/163.85 tff(1064,plain,
% 163.60/163.85 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.85 inference(quant_inst,[status(thm)],[])).
% 163.60/163.85 tff(1065,plain,
% 163.60/163.85 (f7(tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[1064, 138])).
% 163.60/163.85 tff(1066,plain,
% 163.60/163.85 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = f7(tptp_fun_R_5(P!7))),
% 163.60/163.85 inference(symmetry,[status(thm)],[1065])).
% 163.60/163.85 tff(1067,plain,
% 163.60/163.85 (forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> forallprefers(f7(tptp_fun_R_5(P!7)), f7(P!6))),
% 163.60/163.85 inference(monotonicity,[status(thm)],[1066, 175])).
% 163.60/163.85 tff(1068,plain,
% 163.60/163.85 (forallprefers(f7(tptp_fun_R_5(P!7)), f7(P!6)) <=> forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6))),
% 163.60/163.85 inference(symmetry,[status(thm)],[1067])).
% 163.60/163.85 tff(1069,plain,
% 163.60/163.85 ((~forallprefers(f7(tptp_fun_R_5(P!7)), f7(P!6))) <=> (~forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)))),
% 163.60/163.85 inference(monotonicity,[status(thm)],[1068])).
% 163.60/163.85 tff(1070,plain,
% 163.60/163.85 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(tptp_fun_R_5(P!7)), f7(P!6)))),
% 163.60/163.85 inference(quant_inst,[status(thm)],[])).
% 163.60/163.85 tff(1071,plain,
% 163.60/163.85 (~forallprefers(f7(tptp_fun_R_5(P!7)), f7(P!6))),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[1070, 187])).
% 163.60/163.85 tff(1072,plain,
% 163.60/163.85 (~forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6))),
% 163.60/163.85 inference(modus_ponens,[status(thm)],[1071, 1069])).
% 163.60/163.85 tff(1073,plain,
% 163.60/163.85 ((~(forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false))))))) | forallprefers(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)), lazy_impl(prop(P!6), P!6)) | (~((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false))))))),
% 163.60/163.85 inference(tautology,[status(thm)],[])).
% 163.60/163.85 tff(1074,plain,
% 163.60/163.85 (~((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)))))),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[1073, 1072, 1063])).
% 163.60/163.85 tff(1075,plain,
% 163.60/163.85 (((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false))))) | (d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))),
% 163.60/163.85 inference(tautology,[status(thm)],[])).
% 163.60/163.85 tff(1076,plain,
% 163.60/163.85 (d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6)))),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[1075, 1074])).
% 163.60/163.85 tff(1077,plain,
% 163.60/163.85 ((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6)))),
% 163.60/163.85 inference(tautology,[status(thm)],[])).
% 163.60/163.85 tff(1078,plain,
% 163.60/163.85 (d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6)))),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[1077, 1076])).
% 163.60/163.85 tff(1079,plain,
% 163.60/163.85 (d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[1078, 1050])).
% 163.60/163.85 tff(1080,plain,
% 163.60/163.85 (((~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false))))) | ((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 163.60/163.85 inference(tautology,[status(thm)],[])).
% 163.60/163.85 tff(1081,plain,
% 163.60/163.85 ((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[1080, 1074])).
% 163.60/163.85 tff(1082,plain,
% 163.60/163.85 ((~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.60/163.85 inference(tautology,[status(thm)],[])).
% 163.60/163.85 tff(1083,plain,
% 163.60/163.85 ((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[1082, 1081])).
% 163.60/163.85 tff(1084,plain,
% 163.60/163.85 (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[1083, 1079, 1056, 1050])).
% 163.60/163.85 tff(1085,plain,
% 163.60/163.85 ($false),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[1084, 1044])).
% 163.60/163.85 tff(1086,plain,((~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err)) | (~(impl(true, tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))) | (~(prop(tptp_fun_R_5(P!7)) = true))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.85 tff(1087,plain,
% 163.60/163.85 (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[1086, 973, 962, 961])).
% 163.60/163.85 tff(1088,plain,
% 163.60/163.85 ((~((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true))) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)),
% 163.60/163.85 inference(tautology,[status(thm)],[])).
% 163.60/163.85 tff(1089,plain,
% 163.60/163.85 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[1088, 1087, 1015])).
% 163.60/163.85 tff(1090,plain,
% 163.60/163.85 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = impl(false, tptp_fun_R_5(P!7))),
% 163.60/163.85 inference(monotonicity,[status(thm)],[1089])).
% 163.60/163.85 tff(1091,plain,
% 163.60/163.85 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = true),
% 163.60/163.85 inference(transitivity,[status(thm)],[975, 1090, 963])).
% 163.60/163.85 tff(1092,plain,
% 163.60/163.85 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(true)),
% 163.60/163.85 inference(monotonicity,[status(thm)],[1091])).
% 163.60/163.85 tff(1093,plain,
% 163.60/163.85 (phi(true) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.85 inference(symmetry,[status(thm)],[1092])).
% 163.60/163.85 tff(1094,plain,
% 163.60/163.85 (true = err),
% 163.60/163.85 inference(transitivity,[status(thm)],[724, 1093, 973])).
% 163.60/163.85 tff(1095,plain,
% 163.60/163.85 ($false),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[280, 1094])).
% 163.60/163.85 tff(1096,plain,((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) | (~(impl(false, tptp_fun_R_5(P!7)) = true)) | (~(impl(true, tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))) | (~(prop(tptp_fun_R_5(P!7)) = true))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.85 tff(1097,plain,
% 163.60/163.85 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[1096, 963, 962, 961])).
% 163.60/163.85 tff(1098,plain,
% 163.60/163.85 ((~![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R))))))) | (~((~(f5(P!7, tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))) | (~![X1: $i] : (~forallprefers(f4(P!7, X1, tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))))))),
% 163.60/163.85 inference(quant_inst,[status(thm)],[])).
% 163.60/163.85 tff(1099,plain,
% 163.60/163.85 (~((~(f5(P!7, tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))) | (~![X1: $i] : (~forallprefers(f4(P!7, X1, tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))))),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[1098, 99])).
% 163.60/163.85 tff(1100,plain,
% 163.60/163.85 (((~(f5(P!7, tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))) | (~![X1: $i] : (~forallprefers(f4(P!7, X1, tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))))) | (f5(P!7, tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 163.60/163.85 inference(tautology,[status(thm)],[])).
% 163.60/163.85 tff(1101,plain,
% 163.60/163.85 (f5(P!7, tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.85 inference(unit_resolution,[status(thm)],[1100, 1099])).
% 163.60/163.85 tff(1102,plain,
% 163.60/163.85 (f5(P!7, tptp_fun_R_5(P!7)) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 163.60/163.85 inference(transitivity,[status(thm)],[1101, 1097])).
% 163.60/163.85 tff(1103,plain,
% 163.60/163.85 (phi(f5(P!7, tptp_fun_R_5(P!7))) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.85 inference(monotonicity,[status(thm)],[1102])).
% 163.60/163.85 tff(1104,plain,
% 163.60/163.85 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(f5(P!7, tptp_fun_R_5(P!7)))),
% 163.60/163.85 inference(symmetry,[status(thm)],[1103])).
% 163.60/163.85 tff(1105,plain,
% 163.60/163.85 (phi(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.85 inference(monotonicity,[status(thm)],[976])).
% 163.60/163.85 tff(1106,plain,
% 163.60/163.85 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = true)) | (~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = true)) | (~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false)))))))),
% 163.60/163.85 inference(rewrite,[status(thm)],[])).
% 163.60/163.85 tff(1107,plain,
% 163.60/163.85 ((forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~((~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = true)))) | (~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))))))) <=> (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = true)) | (~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false))))))),
% 163.60/163.85 inference(rewrite,[status(thm)],[])).
% 163.60/163.85 tff(1108,plain,
% 163.60/163.85 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~((~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = true)))) | (~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = true)) | (~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false)))))))),
% 163.60/163.86 inference(monotonicity,[status(thm)],[1107])).
% 163.60/163.86 tff(1109,plain,
% 163.60/163.86 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~((~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = true)))) | (~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = true)) | (~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false)))))))),
% 163.60/163.86 inference(transitivity,[status(thm)],[1108, 1106])).
% 163.60/163.86 tff(1110,plain,
% 163.60/163.86 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~((~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = true)))) | (~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))))))))),
% 163.60/163.86 inference(quant_inst,[status(thm)],[])).
% 163.60/163.86 tff(1111,plain,
% 163.60/163.86 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = true)) | (~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false))))))),
% 163.60/163.86 inference(modus_ponens,[status(thm)],[1110, 1109])).
% 163.60/163.86 tff(1112,plain,
% 163.60/163.86 (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = true)) | (~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false)))))),
% 163.60/163.86 inference(unit_resolution,[status(thm)],[1111, 165])).
% 163.60/163.86 tff(1113,plain,
% 163.60/163.86 ((~![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))) | (f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.86 inference(quant_inst,[status(thm)],[])).
% 163.60/163.86 tff(1114,plain,
% 163.60/163.86 (f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.86 inference(unit_resolution,[status(thm)],[1113, 7])).
% 163.60/163.86 tff(1115,plain,
% 163.60/163.86 (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7))),
% 163.60/163.86 inference(symmetry,[status(thm)],[1114])).
% 163.60/163.86 tff(1116,plain,
% 163.60/163.86 (impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), true)),
% 163.60/163.86 inference(monotonicity,[status(thm)],[963])).
% 163.60/163.86 tff(1117,plain,
% 163.60/163.86 (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7)))),
% 163.60/163.86 inference(symmetry,[status(thm)],[1116])).
% 163.60/163.86 tff(1118,assumption,(~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = phi(apply(P!7, tptp_fun_X_3(P!7))))), introduced(assumption)).
% 163.60/163.86 tff(1119,plain,
% 163.60/163.86 (bool(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.86 inference(unit_resolution,[status(thm)],[873, 1118])).
% 163.60/163.86 tff(1120,plain,
% 163.60/163.86 ((~![X: $i] : ((prop(X) = true) <=> bool(X))) | ((prop(apply(P!7, tptp_fun_X_3(P!7))) = true) <=> bool(apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.86 inference(quant_inst,[status(thm)],[])).
% 163.60/163.86 tff(1121,plain,
% 163.60/163.86 ((prop(apply(P!7, tptp_fun_X_3(P!7))) = true) <=> bool(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.86 inference(unit_resolution,[status(thm)],[1120, 19])).
% 163.60/163.86 tff(1122,plain,
% 163.60/163.86 ((~((prop(apply(P!7, tptp_fun_X_3(P!7))) = true) <=> bool(apply(P!7, tptp_fun_X_3(P!7))))) | (prop(apply(P!7, tptp_fun_X_3(P!7))) = true) | (~bool(apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.86 inference(tautology,[status(thm)],[])).
% 163.60/163.86 tff(1123,plain,
% 163.60/163.86 ((prop(apply(P!7, tptp_fun_X_3(P!7))) = true) | (~bool(apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.86 inference(unit_resolution,[status(thm)],[1122, 1121])).
% 163.60/163.86 tff(1124,plain,
% 163.60/163.86 (prop(apply(P!7, tptp_fun_X_3(P!7))) = true),
% 163.60/163.86 inference(unit_resolution,[status(thm)],[1123, 1119])).
% 163.60/163.86 tff(1125,assumption,(phi(apply(P!7, tptp_fun_X_3(P!7))) = err), introduced(assumption)).
% 163.60/163.86 tff(1126,plain,
% 163.60/163.86 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, apply(P!7, tptp_fun_X_3(P!7))) = phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.86 inference(quant_inst,[status(thm)],[])).
% 163.60/163.86 tff(1127,plain,
% 163.60/163.86 (lazy_impl(true, apply(P!7, tptp_fun_X_3(P!7))) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.86 inference(unit_resolution,[status(thm)],[1126, 118])).
% 163.60/163.86 tff(1128,assumption,(prop(apply(P!7, tptp_fun_X_3(P!7))) = true), introduced(assumption)).
% 163.60/163.86 tff(1129,plain,
% 163.60/163.86 (lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = lazy_impl(true, apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.86 inference(monotonicity,[status(thm)],[1128])).
% 163.60/163.86 tff(1130,plain,
% 163.60/163.86 (lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = err),
% 163.60/163.86 inference(transitivity,[status(thm)],[1129, 1127, 1125])).
% 163.60/163.86 tff(1131,plain,
% 163.60/163.86 (bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) <=> bool(err)),
% 163.60/163.86 inference(monotonicity,[status(thm)],[1130])).
% 163.60/163.86 tff(1132,plain,
% 163.60/163.86 (bool(err) <=> bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.86 inference(symmetry,[status(thm)],[1131])).
% 163.60/163.86 tff(1133,plain,
% 163.60/163.86 ((~bool(err)) <=> (~bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))))),
% 163.60/163.86 inference(monotonicity,[status(thm)],[1132])).
% 163.60/163.86 tff(1134,plain,
% 163.60/163.86 (~bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.86 inference(modus_ponens,[status(thm)],[1043, 1133])).
% 163.60/163.86 tff(1135,plain,
% 163.60/163.86 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))))) | (~((~(false = true)) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = false))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))))) | (~((~(false = true)) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = false)))))))),
% 163.60/163.86 inference(rewrite,[status(thm)],[])).
% 163.60/163.86 tff(1136,plain,
% 163.60/163.86 ((forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~((~(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = false)) | (~(false = true)))) | (~(d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))))))) <=> (forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))))) | (~((~(false = true)) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = false))))))),
% 163.60/163.86 inference(rewrite,[status(thm)],[])).
% 163.60/163.86 tff(1137,plain,
% 163.60/163.86 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~((~(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = false)) | (~(false = true)))) | (~(d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))))) | (~((~(false = true)) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = false)))))))),
% 163.60/163.86 inference(monotonicity,[status(thm)],[1136])).
% 163.60/163.86 tff(1138,plain,
% 163.60/163.86 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~((~(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = false)) | (~(false = true)))) | (~(d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))))) | (~((~(false = true)) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = false)))))))),
% 163.60/163.86 inference(transitivity,[status(thm)],[1137, 1135])).
% 163.60/163.86 tff(1139,plain,
% 163.60/163.86 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~((~(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = false)) | (~(false = true)))) | (~(d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))))))))),
% 163.60/163.86 inference(quant_inst,[status(thm)],[])).
% 163.60/163.86 tff(1140,plain,
% 163.60/163.86 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))))) | (~((~(false = true)) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = false))))))),
% 163.60/163.86 inference(modus_ponens,[status(thm)],[1139, 1138])).
% 163.60/163.86 tff(1141,plain,
% 163.60/163.86 (forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))))) | (~((~(false = true)) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = false)))))),
% 163.60/163.86 inference(unit_resolution,[status(thm)],[1140, 165])).
% 163.60/163.86 tff(1142,plain,
% 163.60/163.86 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(apply(P!7, tptp_fun_X_3(P!7))) = lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.86 inference(quant_inst,[status(thm)],[])).
% 163.60/163.86 tff(1143,plain,
% 163.60/163.86 (f7(apply(P!7, tptp_fun_X_3(P!7))) = lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.86 inference(unit_resolution,[status(thm)],[1142, 138])).
% 163.60/163.86 tff(1144,plain,
% 163.60/163.86 (lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = f7(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.86 inference(symmetry,[status(thm)],[1143])).
% 163.60/163.86 tff(1145,plain,
% 163.60/163.86 (forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))), false) <=> forallprefers(f7(apply(P!7, tptp_fun_X_3(P!7))), f7(P!6))),
% 163.60/163.86 inference(monotonicity,[status(thm)],[1144, 463])).
% 163.60/163.86 tff(1146,plain,
% 163.60/163.86 (forallprefers(f7(apply(P!7, tptp_fun_X_3(P!7))), f7(P!6)) <=> forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))), false)),
% 163.60/163.86 inference(symmetry,[status(thm)],[1145])).
% 163.60/163.86 tff(1147,plain,
% 163.60/163.86 ((~forallprefers(f7(apply(P!7, tptp_fun_X_3(P!7))), f7(P!6))) <=> (~forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))), false))),
% 163.60/163.86 inference(monotonicity,[status(thm)],[1146])).
% 163.60/163.86 tff(1148,plain,
% 163.60/163.86 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(apply(P!7, tptp_fun_X_3(P!7))), f7(P!6)))),
% 163.60/163.86 inference(quant_inst,[status(thm)],[])).
% 163.60/163.86 tff(1149,plain,
% 163.60/163.86 (~forallprefers(f7(apply(P!7, tptp_fun_X_3(P!7))), f7(P!6))),
% 163.60/163.86 inference(unit_resolution,[status(thm)],[1148, 187])).
% 163.60/163.86 tff(1150,plain,
% 163.60/163.86 (~forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))), false)),
% 163.60/163.86 inference(modus_ponens,[status(thm)],[1149, 1147])).
% 163.60/163.86 tff(1151,plain,
% 163.60/163.86 ((~(forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))), false) <=> ((~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))))) | (~((~(false = true)) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = false))))))) | forallprefers(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))), false) | (~((~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))))) | (~((~(false = true)) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = false))))))),
% 163.60/163.86 inference(tautology,[status(thm)],[])).
% 163.60/163.86 tff(1152,plain,
% 163.60/163.86 (~((~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))))) | (~((~(false = true)) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = false)))))),
% 163.60/163.86 inference(unit_resolution,[status(thm)],[1151, 1150, 1141])).
% 163.60/163.86 tff(1153,plain,
% 163.60/163.86 (((~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))))) | (~((~(false = true)) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = false))))) | ((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))))),
% 163.60/163.86 inference(tautology,[status(thm)],[])).
% 163.60/163.86 tff(1154,plain,
% 163.60/163.86 ((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))))),
% 163.60/163.86 inference(unit_resolution,[status(thm)],[1153, 1152])).
% 163.60/163.86 tff(1155,plain,
% 163.60/163.86 (((~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))))) | (~((~(false = true)) | (~(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))) = false))))) | ((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))))),
% 163.60/163.86 inference(tautology,[status(thm)],[])).
% 163.60/163.86 tff(1156,plain,
% 163.60/163.86 ((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.86 inference(unit_resolution,[status(thm)],[1155, 1152])).
% 163.60/163.86 tff(1157,plain,
% 163.60/163.86 ((~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))))) | (~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.87 inference(tautology,[status(thm)],[])).
% 163.60/163.87 tff(1158,plain,
% 163.60/163.87 ((~((~d(false)) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))))) | d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1157, 27])).
% 163.60/163.87 tff(1159,plain,
% 163.60/163.87 (d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1158, 1156])).
% 163.60/163.87 tff(1160,plain,
% 163.60/163.87 ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))))) | (~d(false)) | (~bool(false)) | bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))))),
% 163.60/163.87 inference(tautology,[status(thm)],[])).
% 163.60/163.87 tff(1161,plain,
% 163.60/163.87 ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))))) | bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))) | (~d(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7)))))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1160, 27, 72])).
% 163.60/163.87 tff(1162,plain,
% 163.60/163.87 (bool(lazy_impl(prop(apply(P!7, tptp_fun_X_3(P!7))), apply(P!7, tptp_fun_X_3(P!7))))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1161, 1159, 1154])).
% 163.60/163.87 tff(1163,plain,
% 163.60/163.87 ($false),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1162, 1134])).
% 163.60/163.87 tff(1164,plain,((~(prop(apply(P!7, tptp_fun_X_3(P!7))) = true)) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.87 tff(1165,plain,
% 163.60/163.87 (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1164, 1124])).
% 163.60/163.87 tff(1166,plain,
% 163.60/163.87 ((d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))) | (phi(apply(P!7, tptp_fun_X_3(P!7))) = err)),
% 163.60/163.87 inference(tautology,[status(thm)],[])).
% 163.60/163.87 tff(1167,plain,
% 163.60/163.87 (d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1166, 1165])).
% 163.60/163.87 tff(1168,plain,
% 163.60/163.87 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))))) | (~(d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))))) | (~(d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)))))),
% 163.60/163.87 inference(rewrite,[status(thm)],[])).
% 163.60/163.87 tff(1169,plain,
% 163.60/163.87 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))))) | (~(d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)))))),
% 163.60/163.87 inference(quant_inst,[status(thm)],[])).
% 163.60/163.87 tff(1170,plain,
% 163.60/163.87 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))))) | (~(d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))))),
% 163.60/163.87 inference(modus_ponens,[status(thm)],[1169, 1168])).
% 163.60/163.87 tff(1171,plain,
% 163.60/163.87 ((~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))))) | (~(d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1170, 39])).
% 163.60/163.87 tff(1172,plain,
% 163.60/163.87 (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1171, 1167])).
% 163.60/163.87 tff(1173,plain,
% 163.60/163.87 (d(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[765, 1172])).
% 163.60/163.87 tff(1174,plain,
% 163.60/163.87 (phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[744, 1172])).
% 163.60/163.87 tff(1175,plain,
% 163.60/163.87 (lazy_impl(true, impl(false, tptp_fun_R_5(P!7))) = lazy_impl(true, true)),
% 163.60/163.87 inference(monotonicity,[status(thm)],[963])).
% 163.60/163.87 tff(1176,plain,
% 163.60/163.87 (lazy_impl(true, impl(false, tptp_fun_R_5(P!7))) = true),
% 163.60/163.87 inference(transitivity,[status(thm)],[1175, 236, 234])).
% 163.60/163.87 tff(1177,plain,
% 163.60/163.87 (impl(lazy_impl(true, impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = impl(true, tptp_fun_R_5(P!7))),
% 163.60/163.87 inference(monotonicity,[status(thm)],[1176])).
% 163.60/163.87 tff(1178,plain,
% 163.60/163.87 (impl(lazy_impl(true, impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 163.60/163.87 inference(transitivity,[status(thm)],[1177, 962])).
% 163.60/163.87 tff(1179,plain,
% 163.60/163.87 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(lazy_impl(true, impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.87 inference(monotonicity,[status(thm)],[1178])).
% 163.60/163.87 tff(1180,plain,
% 163.60/163.87 (^[P: $i, Q: $i, R: $i] : refl((f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R))) <=> (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R))))),
% 163.60/163.87 inference(bind,[status(th)],[])).
% 163.60/163.87 tff(1181,plain,
% 163.60/163.87 (![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R))) <=> ![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))),
% 163.60/163.87 inference(quant_intro,[status(thm)],[1180])).
% 163.60/163.87 tff(1182,plain,
% 163.60/163.87 (![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R))) <=> ![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))),
% 163.60/163.87 inference(rewrite,[status(thm)],[])).
% 163.60/163.87 tff(1183,axiom,(![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','def_f2')).
% 163.60/163.87 tff(1184,plain,
% 163.60/163.87 (![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))),
% 163.60/163.87 inference(modus_ponens,[status(thm)],[1183, 1182])).
% 163.60/163.87 tff(1185,plain,(
% 163.60/163.87 ![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))),
% 163.60/163.87 inference(skolemize,[status(sab)],[1184])).
% 163.60/163.87 tff(1186,plain,
% 163.60/163.87 (![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))),
% 163.60/163.87 inference(modus_ponens,[status(thm)],[1185, 1181])).
% 163.60/163.87 tff(1187,plain,
% 163.60/163.87 ((~![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))) | (f2(true, false, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(lazy_impl(true, impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))))),
% 163.60/163.87 inference(quant_inst,[status(thm)],[])).
% 163.60/163.87 tff(1188,plain,
% 163.60/163.87 (f2(true, false, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(lazy_impl(true, impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1187, 1186])).
% 163.60/163.87 tff(1189,assumption,(d(apply(P!7, tptp_fun_X_3(P!7)))), introduced(assumption)).
% 163.60/163.87 tff(1190,plain,
% 163.60/163.87 (d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[943, 1189])).
% 163.60/163.87 tff(1191,plain,
% 163.60/163.87 (((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))))) | ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))),
% 163.60/163.87 inference(tautology,[status(thm)],[])).
% 163.60/163.87 tff(1192,plain,
% 163.60/163.87 ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1191, 939])).
% 163.60/163.87 tff(1193,plain,
% 163.60/163.87 ((~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))),
% 163.60/163.87 inference(tautology,[status(thm)],[])).
% 163.60/163.87 tff(1194,plain,
% 163.60/163.87 ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1193, 1192])).
% 163.60/163.87 tff(1195,plain,
% 163.60/163.87 (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1194, 1119, 1189, 1190])).
% 163.60/163.87 tff(1196,plain,
% 163.60/163.87 ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1014, 1195])).
% 163.60/163.87 tff(1197,plain,
% 163.60/163.87 ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = true)),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[868, 1119])).
% 163.60/163.87 tff(1198,assumption,(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))), introduced(assumption)).
% 163.60/163.87 tff(1199,assumption,(apply(P!7, tptp_fun_X_3(P!7)) = true), introduced(assumption)).
% 163.60/163.87 tff(1200,plain,
% 163.60/163.87 (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = impl(true, true)),
% 163.60/163.87 inference(monotonicity,[status(thm)],[1199])).
% 163.60/163.87 tff(1201,plain,
% 163.60/163.87 (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = true),
% 163.60/163.87 inference(transitivity,[status(thm)],[1200, 378])).
% 163.60/163.87 tff(1202,plain,
% 163.60/163.87 (phi(apply(P!7, tptp_fun_X_3(P!7))) = true),
% 163.60/163.87 inference(transitivity,[status(thm)],[1198, 1199])).
% 163.60/163.87 tff(1203,plain,
% 163.60/163.87 ((impl(apply(P!7, tptp_fun_X_3(P!7)), true) = phi(apply(P!7, tptp_fun_X_3(P!7)))) <=> (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = true)),
% 163.60/163.87 inference(monotonicity,[status(thm)],[1202])).
% 163.60/163.87 tff(1204,plain,
% 163.60/163.87 ((~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = phi(apply(P!7, tptp_fun_X_3(P!7))))) <=> (~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = true))),
% 163.60/163.87 inference(monotonicity,[status(thm)],[1203])).
% 163.60/163.87 tff(1205,plain,
% 163.60/163.87 (~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = true)),
% 163.60/163.87 inference(modus_ponens,[status(thm)],[1118, 1204])).
% 163.60/163.87 tff(1206,plain,
% 163.60/163.87 ($false),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1205, 1201])).
% 163.60/163.87 tff(1207,plain,((~(apply(P!7, tptp_fun_X_3(P!7)) = true)) | (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.87 tff(1208,plain,
% 163.60/163.87 (~(apply(P!7, tptp_fun_X_3(P!7)) = true)),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1207, 1118, 1198])).
% 163.60/163.87 tff(1209,plain,
% 163.60/163.87 (apply(P!7, tptp_fun_X_3(P!7)) = false),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[863, 1208, 1197])).
% 163.60/163.87 tff(1210,plain,
% 163.60/163.87 (((~(d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))))) | ((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)))),
% 163.60/163.87 inference(tautology,[status(thm)],[])).
% 163.60/163.87 tff(1211,plain,
% 163.60/163.87 ((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1210, 939])).
% 163.60/163.87 tff(1212,plain,
% 163.60/163.87 ((~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)))) | (~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true))),
% 163.60/163.87 inference(tautology,[status(thm)],[])).
% 163.60/163.87 tff(1213,plain,
% 163.60/163.87 ((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1212, 1211])).
% 163.60/163.87 tff(1214,plain,
% 163.60/163.87 (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1213, 1209])).
% 163.60/163.87 tff(1215,plain,
% 163.60/163.87 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1088, 1214, 1196])).
% 163.60/163.87 tff(1216,plain,
% 163.60/163.87 (f2(true, apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = f2(true, false, tptp_fun_R_5(P!7))),
% 163.60/163.87 inference(monotonicity,[status(thm)],[1215])).
% 163.60/163.87 tff(1217,plain,
% 163.60/163.87 ((~![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))) | (f2(true, apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(lazy_impl(true, impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))))),
% 163.60/163.87 inference(quant_inst,[status(thm)],[])).
% 163.60/163.87 tff(1218,plain,
% 163.60/163.87 (f2(true, apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(lazy_impl(true, impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1217, 1186])).
% 163.60/163.87 tff(1219,plain,
% 163.60/163.87 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(lazy_impl(true, impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = f2(true, apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.87 inference(symmetry,[status(thm)],[1218])).
% 163.60/163.87 tff(1220,plain,
% 163.60/163.87 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f5(P!7, tptp_fun_R_5(P!7))),
% 163.60/163.87 inference(symmetry,[status(thm)],[1101])).
% 163.60/163.87 tff(1221,plain,
% 163.60/163.87 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 163.60/163.87 inference(quant_inst,[status(thm)],[])).
% 163.60/163.87 tff(1222,plain,
% 163.60/163.87 (lazy_impl(true, f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1221, 118])).
% 163.60/163.87 tff(1223,plain,
% 163.60/163.87 (lazy_impl(true, impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) = lazy_impl(true, f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.87 inference(monotonicity,[status(thm)],[976])).
% 163.60/163.87 tff(1224,plain,
% 163.60/163.87 (lazy_impl(true, impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) = f5(P!7, tptp_fun_R_5(P!7))),
% 163.60/163.87 inference(transitivity,[status(thm)],[1223, 1222, 1220])).
% 163.60/163.87 tff(1225,plain,
% 163.60/163.87 (impl(lazy_impl(true, impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.87 inference(monotonicity,[status(thm)],[1224])).
% 163.60/163.87 tff(1226,plain,
% 163.60/163.87 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = impl(lazy_impl(true, impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 163.60/163.87 inference(symmetry,[status(thm)],[1225])).
% 163.60/163.87 tff(1227,plain,
% 163.60/163.87 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(lazy_impl(true, impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.87 inference(monotonicity,[status(thm)],[1226])).
% 163.60/163.87 tff(1228,plain,
% 163.60/163.87 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.87 inference(transitivity,[status(thm)],[1227, 1219, 1216, 1188, 1179])).
% 163.60/163.87 tff(1229,plain,
% 163.60/163.87 ((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true) <=> (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = true)),
% 163.60/163.87 inference(monotonicity,[status(thm)],[1228])).
% 163.60/163.87 tff(1230,plain,
% 163.60/163.87 ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = true) <=> (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)),
% 163.60/163.87 inference(symmetry,[status(thm)],[1229])).
% 163.60/163.87 tff(1231,plain,
% 163.60/163.87 ((false = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) <=> (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)),
% 163.60/163.87 inference(commutativity,[status(thm)],[])).
% 163.60/163.87 tff(1232,plain,
% 163.60/163.87 ((d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))) | (~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.60/163.87 inference(tautology,[status(thm)],[])).
% 163.60/163.87 tff(1233,plain,
% 163.60/163.87 (d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1232, 1079])).
% 163.60/163.87 tff(1234,plain,
% 163.60/163.87 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)))))),
% 163.60/163.87 inference(rewrite,[status(thm)],[])).
% 163.60/163.87 tff(1235,plain,
% 163.60/163.87 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)))))),
% 163.60/163.87 inference(quant_inst,[status(thm)],[])).
% 163.60/163.87 tff(1236,plain,
% 163.60/163.87 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~(d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))))),
% 163.60/163.87 inference(modus_ponens,[status(thm)],[1235, 1234])).
% 163.60/163.87 tff(1237,plain,
% 163.60/163.87 (~((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1236, 39, 1233])).
% 163.60/163.87 tff(1238,plain,
% 163.60/163.87 (((~d(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.87 inference(tautology,[status(thm)],[])).
% 163.60/163.87 tff(1239,plain,
% 163.60/163.87 (phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1238, 1237])).
% 163.60/163.87 tff(1240,plain,
% 163.60/163.87 (f6(P!7, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.87 inference(transitivity,[status(thm)],[565, 1227, 1219, 1216, 1188, 1179])).
% 163.60/163.87 tff(1241,plain,
% 163.60/163.87 (phi(f6(P!7, tptp_fun_R_5(P!7))) = phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.87 inference(monotonicity,[status(thm)],[1240])).
% 163.60/163.87 tff(1242,plain,
% 163.60/163.87 (exists2(P!7) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.87 inference(transitivity,[status(thm)],[720, 1241, 1239])).
% 163.60/163.87 tff(1243,plain,
% 163.60/163.87 (exists1(P!7) = false),
% 163.60/163.87 inference(transitivity,[status(thm)],[742, 1198, 1209])).
% 163.60/163.87 tff(1244,plain,
% 163.60/163.87 ((exists1(P!7) = exists2(P!7)) <=> (false = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.87 inference(monotonicity,[status(thm)],[1243, 1242])).
