%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW098+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 31.91s 32.07s
% Output : Proof 32.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW098+1 : TPTP v9.0.0. Released v5.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 11:14:41 EDT 2025
% 0.12/0.34 % CPUTime :
% 31.91/32.07 % SZS status Theorem
% 31.91/32.07 % SZS output start Proof
% 31.91/32.07 tff(tptp_fun_R_2_type, type, (
% 31.91/32.07 tptp_fun_R_2: ( $i * $i ) > $i)).
% 31.91/32.07 tff(tptp_fun_P_8_type, type, (
% 31.91/32.07 tptp_fun_P_8: $i)).
% 31.91/32.07 tff(tptp_fun_Q_7_type, type, (
% 31.91/32.07 tptp_fun_Q_7: $i)).
% 31.91/32.07 tff(impl_type, type, (
% 31.91/32.07 impl: ( $i * $i ) > $i)).
% 31.91/32.07 tff(true_type, type, (
% 31.91/32.07 true: $i)).
% 31.91/32.07 tff(bool_type, type, (
% 31.91/32.07 bool: $i > $o)).
% 31.91/32.07 tff(false_type, type, (
% 31.91/32.07 false: $i)).
% 31.91/32.07 tff(prop_type, type, (
% 31.91/32.07 prop: $i > $i)).
% 31.91/32.07 tff(lazy_impl_type, type, (
% 31.91/32.07 lazy_impl: ( $i * $i ) > $i)).
% 31.91/32.07 tff(d_type, type, (
% 31.91/32.07 d: $i > $o)).
% 31.91/32.07 tff(forallprefers_type, type, (
% 31.91/32.07 forallprefers: ( $i * $i ) > $o)).
% 31.91/32.07 tff(f3_type, type, (
% 31.91/32.07 f3: ( $i * $i * $i ) > $i)).
% 31.91/32.07 tff(phi_type, type, (
% 31.91/32.07 phi: $i > $i)).
% 31.91/32.07 tff(or1_type, type, (
% 31.91/32.07 or1: ( $i * $i ) > $i)).
% 31.91/32.07 tff(or2_type, type, (
% 31.91/32.07 or2: ( $i * $i ) > $i)).
% 31.91/32.07 tff(err_type, type, (
% 31.91/32.07 err: $i)).
% 31.91/32.07 tff(f7_type, type, (
% 31.91/32.07 f7: $i > $i)).
% 31.91/32.07 tff(tptp_fun_P_6_type, type, (
% 31.91/32.07 tptp_fun_P_6: $i)).
% 31.91/32.07 tff(not1_type, type, (
% 31.91/32.07 not1: $i > $i)).
% 31.91/32.07 tff(false2_type, type, (
% 31.91/32.07 false2: $i)).
% 31.91/32.07 tff(f1_type, type, (
% 31.91/32.07 f1: ( $i * $i * $i ) > $i)).
% 31.91/32.07 tff(1,plain,
% 31.91/32.07 (^[B: $i] : refl((lazy_impl(false, B) = true) <=> (lazy_impl(false, B) = true))),
% 31.91/32.07 inference(bind,[status(th)],[])).
% 31.91/32.07 tff(2,plain,
% 31.91/32.07 (![B: $i] : (lazy_impl(false, B) = true) <=> ![B: $i] : (lazy_impl(false, B) = true)),
% 31.91/32.07 inference(quant_intro,[status(thm)],[1])).
% 31.91/32.07 tff(3,plain,
% 31.91/32.07 (![B: $i] : (lazy_impl(false, B) = true) <=> ![B: $i] : (lazy_impl(false, B) = true)),
% 31.91/32.07 inference(rewrite,[status(thm)],[])).
% 31.91/32.07 tff(4,axiom,(![B: $i] : (lazy_impl(false, B) = true)), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','lazy_impl_axiom2')).
% 31.91/32.07 tff(5,plain,
% 31.91/32.07 (![B: $i] : (lazy_impl(false, B) = true)),
% 31.91/32.07 inference(modus_ponens,[status(thm)],[4, 3])).
% 31.91/32.07 tff(6,plain,(
% 31.91/32.07 ![B: $i] : (lazy_impl(false, B) = true)),
% 31.91/32.07 inference(skolemize,[status(sab)],[5])).
% 31.91/32.07 tff(7,plain,
% 31.91/32.07 (![B: $i] : (lazy_impl(false, B) = true)),
% 31.91/32.07 inference(modus_ponens,[status(thm)],[6, 2])).
% 31.91/32.07 tff(8,plain,
% 31.91/32.07 ((~![B: $i] : (lazy_impl(false, B) = true)) | (lazy_impl(false, impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)),
% 31.91/32.07 inference(quant_inst,[status(thm)],[])).
% 31.91/32.07 tff(9,plain,
% 31.91/32.07 (lazy_impl(false, impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true),
% 31.91/32.07 inference(unit_resolution,[status(thm)],[8, 7])).
% 31.91/32.07 tff(10,assumption,(prop(tptp_fun_R_2(Q!7, P!8)) = false), introduced(assumption)).
% 31.91/32.07 tff(11,plain,
% 31.91/32.07 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = lazy_impl(false, impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))),
% 31.91/32.07 inference(monotonicity,[status(thm)],[10])).
% 31.91/32.07 tff(12,plain,
% 31.91/32.07 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true),
% 31.91/32.07 inference(transitivity,[status(thm)],[11, 9])).
% 31.91/32.07 tff(13,plain,
% 31.91/32.07 (^[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)))))))),
% 31.91/32.07 inference(bind,[status(th)],[])).
% 31.91/32.07 tff(14,plain,
% 31.91/32.07 (![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))))))),
% 31.91/32.07 inference(quant_intro,[status(thm)],[13])).
% 31.91/32.07 tff(15,plain,
% 31.91/32.07 (^[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)))))))),
% 31.91/32.07 inference(bind,[status(th)],[])).
% 31.91/32.07 tff(16,plain,
% 31.91/32.07 (![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))))))),
% 31.91/32.07 inference(quant_intro,[status(thm)],[15])).
% 31.91/32.07 tff(17,plain,
% 31.91/32.07 (![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))))),
% 31.91/32.07 inference(rewrite,[status(thm)],[])).
% 31.91/32.07 tff(18,plain,
% 31.91/32.07 (^[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)))))),
% 31.91/32.07 inference(bind,[status(th)],[])).
% 31.91/32.07 tff(19,plain,
% 31.91/32.07 (![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))))),
% 31.91/32.07 inference(quant_intro,[status(thm)],[18])).
% 31.91/32.07 tff(20,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/sandbox/benchmark/Axioms/SWV012+0.ax','def_forallprefers')).
% 31.91/32.07 tff(21,plain,
% 31.91/32.07 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 31.91/32.07 inference(modus_ponens,[status(thm)],[20, 19])).
% 31.91/32.07 tff(22,plain,
% 31.91/32.07 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 31.91/32.07 inference(modus_ponens,[status(thm)],[21, 17])).
% 31.91/32.07 tff(23,plain,(
% 31.91/32.07 ![X: $i, Y: $i] : (forallprefers(X, Y) <=> (((X = false) & (Y = true)) | ((~d(X)) & d(Y)) | (d(X) & d(Y) & (~bool(X)) & bool(Y))))),
% 31.91/32.07 inference(skolemize,[status(sab)],[22])).
% 31.91/32.07 tff(24,plain,
% 31.91/32.07 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))),
% 31.91/32.07 inference(modus_ponens,[status(thm)],[23, 16])).
% 31.91/32.07 tff(25,plain,
% 31.91/32.07 (![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))),
% 31.91/32.07 inference(modus_ponens,[status(thm)],[24, 14])).
% 31.91/32.07 tff(26,plain,
% 31.91/32.07 (((~![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_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))))))) <=> ((~![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_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))))))),
% 31.91/32.08 inference(rewrite,[status(thm)],[])).
% 31.91/32.08 tff(27,plain,
% 31.91/32.08 ((forallprefers(false, lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((~((~(false = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | bool(false) | (~d(false)))))) <=> (forallprefers(false, lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))))))),
% 31.91/32.08 inference(rewrite,[status(thm)],[])).
% 31.91/32.08 tff(28,plain,
% 31.91/32.08 (((~![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_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((~((~(false = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | 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_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))))))),
% 31.91/32.08 inference(monotonicity,[status(thm)],[27])).
% 31.91/32.08 tff(29,plain,
% 31.91/32.08 (((~![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_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((~((~(false = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | 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_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))))))),
% 31.91/32.08 inference(transitivity,[status(thm)],[28, 26])).
% 31.91/32.08 tff(30,plain,
% 31.91/32.08 ((~![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_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((~((~(false = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | bool(false) | (~d(false))))))),
% 31.91/32.08 inference(quant_inst,[status(thm)],[])).
% 31.91/32.08 tff(31,plain,
% 31.91/32.08 ((~![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_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))))))),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[30, 29])).
% 31.91/32.08 tff(32,plain,
% 31.91/32.08 (forallprefers(false, lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))))),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[31, 25])).
% 31.91/32.08 tff(33,plain,
% 31.91/32.08 (^[P: $i, Q: $i, R: $i] : refl((f3(P, Q, R) = lazy_impl(prop(R), impl(impl(P, R), impl(impl(Q, R), R)))) <=> (f3(P, Q, R) = lazy_impl(prop(R), impl(impl(P, R), impl(impl(Q, R), R)))))),
% 31.91/32.08 inference(bind,[status(th)],[])).
% 31.91/32.08 tff(34,plain,
% 31.91/32.08 (![P: $i, Q: $i, R: $i] : (f3(P, Q, R) = lazy_impl(prop(R), impl(impl(P, R), impl(impl(Q, R), R)))) <=> ![P: $i, Q: $i, R: $i] : (f3(P, Q, R) = lazy_impl(prop(R), impl(impl(P, R), impl(impl(Q, R), R))))),
% 31.91/32.08 inference(quant_intro,[status(thm)],[33])).
% 31.91/32.08 tff(35,plain,
% 31.91/32.08 (![P: $i, Q: $i, R: $i] : (f3(P, Q, R) = lazy_impl(prop(R), impl(impl(P, R), impl(impl(Q, R), R)))) <=> ![P: $i, Q: $i, R: $i] : (f3(P, Q, R) = lazy_impl(prop(R), impl(impl(P, R), impl(impl(Q, R), R))))),
% 31.91/32.08 inference(rewrite,[status(thm)],[])).
% 31.91/32.08 tff(36,axiom,(![P: $i, Q: $i, R: $i] : (f3(P, Q, R) = lazy_impl(prop(R), impl(impl(P, R), impl(impl(Q, R), R))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_f3')).
% 31.91/32.08 tff(37,plain,
% 31.91/32.08 (![P: $i, Q: $i, R: $i] : (f3(P, Q, R) = lazy_impl(prop(R), impl(impl(P, R), impl(impl(Q, R), R))))),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[36, 35])).
% 31.91/32.08 tff(38,plain,(
% 31.91/32.08 ![P: $i, Q: $i, R: $i] : (f3(P, Q, R) = lazy_impl(prop(R), impl(impl(P, R), impl(impl(Q, R), R))))),
% 31.91/32.08 inference(skolemize,[status(sab)],[37])).
% 31.91/32.08 tff(39,plain,
% 31.91/32.08 (![P: $i, Q: $i, R: $i] : (f3(P, Q, R) = lazy_impl(prop(R), impl(impl(P, R), impl(impl(Q, R), R))))),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[38, 34])).
% 31.91/32.08 tff(40,plain,
% 31.91/32.08 ((~![P: $i, Q: $i, R: $i] : (f3(P, Q, R) = lazy_impl(prop(R), impl(impl(P, R), impl(impl(Q, R), R))))) | (f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))),
% 31.91/32.08 inference(quant_inst,[status(thm)],[])).
% 31.91/32.08 tff(41,plain,
% 31.91/32.08 (f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[40, 39])).
% 31.91/32.08 tff(42,plain,
% 31.91/32.08 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))),
% 31.91/32.08 inference(symmetry,[status(thm)],[41])).
% 31.91/32.08 tff(43,assumption,(~(Q!7 = false)), introduced(assumption)).
% 31.91/32.08 tff(44,assumption,(~(or1(P!8, Q!7) = phi(Q!7))), introduced(assumption)).
% 31.91/32.08 tff(45,plain,
% 31.91/32.08 ((or2(P!8, Q!7) = or1(P!8, Q!7)) <=> (or1(P!8, Q!7) = or2(P!8, Q!7))),
% 31.91/32.08 inference(commutativity,[status(thm)],[])).
% 31.91/32.08 tff(46,assumption,(~bool(P!8)), introduced(assumption)).
% 31.91/32.08 tff(47,plain,
% 31.91/32.08 (^[A: $i, B: $i] : refl((bool(A) | (or1(A, B) = phi(A))) <=> (bool(A) | (or1(A, B) = phi(A))))),
% 31.91/32.08 inference(bind,[status(th)],[])).
% 31.91/32.08 tff(48,plain,
% 31.91/32.08 (![A: $i, B: $i] : (bool(A) | (or1(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (or1(A, B) = phi(A)))),
% 31.91/32.08 inference(quant_intro,[status(thm)],[47])).
% 31.91/32.08 tff(49,plain,
% 31.91/32.08 (![A: $i, B: $i] : (bool(A) | (or1(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (or1(A, B) = phi(A)))),
% 31.91/32.08 inference(rewrite,[status(thm)],[])).
% 31.91/32.08 tff(50,plain,
% 31.91/32.08 (^[A: $i, B: $i] : rewrite(((~bool(A)) => (or1(A, B) = phi(A))) <=> (bool(A) | (or1(A, B) = phi(A))))),
% 31.91/32.08 inference(bind,[status(th)],[])).
% 31.91/32.08 tff(51,plain,
% 31.91/32.08 (![A: $i, B: $i] : ((~bool(A)) => (or1(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (or1(A, B) = phi(A)))),
% 31.91/32.08 inference(quant_intro,[status(thm)],[50])).
% 31.91/32.08 tff(52,axiom,(![A: $i, B: $i] : ((~bool(A)) => (or1(A, B) = phi(A)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','or1_axiom1')).
% 31.91/32.08 tff(53,plain,
% 31.91/32.08 (![A: $i, B: $i] : (bool(A) | (or1(A, B) = phi(A)))),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[52, 51])).
% 31.91/32.08 tff(54,plain,
% 31.91/32.08 (![A: $i, B: $i] : (bool(A) | (or1(A, B) = phi(A)))),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[53, 49])).
% 31.91/32.08 tff(55,plain,(
% 31.91/32.08 ![A: $i, B: $i] : (bool(A) | (or1(A, B) = phi(A)))),
% 31.91/32.08 inference(skolemize,[status(sab)],[54])).
% 31.91/32.08 tff(56,plain,
% 31.91/32.08 (![A: $i, B: $i] : (bool(A) | (or1(A, B) = phi(A)))),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[55, 48])).
% 31.91/32.08 tff(57,plain,
% 31.91/32.08 (((~![A: $i, B: $i] : (bool(A) | (or1(A, B) = phi(A)))) | (bool(P!8) | (or1(P!8, Q!7) = phi(P!8)))) <=> ((~![A: $i, B: $i] : (bool(A) | (or1(A, B) = phi(A)))) | bool(P!8) | (or1(P!8, Q!7) = phi(P!8)))),
% 31.91/32.08 inference(rewrite,[status(thm)],[])).
% 31.91/32.08 tff(58,plain,
% 31.91/32.08 ((~![A: $i, B: $i] : (bool(A) | (or1(A, B) = phi(A)))) | (bool(P!8) | (or1(P!8, Q!7) = phi(P!8)))),
% 31.91/32.08 inference(quant_inst,[status(thm)],[])).
% 31.91/32.08 tff(59,plain,
% 31.91/32.08 ((~![A: $i, B: $i] : (bool(A) | (or1(A, B) = phi(A)))) | bool(P!8) | (or1(P!8, Q!7) = phi(P!8))),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[58, 57])).
% 31.91/32.08 tff(60,plain,
% 31.91/32.08 (bool(P!8) | (or1(P!8, Q!7) = phi(P!8))),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[59, 56])).
% 31.91/32.08 tff(61,plain,
% 31.91/32.08 (or1(P!8, Q!7) = phi(P!8)),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[60, 46])).
% 31.91/32.08 tff(62,plain,
% 31.91/32.08 (phi(P!8) = or1(P!8, Q!7)),
% 31.91/32.08 inference(symmetry,[status(thm)],[61])).
% 31.91/32.08 tff(63,plain,
% 31.91/32.08 (^[X: $i] : refl((bool(X) <=> ((X = false) | (X = true))) <=> (bool(X) <=> ((X = false) | (X = true))))),
% 31.91/32.08 inference(bind,[status(th)],[])).
% 31.91/32.08 tff(64,plain,
% 31.91/32.08 (![X: $i] : (bool(X) <=> ((X = false) | (X = true))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 31.91/32.08 inference(quant_intro,[status(thm)],[63])).
% 31.91/32.08 tff(65,plain,
% 31.91/32.08 (![X: $i] : (bool(X) <=> ((X = false) | (X = true))) <=> ![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 31.91/32.08 inference(rewrite,[status(thm)],[])).
% 31.91/32.08 tff(66,axiom,(![X: $i] : (bool(X) <=> ((X = false) | (X = true)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_bool')).
% 31.91/32.08 tff(67,plain,
% 31.91/32.08 (![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[66, 65])).
% 31.91/32.08 tff(68,plain,(
% 31.91/32.08 ![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 31.91/32.08 inference(skolemize,[status(sab)],[67])).
% 31.91/32.08 tff(69,plain,
% 31.91/32.08 (![X: $i] : (bool(X) <=> ((X = false) | (X = true)))),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[68, 64])).
% 31.91/32.08 tff(70,plain,
% 31.91/32.08 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(phi(P!8)) <=> ((phi(P!8) = false) | (phi(P!8) = true)))),
% 31.91/32.08 inference(quant_inst,[status(thm)],[])).
% 31.91/32.08 tff(71,plain,
% 31.91/32.08 (bool(phi(P!8)) <=> ((phi(P!8) = false) | (phi(P!8) = true))),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[70, 69])).
% 31.91/32.08 tff(72,plain,
% 31.91/32.08 (^[A: $i, B: $i] : refl((bool(A) | (impl(A, B) = phi(A))) <=> (bool(A) | (impl(A, B) = phi(A))))),
% 31.91/32.08 inference(bind,[status(th)],[])).
% 31.91/32.08 tff(73,plain,
% 31.91/32.08 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 31.91/32.08 inference(quant_intro,[status(thm)],[72])).
% 31.91/32.08 tff(74,plain,
% 31.91/32.08 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 31.91/32.08 inference(rewrite,[status(thm)],[])).
% 31.91/32.08 tff(75,plain,
% 31.91/32.08 (^[A: $i, B: $i] : rewrite(((~bool(A)) => (impl(A, B) = phi(A))) <=> (bool(A) | (impl(A, B) = phi(A))))),
% 31.91/32.08 inference(bind,[status(th)],[])).
% 31.91/32.08 tff(76,plain,
% 31.91/32.08 (![A: $i, B: $i] : ((~bool(A)) => (impl(A, B) = phi(A))) <=> ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 31.91/32.08 inference(quant_intro,[status(thm)],[75])).
% 31.91/32.08 tff(77,axiom,(![A: $i, B: $i] : ((~bool(A)) => (impl(A, B) = phi(A)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','impl_axiom1')).
% 31.91/32.08 tff(78,plain,
% 31.91/32.08 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[77, 76])).
% 31.91/32.08 tff(79,plain,
% 31.91/32.08 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[78, 74])).
% 31.91/32.08 tff(80,plain,(
% 31.91/32.08 ![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 31.91/32.08 inference(skolemize,[status(sab)],[79])).
% 31.91/32.08 tff(81,plain,
% 31.91/32.08 (![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[80, 73])).
% 31.91/32.08 tff(82,plain,
% 31.91/32.08 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(P!8) | (impl(P!8, tptp_fun_R_2(Q!7, P!8)) = phi(P!8)))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(P!8) | (impl(P!8, tptp_fun_R_2(Q!7, P!8)) = phi(P!8)))),
% 31.91/32.08 inference(rewrite,[status(thm)],[])).
% 31.91/32.08 tff(83,plain,
% 31.91/32.08 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(P!8) | (impl(P!8, tptp_fun_R_2(Q!7, P!8)) = phi(P!8)))),
% 31.91/32.08 inference(quant_inst,[status(thm)],[])).
% 31.91/32.08 tff(84,plain,
% 31.91/32.08 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(P!8) | (impl(P!8, tptp_fun_R_2(Q!7, P!8)) = phi(P!8))),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[83, 82])).
% 31.91/32.08 tff(85,plain,
% 31.91/32.08 (bool(P!8) | (impl(P!8, tptp_fun_R_2(Q!7, P!8)) = phi(P!8))),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[84, 81])).
% 31.91/32.08 tff(86,plain,
% 31.91/32.08 (impl(P!8, tptp_fun_R_2(Q!7, P!8)) = phi(P!8)),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[85, 46])).
% 31.91/32.08 tff(87,plain,
% 31.91/32.08 (phi(P!8) = impl(P!8, tptp_fun_R_2(Q!7, P!8))),
% 31.91/32.08 inference(symmetry,[status(thm)],[86])).
% 31.91/32.08 tff(88,plain,
% 31.91/32.08 ((phi(P!8) = false) <=> (impl(P!8, tptp_fun_R_2(Q!7, P!8)) = false)),
% 31.91/32.08 inference(monotonicity,[status(thm)],[87])).
% 31.91/32.08 tff(89,plain,
% 31.91/32.08 ((impl(P!8, tptp_fun_R_2(Q!7, P!8)) = false) <=> (phi(P!8) = false)),
% 31.91/32.08 inference(symmetry,[status(thm)],[88])).
% 31.91/32.08 tff(90,plain,
% 31.91/32.08 ((~(impl(P!8, tptp_fun_R_2(Q!7, P!8)) = false)) <=> (~(phi(P!8) = false))),
% 31.91/32.08 inference(monotonicity,[status(thm)],[89])).
% 31.91/32.08 tff(91,plain,
% 31.91/32.08 ((false = P!8) <=> (P!8 = false)),
% 31.91/32.08 inference(commutativity,[status(thm)],[])).
% 31.91/32.08 tff(92,assumption,(impl(P!8, tptp_fun_R_2(Q!7, P!8)) = false), introduced(assumption)).
% 31.91/32.08 tff(93,plain,
% 31.91/32.08 (phi(P!8) = false),
% 31.91/32.08 inference(transitivity,[status(thm)],[87, 92])).
% 31.91/32.08 tff(94,plain,
% 31.91/32.08 ((phi(P!8) = P!8) <=> (false = P!8)),
% 31.91/32.08 inference(monotonicity,[status(thm)],[93])).
% 31.91/32.08 tff(95,plain,
% 31.91/32.08 ((phi(P!8) = P!8) <=> (P!8 = false)),
% 31.91/32.08 inference(transitivity,[status(thm)],[94, 91])).
% 31.91/32.08 tff(96,plain,
% 31.91/32.08 ((P!8 = false) <=> (phi(P!8) = P!8)),
% 31.91/32.08 inference(symmetry,[status(thm)],[95])).
% 31.91/32.08 tff(97,plain,
% 31.91/32.08 ((~(P!8 = false)) <=> (~(phi(P!8) = P!8))),
% 31.91/32.08 inference(monotonicity,[status(thm)],[96])).
% 31.91/32.08 tff(98,plain,
% 31.91/32.08 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(P!8) <=> ((P!8 = false) | (P!8 = true)))),
% 31.91/32.08 inference(quant_inst,[status(thm)],[])).
% 31.91/32.08 tff(99,plain,
% 31.91/32.08 (bool(P!8) <=> ((P!8 = false) | (P!8 = true))),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[98, 69])).
% 31.91/32.08 tff(100,plain,
% 31.91/32.08 ((~(bool(P!8) <=> ((P!8 = false) | (P!8 = true)))) | bool(P!8) | (~((P!8 = false) | (P!8 = true)))),
% 31.91/32.08 inference(tautology,[status(thm)],[])).
% 31.91/32.08 tff(101,plain,
% 31.91/32.08 ((~(bool(P!8) <=> ((P!8 = false) | (P!8 = true)))) | (~((P!8 = false) | (P!8 = true)))),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[100, 46])).
% 31.91/32.08 tff(102,plain,
% 31.91/32.08 (~((P!8 = false) | (P!8 = true))),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[101, 99])).
% 31.91/32.08 tff(103,plain,
% 31.91/32.08 (((P!8 = false) | (P!8 = true)) | (~(P!8 = false))),
% 31.91/32.08 inference(tautology,[status(thm)],[])).
% 31.91/32.08 tff(104,plain,
% 31.91/32.08 (~(P!8 = false)),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[103, 102])).
% 31.91/32.08 tff(105,plain,
% 31.91/32.08 (~(phi(P!8) = P!8)),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[104, 97])).
% 31.91/32.08 tff(106,plain,
% 31.91/32.08 (((~d(P!8)) | (~(phi(P!8) = P!8))) | (phi(P!8) = P!8)),
% 31.91/32.08 inference(tautology,[status(thm)],[])).
% 31.91/32.08 tff(107,plain,
% 31.91/32.08 ((~d(P!8)) | (~(phi(P!8) = P!8))),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[106, 105])).
% 31.91/32.08 tff(108,plain,
% 31.91/32.08 ((phi(P!8) = err) <=> (false = err)),
% 31.91/32.08 inference(monotonicity,[status(thm)],[93])).