% 163.60/163.87 tff(1245,plain,
% 163.60/163.87 ((exists1(P!7) = exists2(P!7)) <=> (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)),
% 163.60/163.87 inference(transitivity,[status(thm)],[1244, 1231])).
% 163.60/163.87 tff(1246,plain,
% 163.60/163.87 ((~(exists1(P!7) = exists2(P!7))) <=> (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false))),
% 163.60/163.87 inference(monotonicity,[status(thm)],[1245])).
% 163.60/163.87 tff(1247,plain,
% 163.60/163.87 (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)),
% 163.60/163.87 inference(modus_ponens,[status(thm)],[760, 1246])).
% 163.60/163.87 tff(1248,plain,
% 163.60/163.87 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) <=> ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = true)))),
% 163.60/163.87 inference(quant_inst,[status(thm)],[])).
% 163.60/163.87 tff(1249,plain,
% 163.60/163.87 (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) <=> ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = true))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1248, 218])).
% 163.60/163.87 tff(1250,plain,
% 163.60/163.87 ((~(bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) <=> ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = true)))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = true))),
% 163.60/163.87 inference(tautology,[status(thm)],[])).
% 163.60/163.87 tff(1251,plain,
% 163.60/163.87 ((~(bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) <=> ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = true)))) | ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = true))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1250, 1084])).
% 163.60/163.87 tff(1252,plain,
% 163.60/163.87 ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = true)),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1251, 1249])).
% 163.60/163.87 tff(1253,plain,
% 163.60/163.87 ((~((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = true))) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = true)),
% 163.60/163.87 inference(tautology,[status(thm)],[])).
% 163.60/163.87 tff(1254,plain,
% 163.60/163.87 ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = true)),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1253, 1252])).
% 163.60/163.87 tff(1255,plain,
% 163.60/163.87 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = true),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1254, 1247])).
% 163.60/163.87 tff(1256,plain,
% 163.60/163.87 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true),
% 163.60/163.87 inference(modus_ponens,[status(thm)],[1255, 1230])).
% 163.60/163.87 tff(1257,plain,
% 163.60/163.87 (lazy_impl(true, impl(false, false)) = lazy_impl(true, true)),
% 163.60/163.87 inference(monotonicity,[status(thm)],[392])).
% 163.60/163.87 tff(1258,plain,
% 163.60/163.87 (lazy_impl(true, impl(false, false)) = true),
% 163.60/163.87 inference(transitivity,[status(thm)],[1257, 236, 234])).
% 163.60/163.87 tff(1259,plain,
% 163.60/163.87 (impl(lazy_impl(true, impl(false, false)), false) = impl(true, false)),
% 163.60/163.87 inference(monotonicity,[status(thm)],[1258])).
% 163.60/163.87 tff(1260,plain,
% 163.60/163.87 (impl(lazy_impl(true, impl(false, false)), false) = false),
% 163.60/163.87 inference(transitivity,[status(thm)],[1259, 86])).
% 163.60/163.87 tff(1261,plain,
% 163.60/163.87 (lazy_impl(prop(false), impl(lazy_impl(true, impl(false, false)), false)) = lazy_impl(true, false)),
% 163.60/163.87 inference(monotonicity,[status(thm)],[109, 1260])).
% 163.60/163.87 tff(1262,plain,
% 163.60/163.87 ((~![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))) | (f2(true, false, false) = lazy_impl(prop(false), impl(lazy_impl(true, impl(false, false)), false)))),
% 163.60/163.87 inference(quant_inst,[status(thm)],[])).
% 163.60/163.87 tff(1263,plain,
% 163.60/163.87 (f2(true, false, false) = lazy_impl(prop(false), impl(lazy_impl(true, impl(false, false)), false))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1262, 1186])).
% 163.60/163.87 tff(1264,plain,
% 163.60/163.87 (d(apply(P!7, tptp_fun_X_4(false, P!7)))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[797, 1189])).
% 163.60/163.87 tff(1265,plain,
% 163.60/163.87 (((~(d(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))))) | (~((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)))) | (~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))))) | ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))))),
% 163.60/163.87 inference(tautology,[status(thm)],[])).
% 163.60/163.87 tff(1266,plain,
% 163.60/163.87 ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1265, 793])).
% 163.60/163.87 tff(1267,plain,
% 163.60/163.87 ((~((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7)))))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))),
% 163.60/163.87 inference(tautology,[status(thm)],[])).
% 163.60/163.87 tff(1268,plain,
% 163.60/163.87 ((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~bool(apply(P!7, tptp_fun_X_3(P!7)))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~d(apply(P!7, tptp_fun_X_4(false, P!7))))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1267, 1266])).
% 163.60/163.87 tff(1269,plain,
% 163.60/163.87 (bool(apply(P!7, tptp_fun_X_4(false, P!7)))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1268, 1119, 1189, 1264])).
% 163.60/163.87 tff(1270,plain,
% 163.60/163.87 ((~(bool(apply(P!7, tptp_fun_X_4(false, P!7))) <=> ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = true)))) | ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = true))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[852, 1269])).
% 163.60/163.87 tff(1271,plain,
% 163.60/163.87 ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = true)),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1270, 763])).
% 163.60/163.87 tff(1272,plain,
% 163.60/163.87 (~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[861, 1209])).
% 163.60/163.87 tff(1273,plain,
% 163.60/163.87 (apply(P!7, tptp_fun_X_4(false, P!7)) = false),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[855, 1272, 1271])).
% 163.60/163.87 tff(1274,plain,
% 163.60/163.87 (f2(true, apply(P!7, tptp_fun_X_4(false, P!7)), false) = f2(true, false, false)),
% 163.60/163.87 inference(monotonicity,[status(thm)],[1273])).
% 163.60/163.87 tff(1275,plain,
% 163.60/163.87 ((~![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))) | (f2(true, apply(P!7, tptp_fun_X_4(false, P!7)), false) = lazy_impl(prop(false), impl(lazy_impl(true, impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)), false)))),
% 163.60/163.87 inference(quant_inst,[status(thm)],[])).
% 163.60/163.87 tff(1276,plain,
% 163.60/163.87 (f2(true, apply(P!7, tptp_fun_X_4(false, P!7)), false) = lazy_impl(prop(false), impl(lazy_impl(true, impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)), false))),
% 163.60/163.87 inference(unit_resolution,[status(thm)],[1275, 1186])).
% 163.60/163.87 tff(1277,plain,
% 163.60/163.87 (lazy_impl(prop(false), impl(lazy_impl(true, impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)), false)) = f2(true, apply(P!7, tptp_fun_X_4(false, P!7)), false)),
% 163.60/163.88 inference(symmetry,[status(thm)],[1276])).
% 163.60/163.88 tff(1278,plain,
% 163.60/163.88 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, f4(P!7, tptp_fun_X_4(false, P!7), false)) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.60/163.88 inference(quant_inst,[status(thm)],[])).
% 163.60/163.88 tff(1279,plain,
% 163.60/163.88 (lazy_impl(true, f4(P!7, tptp_fun_X_4(false, P!7), false)) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 163.60/163.88 inference(unit_resolution,[status(thm)],[1278, 118])).
% 163.60/163.88 tff(1280,plain,
% 163.60/163.88 (lazy_impl(true, impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) = lazy_impl(true, f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 163.60/163.88 inference(monotonicity,[status(thm)],[810])).
% 163.60/163.88 tff(1281,plain,
% 163.60/163.88 (lazy_impl(true, impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)) = f5(P!7, false)),
% 163.60/163.88 inference(transitivity,[status(thm)],[1280, 1279, 104])).
% 163.60/163.88 tff(1282,plain,
% 163.60/163.88 (impl(lazy_impl(true, impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)), false) = impl(f5(P!7, false), false)),
% 163.60/163.88 inference(monotonicity,[status(thm)],[1281])).
% 163.60/163.88 tff(1283,plain,
% 163.60/163.88 (impl(f5(P!7, false), false) = impl(lazy_impl(true, impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)), false)),
% 163.60/163.88 inference(symmetry,[status(thm)],[1282])).
% 163.60/163.88 tff(1284,plain,
% 163.60/163.88 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = lazy_impl(prop(false), impl(lazy_impl(true, impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)), false))),
% 163.60/163.88 inference(monotonicity,[status(thm)],[1283])).
% 163.60/163.88 tff(1285,plain,
% 163.60/163.88 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = false),
% 163.60/163.88 inference(transitivity,[status(thm)],[1284, 1277, 1274, 1263, 1261, 130, 45])).
% 163.60/163.88 tff(1286,plain,
% 163.60/163.88 (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)),
% 163.60/163.88 inference(unit_resolution,[status(thm)],[636, 1285])).
% 163.60/163.88 tff(1287,plain,
% 163.60/163.88 ($false),
% 163.60/163.88 inference(unit_resolution,[status(thm)],[1286, 1256])).
% 163.60/163.88 tff(1288,plain,((impl(apply(P!7, tptp_fun_X_3(P!7)), true) = phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~(impl(true, tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))) | (~(impl(false, tptp_fun_R_5(P!7)) = true)) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))) | (~d(apply(P!7, tptp_fun_X_3(P!7))))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.88 tff(1289,plain,
% 163.60/163.88 ($false),
% 163.60/163.88 inference(unit_resolution,[status(thm)],[1288, 1174, 1173, 963, 962, 1118])).
% 163.60/163.88 tff(1290,plain,((impl(apply(P!7, tptp_fun_X_3(P!7)), true) = phi(apply(P!7, tptp_fun_X_3(P!7)))) | (~(impl(false, tptp_fun_R_5(P!7)) = true)) | (~(impl(true, tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.88 tff(1291,plain,
% 163.60/163.88 (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.88 inference(unit_resolution,[status(thm)],[1290, 963, 962])).
% 163.60/163.88 tff(1292,plain,
% 163.60/163.88 (phi(apply(P!7, tptp_fun_X_3(P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), true)),
% 163.60/163.88 inference(symmetry,[status(thm)],[1291])).
% 163.60/163.88 tff(1293,plain,
% 163.60/163.88 (apply(P!7, tptp_fun_X_3(P!7)) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.88 inference(symmetry,[status(thm)],[1198])).
% 163.60/163.88 tff(1294,plain,
% 163.60/163.88 (apply(P!7, tptp_fun_X_3(P!7)) = impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7)))),
% 163.60/163.88 inference(transitivity,[status(thm)],[1293, 1292, 1117])).
% 163.60/163.88 tff(1295,plain,
% 163.60/163.88 (impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7)) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 163.60/163.88 inference(monotonicity,[status(thm)],[1294])).
% 163.60/163.88 tff(1296,plain,
% 163.60/163.88 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_3(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.88 inference(symmetry,[status(thm)],[1295])).
% 163.60/163.88 tff(1297,plain,
% 163.60/163.88 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7))),
% 163.60/163.88 inference(transitivity,[status(thm)],[1296, 1115])).
% 163.60/163.88 tff(1298,plain,
% 163.60/163.88 (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> forallprefers(f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.88 inference(monotonicity,[status(thm)],[1297, 976])).
% 163.60/163.88 tff(1299,plain,
% 163.60/163.88 (forallprefers(f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.88 inference(symmetry,[status(thm)],[1298])).
% 163.60/163.88 tff(1300,plain,
% 163.60/163.88 ((~forallprefers(f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> (~forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))))),
% 163.60/163.88 inference(monotonicity,[status(thm)],[1299])).
% 163.60/163.88 tff(1301,plain,
% 163.60/163.88 (((~(f5(P!7, tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))) | (~![X1: $i] : (~forallprefers(f4(P!7, X1, tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))))) | ![X1: $i] : (~forallprefers(f4(P!7, X1, tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 163.60/163.88 inference(tautology,[status(thm)],[])).
% 163.60/163.88 tff(1302,plain,
% 163.60/163.88 (![X1: $i] : (~forallprefers(f4(P!7, X1, tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 163.60/163.88 inference(unit_resolution,[status(thm)],[1301, 1099])).
% 163.60/163.88 tff(1303,plain,
% 163.60/163.88 ((~![X1: $i] : (~forallprefers(f4(P!7, X1, tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))) | (~forallprefers(f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 163.60/163.88 inference(quant_inst,[status(thm)],[])).
% 163.60/163.88 tff(1304,plain,
% 163.60/163.88 (~forallprefers(f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.88 inference(unit_resolution,[status(thm)],[1303, 1302])).
% 163.60/163.88 tff(1305,plain,
% 163.60/163.88 (~forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.88 inference(modus_ponens,[status(thm)],[1304, 1300])).
% 163.60/163.88 tff(1306,plain,
% 163.60/163.88 ((~(forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> ((~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = true)) | (~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false))))))) | forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)), impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) | (~((~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = true)) | (~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false))))))),
% 163.60/163.88 inference(tautology,[status(thm)],[])).
% 163.60/163.88 tff(1307,plain,
% 163.60/163.88 (~((~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = true)) | (~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false)))))),
% 163.60/163.88 inference(unit_resolution,[status(thm)],[1306, 1305, 1112])).
% 163.60/163.88 tff(1308,plain,
% 163.60/163.88 (((~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = true)) | (~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false))))) | ((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))))),
% 163.60/163.88 inference(tautology,[status(thm)],[])).
% 163.60/163.88 tff(1309,plain,
% 163.60/163.88 ((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))))),
% 163.60/163.88 inference(unit_resolution,[status(thm)],[1308, 1307])).
% 163.60/163.88 tff(1310,plain,
% 163.60/163.88 (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = apply(P!7, tptp_fun_X_3(P!7))),
% 163.60/163.88 inference(transitivity,[status(thm)],[1291, 1198])).
% 163.60/163.88 tff(1311,plain,
% 163.60/163.88 (phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.88 inference(monotonicity,[status(thm)],[1310])).
% 163.60/163.88 tff(1312,plain,
% 163.60/163.88 (apply(P!7, tptp_fun_X_3(P!7)) = impl(apply(P!7, tptp_fun_X_3(P!7)), true)),
% 163.60/163.88 inference(transitivity,[status(thm)],[1293, 1292])).
% 163.60/163.88 tff(1313,plain,
% 163.60/163.88 (bool(apply(P!7, tptp_fun_X_3(P!7))) <=> bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true))),
% 163.60/163.88 inference(monotonicity,[status(thm)],[1312])).
% 163.60/163.88 tff(1314,plain,
% 163.60/163.88 ((~bool(apply(P!7, tptp_fun_X_3(P!7)))) <=> (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))),
% 163.60/163.88 inference(monotonicity,[status(thm)],[1313])).
% 163.60/163.88 tff(1315,assumption,(~bool(apply(P!7, tptp_fun_X_3(P!7)))), introduced(assumption)).
% 163.60/163.88 tff(1316,plain,
% 163.60/163.88 (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true))),
% 163.60/163.88 inference(modus_ponens,[status(thm)],[1315, 1314])).
% 163.60/163.88 tff(1317,plain,
% 163.60/163.88 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), tptp_fun_R_5(P!7)) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), tptp_fun_R_5(P!7)) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true))))),
% 163.60/163.88 inference(rewrite,[status(thm)],[])).
% 163.60/163.88 tff(1318,plain,
% 163.60/163.88 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), tptp_fun_R_5(P!7)) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true))))),
% 163.60/163.88 inference(quant_inst,[status(thm)],[])).
% 163.60/163.88 tff(1319,plain,
% 163.60/163.88 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), tptp_fun_R_5(P!7)) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))),
% 163.60/163.88 inference(modus_ponens,[status(thm)],[1318, 1317])).
% 163.60/163.88 tff(1320,plain,
% 163.60/163.88 (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), tptp_fun_R_5(P!7)) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))),
% 163.60/163.88 inference(unit_resolution,[status(thm)],[1319, 332])).
% 163.60/163.88 tff(1321,plain,
% 163.60/163.88 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), tptp_fun_R_5(P!7)) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true))),
% 163.60/163.88 inference(unit_resolution,[status(thm)],[1320, 1316])).
% 163.60/163.88 tff(1322,plain,
% 163.60/163.88 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), tptp_fun_R_5(P!7))),
% 163.60/163.88 inference(monotonicity,[status(thm)],[1116])).
% 163.60/163.88 tff(1323,plain,
% 163.60/163.88 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_3(P!7)), true)),
% 163.60/163.88 inference(transitivity,[status(thm)],[1322, 1321, 1311, 1292])).
% 163.60/163.88 tff(1324,plain,
% 163.60/163.88 (bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) <=> bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true))),
% 163.60/163.88 inference(monotonicity,[status(thm)],[1323])).
% 163.60/163.88 tff(1325,plain,
% 163.60/163.88 (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) <=> bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.88 inference(symmetry,[status(thm)],[1324])).
% 163.60/163.88 tff(1326,plain,
% 163.60/163.88 ((~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true))) <=> (~bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))))),
% 163.60/163.88 inference(monotonicity,[status(thm)],[1325])).
% 163.60/163.88 tff(1327,plain,
% 163.60/163.88 (~bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.88 inference(modus_ponens,[status(thm)],[1316, 1326])).
% 163.60/163.88 tff(1328,plain,
% 163.60/163.88 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = apply(P!7, tptp_fun_X_3(P!7))),
% 163.60/163.88 inference(transitivity,[status(thm)],[1322, 1321, 1311, 1198])).
% 163.60/163.88 tff(1329,plain,
% 163.60/163.88 (d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) <=> d(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.88 inference(monotonicity,[status(thm)],[1328])).
% 163.60/163.88 tff(1330,plain,
% 163.60/163.88 (d(apply(P!7, tptp_fun_X_3(P!7))) <=> d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.88 inference(symmetry,[status(thm)],[1329])).
% 163.60/163.88 tff(1331,plain,
% 163.60/163.88 (d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.88 inference(modus_ponens,[status(thm)],[1189, 1330])).
% 163.60/163.88 tff(1332,plain,
% 163.60/163.88 (d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.88 inference(monotonicity,[status(thm)],[976])).
% 163.60/163.88 tff(1333,plain,
% 163.60/163.88 ((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) <=> (~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 163.60/163.88 inference(monotonicity,[status(thm)],[1332])).
% 163.60/163.88 tff(1334,assumption,((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))))), introduced(assumption)).
% 163.60/163.88 tff(1335,assumption,(~bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))), introduced(assumption)).
% 163.60/163.88 tff(1336,assumption,(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))), introduced(assumption)).
% 163.60/163.88 tff(1337,assumption,(bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))), introduced(assumption)).
% 163.60/163.88 tff(1338,plain,
% 163.60/163.88 ((~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))))),
% 163.60/163.88 inference(tautology,[status(thm)],[])).
% 163.60/163.88 tff(1339,plain,
% 163.60/163.88 (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.88 inference(unit_resolution,[status(thm)],[1338, 1337, 1336, 1335, 1334])).
% 163.60/163.88 tff(1340,plain,
% 163.60/163.88 (~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.88 inference(modus_ponens,[status(thm)],[1339, 1333])).
% 163.60/163.88 tff(1341,plain,
% 163.60/163.88 (((~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))) | d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.88 inference(tautology,[status(thm)],[])).
% 163.60/163.88 tff(1342,plain,
% 163.60/163.88 ((~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 163.60/163.88 inference(unit_resolution,[status(thm)],[1341, 1340])).
% 163.60/163.88 tff(1343,plain,
% 163.60/163.88 (~(d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err)))),
% 163.60/163.88 inference(unit_resolution,[status(thm)],[970, 1342])).
% 163.60/163.88 tff(1344,plain,
% 163.60/163.88 (bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> bool(f5(P!7, tptp_fun_R_5(P!7)))),
% 163.60/163.88 inference(monotonicity,[status(thm)],[1220])).
% 163.60/163.88 tff(1345,plain,
% 163.60/163.88 (bool(f5(P!7, tptp_fun_R_5(P!7))) <=> bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 163.60/163.88 inference(symmetry,[status(thm)],[1344])).
% 163.60/163.88 tff(1346,assumption,(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), introduced(assumption)).
% 163.60/163.88 tff(1347,plain,
% 163.60/163.88 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.88 inference(symmetry,[status(thm)],[1346])).
% 163.60/163.88 tff(1348,plain,
% 163.60/163.88 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = f5(P!7, tptp_fun_R_5(P!7))),
% 163.60/163.88 inference(transitivity,[status(thm)],[1347, 1220])).
% 163.60/163.88 tff(1349,plain,
% 163.60/163.88 (bool(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> bool(f5(P!7, tptp_fun_R_5(P!7)))),
% 163.60/163.88 inference(monotonicity,[status(thm)],[1348])).
% 163.60/163.88 tff(1350,plain,
% 163.60/163.88 (bool(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 163.60/163.88 inference(transitivity,[status(thm)],[1349, 1345])).
% 163.60/163.88 tff(1351,plain,
% 163.60/163.88 (bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> bool(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.88 inference(monotonicity,[status(thm)],[976])).
% 163.60/163.88 tff(1352,plain,
% 163.60/163.88 (bool(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.88 inference(modus_ponens,[status(thm)],[1337, 1351])).
% 163.60/163.88 tff(1353,plain,
% 163.60/163.88 (bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 163.60/163.88 inference(modus_ponens,[status(thm)],[1352, 1350])).
% 163.60/163.88 tff(1354,assumption,(~(bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true)))), introduced(assumption)).
% 163.60/163.88 tff(1355,plain,
% 163.60/163.88 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true)))),
% 163.60/163.88 inference(quant_inst,[status(thm)],[])).
% 163.60/163.88 tff(1356,plain,
% 163.60/163.88 ($false),
% 163.60/163.88 inference(unit_resolution,[status(thm)],[1355, 218, 1354])).
% 163.60/163.88 tff(1357,plain,(bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.88 tff(1358,plain,
% 163.60/163.88 ((~(bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true)))) | (~bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))) | ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true))),
% 163.60/163.88 inference(tautology,[status(thm)],[])).
% 163.60/163.88 tff(1359,plain,
% 163.60/163.88 ((~bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))) | ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true))),
% 163.60/163.88 inference(unit_resolution,[status(thm)],[1358, 1357])).
% 163.60/163.88 tff(1360,plain,
% 163.60/163.88 ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true)),
% 163.60/163.88 inference(unit_resolution,[status(thm)],[1359, 1353])).
% 163.60/163.88 tff(1361,assumption,((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true)), introduced(assumption)).
% 163.60/163.88 tff(1362,plain,
% 163.60/163.88 ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) <=> (err = false)),
% 163.60/163.88 inference(monotonicity,[status(thm)],[1016])).
% 163.60/163.88 tff(1363,plain,
% 163.60/163.88 ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) <=> (false = err)),
% 163.60/163.88 inference(transitivity,[status(thm)],[1362, 1032])).
% 163.60/163.88 tff(1364,plain,
% 163.60/163.88 ((false = err) <=> (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false)),
% 163.60/163.88 inference(symmetry,[status(thm)],[1363])).
% 163.60/163.88 tff(1365,plain,
% 163.60/163.88 ((~(false = err)) <=> (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false))),
% 163.60/163.88 inference(monotonicity,[status(thm)],[1364])).
% 163.60/163.88 tff(1366,plain,
% 163.60/163.88 (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false)),
% 163.60/163.88 inference(modus_ponens,[status(thm)],[692, 1365])).
% 163.60/163.88 tff(1367,plain,
% 163.60/163.88 ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true) <=> (err = true)),
% 163.60/163.88 inference(monotonicity,[status(thm)],[1016])).
% 163.60/163.88 tff(1368,plain,
% 163.60/163.88 ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true) <=> (true = err)),
% 163.60/163.88 inference(transitivity,[status(thm)],[1367, 1036])).
% 163.60/163.88 tff(1369,plain,
% 163.60/163.88 ((true = err) <=> (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true)),
% 163.60/163.88 inference(symmetry,[status(thm)],[1368])).
% 163.60/163.88 tff(1370,plain,
% 163.60/163.88 ((~(true = err)) <=> (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true))),
% 163.60/163.88 inference(monotonicity,[status(thm)],[1369])).
% 163.60/163.88 tff(1371,plain,
% 163.60/163.88 (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true)),
% 163.60/163.88 inference(modus_ponens,[status(thm)],[280, 1370])).
% 163.60/163.88 tff(1372,plain,
% 163.60/163.88 ((~((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true))) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true)),
% 163.60/163.88 inference(tautology,[status(thm)],[])).
% 163.60/163.88 tff(1373,plain,
% 163.60/163.88 ($false),
% 163.60/163.88 inference(unit_resolution,[status(thm)],[1372, 1371, 1366, 1361])).
% 163.60/163.88 tff(1374,plain,((~((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.89 tff(1375,plain,
% 163.60/163.89 (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err)),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[1374, 1360])).
% 163.60/163.89 tff(1376,plain,
% 163.60/163.89 ($false),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[972, 1375, 1343])).
% 163.60/163.89 tff(1377,plain,((~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))))))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.89 tff(1378,plain,
% 163.60/163.89 (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[1377, 1331, 1097, 1327, 1309])).
% 163.60/163.89 tff(1379,plain,
% 163.60/163.89 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) | (impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) | (impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))),
% 163.60/163.89 inference(rewrite,[status(thm)],[])).
% 163.60/163.89 tff(1380,plain,
% 163.60/163.89 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) | (impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))),
% 163.60/163.89 inference(quant_inst,[status(thm)],[])).
% 163.60/163.89 tff(1381,plain,
% 163.60/163.89 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) | (impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))))),
% 163.60/163.89 inference(modus_ponens,[status(thm)],[1380, 1379])).
% 163.60/163.89 tff(1382,plain,
% 163.60/163.89 (bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) | (impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))))),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[1381, 332])).
% 163.60/163.89 tff(1383,plain,
% 163.60/163.89 (impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[1382, 1378])).
% 163.60/163.89 tff(1384,plain,
% 163.60/163.89 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), impl(true, tptp_fun_R_5(P!7))) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(monotonicity,[status(thm)],[962])).
% 163.60/163.89 tff(1385,plain,
% 163.60/163.89 (impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), impl(true, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(monotonicity,[status(thm)],[1384])).
% 163.60/163.89 tff(1386,plain,
% 163.60/163.89 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), impl(true, tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(symmetry,[status(thm)],[1384])).
% 163.60/163.89 tff(1387,plain,
% 163.60/163.89 (f5(P!7, tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), impl(true, tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(transitivity,[status(thm)],[1101, 1097, 975, 1386])).
% 163.60/163.89 tff(1388,plain,
% 163.60/163.89 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), impl(true, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(monotonicity,[status(thm)],[1387])).
% 163.60/163.89 tff(1389,plain,
% 163.60/163.89 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(transitivity,[status(thm)],[1388, 1385, 1383, 1105, 1104])).
% 163.60/163.89 tff(1390,plain,
% 163.60/163.89 ((d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err))) | (~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))),
% 163.60/163.89 inference(tautology,[status(thm)],[])).
% 163.60/163.89 tff(1391,plain,
% 163.60/163.89 (d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = err))),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[1390, 1190])).
% 163.60/163.89 tff(1392,plain,
% 163.60/163.89 (~((~d(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))))),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[991, 39, 1391])).
% 163.60/163.89 tff(1393,plain,
% 163.60/163.89 (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[994, 1392])).
% 163.60/163.89 tff(1394,plain,
% 163.60/163.89 (((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | ((~bool(true)) | (impl(false, true) = true))) <=> ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | (~bool(true)) | (impl(false, true) = true))),
% 163.60/163.89 inference(rewrite,[status(thm)],[])).
% 163.60/163.89 tff(1395,plain,
% 163.60/163.89 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | ((~bool(true)) | (impl(false, true) = true))),
% 163.60/163.89 inference(quant_inst,[status(thm)],[])).
% 163.60/163.89 tff(1396,plain,
% 163.60/163.89 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | (~bool(true)) | (impl(false, true) = true)),
% 163.60/163.89 inference(modus_ponens,[status(thm)],[1395, 1394])).
% 163.60/163.89 tff(1397,plain,
% 163.60/163.89 (impl(false, true) = true),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[1396, 388, 252])).
% 163.60/163.89 tff(1398,plain,
% 163.60/163.89 (f5(P!7, tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), impl(true, tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(transitivity,[status(thm)],[1101, 1346, 975, 1386])).
% 163.60/163.89 tff(1399,plain,
% 163.60/163.89 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), impl(true, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(monotonicity,[status(thm)],[1398])).
% 163.60/163.89 tff(1400,plain,
% 163.60/163.89 (impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), impl(true, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(symmetry,[status(thm)],[1399])).
% 163.60/163.89 tff(1401,plain,
% 163.60/163.89 (impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), impl(true, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(symmetry,[status(thm)],[1385])).
% 163.60/163.89 tff(1402,assumption,(~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))), introduced(assumption)).
% 163.60/163.89 tff(1403,plain,
% 163.60/163.89 (impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[1382, 1402])).
% 163.60/163.89 tff(1404,plain,
% 163.60/163.89 (phi(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) = impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(symmetry,[status(thm)],[1403])).
% 163.60/163.89 tff(1405,plain,
% 163.60/163.89 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(symmetry,[status(thm)],[1105])).
% 163.60/163.89 tff(1406,plain,
% 163.60/163.89 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(transitivity,[status(thm)],[1399, 1385, 1403, 1105, 1346])).
% 163.60/163.89 tff(1407,plain,
% 163.60/163.89 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(true, f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(monotonicity,[status(thm)],[961, 1406])).
% 163.60/163.89 tff(1408,plain,
% 163.60/163.89 (true = prop(tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(symmetry,[status(thm)],[961])).
% 163.60/163.89 tff(1409,plain,
% 163.60/163.89 (lazy_impl(true, impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(monotonicity,[status(thm)],[1408])).
% 163.60/163.89 tff(1410,plain,
% 163.60/163.89 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.60/163.89 inference(quant_inst,[status(thm)],[])).
% 163.60/163.89 tff(1411,plain,
% 163.60/163.89 (lazy_impl(true, impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[1410, 118])).
% 163.60/163.89 tff(1412,plain,
% 163.60/163.89 (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(true, impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(symmetry,[status(thm)],[1411])).
% 163.60/163.89 tff(1413,plain,
% 163.60/163.89 (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(transitivity,[status(thm)],[1412, 1409, 1407, 1222, 1405, 1404, 1401, 1400])).
% 163.60/163.89 tff(1414,plain,
% 163.60/163.89 (f5(P!7, tptp_fun_R_5(P!7)) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(transitivity,[status(thm)],[1101, 1346])).
% 163.60/163.89 tff(1415,plain,
% 163.60/163.89 (phi(f5(P!7, tptp_fun_R_5(P!7))) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(monotonicity,[status(thm)],[1414])).
% 163.60/163.89 tff(1416,plain,
% 163.60/163.89 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(f5(P!7, tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(symmetry,[status(thm)],[1415])).
% 163.60/163.89 tff(1417,plain,
% 163.60/163.89 (phi(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) = phi(f5(P!7, tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(transitivity,[status(thm)],[1105, 1416])).
% 163.60/163.89 tff(1418,plain,
% 163.60/163.89 (impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(transitivity,[status(thm)],[1401, 1400])).
% 163.60/163.89 tff(1419,plain,
% 163.60/163.89 ((impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) <=> (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7))))),
% 163.60/163.89 inference(monotonicity,[status(thm)],[1418, 1417])).
% 163.60/163.89 tff(1420,plain,
% 163.60/163.89 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(modus_ponens,[status(thm)],[1403, 1419])).
% 163.60/163.89 tff(1421,assumption,(~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)), introduced(assumption)).
% 163.60/163.89 tff(1422,assumption,(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))), introduced(assumption)).
% 163.60/163.89 tff(1423,assumption,(impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))), introduced(assumption)).
% 163.60/163.89 tff(1424,plain,
% 163.60/163.89 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(transitivity,[status(thm)],[1399, 1385, 1423, 1105, 1346])).
% 163.60/163.89 tff(1425,plain,
% 163.60/163.89 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(true, f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(monotonicity,[status(thm)],[961, 1424])).
% 163.60/163.89 tff(1426,plain,
% 163.60/163.89 (f6(P!7, tptp_fun_R_5(P!7)) = f5(P!7, tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(transitivity,[status(thm)],[565, 1425, 1222, 1220])).
% 163.60/163.89 tff(1427,plain,
% 163.60/163.89 (phi(f6(P!7, tptp_fun_R_5(P!7))) = phi(f5(P!7, tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(monotonicity,[status(thm)],[1426])).
% 163.60/163.89 tff(1428,plain,
% 163.60/163.89 (phi(f5(P!7, tptp_fun_R_5(P!7))) = phi(f6(P!7, tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(symmetry,[status(thm)],[1427])).
% 163.60/163.89 tff(1429,assumption,(~bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))), introduced(assumption)).
% 163.60/163.89 tff(1430,plain,
% 163.60/163.89 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[1007, 1429])).
% 163.60/163.89 tff(1431,plain,
% 163.60/163.89 (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(symmetry,[status(thm)],[1430])).
% 163.60/163.89 tff(1432,plain,
% 163.60/163.89 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 163.60/163.89 inference(symmetry,[status(thm)],[1422])).
% 163.60/163.89 tff(1433,plain,
% 163.60/163.89 (^[X1: $i, X2: $i] : refl((bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2))) <=> (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2))))),
% 163.60/163.89 inference(bind,[status(th)],[])).
% 163.60/163.89 tff(1434,plain,
% 163.60/163.89 (![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2))) <=> ![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))),
% 163.60/163.89 inference(quant_intro,[status(thm)],[1433])).
% 163.60/163.89 tff(1435,plain,
% 163.60/163.89 (^[X1: $i, X2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~bool(apply(P!7, X1))) & (~bool(apply(P!7, X2)))) <=> (~(bool(apply(P!7, X1)) | bool(apply(P!7, X2))))), ((~((~bool(apply(P!7, X1))) & (~bool(apply(P!7, X2))))) <=> (~(~(bool(apply(P!7, X1)) | bool(apply(P!7, X2))))))), rewrite((~(~(bool(apply(P!7, X1)) | bool(apply(P!7, X2))))) <=> (bool(apply(P!7, X1)) | bool(apply(P!7, X2)))), ((~((~bool(apply(P!7, X1))) & (~bool(apply(P!7, X2))))) <=> (bool(apply(P!7, X1)) | bool(apply(P!7, X2))))), (((~((~bool(apply(P!7, X1))) & (~bool(apply(P!7, X2))))) | (apply(P!7, X1) = apply(P!7, X2))) <=> ((bool(apply(P!7, X1)) | bool(apply(P!7, X2))) | (apply(P!7, X1) = apply(P!7, X2))))), rewrite(((bool(apply(P!7, X1)) | bool(apply(P!7, X2))) | (apply(P!7, X1) = apply(P!7, X2))) <=> (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))), (((~((~bool(apply(P!7, X1))) & (~bool(apply(P!7, X2))))) | (apply(P!7, X1) = apply(P!7, X2))) <=> (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))))),
% 163.60/163.89 inference(bind,[status(th)],[])).
% 163.60/163.89 tff(1436,plain,
% 163.60/163.89 (![X1: $i, X2: $i] : ((~((~bool(apply(P!7, X1))) & (~bool(apply(P!7, X2))))) | (apply(P!7, X1) = apply(P!7, X2))) <=> ![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))),
% 163.60/163.89 inference(quant_intro,[status(thm)],[1435])).
% 163.60/163.89 tff(1437,plain,
% 163.60/163.89 (![X1: $i, X2: $i] : ((~((~bool(apply(P!7, X1))) & (~bool(apply(P!7, X2))))) | (apply(P!7, X1) = apply(P!7, X2)))),
% 163.60/163.89 inference(and_elim,[status(thm)],[759])).
% 163.60/163.89 tff(1438,plain,
% 163.60/163.89 (![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))),
% 163.60/163.89 inference(modus_ponens,[status(thm)],[1437, 1436])).
% 163.60/163.89 tff(1439,plain,
% 163.60/163.89 (![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))),
% 163.60/163.89 inference(modus_ponens,[status(thm)],[1438, 1434])).
% 163.60/163.89 tff(1440,plain,
% 163.60/163.89 (((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (apply(P!7, tptp_fun_X_3(P!7)) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))) <=> ((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (apply(P!7, tptp_fun_X_3(P!7)) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))),
% 163.60/163.89 inference(rewrite,[status(thm)],[])).
% 163.60/163.89 tff(1441,plain,
% 163.60/163.89 ((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (apply(P!7, tptp_fun_X_3(P!7)) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))))),
% 163.60/163.89 inference(quant_inst,[status(thm)],[])).
% 163.60/163.89 tff(1442,plain,
% 163.60/163.89 ((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (apply(P!7, tptp_fun_X_3(P!7)) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 163.60/163.89 inference(modus_ponens,[status(thm)],[1441, 1440])).
% 163.60/163.89 tff(1443,plain,
% 163.60/163.89 (bool(apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (apply(P!7, tptp_fun_X_3(P!7)) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[1442, 1439])).
% 163.60/163.89 tff(1444,plain,
% 163.60/163.89 (apply(P!7, tptp_fun_X_3(P!7)) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[1443, 1429, 1315])).
% 163.60/163.89 tff(1445,plain,
% 163.60/163.89 (exists1(P!7) = exists2(P!7)),
% 163.60/163.89 inference(transitivity,[status(thm)],[742, 1198, 1444, 1432, 1431, 976, 1347, 1416, 1428, 721])).
% 163.60/163.89 tff(1446,plain,
% 163.60/163.89 ($false),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[760, 1445])).
% 163.60/163.89 tff(1447,plain,(bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))) | (~(impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))))) | (~(impl(true, tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))) | (~(prop(tptp_fun_R_5(P!7)) = true)) | bool(apply(P!7, tptp_fun_X_3(P!7)))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.89 tff(1448,plain,
% 163.60/163.89 (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[1447, 1403, 1422, 1198, 1346, 962, 961, 1315])).
% 163.60/163.89 tff(1449,plain,
% 163.60/163.89 ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[1014, 1448])).
% 163.60/163.89 tff(1450,plain,
% 163.60/163.89 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[1088, 1449, 1421])).
% 163.60/163.89 tff(1451,plain,
% 163.60/163.89 (impl(true, false) = impl(lazy_impl(true, impl(false, false)), false)),
% 163.60/163.89 inference(symmetry,[status(thm)],[1259])).
% 163.60/163.89 tff(1452,plain,
% 163.60/163.89 (false = impl(true, false)),
% 163.60/163.89 inference(symmetry,[status(thm)],[86])).
% 163.60/163.89 tff(1453,plain,
% 163.60/163.89 (false = impl(lazy_impl(true, impl(false, false)), false)),
% 163.60/163.89 inference(transitivity,[status(thm)],[1452, 1451])).
% 163.60/163.89 tff(1454,plain,
% 163.60/163.89 (lazy_impl(true, false) = lazy_impl(prop(false), impl(lazy_impl(true, impl(false, false)), false))),
% 163.60/163.89 inference(monotonicity,[status(thm)],[110, 1453])).
% 163.60/163.89 tff(1455,plain,
% 163.60/163.89 (lazy_impl(prop(false), impl(lazy_impl(true, impl(false, false)), false)) = lazy_impl(true, false)),
% 163.60/163.89 inference(symmetry,[status(thm)],[1454])).
% 163.60/163.89 tff(1456,assumption,(tptp_fun_R_5(P!7) = false), introduced(assumption)).
% 163.60/163.89 tff(1457,plain,
% 163.60/163.89 (false = tptp_fun_R_5(P!7)),
% 163.60/163.89 inference(symmetry,[status(thm)],[1456])).
% 163.60/163.89 tff(1458,assumption,(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false), introduced(assumption)).
% 163.60/163.89 tff(1459,plain,
% 163.60/163.89 (false = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))),
% 163.60/163.89 inference(symmetry,[status(thm)],[1458])).
% 163.60/163.89 tff(1460,plain,
% 163.60/163.89 (f2(true, false, false) = f2(true, apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(monotonicity,[status(thm)],[1459, 1457])).
% 163.60/163.89 tff(1461,plain,
% 163.60/163.89 (f2(true, apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = f2(true, false, false)),
% 163.60/163.89 inference(symmetry,[status(thm)],[1460])).
% 163.60/163.89 tff(1462,plain,
% 163.60/163.89 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(lazy_impl(true, impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(monotonicity,[status(thm)],[1225])).
% 163.60/163.89 tff(1463,plain,
% 163.60/163.89 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(lazy_impl(true, impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(symmetry,[status(thm)],[1462])).
% 163.60/163.89 tff(1464,plain,
% 163.60/163.89 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(true, impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(monotonicity,[status(thm)],[961])).
% 163.60/163.89 tff(1465,plain,
% 163.60/163.89 (lazy_impl(true, impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(symmetry,[status(thm)],[1464])).
% 163.60/163.89 tff(1466,assumption,(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), introduced(assumption)).
% 163.60/163.89 tff(1467,plain,
% 163.60/163.89 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(symmetry,[status(thm)],[1466])).
% 163.60/163.89 tff(1468,assumption,(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7)))), introduced(assumption)).
% 163.60/163.89 tff(1469,plain,
% 163.60/163.89 (phi(f5(P!7, tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(symmetry,[status(thm)],[1468])).
% 163.60/163.89 tff(1470,plain,
% 163.60/163.89 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = impl(false, false)),
% 163.60/163.89 inference(monotonicity,[status(thm)],[1458, 1456])).
% 163.60/163.89 tff(1471,plain,
% 163.60/163.89 (impl(false, false) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(symmetry,[status(thm)],[1470])).
% 163.60/163.89 tff(1472,plain,
% 163.60/163.89 (true = false),
% 163.60/163.89 inference(transitivity,[status(thm)],[841, 1471, 976, 1347, 1416, 1469, 1467, 1412, 1465, 1463, 1219, 1461, 1263, 1455, 130, 45])).
% 163.60/163.89 tff(1473,plain,
% 163.60/163.89 ($false),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[56, 1472])).
% 163.60/163.89 tff(1474,plain,((~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false)) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7))))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(prop(tptp_fun_R_5(P!7)) = true)) | (~(tptp_fun_R_5(P!7) = false))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.89 tff(1475,plain,
% 163.60/163.89 (~(tptp_fun_R_5(P!7) = false)),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[1474, 1450, 1346, 1420, 961, 1413])).
% 163.60/163.89 tff(1476,plain,
% 163.60/163.89 ((~((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = true))) | (tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = true)),
% 163.60/163.89 inference(tautology,[status(thm)],[])).
% 163.60/163.89 tff(1477,plain,
% 163.60/163.89 (tptp_fun_R_5(P!7) = true),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[1476, 1475, 960])).
% 163.60/163.89 tff(1478,plain,
% 163.60/163.89 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = impl(false, true)),
% 163.60/163.89 inference(monotonicity,[status(thm)],[1450, 1477])).
% 163.60/163.89 tff(1479,plain,
% 163.60/163.89 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true),
% 163.60/163.89 inference(transitivity,[status(thm)],[1346, 975, 1478, 1397])).
% 163.60/163.89 tff(1480,plain,
% 163.60/163.89 (bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) <=> bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 163.60/163.89 inference(transitivity,[status(thm)],[1351, 1349, 1345])).
% 163.60/163.89 tff(1481,plain,
% 163.60/163.89 ((~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) <=> (~bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))))),
% 163.60/163.89 inference(monotonicity,[status(thm)],[1480])).
% 163.60/163.89 tff(1482,plain,
% 163.60/163.89 (~bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 163.60/163.89 inference(modus_ponens,[status(thm)],[1402, 1481])).
% 163.60/163.89 tff(1483,plain,
% 163.60/163.89 ((~(bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true)))) | bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true)))),
% 163.60/163.89 inference(tautology,[status(thm)],[])).
% 163.60/163.89 tff(1484,plain,
% 163.60/163.89 (bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true)))),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[1483, 1357])).
% 163.60/163.89 tff(1485,plain,
% 163.60/163.89 (~((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true))),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[1484, 1482])).
% 163.60/163.89 tff(1486,plain,
% 163.60/163.89 (((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true)) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true))),
% 163.60/163.89 inference(tautology,[status(thm)],[])).
% 163.60/163.89 tff(1487,plain,
% 163.60/163.89 (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true)),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[1486, 1485])).
% 163.60/163.89 tff(1488,plain,
% 163.60/163.89 ($false),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[1487, 1479])).
% 163.60/163.89 tff(1489,plain,(bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = true))) | (~(prop(tptp_fun_R_5(P!7)) = true)) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true) | (~(phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))) | (~(impl(true, tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))) | bool(apply(P!7, tptp_fun_X_3(P!7)))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.89 tff(1490,plain,
% 163.60/163.89 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true),
% 163.60/163.89 inference(unit_resolution,[status(thm)],[1489, 1378, 960, 961, 1097, 1393, 1198, 962, 1315])).
% 163.60/163.89 tff(1491,plain,
% 163.60/163.89 (impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), impl(true, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(symmetry,[status(thm)],[1388])).
% 163.60/163.89 tff(1492,plain,
% 163.60/163.89 (phi(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))) = impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(symmetry,[status(thm)],[1383])).
% 163.60/163.89 tff(1493,plain,
% 163.60/163.89 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(transitivity,[status(thm)],[1388, 1385, 1383, 1105, 1097])).
% 163.60/163.89 tff(1494,plain,
% 163.60/163.89 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(true, f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(monotonicity,[status(thm)],[961, 1493])).
% 163.60/163.89 tff(1495,plain,
% 163.60/163.89 (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(transitivity,[status(thm)],[1412, 1409, 1494, 1222, 1405, 1492, 1401, 1491])).
% 163.60/163.89 tff(1496,plain,
% 163.60/163.89 (true = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))),
% 163.60/163.89 inference(symmetry,[status(thm)],[1017])).
% 163.60/163.89 tff(1497,plain,
% 163.60/163.89 (impl(true, false) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.89 inference(monotonicity,[status(thm)],[1496, 1457])).
% 163.60/163.89 tff(1498,plain,
% 163.60/163.89 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = impl(true, false)),
% 163.60/163.89 inference(symmetry,[status(thm)],[1497])).
% 163.60/163.89 tff(1499,plain,
% 163.60/163.89 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(f5(P!7, tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(monotonicity,[status(thm)],[1348])).
% 163.60/163.89 tff(1500,plain,
% 163.60/163.89 (phi(f5(P!7, tptp_fun_R_5(P!7))) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(symmetry,[status(thm)],[1499])).
% 163.60/163.89 tff(1501,plain,
% 163.60/163.89 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(true, impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.89 inference(symmetry,[status(thm)],[1409])).
% 163.60/163.89 tff(1502,plain,
% 163.60/163.89 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false),
% 163.60/163.89 inference(transitivity,[status(thm)],[1501, 1411, 1466, 1468, 1500, 1346, 975, 1498, 86])).
% 163.60/163.89 tff(1503,plain,
% 163.60/163.89 ((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true) <=> (false = true)),
% 163.60/163.89 inference(monotonicity,[status(thm)],[1502])).
% 163.60/163.89 tff(1504,plain,
% 163.60/163.89 ((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true) <=> (true = false)),
% 163.60/163.89 inference(transitivity,[status(thm)],[1503, 239])).
% 163.60/163.89 tff(1505,plain,
% 163.60/163.89 ((true = false) <=> (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)),
% 163.60/163.89 inference(symmetry,[status(thm)],[1504])).
% 163.60/163.89 tff(1506,plain,
% 163.60/163.89 ((~(true = false)) <=> (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true))),
% 163.60/163.89 inference(monotonicity,[status(thm)],[1505])).
% 163.60/163.89 tff(1507,plain,
% 163.60/163.89 (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)),
% 163.60/163.89 inference(modus_ponens,[status(thm)],[56, 1506])).
% 163.60/163.89 tff(1508,plain,
% 163.60/163.89 (lazy_impl(true, impl(true, false)) = lazy_impl(true, false)),
% 163.60/163.89 inference(monotonicity,[status(thm)],[86])).
% 163.60/163.89 tff(1509,plain,
% 163.60/163.89 (lazy_impl(true, impl(true, false)) = false),
% 163.60/163.89 inference(transitivity,[status(thm)],[1508, 130, 45])).
% 163.60/163.89 tff(1510,plain,
% 163.60/163.89 (impl(lazy_impl(true, impl(true, false)), false) = impl(false, false)),
% 163.60/163.89 inference(monotonicity,[status(thm)],[1509])).
% 163.60/163.89 tff(1511,plain,
% 163.60/163.89 (impl(false, false) = impl(lazy_impl(true, impl(true, false)), false)),
% 163.60/163.90 inference(symmetry,[status(thm)],[1510])).
% 163.60/163.90 tff(1512,plain,
% 163.60/163.90 (true = impl(lazy_impl(true, impl(true, false)), false)),
% 163.60/163.90 inference(transitivity,[status(thm)],[841, 1511])).
% 163.60/163.90 tff(1513,plain,
% 163.60/163.90 (lazy_impl(true, true) = lazy_impl(prop(false), impl(lazy_impl(true, impl(true, false)), false))),
% 163.60/163.90 inference(monotonicity,[status(thm)],[110, 1512])).
% 163.60/163.90 tff(1514,plain,
% 163.60/163.90 (lazy_impl(prop(false), impl(lazy_impl(true, impl(true, false)), false)) = lazy_impl(true, true)),
% 163.60/163.90 inference(symmetry,[status(thm)],[1513])).
% 163.60/163.90 tff(1515,plain,
% 163.60/163.90 ((~![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))) | (f2(true, true, false) = lazy_impl(prop(false), impl(lazy_impl(true, impl(true, false)), false)))),
% 163.60/163.90 inference(quant_inst,[status(thm)],[])).
% 163.60/163.90 tff(1516,plain,
% 163.60/163.90 (f2(true, true, false) = lazy_impl(prop(false), impl(lazy_impl(true, impl(true, false)), false))),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1515, 1186])).
% 163.60/163.90 tff(1517,plain,
% 163.60/163.90 (f2(true, true, false) = f2(true, apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.90 inference(monotonicity,[status(thm)],[1496, 1457])).
% 163.60/163.90 tff(1518,plain,
% 163.60/163.90 (f2(true, apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = f2(true, true, false)),
% 163.60/163.90 inference(symmetry,[status(thm)],[1517])).
% 163.60/163.90 tff(1519,plain,
% 163.60/163.90 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true),
% 163.60/163.90 inference(transitivity,[status(thm)],[1463, 1219, 1518, 1516, 1514, 236, 234])).
% 163.60/163.90 tff(1520,plain,
% 163.60/163.90 ($false),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1519, 1507])).
% 163.60/163.90 tff(1521,plain,((~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7))))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(prop(tptp_fun_R_5(P!7)) = true)) | (~(tptp_fun_R_5(P!7) = false))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.90 tff(1522,plain,
% 163.60/163.90 (~(tptp_fun_R_5(P!7) = false)),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1521, 1495, 1097, 1490, 961, 1389])).
% 163.60/163.90 tff(1523,plain,
% 163.60/163.90 (tptp_fun_R_5(P!7) = true),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1476, 1522, 960])).
% 163.60/163.90 tff(1524,plain,
% 163.60/163.90 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = impl(true, tptp_fun_R_5(P!7))),
% 163.60/163.90 inference(monotonicity,[status(thm)],[1490])).
% 163.60/163.90 tff(1525,plain,
% 163.60/163.90 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true),
% 163.60/163.90 inference(transitivity,[status(thm)],[1097, 975, 1524, 962, 1523])).
% 163.60/163.90 tff(1526,plain,
% 163.60/163.90 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.90 inference(symmetry,[status(thm)],[1097])).
% 163.60/163.90 tff(1527,plain,
% 163.60/163.90 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = f5(P!7, tptp_fun_R_5(P!7))),
% 163.60/163.90 inference(transitivity,[status(thm)],[1526, 1220])).
% 163.60/163.90 tff(1528,plain,
% 163.60/163.90 (bool(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> bool(f5(P!7, tptp_fun_R_5(P!7)))),
% 163.60/163.90 inference(monotonicity,[status(thm)],[1527])).
% 163.60/163.90 tff(1529,plain,
% 163.60/163.90 (bool(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 163.60/163.90 inference(transitivity,[status(thm)],[1528, 1345])).
% 163.60/163.90 tff(1530,plain,
% 163.60/163.90 ((~bool(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> (~bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))))),
% 163.60/163.90 inference(monotonicity,[status(thm)],[1529])).
% 163.60/163.90 tff(1531,plain,
% 163.60/163.90 ((~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) <=> (~bool(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 163.60/163.90 inference(monotonicity,[status(thm)],[1351])).
% 163.60/163.90 tff(1532,plain,
% 163.60/163.90 (~bool(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.90 inference(modus_ponens,[status(thm)],[1378, 1531])).
% 163.60/163.90 tff(1533,plain,
% 163.60/163.90 (~bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 163.60/163.90 inference(modus_ponens,[status(thm)],[1532, 1530])).
% 163.60/163.90 tff(1534,plain,
% 163.60/163.90 (~((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true))),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1484, 1533])).
% 163.60/163.90 tff(1535,plain,
% 163.60/163.90 (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true)),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1486, 1534])).
% 163.60/163.90 tff(1536,plain,
% 163.60/163.90 ($false),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1535, 1525])).
% 163.60/163.90 tff(1537,plain,(bool(apply(P!7, tptp_fun_X_3(P!7))) | (~(impl(true, tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))) | (~((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = true))) | (~(prop(tptp_fun_R_5(P!7)) = true)) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))) | (~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(impl(false, tptp_fun_R_5(P!7)) = true))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.90 tff(1538,plain,
% 163.60/163.90 (bool(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1537, 745, 927, 959, 954, 766, 949])).
% 163.60/163.90 tff(1539,plain,
% 163.60/163.90 (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1194, 1538, 766, 944])).
% 163.60/163.90 tff(1540,plain,
% 163.60/163.90 ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1014, 1539])).
% 163.60/163.90 tff(1541,plain,
% 163.60/163.90 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) <=> ((impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = true)))),
% 163.60/163.90 inference(quant_inst,[status(thm)],[])).
% 163.60/163.90 tff(1542,plain,
% 163.60/163.90 (bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) <=> ((impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = true))),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1541, 218])).
% 163.60/163.90 tff(1543,plain,
% 163.60/163.90 (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1290, 949, 954])).
% 163.60/163.90 tff(1544,assumption,(apply(P!7, tptp_fun_X_3(P!7)) = false), introduced(assumption)).
% 163.60/163.90 tff(1545,assumption,(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = phi(apply(P!7, tptp_fun_X_3(P!7)))), introduced(assumption)).
% 163.60/163.90 tff(1546,plain,
% 163.60/163.90 (impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)) = impl(apply(P!7, tptp_fun_X_3(P!7)), true)),
% 163.60/163.90 inference(monotonicity,[status(thm)],[1397])).
% 163.60/163.90 tff(1547,plain,
% 163.60/163.90 (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true))),
% 163.60/163.90 inference(symmetry,[status(thm)],[1546])).
% 163.60/163.90 tff(1548,plain,
% 163.60/163.90 (phi(apply(P!7, tptp_fun_X_3(P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), true)),
% 163.60/163.90 inference(symmetry,[status(thm)],[1545])).
% 163.60/163.90 tff(1549,plain,
% 163.60/163.90 (apply(P!7, tptp_fun_X_3(P!7)) = impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true))),
% 163.60/163.90 inference(transitivity,[status(thm)],[1293, 1548, 1547])).
% 163.60/163.90 tff(1550,plain,
% 163.60/163.90 (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)),
% 163.60/163.90 inference(monotonicity,[status(thm)],[1549])).
% 163.60/163.90 tff(1551,plain,
% 163.60/163.90 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true) = impl(apply(P!7, tptp_fun_X_3(P!7)), true)),
% 163.60/163.90 inference(symmetry,[status(thm)],[1550])).
% 163.60/163.90 tff(1552,plain,
% 163.60/163.90 (impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)) = false),
% 163.60/163.90 inference(transitivity,[status(thm)],[1546, 1545, 1198, 1544])).
% 163.60/163.90 tff(1553,plain,
% 163.60/163.90 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true) = impl(false, true)),
% 163.60/163.90 inference(monotonicity,[status(thm)],[1552])).
% 163.60/163.90 tff(1554,plain,
% 163.60/163.90 (impl(false, true) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)),
% 163.60/163.90 inference(symmetry,[status(thm)],[1553])).
% 163.60/163.90 tff(1555,plain,
% 163.60/163.90 (true = impl(false, true)),
% 163.60/163.90 inference(symmetry,[status(thm)],[1397])).
% 163.60/163.90 tff(1556,plain,
% 163.60/163.90 (true = false),
% 163.60/163.90 inference(transitivity,[status(thm)],[1555, 1554, 1551, 1545, 1198, 1544])).
% 163.60/163.90 tff(1557,plain,
% 163.60/163.90 ($false),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[56, 1556])).
% 163.60/163.90 tff(1558,plain,((~(apply(P!7, tptp_fun_X_3(P!7)) = false)) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = phi(apply(P!7, tptp_fun_X_3(P!7)))))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.90 tff(1559,plain,
% 163.60/163.90 (~(apply(P!7, tptp_fun_X_3(P!7)) = false)),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1558, 745, 1543])).
% 163.60/163.90 tff(1560,plain,
% 163.60/163.90 ((apply(P!7, tptp_fun_X_3(P!7)) = false) | (apply(P!7, tptp_fun_X_3(P!7)) = true)),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[868, 1538])).
% 163.60/163.90 tff(1561,plain,
% 163.60/163.90 (apply(P!7, tptp_fun_X_3(P!7)) = true),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[863, 1560, 1559])).
% 163.60/163.90 tff(1562,plain,
% 163.60/163.90 (impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), true)),
% 163.60/163.90 inference(monotonicity,[status(thm)],[949])).
% 163.60/163.90 tff(1563,plain,
% 163.60/163.90 (impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))) = true),
% 163.60/163.90 inference(transitivity,[status(thm)],[1562, 1543, 745, 1561])).
% 163.60/163.90 tff(1564,plain,
% 163.60/163.90 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = impl(true, tptp_fun_R_5(P!7))),
% 163.60/163.90 inference(monotonicity,[status(thm)],[1563])).
% 163.60/163.90 tff(1565,plain,
% 163.60/163.90 (impl(true, tptp_fun_R_5(P!7)) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 163.60/163.90 inference(symmetry,[status(thm)],[1564])).
% 163.60/163.90 tff(1566,plain,
% 163.60/163.90 (tptp_fun_R_5(P!7) = impl(true, tptp_fun_R_5(P!7))),
% 163.60/163.90 inference(symmetry,[status(thm)],[954])).
% 163.60/163.90 tff(1567,plain,
% 163.60/163.90 (tptp_fun_R_5(P!7) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 163.60/163.90 inference(transitivity,[status(thm)],[1566, 1565])).
% 163.60/163.90 tff(1568,plain,
% 163.60/163.90 (bool(tptp_fun_R_5(P!7)) <=> bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.90 inference(monotonicity,[status(thm)],[1567])).
% 163.60/163.90 tff(1569,plain,
% 163.60/163.90 (bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.90 inference(modus_ponens,[status(thm)],[922, 1568])).
% 163.60/163.90 tff(1570,plain,
% 163.60/163.90 ((~(bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) <=> ((impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = true)))) | (~bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))) | ((impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = true))),
% 163.60/163.90 inference(tautology,[status(thm)],[])).
% 163.60/163.90 tff(1571,plain,
% 163.60/163.90 ((~(bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) <=> ((impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = true)))) | ((impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = true))),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1570, 1569])).
% 163.60/163.90 tff(1572,plain,
% 163.60/163.90 ((impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = true)),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1571, 1542])).
% 163.60/163.90 tff(1573,plain,
% 163.60/163.90 ((true = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) <=> (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = true)),
% 163.60/163.90 inference(commutativity,[status(thm)],[])).
% 163.60/163.90 tff(1574,plain,
% 163.60/163.90 (f2(true, apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = f2(true, false, tptp_fun_R_5(P!7))),
% 163.60/163.90 inference(monotonicity,[status(thm)],[1458])).
% 163.60/163.90 tff(1575,plain,
% 163.60/163.90 (f6(P!7, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.90 inference(transitivity,[status(thm)],[565, 1227, 1219, 1574, 1188, 1179])).
% 163.60/163.90 tff(1576,plain,
% 163.60/163.90 (phi(f6(P!7, tptp_fun_R_5(P!7))) = phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.90 inference(monotonicity,[status(thm)],[1575])).
% 163.60/163.90 tff(1577,plain,
% 163.60/163.90 (exists2(P!7) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.90 inference(transitivity,[status(thm)],[720, 1576, 1239])).
% 163.60/163.90 tff(1578,plain,
% 163.60/163.90 (exists1(P!7) = true),
% 163.60/163.90 inference(transitivity,[status(thm)],[742, 1198, 1199])).
% 163.60/163.90 tff(1579,plain,
% 163.60/163.90 ((exists1(P!7) = exists2(P!7)) <=> (true = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.90 inference(monotonicity,[status(thm)],[1578, 1577])).
% 163.60/163.90 tff(1580,plain,
% 163.60/163.90 ((exists1(P!7) = exists2(P!7)) <=> (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = true)),
% 163.60/163.90 inference(transitivity,[status(thm)],[1579, 1573])).
% 163.60/163.90 tff(1581,plain,
% 163.60/163.90 ((~(exists1(P!7) = exists2(P!7))) <=> (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = true))),
% 163.60/163.90 inference(monotonicity,[status(thm)],[1580])).
% 163.60/163.90 tff(1582,plain,
% 163.60/163.90 (~(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = true)),
% 163.60/163.90 inference(modus_ponens,[status(thm)],[760, 1581])).
% 163.60/163.90 tff(1583,plain,
% 163.60/163.90 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1254, 1582])).
% 163.60/163.90 tff(1584,plain,
% 163.60/163.90 (impl(true, impl(false, tptp_fun_R_5(P!7))) = impl(true, true)),
% 163.60/163.90 inference(monotonicity,[status(thm)],[963])).
% 163.60/163.90 tff(1585,plain,
% 163.60/163.90 (impl(true, impl(false, tptp_fun_R_5(P!7))) = true),
% 163.60/163.90 inference(transitivity,[status(thm)],[1584, 378])).
% 163.60/163.90 tff(1586,plain,
% 163.60/163.90 (impl(impl(true, impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = impl(true, tptp_fun_R_5(P!7))),
% 163.60/163.90 inference(monotonicity,[status(thm)],[1585])).
% 163.60/163.90 tff(1587,plain,
% 163.60/163.90 (impl(true, tptp_fun_R_5(P!7)) = impl(impl(true, impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 163.60/163.90 inference(symmetry,[status(thm)],[1586])).
% 163.60/163.90 tff(1588,plain,
% 163.60/163.90 (tptp_fun_R_5(P!7) = impl(impl(true, impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 163.60/163.90 inference(transitivity,[status(thm)],[1020, 1587])).
% 163.60/163.90 tff(1589,plain,
% 163.60/163.90 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(true, impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.90 inference(monotonicity,[status(thm)],[1588])).
% 163.60/163.90 tff(1590,plain,
% 163.60/163.90 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(true, impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.90 inference(symmetry,[status(thm)],[1589])).
% 163.60/163.90 tff(1591,plain,
% 163.60/163.90 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(true, false, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(true, impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))))),
% 163.60/163.90 inference(quant_inst,[status(thm)],[])).
% 163.60/163.90 tff(1592,plain,
% 163.60/163.90 (f1(true, false, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(true, impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1591, 356])).
% 163.60/163.90 tff(1593,plain,
% 163.60/163.90 (true = apply(P!7, tptp_fun_X_3(P!7))),
% 163.60/163.90 inference(symmetry,[status(thm)],[1199])).
% 163.60/163.90 tff(1594,plain,
% 163.60/163.90 (true = impl(apply(P!7, tptp_fun_X_3(P!7)), true)),
% 163.60/163.90 inference(transitivity,[status(thm)],[1593, 1293, 1292])).
% 163.60/163.90 tff(1595,plain,
% 163.60/163.90 (f1(true, false, tptp_fun_R_5(P!7)) = f1(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false, tptp_fun_R_5(P!7))),
% 163.60/163.90 inference(monotonicity,[status(thm)],[1594])).
% 163.60/163.90 tff(1596,plain,
% 163.60/163.90 (f1(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false, tptp_fun_R_5(P!7)) = f1(true, false, tptp_fun_R_5(P!7))),
% 163.60/163.90 inference(symmetry,[status(thm)],[1595])).
% 163.60/163.90 tff(1597,plain,
% 163.60/163.90 (f1(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false, tptp_fun_R_5(P!7)) = f1(apply(P!7, tptp_fun_X_3(P!7)), false, tptp_fun_R_5(P!7))),
% 163.60/163.90 inference(monotonicity,[status(thm)],[1310])).