% 31.91/32.08 tff(109,plain,
% 31.91/32.08 ((false = err) <=> (phi(P!8) = err)),
% 31.91/32.08 inference(symmetry,[status(thm)],[108])).
% 31.91/32.08 tff(110,plain,
% 31.91/32.08 ((~(false = err)) <=> (~(phi(P!8) = err))),
% 31.91/32.08 inference(monotonicity,[status(thm)],[109])).
% 31.91/32.08 tff(111,plain,
% 31.91/32.08 ((~(false = err)) <=> (~(false = err))),
% 31.91/32.08 inference(rewrite,[status(thm)],[])).
% 31.91/32.08 tff(112,axiom,(((~(true = false)) & (~(true = err))) & (~(false = err))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','distinct_false_true_err')).
% 31.91/32.08 tff(113,plain,
% 31.91/32.08 (~(false = err)),
% 31.91/32.08 inference(and_elim,[status(thm)],[112])).
% 31.91/32.08 tff(114,plain,
% 31.91/32.08 (~(false = err)),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[113, 111])).
% 31.91/32.08 tff(115,plain,
% 31.91/32.08 (~(phi(P!8) = err)),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[114, 110])).
% 31.91/32.08 tff(116,plain,
% 31.91/32.08 ((d(P!8) | (~(phi(P!8) = err))) | (phi(P!8) = err)),
% 31.91/32.08 inference(tautology,[status(thm)],[])).
% 31.91/32.08 tff(117,plain,
% 31.91/32.08 (d(P!8) | (~(phi(P!8) = err))),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[116, 115])).
% 31.91/32.08 tff(118,plain,
% 31.91/32.08 (^[X: $i] : refl(((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))) <=> ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))))),
% 31.91/32.08 inference(bind,[status(th)],[])).
% 31.91/32.08 tff(119,plain,
% 31.91/32.08 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err))))) <=> ![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 31.91/32.08 inference(quant_intro,[status(thm)],[118])).
% 31.91/32.08 tff(120,plain,
% 31.91/32.08 (^[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)))))))),
% 31.91/32.08 inference(bind,[status(th)],[])).
% 31.91/32.08 tff(121,plain,
% 31.91/32.08 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 31.91/32.08 inference(quant_intro,[status(thm)],[120])).
% 31.91/32.08 tff(122,plain,
% 31.91/32.08 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err))) <=> ![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 31.91/32.08 inference(rewrite,[status(thm)],[])).
% 31.91/32.08 tff(123,axiom,(![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_phi')).
% 31.91/32.08 tff(124,plain,
% 31.91/32.08 (![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[123, 122])).
% 31.91/32.08 tff(125,plain,(
% 31.91/32.08 ![X: $i] : ((d(X) & (phi(X) = X)) | ((~d(X)) & (phi(X) = err)))),
% 31.91/32.08 inference(skolemize,[status(sab)],[124])).
% 31.91/32.08 tff(126,plain,
% 31.91/32.08 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[125, 121])).
% 31.91/32.08 tff(127,plain,
% 31.91/32.08 (![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[126, 119])).
% 31.91/32.08 tff(128,plain,
% 31.91/32.08 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(P!8)) | (~(phi(P!8) = P!8)))) | (~(d(P!8) | (~(phi(P!8) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(P!8)) | (~(phi(P!8) = P!8)))) | (~(d(P!8) | (~(phi(P!8) = err)))))),
% 31.91/32.08 inference(rewrite,[status(thm)],[])).
% 31.91/32.08 tff(129,plain,
% 31.91/32.08 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(P!8)) | (~(phi(P!8) = P!8)))) | (~(d(P!8) | (~(phi(P!8) = err)))))),
% 31.91/32.08 inference(quant_inst,[status(thm)],[])).
% 31.91/32.08 tff(130,plain,
% 31.91/32.08 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(P!8)) | (~(phi(P!8) = P!8)))) | (~(d(P!8) | (~(phi(P!8) = err))))),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[129, 128])).
% 31.91/32.08 tff(131,plain,
% 31.91/32.08 ((~((~d(P!8)) | (~(phi(P!8) = P!8)))) | (~(d(P!8) | (~(phi(P!8) = err))))),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[130, 127])).
% 31.91/32.08 tff(132,plain,
% 31.91/32.08 ($false),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[131, 117, 107])).
% 31.91/32.08 tff(133,plain,(bool(P!8) | (~(impl(P!8, tptp_fun_R_2(Q!7, P!8)) = false))), inference(lemma,lemma(discharge,[]))).
% 31.91/32.08 tff(134,plain,
% 31.91/32.08 (~(impl(P!8, tptp_fun_R_2(Q!7, P!8)) = false)),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[133, 46])).
% 31.91/32.08 tff(135,plain,
% 31.91/32.08 (~(phi(P!8) = false)),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[134, 90])).
% 31.91/32.08 tff(136,plain,
% 31.91/32.08 (((P!8 = false) | (P!8 = true)) | (~(P!8 = true))),
% 31.91/32.08 inference(tautology,[status(thm)],[])).
% 31.91/32.08 tff(137,plain,
% 31.91/32.08 (~(P!8 = true)),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[136, 102])).
% 31.91/32.08 tff(138,plain,
% 31.91/32.08 ((true = P!8) <=> (P!8 = true)),
% 31.91/32.08 inference(commutativity,[status(thm)],[])).
% 31.91/32.08 tff(139,assumption,(phi(P!8) = true), introduced(assumption)).
% 31.91/32.08 tff(140,plain,
% 31.91/32.08 ((phi(P!8) = P!8) <=> (true = P!8)),
% 31.91/32.08 inference(monotonicity,[status(thm)],[139])).
% 31.91/32.08 tff(141,plain,
% 31.91/32.08 ((phi(P!8) = P!8) <=> (P!8 = true)),
% 31.91/32.08 inference(transitivity,[status(thm)],[140, 138])).
% 31.91/32.08 tff(142,plain,
% 31.91/32.08 ((P!8 = true) <=> (phi(P!8) = P!8)),
% 31.91/32.08 inference(symmetry,[status(thm)],[141])).
% 31.91/32.08 tff(143,plain,
% 31.91/32.08 ((~(P!8 = true)) <=> (~(phi(P!8) = P!8))),
% 31.91/32.08 inference(monotonicity,[status(thm)],[142])).
% 31.91/32.08 tff(144,assumption,(~(P!8 = true)), introduced(assumption)).
% 31.91/32.08 tff(145,plain,
% 31.91/32.08 (~(phi(P!8) = P!8)),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[144, 143])).
% 31.91/32.08 tff(146,plain,
% 31.91/32.08 ((~d(P!8)) | (~(phi(P!8) = P!8))),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[106, 145])).
% 31.91/32.08 tff(147,plain,
% 31.91/32.08 ((phi(P!8) = err) <=> (true = err)),
% 31.91/32.08 inference(monotonicity,[status(thm)],[139])).
% 31.91/32.08 tff(148,plain,
% 31.91/32.08 ((true = err) <=> (phi(P!8) = err)),
% 31.91/32.08 inference(symmetry,[status(thm)],[147])).
% 31.91/32.08 tff(149,plain,
% 31.91/32.08 ((~(true = err)) <=> (~(phi(P!8) = err))),
% 31.91/32.08 inference(monotonicity,[status(thm)],[148])).
% 31.91/32.08 tff(150,plain,
% 31.91/32.08 ((~(true = err)) <=> (~(true = err))),
% 31.91/32.08 inference(rewrite,[status(thm)],[])).
% 31.91/32.08 tff(151,plain,
% 31.91/32.08 ((~(true = false)) & (~(true = err))),
% 31.91/32.08 inference(and_elim,[status(thm)],[112])).
% 31.91/32.08 tff(152,plain,
% 31.91/32.08 (~(true = err)),
% 31.91/32.08 inference(and_elim,[status(thm)],[151])).
% 31.91/32.08 tff(153,plain,
% 31.91/32.08 (~(true = err)),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[152, 150])).
% 31.91/32.08 tff(154,plain,
% 31.91/32.08 (~(phi(P!8) = err)),
% 31.91/32.08 inference(modus_ponens,[status(thm)],[153, 149])).
% 31.91/32.08 tff(155,plain,
% 31.91/32.08 (d(P!8) | (~(phi(P!8) = err))),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[116, 154])).
% 31.91/32.08 tff(156,plain,
% 31.91/32.08 ($false),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[131, 155, 146])).
% 31.91/32.08 tff(157,plain,((~(phi(P!8) = true)) | (P!8 = true)), inference(lemma,lemma(discharge,[]))).
% 31.91/32.08 tff(158,plain,
% 31.91/32.08 (~(phi(P!8) = true)),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[157, 137])).
% 31.91/32.08 tff(159,plain,
% 31.91/32.08 ((~((phi(P!8) = false) | (phi(P!8) = true))) | (phi(P!8) = false) | (phi(P!8) = true)),
% 31.91/32.08 inference(tautology,[status(thm)],[])).
% 31.91/32.08 tff(160,plain,
% 31.91/32.08 (~((phi(P!8) = false) | (phi(P!8) = true))),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[159, 158, 135])).
% 31.91/32.08 tff(161,plain,
% 31.91/32.08 ((~(bool(phi(P!8)) <=> ((phi(P!8) = false) | (phi(P!8) = true)))) | (~bool(phi(P!8))) | ((phi(P!8) = false) | (phi(P!8) = true))),
% 31.91/32.08 inference(tautology,[status(thm)],[])).
% 31.91/32.08 tff(162,plain,
% 31.91/32.08 (~bool(phi(P!8))),
% 31.91/32.08 inference(unit_resolution,[status(thm)],[161, 160, 71])).
% 31.91/32.08 tff(163,plain,
% 31.91/32.08 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(phi(P!8)) | (impl(phi(P!8), phi(P!8)) = phi(phi(P!8))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(phi(P!8)) | (impl(phi(P!8), phi(P!8)) = phi(phi(P!8))))),
% 31.91/32.09 inference(rewrite,[status(thm)],[])).
% 31.91/32.09 tff(164,plain,
% 31.91/32.09 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(phi(P!8)) | (impl(phi(P!8), phi(P!8)) = phi(phi(P!8))))),
% 31.91/32.09 inference(quant_inst,[status(thm)],[])).
% 31.91/32.09 tff(165,plain,
% 31.91/32.09 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(phi(P!8)) | (impl(phi(P!8), phi(P!8)) = phi(phi(P!8)))),
% 31.91/32.09 inference(modus_ponens,[status(thm)],[164, 163])).
% 31.91/32.09 tff(166,plain,
% 31.91/32.09 (bool(phi(P!8)) | (impl(phi(P!8), phi(P!8)) = phi(phi(P!8)))),
% 31.91/32.09 inference(unit_resolution,[status(thm)],[165, 81])).
% 31.91/32.09 tff(167,plain,
% 31.91/32.09 (impl(phi(P!8), phi(P!8)) = phi(phi(P!8))),
% 31.91/32.09 inference(unit_resolution,[status(thm)],[166, 162])).
% 31.91/32.09 tff(168,plain,
% 31.91/32.09 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(P!8) | (impl(P!8, phi(f7(P!6))) = phi(P!8)))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(P!8) | (impl(P!8, phi(f7(P!6))) = phi(P!8)))),
% 31.91/32.09 inference(rewrite,[status(thm)],[])).
% 31.91/32.09 tff(169,plain,
% 31.91/32.09 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(P!8) | (impl(P!8, phi(f7(P!6))) = phi(P!8)))),
% 31.91/32.09 inference(quant_inst,[status(thm)],[])).
% 31.91/32.09 tff(170,plain,
% 31.91/32.09 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(P!8) | (impl(P!8, phi(f7(P!6))) = phi(P!8))),
% 31.91/32.09 inference(modus_ponens,[status(thm)],[169, 168])).
% 31.91/32.09 tff(171,plain,
% 31.91/32.09 (bool(P!8) | (impl(P!8, phi(f7(P!6))) = phi(P!8))),
% 31.91/32.09 inference(unit_resolution,[status(thm)],[170, 81])).
% 31.91/32.09 tff(172,plain,
% 31.91/32.09 (impl(P!8, phi(f7(P!6))) = phi(P!8)),
% 31.91/32.09 inference(unit_resolution,[status(thm)],[171, 46])).
% 31.91/32.09 tff(173,plain,
% 31.91/32.09 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(P!8) | (impl(P!8, impl(P!8, phi(f7(P!6)))) = phi(P!8)))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(P!8) | (impl(P!8, impl(P!8, phi(f7(P!6)))) = phi(P!8)))),
% 31.91/32.09 inference(rewrite,[status(thm)],[])).
% 31.91/32.09 tff(174,plain,
% 31.91/32.09 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(P!8) | (impl(P!8, impl(P!8, phi(f7(P!6)))) = phi(P!8)))),
% 31.91/32.09 inference(quant_inst,[status(thm)],[])).
% 31.91/32.09 tff(175,plain,
% 31.91/32.09 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(P!8) | (impl(P!8, impl(P!8, phi(f7(P!6)))) = phi(P!8))),
% 31.91/32.09 inference(modus_ponens,[status(thm)],[174, 173])).
% 31.91/32.09 tff(176,plain,
% 31.91/32.09 (bool(P!8) | (impl(P!8, impl(P!8, phi(f7(P!6)))) = phi(P!8))),
% 31.91/32.09 inference(unit_resolution,[status(thm)],[175, 81])).
% 31.91/32.09 tff(177,plain,
% 31.91/32.09 (impl(P!8, impl(P!8, phi(f7(P!6)))) = phi(P!8)),
% 31.91/32.09 inference(unit_resolution,[status(thm)],[176, 46])).
% 31.91/32.09 tff(178,plain,
% 31.91/32.09 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(phi(P!8)) | (impl(phi(P!8), tptp_fun_R_2(Q!7, P!8)) = phi(phi(P!8))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(phi(P!8)) | (impl(phi(P!8), tptp_fun_R_2(Q!7, P!8)) = phi(phi(P!8))))),
% 31.91/32.09 inference(rewrite,[status(thm)],[])).
% 31.91/32.09 tff(179,plain,
% 31.91/32.09 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(phi(P!8)) | (impl(phi(P!8), tptp_fun_R_2(Q!7, P!8)) = phi(phi(P!8))))),
% 31.91/32.09 inference(quant_inst,[status(thm)],[])).
% 31.91/32.09 tff(180,plain,
% 31.91/32.09 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(phi(P!8)) | (impl(phi(P!8), tptp_fun_R_2(Q!7, P!8)) = phi(phi(P!8)))),
% 31.91/32.09 inference(modus_ponens,[status(thm)],[179, 178])).
% 31.91/32.09 tff(181,plain,
% 31.91/32.09 (bool(phi(P!8)) | (impl(phi(P!8), tptp_fun_R_2(Q!7, P!8)) = phi(phi(P!8)))),
% 31.91/32.09 inference(unit_resolution,[status(thm)],[180, 81])).
% 31.91/32.09 tff(182,plain,
% 31.91/32.09 (impl(phi(P!8), tptp_fun_R_2(Q!7, P!8)) = phi(phi(P!8))),
% 31.91/32.09 inference(unit_resolution,[status(thm)],[181, 162])).
% 31.91/32.09 tff(183,plain,
% 31.91/32.09 (bool(phi(P!8)) <=> bool(impl(P!8, tptp_fun_R_2(Q!7, P!8)))),
% 31.91/32.09 inference(monotonicity,[status(thm)],[87])).
% 31.91/32.09 tff(184,plain,
% 31.91/32.09 ((~bool(phi(P!8))) <=> (~bool(impl(P!8, tptp_fun_R_2(Q!7, P!8))))),
% 31.91/32.09 inference(monotonicity,[status(thm)],[183])).
% 31.91/32.09 tff(185,plain,
% 31.91/32.09 (~bool(impl(P!8, tptp_fun_R_2(Q!7, P!8)))),
% 31.91/32.09 inference(modus_ponens,[status(thm)],[162, 184])).
% 31.91/32.09 tff(186,plain,
% 31.91/32.09 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(P!8, tptp_fun_R_2(Q!7, P!8))) | (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = phi(impl(P!8, tptp_fun_R_2(Q!7, P!8)))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(P!8, tptp_fun_R_2(Q!7, P!8))) | (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = phi(impl(P!8, tptp_fun_R_2(Q!7, P!8)))))),
% 31.91/32.09 inference(rewrite,[status(thm)],[])).
% 31.91/32.09 tff(187,plain,
% 31.91/32.09 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(P!8, tptp_fun_R_2(Q!7, P!8))) | (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = phi(impl(P!8, tptp_fun_R_2(Q!7, P!8)))))),
% 31.91/32.09 inference(quant_inst,[status(thm)],[])).
% 31.91/32.09 tff(188,plain,
% 31.91/32.09 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(P!8, tptp_fun_R_2(Q!7, P!8))) | (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = phi(impl(P!8, tptp_fun_R_2(Q!7, P!8))))),
% 31.91/32.09 inference(modus_ponens,[status(thm)],[187, 186])).
% 31.91/32.09 tff(189,plain,
% 31.91/32.09 (bool(impl(P!8, tptp_fun_R_2(Q!7, P!8))) | (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = phi(impl(P!8, tptp_fun_R_2(Q!7, P!8))))),
% 31.91/32.09 inference(unit_resolution,[status(thm)],[188, 81])).
% 31.91/32.09 tff(190,plain,
% 31.91/32.09 (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = phi(impl(P!8, tptp_fun_R_2(Q!7, P!8)))),
% 31.91/32.09 inference(unit_resolution,[status(thm)],[189, 185])).
% 31.91/32.09 tff(191,plain,
% 31.91/32.09 ((true = impl(P!8, tptp_fun_R_2(Q!7, P!8))) <=> (impl(P!8, tptp_fun_R_2(Q!7, P!8)) = true)),
% 31.91/32.09 inference(commutativity,[status(thm)],[])).
% 31.91/32.09 tff(192,plain,
% 31.91/32.09 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) <=> ((lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false) | (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true)))),
% 31.91/32.09 inference(quant_inst,[status(thm)],[])).
% 31.91/32.09 tff(193,plain,
% 31.91/32.09 (bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) <=> ((lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false) | (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true))),
% 31.91/32.09 inference(unit_resolution,[status(thm)],[192, 69])).
% 31.91/32.09 tff(194,plain,
% 31.91/32.09 (d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.91/32.09 inference(monotonicity,[status(thm)],[42])).
% 31.91/32.09 tff(195,plain,
% 31.91/32.09 (d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) <=> d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))),
% 31.91/32.09 inference(symmetry,[status(thm)],[194])).
% 31.91/32.09 tff(196,plain,
% 31.91/32.09 (lazy_impl(false, impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))),
% 31.91/32.09 inference(symmetry,[status(thm)],[11])).
% 31.91/32.09 tff(197,plain,
% 31.91/32.09 (true = lazy_impl(false, impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))),
% 31.91/32.09 inference(symmetry,[status(thm)],[9])).
% 31.91/32.09 tff(198,plain,
% 31.91/32.09 (true = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))),
% 31.91/32.09 inference(transitivity,[status(thm)],[197, 196, 42])).
% 31.91/32.09 tff(199,plain,
% 31.91/32.09 (d(true) <=> d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.91/32.09 inference(monotonicity,[status(thm)],[198])).
% 31.91/32.09 tff(200,plain,
% 31.91/32.09 (d(true) <=> d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))),
% 31.91/32.09 inference(transitivity,[status(thm)],[199, 195])).
% 31.91/32.09 tff(201,plain,
% 31.91/32.09 (d(true) <=> d(true)),
% 31.91/32.09 inference(rewrite,[status(thm)],[])).
% 31.91/32.09 tff(202,axiom,((d(true) & d(false)) & d(err)), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','false_true_err_in_d')).
% 31.91/32.09 tff(203,plain,
% 31.91/32.09 (d(true) & d(false)),
% 31.91/32.09 inference(and_elim,[status(thm)],[202])).
% 31.91/32.09 tff(204,plain,
% 31.91/32.09 (d(true)),
% 31.91/32.09 inference(and_elim,[status(thm)],[203])).
% 31.91/32.09 tff(205,plain,
% 31.91/32.09 (d(true)),
% 31.91/32.09 inference(modus_ponens,[status(thm)],[204, 201])).
% 31.91/32.09 tff(206,plain,
% 31.91/32.09 (d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))),
% 31.91/32.09 inference(modus_ponens,[status(thm)],[205, 200])).
% 31.91/32.09 tff(207,plain,
% 31.91/32.09 (bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> bool(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.91/32.09 inference(monotonicity,[status(thm)],[42])).
% 31.91/32.09 tff(208,plain,
% 31.91/32.09 (bool(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) <=> bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))),
% 31.91/32.09 inference(symmetry,[status(thm)],[207])).
% 31.91/32.09 tff(209,plain,
% 31.91/32.09 (f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)) = true),
% 31.91/32.09 inference(transitivity,[status(thm)],[41, 11, 9])).
% 31.91/32.09 tff(210,plain,
% 31.91/32.09 (bool(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) <=> bool(true)),
% 31.91/32.09 inference(monotonicity,[status(thm)],[209])).
% 31.91/32.09 tff(211,plain,
% 31.91/32.09 (bool(true) <=> bool(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.91/32.09 inference(symmetry,[status(thm)],[210])).
% 31.91/32.09 tff(212,plain,
% 31.91/32.09 (bool(true) <=> bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))),
% 31.91/32.09 inference(transitivity,[status(thm)],[211, 208])).
% 31.91/32.09 tff(213,plain,
% 31.91/32.09 ((false = true) <=> (true = false)),
% 31.91/32.09 inference(commutativity,[status(thm)],[])).
% 31.91/32.09 tff(214,plain,
% 31.91/32.09 ((d(true) | (~(phi(true) = err))) | (~d(true))),
% 31.91/32.09 inference(tautology,[status(thm)],[])).
% 31.91/32.09 tff(215,plain,
% 31.91/32.09 (d(true) | (~(phi(true) = err))),
% 31.91/32.09 inference(unit_resolution,[status(thm)],[214, 205])).
% 31.91/32.09 tff(216,plain,
% 31.91/32.09 (((~![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)))))),
% 31.91/32.09 inference(rewrite,[status(thm)],[])).
% 31.91/32.09 tff(217,plain,
% 31.91/32.09 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(true)) | (~(phi(true) = true)))) | (~(d(true) | (~(phi(true) = err)))))),
% 31.91/32.09 inference(quant_inst,[status(thm)],[])).
% 31.91/32.09 tff(218,plain,
% 31.91/32.09 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(true)) | (~(phi(true) = true)))) | (~(d(true) | (~(phi(true) = err))))),
% 31.91/32.09 inference(modus_ponens,[status(thm)],[217, 216])).
% 31.91/32.09 tff(219,plain,
% 31.91/32.09 (~((~d(true)) | (~(phi(true) = true)))),
% 31.91/32.09 inference(unit_resolution,[status(thm)],[218, 127, 215])).
% 31.91/32.09 tff(220,plain,
% 31.91/32.09 (((~d(true)) | (~(phi(true) = true))) | (phi(true) = true)),
% 31.91/32.09 inference(tautology,[status(thm)],[])).
% 31.91/32.09 tff(221,plain,
% 31.91/32.09 (phi(true) = true),
% 31.91/32.09 inference(unit_resolution,[status(thm)],[220, 219])).
% 31.91/32.09 tff(222,plain,
% 31.91/32.09 ((not1(true) = false) <=> (not1(true) = false)),
% 31.91/32.09 inference(rewrite,[status(thm)],[])).
% 31.91/32.09 tff(223,axiom,(not1(true) = false), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','not1_axiom3')).
% 31.91/32.09 tff(224,plain,
% 31.91/32.09 (not1(true) = false),
% 31.91/32.09 inference(modus_ponens,[status(thm)],[223, 222])).
% 31.91/32.09 tff(225,plain,
% 31.91/32.09 ((not1(true) = phi(true)) <=> (false = true)),
% 31.91/32.09 inference(monotonicity,[status(thm)],[224, 221])).
% 31.91/32.09 tff(226,plain,
% 31.91/32.09 ((not1(true) = phi(true)) <=> (true = false)),
% 31.91/32.09 inference(transitivity,[status(thm)],[225, 213])).
% 31.91/32.09 tff(227,plain,
% 31.91/32.09 ((true = false) <=> (not1(true) = phi(true))),
% 31.91/32.09 inference(symmetry,[status(thm)],[226])).
% 31.91/32.09 tff(228,plain,
% 31.91/32.09 ((~(true = false)) <=> (~(not1(true) = phi(true)))),
% 31.91/32.09 inference(monotonicity,[status(thm)],[227])).
% 31.91/32.09 tff(229,plain,
% 31.91/32.09 ((~(true = false)) <=> (~(true = false))),
% 31.91/32.09 inference(rewrite,[status(thm)],[])).
% 31.91/32.09 tff(230,plain,
% 31.91/32.09 (~(true = false)),
% 31.91/32.09 inference(and_elim,[status(thm)],[151])).
% 31.91/32.09 tff(231,plain,
% 31.91/32.09 (~(true = false)),
% 31.91/32.09 inference(modus_ponens,[status(thm)],[230, 229])).
% 31.91/32.09 tff(232,plain,
% 31.91/32.09 (~(not1(true) = phi(true))),
% 31.91/32.09 inference(modus_ponens,[status(thm)],[231, 228])).
% 31.91/32.09 tff(233,plain,
% 31.91/32.09 (^[A: $i] : refl((bool(A) | (not1(A) = phi(A))) <=> (bool(A) | (not1(A) = phi(A))))),
% 31.91/32.09 inference(bind,[status(th)],[])).