% 163.60/163.90 tff(1598,plain,
% 163.60/163.90 (f1(apply(P!7, tptp_fun_X_3(P!7)), false, tptp_fun_R_5(P!7)) = f1(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false, tptp_fun_R_5(P!7))),
% 163.60/163.90 inference(symmetry,[status(thm)],[1597])).
% 163.60/163.90 tff(1599,plain,
% 163.60/163.90 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(apply(P!7, tptp_fun_X_3(P!7)), false, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))))),
% 163.60/163.90 inference(quant_inst,[status(thm)],[])).
% 163.60/163.90 tff(1600,plain,
% 163.60/163.90 (f1(apply(P!7, tptp_fun_X_3(P!7)), false, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1599, 356])).
% 163.60/163.90 tff(1601,plain,
% 163.60/163.90 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = f1(apply(P!7, tptp_fun_X_3(P!7)), false, tptp_fun_R_5(P!7))),
% 163.60/163.90 inference(symmetry,[status(thm)],[1600])).
% 163.60/163.90 tff(1602,plain,
% 163.60/163.90 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = lazy_impl(true, impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.90 inference(monotonicity,[status(thm)],[961])).
% 163.60/163.90 tff(1603,plain,
% 163.60/163.90 (lazy_impl(true, impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.90 inference(symmetry,[status(thm)],[1602])).
% 163.60/163.90 tff(1604,plain,
% 163.60/163.90 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))))),
% 163.60/163.90 inference(quant_inst,[status(thm)],[])).
% 163.60/163.90 tff(1605,plain,
% 163.60/163.90 (lazy_impl(true, impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1604, 118])).
% 163.60/163.90 tff(1606,plain,
% 163.60/163.90 (phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = lazy_impl(true, impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.90 inference(symmetry,[status(thm)],[1605])).
% 163.60/163.90 tff(1607,plain,
% 163.60/163.90 (((~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = true)) | (~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false))))) | (d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))),
% 163.60/163.90 inference(tautology,[status(thm)],[])).
% 163.60/163.90 tff(1608,plain,
% 163.60/163.90 (d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))))),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1607, 1307])).
% 163.60/163.90 tff(1609,plain,
% 163.60/163.90 (d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.90 inference(symmetry,[status(thm)],[1332])).
% 163.60/163.90 tff(1610,plain,
% 163.60/163.90 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = impl(false, tptp_fun_R_5(P!7))),
% 163.60/163.90 inference(monotonicity,[status(thm)],[1458])).
% 163.60/163.90 tff(1611,plain,
% 163.60/163.90 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = true),
% 163.60/163.90 inference(transitivity,[status(thm)],[975, 1610, 963])).
% 163.60/163.90 tff(1612,plain,
% 163.60/163.90 (d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> d(true)),
% 163.60/163.90 inference(monotonicity,[status(thm)],[1611])).
% 163.60/163.90 tff(1613,plain,
% 163.60/163.90 (d(true) <=> d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.90 inference(symmetry,[status(thm)],[1612])).
% 163.60/163.90 tff(1614,plain,
% 163.60/163.90 (d(true) <=> d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.90 inference(transitivity,[status(thm)],[1613, 1609])).
% 163.60/163.90 tff(1615,plain,
% 163.60/163.90 (d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.90 inference(modus_ponens,[status(thm)],[226, 1614])).
% 163.60/163.90 tff(1616,plain,
% 163.60/163.90 ((~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))))),
% 163.60/163.90 inference(tautology,[status(thm)],[])).
% 163.60/163.90 tff(1617,plain,
% 163.60/163.90 (d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1616, 1615, 1608])).
% 163.60/163.90 tff(1618,plain,
% 163.60/163.90 ((d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = err))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))))),
% 163.60/163.90 inference(tautology,[status(thm)],[])).
% 163.60/163.90 tff(1619,plain,
% 163.60/163.90 (d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = err))),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1618, 1617])).
% 163.60/163.90 tff(1620,plain,
% 163.60/163.90 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))))) | (~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))))) | (~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = err)))))),
% 163.60/163.90 inference(rewrite,[status(thm)],[])).
% 163.60/163.90 tff(1621,plain,
% 163.60/163.90 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))))) | (~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = err)))))),
% 163.60/163.90 inference(quant_inst,[status(thm)],[])).
% 163.60/163.90 tff(1622,plain,
% 163.60/163.90 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))))) | (~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = err))))),
% 163.60/163.90 inference(modus_ponens,[status(thm)],[1621, 1620])).
% 163.60/163.90 tff(1623,plain,
% 163.60/163.90 ((~((~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))))) | (~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = err))))),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1622, 39])).
% 163.60/163.90 tff(1624,plain,
% 163.60/163.90 (~((~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))))),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1623, 1619])).
% 163.60/163.90 tff(1625,plain,
% 163.60/163.90 (((~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))) | (~(phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))))) | (phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.90 inference(tautology,[status(thm)],[])).
% 163.60/163.90 tff(1626,plain,
% 163.60/163.90 (phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 163.60/163.90 inference(unit_resolution,[status(thm)],[1625, 1624])).
% 163.60/163.90 tff(1627,plain,
% 163.60/163.90 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.90 inference(symmetry,[status(thm)],[1626])).
% 163.60/163.90 tff(1628,assumption,((impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = true)), introduced(assumption)).
% 163.60/163.90 tff(1629,plain,
% 163.60/163.90 (((~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | (~bool(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)))) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))))) | (~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = true)) | (~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false))))) | ((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = true)) | (~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false)))),
% 163.60/163.91 inference(tautology,[status(thm)],[])).
% 163.60/163.91 tff(1630,plain,
% 163.60/163.91 ((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = true)) | (~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false))),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[1629, 1307])).
% 163.60/163.91 tff(1631,plain,
% 163.60/163.91 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = true),
% 163.60/163.91 inference(transitivity,[status(thm)],[1610, 963])).
% 163.60/163.91 tff(1632,plain,
% 163.60/163.91 ((~((~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = true)) | (~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false)))) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = true)) | (~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false))),
% 163.60/163.91 inference(tautology,[status(thm)],[])).
% 163.60/163.91 tff(1633,plain,
% 163.60/163.91 (~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false)),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[1632, 1631, 1630])).
% 163.60/163.91 tff(1634,plain,
% 163.60/163.91 ((~((impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = true))) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = true)),
% 163.60/163.91 inference(tautology,[status(thm)],[])).
% 163.60/163.91 tff(1635,plain,
% 163.60/163.91 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = true),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[1634, 1633, 1628])).
% 163.60/163.91 tff(1636,plain,
% 163.60/163.91 (true = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 163.60/163.91 inference(symmetry,[status(thm)],[1635])).
% 163.60/163.91 tff(1637,plain,
% 163.60/163.91 (true = false),
% 163.60/163.91 inference(transitivity,[status(thm)],[1636, 1627, 1606, 1603, 1601, 1598, 1596, 1592, 1590, 1583])).
% 163.60/163.91 tff(1638,plain,
% 163.60/163.91 ($false),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[56, 1637])).
% 163.60/163.91 tff(1639,plain,((~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false)) | (~(prop(tptp_fun_R_5(P!7)) = true)) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))) | (~(apply(P!7, tptp_fun_X_3(P!7)) = true)) | (~(impl(true, tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))) | (~(impl(false, tptp_fun_R_5(P!7)) = true)) | (~((impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = false) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = true)))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.91 tff(1640,plain,
% 163.60/163.91 (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false)),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[1639, 745, 959, 1561, 954, 949, 1572])).
% 163.60/163.91 tff(1641,plain,
% 163.60/163.91 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[1088, 1640, 1540])).
% 163.60/163.91 tff(1642,plain,
% 163.60/163.91 (impl(true, impl(true, false)) = impl(true, false)),
% 163.60/163.91 inference(monotonicity,[status(thm)],[86])).
% 163.60/163.91 tff(1643,plain,
% 163.60/163.91 (impl(true, impl(true, false)) = false),
% 163.60/163.91 inference(transitivity,[status(thm)],[1642, 86])).
% 163.60/163.91 tff(1644,plain,
% 163.60/163.91 (impl(impl(true, impl(true, false)), false) = impl(false, false)),
% 163.60/163.91 inference(monotonicity,[status(thm)],[1643])).
% 163.60/163.91 tff(1645,plain,
% 163.60/163.91 (impl(impl(true, impl(true, false)), false) = true),
% 163.60/163.91 inference(transitivity,[status(thm)],[1644, 392])).
% 163.60/163.91 tff(1646,plain,
% 163.60/163.91 (lazy_impl(prop(false), impl(impl(true, impl(true, false)), false)) = lazy_impl(true, true)),
% 163.60/163.91 inference(monotonicity,[status(thm)],[109, 1645])).
% 163.60/163.91 tff(1647,plain,
% 163.60/163.91 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(true, true, false) = lazy_impl(prop(false), impl(impl(true, impl(true, false)), false)))),
% 163.60/163.91 inference(quant_inst,[status(thm)],[])).
% 163.60/163.91 tff(1648,plain,
% 163.60/163.91 (f1(true, true, false) = lazy_impl(prop(false), impl(impl(true, impl(true, false)), false))),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[1647, 356])).
% 163.60/163.91 tff(1649,plain,
% 163.60/163.91 (impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))) = true),
% 163.60/163.91 inference(transitivity,[status(thm)],[1116, 1291, 1198, 1199])).
% 163.60/163.91 tff(1650,plain,
% 163.60/163.91 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = impl(true, tptp_fun_R_5(P!7))),
% 163.60/163.91 inference(monotonicity,[status(thm)],[1649])).
% 163.60/163.91 tff(1651,plain,
% 163.60/163.91 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = f5(P!7, tptp_fun_R_5(P!7))),
% 163.60/163.91 inference(transitivity,[status(thm)],[1650, 1019, 976, 1526, 1220])).
% 163.60/163.91 tff(1652,plain,
% 163.60/163.91 (phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = phi(f5(P!7, tptp_fun_R_5(P!7)))),
% 163.60/163.91 inference(monotonicity,[status(thm)],[1651])).
% 163.60/163.91 tff(1653,plain,
% 163.60/163.91 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(true, impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = f1(true, false, tptp_fun_R_5(P!7))),
% 163.60/163.91 inference(symmetry,[status(thm)],[1592])).
% 163.60/163.91 tff(1654,plain,
% 163.60/163.91 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false),
% 163.60/163.91 inference(transitivity,[status(thm)],[1589, 1653, 1595, 1597, 1600, 1602, 1605, 1652, 1103, 1097, 975, 1018, 962, 1456])).
% 163.60/163.91 tff(1655,plain,
% 163.60/163.91 (f1(true, true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = f1(true, true, false)),
% 163.60/163.91 inference(monotonicity,[status(thm)],[1654])).
% 163.60/163.91 tff(1656,plain,
% 163.60/163.91 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(true, true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(true, impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 163.60/163.91 inference(quant_inst,[status(thm)],[])).
% 163.60/163.91 tff(1657,plain,
% 163.60/163.91 (f1(true, true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(true, impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[1656, 356])).
% 163.60/163.91 tff(1658,plain,
% 163.60/163.91 (lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(true, impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = f1(true, true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.91 inference(symmetry,[status(thm)],[1657])).
% 163.60/163.91 tff(1659,plain,
% 163.60/163.91 (((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | ((~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) <=> ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.60/163.91 inference(rewrite,[status(thm)],[])).
% 163.60/163.91 tff(1660,plain,
% 163.60/163.91 ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | ((~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.60/163.91 inference(quant_inst,[status(thm)],[])).
% 163.60/163.91 tff(1661,plain,
% 163.60/163.91 ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.91 inference(modus_ponens,[status(thm)],[1660, 1659])).
% 163.60/163.91 tff(1662,plain,
% 163.60/163.91 (impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[1661, 82, 1084])).
% 163.60/163.91 tff(1663,plain,
% 163.60/163.91 (impl(true, impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.91 inference(monotonicity,[status(thm)],[1662])).
% 163.60/163.91 tff(1664,plain,
% 163.60/163.91 (impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(true, impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.60/163.91 inference(symmetry,[status(thm)],[1663])).
% 163.60/163.91 tff(1665,plain,
% 163.60/163.91 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.91 inference(symmetry,[status(thm)],[1662])).
% 163.60/163.91 tff(1666,plain,
% 163.60/163.91 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.60/163.91 inference(quant_inst,[status(thm)],[])).
% 163.60/163.91 tff(1667,plain,
% 163.60/163.91 (lazy_impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = phi(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[1666, 118])).
% 163.60/163.91 tff(1668,plain,
% 163.60/163.91 (lazy_impl(true, impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = lazy_impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.91 inference(monotonicity,[status(thm)],[1662])).
% 163.60/163.91 tff(1669,plain,
% 163.60/163.91 (lazy_impl(true, impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = impl(true, impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.60/163.91 inference(transitivity,[status(thm)],[1668, 1667, 1239, 1665, 1664])).
% 163.60/163.91 tff(1670,plain,
% 163.60/163.91 (impl(lazy_impl(true, impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(impl(true, impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.91 inference(monotonicity,[status(thm)],[1669])).
% 163.60/163.91 tff(1671,plain,
% 163.60/163.91 (lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(lazy_impl(true, impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(impl(true, impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.60/163.91 inference(monotonicity,[status(thm)],[1670])).
% 163.60/163.91 tff(1672,plain,
% 163.60/163.91 ((~![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))) | (f2(true, true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(lazy_impl(true, impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 163.60/163.91 inference(quant_inst,[status(thm)],[])).
% 163.60/163.91 tff(1673,plain,
% 163.60/163.91 (f2(true, true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(lazy_impl(true, impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[1672, 1186])).
% 163.60/163.91 tff(1674,plain,
% 163.60/163.91 (phi(f5(P!7, tptp_fun_R_5(P!7))) = phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.91 inference(symmetry,[status(thm)],[1652])).
% 163.60/163.91 tff(1675,plain,
% 163.60/163.91 (tptp_fun_R_5(P!7) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.91 inference(transitivity,[status(thm)],[1020, 1019, 976, 1526, 1104, 1674, 1606, 1603, 1601, 1598, 1596, 1592, 1590])).
% 163.60/163.91 tff(1676,plain,
% 163.60/163.91 (f2(true, apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = f2(true, true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.91 inference(monotonicity,[status(thm)],[1017, 1675])).
% 163.60/163.91 tff(1677,plain,
% 163.60/163.91 (f6(P!7, tptp_fun_R_5(P!7)) = true),
% 163.60/163.91 inference(transitivity,[status(thm)],[565, 1227, 1219, 1676, 1673, 1671, 1658, 1655, 1648, 1646, 236, 234])).
% 163.60/163.91 tff(1678,plain,
% 163.60/163.91 (phi(f6(P!7, tptp_fun_R_5(P!7))) = phi(true)),
% 163.60/163.91 inference(monotonicity,[status(thm)],[1677])).
% 163.60/163.91 tff(1679,plain,
% 163.60/163.91 (phi(true) = phi(f6(P!7, tptp_fun_R_5(P!7)))),
% 163.60/163.91 inference(symmetry,[status(thm)],[1678])).
% 163.60/163.91 tff(1680,plain,
% 163.60/163.91 (exists1(P!7) = exists2(P!7)),
% 163.60/163.91 inference(transitivity,[status(thm)],[742, 1198, 1199, 724, 1679, 721])).
% 163.60/163.91 tff(1681,plain,
% 163.60/163.91 ($false),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[760, 1680])).
% 163.60/163.91 tff(1682,plain,((~(tptp_fun_R_5(P!7) = false)) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7)))) | (~(apply(P!7, tptp_fun_X_3(P!7)) = true)) | (~(impl(true, tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))) | (~(impl(false, tptp_fun_R_5(P!7)) = true)) | (~(prop(tptp_fun_R_5(P!7)) = true)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.91 tff(1683,plain,
% 163.60/163.91 (~(tptp_fun_R_5(P!7) = false)),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[1682, 745, 1561, 954, 949, 959, 1641])).
% 163.60/163.91 tff(1684,plain,
% 163.60/163.91 (tptp_fun_R_5(P!7) = true),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[1476, 1683, 927])).
% 163.60/163.91 tff(1685,plain,
% 163.60/163.91 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = impl(true, tptp_fun_R_5(P!7))),
% 163.60/163.91 inference(monotonicity,[status(thm)],[1641])).
% 163.60/163.91 tff(1686,plain,
% 163.60/163.91 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[1096, 949, 954, 959])).
% 163.60/163.91 tff(1687,plain,
% 163.60/163.91 (f5(P!7, tptp_fun_R_5(P!7)) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 163.60/163.91 inference(transitivity,[status(thm)],[1101, 1686])).
% 163.60/163.91 tff(1688,plain,
% 163.60/163.91 (phi(f5(P!7, tptp_fun_R_5(P!7))) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.91 inference(monotonicity,[status(thm)],[1687])).
% 163.60/163.91 tff(1689,plain,
% 163.60/163.91 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.60/163.91 inference(symmetry,[status(thm)],[1686])).
% 163.60/163.91 tff(1690,plain,
% 163.60/163.91 (impl(true, tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.91 inference(symmetry,[status(thm)],[1685])).
% 163.60/163.91 tff(1691,plain,
% 163.60/163.91 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = f5(P!7, tptp_fun_R_5(P!7))),
% 163.60/163.91 inference(transitivity,[status(thm)],[1564, 1690, 976, 1689, 1220])).
% 163.60/163.91 tff(1692,plain,
% 163.60/163.91 (phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = phi(f5(P!7, tptp_fun_R_5(P!7)))),
% 163.60/163.91 inference(monotonicity,[status(thm)],[1691])).
% 163.60/163.91 tff(1693,plain,
% 163.60/163.91 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = lazy_impl(true, impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.91 inference(monotonicity,[status(thm)],[959])).
% 163.60/163.91 tff(1694,plain,
% 163.60/163.91 (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = apply(P!7, tptp_fun_X_3(P!7))),
% 163.60/163.91 inference(transitivity,[status(thm)],[1543, 745])).
% 163.60/163.91 tff(1695,plain,
% 163.60/163.91 (f1(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false, tptp_fun_R_5(P!7)) = f1(apply(P!7, tptp_fun_X_3(P!7)), false, tptp_fun_R_5(P!7))),
% 163.60/163.91 inference(monotonicity,[status(thm)],[1694])).
% 163.60/163.91 tff(1696,plain,
% 163.60/163.91 (phi(apply(P!7, tptp_fun_X_3(P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), true)),
% 163.60/163.91 inference(symmetry,[status(thm)],[1543])).
% 163.60/163.91 tff(1697,plain,
% 163.60/163.91 (true = apply(P!7, tptp_fun_X_3(P!7))),
% 163.60/163.91 inference(symmetry,[status(thm)],[1561])).
% 163.60/163.91 tff(1698,plain,
% 163.60/163.91 (true = impl(apply(P!7, tptp_fun_X_3(P!7)), true)),
% 163.60/163.91 inference(transitivity,[status(thm)],[1697, 746, 1696])).
% 163.60/163.91 tff(1699,plain,
% 163.60/163.91 (f1(true, false, tptp_fun_R_5(P!7)) = f1(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false, tptp_fun_R_5(P!7))),
% 163.60/163.91 inference(monotonicity,[status(thm)],[1698])).
% 163.60/163.91 tff(1700,plain,
% 163.60/163.91 (impl(true, impl(false, tptp_fun_R_5(P!7))) = impl(true, true)),
% 163.60/163.91 inference(monotonicity,[status(thm)],[949])).
% 163.60/163.91 tff(1701,plain,
% 163.60/163.91 (impl(true, impl(false, tptp_fun_R_5(P!7))) = true),
% 163.60/163.91 inference(transitivity,[status(thm)],[1700, 378])).
% 163.60/163.91 tff(1702,plain,
% 163.60/163.91 (impl(impl(true, impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = impl(true, tptp_fun_R_5(P!7))),
% 163.60/163.91 inference(monotonicity,[status(thm)],[1701])).
% 163.60/163.91 tff(1703,plain,
% 163.60/163.91 (impl(true, tptp_fun_R_5(P!7)) = impl(impl(true, impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 163.60/163.91 inference(symmetry,[status(thm)],[1702])).
% 163.60/163.91 tff(1704,plain,
% 163.60/163.91 (tptp_fun_R_5(P!7) = impl(impl(true, impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 163.60/163.91 inference(transitivity,[status(thm)],[1566, 1703])).
% 163.60/163.91 tff(1705,plain,
% 163.60/163.91 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(true, impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.91 inference(monotonicity,[status(thm)],[1704])).
% 163.60/163.91 tff(1706,plain,
% 163.60/163.91 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = true),
% 163.60/163.91 inference(transitivity,[status(thm)],[1705, 1653, 1699, 1695, 1600, 1693, 1605, 1692, 1688, 1686, 975, 1685, 954, 1684])).
% 163.60/163.91 tff(1707,plain,
% 163.60/163.91 (f1(true, true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = f1(true, true, true)),
% 163.60/163.91 inference(monotonicity,[status(thm)],[1706])).
% 163.60/163.91 tff(1708,plain,
% 163.60/163.91 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(true, impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.91 inference(symmetry,[status(thm)],[1705])).
% 163.60/163.91 tff(1709,plain,
% 163.60/163.91 (f1(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false, tptp_fun_R_5(P!7)) = f1(true, false, tptp_fun_R_5(P!7))),
% 163.60/163.91 inference(symmetry,[status(thm)],[1699])).
% 163.60/163.91 tff(1710,plain,
% 163.60/163.91 (f1(apply(P!7, tptp_fun_X_3(P!7)), false, tptp_fun_R_5(P!7)) = f1(impl(apply(P!7, tptp_fun_X_3(P!7)), true), false, tptp_fun_R_5(P!7))),
% 163.60/163.91 inference(symmetry,[status(thm)],[1695])).
% 163.60/163.91 tff(1711,plain,
% 163.60/163.91 (lazy_impl(true, impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.91 inference(symmetry,[status(thm)],[1693])).
% 163.60/163.91 tff(1712,plain,
% 163.60/163.91 (phi(f5(P!7, tptp_fun_R_5(P!7))) = phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.60/163.91 inference(symmetry,[status(thm)],[1692])).
% 163.60/163.91 tff(1713,plain,
% 163.60/163.91 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(f5(P!7, tptp_fun_R_5(P!7)))),
% 163.60/163.91 inference(symmetry,[status(thm)],[1688])).
% 163.60/163.91 tff(1714,plain,
% 163.60/163.91 (tptp_fun_R_5(P!7) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.60/163.91 inference(transitivity,[status(thm)],[1566, 1690, 976, 1689, 1713, 1712, 1606, 1711, 1601, 1710, 1709, 1592, 1708])).
% 163.60/163.91 tff(1715,plain,
% 163.60/163.91 (f2(true, apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = f2(true, true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.60/163.91 inference(monotonicity,[status(thm)],[1641, 1714])).
% 163.60/163.91 tff(1716,plain,
% 163.60/163.91 (f6(P!7, tptp_fun_R_5(P!7)) = true),
% 163.60/163.91 inference(transitivity,[status(thm)],[565, 1227, 1219, 1715, 1673, 1671, 1658, 1707, 921, 919, 236, 234])).
% 163.60/163.91 tff(1717,plain,
% 163.60/163.91 (phi(f6(P!7, tptp_fun_R_5(P!7))) = phi(true)),
% 163.60/163.91 inference(monotonicity,[status(thm)],[1716])).
% 163.60/163.91 tff(1718,plain,
% 163.60/163.91 (phi(true) = phi(f6(P!7, tptp_fun_R_5(P!7)))),
% 163.60/163.91 inference(symmetry,[status(thm)],[1717])).
% 163.60/163.91 tff(1719,plain,
% 163.60/163.91 (exists1(P!7) = exists2(P!7)),
% 163.60/163.91 inference(transitivity,[status(thm)],[742, 745, 1561, 724, 1718, 721])).
% 163.60/163.91 tff(1720,plain,
% 163.60/163.91 ($false),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[760, 1719])).
% 163.60/163.91 tff(1721,plain,(((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))))) | (~bool(tptp_fun_R_5(P!7)))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.91 tff(1722,plain,
% 163.60/163.91 (~bool(tptp_fun_R_5(P!7))),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[1721, 547])).
% 163.60/163.91 tff(1723,plain,
% 163.60/163.91 ((~![X: $i] : (~(bool(X) <=> (prop(X) = false)))) | (~(bool(tptp_fun_R_5(P!7)) <=> (prop(tptp_fun_R_5(P!7)) = false)))),
% 163.60/163.91 inference(quant_inst,[status(thm)],[])).
% 163.60/163.91 tff(1724,plain,
% 163.60/163.91 (~(bool(tptp_fun_R_5(P!7)) <=> (prop(tptp_fun_R_5(P!7)) = false))),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[1723, 206])).
% 163.60/163.91 tff(1725,plain,
% 163.60/163.91 ((bool(tptp_fun_R_5(P!7)) <=> (prop(tptp_fun_R_5(P!7)) = false)) | bool(tptp_fun_R_5(P!7)) | (prop(tptp_fun_R_5(P!7)) = false)),
% 163.60/163.91 inference(tautology,[status(thm)],[])).
% 163.60/163.91 tff(1726,plain,
% 163.60/163.91 (bool(tptp_fun_R_5(P!7)) | (prop(tptp_fun_R_5(P!7)) = false)),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[1725, 1724])).
% 163.60/163.91 tff(1727,plain,
% 163.60/163.91 ($false),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[1726, 1722, 914])).
% 163.60/163.91 tff(1728,plain,((~d(apply(P!7, tptp_fun_X_3(P!7)))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = apply(P!7, tptp_fun_X_3(P!7))))), inference(lemma,lemma(discharge,[]))).
% 163.60/163.91 tff(1729,plain,
% 163.60/163.91 (~(d(apply(P!7, tptp_fun_X_3(P!7))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err)))),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[1171, 1728])).
% 163.60/163.91 tff(1730,plain,
% 163.60/163.91 (phi(apply(P!7, tptp_fun_X_3(P!7))) = err),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[1166, 1729])).
% 163.60/163.91 tff(1731,assumption,(~bool(apply(P!7, tptp_fun_X_4(false, P!7)))), introduced(assumption)).
% 163.60/163.91 tff(1732,plain,
% 163.60/163.91 (~(prop(apply(P!7, tptp_fun_X_3(P!7))) = true)),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[1164, 1730])).
% 163.60/163.91 tff(1733,plain,
% 163.60/163.91 (~bool(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.60/163.91 inference(unit_resolution,[status(thm)],[1123, 1732])).
% 163.60/163.91 tff(1734,plain,
% 163.60/163.91 (((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(false, P!7)) = apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))))) <=> ((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(false, P!7)) = apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))))),
% 163.60/163.91 inference(rewrite,[status(thm)],[])).
% 163.60/163.91 tff(1735,plain,
% 163.60/163.91 ((bool(apply(P!7, tptp_fun_X_4(false, P!7))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(false, P!7)) = apply(P!7, tptp_fun_X_3(P!7)))) <=> (bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(false, P!7)) = apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))))),
% 163.60/163.91 inference(rewrite,[status(thm)],[])).
% 163.60/163.91 tff(1736,plain,
% 163.60/163.91 (((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | (bool(apply(P!7, tptp_fun_X_4(false, P!7))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(false, P!7)) = apply(P!7, tptp_fun_X_3(P!7))))) <=> ((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(false, P!7)) = apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(false, P!7)))))),
% 163.60/163.91 inference(monotonicity,[status(thm)],[1735])).
% 163.60/163.91 tff(1737,plain,
% 163.60/163.91 (((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | (bool(apply(P!7, tptp_fun_X_4(false, P!7))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(false, P!7)) = apply(P!7, tptp_fun_X_3(P!7))))) <=> ((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(false, P!7)) = apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(false, P!7))))),
% 163.60/163.91 inference(transitivity,[status(thm)],[1736, 1734])).
% 163.60/163.91 tff(1738,plain,
% 163.70/163.91 ((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | (bool(apply(P!7, tptp_fun_X_4(false, P!7))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(false, P!7)) = apply(P!7, tptp_fun_X_3(P!7))))),
% 163.70/163.91 inference(quant_inst,[status(thm)],[])).
% 163.70/163.91 tff(1739,plain,
% 163.70/163.91 ((~![X1: $i, X2: $i] : (bool(apply(P!7, X1)) | bool(apply(P!7, X2)) | (apply(P!7, X1) = apply(P!7, X2)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(false, P!7)) = apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(false, P!7)))),
% 163.70/163.91 inference(modus_ponens,[status(thm)],[1738, 1737])).
% 163.70/163.91 tff(1740,plain,
% 163.70/163.91 (bool(apply(P!7, tptp_fun_X_3(P!7))) | (apply(P!7, tptp_fun_X_4(false, P!7)) = apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(false, P!7)))),
% 163.70/163.91 inference(unit_resolution,[status(thm)],[1739, 1439])).
% 163.70/163.91 tff(1741,plain,
% 163.70/163.91 ((apply(P!7, tptp_fun_X_4(false, P!7)) = apply(P!7, tptp_fun_X_3(P!7))) | bool(apply(P!7, tptp_fun_X_4(false, P!7)))),
% 163.70/163.91 inference(unit_resolution,[status(thm)],[1740, 1733])).
% 163.70/163.91 tff(1742,plain,
% 163.70/163.91 (apply(P!7, tptp_fun_X_4(false, P!7)) = apply(P!7, tptp_fun_X_3(P!7))),
% 163.70/163.91 inference(unit_resolution,[status(thm)],[1741, 1731])).
% 163.70/163.91 tff(1743,plain,
% 163.70/163.91 (phi(apply(P!7, tptp_fun_X_4(false, P!7))) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.70/163.91 inference(monotonicity,[status(thm)],[1742])).
% 163.70/163.91 tff(1744,plain,
% 163.70/163.91 (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = phi(apply(P!7, tptp_fun_X_4(false, P!7)))),
% 163.70/163.91 inference(unit_resolution,[status(thm)],[850, 1731])).
% 163.70/163.91 tff(1745,plain,
% 163.70/163.91 (false = lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.70/163.91 inference(symmetry,[status(thm)],[816])).
% 163.70/163.91 tff(1746,plain,
% 163.70/163.91 (false = err),
% 163.70/163.91 inference(transitivity,[status(thm)],[1745, 818, 535, 827, 836, 809, 1744, 1743, 1730])).
% 163.70/163.91 tff(1747,plain,
% 163.70/163.91 ($false),
% 163.70/163.91 inference(unit_resolution,[status(thm)],[692, 1746])).
% 163.70/163.91 tff(1748,plain,(bool(apply(P!7, tptp_fun_X_4(false, P!7))) | (~(lazy_impl(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))), phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = false)) | (~(prop(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) = true))), inference(lemma,lemma(discharge,[]))).
% 163.70/163.91 tff(1749,plain,
% 163.70/163.91 (bool(apply(P!7, tptp_fun_X_4(false, P!7)))),
% 163.70/163.91 inference(unit_resolution,[status(thm)],[1748, 546, 340])).
% 163.70/163.91 tff(1750,plain,
% 163.70/163.91 (~(apply(P!7, tptp_fun_X_4(false, P!7)) = false)),
% 163.70/163.91 inference(unit_resolution,[status(thm)],[844, 546, 340])).
% 163.70/163.91 tff(1751,assumption,(apply(P!7, tptp_fun_X_4(false, P!7)) = true), introduced(assumption)).
% 163.70/163.91 tff(1752,plain,
% 163.70/163.91 (impl(apply(P!7, tptp_fun_X_4(false, P!7)), false) = impl(true, false)),
% 163.70/163.91 inference(monotonicity,[status(thm)],[1751])).
% 163.70/163.91 tff(1753,plain,
% 163.70/163.91 (impl(true, false) = impl(apply(P!7, tptp_fun_X_4(false, P!7)), false)),
% 163.70/163.91 inference(symmetry,[status(thm)],[1752])).
% 163.70/163.91 tff(1754,plain,
% 163.70/163.91 (false = f4(P!7, tptp_fun_X_4(false, P!7), false)),
% 163.70/163.91 inference(transitivity,[status(thm)],[1452, 1753, 810])).
% 163.70/163.91 tff(1755,plain,
% 163.70/163.91 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = phi(apply(P!7, tptp_fun_X_3(P!7)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 163.70/163.91 inference(rewrite,[status(thm)],[])).
% 163.70/163.91 tff(1756,plain,
% 163.70/163.91 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 163.70/163.91 inference(quant_inst,[status(thm)],[])).
% 163.70/163.91 tff(1757,plain,
% 163.70/163.91 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 163.70/163.91 inference(modus_ponens,[status(thm)],[1756, 1755])).
% 163.70/163.91 tff(1758,plain,
% 163.70/163.91 (impl(apply(P!7, tptp_fun_X_3(P!7)), false) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.70/163.91 inference(unit_resolution,[status(thm)],[1757, 332, 1733])).
% 163.70/163.92 tff(1759,plain,
% 163.70/163.92 (phi(apply(P!7, tptp_fun_X_3(P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), false)),
% 163.70/163.92 inference(symmetry,[status(thm)],[1758])).
% 163.70/163.92 tff(1760,plain,
% 163.70/163.92 (err = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.70/163.92 inference(symmetry,[status(thm)],[1730])).
% 163.70/163.92 tff(1761,plain,
% 163.70/163.92 (err = f4(P!7, tptp_fun_X_3(P!7), false)),
% 163.70/163.92 inference(transitivity,[status(thm)],[1760, 1759, 716])).
% 163.70/163.92 tff(1762,plain,
% 163.70/163.92 (forallprefers(err, false) <=> forallprefers(f4(P!7, tptp_fun_X_3(P!7), false), f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 163.70/163.92 inference(monotonicity,[status(thm)],[1761, 1754])).
% 163.70/163.92 tff(1763,plain,
% 163.70/163.92 (forallprefers(f4(P!7, tptp_fun_X_3(P!7), false), f4(P!7, tptp_fun_X_4(false, P!7), false)) <=> forallprefers(err, false)),
% 163.70/163.92 inference(symmetry,[status(thm)],[1762])).
% 163.70/163.92 tff(1764,plain,
% 163.70/163.92 ((~forallprefers(f4(P!7, tptp_fun_X_3(P!7), false), f4(P!7, tptp_fun_X_4(false, P!7), false))) <=> (~forallprefers(err, false))),
% 163.70/163.92 inference(monotonicity,[status(thm)],[1763])).
% 163.70/163.92 tff(1765,plain,
% 163.70/163.92 (~forallprefers(err, false)),
% 163.70/163.92 inference(modus_ponens,[status(thm)],[901, 1764])).
% 163.70/163.92 tff(1766,plain,
% 163.70/163.92 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(err, false) <=> ((~((~(err = false)) | (~(false = true)))) | (~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(err, false) <=> ((~((~(err = false)) | (~(false = true)))) | (~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))))))),
% 163.70/163.92 inference(rewrite,[status(thm)],[])).
% 163.70/163.92 tff(1767,plain,
% 163.70/163.92 ((forallprefers(err, false) <=> ((~((~(err = false)) | (~(false = true)))) | (~(d(err) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(err) | (~d(err)))))) <=> (forallprefers(err, false) <=> ((~((~(err = false)) | (~(false = true)))) | (~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false))))))),
% 163.70/163.92 inference(rewrite,[status(thm)],[])).
% 163.70/163.92 tff(1768,plain,
% 163.70/163.92 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(err, false) <=> ((~((~(err = false)) | (~(false = true)))) | (~(d(err) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(err) | (~d(err))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(err, false) <=> ((~((~(err = false)) | (~(false = true)))) | (~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))))))),
% 163.70/163.92 inference(monotonicity,[status(thm)],[1767])).
% 163.70/163.92 tff(1769,plain,
% 163.70/163.92 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(err, false) <=> ((~((~(err = false)) | (~(false = true)))) | (~(d(err) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(err) | (~d(err))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(err, false) <=> ((~((~(err = false)) | (~(false = true)))) | (~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))))))),
% 163.70/163.92 inference(transitivity,[status(thm)],[1768, 1766])).
% 163.70/163.92 tff(1770,plain,
% 163.70/163.92 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(err, false) <=> ((~((~(err = false)) | (~(false = true)))) | (~(d(err) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(err) | (~d(err))))))),
% 163.70/163.92 inference(quant_inst,[status(thm)],[])).
% 163.70/163.92 tff(1771,plain,
% 163.70/163.92 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(err, false) <=> ((~((~(err = false)) | (~(false = true)))) | (~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false))))))),
% 163.70/163.92 inference(modus_ponens,[status(thm)],[1770, 1769])).
% 163.70/163.92 tff(1772,plain,
% 163.70/163.92 (forallprefers(err, false) <=> ((~((~(err = false)) | (~(false = true)))) | (~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))))),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1771, 165])).
% 163.70/163.92 tff(1773,plain,
% 163.70/163.92 (d(err) <=> d(err)),
% 163.70/163.92 inference(rewrite,[status(thm)],[])).
% 163.70/163.92 tff(1774,plain,
% 163.70/163.92 (d(err)),
% 163.70/163.92 inference(and_elim,[status(thm)],[24])).
% 163.70/163.92 tff(1775,plain,
% 163.70/163.92 (d(err)),
% 163.70/163.92 inference(modus_ponens,[status(thm)],[1774, 1773])).
% 163.70/163.92 tff(1776,plain,
% 163.70/163.92 ((~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))) | (~d(false)) | (~d(err)) | bool(err) | (~bool(false))),
% 163.70/163.92 inference(tautology,[status(thm)],[])).
% 163.70/163.92 tff(1777,plain,
% 163.70/163.92 (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1776, 27, 1775, 72, 1043])).
% 163.70/163.92 tff(1778,plain,
% 163.70/163.92 (((~((~(err = false)) | (~(false = true)))) | (~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false))))) | ((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))),
% 163.70/163.92 inference(tautology,[status(thm)],[])).
% 163.70/163.92 tff(1779,plain,
% 163.70/163.92 ((~((~(err = false)) | (~(false = true)))) | (~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false))))),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1778, 1777])).
% 163.70/163.92 tff(1780,plain,
% 163.70/163.92 ((~(forallprefers(err, false) <=> ((~((~(err = false)) | (~(false = true)))) | (~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false))))))) | forallprefers(err, false) | (~((~((~(err = false)) | (~(false = true)))) | (~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false))))))),
% 163.70/163.92 inference(tautology,[status(thm)],[])).
% 163.70/163.92 tff(1781,plain,
% 163.70/163.92 ((~(forallprefers(err, false) <=> ((~((~(err = false)) | (~(false = true)))) | (~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false))))))) | forallprefers(err, false)),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1780, 1779])).
% 163.70/163.92 tff(1782,plain,
% 163.70/163.92 (forallprefers(err, false)),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1781, 1772])).
% 163.70/163.92 tff(1783,plain,
% 163.70/163.92 ($false),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1782, 1765])).
% 163.70/163.92 tff(1784,plain,(~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)), inference(lemma,lemma(discharge,[]))).
% 163.70/163.92 tff(1785,plain,
% 163.70/163.92 ((~((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = true))) | (apply(P!7, tptp_fun_X_4(false, P!7)) = false)),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[855, 1784])).
% 163.70/163.92 tff(1786,plain,
% 163.70/163.92 (~((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = true))),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1785, 1750])).
% 163.70/163.92 tff(1787,assumption,(~(bool(apply(P!7, tptp_fun_X_4(false, P!7))) <=> ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = true)))), introduced(assumption)).
% 163.70/163.92 tff(1788,plain,
% 163.70/163.92 ($false),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[762, 218, 1787])).
% 163.70/163.92 tff(1789,plain,(bool(apply(P!7, tptp_fun_X_4(false, P!7))) <=> ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = true))), inference(lemma,lemma(discharge,[]))).
% 163.70/163.92 tff(1790,plain,
% 163.70/163.92 ((~bool(apply(P!7, tptp_fun_X_4(false, P!7)))) | ((apply(P!7, tptp_fun_X_4(false, P!7)) = false) | (apply(P!7, tptp_fun_X_4(false, P!7)) = true))),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[852, 1789])).
% 163.70/163.92 tff(1791,plain,
% 163.70/163.92 ($false),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1790, 1786, 1749])).
% 163.70/163.92 tff(1792,plain,(~(lazy_impl(prop(false), impl(f5(P!7, false), false)) = true)), inference(lemma,lemma(discharge,[]))).
% 163.70/163.92 tff(1793,plain,
% 163.70/163.92 ((err = phi(f6(P!7, tptp_fun_R_5(P!7)))) <=> (phi(f6(P!7, tptp_fun_R_5(P!7))) = err)),
% 163.70/163.92 inference(commutativity,[status(thm)],[])).
% 163.70/163.92 tff(1794,plain,
% 163.70/163.92 (exists1(P!7) = err),
% 163.70/163.92 inference(transitivity,[status(thm)],[742, 1730])).
% 163.70/163.92 tff(1795,plain,
% 163.70/163.92 ((exists1(P!7) = exists2(P!7)) <=> (err = phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 163.70/163.92 inference(monotonicity,[status(thm)],[1794, 720])).
% 163.70/163.92 tff(1796,plain,
% 163.70/163.92 ((exists1(P!7) = exists2(P!7)) <=> (phi(f6(P!7, tptp_fun_R_5(P!7))) = err)),
% 163.70/163.92 inference(transitivity,[status(thm)],[1795, 1793])).
% 163.70/163.92 tff(1797,plain,
% 163.70/163.92 ((~(exists1(P!7) = exists2(P!7))) <=> (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err))),
% 163.70/163.92 inference(monotonicity,[status(thm)],[1796])).
% 163.70/163.92 tff(1798,plain,
% 163.70/163.92 (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err)),
% 163.70/163.92 inference(modus_ponens,[status(thm)],[760, 1797])).
% 163.70/163.92 tff(1799,plain,
% 163.70/163.92 ((d(f6(P!7, tptp_fun_R_5(P!7))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err))) | (phi(f6(P!7, tptp_fun_R_5(P!7))) = err)),
% 163.70/163.92 inference(tautology,[status(thm)],[])).
% 163.70/163.92 tff(1800,plain,
% 163.70/163.92 (d(f6(P!7, tptp_fun_R_5(P!7))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err))),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1799, 1798])).
% 163.70/163.92 tff(1801,plain,
% 163.70/163.92 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(f6(P!7, tptp_fun_R_5(P!7)))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7)))))) | (~(d(f6(P!7, tptp_fun_R_5(P!7))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(f6(P!7, tptp_fun_R_5(P!7)))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7)))))) | (~(d(f6(P!7, tptp_fun_R_5(P!7))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err)))))),
% 163.70/163.92 inference(rewrite,[status(thm)],[])).
% 163.70/163.92 tff(1802,plain,
% 163.70/163.92 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(f6(P!7, tptp_fun_R_5(P!7)))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7)))))) | (~(d(f6(P!7, tptp_fun_R_5(P!7))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err)))))),
% 163.70/163.92 inference(quant_inst,[status(thm)],[])).
% 163.70/163.92 tff(1803,plain,
% 163.70/163.92 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(f6(P!7, tptp_fun_R_5(P!7)))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7)))))) | (~(d(f6(P!7, tptp_fun_R_5(P!7))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err))))),
% 163.70/163.92 inference(modus_ponens,[status(thm)],[1802, 1801])).
% 163.70/163.92 tff(1804,plain,
% 163.70/163.92 ((~((~d(f6(P!7, tptp_fun_R_5(P!7)))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7)))))) | (~(d(f6(P!7, tptp_fun_R_5(P!7))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err))))),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1803, 39])).
% 163.70/163.92 tff(1805,plain,
% 163.70/163.92 (~((~d(f6(P!7, tptp_fun_R_5(P!7)))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1804, 1800])).
% 163.70/163.92 tff(1806,plain,
% 163.70/163.92 (((~d(f6(P!7, tptp_fun_R_5(P!7)))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7))))) | (phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7)))),
% 163.70/163.92 inference(tautology,[status(thm)],[])).
% 163.70/163.92 tff(1807,plain,
% 163.70/163.92 (phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7))),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1806, 1805])).
% 163.70/163.92 tff(1808,plain,
% 163.70/163.92 (phi(phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(f6(P!7, tptp_fun_R_5(P!7)))),
% 163.70/163.92 inference(monotonicity,[status(thm)],[1807])).
% 163.70/163.92 tff(1809,plain,
% 163.70/163.92 (bool(phi(f6(P!7, tptp_fun_R_5(P!7)))) <=> bool(f6(P!7, tptp_fun_R_5(P!7)))),
% 163.70/163.92 inference(monotonicity,[status(thm)],[1807])).
% 163.70/163.92 tff(1810,plain,
% 163.70/163.92 (bool(f6(P!7, tptp_fun_R_5(P!7))) <=> bool(phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 163.70/163.92 inference(symmetry,[status(thm)],[1809])).
% 163.70/163.92 tff(1811,plain,
% 163.70/163.92 (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> bool(phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 163.70/163.92 inference(transitivity,[status(thm)],[578, 1810])).
% 163.70/163.92 tff(1812,plain,
% 163.70/163.92 ((~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) <=> (~bool(phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.92 inference(monotonicity,[status(thm)],[1811])).
% 163.70/163.92 tff(1813,assumption,(~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))), introduced(assumption)).
% 163.70/163.92 tff(1814,plain,
% 163.70/163.92 (~bool(phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 163.70/163.92 inference(modus_ponens,[status(thm)],[1813, 1812])).
% 163.70/163.92 tff(1815,plain,
% 163.70/163.92 (^[A: $i, B: $i] : refl((bool(B) | (~bool(A)) | (impl(A, B) = phi(B))) <=> (bool(B) | (~bool(A)) | (impl(A, B) = phi(B))))),
% 163.70/163.92 inference(bind,[status(th)],[])).
% 163.70/163.92 tff(1816,plain,
% 163.70/163.92 (![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B))) <=> ![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))),
% 163.70/163.92 inference(quant_intro,[status(thm)],[1815])).
% 163.70/163.92 tff(1817,plain,
% 163.70/163.92 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((bool(A) & (~bool(B))) <=> (~(bool(B) | (~bool(A))))), ((~(bool(A) & (~bool(B)))) <=> (~(~(bool(B) | (~bool(A))))))), rewrite((~(~(bool(B) | (~bool(A))))) <=> (bool(B) | (~bool(A)))), ((~(bool(A) & (~bool(B)))) <=> (bool(B) | (~bool(A))))), (((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B))) <=> ((bool(B) | (~bool(A))) | (impl(A, B) = phi(B))))), rewrite(((bool(B) | (~bool(A))) | (impl(A, B) = phi(B))) <=> (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))), (((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B))) <=> (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))))),
% 163.70/163.92 inference(bind,[status(th)],[])).
% 163.70/163.92 tff(1818,plain,
% 163.70/163.92 (![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B))) <=> ![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))),
% 163.70/163.92 inference(quant_intro,[status(thm)],[1817])).
% 163.70/163.92 tff(1819,plain,
% 163.70/163.92 (![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B))) <=> ![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B)))),
% 163.70/163.92 inference(rewrite,[status(thm)],[])).
% 163.70/163.92 tff(1820,plain,
% 163.70/163.92 (^[A: $i, B: $i] : rewrite(((bool(A) & (~bool(B))) => (impl(A, B) = phi(B))) <=> ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B))))),
% 163.70/163.92 inference(bind,[status(th)],[])).
% 163.70/163.92 tff(1821,plain,
% 163.70/163.92 (![A: $i, B: $i] : ((bool(A) & (~bool(B))) => (impl(A, B) = phi(B))) <=> ![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B)))),
% 163.70/163.92 inference(quant_intro,[status(thm)],[1820])).
% 163.70/163.92 tff(1822,axiom,(![A: $i, B: $i] : ((bool(A) & (~bool(B))) => (impl(A, B) = phi(B)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV012+0.ax','impl_axiom2')).
% 163.70/163.92 tff(1823,plain,
% 163.70/163.92 (![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B)))),
% 163.70/163.92 inference(modus_ponens,[status(thm)],[1822, 1821])).
% 163.70/163.92 tff(1824,plain,
% 163.70/163.92 (![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B)))),
% 163.70/163.92 inference(modus_ponens,[status(thm)],[1823, 1819])).
% 163.70/163.92 tff(1825,plain,(
% 163.70/163.92 ![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B)))),
% 163.70/163.92 inference(skolemize,[status(sab)],[1824])).
% 163.70/163.92 tff(1826,plain,
% 163.70/163.92 (![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))),
% 163.70/163.92 inference(modus_ponens,[status(thm)],[1825, 1818])).
% 163.70/163.92 tff(1827,plain,
% 163.70/163.92 (![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))),
% 163.70/163.92 inference(modus_ponens,[status(thm)],[1826, 1816])).
% 163.70/163.92 tff(1828,plain,
% 163.70/163.92 (((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | ((~bool(true)) | bool(phi(f6(P!7, tptp_fun_R_5(P!7)))) | (impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(phi(f6(P!7, tptp_fun_R_5(P!7))))))) <=> ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (~bool(true)) | bool(phi(f6(P!7, tptp_fun_R_5(P!7)))) | (impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.92 inference(rewrite,[status(thm)],[])).
% 163.70/163.92 tff(1829,plain,
% 163.70/163.92 ((bool(phi(f6(P!7, tptp_fun_R_5(P!7)))) | (~bool(true)) | (impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> ((~bool(true)) | bool(phi(f6(P!7, tptp_fun_R_5(P!7)))) | (impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.92 inference(rewrite,[status(thm)],[])).
% 163.70/163.92 tff(1830,plain,
% 163.70/163.92 (((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (bool(phi(f6(P!7, tptp_fun_R_5(P!7)))) | (~bool(true)) | (impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(phi(f6(P!7, tptp_fun_R_5(P!7))))))) <=> ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | ((~bool(true)) | bool(phi(f6(P!7, tptp_fun_R_5(P!7)))) | (impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(phi(f6(P!7, tptp_fun_R_5(P!7)))))))),
% 163.70/163.92 inference(monotonicity,[status(thm)],[1829])).
% 163.70/163.92 tff(1831,plain,
% 163.70/163.92 (((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (bool(phi(f6(P!7, tptp_fun_R_5(P!7)))) | (~bool(true)) | (impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(phi(f6(P!7, tptp_fun_R_5(P!7))))))) <=> ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (~bool(true)) | bool(phi(f6(P!7, tptp_fun_R_5(P!7)))) | (impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.92 inference(transitivity,[status(thm)],[1830, 1828])).
% 163.70/163.92 tff(1832,plain,
% 163.70/163.92 ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (bool(phi(f6(P!7, tptp_fun_R_5(P!7)))) | (~bool(true)) | (impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.92 inference(quant_inst,[status(thm)],[])).
% 163.70/163.92 tff(1833,plain,
% 163.70/163.92 ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (~bool(true)) | bool(phi(f6(P!7, tptp_fun_R_5(P!7)))) | (impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.92 inference(modus_ponens,[status(thm)],[1832, 1831])).
% 163.70/163.92 tff(1834,plain,
% 163.70/163.92 (bool(phi(f6(P!7, tptp_fun_R_5(P!7)))) | (impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1833, 1827, 252])).
% 163.70/163.92 tff(1835,plain,
% 163.70/163.92 (impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1834, 1814])).
% 163.70/163.92 tff(1836,plain,
% 163.70/163.92 (impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))) = f6(P!7, tptp_fun_R_5(P!7))),
% 163.70/163.92 inference(transitivity,[status(thm)],[1835, 1808, 1807])).
% 163.70/163.92 tff(1837,plain,
% 163.70/163.92 (bool(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7))))) <=> bool(f6(P!7, tptp_fun_R_5(P!7)))),
% 163.70/163.92 inference(monotonicity,[status(thm)],[1836])).
% 163.70/163.92 tff(1838,plain,
% 163.70/163.92 (bool(f6(P!7, tptp_fun_R_5(P!7))) <=> bool(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.92 inference(symmetry,[status(thm)],[1837])).
% 163.70/163.92 tff(1839,plain,
% 163.70/163.92 ((~bool(f6(P!7, tptp_fun_R_5(P!7)))) <=> (~bool(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.92 inference(monotonicity,[status(thm)],[1838])).
% 163.70/163.92 tff(1840,plain,
% 163.70/163.92 ((~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) <=> (~bool(f6(P!7, tptp_fun_R_5(P!7))))),
% 163.70/163.92 inference(monotonicity,[status(thm)],[578])).
% 163.70/163.92 tff(1841,plain,
% 163.70/163.92 (~bool(f6(P!7, tptp_fun_R_5(P!7)))),
% 163.70/163.92 inference(modus_ponens,[status(thm)],[1813, 1840])).
% 163.70/163.92 tff(1842,plain,
% 163.70/163.92 (~bool(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.92 inference(modus_ponens,[status(thm)],[1841, 1839])).
% 163.70/163.92 tff(1843,plain,
% 163.70/163.92 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7))))) | (impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7))))) | (impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))))))),
% 163.70/163.92 inference(rewrite,[status(thm)],[])).
% 163.70/163.92 tff(1844,plain,
% 163.70/163.92 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7))))) | (impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))))))),
% 163.70/163.92 inference(quant_inst,[status(thm)],[])).
% 163.70/163.92 tff(1845,plain,
% 163.70/163.92 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7))))) | (impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.92 inference(modus_ponens,[status(thm)],[1844, 1843])).
% 163.70/163.92 tff(1846,plain,
% 163.70/163.92 (bool(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7))))) | (impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1845, 332])).
% 163.70/163.92 tff(1847,plain,
% 163.70/163.92 (impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1846, 1842])).
% 163.70/163.92 tff(1848,plain,
% 163.70/163.92 (phi(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7))))) = impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.92 inference(symmetry,[status(thm)],[1847])).
% 163.70/163.92 tff(1849,plain,
% 163.70/163.92 (phi(phi(f6(P!7, tptp_fun_R_5(P!7)))) = impl(true, phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 163.70/163.92 inference(symmetry,[status(thm)],[1835])).
% 163.70/163.92 tff(1850,plain,
% 163.70/163.92 (phi(f6(P!7, tptp_fun_R_5(P!7))) = phi(phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 163.70/163.92 inference(symmetry,[status(thm)],[1808])).
% 163.70/163.92 tff(1851,plain,
% 163.70/163.92 (f6(P!7, tptp_fun_R_5(P!7)) = phi(f6(P!7, tptp_fun_R_5(P!7)))),
% 163.70/163.92 inference(symmetry,[status(thm)],[1807])).
% 163.70/163.92 tff(1852,plain,
% 163.70/163.92 (f6(P!7, tptp_fun_R_5(P!7)) = impl(true, phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 163.70/163.92 inference(transitivity,[status(thm)],[1851, 1850, 1849])).
% 163.70/163.92 tff(1853,plain,
% 163.70/163.92 (phi(f6(P!7, tptp_fun_R_5(P!7))) = phi(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.92 inference(monotonicity,[status(thm)],[1852])).
% 163.70/163.92 tff(1854,plain,
% 163.70/163.92 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)))),
% 163.70/163.92 inference(quant_inst,[status(thm)],[])).
% 163.70/163.92 tff(1855,plain,
% 163.70/163.92 (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true))),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1854, 218])).
% 163.70/163.92 tff(1856,plain,
% 163.70/163.92 ((~(bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)))) | bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)))),
% 163.70/163.92 inference(tautology,[status(thm)],[])).
% 163.70/163.92 tff(1857,plain,
% 163.70/163.92 (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)))),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1856, 1855])).
% 163.70/163.92 tff(1858,plain,
% 163.70/163.92 (~((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true))),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1857, 1813])).
% 163.70/163.92 tff(1859,plain,
% 163.70/163.92 (((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)) | (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true))),
% 163.70/163.92 inference(tautology,[status(thm)],[])).
% 163.70/163.92 tff(1860,plain,
% 163.70/163.92 (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1859, 1858])).
% 163.70/163.92 tff(1861,plain,
% 163.70/163.92 (impl(false, false) = impl(impl(true, impl(true, false)), false)),
% 163.70/163.92 inference(symmetry,[status(thm)],[1644])).
% 163.70/163.92 tff(1862,plain,
% 163.70/163.92 (true = impl(impl(true, impl(true, false)), false)),
% 163.70/163.92 inference(transitivity,[status(thm)],[841, 1861])).
% 163.70/163.92 tff(1863,plain,
% 163.70/163.92 (lazy_impl(true, true) = lazy_impl(prop(false), impl(impl(true, impl(true, false)), false))),
% 163.70/163.92 inference(monotonicity,[status(thm)],[110, 1862])).
% 163.70/163.92 tff(1864,plain,
% 163.70/163.92 (lazy_impl(prop(false), impl(impl(true, impl(true, false)), false)) = lazy_impl(true, true)),
% 163.70/163.92 inference(symmetry,[status(thm)],[1863])).
% 163.70/163.92 tff(1865,assumption,(~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)), introduced(assumption)).
% 163.70/163.92 tff(1866,assumption,(~(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))), introduced(assumption)).
% 163.70/163.92 tff(1867,plain,
% 163.70/163.92 ((~![B: $i] : (lazy_impl(false, B) = true)) | (lazy_impl(false, err) = true)),
% 163.70/163.92 inference(quant_inst,[status(thm)],[])).
% 163.70/163.92 tff(1868,plain,
% 163.70/163.92 (lazy_impl(false, err) = true),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1867, 147])).
% 163.70/163.92 tff(1869,plain,
% 163.70/163.92 ((~![X: $i] : (~(bool(X) <=> (prop(X) = false)))) | (~(bool(err) <=> (prop(err) = false)))),
% 163.70/163.92 inference(quant_inst,[status(thm)],[])).
% 163.70/163.92 tff(1870,plain,
% 163.70/163.92 (~(bool(err) <=> (prop(err) = false))),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1869, 206])).
% 163.70/163.92 tff(1871,plain,
% 163.70/163.92 ((bool(err) <=> (prop(err) = false)) | bool(err) | (prop(err) = false)),
% 163.70/163.92 inference(tautology,[status(thm)],[])).
% 163.70/163.92 tff(1872,plain,
% 163.70/163.92 (prop(err) = false),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1871, 1043, 1870])).
% 163.70/163.92 tff(1873,plain,
% 163.70/163.92 (false = prop(err)),
% 163.70/163.92 inference(symmetry,[status(thm)],[1872])).
% 163.70/163.92 tff(1874,plain,
% 163.70/163.92 (lazy_impl(false, err) = lazy_impl(prop(err), err)),
% 163.70/163.92 inference(monotonicity,[status(thm)],[1873])).
% 163.70/163.92 tff(1875,plain,
% 163.70/163.92 (lazy_impl(prop(err), err) = lazy_impl(false, err)),
% 163.70/163.92 inference(symmetry,[status(thm)],[1874])).
% 163.70/163.92 tff(1876,assumption,(~bool(tptp_fun_R_5(P!7))), introduced(assumption)).
% 163.70/163.92 tff(1877,plain,
% 163.70/163.92 (((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (bool(tptp_fun_R_5(P!7)) | (~bool(f5(P!7, tptp_fun_R_5(P!7)))) | (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))))) <=> ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | bool(tptp_fun_R_5(P!7)) | (~bool(f5(P!7, tptp_fun_R_5(P!7)))) | (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))))),
% 163.70/163.92 inference(rewrite,[status(thm)],[])).
% 163.70/163.92 tff(1878,plain,
% 163.70/163.92 ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (bool(tptp_fun_R_5(P!7)) | (~bool(f5(P!7, tptp_fun_R_5(P!7)))) | (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))))),
% 163.70/163.92 inference(quant_inst,[status(thm)],[])).
% 163.70/163.92 tff(1879,plain,
% 163.70/163.92 ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | bool(tptp_fun_R_5(P!7)) | (~bool(f5(P!7, tptp_fun_R_5(P!7)))) | (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 163.70/163.92 inference(modus_ponens,[status(thm)],[1878, 1877])).
% 163.70/163.92 tff(1880,plain,
% 163.70/163.92 (bool(tptp_fun_R_5(P!7)) | (~bool(f5(P!7, tptp_fun_R_5(P!7)))) | (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1879, 1827])).
% 163.70/163.92 tff(1881,plain,
% 163.70/163.92 (~bool(f5(P!7, tptp_fun_R_5(P!7)))),
% 163.70/163.92 inference(unit_resolution,[status(thm)],[1880, 1876, 1866])).
% 163.70/163.92 tff(1882,plain,
% 163.70/163.92 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(f5(P!7, tptp_fun_R_5(P!7))) | (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(f5(P!7, tptp_fun_R_5(P!7))) | (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.93 inference(rewrite,[status(thm)],[])).
% 163.70/163.93 tff(1883,plain,
% 163.70/163.93 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(f5(P!7, tptp_fun_R_5(P!7))) | (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.93 inference(quant_inst,[status(thm)],[])).
% 163.70/163.93 tff(1884,plain,
% 163.70/163.93 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(f5(P!7, tptp_fun_R_5(P!7))) | (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7))))),
% 163.70/163.93 inference(modus_ponens,[status(thm)],[1883, 1882])).
% 163.70/163.93 tff(1885,plain,
% 163.70/163.93 (bool(f5(P!7, tptp_fun_R_5(P!7))) | (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7))))),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1884, 332])).
% 163.70/163.93 tff(1886,plain,
% 163.70/163.93 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7)))),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1885, 1881])).
% 163.70/163.93 tff(1887,plain,
% 163.70/163.93 (phi(f5(P!7, tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.93 inference(symmetry,[status(thm)],[1886])).
% 163.70/163.93 tff(1888,plain,
% 163.70/163.93 ((d(err) | (~(phi(err) = err))) | (~d(err))),
% 163.70/163.93 inference(tautology,[status(thm)],[])).
% 163.70/163.93 tff(1889,plain,
% 163.70/163.93 (d(err) | (~(phi(err) = err))),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1888, 1775])).
% 163.70/163.93 tff(1890,plain,
% 163.70/163.93 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(err)) | (~(phi(err) = err)))) | (~(d(err) | (~(phi(err) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(err)) | (~(phi(err) = err)))) | (~(d(err) | (~(phi(err) = err)))))),
% 163.70/163.93 inference(rewrite,[status(thm)],[])).
% 163.70/163.93 tff(1891,plain,
% 163.70/163.93 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(err)) | (~(phi(err) = err)))) | (~(d(err) | (~(phi(err) = err)))))),
% 163.70/163.93 inference(quant_inst,[status(thm)],[])).
% 163.70/163.93 tff(1892,plain,
% 163.70/163.93 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(err)) | (~(phi(err) = err)))) | (~(d(err) | (~(phi(err) = err))))),
% 163.70/163.93 inference(modus_ponens,[status(thm)],[1891, 1890])).
% 163.70/163.93 tff(1893,plain,
% 163.70/163.93 (~((~d(err)) | (~(phi(err) = err)))),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1892, 39, 1889])).
% 163.70/163.93 tff(1894,plain,
% 163.70/163.93 (((~d(err)) | (~(phi(err) = err))) | (phi(err) = err)),
% 163.70/163.93 inference(tautology,[status(thm)],[])).
% 163.70/163.93 tff(1895,plain,
% 163.70/163.93 (phi(err) = err),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1894, 1893])).
% 163.70/163.93 tff(1896,assumption,(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))), introduced(assumption)).
% 163.70/163.93 tff(1897,plain,
% 163.70/163.93 (((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (bool(tptp_fun_R_5(P!7)) | (~bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))))) <=> ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | bool(tptp_fun_R_5(P!7)) | (~bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))))),
% 163.70/163.93 inference(rewrite,[status(thm)],[])).
% 163.70/163.93 tff(1898,plain,
% 163.70/163.93 ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (bool(tptp_fun_R_5(P!7)) | (~bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))))),
% 163.70/163.93 inference(quant_inst,[status(thm)],[])).
% 163.70/163.93 tff(1899,plain,
% 163.70/163.93 ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | bool(tptp_fun_R_5(P!7)) | (~bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 163.70/163.93 inference(modus_ponens,[status(thm)],[1898, 1897])).
% 163.70/163.93 tff(1900,plain,
% 163.70/163.93 (bool(tptp_fun_R_5(P!7)) | (~bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))) | (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1899, 1827])).
% 163.70/163.93 tff(1901,plain,
% 163.70/163.93 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1900, 1008, 1876])).
% 163.70/163.93 tff(1902,plain,
% 163.70/163.93 (phi(tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.93 inference(symmetry,[status(thm)],[1901])).