% 31.91/32.09 tff(234,plain,
% 31.91/32.09 (![A: $i] : (bool(A) | (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 31.91/32.09 inference(quant_intro,[status(thm)],[233])).
% 31.91/32.09 tff(235,plain,
% 31.91/32.09 (![A: $i] : (bool(A) | (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 31.91/32.09 inference(rewrite,[status(thm)],[])).
% 31.91/32.09 tff(236,plain,
% 31.91/32.09 (^[A: $i] : rewrite(((~bool(A)) => (not1(A) = phi(A))) <=> (bool(A) | (not1(A) = phi(A))))),
% 31.91/32.09 inference(bind,[status(th)],[])).
% 31.91/32.09 tff(237,plain,
% 31.91/32.09 (![A: $i] : ((~bool(A)) => (not1(A) = phi(A))) <=> ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 31.91/32.09 inference(quant_intro,[status(thm)],[236])).
% 31.91/32.09 tff(238,axiom,(![A: $i] : ((~bool(A)) => (not1(A) = phi(A)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','not1_axiom1')).
% 31.91/32.09 tff(239,plain,
% 31.91/32.09 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 31.91/32.09 inference(modus_ponens,[status(thm)],[238, 237])).
% 31.91/32.09 tff(240,plain,
% 31.91/32.09 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 31.91/32.09 inference(modus_ponens,[status(thm)],[239, 235])).
% 31.91/32.09 tff(241,plain,(
% 31.91/32.09 ![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 31.91/32.09 inference(skolemize,[status(sab)],[240])).
% 31.91/32.09 tff(242,plain,
% 31.91/32.09 (![A: $i] : (bool(A) | (not1(A) = phi(A)))),
% 31.91/32.09 inference(modus_ponens,[status(thm)],[241, 234])).
% 31.91/32.09 tff(243,plain,
% 31.91/32.09 (((~![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)))),
% 31.91/32.09 inference(rewrite,[status(thm)],[])).
% 31.91/32.09 tff(244,plain,
% 31.91/32.09 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(true) | (not1(true) = phi(true)))),
% 31.91/32.09 inference(quant_inst,[status(thm)],[])).
% 31.91/32.09 tff(245,plain,
% 31.91/32.09 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(true) | (not1(true) = phi(true))),
% 31.91/32.09 inference(modus_ponens,[status(thm)],[244, 243])).
% 31.91/32.09 tff(246,plain,
% 31.91/32.09 (bool(true) | (not1(true) = phi(true))),
% 31.91/32.09 inference(unit_resolution,[status(thm)],[245, 242])).
% 31.91/32.09 tff(247,plain,
% 31.91/32.09 (bool(true)),
% 31.91/32.09 inference(unit_resolution,[status(thm)],[246, 232])).
% 31.91/32.09 tff(248,plain,
% 31.91/32.09 (bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))),
% 31.91/32.09 inference(modus_ponens,[status(thm)],[247, 212])).
% 31.91/32.09 tff(249,plain,
% 31.91/32.09 (((~![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(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))), lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((~((~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))))) | (~(d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))))))) <=> ((~![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(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))), lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((~((~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))))) | (~(d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))))))),
% 31.91/32.09 inference(rewrite,[status(thm)],[])).
% 31.91/32.09 tff(250,plain,
% 31.91/32.09 ((forallprefers(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))), lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((~((~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))) | (~(d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))))))) <=> (forallprefers(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))), lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((~((~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))))) | (~(d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))))))),
% 31.91/32.10 inference(rewrite,[status(thm)],[])).
% 31.91/32.10 tff(251,plain,
% 31.91/32.10 (((~![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(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))), lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((~((~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))) | (~(d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, 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(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))), lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((~((~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))))) | (~(d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))))))),
% 31.91/32.10 inference(monotonicity,[status(thm)],[250])).
% 31.91/32.10 tff(252,plain,
% 31.91/32.10 (((~![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(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))), lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((~((~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))) | (~(d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, 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(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))), lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((~((~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))))) | (~(d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))))))),
% 31.91/32.10 inference(transitivity,[status(thm)],[251, 249])).
% 31.91/32.10 tff(253,plain,
% 31.91/32.10 ((~![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(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))), lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((~((~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))) | (~(d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))))))))),
% 31.91/32.10 inference(quant_inst,[status(thm)],[])).
% 31.91/32.10 tff(254,plain,
% 31.91/32.10 ((~![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(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))), lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((~((~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))))) | (~(d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))))))),
% 31.91/32.10 inference(modus_ponens,[status(thm)],[253, 252])).
% 31.91/32.10 tff(255,plain,
% 31.91/32.10 (forallprefers(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))), lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((~((~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))))) | (~(d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))))),
% 31.91/32.10 inference(unit_resolution,[status(thm)],[254, 25])).
% 31.91/32.10 tff(256,plain,
% 31.91/32.10 ((~![P: $i, Q: $i, R: $i] : (f3(P, Q, R) = lazy_impl(prop(R), impl(impl(P, R), impl(impl(Q, R), R))))) | (f3(P!8, Q!7, true) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.91/32.10 inference(quant_inst,[status(thm)],[])).
% 31.91/32.10 tff(257,plain,
% 31.91/32.10 (f3(P!8, Q!7, true) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.91/32.10 inference(unit_resolution,[status(thm)],[256, 39])).
% 31.91/32.10 tff(258,plain,
% 31.91/32.10 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = f3(P!8, Q!7, true)),
% 31.91/32.10 inference(symmetry,[status(thm)],[257])).
% 31.91/32.10 tff(259,plain,
% 31.91/32.10 (forallprefers(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))), lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> forallprefers(f3(P!8, Q!7, true), f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.91/32.10 inference(monotonicity,[status(thm)],[258, 42])).
% 31.91/32.10 tff(260,plain,
% 31.91/32.10 (forallprefers(f3(P!8, Q!7, true), f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) <=> forallprefers(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))), lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))),
% 31.91/32.10 inference(symmetry,[status(thm)],[259])).
% 31.91/32.10 tff(261,plain,
% 31.91/32.10 ((~forallprefers(f3(P!8, Q!7, true), f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))) <=> (~forallprefers(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))), lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))),
% 31.91/32.10 inference(monotonicity,[status(thm)],[260])).
% 31.91/32.10 tff(262,plain,
% 31.91/32.10 (^[P: $i, Q: $i] : refl((~((~(or2(P, Q) = phi(f3(P, Q, tptp_fun_R_2(Q, P))))) | (~![R1: $i] : (~forallprefers(f3(P, Q, R1), f3(P, Q, tptp_fun_R_2(Q, P))))))) <=> (~((~(or2(P, Q) = phi(f3(P, Q, tptp_fun_R_2(Q, P))))) | (~![R1: $i] : (~forallprefers(f3(P, Q, R1), f3(P, Q, tptp_fun_R_2(Q, P))))))))),
% 31.91/32.10 inference(bind,[status(th)],[])).
% 31.91/32.10 tff(263,plain,
% 31.91/32.10 (![P: $i, Q: $i] : (~((~(or2(P, Q) = phi(f3(P, Q, tptp_fun_R_2(Q, P))))) | (~![R1: $i] : (~forallprefers(f3(P, Q, R1), f3(P, Q, tptp_fun_R_2(Q, P))))))) <=> ![P: $i, Q: $i] : (~((~(or2(P, Q) = phi(f3(P, Q, tptp_fun_R_2(Q, P))))) | (~![R1: $i] : (~forallprefers(f3(P, Q, R1), f3(P, Q, tptp_fun_R_2(Q, P)))))))),
% 31.91/32.10 inference(quant_intro,[status(thm)],[262])).
% 31.91/32.10 tff(264,plain,
% 31.91/32.10 (^[P: $i, Q: $i] : rewrite((~((~(or2(P, Q) = phi(f3(P, Q, tptp_fun_R_2(Q, P))))) | (~![R1: $i] : (~forallprefers(f3(P, Q, R1), f3(P, Q, tptp_fun_R_2(Q, P))))))) <=> (~((~(or2(P, Q) = phi(f3(P, Q, tptp_fun_R_2(Q, P))))) | (~![R1: $i] : (~forallprefers(f3(P, Q, R1), f3(P, Q, tptp_fun_R_2(Q, P))))))))),
% 31.91/32.10 inference(bind,[status(th)],[])).
% 31.91/32.10 tff(265,plain,
% 31.91/32.10 (![P: $i, Q: $i] : (~((~(or2(P, Q) = phi(f3(P, Q, tptp_fun_R_2(Q, P))))) | (~![R1: $i] : (~forallprefers(f3(P, Q, R1), f3(P, Q, tptp_fun_R_2(Q, P))))))) <=> ![P: $i, Q: $i] : (~((~(or2(P, Q) = phi(f3(P, Q, tptp_fun_R_2(Q, P))))) | (~![R1: $i] : (~forallprefers(f3(P, Q, R1), f3(P, Q, tptp_fun_R_2(Q, P)))))))),
% 31.91/32.10 inference(quant_intro,[status(thm)],[264])).
% 31.91/32.10 tff(266,plain,
% 31.91/32.10 (![P: $i, Q: $i] : (~((~(or2(P, Q) = phi(f3(P, Q, tptp_fun_R_2(Q, P))))) | (~![R1: $i] : (~forallprefers(f3(P, Q, R1), f3(P, Q, tptp_fun_R_2(Q, P))))))) <=> ![P: $i, Q: $i] : (~((~(or2(P, Q) = phi(f3(P, Q, tptp_fun_R_2(Q, P))))) | (~![R1: $i] : (~forallprefers(f3(P, Q, R1), f3(P, Q, tptp_fun_R_2(Q, P)))))))),
% 31.91/32.10 inference(transitivity,[status(thm)],[265, 263])).
% 31.91/32.10 tff(267,plain,
% 31.91/32.10 (^[P: $i, Q: $i] : rewrite(((or2(P, Q) = phi(f3(P, Q, tptp_fun_R_2(Q, P)))) & ![R1: $i] : (~forallprefers(f3(P, Q, R1), f3(P, Q, tptp_fun_R_2(Q, P))))) <=> (~((~(or2(P, Q) = phi(f3(P, Q, tptp_fun_R_2(Q, P))))) | (~![R1: $i] : (~forallprefers(f3(P, Q, R1), f3(P, Q, tptp_fun_R_2(Q, P))))))))),
% 31.91/32.10 inference(bind,[status(th)],[])).
% 31.91/32.10 tff(268,plain,
% 31.91/32.10 (![P: $i, Q: $i] : ((or2(P, Q) = phi(f3(P, Q, tptp_fun_R_2(Q, P)))) & ![R1: $i] : (~forallprefers(f3(P, Q, R1), f3(P, Q, tptp_fun_R_2(Q, P))))) <=> ![P: $i, Q: $i] : (~((~(or2(P, Q) = phi(f3(P, Q, tptp_fun_R_2(Q, P))))) | (~![R1: $i] : (~forallprefers(f3(P, Q, R1), f3(P, Q, tptp_fun_R_2(Q, P)))))))),
% 31.91/32.10 inference(quant_intro,[status(thm)],[267])).
% 31.91/32.10 tff(269,plain,
% 31.91/32.10 (![P: $i, Q: $i] : ?[R: $i] : ((or2(P, Q) = phi(f3(P, Q, R))) & (~?[R1: $i] : forallprefers(f3(P, Q, R1), f3(P, Q, R)))) <=> ![P: $i, Q: $i] : ?[R: $i] : ((or2(P, Q) = phi(f3(P, Q, R))) & (~?[R1: $i] : forallprefers(f3(P, Q, R1), f3(P, Q, R))))),
% 31.91/32.10 inference(rewrite,[status(thm)],[])).
% 31.91/32.10 tff(270,axiom,(![P: $i, Q: $i] : ?[R: $i] : ((or2(P, Q) = phi(f3(P, Q, R))) & (~?[R1: $i] : forallprefers(f3(P, Q, R1), f3(P, Q, R))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_or2')).
% 31.91/32.10 tff(271,plain,
% 31.91/32.10 (![P: $i, Q: $i] : ?[R: $i] : ((or2(P, Q) = phi(f3(P, Q, R))) & (~?[R1: $i] : forallprefers(f3(P, Q, R1), f3(P, Q, R))))),
% 31.91/32.10 inference(modus_ponens,[status(thm)],[270, 269])).
% 31.91/32.10 tff(272,plain,(
% 31.91/32.10 ![P: $i, Q: $i] : ((or2(P, Q) = phi(f3(P, Q, tptp_fun_R_2(Q, P)))) & ![R1: $i] : (~forallprefers(f3(P, Q, R1), f3(P, Q, tptp_fun_R_2(Q, P)))))),
% 31.91/32.10 inference(skolemize,[status(sab)],[271])).
% 31.91/32.10 tff(273,plain,
% 31.91/32.10 (![P: $i, Q: $i] : (~((~(or2(P, Q) = phi(f3(P, Q, tptp_fun_R_2(Q, P))))) | (~![R1: $i] : (~forallprefers(f3(P, Q, R1), f3(P, Q, tptp_fun_R_2(Q, P)))))))),
% 31.91/32.10 inference(modus_ponens,[status(thm)],[272, 268])).
% 31.91/32.10 tff(274,plain,
% 31.91/32.10 (![P: $i, Q: $i] : (~((~(or2(P, Q) = phi(f3(P, Q, tptp_fun_R_2(Q, P))))) | (~![R1: $i] : (~forallprefers(f3(P, Q, R1), f3(P, Q, tptp_fun_R_2(Q, P)))))))),
% 31.91/32.10 inference(modus_ponens,[status(thm)],[273, 266])).
% 31.91/32.10 tff(275,plain,
% 31.91/32.10 ((~![P: $i, Q: $i] : (~((~(or2(P, Q) = phi(f3(P, Q, tptp_fun_R_2(Q, P))))) | (~![R1: $i] : (~forallprefers(f3(P, Q, R1), f3(P, Q, tptp_fun_R_2(Q, P)))))))) | (~((~(or2(P!8, Q!7) = phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))))) | (~![R1: $i] : (~forallprefers(f3(P!8, Q!7, R1), f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))))))),
% 31.91/32.10 inference(quant_inst,[status(thm)],[])).
% 31.91/32.10 tff(276,plain,
% 31.91/32.10 (~((~(or2(P!8, Q!7) = phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))))) | (~![R1: $i] : (~forallprefers(f3(P!8, Q!7, R1), f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))))))),
% 31.91/32.10 inference(unit_resolution,[status(thm)],[275, 274])).
% 31.91/32.10 tff(277,plain,
% 31.91/32.10 (((~(or2(P!8, Q!7) = phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))))) | (~![R1: $i] : (~forallprefers(f3(P!8, Q!7, R1), f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))))) | ![R1: $i] : (~forallprefers(f3(P!8, Q!7, R1), f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))))),
% 31.91/32.10 inference(tautology,[status(thm)],[])).
% 31.91/32.10 tff(278,plain,
% 31.91/32.10 (![R1: $i] : (~forallprefers(f3(P!8, Q!7, R1), f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))))),
% 31.91/32.10 inference(unit_resolution,[status(thm)],[277, 276])).
% 31.91/32.10 tff(279,plain,
% 31.91/32.10 ((~![R1: $i] : (~forallprefers(f3(P!8, Q!7, R1), f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))))) | (~forallprefers(f3(P!8, Q!7, true), f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))))),
% 31.91/32.10 inference(quant_inst,[status(thm)],[])).
% 31.91/32.10 tff(280,plain,
% 31.91/32.10 (~forallprefers(f3(P!8, Q!7, true), f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.91/32.10 inference(unit_resolution,[status(thm)],[279, 278])).
% 31.91/32.10 tff(281,plain,
% 31.91/32.10 (~forallprefers(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))), lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))),
% 31.91/32.10 inference(modus_ponens,[status(thm)],[280, 261])).
% 31.91/32.10 tff(282,plain,
% 31.91/32.10 ((~(forallprefers(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))), lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((~((~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))))) | (~(d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))))))) | forallprefers(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))), lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) | (~((~((~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))))) | (~(d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))))))),
% 31.91/32.10 inference(tautology,[status(thm)],[])).
% 31.91/32.10 tff(283,plain,
% 31.91/32.10 (~((~((~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))))) | (~(d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))))),
% 31.91/32.10 inference(unit_resolution,[status(thm)],[282, 281, 255])).
% 31.91/32.10 tff(284,plain,
% 31.91/32.10 (((~((~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))))) | (~(d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))))) | (d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))),
% 31.91/32.10 inference(tautology,[status(thm)],[])).
% 31.91/32.10 tff(285,plain,
% 31.91/32.10 (d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))),
% 31.91/32.10 inference(unit_resolution,[status(thm)],[284, 283])).
% 31.91/32.10 tff(286,plain,
% 31.91/32.10 ((~(d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))) | d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))),
% 31.91/32.10 inference(tautology,[status(thm)],[])).
% 31.91/32.10 tff(287,plain,
% 31.91/32.10 (d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))),
% 31.91/32.10 inference(unit_resolution,[status(thm)],[286, 285])).
% 31.91/32.10 tff(288,plain,
% 31.91/32.10 (d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.91/32.10 inference(unit_resolution,[status(thm)],[287, 206])).
% 31.91/32.10 tff(289,plain,
% 31.91/32.10 (((~((~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))))) | (~(d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))))) | ((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))))),
% 31.95/32.11 inference(tautology,[status(thm)],[])).
% 31.95/32.11 tff(290,plain,
% 31.95/32.11 ((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.95/32.11 inference(unit_resolution,[status(thm)],[289, 283])).
% 31.95/32.11 tff(291,plain,
% 31.95/32.11 ((~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.95/32.11 inference(tautology,[status(thm)],[])).
% 31.95/32.11 tff(292,plain,
% 31.95/32.11 ((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.95/32.11 inference(unit_resolution,[status(thm)],[291, 290])).
% 31.95/32.11 tff(293,plain,
% 31.95/32.11 (bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.95/32.11 inference(unit_resolution,[status(thm)],[292, 288, 248, 206])).
% 31.95/32.11 tff(294,plain,
% 31.95/32.11 ((~(bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) <=> ((lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false) | (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true)))) | (~bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | ((lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false) | (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true))),
% 31.95/32.11 inference(tautology,[status(thm)],[])).
% 31.95/32.11 tff(295,plain,
% 31.95/32.11 ((~(bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) <=> ((lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false) | (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true)))) | ((lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false) | (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true))),
% 31.95/32.11 inference(unit_resolution,[status(thm)],[294, 293])).
% 31.95/32.11 tff(296,plain,
% 31.95/32.11 ((lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false) | (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true)),
% 31.95/32.11 inference(unit_resolution,[status(thm)],[295, 193])).
% 31.95/32.11 tff(297,plain,
% 31.95/32.11 (((~((~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))))) | (~(d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))))) | ((~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))),
% 31.95/32.11 inference(tautology,[status(thm)],[])).
% 31.95/32.11 tff(298,plain,
% 31.95/32.11 ((~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true))),
% 31.95/32.11 inference(unit_resolution,[status(thm)],[297, 283])).
% 31.95/32.11 tff(299,plain,
% 31.95/32.11 ((~((~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)))) | (~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true))),
% 31.95/32.11 inference(tautology,[status(thm)],[])).
% 31.95/32.11 tff(300,plain,
% 31.95/32.11 ((~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true))),
% 31.95/32.11 inference(unit_resolution,[status(thm)],[299, 298])).
% 31.95/32.11 tff(301,plain,
% 31.95/32.11 (~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)),
% 31.95/32.11 inference(unit_resolution,[status(thm)],[300, 12])).
% 31.95/32.11 tff(302,plain,
% 31.95/32.11 ((~((lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false) | (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true))) | (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false) | (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true)),
% 31.95/32.11 inference(tautology,[status(thm)],[])).
% 31.95/32.11 tff(303,plain,
% 31.95/32.11 ((~((lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false) | (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true))) | (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true)),
% 31.95/32.11 inference(unit_resolution,[status(thm)],[302, 301])).
% 31.95/32.11 tff(304,plain,
% 31.95/32.11 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true),
% 31.95/32.11 inference(unit_resolution,[status(thm)],[303, 296])).
% 31.95/32.11 tff(305,plain,
% 31.95/32.11 (^[X: $i] : refl(((prop(X) = true) <=> bool(X)) <=> ((prop(X) = true) <=> bool(X)))),
% 31.95/32.11 inference(bind,[status(th)],[])).
% 31.95/32.11 tff(306,plain,
% 31.95/32.11 (![X: $i] : ((prop(X) = true) <=> bool(X)) <=> ![X: $i] : ((prop(X) = true) <=> bool(X))),
% 31.95/32.11 inference(quant_intro,[status(thm)],[305])).
% 31.95/32.11 tff(307,plain,
% 31.95/32.11 (![X: $i] : ((prop(X) = true) <=> bool(X)) <=> ![X: $i] : ((prop(X) = true) <=> bool(X))),
% 31.95/32.11 inference(rewrite,[status(thm)],[])).
% 31.95/32.11 tff(308,axiom,(![X: $i] : ((prop(X) = true) <=> bool(X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','prop_true')).
% 31.95/32.11 tff(309,plain,
% 31.95/32.11 (![X: $i] : ((prop(X) = true) <=> bool(X))),
% 31.95/32.11 inference(modus_ponens,[status(thm)],[308, 307])).
% 31.95/32.11 tff(310,plain,(
% 31.95/32.11 ![X: $i] : ((prop(X) = true) <=> bool(X))),
% 31.95/32.11 inference(skolemize,[status(sab)],[309])).
% 31.95/32.11 tff(311,plain,
% 31.95/32.11 (![X: $i] : ((prop(X) = true) <=> bool(X))),
% 31.95/32.11 inference(modus_ponens,[status(thm)],[310, 306])).
% 31.95/32.11 tff(312,plain,
% 31.95/32.11 ((~![X: $i] : ((prop(X) = true) <=> bool(X))) | ((prop(true) = true) <=> bool(true))),
% 31.95/32.11 inference(quant_inst,[status(thm)],[])).
% 31.95/32.11 tff(313,plain,
% 31.95/32.11 ((prop(true) = true) <=> bool(true)),
% 31.95/32.11 inference(unit_resolution,[status(thm)],[312, 311])).
% 31.95/32.11 tff(314,plain,
% 31.95/32.11 ((~((prop(true) = true) <=> bool(true))) | (prop(true) = true) | (~bool(true))),
% 31.95/32.11 inference(tautology,[status(thm)],[])).
% 31.95/32.11 tff(315,plain,
% 31.95/32.11 ((~((prop(true) = true) <=> bool(true))) | (prop(true) = true)),
% 31.95/32.11 inference(unit_resolution,[status(thm)],[314, 247])).
% 31.95/32.11 tff(316,plain,
% 31.95/32.11 (prop(true) = true),
% 31.95/32.11 inference(unit_resolution,[status(thm)],[315, 313])).
% 31.95/32.11 tff(317,plain,
% 31.95/32.11 (true = prop(true)),
% 31.95/32.11 inference(symmetry,[status(thm)],[316])).
% 31.95/32.11 tff(318,plain,
% 31.95/32.11 (lazy_impl(true, impl(impl(P!8, true), impl(impl(Q!7, true), true))) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.95/32.11 inference(monotonicity,[status(thm)],[317])).
% 31.95/32.11 tff(319,plain,
% 31.95/32.11 (^[B: $i] : refl((lazy_impl(true, B) = phi(B)) <=> (lazy_impl(true, B) = phi(B)))),
% 31.95/32.11 inference(bind,[status(th)],[])).
% 31.95/32.11 tff(320,plain,
% 31.95/32.11 (![B: $i] : (lazy_impl(true, B) = phi(B)) <=> ![B: $i] : (lazy_impl(true, B) = phi(B))),
% 31.95/32.11 inference(quant_intro,[status(thm)],[319])).
% 31.95/32.11 tff(321,plain,
% 31.95/32.11 (![B: $i] : (lazy_impl(true, B) = phi(B)) <=> ![B: $i] : (lazy_impl(true, B) = phi(B))),
% 31.95/32.11 inference(rewrite,[status(thm)],[])).
% 31.95/32.11 tff(322,axiom,(![B: $i] : (lazy_impl(true, B) = phi(B))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','lazy_impl_axiom3')).
% 31.95/32.11 tff(323,plain,
% 31.95/32.11 (![B: $i] : (lazy_impl(true, B) = phi(B))),
% 31.95/32.11 inference(modus_ponens,[status(thm)],[322, 321])).
% 31.95/32.11 tff(324,plain,(
% 31.95/32.11 ![B: $i] : (lazy_impl(true, B) = phi(B))),
% 31.95/32.11 inference(skolemize,[status(sab)],[323])).
% 31.95/32.11 tff(325,plain,
% 31.95/32.11 (![B: $i] : (lazy_impl(true, B) = phi(B))),
% 31.95/32.11 inference(modus_ponens,[status(thm)],[324, 320])).
% 31.95/32.11 tff(326,plain,
% 31.95/32.11 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, impl(impl(P!8, true), impl(impl(Q!7, true), true))) = phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.95/32.11 inference(quant_inst,[status(thm)],[])).
% 31.95/32.11 tff(327,plain,
% 31.95/32.11 (lazy_impl(true, impl(impl(P!8, true), impl(impl(Q!7, true), true))) = phi(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.95/32.11 inference(unit_resolution,[status(thm)],[326, 325])).