% 163.70/163.93 tff(1903,plain,
% 163.70/163.93 ((err = phi(tptp_fun_R_5(P!7))) <=> (phi(tptp_fun_R_5(P!7)) = err)),
% 163.70/163.93 inference(commutativity,[status(thm)],[])).
% 163.70/163.93 tff(1904,plain,
% 163.70/163.93 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))),
% 163.70/163.93 inference(transitivity,[status(thm)],[975, 1901])).
% 163.70/163.93 tff(1905,plain,
% 163.70/163.93 ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> (err = phi(tptp_fun_R_5(P!7)))),
% 163.70/163.93 inference(monotonicity,[status(thm)],[973, 1904])).
% 163.70/163.93 tff(1906,plain,
% 163.70/163.93 ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> (phi(tptp_fun_R_5(P!7)) = err)),
% 163.70/163.93 inference(transitivity,[status(thm)],[1905, 1903])).
% 163.70/163.93 tff(1907,plain,
% 163.70/163.93 ((~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> (~(phi(tptp_fun_R_5(P!7)) = err))),
% 163.70/163.93 inference(monotonicity,[status(thm)],[1906])).
% 163.70/163.93 tff(1908,plain,
% 163.70/163.93 (~(phi(tptp_fun_R_5(P!7)) = err)),
% 163.70/163.93 inference(modus_ponens,[status(thm)],[964, 1907])).
% 163.70/163.93 tff(1909,plain,
% 163.70/163.93 ((d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err))) | (phi(tptp_fun_R_5(P!7)) = err)),
% 163.70/163.93 inference(tautology,[status(thm)],[])).
% 163.70/163.93 tff(1910,plain,
% 163.70/163.93 (d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err))),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1909, 1908])).
% 163.70/163.93 tff(1911,plain,
% 163.70/163.93 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))) | (~(d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))) | (~(d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err)))))),
% 163.70/163.93 inference(rewrite,[status(thm)],[])).
% 163.70/163.93 tff(1912,plain,
% 163.70/163.93 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))) | (~(d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err)))))),
% 163.70/163.93 inference(quant_inst,[status(thm)],[])).
% 163.70/163.93 tff(1913,plain,
% 163.70/163.93 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))) | (~(d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err))))),
% 163.70/163.93 inference(modus_ponens,[status(thm)],[1912, 1911])).
% 163.70/163.93 tff(1914,plain,
% 163.70/163.93 ((~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))) | (~(d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err))))),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1913, 39])).
% 163.70/163.93 tff(1915,plain,
% 163.70/163.93 (~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1914, 1910])).
% 163.70/163.93 tff(1916,plain,
% 163.70/163.93 (((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)))) | (phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))),
% 163.70/163.93 inference(tautology,[status(thm)],[])).
% 163.70/163.93 tff(1917,plain,
% 163.70/163.93 (phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1916, 1915])).
% 163.70/163.93 tff(1918,plain,
% 163.70/163.93 (tptp_fun_R_5(P!7) = phi(tptp_fun_R_5(P!7))),
% 163.70/163.93 inference(symmetry,[status(thm)],[1917])).
% 163.70/163.93 tff(1919,plain,
% 163.70/163.93 (tptp_fun_R_5(P!7) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 163.70/163.93 inference(transitivity,[status(thm)],[1918, 1902, 976])).
% 163.70/163.93 tff(1920,plain,
% 163.70/163.93 (phi(tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.70/163.93 inference(monotonicity,[status(thm)],[1919])).
% 163.70/163.93 tff(1921,plain,
% 163.70/163.93 (phi(tptp_fun_R_5(P!7)) = err),
% 163.70/163.93 inference(transitivity,[status(thm)],[1920, 973])).
% 163.70/163.93 tff(1922,plain,
% 163.70/163.93 ($false),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1908, 1921])).
% 163.70/163.93 tff(1923,plain,((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) | bool(tptp_fun_R_5(P!7))), inference(lemma,lemma(discharge,[]))).
% 163.70/163.93 tff(1924,plain,
% 163.70/163.93 (bool(tptp_fun_R_5(P!7))),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1923, 964])).
% 163.70/163.93 tff(1925,plain,
% 163.70/163.93 (prop(tptp_fun_R_5(P!7)) = true),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[958, 1924])).
% 163.70/163.93 tff(1926,plain,
% 163.70/163.93 (impl(true, tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[953, 1924])).
% 163.70/163.93 tff(1927,plain,
% 163.70/163.93 (impl(false, tptp_fun_R_5(P!7)) = true),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[948, 1924])).
% 163.70/163.93 tff(1928,plain,
% 163.70/163.93 ($false),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1096, 1927, 1926, 964, 1925])).
% 163.70/163.93 tff(1929,plain,(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), inference(lemma,lemma(discharge,[]))).
% 163.70/163.93 tff(1930,plain,
% 163.70/163.93 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.70/163.93 inference(symmetry,[status(thm)],[1929])).
% 163.70/163.93 tff(1931,plain,
% 163.70/163.93 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = f5(P!7, tptp_fun_R_5(P!7))),
% 163.70/163.93 inference(transitivity,[status(thm)],[1930, 1220])).
% 163.70/163.93 tff(1932,plain,
% 163.70/163.93 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(f5(P!7, tptp_fun_R_5(P!7)))),
% 163.70/163.93 inference(monotonicity,[status(thm)],[1931])).
% 163.70/163.93 tff(1933,plain,
% 163.70/163.93 (phi(f5(P!7, tptp_fun_R_5(P!7))) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.70/163.93 inference(symmetry,[status(thm)],[1932])).
% 163.70/163.93 tff(1934,plain,
% 163.70/163.93 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))),
% 163.70/163.93 inference(transitivity,[status(thm)],[1468, 1933, 1929, 975, 1896])).
% 163.70/163.93 tff(1935,plain,
% 163.70/163.93 ($false),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1866, 1934])).
% 163.70/163.93 tff(1936,plain,((impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))) | (~(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7))))) | (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))))), inference(lemma,lemma(discharge,[]))).
% 163.70/163.93 tff(1937,plain,
% 163.70/163.93 (~(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1936, 1886, 1866])).
% 163.70/163.93 tff(1938,plain,
% 163.70/163.93 (~bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1900, 1937, 1876])).
% 163.70/163.93 tff(1939,plain,
% 163.70/163.93 (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (apply(P!7, tptp_fun_X_3(P!7)) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1443, 1733])).
% 163.70/163.93 tff(1940,plain,
% 163.70/163.93 (apply(P!7, tptp_fun_X_3(P!7)) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1939, 1938])).
% 163.70/163.93 tff(1941,plain,
% 163.70/163.93 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = apply(P!7, tptp_fun_X_3(P!7))),
% 163.70/163.93 inference(symmetry,[status(thm)],[1940])).
% 163.70/163.93 tff(1942,plain,
% 163.70/163.93 (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.70/163.93 inference(monotonicity,[status(thm)],[1941])).
% 163.70/163.93 tff(1943,plain,
% 163.70/163.93 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1007, 1938])).
% 163.70/163.93 tff(1944,plain,
% 163.70/163.93 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = err),
% 163.70/163.93 inference(transitivity,[status(thm)],[975, 1943, 1942, 1730])).
% 163.70/163.93 tff(1945,plain,
% 163.70/163.93 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(err)),
% 163.70/163.93 inference(monotonicity,[status(thm)],[1944])).
% 163.70/163.93 tff(1946,plain,
% 163.70/163.93 (f5(P!7, tptp_fun_R_5(P!7)) = err),
% 163.70/163.93 inference(transitivity,[status(thm)],[1101, 1945, 1895])).
% 163.70/163.93 tff(1947,plain,
% 163.70/163.93 (phi(f5(P!7, tptp_fun_R_5(P!7))) = phi(err)),
% 163.70/163.93 inference(monotonicity,[status(thm)],[1946])).
% 163.70/163.93 tff(1948,plain,
% 163.70/163.93 (phi(err) = phi(f5(P!7, tptp_fun_R_5(P!7)))),
% 163.70/163.93 inference(symmetry,[status(thm)],[1947])).
% 163.70/163.93 tff(1949,plain,
% 163.70/163.93 (err = phi(err)),
% 163.70/163.93 inference(symmetry,[status(thm)],[1895])).
% 163.70/163.93 tff(1950,plain,
% 163.70/163.93 (err = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.93 inference(transitivity,[status(thm)],[1949, 1948, 1887])).
% 163.70/163.93 tff(1951,plain,
% 163.70/163.93 (prop(tptp_fun_R_5(P!7)) = false),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1726, 1876])).
% 163.70/163.93 tff(1952,plain,
% 163.70/163.93 (false = prop(tptp_fun_R_5(P!7))),
% 163.70/163.93 inference(symmetry,[status(thm)],[1951])).
% 163.70/163.93 tff(1953,plain,
% 163.70/163.93 (prop(err) = prop(tptp_fun_R_5(P!7))),
% 163.70/163.93 inference(transitivity,[status(thm)],[1872, 1952])).
% 163.70/163.93 tff(1954,plain,
% 163.70/163.93 (lazy_impl(prop(err), err) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.93 inference(monotonicity,[status(thm)],[1953, 1950])).
% 163.70/163.93 tff(1955,plain,
% 163.70/163.93 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(err), err)),
% 163.70/163.93 inference(symmetry,[status(thm)],[1954])).
% 163.70/163.93 tff(1956,plain,
% 163.70/163.93 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true),
% 163.70/163.93 inference(transitivity,[status(thm)],[1955, 1875, 1868])).
% 163.70/163.93 tff(1957,plain,
% 163.70/163.93 ($false),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1865, 1956])).
% 163.70/163.93 tff(1958,plain,(bool(tptp_fun_R_5(P!7)) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true) | (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))), inference(lemma,lemma(discharge,[]))).
% 163.70/163.93 tff(1959,plain,
% 163.70/163.93 (bool(tptp_fun_R_5(P!7))),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1958, 1866, 1865])).
% 163.70/163.93 tff(1960,plain,
% 163.70/163.93 ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = true)),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[926, 1959])).
% 163.70/163.93 tff(1961,plain,
% 163.70/163.93 (prop(tptp_fun_R_5(P!7)) = true),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[958, 1959])).
% 163.70/163.93 tff(1962,plain,
% 163.70/163.93 (impl(false, tptp_fun_R_5(P!7)) = true),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[948, 1959])).
% 163.70/163.93 tff(1963,plain,
% 163.70/163.93 (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[873, 1733])).
% 163.70/163.93 tff(1964,plain,
% 163.70/163.93 (impl(false, tptp_fun_R_5(P!7)) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.93 inference(symmetry,[status(thm)],[1610])).
% 163.70/163.93 tff(1965,plain,
% 163.70/163.93 (true = impl(false, tptp_fun_R_5(P!7))),
% 163.70/163.93 inference(symmetry,[status(thm)],[963])).
% 163.70/163.93 tff(1966,plain,
% 163.70/163.93 (true = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 163.70/163.93 inference(transitivity,[status(thm)],[1965, 1964, 976])).
% 163.70/163.93 tff(1967,assumption,(tptp_fun_R_5(P!7) = true), introduced(assumption)).
% 163.70/163.93 tff(1968,plain,
% 163.70/163.93 (f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7)) = f4(P!7, tptp_fun_X_3(P!7), true)),
% 163.70/163.93 inference(monotonicity,[status(thm)],[1967])).
% 163.70/163.93 tff(1969,plain,
% 163.70/163.93 (f4(P!7, tptp_fun_X_3(P!7), true) = f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7))),
% 163.70/163.93 inference(symmetry,[status(thm)],[1968])).
% 163.70/163.93 tff(1970,plain,
% 163.70/163.93 ((~![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))) | (f4(P!7, tptp_fun_X_3(P!7), true) = impl(apply(P!7, tptp_fun_X_3(P!7)), true))),
% 163.70/163.93 inference(quant_inst,[status(thm)],[])).
% 163.70/163.93 tff(1971,plain,
% 163.70/163.93 (f4(P!7, tptp_fun_X_3(P!7), true) = impl(apply(P!7, tptp_fun_X_3(P!7)), true)),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1970, 7])).
% 163.70/163.93 tff(1972,plain,
% 163.70/163.93 (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = f4(P!7, tptp_fun_X_3(P!7), true)),
% 163.70/163.93 inference(symmetry,[status(thm)],[1971])).
% 163.70/163.93 tff(1973,plain,
% 163.70/163.93 (err = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.70/163.93 inference(symmetry,[status(thm)],[1125])).
% 163.70/163.93 tff(1974,plain,
% 163.70/163.93 (err = impl(apply(P!7, tptp_fun_X_3(P!7)), true)),
% 163.70/163.93 inference(transitivity,[status(thm)],[1973, 1548])).
% 163.70/163.93 tff(1975,plain,
% 163.70/163.93 (phi(err) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true))),
% 163.70/163.93 inference(monotonicity,[status(thm)],[1974])).
% 163.70/163.93 tff(1976,plain,
% 163.70/163.93 (phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) = phi(err)),
% 163.70/163.93 inference(symmetry,[status(thm)],[1975])).
% 163.70/163.93 tff(1977,plain,
% 163.70/163.93 (impl(apply(P!7, tptp_fun_X_3(P!7)), true) = err),
% 163.70/163.93 inference(transitivity,[status(thm)],[1545, 1125])).
% 163.70/163.93 tff(1978,plain,
% 163.70/163.93 (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) <=> bool(err)),
% 163.70/163.93 inference(monotonicity,[status(thm)],[1977])).
% 163.70/163.93 tff(1979,plain,
% 163.70/163.93 (bool(err) <=> bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true))),
% 163.70/163.93 inference(symmetry,[status(thm)],[1978])).
% 163.70/163.93 tff(1980,plain,
% 163.70/163.93 ((~bool(err)) <=> (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))),
% 163.70/163.93 inference(monotonicity,[status(thm)],[1979])).
% 163.70/163.93 tff(1981,plain,
% 163.70/163.93 (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true))),
% 163.70/163.93 inference(modus_ponens,[status(thm)],[1043, 1980])).
% 163.70/163.93 tff(1982,assumption,(bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true))), introduced(assumption)).
% 163.70/163.93 tff(1983,plain,
% 163.70/163.93 ($false),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1982, 1981])).
% 163.70/163.93 tff(1984,plain,((~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))), inference(lemma,lemma(discharge,[]))).
% 163.70/163.93 tff(1985,plain,
% 163.70/163.93 (~bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true))),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1984, 1125, 1545])).
% 163.70/163.93 tff(1986,plain,
% 163.70/163.93 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), true) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), true) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true))))),
% 163.70/163.93 inference(rewrite,[status(thm)],[])).
% 163.70/163.93 tff(1987,plain,
% 163.70/163.93 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), true) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true))))),
% 163.70/163.93 inference(quant_inst,[status(thm)],[])).
% 163.70/163.93 tff(1988,plain,
% 163.70/163.93 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), true) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))),
% 163.70/163.93 inference(modus_ponens,[status(thm)],[1987, 1986])).
% 163.70/163.93 tff(1989,plain,
% 163.70/163.93 (bool(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) | (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), true) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true)))),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1988, 332])).
% 163.70/163.93 tff(1990,plain,
% 163.70/163.93 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), true) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true))),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[1989, 1985])).
% 163.70/163.93 tff(1991,plain,
% 163.70/163.93 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), true) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)),
% 163.70/163.93 inference(monotonicity,[status(thm)],[1547])).
% 163.70/163.93 tff(1992,plain,
% 163.70/163.93 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), true)),
% 163.70/163.93 inference(symmetry,[status(thm)],[1991])).
% 163.70/163.93 tff(1993,plain,
% 163.70/163.93 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true) = f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7))),
% 163.70/163.93 inference(transitivity,[status(thm)],[1992, 1990, 1976, 1895, 1973, 1548, 1972, 1969])).
% 163.70/163.93 tff(1994,plain,
% 163.70/163.93 (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true), true) <=> forallprefers(f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.70/163.93 inference(monotonicity,[status(thm)],[1993, 1966])).
% 163.70/163.93 tff(1995,plain,
% 163.70/163.93 (forallprefers(f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true), true)),
% 163.70/163.93 inference(symmetry,[status(thm)],[1994])).
% 163.70/163.93 tff(1996,plain,
% 163.70/163.93 ((~forallprefers(f4(P!7, tptp_fun_X_3(P!7), tptp_fun_R_5(P!7)), f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) <=> (~forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true), true))),
% 163.70/163.93 inference(monotonicity,[status(thm)],[1995])).
% 163.70/163.93 tff(1997,plain,
% 163.70/163.93 (~forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true), true)),
% 163.70/163.93 inference(modus_ponens,[status(thm)],[1304, 1996])).
% 163.70/163.93 tff(1998,plain,
% 163.70/163.93 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true), true) <=> ((impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true) = false) | (~((~d(true)) | (~bool(true)) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))) | (~((~d(true)) | d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true), true) <=> ((impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true) = false) | (~((~d(true)) | (~bool(true)) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))) | (~((~d(true)) | d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)))))))),
% 163.70/163.93 inference(rewrite,[status(thm)],[])).
% 163.70/163.93 tff(1999,plain,
% 163.70/163.93 ((forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true), true) <=> ((~((~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true) = false)) | (~(true = true)))) | (~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(true)))) | (~((~d(true)) | (~bool(true)) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))))) <=> (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true), true) <=> ((impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true) = false) | (~((~d(true)) | (~bool(true)) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))) | (~((~d(true)) | d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))))),
% 163.70/163.93 inference(rewrite,[status(thm)],[])).
% 163.70/163.93 tff(2000,plain,
% 163.70/163.93 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true), true) <=> ((~((~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true) = false)) | (~(true = true)))) | (~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(true)))) | (~((~d(true)) | (~bool(true)) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true), true) <=> ((impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true) = false) | (~((~d(true)) | (~bool(true)) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))) | (~((~d(true)) | d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)))))))),
% 163.70/163.93 inference(monotonicity,[status(thm)],[1999])).
% 163.70/163.93 tff(2001,plain,
% 163.70/163.93 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true), true) <=> ((~((~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true) = false)) | (~(true = true)))) | (~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(true)))) | (~((~d(true)) | (~bool(true)) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true), true) <=> ((impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true) = false) | (~((~d(true)) | (~bool(true)) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))) | (~((~d(true)) | d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)))))))),
% 163.70/163.93 inference(transitivity,[status(thm)],[2000, 1998])).
% 163.70/163.93 tff(2002,plain,
% 163.70/163.93 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true), true) <=> ((~((~(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true) = false)) | (~(true = true)))) | (~(d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(true)))) | (~((~d(true)) | (~bool(true)) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)))))))),
% 163.70/163.93 inference(quant_inst,[status(thm)],[])).
% 163.70/163.93 tff(2003,plain,
% 163.70/163.93 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true), true) <=> ((impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true) = false) | (~((~d(true)) | (~bool(true)) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))) | (~((~d(true)) | d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))))),
% 163.70/163.93 inference(modus_ponens,[status(thm)],[2002, 2001])).
% 163.70/163.93 tff(2004,plain,
% 163.70/163.93 (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true), true) <=> ((impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true) = false) | (~((~d(true)) | (~bool(true)) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))) | (~((~d(true)) | d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)))))),
% 163.70/163.93 inference(unit_resolution,[status(thm)],[2003, 165])).
% 163.70/163.93 tff(2005,plain,
% 163.70/163.93 (phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true)) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), true)),
% 163.70/163.93 inference(symmetry,[status(thm)],[1990])).
% 163.70/163.93 tff(2006,plain,
% 163.70/163.93 (err = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)),
% 163.70/163.93 inference(transitivity,[status(thm)],[1949, 1975, 2005, 1991])).
% 163.70/163.93 tff(2007,plain,
% 163.70/163.93 (d(err) <=> d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))),
% 163.70/163.93 inference(monotonicity,[status(thm)],[2006])).
% 163.70/163.94 tff(2008,plain,
% 163.70/163.94 (d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))),
% 163.70/163.94 inference(modus_ponens,[status(thm)],[1775, 2007])).
% 163.70/163.94 tff(2009,plain,
% 163.70/163.94 (bool(err) <=> bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))),
% 163.70/163.94 inference(monotonicity,[status(thm)],[2006])).
% 163.70/163.94 tff(2010,plain,
% 163.70/163.94 ((~bool(err)) <=> (~bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)))),
% 163.70/163.94 inference(monotonicity,[status(thm)],[2009])).
% 163.70/163.94 tff(2011,plain,
% 163.70/163.94 (~bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))),
% 163.70/163.94 inference(modus_ponens,[status(thm)],[1043, 2010])).
% 163.70/163.94 tff(2012,plain,
% 163.70/163.94 ((~((~d(true)) | (~bool(true)) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))) | (~d(true)) | (~bool(true)) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)))),
% 163.70/163.94 inference(tautology,[status(thm)],[])).
% 163.70/163.94 tff(2013,plain,
% 163.70/163.94 (~((~d(true)) | (~bool(true)) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2012, 226, 252, 2011, 2008])).
% 163.70/163.94 tff(2014,plain,
% 163.70/163.94 (((impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true) = false) | (~((~d(true)) | (~bool(true)) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))) | (~((~d(true)) | d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))) | ((~d(true)) | (~bool(true)) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))),
% 163.70/163.94 inference(tautology,[status(thm)],[])).
% 163.70/163.94 tff(2015,plain,
% 163.70/163.94 ((impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true) = false) | (~((~d(true)) | (~bool(true)) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))) | (~((~d(true)) | d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2014, 2013])).
% 163.70/163.94 tff(2016,plain,
% 163.70/163.94 ((~(forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true), true) <=> ((impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true) = false) | (~((~d(true)) | (~bool(true)) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))) | (~((~d(true)) | d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))))) | forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true), true) | (~((impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true) = false) | (~((~d(true)) | (~bool(true)) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))) | (~((~d(true)) | d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))))),
% 163.70/163.94 inference(tautology,[status(thm)],[])).
% 163.70/163.94 tff(2017,plain,
% 163.70/163.94 ((~(forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true), true) <=> ((impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true) = false) | (~((~d(true)) | (~bool(true)) | bool(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) | (~d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))) | (~((~d(true)) | d(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))))))) | forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true), true)),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2016, 2015])).
% 163.70/163.94 tff(2018,plain,
% 163.70/163.94 (forallprefers(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true), true)),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2017, 2004])).
% 163.70/163.94 tff(2019,plain,
% 163.70/163.94 ($false),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2018, 1997])).
% 163.70/163.94 tff(2020,plain,((~(tptp_fun_R_5(P!7) = true)) | (~(impl(false, tptp_fun_R_5(P!7)) = true)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false)) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))), inference(lemma,lemma(discharge,[]))).
% 163.70/163.94 tff(2021,plain,
% 163.70/163.94 ((~(tptp_fun_R_5(P!7) = true)) | (~(impl(false, tptp_fun_R_5(P!7)) = true)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false))),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2020, 1963, 1730])).
% 163.70/163.94 tff(2022,plain,
% 163.70/163.94 (~(tptp_fun_R_5(P!7) = true)),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2021, 1458, 963])).
% 163.70/163.94 tff(2023,plain,
% 163.70/163.94 (tptp_fun_R_5(P!7) = false),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[1476, 2022, 960])).
% 163.70/163.94 tff(2024,assumption,(phi(tptp_fun_R_5(P!7)) = err), introduced(assumption)).
% 163.70/163.94 tff(2025,plain,
% 163.70/163.94 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = err),
% 163.70/163.94 inference(transitivity,[status(thm)],[1025, 1024, 2024])).
% 163.70/163.94 tff(2026,plain,
% 163.70/163.94 (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) <=> bool(err)),
% 163.70/163.94 inference(monotonicity,[status(thm)],[2025])).
% 163.70/163.94 tff(2027,plain,
% 163.70/163.94 (bool(err) <=> bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.94 inference(symmetry,[status(thm)],[2026])).
% 163.70/163.94 tff(2028,plain,
% 163.70/163.94 ((~bool(err)) <=> (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.70/163.94 inference(monotonicity,[status(thm)],[2027])).
% 163.70/163.94 tff(2029,plain,
% 163.70/163.94 (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.94 inference(modus_ponens,[status(thm)],[1043, 2028])).
% 163.70/163.94 tff(2030,plain,
% 163.70/163.94 ($false),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[1084, 2029])).
% 163.70/163.94 tff(2031,plain,((~(phi(tptp_fun_R_5(P!7)) = err)) | (~(prop(tptp_fun_R_5(P!7)) = true))), inference(lemma,lemma(discharge,[]))).
% 163.70/163.94 tff(2032,plain,
% 163.70/163.94 (~(phi(tptp_fun_R_5(P!7)) = err)),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2031, 961])).
% 163.70/163.94 tff(2033,plain,
% 163.70/163.94 (d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err))),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[1909, 2032])).
% 163.70/163.94 tff(2034,plain,
% 163.70/163.94 (~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[1914, 2033])).
% 163.70/163.94 tff(2035,plain,
% 163.70/163.94 (phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[1916, 2034])).
% 163.70/163.94 tff(2036,plain,
% 163.70/163.94 (phi(tptp_fun_R_5(P!7)) = false),
% 163.70/163.94 inference(transitivity,[status(thm)],[2035, 2023])).
% 163.70/163.94 tff(2037,plain,
% 163.70/163.94 (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = phi(f6(P!7, tptp_fun_R_5(P!7)))),
% 163.70/163.94 inference(transitivity,[status(thm)],[1412, 1409, 566, 1851])).
% 163.70/163.94 tff(2038,plain,
% 163.70/163.94 ((phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err) <=> (phi(f6(P!7, tptp_fun_R_5(P!7))) = err)),
% 163.70/163.94 inference(monotonicity,[status(thm)],[2037])).
% 163.70/163.94 tff(2039,plain,
% 163.70/163.94 ((phi(f6(P!7, tptp_fun_R_5(P!7))) = err) <=> (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 163.70/163.94 inference(symmetry,[status(thm)],[2038])).
% 163.70/163.94 tff(2040,plain,
% 163.70/163.94 ((~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err)) <=> (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))),
% 163.70/163.94 inference(monotonicity,[status(thm)],[2039])).
% 163.70/163.94 tff(2041,plain,
% 163.70/163.94 (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 163.70/163.94 inference(modus_ponens,[status(thm)],[1798, 2040])).
% 163.70/163.94 tff(2042,plain,
% 163.70/163.94 ((d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))) | (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 163.70/163.94 inference(tautology,[status(thm)],[])).
% 163.70/163.94 tff(2043,plain,
% 163.70/163.94 (d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2042, 2041])).
% 163.70/163.94 tff(2044,plain,
% 163.70/163.94 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~(d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~(d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)))))),
% 163.70/163.94 inference(rewrite,[status(thm)],[])).
% 163.70/163.94 tff(2045,plain,
% 163.70/163.94 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~(d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)))))),
% 163.70/163.94 inference(quant_inst,[status(thm)],[])).
% 163.70/163.94 tff(2046,plain,
% 163.70/163.94 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~(d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))))),
% 163.70/163.94 inference(modus_ponens,[status(thm)],[2045, 2044])).
% 163.70/163.94 tff(2047,plain,
% 163.70/163.94 (~((~d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2046, 39, 2043])).
% 163.70/163.94 tff(2048,plain,
% 163.70/163.94 (((~d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.94 inference(tautology,[status(thm)],[])).
% 163.70/163.94 tff(2049,plain,
% 163.70/163.94 (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2048, 2047])).
% 163.70/163.94 tff(2050,plain,
% 163.70/163.94 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.94 inference(symmetry,[status(thm)],[2049])).
% 163.70/163.94 tff(2051,plain,
% 163.70/163.94 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.94 inference(transitivity,[status(thm)],[2050, 1412, 1409])).
% 163.70/163.94 tff(2052,plain,
% 163.70/163.94 ((impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))) <=> (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false)),
% 163.70/163.94 inference(monotonicity,[status(thm)],[2051, 2036])).
% 163.70/163.94 tff(2053,plain,
% 163.70/163.94 ((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) <=> (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 163.70/163.94 inference(symmetry,[status(thm)],[2052])).
% 163.70/163.94 tff(2054,plain,
% 163.70/163.94 (((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | ((~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true))) <=> ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true))),
% 163.70/163.94 inference(rewrite,[status(thm)],[])).
% 163.70/163.94 tff(2055,plain,
% 163.70/163.94 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | ((~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true))),
% 163.70/163.94 inference(quant_inst,[status(thm)],[])).
% 163.70/163.94 tff(2056,plain,
% 163.70/163.94 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)),
% 163.70/163.94 inference(modus_ponens,[status(thm)],[2055, 2054])).
% 163.70/163.94 tff(2057,plain,
% 163.70/163.94 (impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2056, 388, 1084])).
% 163.70/163.94 tff(2058,plain,
% 163.70/163.94 (lazy_impl(true, impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = lazy_impl(true, true)),
% 163.70/163.94 inference(monotonicity,[status(thm)],[2057])).
% 163.70/163.94 tff(2059,plain,
% 163.70/163.94 (lazy_impl(true, impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = true),
% 163.70/163.94 inference(transitivity,[status(thm)],[2058, 236, 234])).
% 163.70/163.94 tff(2060,plain,
% 163.70/163.94 (impl(lazy_impl(true, impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.94 inference(monotonicity,[status(thm)],[2059])).
% 163.70/163.94 tff(2061,plain,
% 163.70/163.94 (impl(lazy_impl(true, impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.94 inference(transitivity,[status(thm)],[2060, 1662])).
% 163.70/163.94 tff(2062,plain,
% 163.70/163.94 ((~![X: $i] : ((prop(X) = true) <=> bool(X))) | ((prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true) <=> bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.70/163.94 inference(quant_inst,[status(thm)],[])).
% 163.70/163.94 tff(2063,plain,
% 163.70/163.94 ((prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true) <=> bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2062, 19])).
% 163.70/163.94 tff(2064,plain,
% 163.70/163.94 ((~((prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true) <=> bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.70/163.94 inference(tautology,[status(thm)],[])).
% 163.70/163.94 tff(2065,plain,
% 163.70/163.94 ((~((prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true) <=> bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | (prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2064, 1084])).
% 163.70/163.94 tff(2066,plain,
% 163.70/163.94 (prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2065, 2063])).
% 163.70/163.94 tff(2067,plain,
% 163.70/163.94 (lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(lazy_impl(true, impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = lazy_impl(true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.94 inference(monotonicity,[status(thm)],[2066, 2061])).
% 163.70/163.94 tff(2068,plain,
% 163.70/163.94 ((~![P: $i, Q: $i, R: $i] : (f2(P, Q, R) = lazy_impl(prop(R), impl(lazy_impl(P, impl(Q, R)), R)))) | (f2(true, false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(lazy_impl(true, impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 163.70/163.94 inference(quant_inst,[status(thm)],[])).
% 163.70/163.94 tff(2069,plain,
% 163.70/163.94 (f2(true, false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))), impl(lazy_impl(true, impl(false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))), lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2068, 1186])).
% 163.70/163.94 tff(2070,plain,
% 163.70/163.94 (lazy_impl(true, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.94 inference(symmetry,[status(thm)],[1025])).
% 163.70/163.94 tff(2071,plain,
% 163.70/163.94 (phi(tptp_fun_R_5(P!7)) = lazy_impl(true, tptp_fun_R_5(P!7))),
% 163.70/163.94 inference(symmetry,[status(thm)],[1024])).
% 163.70/163.94 tff(2072,plain,
% 163.70/163.94 (tptp_fun_R_5(P!7) = phi(tptp_fun_R_5(P!7))),
% 163.70/163.94 inference(symmetry,[status(thm)],[2035])).
% 163.70/163.94 tff(2073,plain,
% 163.70/163.94 (tptp_fun_R_5(P!7) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.94 inference(transitivity,[status(thm)],[2072, 2071, 2070])).
% 163.70/163.94 tff(2074,plain,
% 163.70/163.94 (f2(true, apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = f2(true, false, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.94 inference(monotonicity,[status(thm)],[1458, 2073])).
% 163.70/163.94 tff(2075,plain,
% 163.70/163.94 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false),
% 163.70/163.94 inference(transitivity,[status(thm)],[1227, 1219, 2074, 2069, 2067, 1667, 1239, 1025, 1024, 2035, 2023])).
% 163.70/163.94 tff(2076,plain,
% 163.70/163.94 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))),
% 163.70/163.94 inference(modus_ponens,[status(thm)],[2075, 2053])).
% 163.70/163.94 tff(2077,plain,
% 163.70/163.94 ($false),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[1866, 2076])).
% 163.70/163.94 tff(2078,plain,((~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false)) | (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))) | (~(prop(tptp_fun_R_5(P!7)) = true)) | (~((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = true))) | (~(impl(false, tptp_fun_R_5(P!7)) = true))), inference(lemma,lemma(discharge,[]))).
% 163.70/163.94 tff(2079,plain,
% 163.70/163.94 (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false)),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2078, 1961, 1866, 1960, 1962])).
% 163.70/163.94 tff(2080,plain,
% 163.70/163.94 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(err) | (impl(err, phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(err)))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(err) | (impl(err, phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(err)))),
% 163.70/163.94 inference(rewrite,[status(thm)],[])).
% 163.70/163.94 tff(2081,plain,
% 163.70/163.94 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(err) | (impl(err, phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(err)))),
% 163.70/163.94 inference(quant_inst,[status(thm)],[])).
% 163.70/163.94 tff(2082,plain,
% 163.70/163.94 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(err) | (impl(err, phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(err))),
% 163.70/163.94 inference(modus_ponens,[status(thm)],[2081, 2080])).
% 163.70/163.94 tff(2083,plain,
% 163.70/163.94 (impl(err, phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(err)),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2082, 332, 1043])).
% 163.70/163.94 tff(2084,plain,
% 163.70/163.94 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), impl(err, true)) = phi(apply(P!7, tptp_fun_X_3(P!7)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), impl(err, true)) = phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 163.70/163.94 inference(rewrite,[status(thm)],[])).
% 163.70/163.94 tff(2085,plain,
% 163.70/163.94 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), impl(err, true)) = phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 163.70/163.94 inference(quant_inst,[status(thm)],[])).
% 163.70/163.94 tff(2086,plain,
% 163.70/163.94 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), impl(err, true)) = phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 163.70/163.94 inference(modus_ponens,[status(thm)],[2085, 2084])).
% 163.70/163.94 tff(2087,plain,
% 163.70/163.94 (bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), impl(err, true)) = phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2086, 332])).
% 163.70/163.94 tff(2088,plain,
% 163.70/163.94 (impl(apply(P!7, tptp_fun_X_3(P!7)), impl(err, true)) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2087, 1733])).
% 163.70/163.94 tff(2089,plain,
% 163.70/163.94 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(err) | (impl(err, true) = phi(err)))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(err) | (impl(err, true) = phi(err)))),
% 163.70/163.94 inference(rewrite,[status(thm)],[])).
% 163.70/163.94 tff(2090,plain,
% 163.70/163.94 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(err) | (impl(err, true) = phi(err)))),
% 163.70/163.94 inference(quant_inst,[status(thm)],[])).
% 163.70/163.94 tff(2091,plain,
% 163.70/163.94 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(err) | (impl(err, true) = phi(err))),
% 163.70/163.94 inference(modus_ponens,[status(thm)],[2090, 2089])).
% 163.70/163.94 tff(2092,plain,
% 163.70/163.94 (impl(err, true) = phi(err)),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2091, 332, 1043])).
% 163.70/163.94 tff(2093,plain,
% 163.70/163.94 (phi(err) = impl(err, true)),
% 163.70/163.94 inference(symmetry,[status(thm)],[2092])).
% 163.70/163.94 tff(2094,plain,
% 163.70/163.94 (impl(err, phi(f6(P!7, tptp_fun_R_5(P!7)))) = impl(err, true)),
% 163.70/163.94 inference(transitivity,[status(thm)],[2083, 2093])).
% 163.70/163.94 tff(2095,plain,
% 163.70/163.94 (impl(apply(P!7, tptp_fun_X_3(P!7)), impl(err, phi(f6(P!7, tptp_fun_R_5(P!7))))) = impl(apply(P!7, tptp_fun_X_3(P!7)), impl(err, true))),
% 163.70/163.94 inference(monotonicity,[status(thm)],[2094])).
% 163.70/163.94 tff(2096,plain,
% 163.70/163.94 (impl(apply(P!7, tptp_fun_X_3(P!7)), impl(err, phi(f6(P!7, tptp_fun_R_5(P!7))))) = err),
% 163.70/163.94 inference(transitivity,[status(thm)],[2095, 2088, 1730])).
% 163.70/163.94 tff(2097,plain,
% 163.70/163.94 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(err, phi(f6(P!7, tptp_fun_R_5(P!7))))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = impl(err, phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 163.70/163.94 inference(monotonicity,[status(thm)],[2096])).
% 163.70/163.94 tff(2098,plain,
% 163.70/163.94 (impl(apply(P!7, tptp_fun_X_3(P!7)), impl(err, true)) = impl(apply(P!7, tptp_fun_X_3(P!7)), impl(err, phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.94 inference(symmetry,[status(thm)],[2095])).
% 163.70/163.94 tff(2099,plain,
% 163.70/163.94 (phi(apply(P!7, tptp_fun_X_3(P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), impl(err, true))),
% 163.70/163.94 inference(symmetry,[status(thm)],[2088])).
% 163.70/163.94 tff(2100,plain,
% 163.70/163.94 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 163.70/163.94 inference(rewrite,[status(thm)],[])).
% 163.70/163.94 tff(2101,plain,
% 163.70/163.94 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7)))))),
% 163.70/163.94 inference(quant_inst,[status(thm)],[])).
% 163.70/163.94 tff(2102,plain,
% 163.70/163.94 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 163.70/163.94 inference(modus_ponens,[status(thm)],[2101, 2100])).
% 163.70/163.94 tff(2103,plain,
% 163.70/163.94 (bool(apply(P!7, tptp_fun_X_3(P!7))) | (impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7))))),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2102, 332])).
% 163.70/163.94 tff(2104,plain,
% 163.70/163.94 (impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.70/163.94 inference(unit_resolution,[status(thm)],[2103, 1733])).
% 163.70/163.94 tff(2105,plain,
% 163.70/163.94 (impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))) = impl(apply(P!7, tptp_fun_X_3(P!7)), impl(err, phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.94 inference(transitivity,[status(thm)],[2104, 2099, 2098])).
% 163.70/163.94 tff(2106,plain,
% 163.70/163.94 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(err, phi(f6(P!7, tptp_fun_R_5(P!7))))), phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 163.70/163.94 inference(monotonicity,[status(thm)],[2105])).
% 163.70/163.94 tff(2107,plain,
% 163.70/163.94 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = err),
% 163.70/163.94 inference(transitivity,[status(thm)],[2106, 2097, 2083, 1895])).
% 163.70/163.94 tff(2108,plain,
% 163.70/163.94 (phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(err)),
% 163.70/163.94 inference(monotonicity,[status(thm)],[2107])).
% 163.70/163.94 tff(2109,plain,
% 163.70/163.94 (phi(err) = phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.94 inference(symmetry,[status(thm)],[2108])).
% 163.70/163.94 tff(2110,plain,
% 163.70/163.94 (err = phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.94 inference(transitivity,[status(thm)],[1949, 2109])).
% 163.70/163.94 tff(2111,assumption,(impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))))), introduced(assumption)).
% 163.70/163.94 tff(2112,plain,
% 163.70/163.94 (phi(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7))))) = impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.94 inference(symmetry,[status(thm)],[2111])).
% 163.70/163.94 tff(2113,assumption,(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(phi(f6(P!7, tptp_fun_R_5(P!7))))), introduced(assumption)).
% 163.70/163.94 tff(2114,plain,
% 163.70/163.94 (phi(phi(f6(P!7, tptp_fun_R_5(P!7)))) = impl(true, phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 163.70/163.94 inference(symmetry,[status(thm)],[2113])).
% 163.70/163.94 tff(2115,plain,
% 163.70/163.94 (f6(P!7, tptp_fun_R_5(P!7)) = impl(true, phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 163.70/163.94 inference(transitivity,[status(thm)],[1851, 1850, 2114])).
% 163.70/163.94 tff(2116,plain,
% 163.70/163.94 (phi(f6(P!7, tptp_fun_R_5(P!7))) = phi(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.94 inference(monotonicity,[status(thm)],[2115])).
% 163.70/163.94 tff(2117,plain,
% 163.70/163.94 (true = prop(tptp_fun_R_5(P!7))),
% 163.70/163.94 inference(symmetry,[status(thm)],[1961])).
% 163.70/163.94 tff(2118,plain,
% 163.70/163.94 (lazy_impl(true, impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.94 inference(monotonicity,[status(thm)],[2117])).
% 163.70/163.94 tff(2119,plain,
% 163.70/163.94 (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.94 inference(transitivity,[status(thm)],[1412, 2118, 566, 1851, 2116, 2112])).
% 163.70/163.94 tff(2120,plain,
% 163.70/163.94 ((phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err) <=> (impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.94 inference(monotonicity,[status(thm)],[2119, 2110])).
% 163.70/163.94 tff(2121,plain,
% 163.70/163.94 ((impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 163.70/163.94 inference(symmetry,[status(thm)],[2120])).
% 163.70/163.94 tff(2122,plain,
% 163.70/163.94 ((~(impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) <=> (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))),
% 163.70/163.94 inference(monotonicity,[status(thm)],[2121])).
% 163.70/163.94 tff(2123,plain,
% 163.70/163.94 (phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = err),
% 163.70/163.94 inference(transitivity,[status(thm)],[2108, 1895])).
% 163.70/163.94 tff(2124,plain,
% 163.70/163.94 (phi(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(f6(P!7, tptp_fun_R_5(P!7)))),
% 163.70/163.94 inference(symmetry,[status(thm)],[2116])).
% 163.70/163.94 tff(2125,plain,
% 163.70/163.94 (impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(f6(P!7, tptp_fun_R_5(P!7)))),
% 163.70/163.94 inference(transitivity,[status(thm)],[2111, 2124])).
% 163.70/163.94 tff(2126,plain,
% 163.70/163.94 ((impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> (phi(f6(P!7, tptp_fun_R_5(P!7))) = err)),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2125, 2123])).
% 163.70/163.95 tff(2127,plain,
% 163.70/163.95 ((phi(f6(P!7, tptp_fun_R_5(P!7))) = err) <=> (impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.95 inference(symmetry,[status(thm)],[2126])).
% 163.70/163.95 tff(2128,plain,
% 163.70/163.95 ((~(phi(f6(P!7, tptp_fun_R_5(P!7))) = err)) <=> (~(impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2127])).
% 163.70/163.95 tff(2129,plain,
% 163.70/163.95 (~(impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.95 inference(modus_ponens,[status(thm)],[1798, 2128])).
% 163.70/163.95 tff(2130,plain,
% 163.70/163.95 (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 163.70/163.95 inference(modus_ponens,[status(thm)],[2129, 2122])).
% 163.70/163.95 tff(2131,plain,
% 163.70/163.95 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), tptp_fun_R_5(P!7)) = phi(impl(apply(P!7, tptp_fun_X_3(P!7)), true))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[1320, 1985])).
% 163.70/163.95 tff(2132,plain,
% 163.70/163.95 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), impl(false, tptp_fun_R_5(P!7))) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)),
% 163.70/163.95 inference(monotonicity,[status(thm)],[1547, 963])).
% 163.70/163.95 tff(2133,plain,
% 163.70/163.95 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), impl(false, tptp_fun_R_5(P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7)))),
% 163.70/163.95 inference(transitivity,[status(thm)],[2132, 1992, 1990, 1976, 1895, 1973, 1548, 1117])).
% 163.70/163.95 tff(2134,plain,
% 163.70/163.95 (impl(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2133])).
% 163.70/163.95 tff(2135,plain,
% 163.70/163.95 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), impl(false, tptp_fun_R_5(P!7)))),
% 163.70/163.95 inference(symmetry,[status(thm)],[2132])).
% 163.70/163.95 tff(2136,plain,
% 163.70/163.95 (impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true) = err),
% 163.70/163.95 inference(transitivity,[status(thm)],[1992, 1990, 1976, 1895])).
% 163.70/163.95 tff(2137,plain,
% 163.70/163.95 (phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)) = phi(err)),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2136])).
% 163.70/163.95 tff(2138,plain,
% 163.70/163.95 (~(prop(apply(P!7, tptp_fun_X_3(P!7))) = true)),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[1164, 1125])).
% 163.70/163.95 tff(2139,plain,
% 163.70/163.95 (~bool(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[1123, 2138])).
% 163.70/163.95 tff(2140,plain,
% 163.70/163.95 (apply(P!7, tptp_fun_X_3(P!7)) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[1443, 1429, 2139])).
% 163.70/163.95 tff(2141,plain,
% 163.70/163.95 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = apply(P!7, tptp_fun_X_3(P!7))),
% 163.70/163.95 inference(symmetry,[status(thm)],[2140])).
% 163.70/163.95 tff(2142,plain,
% 163.70/163.95 (phi(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) = phi(apply(P!7, tptp_fun_X_3(P!7)))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2141])).
% 163.70/163.95 tff(2143,plain,
% 163.70/163.95 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true)),
% 163.70/163.95 inference(transitivity,[status(thm)],[975, 1430, 2142, 1125, 1949, 1975, 2005, 1991])).
% 163.70/163.95 tff(2144,plain,
% 163.70/163.95 (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = phi(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), impl(false, true)), true))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2143])).
% 163.70/163.95 tff(2145,plain,
% 163.70/163.95 (f5(P!7, tptp_fun_R_5(P!7)) = impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), impl(false, tptp_fun_R_5(P!7)))),
% 163.70/163.95 inference(transitivity,[status(thm)],[1101, 2144, 2137, 1975, 2005, 1991, 2135])).
% 163.70/163.95 tff(2146,plain,
% 163.70/163.95 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = impl(impl(impl(apply(P!7, tptp_fun_X_3(P!7)), true), impl(false, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2145])).
% 163.70/163.95 tff(2147,assumption,(~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)), introduced(assumption)).
% 163.70/163.95 tff(2148,plain,
% 163.70/163.95 (d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2042, 2147])).
% 163.70/163.95 tff(2149,plain,
% 163.70/163.95 ((~((~d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (~(d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2046, 39])).
% 163.70/163.95 tff(2150,plain,
% 163.70/163.95 (~((~d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2149, 2148])).
% 163.70/163.95 tff(2151,plain,
% 163.70/163.95 (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2048, 2150])).
% 163.70/163.95 tff(2152,plain,
% 163.70/163.95 (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err),
% 163.70/163.95 inference(transitivity,[status(thm)],[2151, 2146, 2134, 1322, 2131, 1976, 1895])).
% 163.70/163.95 tff(2153,plain,
% 163.70/163.95 ($false),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2147, 2152])).
% 163.70/163.95 tff(2154,plain,(bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err) | (~(impl(false, tptp_fun_R_5(P!7)) = true)) | (~(impl(apply(P!7, tptp_fun_X_3(P!7)), true) = phi(apply(P!7, tptp_fun_X_3(P!7))))) | (~(phi(apply(P!7, tptp_fun_X_3(P!7))) = err))), inference(lemma,lemma(discharge,[]))).
% 163.70/163.95 tff(2155,plain,
% 163.70/163.95 (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))) | (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err) | (~(impl(false, tptp_fun_R_5(P!7)) = true))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2154, 1730, 1963])).
% 163.70/163.95 tff(2156,plain,
% 163.70/163.95 (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2155, 2130, 1962])).
% 163.70/163.95 tff(2157,plain,
% 163.70/163.95 ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[1014, 2156])).
% 163.70/163.95 tff(2158,plain,
% 163.70/163.95 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[1088, 2157, 2079])).
% 163.70/163.95 tff(2159,plain,
% 163.70/163.95 (phi(tptp_fun_R_5(P!7)) = true),
% 163.70/163.95 inference(transitivity,[status(thm)],[2035, 1967])).
% 163.70/163.95 tff(2160,plain,
% 163.70/163.95 ((impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))) <=> (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2051, 2159])).
% 163.70/163.95 tff(2161,plain,
% 163.70/163.95 ((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true) <=> (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 163.70/163.95 inference(symmetry,[status(thm)],[2160])).
% 163.70/163.95 tff(2162,plain,
% 163.70/163.95 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = true),
% 163.70/163.95 inference(transitivity,[status(thm)],[1025, 1024, 2035, 1967])).
% 163.70/163.95 tff(2163,plain,
% 163.70/163.95 (f1(true, true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = f1(true, true, true)),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2162])).
% 163.70/163.95 tff(2164,plain,
% 163.70/163.95 (f2(true, apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = f2(true, true, lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[1017, 2073])).
% 163.70/163.95 tff(2165,plain,
% 163.70/163.95 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true),
% 163.70/163.95 inference(transitivity,[status(thm)],[1227, 1219, 2164, 1673, 1671, 1658, 2163, 921, 919, 236, 234])).
% 163.70/163.95 tff(2166,plain,
% 163.70/163.95 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))),
% 163.70/163.95 inference(modus_ponens,[status(thm)],[2165, 2161])).
% 163.70/163.95 tff(2167,plain,
% 163.70/163.95 ($false),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[1866, 2166])).
% 163.70/163.95 tff(2168,plain,((~(tptp_fun_R_5(P!7) = true)) | (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))) | (~(prop(tptp_fun_R_5(P!7)) = true)) | (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true))), inference(lemma,lemma(discharge,[]))).
% 163.70/163.95 tff(2169,plain,
% 163.70/163.95 (~(tptp_fun_R_5(P!7) = true)),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2168, 2158, 1866, 1961])).
% 163.70/163.95 tff(2170,plain,
% 163.70/163.95 (tptp_fun_R_5(P!7) = false),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[1476, 2169, 1960])).
% 163.70/163.95 tff(2171,plain,
% 163.70/163.95 (tptp_fun_X_4(tptp_fun_R_5(P!7), P!7) = tptp_fun_X_4(false, P!7)),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2170])).
% 163.70/163.95 tff(2172,plain,
% 163.70/163.95 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = apply(P!7, tptp_fun_X_4(false, P!7))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2171])).
% 163.70/163.95 tff(2173,plain,
% 163.70/163.95 ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true) <=> (apply(P!7, tptp_fun_X_4(false, P!7)) = true)),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2172])).
% 163.70/163.95 tff(2174,plain,
% 163.70/163.95 (apply(P!7, tptp_fun_X_4(false, P!7)) = true),
% 163.70/163.95 inference(modus_ponens,[status(thm)],[2158, 2173])).
% 163.70/163.95 tff(2175,plain,
% 163.70/163.95 (true = apply(P!7, tptp_fun_X_4(false, P!7))),
% 163.70/163.95 inference(symmetry,[status(thm)],[2174])).
% 163.70/163.95 tff(2176,plain,
% 163.70/163.95 (f1(true, true, false) = f1(apply(P!7, tptp_fun_X_4(false, P!7)), true, false)),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2175])).
% 163.70/163.95 tff(2177,plain,
% 163.70/163.95 (f1(apply(P!7, tptp_fun_X_4(false, P!7)), true, false) = f1(true, true, false)),
% 163.70/163.95 inference(symmetry,[status(thm)],[2176])).
% 163.70/163.95 tff(2178,plain,
% 163.70/163.95 (false = tptp_fun_R_5(P!7)),
% 163.70/163.95 inference(symmetry,[status(thm)],[2170])).
% 163.70/163.95 tff(2179,plain,
% 163.70/163.95 (apply(P!7, tptp_fun_X_4(false, P!7)) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))),
% 163.70/163.95 inference(symmetry,[status(thm)],[2172])).
% 163.70/163.95 tff(2180,plain,
% 163.70/163.95 (f1(apply(P!7, tptp_fun_X_4(false, P!7)), true, false) = f1(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), true, tptp_fun_R_5(P!7))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2179, 2178])).
% 163.70/163.95 tff(2181,plain,
% 163.70/163.95 (f1(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), true, tptp_fun_R_5(P!7)) = f1(apply(P!7, tptp_fun_X_4(false, P!7)), true, false)),
% 163.70/163.95 inference(symmetry,[status(thm)],[2180])).
% 163.70/163.95 tff(2182,plain,
% 163.70/163.95 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), true, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), impl(true, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))))),
% 163.70/163.95 inference(quant_inst,[status(thm)],[])).
% 163.70/163.95 tff(2183,plain,
% 163.70/163.95 (f1(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), true, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), impl(true, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2182, 356])).
% 163.70/163.95 tff(2184,plain,
% 163.70/163.95 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), impl(true, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = f1(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), true, tptp_fun_R_5(P!7))),
% 163.70/163.95 inference(symmetry,[status(thm)],[2183])).
% 163.70/163.95 tff(2185,plain,
% 163.70/163.95 (d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2042, 2130])).
% 163.70/163.95 tff(2186,plain,
% 163.70/163.95 (~((~d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2046, 39, 2185])).
% 163.70/163.95 tff(2187,plain,
% 163.70/163.95 (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2048, 2186])).
% 163.70/163.95 tff(2188,plain,
% 163.70/163.95 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.95 inference(symmetry,[status(thm)],[2187])).
% 163.70/163.95 tff(2189,plain,
% 163.70/163.95 (impl(true, false) = tptp_fun_R_5(P!7)),
% 163.70/163.95 inference(transitivity,[status(thm)],[86, 2178])).
% 163.70/163.95 tff(2190,plain,
% 163.70/163.95 (impl(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), impl(true, false)) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[1220, 2189])).
% 163.70/163.95 tff(2191,plain,
% 163.70/163.95 (tptp_fun_R_5(P!7) = impl(true, false)),
% 163.70/163.95 inference(transitivity,[status(thm)],[2170, 1452])).
% 163.70/163.95 tff(2192,plain,
% 163.70/163.95 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.70/163.95 inference(transitivity,[status(thm)],[976, 1930])).
% 163.70/163.95 tff(2193,plain,
% 163.70/163.95 (impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = impl(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))), impl(true, false))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2192, 2191])).
% 163.70/163.95 tff(2194,plain,
% 163.70/163.95 (impl(true, tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[953, 1959])).
% 163.70/163.95 tff(2195,plain,
% 163.70/163.95 (impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), impl(true, tptp_fun_R_5(P!7))) = impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2194])).
% 163.70/163.95 tff(2196,plain,
% 163.70/163.95 (impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), impl(true, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2195])).
% 163.70/163.95 tff(2197,plain,
% 163.70/163.95 (impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), impl(true, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)) = f6(P!7, tptp_fun_R_5(P!7))),
% 163.70/163.95 inference(transitivity,[status(thm)],[2196, 2193, 2190, 2188, 1412, 2118, 566])).
% 163.70/163.95 tff(2198,plain,
% 163.70/163.95 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), impl(true, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7))) = lazy_impl(true, f6(P!7, tptp_fun_R_5(P!7)))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[1961, 2197])).
% 163.70/163.95 tff(2199,plain,
% 163.70/163.95 (lazy_impl(true, f6(P!7, tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(impl(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)), impl(true, tptp_fun_R_5(P!7))), tptp_fun_R_5(P!7)))),
% 163.70/163.95 inference(symmetry,[status(thm)],[2198])).
% 163.70/163.95 tff(2200,plain,
% 163.70/163.95 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, f6(P!7, tptp_fun_R_5(P!7))) = phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 163.70/163.95 inference(quant_inst,[status(thm)],[])).
% 163.70/163.95 tff(2201,plain,
% 163.70/163.95 (lazy_impl(true, f6(P!7, tptp_fun_R_5(P!7))) = phi(f6(P!7, tptp_fun_R_5(P!7)))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2200, 118])).
% 163.70/163.95 tff(2202,plain,
% 163.70/163.95 (phi(f6(P!7, tptp_fun_R_5(P!7))) = lazy_impl(true, f6(P!7, tptp_fun_R_5(P!7)))),
% 163.70/163.95 inference(symmetry,[status(thm)],[2201])).
% 163.70/163.95 tff(2203,plain,
% 163.70/163.95 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true),
% 163.70/163.95 inference(transitivity,[status(thm)],[566, 1851, 2202, 2199, 2184, 2181, 2177, 1648, 1864, 236, 234])).
% 163.70/163.95 tff(2204,plain,
% 163.70/163.95 ($false),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[1865, 2203])).
% 163.70/163.95 tff(2205,plain,((impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true) | (~(impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(phi(f6(P!7, tptp_fun_R_5(P!7))))))), inference(lemma,lemma(discharge,[]))).
% 163.70/163.95 tff(2206,plain,
% 163.70/163.95 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2205, 1860, 1847, 1835])).
% 163.70/163.95 tff(2207,plain,
% 163.70/163.95 (phi(tptp_fun_R_5(P!7)) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.95 inference(symmetry,[status(thm)],[2206])).
% 163.70/163.95 tff(2208,plain,
% 163.70/163.95 (false = prop(tptp_fun_R_5(P!7))),
% 163.70/163.95 inference(symmetry,[status(thm)],[571])).
% 163.70/163.95 tff(2209,plain,
% 163.70/163.95 (lazy_impl(false, impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2208])).
% 163.70/163.95 tff(2210,plain,
% 163.70/163.95 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(false, impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.95 inference(symmetry,[status(thm)],[2209])).
% 163.70/163.95 tff(2211,plain,
% 163.70/163.95 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true),
% 163.70/163.95 inference(transitivity,[status(thm)],[2210, 570])).
% 163.70/163.95 tff(2212,plain,
% 163.70/163.95 ($false),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[1865, 2211])).
% 163.70/163.95 tff(2213,plain,((~(prop(tptp_fun_R_5(P!7)) = false)) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)), inference(lemma,lemma(discharge,[]))).
% 163.70/163.95 tff(2214,plain,
% 163.70/163.95 (~(prop(tptp_fun_R_5(P!7)) = false)),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2213, 1860])).
% 163.70/163.95 tff(2215,plain,
% 163.70/163.95 (bool(tptp_fun_R_5(P!7))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[1726, 2214])).
% 163.70/163.95 tff(2216,plain,
% 163.70/163.95 (prop(tptp_fun_R_5(P!7)) = true),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[958, 2215])).
% 163.70/163.95 tff(2217,plain,
% 163.70/163.95 (~(phi(tptp_fun_R_5(P!7)) = err)),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2031, 2216])).
% 163.70/163.95 tff(2218,plain,
% 163.70/163.95 (d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[1909, 2217])).
% 163.70/163.95 tff(2219,plain,
% 163.70/163.95 (~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[1914, 2218])).
% 163.70/163.95 tff(2220,plain,
% 163.70/163.95 (phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[1916, 2219])).
% 163.70/163.95 tff(2221,plain,
% 163.70/163.95 (tptp_fun_R_5(P!7) = phi(tptp_fun_R_5(P!7))),
% 163.70/163.95 inference(symmetry,[status(thm)],[2220])).
% 163.70/163.95 tff(2222,plain,
% 163.70/163.95 (tptp_fun_R_5(P!7) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.95 inference(transitivity,[status(thm)],[2221, 2207])).
% 163.70/163.95 tff(2223,plain,
% 163.70/163.95 (true = prop(tptp_fun_R_5(P!7))),
% 163.70/163.95 inference(symmetry,[status(thm)],[2216])).
% 163.70/163.95 tff(2224,plain,
% 163.70/163.95 (lazy_impl(true, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2223, 2222])).
% 163.70/163.95 tff(2225,plain,
% 163.70/163.95 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = lazy_impl(true, tptp_fun_R_5(P!7))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2216])).
% 163.70/163.95 tff(2226,plain,
% 163.70/163.95 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.95 inference(transitivity,[status(thm)],[2225, 2224, 566, 1851, 1853, 1848])).
% 163.70/163.95 tff(2227,plain,
% 163.70/163.95 (bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) <=> bool(impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2226])).
% 163.70/163.95 tff(2228,plain,
% 163.70/163.95 (bool(impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.95 inference(symmetry,[status(thm)],[2227])).
% 163.70/163.95 tff(2229,plain,
% 163.70/163.95 ((~bool(impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) <=> (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2228])).
% 163.70/163.95 tff(2230,plain,
% 163.70/163.95 (f6(P!7, tptp_fun_R_5(P!7)) = impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.95 inference(transitivity,[status(thm)],[1851, 1853, 1848])).
% 163.70/163.95 tff(2231,plain,
% 163.70/163.95 (bool(f6(P!7, tptp_fun_R_5(P!7))) <=> bool(impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2230])).
% 163.70/163.95 tff(2232,plain,
% 163.70/163.95 ((~bool(f6(P!7, tptp_fun_R_5(P!7)))) <=> (~bool(impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2231])).
% 163.70/163.95 tff(2233,plain,
% 163.70/163.95 (~bool(impl(impl(true, phi(f6(P!7, tptp_fun_R_5(P!7)))), impl(impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.95 inference(modus_ponens,[status(thm)],[1841, 2232])).
% 163.70/163.95 tff(2234,plain,
% 163.70/163.95 (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.95 inference(modus_ponens,[status(thm)],[2233, 2229])).
% 163.70/163.95 tff(2235,plain,
% 163.70/163.95 ($false),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[1084, 2234])).
% 163.70/163.95 tff(2236,plain,(bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))), inference(lemma,lemma(discharge,[]))).
% 163.70/163.95 tff(2237,plain,
% 163.70/163.95 (((~d(f6(P!7, tptp_fun_R_5(P!7)))) | (~(phi(f6(P!7, tptp_fun_R_5(P!7))) = f6(P!7, tptp_fun_R_5(P!7))))) | d(f6(P!7, tptp_fun_R_5(P!7)))),
% 163.70/163.95 inference(tautology,[status(thm)],[])).
% 163.70/163.95 tff(2238,plain,
% 163.70/163.95 (d(f6(P!7, tptp_fun_R_5(P!7)))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2237, 1805])).
% 163.70/163.95 tff(2239,plain,
% 163.70/163.95 (d(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.70/163.95 inference(modus_ponens,[status(thm)],[2238, 568])).
% 163.70/163.95 tff(2240,plain,
% 163.70/163.95 (d(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[622, 2239])).
% 163.70/163.95 tff(2241,plain,
% 163.70/163.95 ((~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | bool(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[627, 2240, 2239])).
% 163.70/163.95 tff(2242,plain,
% 163.70/163.95 (bool(lazy_impl(prop(false), impl(f5(P!7, false), false)))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2241, 2236])).
% 163.70/163.95 tff(2243,plain,
% 163.70/163.95 ((~(bool(lazy_impl(prop(false), impl(f5(P!7, false), false))) <=> ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = true)))) | ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = true))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[629, 2242])).
% 163.70/163.95 tff(2244,plain,
% 163.70/163.95 ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = true)),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2243, 556])).
% 163.70/163.95 tff(2245,plain,
% 163.70/163.95 ((lazy_impl(prop(false), impl(f5(P!7, false), false)) = false) | (lazy_impl(prop(false), impl(f5(P!7, false), false)) = true)),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[638, 2244])).
% 163.70/163.95 tff(2246,plain,
% 163.70/163.95 (lazy_impl(prop(false), impl(f5(P!7, false), false)) = false),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2245, 1792])).
% 163.70/163.95 tff(2247,plain,
% 163.70/163.95 (~(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[636, 2246])).
% 163.70/163.95 tff(2248,plain,
% 163.70/163.95 ((~(bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) <=> ((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)))) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | ((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true))),
% 163.70/163.95 inference(tautology,[status(thm)],[])).
% 163.70/163.95 tff(2249,plain,
% 163.70/163.95 ((~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))) | ((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2248, 1855])).
% 163.70/163.95 tff(2250,plain,
% 163.70/163.95 ((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2249, 2236])).
% 163.70/163.95 tff(2251,plain,
% 163.70/163.95 ((~((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true))) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)),
% 163.70/163.95 inference(tautology,[status(thm)],[])).
% 163.70/163.95 tff(2252,plain,
% 163.70/163.95 ((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false) | (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true)),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2251, 2250])).
% 163.70/163.95 tff(2253,plain,
% 163.70/163.95 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2252, 2247])).
% 163.70/163.95 tff(2254,plain,
% 163.70/163.95 ((~![X: $i] : ((prop(X) = true) <=> bool(X))) | ((prop(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = true) <=> bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 163.70/163.95 inference(quant_inst,[status(thm)],[])).
% 163.70/163.95 tff(2255,plain,
% 163.70/163.95 ((prop(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = true) <=> bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2254, 19])).
% 163.70/163.95 tff(2256,plain,
% 163.70/163.95 ((~((prop(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = true) <=> bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))) | (prop(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = true) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 163.70/163.95 inference(tautology,[status(thm)],[])).