% 31.95/32.11 tff(328,plain,
% 31.95/32.11 (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = lazy_impl(true, impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.95/32.11 inference(symmetry,[status(thm)],[327])).
% 31.95/32.11 tff(329,plain,
% 31.95/32.11 (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true),
% 31.95/32.11 inference(transitivity,[status(thm)],[328, 318, 304])).
% 31.95/32.11 tff(330,plain,
% 31.95/32.11 ((phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err) <=> (true = err)),
% 31.95/32.11 inference(monotonicity,[status(thm)],[329])).
% 31.95/32.11 tff(331,plain,
% 31.95/32.11 ((true = err) <=> (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)),
% 31.95/32.11 inference(symmetry,[status(thm)],[330])).
% 31.95/32.11 tff(332,plain,
% 31.95/32.11 ((~(true = err)) <=> (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err))),
% 31.95/32.11 inference(monotonicity,[status(thm)],[331])).
% 31.95/32.11 tff(333,plain,
% 31.95/32.11 (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)),
% 31.95/32.11 inference(modus_ponens,[status(thm)],[153, 332])).
% 31.95/32.11 tff(334,plain,
% 31.95/32.11 ((d(impl(impl(P!8, true), impl(impl(Q!7, true), true))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err))) | (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)),
% 31.95/32.11 inference(tautology,[status(thm)],[])).
% 31.95/32.11 tff(335,plain,
% 31.95/32.11 (d(impl(impl(P!8, true), impl(impl(Q!7, true), true))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err))),
% 31.95/32.11 inference(unit_resolution,[status(thm)],[334, 333])).
% 31.95/32.11 tff(336,plain,
% 31.95/32.11 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~(d(impl(impl(P!8, true), impl(impl(Q!7, true), true))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)))) | (~((~d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true)))))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~(d(impl(impl(P!8, true), impl(impl(Q!7, true), true))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)))) | (~((~d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true)))))))),
% 31.95/32.11 inference(rewrite,[status(thm)],[])).
% 31.95/32.11 tff(337,plain,
% 31.95/32.11 (((~((~d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true)))))) | (~(d(impl(impl(P!8, true), impl(impl(Q!7, true), true))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err))))) <=> ((~(d(impl(impl(P!8, true), impl(impl(Q!7, true), true))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)))) | (~((~d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true)))))))),
% 31.95/32.11 inference(rewrite,[status(thm)],[])).
% 31.95/32.11 tff(338,plain,
% 31.95/32.11 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true)))))) | (~(d(impl(impl(P!8, true), impl(impl(Q!7, true), true))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~(d(impl(impl(P!8, true), impl(impl(Q!7, true), true))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)))) | (~((~d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true))))))))),
% 31.95/32.11 inference(monotonicity,[status(thm)],[337])).
% 31.95/32.11 tff(339,plain,
% 31.95/32.11 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true)))))) | (~(d(impl(impl(P!8, true), impl(impl(Q!7, true), true))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~(d(impl(impl(P!8, true), impl(impl(Q!7, true), true))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)))) | (~((~d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true)))))))),
% 31.95/32.11 inference(transitivity,[status(thm)],[338, 336])).
% 31.95/32.11 tff(340,plain,
% 31.95/32.11 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true)))))) | (~(d(impl(impl(P!8, true), impl(impl(Q!7, true), true))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)))))),
% 31.95/32.11 inference(quant_inst,[status(thm)],[])).
% 31.95/32.11 tff(341,plain,
% 31.95/32.11 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~(d(impl(impl(P!8, true), impl(impl(Q!7, true), true))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)))) | (~((~d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true))))))),
% 31.95/32.11 inference(modus_ponens,[status(thm)],[340, 339])).
% 31.95/32.11 tff(342,plain,
% 31.95/32.11 ((~(d(impl(impl(P!8, true), impl(impl(Q!7, true), true))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)))) | (~((~d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true))))))),
% 31.95/32.11 inference(unit_resolution,[status(thm)],[341, 127])).
% 31.95/32.11 tff(343,plain,
% 31.95/32.11 (~((~d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true)))))),
% 31.95/32.11 inference(unit_resolution,[status(thm)],[342, 335])).
% 31.95/32.11 tff(344,plain,
% 31.95/32.11 (((~d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.95/32.11 inference(tautology,[status(thm)],[])).
% 31.95/32.11 tff(345,plain,
% 31.95/32.11 (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.95/32.11 inference(unit_resolution,[status(thm)],[344, 343])).
% 31.95/32.11 tff(346,plain,
% 31.95/32.11 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.95/32.11 inference(symmetry,[status(thm)],[345])).
% 31.95/32.11 tff(347,plain,
% 31.95/32.11 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(P!8) | (impl(P!8, true) = phi(P!8)))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(P!8) | (impl(P!8, true) = phi(P!8)))),
% 31.95/32.11 inference(rewrite,[status(thm)],[])).
% 31.95/32.11 tff(348,plain,
% 31.95/32.11 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(P!8) | (impl(P!8, true) = phi(P!8)))),
% 31.95/32.11 inference(quant_inst,[status(thm)],[])).
% 31.95/32.11 tff(349,plain,
% 31.95/32.11 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(P!8) | (impl(P!8, true) = phi(P!8))),
% 31.95/32.11 inference(modus_ponens,[status(thm)],[348, 347])).
% 31.95/32.11 tff(350,plain,
% 31.95/32.11 (bool(P!8) | (impl(P!8, true) = phi(P!8))),
% 31.95/32.11 inference(unit_resolution,[status(thm)],[349, 81])).
% 31.95/32.11 tff(351,plain,
% 31.95/32.11 (impl(P!8, true) = phi(P!8)),
% 31.95/32.11 inference(unit_resolution,[status(thm)],[350, 46])).
% 31.95/32.11 tff(352,plain,
% 31.95/32.11 (impl(P!8, true) = impl(P!8, tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.11 inference(transitivity,[status(thm)],[351, 87])).
% 31.95/32.11 tff(353,plain,
% 31.95/32.11 (bool(impl(P!8, true)) <=> bool(impl(P!8, tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.11 inference(monotonicity,[status(thm)],[352])).
% 31.95/32.11 tff(354,plain,
% 31.95/32.11 (bool(impl(P!8, tptp_fun_R_2(Q!7, P!8))) <=> bool(impl(P!8, true))),
% 31.95/32.11 inference(symmetry,[status(thm)],[353])).
% 31.95/32.11 tff(355,plain,
% 31.95/32.11 (bool(phi(P!8)) <=> bool(impl(P!8, true))),
% 31.95/32.11 inference(transitivity,[status(thm)],[183, 354])).
% 31.95/32.11 tff(356,plain,
% 31.95/32.11 ((~bool(phi(P!8))) <=> (~bool(impl(P!8, true)))),
% 31.95/32.11 inference(monotonicity,[status(thm)],[355])).
% 31.95/32.11 tff(357,plain,
% 31.95/32.11 ((phi(P!8) = true) <=> (impl(P!8, tptp_fun_R_2(Q!7, P!8)) = true)),
% 31.95/32.11 inference(monotonicity,[status(thm)],[87])).
% 31.95/32.11 tff(358,plain,
% 31.95/32.11 ((impl(P!8, tptp_fun_R_2(Q!7, P!8)) = true) <=> (phi(P!8) = true)),
% 31.95/32.11 inference(symmetry,[status(thm)],[357])).
% 31.95/32.11 tff(359,plain,
% 31.95/32.11 ((~(impl(P!8, tptp_fun_R_2(Q!7, P!8)) = true)) <=> (~(phi(P!8) = true))),
% 31.95/32.11 inference(monotonicity,[status(thm)],[358])).
% 31.95/32.11 tff(360,plain,
% 31.95/32.11 ((phi(P!8) = impl(P!8, tptp_fun_R_2(Q!7, P!8))) <=> (impl(P!8, tptp_fun_R_2(Q!7, P!8)) = phi(P!8))),
% 31.95/32.11 inference(commutativity,[status(thm)],[])).
% 31.95/32.11 tff(361,assumption,(impl(P!8, tptp_fun_R_2(Q!7, P!8)) = true), introduced(assumption)).
% 31.95/32.11 tff(362,plain,
% 31.95/32.11 (true = impl(P!8, tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.11 inference(symmetry,[status(thm)],[361])).
% 31.95/32.11 tff(363,plain,
% 31.95/32.11 (phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = phi(true)),
% 31.95/32.11 inference(monotonicity,[status(thm)],[209])).
% 31.95/32.11 tff(364,plain,
% 31.95/32.11 (((~(or2(P!8, Q!7) = phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))))) | (~![R1: $i] : (~forallprefers(f3(P!8, Q!7, R1), f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))))) | (or2(P!8, Q!7) = phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))))),
% 31.95/32.12 inference(tautology,[status(thm)],[])).
% 31.95/32.12 tff(365,plain,
% 31.95/32.12 (or2(P!8, Q!7) = phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[364, 276])).
% 31.95/32.12 tff(366,plain,
% 31.95/32.12 (or2(P!8, Q!7) = impl(P!8, tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.12 inference(transitivity,[status(thm)],[365, 363, 221, 362])).
% 31.95/32.12 tff(367,plain,
% 31.95/32.12 ((or1(P!8, Q!7) = or2(P!8, Q!7)) <=> (phi(P!8) = impl(P!8, tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.12 inference(monotonicity,[status(thm)],[61, 366])).
% 31.95/32.12 tff(368,plain,
% 31.95/32.12 ((or1(P!8, Q!7) = or2(P!8, Q!7)) <=> (impl(P!8, tptp_fun_R_2(Q!7, P!8)) = phi(P!8))),
% 31.95/32.12 inference(transitivity,[status(thm)],[367, 360])).
% 31.95/32.12 tff(369,plain,
% 31.95/32.12 ((impl(P!8, tptp_fun_R_2(Q!7, P!8)) = phi(P!8)) <=> (or1(P!8, Q!7) = or2(P!8, Q!7))),
% 31.95/32.12 inference(symmetry,[status(thm)],[368])).
% 31.95/32.12 tff(370,plain,
% 31.95/32.12 (or1(P!8, Q!7) = or2(P!8, Q!7)),
% 31.95/32.12 inference(modus_ponens,[status(thm)],[86, 369])).
% 31.95/32.12 tff(371,plain,
% 31.95/32.12 ((~![P: $i, Q: $i] : (or1(P, Q) = or2(P, Q))) <=> (~![P: $i, Q: $i] : (or1(P, Q) = or2(P, Q)))),
% 31.95/32.12 inference(rewrite,[status(thm)],[])).
% 31.95/32.12 tff(372,axiom,(~![P: $i, Q: $i] : (or1(P, Q) = or2(P, Q))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','or1_or2')).
% 31.95/32.12 tff(373,plain,
% 31.95/32.12 (~![P: $i, Q: $i] : (or1(P, Q) = or2(P, Q))),
% 31.95/32.12 inference(modus_ponens,[status(thm)],[372, 371])).
% 31.95/32.12 tff(374,plain,
% 31.95/32.12 (~![P: $i, Q: $i] : (or1(P, Q) = or2(P, Q))),
% 31.95/32.12 inference(modus_ponens,[status(thm)],[373, 371])).
% 31.95/32.12 tff(375,plain,
% 31.95/32.12 (~![P: $i, Q: $i] : (or1(P, Q) = or2(P, Q))),
% 31.95/32.12 inference(modus_ponens,[status(thm)],[374, 371])).
% 31.95/32.12 tff(376,plain,
% 31.95/32.12 (~![P: $i, Q: $i] : (or1(P, Q) = or2(P, Q))),
% 31.95/32.12 inference(modus_ponens,[status(thm)],[375, 371])).
% 31.95/32.12 tff(377,plain,(
% 31.95/32.12 ~(or1(P!8, Q!7) = or2(P!8, Q!7))),
% 31.95/32.12 inference(skolemize,[status(sab)],[376])).
% 31.95/32.12 tff(378,plain,
% 31.95/32.12 ($false),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[377, 370])).
% 31.95/32.12 tff(379,plain,(bool(P!8) | (~(impl(P!8, tptp_fun_R_2(Q!7, P!8)) = true)) | (~(prop(tptp_fun_R_2(Q!7, P!8)) = false))), inference(lemma,lemma(discharge,[]))).
% 31.95/32.12 tff(380,plain,
% 31.95/32.12 (~(impl(P!8, tptp_fun_R_2(Q!7, P!8)) = true)),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[379, 10, 46])).
% 31.95/32.12 tff(381,plain,
% 31.95/32.12 (~(phi(P!8) = true)),
% 31.95/32.12 inference(modus_ponens,[status(thm)],[380, 359])).
% 31.95/32.12 tff(382,plain,
% 31.95/32.12 (~((phi(P!8) = false) | (phi(P!8) = true))),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[159, 381, 135])).
% 31.95/32.12 tff(383,plain,
% 31.95/32.12 (~bool(phi(P!8))),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[161, 382, 71])).
% 31.95/32.12 tff(384,plain,
% 31.95/32.12 (~bool(impl(P!8, true))),
% 31.95/32.12 inference(modus_ponens,[status(thm)],[383, 356])).
% 31.95/32.12 tff(385,plain,
% 31.95/32.12 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(P!8, true)) | (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(P!8, true))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(P!8, true)) | (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(P!8, true))))),
% 31.95/32.12 inference(rewrite,[status(thm)],[])).
% 31.95/32.12 tff(386,plain,
% 31.95/32.12 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(P!8, true)) | (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(P!8, true))))),
% 31.95/32.12 inference(quant_inst,[status(thm)],[])).
% 31.95/32.12 tff(387,plain,
% 31.95/32.12 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(P!8, true)) | (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(P!8, true)))),
% 31.95/32.12 inference(modus_ponens,[status(thm)],[386, 385])).
% 31.95/32.12 tff(388,plain,
% 31.95/32.12 (bool(impl(P!8, true)) | (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(P!8, true)))),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[387, 81])).
% 31.95/32.12 tff(389,plain,
% 31.95/32.12 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(P!8, true))),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[388, 384])).
% 31.95/32.12 tff(390,plain,
% 31.95/32.12 (phi(impl(P!8, true)) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.95/32.12 inference(symmetry,[status(thm)],[389])).
% 31.95/32.12 tff(391,plain,
% 31.95/32.12 (phi(P!8) = impl(P!8, true)),
% 31.95/32.12 inference(symmetry,[status(thm)],[351])).
% 31.95/32.12 tff(392,plain,
% 31.95/32.12 (phi(phi(P!8)) = phi(impl(P!8, true))),
% 31.95/32.12 inference(monotonicity,[status(thm)],[391])).
% 31.95/32.12 tff(393,plain,
% 31.95/32.12 (phi(phi(P!8)) = true),
% 31.95/32.12 inference(transitivity,[status(thm)],[392, 390, 346, 328, 318, 304])).
% 31.95/32.12 tff(394,plain,
% 31.95/32.12 ((phi(phi(P!8)) = phi(P!8)) <=> (true = impl(P!8, tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.12 inference(monotonicity,[status(thm)],[393, 87])).
% 31.95/32.12 tff(395,plain,
% 31.95/32.12 ((phi(phi(P!8)) = phi(P!8)) <=> (impl(P!8, tptp_fun_R_2(Q!7, P!8)) = true)),
% 31.95/32.12 inference(transitivity,[status(thm)],[394, 191])).
% 31.95/32.12 tff(396,plain,
% 31.95/32.12 ((impl(P!8, tptp_fun_R_2(Q!7, P!8)) = true) <=> (phi(phi(P!8)) = phi(P!8))),
% 31.95/32.12 inference(symmetry,[status(thm)],[395])).
% 31.95/32.12 tff(397,plain,
% 31.95/32.12 ((~(impl(P!8, tptp_fun_R_2(Q!7, P!8)) = true)) <=> (~(phi(phi(P!8)) = phi(P!8)))),
% 31.95/32.12 inference(monotonicity,[status(thm)],[396])).
% 31.95/32.12 tff(398,plain,
% 31.95/32.12 (~(phi(phi(P!8)) = phi(P!8))),
% 31.95/32.12 inference(modus_ponens,[status(thm)],[380, 397])).
% 31.95/32.12 tff(399,assumption,(impl(P!8, tptp_fun_R_2(Q!7, P!8)) = phi(P!8)), introduced(assumption)).
% 31.95/32.12 tff(400,plain,
% 31.95/32.12 (phi(P!8) = impl(P!8, tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.12 inference(symmetry,[status(thm)],[399])).
% 31.95/32.12 tff(401,plain,
% 31.95/32.12 ((phi(P!8) = phi(phi(P!8))) <=> (phi(phi(P!8)) = phi(P!8))),
% 31.95/32.12 inference(commutativity,[status(thm)],[])).
% 31.95/32.12 tff(402,assumption,(~(phi(phi(P!8)) = phi(P!8))), introduced(assumption)).
% 31.95/32.12 tff(403,plain,
% 31.95/32.12 (((~d(phi(P!8))) | (~(phi(phi(P!8)) = phi(P!8)))) | (phi(phi(P!8)) = phi(P!8))),
% 31.95/32.12 inference(tautology,[status(thm)],[])).
% 31.95/32.12 tff(404,plain,
% 31.95/32.12 ((~d(phi(P!8))) | (~(phi(phi(P!8)) = phi(P!8)))),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[403, 402])).
% 31.95/32.12 tff(405,plain,
% 31.95/32.12 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(phi(P!8))) | (~(phi(phi(P!8)) = phi(P!8))))) | (~(d(phi(P!8)) | (~(phi(phi(P!8)) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(phi(P!8))) | (~(phi(phi(P!8)) = phi(P!8))))) | (~(d(phi(P!8)) | (~(phi(phi(P!8)) = err)))))),
% 31.95/32.12 inference(rewrite,[status(thm)],[])).
% 31.95/32.12 tff(406,plain,
% 31.95/32.12 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(phi(P!8))) | (~(phi(phi(P!8)) = phi(P!8))))) | (~(d(phi(P!8)) | (~(phi(phi(P!8)) = err)))))),
% 31.95/32.12 inference(quant_inst,[status(thm)],[])).
% 31.95/32.12 tff(407,plain,
% 31.95/32.12 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(phi(P!8))) | (~(phi(phi(P!8)) = phi(P!8))))) | (~(d(phi(P!8)) | (~(phi(phi(P!8)) = err))))),
% 31.95/32.12 inference(modus_ponens,[status(thm)],[406, 405])).
% 31.95/32.12 tff(408,plain,
% 31.95/32.12 ((~((~d(phi(P!8))) | (~(phi(phi(P!8)) = phi(P!8))))) | (~(d(phi(P!8)) | (~(phi(phi(P!8)) = err))))),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[407, 127])).
% 31.95/32.12 tff(409,plain,
% 31.95/32.12 (~(d(phi(P!8)) | (~(phi(phi(P!8)) = err)))),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[408, 404])).
% 31.95/32.12 tff(410,plain,
% 31.95/32.12 ((d(phi(P!8)) | (~(phi(phi(P!8)) = err))) | (phi(phi(P!8)) = err)),
% 31.95/32.12 inference(tautology,[status(thm)],[])).
% 31.95/32.12 tff(411,plain,
% 31.95/32.12 (phi(phi(P!8)) = err),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[410, 409])).
% 31.95/32.12 tff(412,plain,
% 31.95/32.12 (err = phi(phi(P!8))),
% 31.95/32.12 inference(symmetry,[status(thm)],[411])).
% 31.95/32.12 tff(413,plain,
% 31.95/32.12 ((phi(P!8) = err) <=> (phi(P!8) = phi(phi(P!8)))),
% 31.95/32.12 inference(monotonicity,[status(thm)],[412])).
% 31.95/32.12 tff(414,plain,
% 31.95/32.12 ((phi(P!8) = err) <=> (phi(phi(P!8)) = phi(P!8))),
% 31.95/32.12 inference(transitivity,[status(thm)],[413, 401])).
% 31.95/32.12 tff(415,plain,
% 31.95/32.12 ((phi(phi(P!8)) = phi(P!8)) <=> (phi(P!8) = err)),
% 31.95/32.12 inference(symmetry,[status(thm)],[414])).
% 31.95/32.12 tff(416,plain,
% 31.95/32.12 ((~(phi(phi(P!8)) = phi(P!8))) <=> (~(phi(P!8) = err))),
% 31.95/32.12 inference(monotonicity,[status(thm)],[415])).
% 31.95/32.12 tff(417,plain,
% 31.95/32.12 (~(phi(P!8) = err)),
% 31.95/32.12 inference(modus_ponens,[status(thm)],[402, 416])).
% 31.95/32.12 tff(418,plain,
% 31.95/32.12 (d(P!8) | (~(phi(P!8) = err))),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[116, 417])).
% 31.95/32.12 tff(419,plain,
% 31.95/32.12 (~((~d(P!8)) | (~(phi(P!8) = P!8)))),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[131, 418])).
% 31.95/32.12 tff(420,plain,
% 31.95/32.12 (phi(P!8) = P!8),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[106, 419])).
% 31.95/32.12 tff(421,plain,
% 31.95/32.12 (P!8 = phi(P!8)),
% 31.95/32.12 inference(symmetry,[status(thm)],[420])).
% 31.95/32.12 tff(422,plain,
% 31.95/32.12 (P!8 = impl(P!8, tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.12 inference(transitivity,[status(thm)],[421, 400])).
% 31.95/32.12 tff(423,plain,
% 31.95/32.12 (phi(P!8) = phi(impl(P!8, tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.12 inference(monotonicity,[status(thm)],[422])).
% 31.95/32.12 tff(424,plain,
% 31.95/32.12 (phi(impl(P!8, tptp_fun_R_2(Q!7, P!8))) = phi(P!8)),
% 31.95/32.12 inference(symmetry,[status(thm)],[423])).
% 31.95/32.12 tff(425,plain,
% 31.95/32.12 (phi(impl(P!8, tptp_fun_R_2(Q!7, P!8))) = phi(phi(P!8))),
% 31.95/32.12 inference(monotonicity,[status(thm)],[399])).
% 31.95/32.12 tff(426,plain,
% 31.95/32.12 (phi(phi(P!8)) = phi(impl(P!8, tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.12 inference(symmetry,[status(thm)],[425])).
% 31.95/32.12 tff(427,plain,
% 31.95/32.12 (phi(phi(P!8)) = phi(P!8)),
% 31.95/32.12 inference(transitivity,[status(thm)],[426, 424])).
% 31.95/32.12 tff(428,plain,
% 31.95/32.12 ($false),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[402, 427])).
% 31.95/32.12 tff(429,plain,((phi(phi(P!8)) = phi(P!8)) | (~(impl(P!8, tptp_fun_R_2(Q!7, P!8)) = phi(P!8)))), inference(lemma,lemma(discharge,[]))).
% 31.95/32.12 tff(430,plain,
% 31.95/32.12 (phi(phi(P!8)) = phi(P!8)),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[429, 86])).
% 31.95/32.12 tff(431,plain,
% 31.95/32.12 ($false),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[430, 398])).
% 31.95/32.12 tff(432,plain,((~(prop(tptp_fun_R_2(Q!7, P!8)) = false)) | bool(P!8)), inference(lemma,lemma(discharge,[]))).
% 31.95/32.12 tff(433,plain,
% 31.95/32.12 (~(prop(tptp_fun_R_2(Q!7, P!8)) = false)),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[432, 46])).
% 31.95/32.12 tff(434,plain,
% 31.95/32.12 (^[X: $i] : refl((~(bool(X) <=> (prop(X) = false))) <=> (~(bool(X) <=> (prop(X) = false))))),
% 31.95/32.12 inference(bind,[status(th)],[])).
% 31.95/32.12 tff(435,plain,
% 31.95/32.12 (![X: $i] : (~(bool(X) <=> (prop(X) = false))) <=> ![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 31.95/32.12 inference(quant_intro,[status(thm)],[434])).
% 31.95/32.12 tff(436,plain,
% 31.95/32.12 (![X: $i] : (~(bool(X) <=> (prop(X) = false))) <=> ![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 31.95/32.12 inference(rewrite,[status(thm)],[])).
% 31.95/32.12 tff(437,plain,
% 31.95/32.12 (^[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)))))),
% 31.95/32.12 inference(bind,[status(th)],[])).
% 31.95/32.12 tff(438,plain,
% 31.95/32.12 (![X: $i] : ((prop(X) = false) <=> (~bool(X))) <=> ![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 31.95/32.12 inference(quant_intro,[status(thm)],[437])).
% 31.95/32.12 tff(439,axiom,(![X: $i] : ((prop(X) = false) <=> (~bool(X)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','prop_false')).
% 31.95/32.12 tff(440,plain,
% 31.95/32.12 (![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 31.95/32.12 inference(modus_ponens,[status(thm)],[439, 438])).
% 31.95/32.12 tff(441,plain,
% 31.95/32.12 (![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 31.95/32.12 inference(modus_ponens,[status(thm)],[440, 436])).
% 31.95/32.12 tff(442,plain,(
% 31.95/32.12 ![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 31.95/32.12 inference(skolemize,[status(sab)],[441])).
% 31.95/32.12 tff(443,plain,
% 31.95/32.12 (![X: $i] : (~(bool(X) <=> (prop(X) = false)))),
% 31.95/32.12 inference(modus_ponens,[status(thm)],[442, 435])).
% 31.95/32.12 tff(444,plain,
% 31.95/32.12 ((~![X: $i] : (~(bool(X) <=> (prop(X) = false)))) | (~(bool(tptp_fun_R_2(Q!7, P!8)) <=> (prop(tptp_fun_R_2(Q!7, P!8)) = false)))),
% 31.95/32.12 inference(quant_inst,[status(thm)],[])).
% 31.95/32.12 tff(445,plain,
% 31.95/32.12 (~(bool(tptp_fun_R_2(Q!7, P!8)) <=> (prop(tptp_fun_R_2(Q!7, P!8)) = false))),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[444, 443])).
% 31.95/32.12 tff(446,plain,
% 31.95/32.12 ((bool(tptp_fun_R_2(Q!7, P!8)) <=> (prop(tptp_fun_R_2(Q!7, P!8)) = false)) | bool(tptp_fun_R_2(Q!7, P!8)) | (prop(tptp_fun_R_2(Q!7, P!8)) = false)),
% 31.95/32.12 inference(tautology,[status(thm)],[])).
% 31.95/32.12 tff(447,plain,
% 31.95/32.12 (bool(tptp_fun_R_2(Q!7, P!8)) | (prop(tptp_fun_R_2(Q!7, P!8)) = false)),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[446, 445])).
% 31.95/32.12 tff(448,plain,
% 31.95/32.12 (bool(tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[447, 433])).
% 31.95/32.12 tff(449,plain,
% 31.95/32.12 ((~![X: $i] : ((prop(X) = true) <=> bool(X))) | ((prop(tptp_fun_R_2(Q!7, P!8)) = true) <=> bool(tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.12 inference(quant_inst,[status(thm)],[])).
% 31.95/32.12 tff(450,plain,
% 31.95/32.12 ((prop(tptp_fun_R_2(Q!7, P!8)) = true) <=> bool(tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[449, 311])).
% 31.95/32.12 tff(451,plain,
% 31.95/32.12 ((~((prop(tptp_fun_R_2(Q!7, P!8)) = true) <=> bool(tptp_fun_R_2(Q!7, P!8)))) | (prop(tptp_fun_R_2(Q!7, P!8)) = true) | (~bool(tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.12 inference(tautology,[status(thm)],[])).
% 31.95/32.12 tff(452,plain,
% 31.95/32.12 ((prop(tptp_fun_R_2(Q!7, P!8)) = true) | (~bool(tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[451, 450])).
% 31.95/32.12 tff(453,plain,
% 31.95/32.12 (prop(tptp_fun_R_2(Q!7, P!8)) = true),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[452, 448])).
% 31.95/32.12 tff(454,plain,
% 31.95/32.12 (~bool(impl(P!8, true))),
% 31.95/32.12 inference(modus_ponens,[status(thm)],[162, 356])).
% 31.95/32.12 tff(455,plain,
% 31.95/32.12 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(P!8, true))),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[388, 454])).
% 31.95/32.12 tff(456,plain,
% 31.95/32.12 ((err = phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))) <=> (phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = err)),
% 31.95/32.12 inference(commutativity,[status(thm)],[])).
% 31.95/32.12 tff(457,plain,
% 31.95/32.12 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))))),
% 31.95/32.12 inference(quant_inst,[status(thm)],[])).
% 31.95/32.12 tff(458,plain,
% 31.95/32.12 (lazy_impl(true, impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[457, 325])).
% 31.95/32.12 tff(459,assumption,(prop(tptp_fun_R_2(Q!7, P!8)) = true), introduced(assumption)).
% 31.95/32.12 tff(460,plain,
% 31.95/32.12 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = lazy_impl(true, impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.12 inference(monotonicity,[status(thm)],[459])).
% 31.95/32.12 tff(461,assumption,(impl(P!8, impl(P!8, phi(f7(P!6)))) = phi(P!8)), introduced(assumption)).
% 31.95/32.12 tff(462,assumption,(impl(P!8, phi(f7(P!6))) = phi(P!8)), introduced(assumption)).
% 31.95/32.12 tff(463,plain,
% 31.95/32.12 (phi(P!8) = impl(P!8, phi(f7(P!6)))),
% 31.95/32.12 inference(symmetry,[status(thm)],[462])).
% 31.95/32.12 tff(464,plain,
% 31.95/32.12 (impl(P!8, tptp_fun_R_2(Q!7, P!8)) = impl(P!8, phi(f7(P!6)))),
% 31.95/32.12 inference(transitivity,[status(thm)],[399, 463])).
% 31.95/32.12 tff(465,plain,
% 31.95/32.12 (impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))) = impl(P!8, impl(P!8, phi(f7(P!6))))),
% 31.95/32.12 inference(monotonicity,[status(thm)],[464])).
% 31.95/32.12 tff(466,plain,
% 31.95/32.12 (impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))) = phi(P!8)),
% 31.95/32.12 inference(transitivity,[status(thm)],[465, 461])).
% 31.95/32.12 tff(467,plain,
% 31.95/32.12 (impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)) = impl(phi(P!8), tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.12 inference(monotonicity,[status(thm)],[466])).
% 31.95/32.12 tff(468,plain,
% 31.95/32.12 (impl(phi(P!8), tptp_fun_R_2(Q!7, P!8)) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.12 inference(symmetry,[status(thm)],[467])).
% 31.95/32.12 tff(469,assumption,(impl(phi(P!8), tptp_fun_R_2(Q!7, P!8)) = phi(phi(P!8))), introduced(assumption)).
% 31.95/32.12 tff(470,plain,
% 31.95/32.12 (phi(phi(P!8)) = impl(phi(P!8), tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.12 inference(symmetry,[status(thm)],[469])).
% 31.95/32.12 tff(471,assumption,(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = phi(impl(P!8, tptp_fun_R_2(Q!7, P!8)))), introduced(assumption)).
% 31.95/32.12 tff(472,plain,
% 31.95/32.12 (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.12 inference(transitivity,[status(thm)],[471, 425, 470, 468])).
% 31.95/32.12 tff(473,plain,
% 31.95/32.12 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.12 inference(monotonicity,[status(thm)],[472])).
% 31.95/32.12 tff(474,plain,
% 31.95/32.12 (f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)) = phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.12 inference(transitivity,[status(thm)],[41, 473, 460, 458])).
% 31.95/32.12 tff(475,assumption,(~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))), introduced(assumption)).
% 31.95/32.12 tff(476,plain,
% 31.95/32.12 (((~d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))))) | (phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.12 inference(tautology,[status(thm)],[])).
% 31.95/32.12 tff(477,plain,
% 31.95/32.12 ((~d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))))),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[476, 475])).
% 31.95/32.12 tff(478,plain,
% 31.95/32.12 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))))) | (~(d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))))) | (~(d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err)))))),
% 31.95/32.12 inference(rewrite,[status(thm)],[])).
% 31.95/32.12 tff(479,plain,
% 31.95/32.12 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))))) | (~(d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err)))))),
% 31.95/32.12 inference(quant_inst,[status(thm)],[])).
% 31.95/32.12 tff(480,plain,
% 31.95/32.12 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))))) | (~(d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err))))),
% 31.95/32.12 inference(modus_ponens,[status(thm)],[479, 478])).
% 31.95/32.12 tff(481,plain,
% 31.95/32.12 ((~((~d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))))) | (~(d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err))))),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[480, 127])).
% 31.95/32.12 tff(482,plain,
% 31.95/32.12 (~(d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err)))),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[481, 477])).
% 31.95/32.12 tff(483,plain,
% 31.95/32.12 ((d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err))) | (phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err)),
% 31.95/32.12 inference(tautology,[status(thm)],[])).
% 31.95/32.12 tff(484,plain,
% 31.95/32.12 (phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[483, 482])).
% 31.95/32.12 tff(485,plain,
% 31.95/32.12 ((phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) <=> (err = phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))))),
% 31.95/32.12 inference(monotonicity,[status(thm)],[484, 474])).
% 31.95/32.12 tff(486,plain,
% 31.95/32.12 ((phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) <=> (phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = err)),
% 31.95/32.12 inference(transitivity,[status(thm)],[485, 456])).
% 31.95/32.12 tff(487,plain,
% 31.95/32.12 ((~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))) <=> (~(phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = err))),
% 31.95/32.12 inference(monotonicity,[status(thm)],[486])).
% 31.95/32.12 tff(488,plain,
% 31.95/32.12 (~(phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = err)),
% 31.95/32.12 inference(modus_ponens,[status(thm)],[475, 487])).
% 31.95/32.12 tff(489,plain,
% 31.95/32.12 ((d(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) | (~(phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = err))) | (phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = err)),
% 31.95/32.12 inference(tautology,[status(thm)],[])).
% 31.95/32.12 tff(490,plain,
% 31.95/32.12 (d(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) | (~(phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = err))),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[489, 488])).
% 31.95/32.12 tff(491,plain,
% 31.95/32.12 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))) | (~(phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))))) | (~(d(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) | (~(phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))) | (~(phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))))) | (~(d(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) | (~(phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = err)))))),
% 31.95/32.12 inference(rewrite,[status(thm)],[])).
% 31.95/32.12 tff(492,plain,
% 31.95/32.12 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))) | (~(phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))))) | (~(d(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) | (~(phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = err)))))),
% 31.95/32.12 inference(quant_inst,[status(thm)],[])).
% 31.95/32.12 tff(493,plain,
% 31.95/32.12 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))) | (~(phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))))) | (~(d(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) | (~(phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = err))))),
% 31.95/32.12 inference(modus_ponens,[status(thm)],[492, 491])).
% 31.95/32.12 tff(494,plain,
% 31.95/32.12 ((~((~d(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))) | (~(phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))))) | (~(d(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) | (~(phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = err))))),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[493, 127])).
% 31.95/32.12 tff(495,plain,
% 31.95/32.12 (~((~d(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))) | (~(phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))))),
% 31.95/32.12 inference(unit_resolution,[status(thm)],[494, 490])).
% 31.95/32.12 tff(496,plain,
% 31.95/32.12 (((~d(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))) | (~(phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))))) | (phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.12 inference(tautology,[status(thm)],[])).
% 31.95/32.12 tff(497,plain,
% 31.95/32.12 (phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.13 inference(unit_resolution,[status(thm)],[496, 495])).
% 31.95/32.13 tff(498,assumption,(impl(P!8, true) = phi(P!8)), introduced(assumption)).
% 31.95/32.13 tff(499,plain,
% 31.95/32.13 (phi(impl(P!8, true)) = phi(phi(P!8))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[498])).
% 31.95/32.13 tff(500,assumption,(impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(P!8, true))), introduced(assumption)).
% 31.95/32.13 tff(501,plain,
% 31.95/32.13 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.13 inference(transitivity,[status(thm)],[500, 499, 470, 468])).
% 31.95/32.13 tff(502,plain,
% 31.95/32.13 (true = prop(tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.13 inference(symmetry,[status(thm)],[459])).
% 31.95/32.13 tff(503,plain,
% 31.95/32.13 (prop(true) = prop(tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.13 inference(transitivity,[status(thm)],[316, 502])).
% 31.95/32.13 tff(504,plain,
% 31.95/32.13 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[503, 501])).
% 31.95/32.13 tff(505,plain,
% 31.95/32.13 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.13 inference(transitivity,[status(thm)],[504, 460, 458, 497])).
% 31.95/32.13 tff(506,plain,
% 31.95/32.13 (d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) <=> d(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[505])).
% 31.95/32.13 tff(507,plain,
% 31.95/32.13 (d(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) <=> d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.95/32.13 inference(symmetry,[status(thm)],[506])).
% 31.95/32.13 tff(508,plain,
% 31.95/32.13 (((~d(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))) | (~(phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))))) | d(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.13 inference(tautology,[status(thm)],[])).
% 31.95/32.13 tff(509,plain,
% 31.95/32.13 (d(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.13 inference(unit_resolution,[status(thm)],[508, 495])).
% 31.95/32.13 tff(510,plain,
% 31.95/32.13 (d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.95/32.13 inference(modus_ponens,[status(thm)],[509, 507])).
% 31.95/32.13 tff(511,plain,
% 31.95/32.13 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.95/32.13 inference(symmetry,[status(thm)],[504])).
% 31.95/32.13 tff(512,plain,
% 31.95/32.13 (f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.95/32.13 inference(transitivity,[status(thm)],[41, 473, 511])).
% 31.95/32.13 tff(513,plain,
% 31.95/32.13 (d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) <=> d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[512])).
% 31.95/32.13 tff(514,plain,
% 31.95/32.13 ((~d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))) <=> (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[513])).
% 31.95/32.13 tff(515,plain,
% 31.95/32.13 ((d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err))) | (~d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))))),
% 31.95/32.13 inference(tautology,[status(thm)],[])).
% 31.95/32.13 tff(516,plain,
% 31.95/32.13 (~d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.13 inference(unit_resolution,[status(thm)],[515, 482])).
% 31.95/32.13 tff(517,plain,
% 31.95/32.13 (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.95/32.13 inference(modus_ponens,[status(thm)],[516, 514])).
% 31.95/32.13 tff(518,plain,
% 31.95/32.13 ($false),
% 31.95/32.13 inference(unit_resolution,[status(thm)],[517, 510])).
% 31.95/32.13 tff(519,plain,((phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) | (~(prop(tptp_fun_R_2(Q!7, P!8)) = true)) | (~(impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(P!8, true)))) | (~(impl(phi(P!8), tptp_fun_R_2(Q!7, P!8)) = phi(phi(P!8)))) | (~(impl(P!8, impl(P!8, phi(f7(P!6)))) = phi(P!8))) | (~(impl(P!8, tptp_fun_R_2(Q!7, P!8)) = phi(P!8))) | (~(impl(P!8, phi(f7(P!6))) = phi(P!8))) | (~(impl(P!8, true) = phi(P!8))) | (~(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = phi(impl(P!8, tptp_fun_R_2(Q!7, P!8)))))), inference(lemma,lemma(discharge,[]))).
% 31.95/32.13 tff(520,plain,
% 31.95/32.13 (phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.13 inference(unit_resolution,[status(thm)],[519, 453, 455, 182, 177, 86, 172, 351, 190])).
% 31.95/32.13 tff(521,plain,
% 31.95/32.13 ((impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)) = phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))) <=> (phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.13 inference(commutativity,[status(thm)],[])).
% 31.95/32.13 tff(522,plain,
% 31.95/32.13 (lazy_impl(true, impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[502])).
% 31.95/32.13 tff(523,plain,
% 31.95/32.13 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = lazy_impl(true, impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.13 inference(symmetry,[status(thm)],[522])).
% 31.95/32.13 tff(524,assumption,(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))), introduced(assumption)).
% 31.95/32.13 tff(525,plain,
% 31.95/32.13 (or2(P!8, Q!7) = phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.13 inference(transitivity,[status(thm)],[365, 524, 41, 473, 523, 458])).
% 31.95/32.13 tff(526,assumption,(phi(P!8) = P!8), introduced(assumption)).
% 31.95/32.13 tff(527,plain,
% 31.95/32.13 (P!8 = phi(P!8)),
% 31.95/32.13 inference(symmetry,[status(thm)],[526])).
% 31.95/32.13 tff(528,plain,
% 31.95/32.13 (phi(P!8) = phi(phi(P!8))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[527])).
% 31.95/32.13 tff(529,assumption,(or1(P!8, Q!7) = phi(P!8)), introduced(assumption)).
% 31.95/32.13 tff(530,plain,
% 31.95/32.13 (or1(P!8, Q!7) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.13 inference(transitivity,[status(thm)],[529, 528, 470, 468])).
% 31.95/32.13 tff(531,plain,
% 31.95/32.13 ((or1(P!8, Q!7) = or2(P!8, Q!7)) <=> (impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)) = phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[530, 525])).
% 31.95/32.13 tff(532,plain,
% 31.95/32.13 ((or1(P!8, Q!7) = or2(P!8, Q!7)) <=> (phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.13 inference(transitivity,[status(thm)],[531, 521])).
% 31.95/32.13 tff(533,plain,
% 31.95/32.13 ((phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) <=> (or1(P!8, Q!7) = or2(P!8, Q!7))),
% 31.95/32.13 inference(symmetry,[status(thm)],[532])).
% 31.95/32.13 tff(534,plain,
% 31.95/32.13 (impl(P!8, phi(P!8)) = impl(P!8, impl(P!8, phi(f7(P!6))))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[463])).
% 31.95/32.13 tff(535,plain,
% 31.95/32.13 (impl(P!8, phi(P!8)) = impl(P!8, phi(f7(P!6)))),
% 31.95/32.13 inference(transitivity,[status(thm)],[534, 461, 463])).
% 31.95/32.13 tff(536,plain,
% 31.95/32.13 (impl(P!8, impl(P!8, phi(P!8))) = impl(P!8, impl(P!8, phi(f7(P!6))))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[535])).
% 31.95/32.13 tff(537,plain,
% 31.95/32.13 (impl(P!8, impl(P!8, phi(P!8))) = phi(P!8)),
% 31.95/32.13 inference(transitivity,[status(thm)],[536, 461])).
% 31.95/32.13 tff(538,plain,
% 31.95/32.13 (impl(impl(P!8, impl(P!8, phi(P!8))), phi(P!8)) = impl(phi(P!8), phi(P!8))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[537])).
% 31.95/32.13 tff(539,plain,
% 31.95/32.13 (impl(phi(P!8), phi(P!8)) = impl(impl(P!8, impl(P!8, phi(P!8))), phi(P!8))),
% 31.95/32.13 inference(symmetry,[status(thm)],[538])).
% 31.95/32.13 tff(540,assumption,(impl(phi(P!8), phi(P!8)) = phi(phi(P!8))), introduced(assumption)).
% 31.95/32.13 tff(541,plain,
% 31.95/32.13 (phi(phi(P!8)) = impl(phi(P!8), phi(P!8))),
% 31.95/32.13 inference(symmetry,[status(thm)],[540])).
% 31.95/32.13 tff(542,plain,
% 31.95/32.13 (phi(P!8) = impl(impl(P!8, impl(P!8, phi(P!8))), phi(P!8))),
% 31.95/32.13 inference(transitivity,[status(thm)],[528, 541, 539])).
% 31.95/32.13 tff(543,plain,
% 31.95/32.13 (phi(phi(P!8)) = phi(impl(impl(P!8, impl(P!8, phi(P!8))), phi(P!8)))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[542])).
% 31.95/32.13 tff(544,plain,
% 31.95/32.13 (phi(impl(impl(P!8, impl(P!8, phi(P!8))), phi(P!8))) = phi(phi(P!8))),
% 31.95/32.13 inference(symmetry,[status(thm)],[543])).
% 31.95/32.13 tff(545,plain,
% 31.95/32.13 (impl(impl(P!8, impl(P!8, phi(P!8))), phi(P!8)) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.13 inference(transitivity,[status(thm)],[538, 540, 470, 468])).
% 31.95/32.13 tff(546,plain,
% 31.95/32.13 (phi(impl(impl(P!8, impl(P!8, phi(P!8))), phi(P!8))) = phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[545])).
% 31.95/32.13 tff(547,plain,
% 31.95/32.13 (phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = phi(impl(impl(P!8, impl(P!8, phi(P!8))), phi(P!8)))),
% 31.95/32.13 inference(symmetry,[status(thm)],[546])).
% 31.95/32.13 tff(548,plain,
% 31.95/32.13 (phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.13 inference(transitivity,[status(thm)],[547, 544, 470, 468])).
% 31.95/32.13 tff(549,plain,
% 31.95/32.13 (or1(P!8, Q!7) = or2(P!8, Q!7)),
% 31.95/32.13 inference(modus_ponens,[status(thm)],[548, 533])).
% 31.95/32.13 tff(550,plain,
% 31.95/32.13 ($false),
% 31.95/32.13 inference(unit_resolution,[status(thm)],[377, 549])).
% 31.95/32.13 tff(551,plain,((~(phi(P!8) = P!8)) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))) | (~(prop(tptp_fun_R_2(Q!7, P!8)) = true)) | (~(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = phi(impl(P!8, tptp_fun_R_2(Q!7, P!8))))) | (~(impl(phi(P!8), tptp_fun_R_2(Q!7, P!8)) = phi(phi(P!8)))) | (~(impl(P!8, impl(P!8, phi(f7(P!6)))) = phi(P!8))) | (~(impl(P!8, tptp_fun_R_2(Q!7, P!8)) = phi(P!8))) | (~(impl(P!8, phi(f7(P!6))) = phi(P!8))) | (~(or1(P!8, Q!7) = phi(P!8))) | (~(impl(phi(P!8), phi(P!8)) = phi(phi(P!8))))), inference(lemma,lemma(discharge,[]))).
% 31.95/32.13 tff(552,plain,
% 31.95/32.13 (~(phi(P!8) = P!8)),
% 31.95/32.13 inference(unit_resolution,[status(thm)],[551, 520, 453, 190, 182, 177, 86, 172, 61, 167])).
% 31.95/32.13 tff(553,plain,
% 31.95/32.13 ((~d(P!8)) | (~(phi(P!8) = P!8))),
% 31.95/32.13 inference(unit_resolution,[status(thm)],[106, 552])).
% 31.95/32.13 tff(554,plain,
% 31.95/32.13 (~(d(P!8) | (~(phi(P!8) = err)))),
% 31.95/32.13 inference(unit_resolution,[status(thm)],[131, 553])).
% 31.95/32.13 tff(555,plain,
% 31.95/32.13 (phi(P!8) = err),
% 31.95/32.13 inference(unit_resolution,[status(thm)],[116, 554])).
% 31.95/32.13 tff(556,plain,
% 31.95/32.13 (err = phi(P!8)),
% 31.95/32.13 inference(symmetry,[status(thm)],[555])).
% 31.95/32.13 tff(557,plain,
% 31.95/32.13 (d(err) <=> d(err)),
% 31.95/32.13 inference(rewrite,[status(thm)],[])).
% 31.95/32.13 tff(558,plain,
% 31.95/32.13 (d(err)),
% 31.95/32.13 inference(and_elim,[status(thm)],[202])).
% 31.95/32.13 tff(559,plain,
% 31.95/32.13 (d(err)),
% 31.95/32.13 inference(modus_ponens,[status(thm)],[558, 557])).
% 31.95/32.13 tff(560,plain,
% 31.95/32.13 ((d(err) | (~(phi(err) = err))) | (~d(err))),
% 31.95/32.13 inference(tautology,[status(thm)],[])).
% 31.95/32.13 tff(561,plain,
% 31.95/32.13 (d(err) | (~(phi(err) = err))),
% 31.95/32.13 inference(unit_resolution,[status(thm)],[560, 559])).
% 31.95/32.13 tff(562,plain,
% 31.95/32.13 (((~![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)))))),
% 31.95/32.13 inference(rewrite,[status(thm)],[])).
% 31.95/32.13 tff(563,plain,
% 31.95/32.13 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(err)) | (~(phi(err) = err)))) | (~(d(err) | (~(phi(err) = err)))))),
% 31.95/32.13 inference(quant_inst,[status(thm)],[])).
% 31.95/32.13 tff(564,plain,
% 31.95/32.13 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(err)) | (~(phi(err) = err)))) | (~(d(err) | (~(phi(err) = err))))),
% 31.95/32.13 inference(modus_ponens,[status(thm)],[563, 562])).
% 31.95/32.13 tff(565,plain,
% 31.95/32.13 (~((~d(err)) | (~(phi(err) = err)))),
% 31.95/32.13 inference(unit_resolution,[status(thm)],[564, 127, 561])).
% 31.95/32.13 tff(566,plain,
% 31.95/32.13 (((~d(err)) | (~(phi(err) = err))) | (phi(err) = err)),
% 31.95/32.13 inference(tautology,[status(thm)],[])).
% 31.95/32.13 tff(567,plain,
% 31.95/32.13 (phi(err) = err),
% 31.95/32.13 inference(unit_resolution,[status(thm)],[566, 565])).
% 31.95/32.13 tff(568,plain,
% 31.95/32.13 (phi(err) = phi(phi(P!8))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[556])).
% 31.95/32.13 tff(569,plain,
% 31.95/32.13 (phi(phi(P!8)) = phi(err)),
% 31.95/32.13 inference(symmetry,[status(thm)],[568])).
% 31.95/32.13 tff(570,plain,
% 31.95/32.13 (phi(P!8) = impl(P!8, phi(f7(P!6)))),
% 31.95/32.13 inference(symmetry,[status(thm)],[172])).
% 31.95/32.13 tff(571,plain,
% 31.95/32.13 (impl(P!8, tptp_fun_R_2(Q!7, P!8)) = impl(P!8, phi(f7(P!6)))),
% 31.95/32.13 inference(transitivity,[status(thm)],[86, 570])).
% 31.95/32.13 tff(572,plain,
% 31.95/32.13 (impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))) = impl(P!8, impl(P!8, phi(f7(P!6))))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[571])).
% 31.95/32.13 tff(573,plain,
% 31.95/32.13 (impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))) = phi(P!8)),
% 31.95/32.13 inference(transitivity,[status(thm)],[572, 177])).
% 31.95/32.13 tff(574,plain,
% 31.95/32.13 (impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)) = impl(phi(P!8), tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[573])).
% 31.95/32.13 tff(575,plain,
% 31.95/32.13 (impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)) = or1(P!8, Q!7)),
% 31.95/32.13 inference(transitivity,[status(thm)],[574, 182, 569, 567, 556, 62])).
% 31.95/32.13 tff(576,plain,
% 31.95/32.13 (phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = or2(P!8, Q!7)),
% 31.95/32.13 inference(symmetry,[status(thm)],[365])).
% 31.95/32.13 tff(577,plain,
% 31.95/32.13 (f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)) = phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.13 inference(symmetry,[status(thm)],[520])).