% 163.70/163.95 tff(2257,plain,
% 163.70/163.95 ((prop(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = true) | (~bool(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2256, 2255])).
% 163.70/163.95 tff(2258,plain,
% 163.70/163.95 (prop(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) = true),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2257, 2236])).
% 163.70/163.95 tff(2259,plain,
% 163.70/163.95 (phi(f6(P!7, tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.95 inference(transitivity,[status(thm)],[1807, 565])).
% 163.70/163.95 tff(2260,plain,
% 163.70/163.95 (prop(phi(f6(P!7, tptp_fun_R_5(P!7)))) = prop(lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2259])).
% 163.70/163.95 tff(2261,plain,
% 163.70/163.95 (prop(phi(f6(P!7, tptp_fun_R_5(P!7)))) = true),
% 163.70/163.95 inference(transitivity,[status(thm)],[2260, 2258])).
% 163.70/163.95 tff(2262,plain,
% 163.70/163.95 (lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = lazy_impl(true, f6(P!7, tptp_fun_R_5(P!7)))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2261, 1807])).
% 163.70/163.95 tff(2263,plain,
% 163.70/163.95 (lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = false),
% 163.70/163.95 inference(transitivity,[status(thm)],[2262, 2201, 1807, 565, 2253])).
% 163.70/163.95 tff(2264,plain,
% 163.70/163.95 (tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7) = tptp_fun_X_4(false, P!7)),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2263])).
% 163.70/163.95 tff(2265,plain,
% 163.70/163.95 (f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = f4(P!7, tptp_fun_X_4(false, P!7), false)),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2264, 2263])).
% 163.70/163.95 tff(2266,plain,
% 163.70/163.95 (d(f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> d(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 163.70/163.95 inference(monotonicity,[status(thm)],[2265])).
% 163.70/163.95 tff(2267,plain,
% 163.70/163.95 (d(f4(P!7, tptp_fun_X_4(false, P!7), false)) <=> d(f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.95 inference(symmetry,[status(thm)],[2266])).
% 163.70/163.95 tff(2268,plain,
% 163.70/163.95 (~(prop(tptp_fun_R_5(P!7)) = false)),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[2213, 2247])).
% 163.70/163.95 tff(2269,plain,
% 163.70/163.95 (bool(tptp_fun_R_5(P!7))),
% 163.70/163.95 inference(unit_resolution,[status(thm)],[1726, 2268])).
% 163.70/163.95 tff(2270,plain,
% 163.70/163.95 (prop(tptp_fun_R_5(P!7)) = true),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[958, 2269])).
% 163.70/163.96 tff(2271,plain,
% 163.70/163.96 (~(phi(tptp_fun_R_5(P!7)) = err)),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[2031, 2270])).
% 163.70/163.96 tff(2272,plain,
% 163.70/163.96 (d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err))),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[1909, 2271])).
% 163.70/163.96 tff(2273,plain,
% 163.70/163.96 (~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[1913, 39, 2272])).
% 163.70/163.96 tff(2274,plain,
% 163.70/163.96 (phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[1916, 2273])).
% 163.70/163.96 tff(2275,plain,
% 163.70/163.96 (true = prop(tptp_fun_R_5(P!7))),
% 163.70/163.96 inference(symmetry,[status(thm)],[2270])).
% 163.70/163.96 tff(2276,plain,
% 163.70/163.96 (lazy_impl(true, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.96 inference(monotonicity,[status(thm)],[2275])).
% 163.70/163.96 tff(2277,plain,
% 163.70/163.96 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = lazy_impl(true, tptp_fun_R_5(P!7))),
% 163.70/163.96 inference(symmetry,[status(thm)],[2276])).
% 163.70/163.96 tff(2278,plain,
% 163.70/163.96 (phi(tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.96 inference(transitivity,[status(thm)],[2071, 2276])).
% 163.70/163.96 tff(2279,plain,
% 163.70/163.96 (lazy_impl(true, impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.96 inference(monotonicity,[status(thm)],[2275])).
% 163.70/163.96 tff(2280,plain,
% 163.70/163.96 (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false),
% 163.70/163.96 inference(transitivity,[status(thm)],[1412, 2279, 2253])).
% 163.70/163.96 tff(2281,plain,
% 163.70/163.96 ((phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err) <=> (false = err)),
% 163.70/163.96 inference(monotonicity,[status(thm)],[2280])).
% 163.70/163.96 tff(2282,plain,
% 163.70/163.96 ((false = err) <=> (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 163.70/163.96 inference(symmetry,[status(thm)],[2281])).
% 163.70/163.96 tff(2283,plain,
% 163.70/163.96 ((~(false = err)) <=> (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))),
% 163.70/163.96 inference(monotonicity,[status(thm)],[2282])).
% 163.70/163.96 tff(2284,plain,
% 163.70/163.96 (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 163.70/163.96 inference(modus_ponens,[status(thm)],[692, 2283])).
% 163.70/163.96 tff(2285,plain,
% 163.70/163.96 (d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[2042, 2284])).
% 163.70/163.96 tff(2286,plain,
% 163.70/163.96 (~((~d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[2046, 39, 2285])).
% 163.70/163.96 tff(2287,plain,
% 163.70/163.96 (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[2048, 2286])).
% 163.70/163.96 tff(2288,plain,
% 163.70/163.96 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.96 inference(symmetry,[status(thm)],[2287])).
% 163.70/163.96 tff(2289,plain,
% 163.70/163.96 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false),
% 163.70/163.96 inference(transitivity,[status(thm)],[2288, 1412, 2279, 2253])).
% 163.70/163.96 tff(2290,plain,
% 163.70/163.96 ((impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))) <=> (false = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.96 inference(monotonicity,[status(thm)],[2289, 2278])).
% 163.70/163.96 tff(2291,plain,
% 163.70/163.96 ((impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))) <=> (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)),
% 163.70/163.96 inference(transitivity,[status(thm)],[2290, 1231])).
% 163.70/163.96 tff(2292,plain,
% 163.70/163.96 (bool(tptp_fun_R_5(P!7))),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[1958, 1865, 1866])).
% 163.70/163.96 tff(2293,plain,
% 163.70/163.96 (prop(tptp_fun_R_5(P!7)) = true),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[958, 2292])).
% 163.70/163.96 tff(2294,plain,
% 163.70/163.96 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = lazy_impl(true, tptp_fun_R_5(P!7))),
% 163.70/163.96 inference(monotonicity,[status(thm)],[2293])).
% 163.70/163.96 tff(2295,plain,
% 163.70/163.96 (lazy_impl(true, tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.96 inference(symmetry,[status(thm)],[2294])).
% 163.70/163.96 tff(2296,plain,
% 163.70/163.96 (phi(tptp_fun_R_5(P!7)) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.96 inference(transitivity,[status(thm)],[2071, 2295])).
% 163.70/163.96 tff(2297,plain,
% 163.70/163.96 (lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[2252, 1865])).
% 163.70/163.96 tff(2298,plain,
% 163.70/163.96 (true = prop(tptp_fun_R_5(P!7))),
% 163.70/163.96 inference(symmetry,[status(thm)],[2293])).
% 163.70/163.96 tff(2299,plain,
% 163.70/163.96 (lazy_impl(true, impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.96 inference(monotonicity,[status(thm)],[2298])).
% 163.70/163.96 tff(2300,plain,
% 163.70/163.96 (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = false),
% 163.70/163.96 inference(transitivity,[status(thm)],[1412, 2299, 2297])).
% 163.70/163.96 tff(2301,plain,
% 163.70/163.96 ((phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err) <=> (false = err)),
% 163.70/163.96 inference(monotonicity,[status(thm)],[2300])).
% 163.70/163.96 tff(2302,plain,
% 163.70/163.96 ((false = err) <=> (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 163.70/163.96 inference(symmetry,[status(thm)],[2301])).
% 163.70/163.96 tff(2303,plain,
% 163.70/163.96 ((~(false = err)) <=> (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))),
% 163.70/163.96 inference(monotonicity,[status(thm)],[2302])).
% 163.70/163.96 tff(2304,plain,
% 163.70/163.96 (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err)),
% 163.70/163.96 inference(modus_ponens,[status(thm)],[692, 2303])).
% 163.70/163.96 tff(2305,plain,
% 163.70/163.96 (d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = err))),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[2042, 2304])).
% 163.70/163.96 tff(2306,plain,
% 163.70/163.96 (~((~d(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))))),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[2046, 39, 2305])).
% 163.70/163.96 tff(2307,plain,
% 163.70/163.96 (phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[2048, 2306])).
% 163.70/163.96 tff(2308,plain,
% 163.70/163.96 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.96 inference(symmetry,[status(thm)],[2307])).
% 163.70/163.96 tff(2309,plain,
% 163.70/163.96 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false),
% 163.70/163.96 inference(transitivity,[status(thm)],[2308, 1412, 2299, 2297])).
% 163.70/163.96 tff(2310,plain,
% 163.70/163.96 ((impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))) <=> (false = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))),
% 163.70/163.96 inference(monotonicity,[status(thm)],[2309, 2296])).
% 163.70/163.96 tff(2311,plain,
% 163.70/163.96 ((impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))) <=> (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)),
% 163.70/163.96 inference(transitivity,[status(thm)],[2310, 1231])).
% 163.70/163.96 tff(2312,plain,
% 163.70/163.96 ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) <=> (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))),
% 163.70/163.96 inference(symmetry,[status(thm)],[2311])).
% 163.70/163.96 tff(2313,plain,
% 163.70/163.96 ((tptp_fun_R_5(P!7) = false) | (tptp_fun_R_5(P!7) = true)),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[926, 2292])).
% 163.70/163.96 tff(2314,plain,
% 163.70/163.96 (impl(false, tptp_fun_R_5(P!7)) = true),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[948, 2292])).
% 163.70/163.96 tff(2315,plain,
% 163.70/163.96 (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false)),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[2078, 2293, 1866, 2313, 2314])).
% 163.70/163.96 tff(2316,plain,
% 163.70/163.96 (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[2155, 2304, 2314])).
% 163.70/163.96 tff(2317,plain,
% 163.70/163.96 ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[1014, 2316])).
% 163.70/163.96 tff(2318,plain,
% 163.70/163.96 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[1088, 2317, 2315])).
% 163.70/163.96 tff(2319,plain,
% 163.70/163.96 (~(tptp_fun_R_5(P!7) = true)),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[2168, 2318, 1866, 2293])).
% 163.70/163.96 tff(2320,plain,
% 163.70/163.96 (tptp_fun_R_5(P!7) = false),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[1476, 2319, 2313])).
% 163.70/163.96 tff(2321,plain,
% 163.70/163.96 (~(phi(tptp_fun_R_5(P!7)) = err)),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[2031, 2293])).
% 163.70/163.96 tff(2322,plain,
% 163.70/163.96 (d(tptp_fun_R_5(P!7)) | (~(phi(tptp_fun_R_5(P!7)) = err))),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[1909, 2321])).
% 163.70/163.96 tff(2323,plain,
% 163.70/163.96 (~((~d(tptp_fun_R_5(P!7))) | (~(phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7))))),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[1913, 39, 2322])).
% 163.70/163.96 tff(2324,plain,
% 163.70/163.96 (phi(tptp_fun_R_5(P!7)) = tptp_fun_R_5(P!7)),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[1916, 2323])).
% 163.70/163.96 tff(2325,plain,
% 163.70/163.96 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false),
% 163.70/163.96 inference(transitivity,[status(thm)],[2294, 1024, 2324, 2320])).
% 163.70/163.96 tff(2326,plain,
% 163.70/163.96 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))),
% 163.70/163.96 inference(modus_ponens,[status(thm)],[2325, 2312])).
% 163.70/163.96 tff(2327,plain,
% 163.70/163.96 ($false),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[1866, 2326])).
% 163.70/163.96 tff(2328,plain,((lazy_impl(prop(tptp_fun_R_5(P!7)), impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = true) | (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7)))), inference(lemma,lemma(discharge,[]))).
% 163.70/163.96 tff(2329,plain,
% 163.70/163.96 (impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(tptp_fun_R_5(P!7))),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[2328, 2247])).
% 163.70/163.96 tff(2330,plain,
% 163.70/163.96 (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false),
% 163.70/163.96 inference(modus_ponens,[status(thm)],[2329, 2291])).
% 163.70/163.96 tff(2331,plain,
% 163.70/163.96 (false = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.96 inference(symmetry,[status(thm)],[2330])).
% 163.70/163.96 tff(2332,plain,
% 163.70/163.96 (false = tptp_fun_R_5(P!7)),
% 163.70/163.96 inference(transitivity,[status(thm)],[2331, 2277, 1024, 2274])).
% 163.70/163.96 tff(2333,plain,
% 163.70/163.96 (tptp_fun_R_5(P!7) = phi(tptp_fun_R_5(P!7))),
% 163.70/163.96 inference(symmetry,[status(thm)],[2274])).
% 163.70/163.96 tff(2334,plain,
% 163.70/163.96 (tptp_fun_R_5(P!7) = false),
% 163.70/163.96 inference(transitivity,[status(thm)],[2333, 2071, 2276, 2330])).
% 163.70/163.96 tff(2335,plain,
% 163.70/163.96 (tptp_fun_X_4(tptp_fun_R_5(P!7), P!7) = tptp_fun_X_4(false, P!7)),
% 163.70/163.96 inference(monotonicity,[status(thm)],[2334])).
% 163.70/163.96 tff(2336,plain,
% 163.70/163.96 (tptp_fun_X_4(false, P!7) = tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)),
% 163.70/163.96 inference(symmetry,[status(thm)],[2335])).
% 163.70/163.96 tff(2337,plain,
% 163.70/163.96 (f4(P!7, tptp_fun_X_4(false, P!7), false) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))),
% 163.70/163.96 inference(monotonicity,[status(thm)],[2336, 2332])).
% 163.70/163.96 tff(2338,plain,
% 163.70/163.96 (f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)) = f4(P!7, tptp_fun_X_4(false, P!7), false)),
% 163.70/163.96 inference(symmetry,[status(thm)],[2337])).
% 163.70/163.96 tff(2339,plain,
% 163.70/163.96 (d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> d(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 163.70/163.96 inference(monotonicity,[status(thm)],[2338])).
% 163.70/163.96 tff(2340,plain,
% 163.70/163.96 (d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) <=> d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.96 inference(transitivity,[status(thm)],[2339, 2267, 12])).
% 163.70/163.96 tff(2341,plain,
% 163.70/163.96 (tptp_fun_R_5(P!7) = lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))),
% 163.70/163.96 inference(transitivity,[status(thm)],[2333, 2071, 2276])).
% 163.70/163.96 tff(2342,plain,
% 163.70/163.96 ((tptp_fun_R_5(P!7) = false) <=> (lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false)),
% 163.70/163.96 inference(monotonicity,[status(thm)],[2341])).
% 163.70/163.96 tff(2343,plain,
% 163.70/163.96 ((lazy_impl(prop(tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = false) <=> (tptp_fun_R_5(P!7) = false)),
% 163.70/163.96 inference(symmetry,[status(thm)],[2342])).
% 163.70/163.96 tff(2344,plain,
% 163.70/163.96 (tptp_fun_R_5(P!7) = false),
% 163.70/163.96 inference(modus_ponens,[status(thm)],[2330, 2343])).
% 163.70/163.96 tff(2345,plain,
% 163.70/163.96 (impl(false, tptp_fun_R_5(P!7)) = true),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[948, 2269])).
% 163.70/163.96 tff(2346,plain,
% 163.70/163.96 (bool(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)))),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[2155, 2284, 2345])).
% 163.70/163.96 tff(2347,plain,
% 163.70/163.96 ((apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false) | (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[1014, 2346])).
% 163.70/163.96 tff(2348,plain,
% 163.70/163.96 (apply(P!7, tptp_fun_X_4(false, P!7)) = apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7))),
% 163.70/163.96 inference(monotonicity,[status(thm)],[2336])).
% 163.70/163.96 tff(2349,plain,
% 163.70/163.96 ((apply(P!7, tptp_fun_X_4(false, P!7)) = true) <=> (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)),
% 163.70/163.96 inference(monotonicity,[status(thm)],[2348])).
% 163.70/163.96 tff(2350,plain,
% 163.70/163.96 ((~(apply(P!7, tptp_fun_X_4(false, P!7)) = true)) <=> (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true))),
% 163.70/163.96 inference(monotonicity,[status(thm)],[2349])).
% 163.70/163.96 tff(2351,plain,
% 163.70/163.96 (~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = true)),
% 163.70/163.96 inference(modus_ponens,[status(thm)],[1784, 2350])).
% 163.70/163.96 tff(2352,plain,
% 163.70/163.96 (apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[1088, 2351, 2347])).
% 163.70/163.96 tff(2353,plain,
% 163.70/163.96 ((~(apply(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7)) = false)) | (~(phi(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7))) = impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)))) | (~(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7))))) | (~(prop(tptp_fun_R_5(P!7)) = true)) | (~(tptp_fun_R_5(P!7) = false))),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[1474, 1929])).
% 163.70/163.96 tff(2354,plain,
% 163.70/163.96 (~(impl(f5(P!7, tptp_fun_R_5(P!7)), tptp_fun_R_5(P!7)) = phi(f5(P!7, tptp_fun_R_5(P!7))))),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[2353, 2352, 2344, 2270, 2287])).
% 163.70/163.96 tff(2355,plain,
% 163.70/163.96 (bool(f5(P!7, tptp_fun_R_5(P!7)))),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[1885, 2354])).
% 163.70/163.96 tff(2356,assumption,(bool(f5(P!7, tptp_fun_R_5(P!7)))), introduced(assumption)).
% 163.70/163.96 tff(2357,plain,
% 163.70/163.96 (bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 163.70/163.96 inference(modus_ponens,[status(thm)],[2356, 1345])).
% 163.70/163.96 tff(2358,assumption,(~bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))), introduced(assumption)).
% 163.70/163.96 tff(2359,plain,
% 163.70/163.96 ($false),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[2358, 2357])).
% 163.70/163.96 tff(2360,plain,((~bool(f5(P!7, tptp_fun_R_5(P!7)))) | bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))), inference(lemma,lemma(discharge,[]))).
% 163.70/163.96 tff(2361,plain,
% 163.70/163.96 (bool(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))))),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[2360, 2355])).
% 163.70/163.96 tff(2362,plain,
% 163.70/163.96 ((phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = false) | (phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = true)),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[1359, 2361])).
% 163.70/163.96 tff(2363,plain,
% 163.70/163.96 (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err)),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[1374, 2362])).
% 163.70/163.96 tff(2364,plain,
% 163.70/163.96 (d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = err))),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[972, 2363])).
% 163.70/163.96 tff(2365,plain,
% 163.70/163.96 (~((~d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))) | (~(phi(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7))) = f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))))),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[970, 2364])).
% 163.70/163.96 tff(2366,plain,
% 163.70/163.96 (d(f4(P!7, tptp_fun_X_4(tptp_fun_R_5(P!7), P!7), tptp_fun_R_5(P!7)))),
% 163.70/163.96 inference(unit_resolution,[status(thm)],[1341, 2365])).
% 163.70/163.96 tff(2367,plain,
% 163.70/163.96 (d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.96 inference(modus_ponens,[status(thm)],[2366, 2340])).
% 163.70/163.96 tff(2368,plain,
% 163.70/163.96 (bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> bool(f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.96 inference(monotonicity,[status(thm)],[10])).
% 163.70/163.96 tff(2369,plain,
% 163.70/163.96 (bool(f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.96 inference(symmetry,[status(thm)],[2368])).
% 163.70/163.96 tff(2370,plain,
% 163.70/163.96 (bool(f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> bool(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 163.70/163.96 inference(monotonicity,[status(thm)],[2265])).
% 163.70/163.96 tff(2371,plain,
% 163.70/163.96 (bool(f4(P!7, tptp_fun_X_4(false, P!7), false)) <=> bool(f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.96 inference(symmetry,[status(thm)],[2370])).
% 163.70/163.96 tff(2372,plain,
% 163.70/163.96 (f5(P!7, false) = f5(P!7, tptp_fun_R_5(P!7))),
% 163.70/163.96 inference(monotonicity,[status(thm)],[2332])).
% 163.70/163.96 tff(2373,plain,
% 163.70/163.96 (f5(P!7, tptp_fun_R_5(P!7)) = f5(P!7, false)),
% 163.70/163.96 inference(symmetry,[status(thm)],[2372])).
% 163.70/163.96 tff(2374,plain,
% 163.70/163.96 (f4(P!7, tptp_fun_X_4(false, P!7), false) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 163.70/163.96 inference(transitivity,[status(thm)],[2337, 1930, 1220, 2373, 103])).
% 163.70/163.96 tff(2375,plain,
% 163.70/163.96 (bool(f4(P!7, tptp_fun_X_4(false, P!7), false)) <=> bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.70/163.96 inference(monotonicity,[status(thm)],[2374])).
% 163.70/163.96 tff(2376,plain,
% 163.70/163.96 (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) <=> bool(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 163.70/163.96 inference(symmetry,[status(thm)],[2375])).
% 163.70/163.96 tff(2377,plain,
% 163.70/163.96 (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false))) <=> bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.96 inference(transitivity,[status(thm)],[2376, 2371, 2369])).
% 163.70/163.96 tff(2378,plain,
% 163.70/163.96 (f5(P!7, tptp_fun_R_5(P!7)) = phi(f4(P!7, tptp_fun_X_4(false, P!7), false))),
% 163.70/163.96 inference(transitivity,[status(thm)],[2373, 103])).
% 163.70/163.96 tff(2379,plain,
% 163.70/163.96 (bool(f5(P!7, tptp_fun_R_5(P!7))) <=> bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.70/163.96 inference(monotonicity,[status(thm)],[2378])).
% 163.70/163.96 tff(2380,plain,
% 163.70/163.96 (bool(phi(f4(P!7, tptp_fun_X_4(false, P!7), false)))),
% 163.70/163.96 inference(modus_ponens,[status(thm)],[2355, 2379])).
% 163.70/163.96 tff(2381,plain,
% 163.70/163.96 (bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.96 inference(modus_ponens,[status(thm)],[2380, 2377])).
% 163.70/163.96 tff(2382,plain,
% 163.70/163.96 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(err, impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> ((~((~(err = false)) | (~(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = true)))) | (~(d(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))) | (~((~d(err)) | bool(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(err, impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> ((~((~(err = false)) | (~(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = true)))) | (~(d(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))) | (~((~d(err)) | bool(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))))))),
% 163.70/163.96 inference(rewrite,[status(thm)],[])).
% 163.70/163.96 tff(2383,plain,
% 163.70/163.96 ((forallprefers(err, impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> ((~((~(err = false)) | (~(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = true)))) | (~(d(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | bool(err) | (~d(err)))))) <=> (forallprefers(err, impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> ((~((~(err = false)) | (~(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = true)))) | (~(d(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))) | (~((~d(err)) | bool(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))))))),
% 163.70/163.96 inference(rewrite,[status(thm)],[])).
% 163.70/163.96 tff(2384,plain,
% 163.70/163.96 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(err, impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> ((~((~(err = false)) | (~(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = true)))) | (~(d(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | bool(err) | (~d(err))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(err, impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> ((~((~(err = false)) | (~(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = true)))) | (~(d(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))) | (~((~d(err)) | bool(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))))))),
% 163.70/163.96 inference(monotonicity,[status(thm)],[2383])).
% 163.70/163.96 tff(2385,plain,
% 163.70/163.96 (((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(err, impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> ((~((~(err = false)) | (~(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = true)))) | (~(d(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | bool(err) | (~d(err))))))) <=> ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(err, impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> ((~((~(err = false)) | (~(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = true)))) | (~(d(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))) | (~((~d(err)) | bool(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))))))),
% 163.70/163.96 inference(transitivity,[status(thm)],[2384, 2382])).
% 163.70/163.96 tff(2386,plain,
% 163.70/163.96 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(err, impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> ((~((~(err = false)) | (~(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = true)))) | (~(d(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))) | (~((~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | bool(err) | (~d(err))))))),
% 163.70/163.97 inference(quant_inst,[status(thm)],[])).
% 163.70/163.97 tff(2387,plain,
% 163.70/163.97 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | (forallprefers(err, impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> ((~((~(err = false)) | (~(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = true)))) | (~(d(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))) | (~((~d(err)) | bool(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))))))),
% 163.70/163.97 inference(modus_ponens,[status(thm)],[2386, 2385])).
% 163.70/163.97 tff(2388,plain,
% 163.70/163.97 (forallprefers(err, impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> ((~((~(err = false)) | (~(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = true)))) | (~(d(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))) | (~((~d(err)) | bool(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))))),
% 163.70/163.97 inference(unit_resolution,[status(thm)],[2387, 165])).
% 163.70/163.97 tff(2389,plain,
% 163.70/163.97 (lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))) = phi(f6(P!7, tptp_fun_R_5(P!7)))),
% 163.70/163.97 inference(transitivity,[status(thm)],[2262, 2201])).
% 163.70/163.97 tff(2390,plain,
% 163.70/163.97 (f4(P!7, tptp_fun_X_3(P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = f4(P!7, tptp_fun_X_3(P!7), phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 163.70/163.97 inference(monotonicity,[status(thm)],[2389])).
% 163.70/163.97 tff(2391,plain,
% 163.70/163.97 (f4(P!7, tptp_fun_X_3(P!7), phi(f6(P!7, tptp_fun_R_5(P!7)))) = f4(P!7, tptp_fun_X_3(P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.97 inference(symmetry,[status(thm)],[2390])).
% 163.70/163.97 tff(2392,plain,
% 163.70/163.97 ((~![P: $i, X: $i, R: $i] : (f4(P, X, R) = impl(apply(P, X), R))) | (f4(P!7, tptp_fun_X_3(P!7), phi(f6(P!7, tptp_fun_R_5(P!7)))) = impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.97 inference(quant_inst,[status(thm)],[])).
% 163.70/163.97 tff(2393,plain,
% 163.70/163.97 (f4(P!7, tptp_fun_X_3(P!7), phi(f6(P!7, tptp_fun_R_5(P!7)))) = impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 163.70/163.97 inference(unit_resolution,[status(thm)],[2392, 7])).
% 163.70/163.97 tff(2394,plain,
% 163.70/163.97 (impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7)))) = f4(P!7, tptp_fun_X_3(P!7), phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 163.70/163.97 inference(symmetry,[status(thm)],[2393])).
% 163.70/163.97 tff(2395,plain,
% 163.70/163.97 (phi(apply(P!7, tptp_fun_X_3(P!7))) = impl(apply(P!7, tptp_fun_X_3(P!7)), phi(f6(P!7, tptp_fun_R_5(P!7))))),
% 163.70/163.97 inference(symmetry,[status(thm)],[2104])).
% 163.70/163.97 tff(2396,plain,
% 163.70/163.97 (err = f4(P!7, tptp_fun_X_3(P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))),
% 163.70/163.97 inference(transitivity,[status(thm)],[1760, 2395, 2394, 2391])).
% 163.70/163.97 tff(2397,plain,
% 163.70/163.97 (forallprefers(err, impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> forallprefers(f4(P!7, tptp_fun_X_3(P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))), f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.97 inference(monotonicity,[status(thm)],[2396, 10])).
% 163.70/163.97 tff(2398,plain,
% 163.70/163.97 (forallprefers(f4(P!7, tptp_fun_X_3(P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))), f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> forallprefers(err, impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.97 inference(symmetry,[status(thm)],[2397])).
% 163.70/163.97 tff(2399,plain,
% 163.70/163.97 ((~forallprefers(f4(P!7, tptp_fun_X_3(P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))), f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) <=> (~forallprefers(err, impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))),
% 163.70/163.97 inference(monotonicity,[status(thm)],[2398])).
% 163.70/163.97 tff(2400,plain,
% 163.70/163.97 ((~![P: $i, R: $i] : (~((~(f5(P, R) = phi(f4(P, tptp_fun_X_4(R, P), R)))) | (~![X1: $i] : (~forallprefers(f4(P, X1, R), f4(P, tptp_fun_X_4(R, P), R))))))) | (~((~(f5(P!7, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))) | (~![X1: $i] : (~forallprefers(f4(P!7, X1, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))), f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))))),
% 163.70/163.97 inference(quant_inst,[status(thm)],[])).
% 163.70/163.97 tff(2401,plain,
% 163.70/163.97 (~((~(f5(P!7, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))) | (~![X1: $i] : (~forallprefers(f4(P!7, X1, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))), f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))))),
% 163.70/163.97 inference(unit_resolution,[status(thm)],[2400, 99])).
% 163.70/163.97 tff(2402,plain,
% 163.70/163.97 (((~(f5(P!7, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = phi(f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))) | (~![X1: $i] : (~forallprefers(f4(P!7, X1, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))), f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))) | ![X1: $i] : (~forallprefers(f4(P!7, X1, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))), f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))),
% 163.70/163.97 inference(tautology,[status(thm)],[])).
% 163.70/163.97 tff(2403,plain,
% 163.70/163.97 (![X1: $i] : (~forallprefers(f4(P!7, X1, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))), f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))),
% 163.70/163.97 inference(unit_resolution,[status(thm)],[2402, 2401])).
% 163.70/163.97 tff(2404,plain,
% 163.70/163.97 ((~![X1: $i] : (~forallprefers(f4(P!7, X1, lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))), f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))) | (~forallprefers(f4(P!7, tptp_fun_X_3(P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))), f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))),
% 163.70/163.97 inference(quant_inst,[status(thm)],[])).
% 163.70/163.97 tff(2405,plain,
% 163.70/163.97 (~forallprefers(f4(P!7, tptp_fun_X_3(P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))), f4(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.97 inference(unit_resolution,[status(thm)],[2404, 2403])).
% 163.70/163.97 tff(2406,plain,
% 163.70/163.97 (~forallprefers(err, impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))),
% 163.70/163.97 inference(modus_ponens,[status(thm)],[2405, 2399])).
% 163.70/163.97 tff(2407,plain,
% 163.70/163.97 ((~(forallprefers(err, impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) <=> ((~((~(err = false)) | (~(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = true)))) | (~(d(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))) | (~((~d(err)) | bool(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))))))) | forallprefers(err, impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))) | (~((~((~(err = false)) | (~(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = true)))) | (~(d(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))) | (~((~d(err)) | bool(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))))))),
% 163.70/163.97 inference(tautology,[status(thm)],[])).
% 163.70/163.97 tff(2408,plain,
% 163.70/163.97 (~((~((~(err = false)) | (~(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = true)))) | (~(d(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))) | (~((~d(err)) | bool(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))))),
% 163.70/163.97 inference(unit_resolution,[status(thm)],[2407, 2406, 2388])).
% 163.70/163.97 tff(2409,plain,
% 163.70/163.97 (((~((~(err = false)) | (~(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))) = true)))) | (~(d(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))) | (~((~d(err)) | bool(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))))) | ((~d(err)) | bool(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))),
% 163.70/163.97 inference(tautology,[status(thm)],[])).
% 163.70/163.97 tff(2410,plain,
% 163.70/163.97 ((~d(err)) | bool(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))),
% 163.70/163.98 inference(unit_resolution,[status(thm)],[2409, 2408])).
% 163.70/163.98 tff(2411,plain,
% 163.70/163.98 ((~((~d(err)) | bool(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))) | (~d(err)) | bool(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))),
% 163.70/163.98 inference(tautology,[status(thm)],[])).
% 163.70/163.98 tff(2412,plain,
% 163.70/163.98 ((~((~d(err)) | bool(err) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))))) | (~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))),
% 163.70/163.98 inference(unit_resolution,[status(thm)],[2411, 1775, 1043])).
% 163.70/163.98 tff(2413,plain,
% 163.70/163.98 ((~d(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7))))))) | (~bool(impl(apply(P!7, tptp_fun_X_4(lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))), P!7)), lazy_impl(prop(phi(f6(P!7, tptp_fun_R_5(P!7)))), phi(f6(P!7, tptp_fun_R_5(P!7)))))))),
% 163.70/163.98 inference(unit_resolution,[status(thm)],[2412, 2410])).
% 163.70/163.98 tff(2414,plain,
% 163.70/163.98 ($false),
% 163.70/163.98 inference(unit_resolution,[status(thm)],[2413, 2381, 2367])).
% 163.70/163.98 % SZS output end Proof
% 163.70/163.98 % E exiting
%------------------------------------------------------------------------------