% 31.95/32.13 tff(578,plain,
% 31.95/32.13 (impl(phi(P!8), tptp_fun_R_2(Q!7, P!8)) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.13 inference(symmetry,[status(thm)],[574])).
% 31.95/32.13 tff(579,plain,
% 31.95/32.13 (phi(phi(P!8)) = impl(phi(P!8), tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.13 inference(symmetry,[status(thm)],[182])).
% 31.95/32.13 tff(580,plain,
% 31.95/32.13 (phi(impl(P!8, tptp_fun_R_2(Q!7, P!8))) = phi(phi(P!8))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[86])).
% 31.95/32.13 tff(581,plain,
% 31.95/32.13 (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.13 inference(transitivity,[status(thm)],[190, 580, 579, 578])).
% 31.95/32.13 tff(582,plain,
% 31.95/32.13 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[581])).
% 31.95/32.13 tff(583,plain,
% 31.95/32.13 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))),
% 31.95/32.13 inference(symmetry,[status(thm)],[582])).
% 31.95/32.13 tff(584,plain,
% 31.95/32.13 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = lazy_impl(true, impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[453])).
% 31.95/32.13 tff(585,plain,
% 31.95/32.13 (lazy_impl(true, impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.13 inference(symmetry,[status(thm)],[584])).
% 31.95/32.13 tff(586,plain,
% 31.95/32.13 (phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = lazy_impl(true, impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.13 inference(symmetry,[status(thm)],[458])).
% 31.95/32.13 tff(587,plain,
% 31.95/32.13 (phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = or2(P!8, Q!7)),
% 31.95/32.13 inference(transitivity,[status(thm)],[586, 585, 583, 42, 577, 576])).
% 31.95/32.13 tff(588,plain,
% 31.95/32.13 ((phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) <=> (or2(P!8, Q!7) = or1(P!8, Q!7))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[587, 575])).
% 31.95/32.13 tff(589,plain,
% 31.95/32.13 ((phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) <=> (or1(P!8, Q!7) = or2(P!8, Q!7))),
% 31.95/32.13 inference(transitivity,[status(thm)],[588, 45])).
% 31.95/32.13 tff(590,plain,
% 31.95/32.13 ((or1(P!8, Q!7) = or2(P!8, Q!7)) <=> (phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.13 inference(symmetry,[status(thm)],[589])).
% 31.95/32.13 tff(591,plain,
% 31.95/32.13 ((~(or1(P!8, Q!7) = or2(P!8, Q!7))) <=> (~(phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[590])).
% 31.95/32.13 tff(592,plain,
% 31.95/32.13 (~(phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.95/32.13 inference(modus_ponens,[status(thm)],[377, 591])).
% 31.95/32.13 tff(593,plain,
% 31.95/32.13 (impl(P!8, phi(P!8)) = impl(P!8, impl(P!8, phi(f7(P!6))))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[570])).
% 31.95/32.13 tff(594,plain,
% 31.95/32.13 (impl(P!8, phi(P!8)) = impl(P!8, phi(f7(P!6)))),
% 31.95/32.13 inference(transitivity,[status(thm)],[593, 177, 570])).
% 31.95/32.13 tff(595,plain,
% 31.95/32.13 (impl(P!8, impl(P!8, phi(P!8))) = impl(P!8, impl(P!8, phi(f7(P!6))))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[594])).
% 31.95/32.13 tff(596,plain,
% 31.95/32.13 (impl(P!8, impl(P!8, phi(f7(P!6)))) = impl(P!8, impl(P!8, phi(P!8)))),
% 31.95/32.13 inference(symmetry,[status(thm)],[595])).
% 31.95/32.13 tff(597,plain,
% 31.95/32.13 (phi(P!8) = impl(P!8, impl(P!8, phi(f7(P!6))))),
% 31.95/32.13 inference(symmetry,[status(thm)],[177])).
% 31.95/32.13 tff(598,plain,
% 31.95/32.13 (phi(P!8) = impl(P!8, impl(P!8, phi(P!8)))),
% 31.95/32.13 inference(transitivity,[status(thm)],[597, 596])).
% 31.95/32.13 tff(599,plain,
% 31.95/32.13 (impl(phi(P!8), phi(P!8)) = impl(impl(P!8, impl(P!8, phi(P!8))), phi(P!8))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[598])).
% 31.95/32.13 tff(600,plain,
% 31.95/32.13 (impl(impl(P!8, impl(P!8, phi(P!8))), phi(P!8)) = impl(phi(P!8), phi(P!8))),
% 31.95/32.13 inference(symmetry,[status(thm)],[599])).
% 31.95/32.13 tff(601,plain,
% 31.95/32.13 (impl(impl(P!8, impl(P!8, phi(P!8))), phi(P!8)) = phi(P!8)),
% 31.95/32.13 inference(transitivity,[status(thm)],[600, 167, 569, 567, 556])).
% 31.95/32.13 tff(602,plain,
% 31.95/32.13 (phi(impl(impl(P!8, impl(P!8, phi(P!8))), phi(P!8))) = phi(phi(P!8))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[601])).
% 31.95/32.13 tff(603,plain,
% 31.95/32.13 (phi(phi(P!8)) = impl(phi(P!8), phi(P!8))),
% 31.95/32.13 inference(symmetry,[status(thm)],[167])).
% 31.95/32.13 tff(604,plain,
% 31.95/32.13 (impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)) = impl(impl(P!8, impl(P!8, phi(P!8))), phi(P!8))),
% 31.95/32.13 inference(transitivity,[status(thm)],[574, 182, 603, 599])).
% 31.95/32.13 tff(605,plain,
% 31.95/32.13 (phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = phi(impl(impl(P!8, impl(P!8, phi(P!8))), phi(P!8)))),
% 31.95/32.13 inference(monotonicity,[status(thm)],[604])).
% 31.95/32.13 tff(606,plain,
% 31.95/32.13 (phi(impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, impl(P!8, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))),
% 31.95/32.13 inference(transitivity,[status(thm)],[605, 602, 579, 578])).
% 31.95/32.13 tff(607,plain,
% 31.95/32.13 ($false),
% 31.95/32.13 inference(unit_resolution,[status(thm)],[606, 592])).
% 31.95/32.13 tff(608,plain,(bool(P!8)), inference(lemma,lemma(discharge,[]))).
% 31.95/32.13 tff(609,plain,
% 31.95/32.13 (^[A: $i, B: $i] : refl((bool(B) | (~bool(A)) | (or1(A, B) = phi(B))) <=> (bool(B) | (~bool(A)) | (or1(A, B) = phi(B))))),
% 31.95/32.13 inference(bind,[status(th)],[])).
% 31.95/32.13 tff(610,plain,
% 31.95/32.13 (![A: $i, B: $i] : (bool(B) | (~bool(A)) | (or1(A, B) = phi(B))) <=> ![A: $i, B: $i] : (bool(B) | (~bool(A)) | (or1(A, B) = phi(B)))),
% 31.95/32.13 inference(quant_intro,[status(thm)],[609])).
% 31.95/32.13 tff(611,plain,
% 31.95/32.13 (^[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)))) | (or1(A, B) = phi(B))) <=> ((bool(B) | (~bool(A))) | (or1(A, B) = phi(B))))), rewrite(((bool(B) | (~bool(A))) | (or1(A, B) = phi(B))) <=> (bool(B) | (~bool(A)) | (or1(A, B) = phi(B)))), (((~(bool(A) & (~bool(B)))) | (or1(A, B) = phi(B))) <=> (bool(B) | (~bool(A)) | (or1(A, B) = phi(B)))))),
% 31.95/32.13 inference(bind,[status(th)],[])).
% 31.95/32.13 tff(612,plain,
% 31.95/32.13 (![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (or1(A, B) = phi(B))) <=> ![A: $i, B: $i] : (bool(B) | (~bool(A)) | (or1(A, B) = phi(B)))),
% 31.95/32.13 inference(quant_intro,[status(thm)],[611])).
% 31.95/32.13 tff(613,plain,
% 31.95/32.13 (![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (or1(A, B) = phi(B))) <=> ![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (or1(A, B) = phi(B)))),
% 31.95/32.13 inference(rewrite,[status(thm)],[])).
% 31.95/32.13 tff(614,plain,
% 31.95/32.13 (^[A: $i, B: $i] : rewrite(((bool(A) & (~bool(B))) => (or1(A, B) = phi(B))) <=> ((~(bool(A) & (~bool(B)))) | (or1(A, B) = phi(B))))),
% 31.95/32.13 inference(bind,[status(th)],[])).
% 31.95/32.13 tff(615,plain,
% 31.95/32.13 (![A: $i, B: $i] : ((bool(A) & (~bool(B))) => (or1(A, B) = phi(B))) <=> ![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (or1(A, B) = phi(B)))),
% 31.95/32.13 inference(quant_intro,[status(thm)],[614])).
% 31.95/32.13 tff(616,axiom,(![A: $i, B: $i] : ((bool(A) & (~bool(B))) => (or1(A, B) = phi(B)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','or1_axiom2')).
% 31.95/32.13 tff(617,plain,
% 31.95/32.13 (![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (or1(A, B) = phi(B)))),
% 31.95/32.13 inference(modus_ponens,[status(thm)],[616, 615])).
% 31.95/32.13 tff(618,plain,
% 31.95/32.13 (![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (or1(A, B) = phi(B)))),
% 31.95/32.13 inference(modus_ponens,[status(thm)],[617, 613])).
% 31.95/32.13 tff(619,plain,(
% 31.95/32.13 ![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (or1(A, B) = phi(B)))),
% 31.95/32.13 inference(skolemize,[status(sab)],[618])).
% 31.95/32.13 tff(620,plain,
% 31.95/32.13 (![A: $i, B: $i] : (bool(B) | (~bool(A)) | (or1(A, B) = phi(B)))),
% 31.95/32.13 inference(modus_ponens,[status(thm)],[619, 612])).
% 31.95/32.13 tff(621,plain,
% 31.95/32.13 (![A: $i, B: $i] : (bool(B) | (~bool(A)) | (or1(A, B) = phi(B)))),
% 31.95/32.13 inference(modus_ponens,[status(thm)],[620, 610])).
% 31.95/32.13 tff(622,plain,
% 31.95/32.13 (((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (or1(A, B) = phi(B)))) | (bool(Q!7) | (~bool(P!8)) | (or1(P!8, Q!7) = phi(Q!7)))) <=> ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (or1(A, B) = phi(B)))) | bool(Q!7) | (~bool(P!8)) | (or1(P!8, Q!7) = phi(Q!7)))),
% 31.95/32.13 inference(rewrite,[status(thm)],[])).
% 31.95/32.13 tff(623,plain,
% 31.95/32.13 ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (or1(A, B) = phi(B)))) | (bool(Q!7) | (~bool(P!8)) | (or1(P!8, Q!7) = phi(Q!7)))),
% 31.95/32.13 inference(quant_inst,[status(thm)],[])).
% 31.95/32.13 tff(624,plain,
% 31.95/32.13 ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (or1(A, B) = phi(B)))) | bool(Q!7) | (~bool(P!8)) | (or1(P!8, Q!7) = phi(Q!7))),
% 31.95/32.13 inference(modus_ponens,[status(thm)],[623, 622])).
% 31.95/32.13 tff(625,plain,
% 31.95/32.13 (bool(Q!7) | (~bool(P!8)) | (or1(P!8, Q!7) = phi(Q!7))),
% 31.95/32.13 inference(unit_resolution,[status(thm)],[624, 621])).
% 31.95/32.13 tff(626,plain,
% 31.95/32.13 (bool(Q!7) | (or1(P!8, Q!7) = phi(Q!7))),
% 31.95/32.13 inference(unit_resolution,[status(thm)],[625, 608])).
% 31.95/32.13 tff(627,plain,
% 31.95/32.13 (bool(Q!7)),
% 31.95/32.13 inference(unit_resolution,[status(thm)],[626, 44])).
% 31.95/32.13 tff(628,plain,
% 31.95/32.13 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(Q!7) <=> ((Q!7 = false) | (Q!7 = true)))),
% 31.95/32.13 inference(quant_inst,[status(thm)],[])).
% 31.95/32.13 tff(629,plain,
% 31.95/32.13 (bool(Q!7) <=> ((Q!7 = false) | (Q!7 = true))),
% 31.95/32.13 inference(unit_resolution,[status(thm)],[628, 69])).
% 31.95/32.13 tff(630,plain,
% 31.95/32.13 ((~(bool(Q!7) <=> ((Q!7 = false) | (Q!7 = true)))) | (~bool(Q!7)) | ((Q!7 = false) | (Q!7 = true))),
% 31.95/32.13 inference(tautology,[status(thm)],[])).
% 31.95/32.13 tff(631,plain,
% 31.95/32.13 ((~bool(Q!7)) | ((Q!7 = false) | (Q!7 = true))),
% 31.95/32.13 inference(unit_resolution,[status(thm)],[630, 629])).
% 31.95/32.13 tff(632,plain,
% 31.95/32.13 ((Q!7 = false) | (Q!7 = true)),
% 31.95/32.13 inference(unit_resolution,[status(thm)],[631, 627])).
% 31.95/32.13 tff(633,plain,
% 31.95/32.13 ((~((Q!7 = false) | (Q!7 = true))) | (Q!7 = false) | (Q!7 = true)),
% 31.95/32.14 inference(tautology,[status(thm)],[])).
% 31.95/32.14 tff(634,plain,
% 31.95/32.14 (Q!7 = true),
% 31.95/32.14 inference(unit_resolution,[status(thm)],[633, 632, 43])).
% 31.95/32.14 tff(635,plain,
% 31.95/32.14 (phi(Q!7) = phi(true)),
% 31.95/32.14 inference(monotonicity,[status(thm)],[634])).
% 31.95/32.14 tff(636,plain,
% 31.95/32.14 (phi(true) = phi(Q!7)),
% 31.95/32.14 inference(symmetry,[status(thm)],[635])).
% 31.95/32.14 tff(637,plain,
% 31.95/32.14 (true = phi(true)),
% 31.95/32.14 inference(symmetry,[status(thm)],[221])).
% 31.95/32.14 tff(638,plain,
% 31.95/32.14 (^[B: $i] : refl(((~bool(B)) | (or1(false, B) = B)) <=> ((~bool(B)) | (or1(false, B) = B)))),
% 31.95/32.14 inference(bind,[status(th)],[])).
% 31.95/32.14 tff(639,plain,
% 31.95/32.14 (![B: $i] : ((~bool(B)) | (or1(false, B) = B)) <=> ![B: $i] : ((~bool(B)) | (or1(false, B) = B))),
% 31.95/32.14 inference(quant_intro,[status(thm)],[638])).
% 31.95/32.14 tff(640,plain,
% 31.95/32.14 (![B: $i] : ((~bool(B)) | (or1(false, B) = B)) <=> ![B: $i] : ((~bool(B)) | (or1(false, B) = B))),
% 31.95/32.14 inference(rewrite,[status(thm)],[])).
% 31.95/32.14 tff(641,plain,
% 31.95/32.14 (^[B: $i] : rewrite((bool(B) => (or1(false, B) = B)) <=> ((~bool(B)) | (or1(false, B) = B)))),
% 31.95/32.14 inference(bind,[status(th)],[])).
% 31.95/32.14 tff(642,plain,
% 31.95/32.14 (![B: $i] : (bool(B) => (or1(false, B) = B)) <=> ![B: $i] : ((~bool(B)) | (or1(false, B) = B))),
% 31.95/32.14 inference(quant_intro,[status(thm)],[641])).
% 31.95/32.14 tff(643,axiom,(![B: $i] : (bool(B) => (or1(false, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','or1_axiom4')).
% 31.95/32.14 tff(644,plain,
% 31.95/32.14 (![B: $i] : ((~bool(B)) | (or1(false, B) = B))),
% 31.95/32.14 inference(modus_ponens,[status(thm)],[643, 642])).
% 31.95/32.14 tff(645,plain,
% 31.95/32.14 (![B: $i] : ((~bool(B)) | (or1(false, B) = B))),
% 31.95/32.14 inference(modus_ponens,[status(thm)],[644, 640])).
% 31.95/32.14 tff(646,plain,(
% 31.95/32.14 ![B: $i] : ((~bool(B)) | (or1(false, B) = B))),
% 31.95/32.14 inference(skolemize,[status(sab)],[645])).
% 31.95/32.14 tff(647,plain,
% 31.95/32.14 (![B: $i] : ((~bool(B)) | (or1(false, B) = B))),
% 31.95/32.14 inference(modus_ponens,[status(thm)],[646, 639])).
% 31.95/32.14 tff(648,plain,
% 31.95/32.14 (((~![B: $i] : ((~bool(B)) | (or1(false, B) = B))) | ((~bool(true)) | (or1(false, true) = true))) <=> ((~![B: $i] : ((~bool(B)) | (or1(false, B) = B))) | (~bool(true)) | (or1(false, true) = true))),
% 31.95/32.14 inference(rewrite,[status(thm)],[])).
% 31.95/32.14 tff(649,plain,
% 31.95/32.14 ((~![B: $i] : ((~bool(B)) | (or1(false, B) = B))) | ((~bool(true)) | (or1(false, true) = true))),
% 31.95/32.14 inference(quant_inst,[status(thm)],[])).
% 31.95/32.14 tff(650,plain,
% 31.95/32.14 ((~![B: $i] : ((~bool(B)) | (or1(false, B) = B))) | (~bool(true)) | (or1(false, true) = true)),
% 31.95/32.14 inference(modus_ponens,[status(thm)],[649, 648])).
% 31.95/32.14 tff(651,plain,
% 31.95/32.14 (or1(false, true) = true),
% 31.95/32.14 inference(unit_resolution,[status(thm)],[650, 647, 247])).
% 31.95/32.14 tff(652,plain,
% 31.95/32.14 (^[B: $i] : refl(((~bool(B)) | (or1(true, B) = true)) <=> ((~bool(B)) | (or1(true, B) = true)))),
% 31.95/32.14 inference(bind,[status(th)],[])).
% 31.95/32.14 tff(653,plain,
% 31.95/32.14 (![B: $i] : ((~bool(B)) | (or1(true, B) = true)) <=> ![B: $i] : ((~bool(B)) | (or1(true, B) = true))),
% 31.95/32.14 inference(quant_intro,[status(thm)],[652])).
% 31.95/32.14 tff(654,plain,
% 31.95/32.14 (![B: $i] : ((~bool(B)) | (or1(true, B) = true)) <=> ![B: $i] : ((~bool(B)) | (or1(true, B) = true))),
% 31.95/32.14 inference(rewrite,[status(thm)],[])).
% 31.95/32.14 tff(655,plain,
% 31.95/32.14 (^[B: $i] : rewrite((bool(B) => (or1(true, B) = true)) <=> ((~bool(B)) | (or1(true, B) = true)))),
% 31.95/32.14 inference(bind,[status(th)],[])).
% 31.95/32.14 tff(656,plain,
% 31.95/32.14 (![B: $i] : (bool(B) => (or1(true, B) = true)) <=> ![B: $i] : ((~bool(B)) | (or1(true, B) = true))),
% 31.95/32.14 inference(quant_intro,[status(thm)],[655])).
% 31.95/32.14 tff(657,axiom,(![B: $i] : (bool(B) => (or1(true, B) = true))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','or1_axiom3')).
% 31.95/32.14 tff(658,plain,
% 31.95/32.14 (![B: $i] : ((~bool(B)) | (or1(true, B) = true))),
% 31.95/32.14 inference(modus_ponens,[status(thm)],[657, 656])).
% 31.95/32.14 tff(659,plain,
% 31.95/32.14 (![B: $i] : ((~bool(B)) | (or1(true, B) = true))),
% 31.95/32.14 inference(modus_ponens,[status(thm)],[658, 654])).
% 31.95/32.14 tff(660,plain,(
% 31.95/32.14 ![B: $i] : ((~bool(B)) | (or1(true, B) = true))),
% 31.95/32.14 inference(skolemize,[status(sab)],[659])).
% 31.95/32.14 tff(661,plain,
% 31.95/32.14 (![B: $i] : ((~bool(B)) | (or1(true, B) = true))),
% 31.95/32.14 inference(modus_ponens,[status(thm)],[660, 653])).
% 31.95/32.14 tff(662,plain,
% 31.95/32.14 (((~![B: $i] : ((~bool(B)) | (or1(true, B) = true))) | ((~bool(Q!7)) | (or1(true, Q!7) = true))) <=> ((~![B: $i] : ((~bool(B)) | (or1(true, B) = true))) | (~bool(Q!7)) | (or1(true, Q!7) = true))),
% 31.95/32.14 inference(rewrite,[status(thm)],[])).
% 31.95/32.14 tff(663,plain,
% 31.95/32.14 ((~![B: $i] : ((~bool(B)) | (or1(true, B) = true))) | ((~bool(Q!7)) | (or1(true, Q!7) = true))),
% 31.95/32.14 inference(quant_inst,[status(thm)],[])).
% 31.95/32.14 tff(664,plain,
% 31.95/32.14 ((~![B: $i] : ((~bool(B)) | (or1(true, B) = true))) | (~bool(Q!7)) | (or1(true, Q!7) = true)),
% 31.95/32.14 inference(modus_ponens,[status(thm)],[663, 662])).
% 31.95/32.14 tff(665,plain,
% 31.95/32.14 ((~bool(Q!7)) | (or1(true, Q!7) = true)),
% 31.95/32.14 inference(unit_resolution,[status(thm)],[664, 661])).
% 31.95/32.14 tff(666,plain,
% 31.95/32.14 (or1(true, Q!7) = true),
% 31.95/32.14 inference(unit_resolution,[status(thm)],[665, 627])).
% 31.95/32.14 tff(667,assumption,(P!8 = true), introduced(assumption)).
% 31.95/32.14 tff(668,plain,
% 31.95/32.14 (or1(P!8, Q!7) = or1(true, Q!7)),
% 31.95/32.14 inference(monotonicity,[status(thm)],[667])).
% 31.95/32.14 tff(669,plain,
% 31.95/32.14 (or1(P!8, Q!7) = phi(Q!7)),
% 31.95/32.14 inference(transitivity,[status(thm)],[668, 666, 637, 636])).
% 31.95/32.14 tff(670,plain,
% 31.95/32.14 ($false),
% 31.95/32.14 inference(unit_resolution,[status(thm)],[44, 669])).
% 31.95/32.14 tff(671,plain,((or1(P!8, Q!7) = phi(Q!7)) | (~(P!8 = true)) | (Q!7 = false)), inference(lemma,lemma(discharge,[]))).
% 31.95/32.14 tff(672,plain,
% 31.95/32.14 (~(P!8 = true)),
% 31.95/32.14 inference(unit_resolution,[status(thm)],[671, 44, 43])).
% 31.95/32.14 tff(673,plain,
% 31.95/32.14 ((~(bool(P!8) <=> ((P!8 = false) | (P!8 = true)))) | (~bool(P!8)) | ((P!8 = false) | (P!8 = true))),
% 31.95/32.14 inference(tautology,[status(thm)],[])).
% 31.95/32.14 tff(674,plain,
% 31.95/32.14 ((~(bool(P!8) <=> ((P!8 = false) | (P!8 = true)))) | ((P!8 = false) | (P!8 = true))),
% 31.95/32.14 inference(unit_resolution,[status(thm)],[673, 608])).
% 31.95/32.14 tff(675,plain,
% 31.95/32.14 ((P!8 = false) | (P!8 = true)),
% 31.95/32.14 inference(unit_resolution,[status(thm)],[674, 99])).
% 31.95/32.14 tff(676,plain,
% 31.95/32.14 ((~((P!8 = false) | (P!8 = true))) | (P!8 = false) | (P!8 = true)),
% 31.95/32.14 inference(tautology,[status(thm)],[])).
% 31.95/32.14 tff(677,plain,
% 31.95/32.14 ((P!8 = false) | (P!8 = true)),
% 31.95/32.14 inference(unit_resolution,[status(thm)],[676, 675])).
% 31.95/32.14 tff(678,plain,
% 31.95/32.14 (P!8 = false),
% 31.95/32.14 inference(unit_resolution,[status(thm)],[677, 672])).
% 31.95/32.14 tff(679,plain,
% 31.95/32.14 (or1(P!8, Q!7) = or1(false, true)),
% 31.95/32.14 inference(monotonicity,[status(thm)],[678, 634])).
% 31.95/32.14 tff(680,plain,
% 31.95/32.14 (or1(P!8, Q!7) = phi(Q!7)),
% 31.95/32.14 inference(transitivity,[status(thm)],[679, 651, 637, 636])).
% 31.95/32.14 tff(681,plain,
% 31.95/32.14 ($false),
% 31.95/32.14 inference(unit_resolution,[status(thm)],[44, 680])).
% 31.95/32.14 tff(682,plain,((or1(P!8, Q!7) = phi(Q!7)) | (Q!7 = false)), inference(lemma,lemma(discharge,[]))).
% 31.95/32.14 tff(683,plain,
% 31.95/32.14 (or1(P!8, Q!7) = phi(Q!7)),
% 31.95/32.14 inference(unit_resolution,[status(thm)],[682, 43])).
% 31.95/32.14 tff(684,plain,
% 31.95/32.14 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true)))),
% 31.95/32.14 inference(quant_inst,[status(thm)],[])).
% 31.95/32.14 tff(685,plain,
% 31.95/32.14 (lazy_impl(true, impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true))),
% 31.95/32.14 inference(unit_resolution,[status(thm)],[684, 325])).
% 31.95/32.14 tff(686,plain,
% 31.95/32.14 (^[B: $i] : refl(((~bool(B)) | (impl(false, B) = true)) <=> ((~bool(B)) | (impl(false, B) = true)))),
% 31.95/32.14 inference(bind,[status(th)],[])).
% 31.98/32.14 tff(687,plain,
% 31.98/32.14 (![B: $i] : ((~bool(B)) | (impl(false, B) = true)) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 31.98/32.14 inference(quant_intro,[status(thm)],[686])).
% 31.98/32.14 tff(688,plain,
% 31.98/32.14 (![B: $i] : ((~bool(B)) | (impl(false, B) = true)) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 31.98/32.14 inference(rewrite,[status(thm)],[])).
% 31.98/32.14 tff(689,plain,
% 31.98/32.14 (^[B: $i] : rewrite((bool(B) => (impl(false, B) = true)) <=> ((~bool(B)) | (impl(false, B) = true)))),
% 31.98/32.14 inference(bind,[status(th)],[])).
% 31.98/32.14 tff(690,plain,
% 31.98/32.14 (![B: $i] : (bool(B) => (impl(false, B) = true)) <=> ![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 31.98/32.14 inference(quant_intro,[status(thm)],[689])).
% 31.98/32.14 tff(691,axiom,(![B: $i] : (bool(B) => (impl(false, B) = true))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','impl_axiom3')).
% 31.98/32.14 tff(692,plain,
% 31.98/32.14 (![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 31.98/32.14 inference(modus_ponens,[status(thm)],[691, 690])).
% 31.98/32.14 tff(693,plain,
% 31.98/32.14 (![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 31.98/32.14 inference(modus_ponens,[status(thm)],[692, 688])).
% 31.98/32.14 tff(694,plain,(
% 31.98/32.14 ![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 31.98/32.14 inference(skolemize,[status(sab)],[693])).
% 31.98/32.14 tff(695,plain,
% 31.98/32.14 (![B: $i] : ((~bool(B)) | (impl(false, B) = true))),
% 31.98/32.14 inference(modus_ponens,[status(thm)],[694, 687])).
% 31.98/32.14 tff(696,plain,
% 31.98/32.14 (((~![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))),
% 31.98/32.14 inference(rewrite,[status(thm)],[])).
% 31.98/32.14 tff(697,plain,
% 31.98/32.14 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | ((~bool(true)) | (impl(false, true) = true))),
% 31.98/32.14 inference(quant_inst,[status(thm)],[])).
% 31.98/32.14 tff(698,plain,
% 31.98/32.14 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | (~bool(true)) | (impl(false, true) = true)),
% 31.98/32.14 inference(modus_ponens,[status(thm)],[697, 696])).
% 31.98/32.14 tff(699,plain,
% 31.98/32.14 (impl(false, true) = true),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[698, 695, 247])).
% 31.98/32.14 tff(700,plain,
% 31.98/32.14 (impl(Q!7, impl(false, true)) = impl(Q!7, true)),
% 31.98/32.14 inference(monotonicity,[status(thm)],[699])).
% 31.98/32.14 tff(701,plain,
% 31.98/32.14 (impl(impl(Q!7, impl(false, true)), true) = impl(impl(Q!7, true), true)),
% 31.98/32.14 inference(monotonicity,[status(thm)],[700])).
% 31.98/32.14 tff(702,plain,
% 31.98/32.14 (lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = lazy_impl(true, impl(impl(Q!7, true), true))),
% 31.98/32.14 inference(monotonicity,[status(thm)],[316, 701])).
% 31.98/32.14 tff(703,plain,
% 31.98/32.14 (impl(impl(Q!7, true), true) = impl(impl(Q!7, impl(false, true)), true)),
% 31.98/32.14 inference(symmetry,[status(thm)],[701])).
% 31.98/32.14 tff(704,plain,
% 31.98/32.14 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, true) = phi(true))),
% 31.98/32.14 inference(quant_inst,[status(thm)],[])).
% 31.98/32.14 tff(705,plain,
% 31.98/32.14 (lazy_impl(true, true) = phi(true)),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[704, 325])).
% 31.98/32.14 tff(706,plain,
% 31.98/32.14 (lazy_impl(prop(true), true) = lazy_impl(true, true)),
% 31.98/32.14 inference(monotonicity,[status(thm)],[316])).
% 31.98/32.14 tff(707,plain,
% 31.98/32.14 (^[P: $i] : refl((f7(P) = lazy_impl(prop(P), P)) <=> (f7(P) = lazy_impl(prop(P), P)))),
% 31.98/32.14 inference(bind,[status(th)],[])).
% 31.98/32.14 tff(708,plain,
% 31.98/32.14 (![P: $i] : (f7(P) = lazy_impl(prop(P), P)) <=> ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 31.98/32.14 inference(quant_intro,[status(thm)],[707])).
% 31.98/32.14 tff(709,plain,
% 31.98/32.14 (![P: $i] : (f7(P) = lazy_impl(prop(P), P)) <=> ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 31.98/32.14 inference(rewrite,[status(thm)],[])).
% 31.98/32.14 tff(710,axiom,(![P: $i] : (f7(P) = lazy_impl(prop(P), P))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_f7')).
% 31.98/32.14 tff(711,plain,
% 31.98/32.14 (![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 31.98/32.14 inference(modus_ponens,[status(thm)],[710, 709])).
% 31.98/32.14 tff(712,plain,(
% 31.98/32.14 ![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 31.98/32.14 inference(skolemize,[status(sab)],[711])).
% 31.98/32.14 tff(713,plain,
% 31.98/32.14 (![P: $i] : (f7(P) = lazy_impl(prop(P), P))),
% 31.98/32.14 inference(modus_ponens,[status(thm)],[712, 708])).
% 31.98/32.14 tff(714,plain,
% 31.98/32.14 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(true) = lazy_impl(prop(true), true))),
% 31.98/32.14 inference(quant_inst,[status(thm)],[])).
% 31.98/32.14 tff(715,plain,
% 31.98/32.14 (f7(true) = lazy_impl(prop(true), true)),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[714, 713])).
% 31.98/32.14 tff(716,assumption,(P!6 = true), introduced(assumption)).
% 31.98/32.14 tff(717,plain,
% 31.98/32.14 (f7(P!6) = f7(true)),
% 31.98/32.14 inference(monotonicity,[status(thm)],[716])).
% 31.98/32.14 tff(718,plain,
% 31.98/32.14 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(P!6) = lazy_impl(prop(P!6), P!6))),
% 31.98/32.14 inference(quant_inst,[status(thm)],[])).
% 31.98/32.14 tff(719,plain,
% 31.98/32.14 (f7(P!6) = lazy_impl(prop(P!6), P!6)),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[718, 713])).
% 31.98/32.14 tff(720,plain,
% 31.98/32.14 (lazy_impl(prop(P!6), P!6) = f7(P!6)),
% 31.98/32.14 inference(symmetry,[status(thm)],[719])).
% 31.98/32.14 tff(721,plain,
% 31.98/32.14 (lazy_impl(prop(P!6), P!6) = true),
% 31.98/32.14 inference(transitivity,[status(thm)],[720, 717, 715, 706, 705, 221])).
% 31.98/32.14 tff(722,plain,
% 31.98/32.14 (((~![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))))))))),
% 31.98/32.14 inference(rewrite,[status(thm)],[])).
% 31.98/32.14 tff(723,plain,
% 31.98/32.14 ((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)))))))),
% 31.98/32.14 inference(rewrite,[status(thm)],[])).
% 31.98/32.14 tff(724,plain,
% 31.98/32.14 (((~![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))))))))),
% 31.98/32.14 inference(monotonicity,[status(thm)],[723])).
% 31.98/32.14 tff(725,plain,
% 31.98/32.14 (((~![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))))))))),
% 31.98/32.14 inference(transitivity,[status(thm)],[724, 722])).
% 31.98/32.14 tff(726,plain,
% 31.98/32.14 ((~![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))))))),
% 31.98/32.14 inference(quant_inst,[status(thm)],[])).
% 31.98/32.14 tff(727,plain,
% 31.98/32.14 ((~![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)))))))),
% 31.98/32.14 inference(modus_ponens,[status(thm)],[726, 725])).
% 31.98/32.14 tff(728,plain,
% 31.98/32.14 (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))))))),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[727, 25])).
% 31.98/32.14 tff(729,plain,
% 31.98/32.14 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(false) = lazy_impl(prop(false), false))),
% 31.98/32.14 inference(quant_inst,[status(thm)],[])).
% 31.98/32.14 tff(730,plain,
% 31.98/32.14 (f7(false) = lazy_impl(prop(false), false)),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[729, 713])).
% 31.98/32.14 tff(731,plain,
% 31.98/32.14 (lazy_impl(prop(false), false) = f7(false)),
% 31.98/32.14 inference(symmetry,[status(thm)],[730])).
% 31.98/32.14 tff(732,plain,
% 31.98/32.14 ((~![X: $i] : ((prop(X) = true) <=> bool(X))) | ((prop(false) = true) <=> bool(false))),
% 31.98/32.14 inference(quant_inst,[status(thm)],[])).
% 31.98/32.14 tff(733,plain,
% 31.98/32.14 ((prop(false) = true) <=> bool(false)),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[732, 311])).
% 31.98/32.14 tff(734,plain,
% 31.98/32.14 (d(false) <=> d(false)),
% 31.98/32.14 inference(rewrite,[status(thm)],[])).
% 31.98/32.14 tff(735,plain,
% 31.98/32.14 (d(false)),
% 31.98/32.14 inference(and_elim,[status(thm)],[203])).
% 31.98/32.14 tff(736,plain,
% 31.98/32.14 (d(false)),
% 31.98/32.14 inference(modus_ponens,[status(thm)],[735, 734])).
% 31.98/32.14 tff(737,plain,
% 31.98/32.14 ((d(false) | (~(phi(false) = err))) | (~d(false))),
% 31.98/32.14 inference(tautology,[status(thm)],[])).
% 31.98/32.14 tff(738,plain,
% 31.98/32.14 (d(false) | (~(phi(false) = err))),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[737, 736])).
% 31.98/32.14 tff(739,plain,
% 31.98/32.14 (((~![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)))))),
% 31.98/32.14 inference(rewrite,[status(thm)],[])).
% 31.98/32.14 tff(740,plain,
% 31.98/32.14 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(false)) | (~(phi(false) = false)))) | (~(d(false) | (~(phi(false) = err)))))),
% 31.98/32.14 inference(quant_inst,[status(thm)],[])).
% 31.98/32.14 tff(741,plain,
% 31.98/32.14 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(false)) | (~(phi(false) = false)))) | (~(d(false) | (~(phi(false) = err))))),
% 31.98/32.14 inference(modus_ponens,[status(thm)],[740, 739])).
% 31.98/32.14 tff(742,plain,
% 31.98/32.14 (~((~d(false)) | (~(phi(false) = false)))),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[741, 127, 738])).
% 31.98/32.14 tff(743,plain,
% 31.98/32.14 (((~d(false)) | (~(phi(false) = false))) | (phi(false) = false)),
% 31.98/32.14 inference(tautology,[status(thm)],[])).
% 31.98/32.14 tff(744,plain,
% 31.98/32.14 (phi(false) = false),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[743, 742])).
% 31.98/32.14 tff(745,plain,
% 31.98/32.14 ((not1(false) = true) <=> (not1(false) = true)),
% 31.98/32.14 inference(rewrite,[status(thm)],[])).
% 31.98/32.14 tff(746,axiom,(not1(false) = true), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','not1_axiom2')).
% 31.98/32.14 tff(747,plain,
% 31.98/32.14 (not1(false) = true),
% 31.98/32.14 inference(modus_ponens,[status(thm)],[746, 745])).
% 31.98/32.14 tff(748,plain,
% 31.98/32.14 ((not1(false) = phi(false)) <=> (true = false)),
% 31.98/32.14 inference(monotonicity,[status(thm)],[747, 744])).
% 31.98/32.14 tff(749,plain,
% 31.98/32.14 ((true = false) <=> (not1(false) = phi(false))),
% 31.98/32.14 inference(symmetry,[status(thm)],[748])).
% 31.98/32.14 tff(750,plain,
% 31.98/32.14 ((~(true = false)) <=> (~(not1(false) = phi(false)))),
% 31.98/32.14 inference(monotonicity,[status(thm)],[749])).
% 31.98/32.14 tff(751,plain,
% 31.98/32.14 (~(not1(false) = phi(false))),
% 31.98/32.14 inference(modus_ponens,[status(thm)],[231, 750])).
% 31.98/32.14 tff(752,plain,
% 31.98/32.14 (((~![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)))),
% 31.98/32.14 inference(rewrite,[status(thm)],[])).
% 31.98/32.14 tff(753,plain,
% 31.98/32.14 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | (bool(false) | (not1(false) = phi(false)))),
% 31.98/32.14 inference(quant_inst,[status(thm)],[])).
% 31.98/32.14 tff(754,plain,
% 31.98/32.14 ((~![A: $i] : (bool(A) | (not1(A) = phi(A)))) | bool(false) | (not1(false) = phi(false))),
% 31.98/32.14 inference(modus_ponens,[status(thm)],[753, 752])).
% 31.98/32.14 tff(755,plain,
% 31.98/32.14 (bool(false) | (not1(false) = phi(false))),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[754, 242])).
% 31.98/32.14 tff(756,plain,
% 31.98/32.14 (bool(false)),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[755, 751])).
% 31.98/32.14 tff(757,plain,
% 31.98/32.14 ((~((prop(false) = true) <=> bool(false))) | (prop(false) = true) | (~bool(false))),
% 31.98/32.14 inference(tautology,[status(thm)],[])).
% 31.98/32.14 tff(758,plain,
% 31.98/32.14 ((~((prop(false) = true) <=> bool(false))) | (prop(false) = true)),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[757, 756])).
% 31.98/32.14 tff(759,plain,
% 31.98/32.14 (prop(false) = true),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[758, 733])).
% 31.98/32.14 tff(760,plain,
% 31.98/32.14 (lazy_impl(prop(false), false) = lazy_impl(true, false)),
% 31.98/32.14 inference(monotonicity,[status(thm)],[759])).
% 31.98/32.14 tff(761,plain,
% 31.98/32.14 (lazy_impl(true, false) = lazy_impl(prop(false), false)),
% 31.98/32.14 inference(symmetry,[status(thm)],[760])).
% 31.98/32.14 tff(762,plain,
% 31.98/32.14 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, false) = phi(false))),
% 31.98/32.14 inference(quant_inst,[status(thm)],[])).
% 31.98/32.14 tff(763,plain,
% 31.98/32.14 (lazy_impl(true, false) = phi(false)),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[762, 325])).
% 31.98/32.14 tff(764,plain,
% 31.98/32.14 (phi(false) = lazy_impl(true, false)),
% 31.98/32.14 inference(symmetry,[status(thm)],[763])).
% 31.98/32.14 tff(765,plain,
% 31.98/32.14 (false = phi(false)),
% 31.98/32.14 inference(symmetry,[status(thm)],[744])).
% 31.98/32.14 tff(766,plain,
% 31.98/32.14 (false = f7(false)),
% 31.98/32.14 inference(transitivity,[status(thm)],[765, 764, 761, 731])).
% 31.98/32.14 tff(767,plain,
% 31.98/32.14 (forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> forallprefers(f7(false), f7(P!6))),
% 31.98/32.14 inference(monotonicity,[status(thm)],[766, 720])).
% 31.98/32.14 tff(768,plain,
% 31.98/32.14 (forallprefers(f7(false), f7(P!6)) <=> forallprefers(false, lazy_impl(prop(P!6), P!6))),
% 31.98/32.14 inference(symmetry,[status(thm)],[767])).
% 31.98/32.14 tff(769,plain,
% 31.98/32.14 ((~forallprefers(f7(false), f7(P!6))) <=> (~forallprefers(false, lazy_impl(prop(P!6), P!6)))),
% 31.98/32.14 inference(monotonicity,[status(thm)],[768])).
% 31.98/32.14 tff(770,plain,
% 31.98/32.14 (^[P1: $i] : refl((~forallprefers(f7(P1), f7(P!6))) <=> (~forallprefers(f7(P1), f7(P!6))))),
% 31.98/32.14 inference(bind,[status(th)],[])).
% 31.98/32.14 tff(771,plain,
% 31.98/32.14 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6))) <=> ![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 31.98/32.14 inference(quant_intro,[status(thm)],[770])).
% 31.98/32.14 tff(772,plain,
% 31.98/32.14 (((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))))),
% 31.98/32.14 inference(rewrite,[status(thm)],[])).
% 31.98/32.14 tff(773,plain,
% 31.98/32.14 (?[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))))),
% 31.98/32.14 inference(rewrite,[status(thm)],[])).
% 31.98/32.14 tff(774,axiom,(?[P: $i] : ((false2 = phi(f7(P))) & (~?[P1: $i] : forallprefers(f7(P1), f7(P))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','def_false2')).
% 31.98/32.14 tff(775,plain,
% 31.98/32.14 (?[P: $i] : ((false2 = phi(f7(P))) & (~?[P1: $i] : forallprefers(f7(P1), f7(P))))),
% 31.98/32.14 inference(modus_ponens,[status(thm)],[774, 773])).
% 31.98/32.14 tff(776,plain,
% 31.98/32.14 ((false2 = phi(f7(P!6))) & ![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 31.98/32.14 inference(modus_ponens,[status(thm)],[775, 772])).
% 31.98/32.14 tff(777,plain,
% 31.98/32.14 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 31.98/32.14 inference(and_elim,[status(thm)],[776])).
% 31.98/32.14 tff(778,plain,
% 31.98/32.14 (![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))),
% 31.98/32.14 inference(modus_ponens,[status(thm)],[777, 771])).
% 31.98/32.14 tff(779,plain,
% 31.98/32.14 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(false), f7(P!6)))),
% 31.98/32.14 inference(quant_inst,[status(thm)],[])).
% 31.98/32.14 tff(780,plain,
% 31.98/32.14 (~forallprefers(f7(false), f7(P!6))),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[779, 778])).
% 31.98/32.14 tff(781,plain,
% 31.98/32.14 (~forallprefers(false, lazy_impl(prop(P!6), P!6))),
% 31.98/32.14 inference(modus_ponens,[status(thm)],[780, 769])).
% 31.98/32.14 tff(782,plain,
% 31.98/32.14 ((~(forallprefers(false, lazy_impl(prop(P!6), P!6)) <=> ((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6)))))))) | forallprefers(false, lazy_impl(prop(P!6), P!6)) | (~((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6)))))))),
% 31.98/32.14 inference(tautology,[status(thm)],[])).
% 31.98/32.14 tff(783,plain,
% 31.98/32.14 (~((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))))))),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[782, 781, 728])).
% 31.98/32.14 tff(784,plain,
% 31.98/32.14 (((lazy_impl(prop(P!6), P!6) = true) | (~(d(false) | (~d(lazy_impl(prop(P!6), P!6))))) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6)))))) | (~(lazy_impl(prop(P!6), P!6) = true))),
% 31.98/32.14 inference(tautology,[status(thm)],[])).
% 31.98/32.14 tff(785,plain,
% 31.98/32.14 (~(lazy_impl(prop(P!6), P!6) = true)),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[784, 783])).
% 31.98/32.14 tff(786,plain,
% 31.98/32.14 ($false),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[785, 721])).
% 31.98/32.14 tff(787,plain,(~(P!6 = true)), inference(lemma,lemma(discharge,[]))).
% 31.98/32.14 tff(788,plain,
% 31.98/32.14 ((~![B: $i] : (lazy_impl(false, B) = true)) | (lazy_impl(false, P!6) = true)),
% 31.98/32.14 inference(quant_inst,[status(thm)],[])).
% 31.98/32.14 tff(789,plain,
% 31.98/32.14 (lazy_impl(false, P!6) = true),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[788, 7])).
% 31.98/32.14 tff(790,assumption,(prop(P!6) = false), introduced(assumption)).
% 31.98/32.14 tff(791,plain,
% 31.98/32.14 (lazy_impl(prop(P!6), P!6) = lazy_impl(false, P!6)),
% 31.98/32.14 inference(monotonicity,[status(thm)],[790])).
% 31.98/32.14 tff(792,plain,
% 31.98/32.14 (lazy_impl(prop(P!6), P!6) = true),
% 31.98/32.14 inference(transitivity,[status(thm)],[791, 789])).
% 31.98/32.14 tff(793,plain,
% 31.98/32.14 ($false),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[785, 792])).
% 31.98/32.14 tff(794,plain,(~(prop(P!6) = false)), inference(lemma,lemma(discharge,[]))).
% 31.98/32.14 tff(795,plain,
% 31.98/32.14 ((~![X: $i] : (~(bool(X) <=> (prop(X) = false)))) | (~(bool(P!6) <=> (prop(P!6) = false)))),
% 31.98/32.14 inference(quant_inst,[status(thm)],[])).
% 31.98/32.14 tff(796,plain,
% 31.98/32.14 (~(bool(P!6) <=> (prop(P!6) = false))),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[795, 443])).
% 31.98/32.14 tff(797,plain,
% 31.98/32.14 ((bool(P!6) <=> (prop(P!6) = false)) | bool(P!6) | (prop(P!6) = false)),
% 31.98/32.14 inference(tautology,[status(thm)],[])).
% 31.98/32.14 tff(798,plain,
% 31.98/32.14 (bool(P!6) | (prop(P!6) = false)),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[797, 796])).
% 31.98/32.14 tff(799,plain,
% 31.98/32.14 (bool(P!6)),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[798, 794])).
% 31.98/32.14 tff(800,plain,
% 31.98/32.14 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(P!6) <=> ((P!6 = false) | (P!6 = true)))),
% 31.98/32.14 inference(quant_inst,[status(thm)],[])).
% 31.98/32.14 tff(801,plain,
% 31.98/32.14 (bool(P!6) <=> ((P!6 = false) | (P!6 = true))),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[800, 69])).
% 31.98/32.14 tff(802,plain,
% 31.98/32.14 ((~(bool(P!6) <=> ((P!6 = false) | (P!6 = true)))) | (~bool(P!6)) | ((P!6 = false) | (P!6 = true))),
% 31.98/32.14 inference(tautology,[status(thm)],[])).
% 31.98/32.14 tff(803,plain,
% 31.98/32.14 ((~bool(P!6)) | ((P!6 = false) | (P!6 = true))),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[802, 801])).
% 31.98/32.14 tff(804,plain,
% 31.98/32.14 ((P!6 = false) | (P!6 = true)),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[803, 799])).
% 31.98/32.14 tff(805,plain,
% 31.98/32.14 ((~((P!6 = false) | (P!6 = true))) | (P!6 = false) | (P!6 = true)),
% 31.98/32.14 inference(tautology,[status(thm)],[])).
% 31.98/32.14 tff(806,plain,
% 31.98/32.14 ((P!6 = false) | (P!6 = true)),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[805, 804])).
% 31.98/32.14 tff(807,plain,
% 31.98/32.14 (P!6 = false),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[806, 787])).
% 31.98/32.14 tff(808,plain,
% 31.98/32.14 (((~![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))),
% 31.98/32.14 inference(rewrite,[status(thm)],[])).
% 31.98/32.14 tff(809,plain,
% 31.98/32.14 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | ((~bool(false)) | (impl(false, false) = true))),
% 31.98/32.14 inference(quant_inst,[status(thm)],[])).
% 31.98/32.14 tff(810,plain,
% 31.98/32.14 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | (~bool(false)) | (impl(false, false) = true)),
% 31.98/32.14 inference(modus_ponens,[status(thm)],[809, 808])).
% 31.98/32.14 tff(811,plain,
% 31.98/32.14 (impl(false, false) = true),
% 31.98/32.14 inference(unit_resolution,[status(thm)],[810, 695, 756])).
% 31.98/32.14 tff(812,plain,
% 31.98/32.15 (impl(impl(Q!7, true), impl(false, false)) = impl(impl(Q!7, true), true)),
% 31.98/32.15 inference(monotonicity,[status(thm)],[811])).
% 31.98/32.15 tff(813,plain,
% 31.98/32.15 (impl(impl(Q!7, true), true) = impl(impl(Q!7, true), impl(false, false))),
% 31.98/32.15 inference(symmetry,[status(thm)],[812])).
% 31.98/32.15 tff(814,plain,
% 31.98/32.15 (((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | ((~bool(P!6)) | (impl(false, P!6) = true))) <=> ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | (~bool(P!6)) | (impl(false, P!6) = true))),
% 31.98/32.15 inference(rewrite,[status(thm)],[])).
% 31.98/32.15 tff(815,plain,
% 31.98/32.15 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | ((~bool(P!6)) | (impl(false, P!6) = true))),
% 31.98/32.15 inference(quant_inst,[status(thm)],[])).
% 31.98/32.15 tff(816,plain,
% 31.98/32.15 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | (~bool(P!6)) | (impl(false, P!6) = true)),
% 31.98/32.15 inference(modus_ponens,[status(thm)],[815, 814])).
% 31.98/32.15 tff(817,plain,
% 31.98/32.15 ((~bool(P!6)) | (impl(false, P!6) = true)),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[816, 695])).
% 31.98/32.15 tff(818,plain,
% 31.98/32.15 (impl(false, P!6) = true),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[817, 799])).
% 31.98/32.15 tff(819,plain,
% 31.98/32.15 (impl(impl(Q!7, true), impl(false, P!6)) = impl(impl(Q!7, true), true)),
% 31.98/32.15 inference(monotonicity,[status(thm)],[818])).
% 31.98/32.15 tff(820,plain,
% 31.98/32.15 (impl(impl(Q!7, true), impl(false, P!6)) = impl(impl(Q!7, true), impl(false, false))),
% 31.98/32.15 inference(transitivity,[status(thm)],[819, 813])).
% 31.98/32.15 tff(821,plain,
% 31.98/32.15 (impl(impl(impl(Q!7, true), impl(false, P!6)), P!6) = impl(impl(impl(Q!7, true), impl(false, false)), false)),
% 31.98/32.15 inference(monotonicity,[status(thm)],[820, 807])).
% 31.98/32.15 tff(822,plain,
% 31.98/32.15 (impl(impl(Q!7, true), true) = impl(impl(Q!7, true), impl(false, P!6))),
% 31.98/32.15 inference(symmetry,[status(thm)],[819])).
% 31.98/32.15 tff(823,plain,
% 31.98/32.15 (impl(impl(impl(Q!7, true), true), P!6) = impl(impl(impl(Q!7, true), impl(false, P!6)), P!6)),
% 31.98/32.15 inference(monotonicity,[status(thm)],[822])).
% 31.98/32.15 tff(824,assumption,(~bool(impl(impl(Q!7, true), true))), introduced(assumption)).
% 31.98/32.15 tff(825,plain,
% 31.98/32.15 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(impl(Q!7, true), true)) | (impl(impl(impl(Q!7, true), true), P!6) = phi(impl(impl(Q!7, true), true))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(impl(Q!7, true), true)) | (impl(impl(impl(Q!7, true), true), P!6) = phi(impl(impl(Q!7, true), true))))),
% 31.98/32.15 inference(rewrite,[status(thm)],[])).
% 31.98/32.15 tff(826,plain,
% 31.98/32.15 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(impl(Q!7, true), true)) | (impl(impl(impl(Q!7, true), true), P!6) = phi(impl(impl(Q!7, true), true))))),
% 31.98/32.15 inference(quant_inst,[status(thm)],[])).
% 31.98/32.15 tff(827,plain,
% 31.98/32.15 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(impl(Q!7, true), true)) | (impl(impl(impl(Q!7, true), true), P!6) = phi(impl(impl(Q!7, true), true)))),
% 31.98/32.15 inference(modus_ponens,[status(thm)],[826, 825])).
% 31.98/32.15 tff(828,plain,
% 31.98/32.15 (bool(impl(impl(Q!7, true), true)) | (impl(impl(impl(Q!7, true), true), P!6) = phi(impl(impl(Q!7, true), true)))),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[827, 81])).
% 31.98/32.15 tff(829,plain,
% 31.98/32.15 (impl(impl(impl(Q!7, true), true), P!6) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[828, 824])).
% 31.98/32.15 tff(830,plain,
% 31.98/32.15 (phi(impl(impl(Q!7, true), true)) = impl(impl(impl(Q!7, true), true), P!6)),
% 31.98/32.15 inference(symmetry,[status(thm)],[829])).
% 31.98/32.15 tff(831,assumption,(~(impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true)))), introduced(assumption)).
% 31.98/32.15 tff(832,plain,
% 31.98/32.15 ((impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8)))) <=> (phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.15 inference(commutativity,[status(thm)],[])).
% 31.98/32.15 tff(833,plain,
% 31.98/32.15 ((impl(impl(Q!7, true), true) = phi(impl(impl(Q!7, true), true))) <=> (phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))),
% 31.98/32.15 inference(commutativity,[status(thm)],[])).
% 31.98/32.15 tff(834,plain,
% 31.98/32.15 (^[B: $i] : refl(((~bool(B)) | (impl(true, B) = B)) <=> ((~bool(B)) | (impl(true, B) = B)))),
% 31.98/32.15 inference(bind,[status(th)],[])).
% 31.98/32.15 tff(835,plain,
% 31.98/32.15 (![B: $i] : ((~bool(B)) | (impl(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 31.98/32.15 inference(quant_intro,[status(thm)],[834])).
% 31.98/32.15 tff(836,plain,
% 31.98/32.15 (![B: $i] : ((~bool(B)) | (impl(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 31.98/32.15 inference(rewrite,[status(thm)],[])).
% 31.98/32.15 tff(837,plain,
% 31.98/32.15 (^[B: $i] : rewrite((bool(B) => (impl(true, B) = B)) <=> ((~bool(B)) | (impl(true, B) = B)))),
% 31.98/32.15 inference(bind,[status(th)],[])).
% 31.98/32.15 tff(838,plain,
% 31.98/32.15 (![B: $i] : (bool(B) => (impl(true, B) = B)) <=> ![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 31.98/32.15 inference(quant_intro,[status(thm)],[837])).
% 31.98/32.15 tff(839,axiom,(![B: $i] : (bool(B) => (impl(true, B) = B))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','impl_axiom4')).
% 31.98/32.15 tff(840,plain,
% 31.98/32.15 (![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 31.98/32.15 inference(modus_ponens,[status(thm)],[839, 838])).
% 31.98/32.15 tff(841,plain,
% 31.98/32.15 (![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 31.98/32.15 inference(modus_ponens,[status(thm)],[840, 836])).
% 31.98/32.15 tff(842,plain,(
% 31.98/32.15 ![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 31.98/32.15 inference(skolemize,[status(sab)],[841])).
% 31.98/32.15 tff(843,plain,
% 31.98/32.15 (![B: $i] : ((~bool(B)) | (impl(true, B) = B))),
% 31.98/32.15 inference(modus_ponens,[status(thm)],[842, 835])).
% 31.98/32.15 tff(844,plain,
% 31.98/32.15 (((~![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))),
% 31.98/32.15 inference(rewrite,[status(thm)],[])).
% 31.98/32.15 tff(845,plain,
% 31.98/32.15 ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | ((~bool(true)) | (impl(true, true) = true))),
% 31.98/32.15 inference(quant_inst,[status(thm)],[])).
% 31.98/32.15 tff(846,plain,
% 31.98/32.15 ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | (~bool(true)) | (impl(true, true) = true)),
% 31.98/32.15 inference(modus_ponens,[status(thm)],[845, 844])).
% 31.98/32.15 tff(847,plain,
% 31.98/32.15 (impl(true, true) = true),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[846, 843, 247])).
% 31.98/32.15 tff(848,plain,
% 31.98/32.15 (impl(P!8, true) = impl(true, true)),
% 31.98/32.15 inference(monotonicity,[status(thm)],[667])).
% 31.98/32.15 tff(849,plain,
% 31.98/32.15 (impl(P!8, true) = true),
% 31.98/32.15 inference(transitivity,[status(thm)],[848, 847])).
% 31.98/32.15 tff(850,plain,
% 31.98/32.15 (bool(impl(P!8, true)) <=> bool(true)),
% 31.98/32.15 inference(monotonicity,[status(thm)],[849])).
% 31.98/32.15 tff(851,plain,
% 31.98/32.15 (bool(true) <=> bool(impl(P!8, true))),
% 31.98/32.15 inference(symmetry,[status(thm)],[850])).
% 31.98/32.15 tff(852,plain,
% 31.98/32.15 (bool(impl(P!8, true))),
% 31.98/32.15 inference(modus_ponens,[status(thm)],[247, 851])).
% 31.98/32.15 tff(853,plain,
% 31.98/32.15 (^[A: $i, B: $i] : refl((bool(B) | (~bool(A)) | (impl(A, B) = phi(B))) <=> (bool(B) | (~bool(A)) | (impl(A, B) = phi(B))))),
% 31.98/32.15 inference(bind,[status(th)],[])).
% 31.98/32.15 tff(854,plain,
% 31.98/32.15 (![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)))),
% 31.98/32.15 inference(quant_intro,[status(thm)],[853])).
% 31.98/32.15 tff(855,plain,
% 31.98/32.15 (^[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)))))),
% 31.98/32.15 inference(bind,[status(th)],[])).
% 31.98/32.15 tff(856,plain,
% 31.98/32.15 (![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)))),
% 31.98/32.15 inference(quant_intro,[status(thm)],[855])).
% 31.98/32.15 tff(857,plain,
% 31.98/32.15 (![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)))),
% 31.98/32.15 inference(rewrite,[status(thm)],[])).
% 31.98/32.15 tff(858,plain,
% 31.98/32.15 (^[A: $i, B: $i] : rewrite(((bool(A) & (~bool(B))) => (impl(A, B) = phi(B))) <=> ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B))))),
% 31.98/32.15 inference(bind,[status(th)],[])).
% 31.98/32.15 tff(859,plain,
% 31.98/32.15 (![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)))),
% 31.98/32.15 inference(quant_intro,[status(thm)],[858])).
% 31.98/32.15 tff(860,axiom,(![A: $i, B: $i] : ((bool(A) & (~bool(B))) => (impl(A, B) = phi(B)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax','impl_axiom2')).
% 31.98/32.15 tff(861,plain,
% 31.98/32.15 (![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B)))),
% 31.98/32.15 inference(modus_ponens,[status(thm)],[860, 859])).
% 31.98/32.15 tff(862,plain,
% 31.98/32.15 (![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B)))),
% 31.98/32.15 inference(modus_ponens,[status(thm)],[861, 857])).
% 31.98/32.15 tff(863,plain,(
% 31.98/32.15 ![A: $i, B: $i] : ((~(bool(A) & (~bool(B)))) | (impl(A, B) = phi(B)))),
% 31.98/32.15 inference(skolemize,[status(sab)],[862])).
% 31.98/32.15 tff(864,plain,
% 31.98/32.15 (![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))),
% 31.98/32.15 inference(modus_ponens,[status(thm)],[863, 856])).
% 31.98/32.15 tff(865,plain,
% 31.98/32.15 (![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))),
% 31.98/32.15 inference(modus_ponens,[status(thm)],[864, 854])).
% 31.98/32.15 tff(866,plain,
% 31.98/32.15 (((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (bool(impl(impl(Q!7, true), true)) | (~bool(impl(P!8, true))) | (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true))))) <=> ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | bool(impl(impl(Q!7, true), true)) | (~bool(impl(P!8, true))) | (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true))))),
% 31.98/32.15 inference(rewrite,[status(thm)],[])).
% 31.98/32.15 tff(867,plain,
% 31.98/32.15 ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (bool(impl(impl(Q!7, true), true)) | (~bool(impl(P!8, true))) | (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true))))),
% 31.98/32.15 inference(quant_inst,[status(thm)],[])).
% 31.98/32.15 tff(868,plain,
% 31.98/32.15 ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | bool(impl(impl(Q!7, true), true)) | (~bool(impl(P!8, true))) | (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true)))),
% 31.98/32.15 inference(modus_ponens,[status(thm)],[867, 866])).
% 31.98/32.15 tff(869,plain,
% 31.98/32.15 (bool(impl(impl(Q!7, true), true)) | (~bool(impl(P!8, true))) | (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true)))),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[868, 865])).
% 31.98/32.15 tff(870,plain,
% 31.98/32.15 (bool(impl(impl(Q!7, true), true))),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[869, 831, 852])).
% 31.98/32.15 tff(871,plain,
% 31.98/32.15 (((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | ((~bool(impl(impl(Q!7, true), true))) | (impl(true, impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)))) <=> ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | (~bool(impl(impl(Q!7, true), true))) | (impl(true, impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)))),
% 31.98/32.15 inference(rewrite,[status(thm)],[])).
% 31.98/32.15 tff(872,plain,
% 31.98/32.15 ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | ((~bool(impl(impl(Q!7, true), true))) | (impl(true, impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)))),
% 31.98/32.15 inference(quant_inst,[status(thm)],[])).
% 31.98/32.15 tff(873,plain,
% 31.98/32.15 ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | (~bool(impl(impl(Q!7, true), true))) | (impl(true, impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))),
% 31.98/32.15 inference(modus_ponens,[status(thm)],[872, 871])).
% 31.98/32.15 tff(874,plain,
% 31.98/32.15 ((~bool(impl(impl(Q!7, true), true))) | (impl(true, impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[873, 843])).
% 31.98/32.15 tff(875,plain,
% 31.98/32.15 (impl(true, impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[874, 870])).
% 31.98/32.15 tff(876,plain,
% 31.98/32.15 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = impl(true, impl(impl(Q!7, true), true))),
% 31.98/32.15 inference(monotonicity,[status(thm)],[849])).
% 31.98/32.15 tff(877,plain,
% 31.98/32.15 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)),
% 31.98/32.15 inference(transitivity,[status(thm)],[876, 875])).
% 31.98/32.15 tff(878,plain,
% 31.98/32.15 ((impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true))) <=> (impl(impl(Q!7, true), true) = phi(impl(impl(Q!7, true), true)))),
% 31.98/32.15 inference(monotonicity,[status(thm)],[877])).
% 31.98/32.15 tff(879,plain,
% 31.98/32.15 ((impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true))) <=> (phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))),
% 31.98/32.15 inference(transitivity,[status(thm)],[878, 833])).
% 31.98/32.15 tff(880,plain,
% 31.98/32.15 ((phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)) <=> (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true)))),
% 31.98/32.15 inference(symmetry,[status(thm)],[879])).
% 31.98/32.15 tff(881,plain,
% 31.98/32.15 (f7(P!6) = f7(false)),
% 31.98/32.15 inference(monotonicity,[status(thm)],[807])).
% 31.98/32.15 tff(882,plain,
% 31.98/32.15 (f7(false) = f7(P!6)),
% 31.98/32.15 inference(symmetry,[status(thm)],[881])).
% 31.98/32.15 tff(883,plain,
% 31.98/32.15 (false = f7(P!6)),
% 31.98/32.15 inference(transitivity,[status(thm)],[765, 764, 761, 731, 882])).
% 31.98/32.15 tff(884,plain,
% 31.98/32.15 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(impl(impl(Q!7, true), true)) = lazy_impl(prop(impl(impl(Q!7, true), true)), impl(impl(Q!7, true), true)))),
% 31.98/32.15 inference(quant_inst,[status(thm)],[])).
% 31.98/32.15 tff(885,plain,
% 31.98/32.15 (f7(impl(impl(Q!7, true), true)) = lazy_impl(prop(impl(impl(Q!7, true), true)), impl(impl(Q!7, true), true))),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[884, 713])).
% 31.98/32.15 tff(886,plain,
% 31.98/32.15 (lazy_impl(prop(impl(impl(Q!7, true), true)), impl(impl(Q!7, true), true)) = f7(impl(impl(Q!7, true), true))),
% 31.98/32.15 inference(symmetry,[status(thm)],[885])).
% 31.98/32.15 tff(887,plain,
% 31.98/32.15 ((~![X: $i] : ((prop(X) = true) <=> bool(X))) | ((prop(impl(impl(Q!7, true), true)) = true) <=> bool(impl(impl(Q!7, true), true)))),
% 31.98/32.15 inference(quant_inst,[status(thm)],[])).
% 31.98/32.15 tff(888,plain,
% 31.98/32.15 ((prop(impl(impl(Q!7, true), true)) = true) <=> bool(impl(impl(Q!7, true), true))),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[887, 311])).
% 31.98/32.15 tff(889,assumption,(~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true)))), introduced(assumption)).
% 31.98/32.15 tff(890,plain,
% 31.98/32.15 (impl(impl(Q!7, true), impl(false, true)) = impl(impl(Q!7, true), true)),
% 31.98/32.15 inference(monotonicity,[status(thm)],[699])).
% 31.98/32.15 tff(891,plain,
% 31.98/32.15 (impl(impl(impl(Q!7, true), impl(false, true)), true) = impl(impl(impl(Q!7, true), true), true)),
% 31.98/32.15 inference(monotonicity,[status(thm)],[890])).
% 31.98/32.15 tff(892,plain,
% 31.98/32.15 (impl(impl(impl(Q!7, true), true), true) = impl(impl(impl(Q!7, true), impl(false, true)), true)),
% 31.98/32.15 inference(symmetry,[status(thm)],[891])).
% 31.98/32.15 tff(893,plain,
% 31.98/32.15 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(impl(Q!7, true), true)) | (impl(impl(impl(Q!7, true), true), true) = phi(impl(impl(Q!7, true), true))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(impl(Q!7, true), true)) | (impl(impl(impl(Q!7, true), true), true) = phi(impl(impl(Q!7, true), true))))),
% 31.98/32.15 inference(rewrite,[status(thm)],[])).
% 31.98/32.15 tff(894,plain,
% 31.98/32.15 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(impl(Q!7, true), true)) | (impl(impl(impl(Q!7, true), true), true) = phi(impl(impl(Q!7, true), true))))),
% 31.98/32.15 inference(quant_inst,[status(thm)],[])).
% 31.98/32.15 tff(895,plain,
% 31.98/32.15 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(impl(Q!7, true), true)) | (impl(impl(impl(Q!7, true), true), true) = phi(impl(impl(Q!7, true), true)))),
% 31.98/32.15 inference(modus_ponens,[status(thm)],[894, 893])).
% 31.98/32.15 tff(896,plain,
% 31.98/32.15 (bool(impl(impl(Q!7, true), true)) | (impl(impl(impl(Q!7, true), true), true) = phi(impl(impl(Q!7, true), true)))),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[895, 81])).
% 31.98/32.15 tff(897,plain,
% 31.98/32.15 (impl(impl(impl(Q!7, true), true), true) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[896, 824])).
% 31.98/32.15 tff(898,plain,
% 31.98/32.15 (phi(impl(impl(Q!7, true), true)) = impl(impl(impl(Q!7, true), true), true)),
% 31.98/32.15 inference(symmetry,[status(thm)],[897])).
% 31.98/32.15 tff(899,plain,
% 31.98/32.15 ((err = phi(impl(impl(Q!7, true), true))) <=> (phi(impl(impl(Q!7, true), true)) = err)),
% 31.98/32.15 inference(commutativity,[status(thm)],[])).
% 31.98/32.15 tff(900,assumption,(bool(impl(P!8, true))), introduced(assumption)).
% 31.98/32.15 tff(901,plain,
% 31.98/32.15 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[869, 824, 900])).
% 31.98/32.15 tff(902,plain,
% 31.98/32.15 ((~d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[344, 889])).
% 31.98/32.15 tff(903,plain,
% 31.98/32.15 (~(d(impl(impl(P!8, true), impl(impl(Q!7, true), true))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)))),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[342, 902])).
% 31.98/32.15 tff(904,plain,
% 31.98/32.15 (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[334, 903])).
% 31.98/32.15 tff(905,plain,
% 31.98/32.15 ((phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true))) <=> (err = phi(impl(impl(Q!7, true), true)))),
% 31.98/32.15 inference(monotonicity,[status(thm)],[904, 901])).
% 31.98/32.15 tff(906,plain,
% 31.98/32.15 ((phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true))) <=> (phi(impl(impl(Q!7, true), true)) = err)),
% 31.98/32.15 inference(transitivity,[status(thm)],[905, 899])).
% 31.98/32.15 tff(907,plain,
% 31.98/32.15 ((~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true)))) <=> (~(phi(impl(impl(Q!7, true), true)) = err))),
% 31.98/32.15 inference(monotonicity,[status(thm)],[906])).
% 31.98/32.15 tff(908,plain,
% 31.98/32.15 (~(phi(impl(impl(Q!7, true), true)) = err)),
% 31.98/32.15 inference(modus_ponens,[status(thm)],[889, 907])).
% 31.98/32.15 tff(909,plain,
% 31.98/32.15 ((d(impl(impl(Q!7, true), true)) | (~(phi(impl(impl(Q!7, true), true)) = err))) | (phi(impl(impl(Q!7, true), true)) = err)),
% 31.98/32.15 inference(tautology,[status(thm)],[])).
% 31.98/32.15 tff(910,plain,
% 31.98/32.15 (d(impl(impl(Q!7, true), true)) | (~(phi(impl(impl(Q!7, true), true)) = err))),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[909, 908])).
% 31.98/32.15 tff(911,plain,
% 31.98/32.15 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(impl(Q!7, true), true))) | (~(phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))))) | (~(d(impl(impl(Q!7, true), true)) | (~(phi(impl(impl(Q!7, true), true)) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(impl(Q!7, true), true))) | (~(phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))))) | (~(d(impl(impl(Q!7, true), true)) | (~(phi(impl(impl(Q!7, true), true)) = err)))))),
% 31.98/32.15 inference(rewrite,[status(thm)],[])).
% 31.98/32.15 tff(912,plain,
% 31.98/32.15 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(impl(Q!7, true), true))) | (~(phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))))) | (~(d(impl(impl(Q!7, true), true)) | (~(phi(impl(impl(Q!7, true), true)) = err)))))),
% 31.98/32.15 inference(quant_inst,[status(thm)],[])).
% 31.98/32.15 tff(913,plain,
% 31.98/32.15 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(impl(Q!7, true), true))) | (~(phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))))) | (~(d(impl(impl(Q!7, true), true)) | (~(phi(impl(impl(Q!7, true), true)) = err))))),
% 31.98/32.15 inference(modus_ponens,[status(thm)],[912, 911])).
% 31.98/32.15 tff(914,plain,
% 31.98/32.15 ((~((~d(impl(impl(Q!7, true), true))) | (~(phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))))) | (~(d(impl(impl(Q!7, true), true)) | (~(phi(impl(impl(Q!7, true), true)) = err))))),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[913, 127])).
% 31.98/32.15 tff(915,plain,
% 31.98/32.15 (~((~d(impl(impl(Q!7, true), true))) | (~(phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))))),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[914, 910])).
% 31.98/32.15 tff(916,plain,
% 31.98/32.15 (((~d(impl(impl(Q!7, true), true))) | (~(phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)))) | (phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))),
% 31.98/32.15 inference(tautology,[status(thm)],[])).
% 31.98/32.15 tff(917,plain,
% 31.98/32.15 (phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[916, 915])).
% 31.98/32.15 tff(918,plain,
% 31.98/32.15 (impl(impl(impl(Q!7, true), impl(false, P!6)), P!6) = impl(impl(impl(Q!7, true), true), P!6)),
% 31.98/32.15 inference(monotonicity,[status(thm)],[819])).
% 31.98/32.15 tff(919,plain,
% 31.98/32.15 (false = P!6),
% 31.98/32.15 inference(symmetry,[status(thm)],[807])).
% 31.98/32.15 tff(920,plain,
% 31.98/32.15 (impl(impl(Q!7, true), impl(false, false)) = impl(impl(Q!7, true), impl(false, P!6))),
% 31.98/32.15 inference(transitivity,[status(thm)],[812, 822])).
% 31.98/32.15 tff(921,plain,
% 31.98/32.15 (impl(impl(impl(Q!7, true), impl(false, false)), false) = impl(impl(impl(Q!7, true), impl(false, P!6)), P!6)),
% 31.98/32.15 inference(monotonicity,[status(thm)],[920, 919])).
% 31.98/32.15 tff(922,plain,
% 31.98/32.15 (impl(impl(impl(Q!7, true), impl(false, false)), false) = impl(impl(Q!7, true), true)),
% 31.98/32.15 inference(transitivity,[status(thm)],[921, 918, 829, 917])).
% 31.98/32.15 tff(923,plain,
% 31.98/32.15 (phi(impl(impl(impl(Q!7, true), impl(false, false)), false)) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.15 inference(monotonicity,[status(thm)],[922])).
% 31.98/32.15 tff(924,plain,
% 31.98/32.15 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, impl(impl(impl(Q!7, true), impl(false, false)), false)) = phi(impl(impl(impl(Q!7, true), impl(false, false)), false)))),
% 31.98/32.15 inference(quant_inst,[status(thm)],[])).
% 31.98/32.15 tff(925,plain,
% 31.98/32.15 (lazy_impl(true, impl(impl(impl(Q!7, true), impl(false, false)), false)) = phi(impl(impl(impl(Q!7, true), impl(false, false)), false))),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[924, 325])).
% 31.98/32.15 tff(926,plain,
% 31.98/32.15 (lazy_impl(prop(false), impl(impl(impl(Q!7, true), impl(false, false)), false)) = lazy_impl(true, impl(impl(impl(Q!7, true), impl(false, false)), false))),
% 31.98/32.15 inference(monotonicity,[status(thm)],[759])).
% 31.98/32.15 tff(927,plain,
% 31.98/32.15 (impl(impl(impl(Q!7, true), impl(false, P!6)), P!6) = impl(impl(impl(Q!7, true), impl(false, false)), false)),
% 31.98/32.15 inference(symmetry,[status(thm)],[921])).
% 31.98/32.15 tff(928,plain,
% 31.98/32.15 (impl(impl(impl(Q!7, true), true), P!6) = impl(impl(impl(Q!7, true), impl(false, P!6)), P!6)),
% 31.98/32.15 inference(symmetry,[status(thm)],[918])).
% 31.98/32.15 tff(929,plain,
% 31.98/32.15 (impl(impl(impl(Q!7, true), impl(false, true)), true) = impl(impl(impl(Q!7, true), impl(false, false)), false)),
% 31.98/32.15 inference(transitivity,[status(thm)],[891, 897, 830, 928, 927])).
% 31.98/32.15 tff(930,plain,
% 31.98/32.15 (true = prop(false)),
% 31.98/32.15 inference(symmetry,[status(thm)],[759])).
% 31.98/32.15 tff(931,plain,
% 31.98/32.15 (prop(true) = prop(false)),
% 31.98/32.15 inference(transitivity,[status(thm)],[316, 930])).
% 31.98/32.15 tff(932,plain,
% 31.98/32.15 (lazy_impl(prop(true), impl(impl(impl(Q!7, true), impl(false, true)), true)) = lazy_impl(prop(false), impl(impl(impl(Q!7, true), impl(false, false)), false))),
% 31.98/32.15 inference(monotonicity,[status(thm)],[931, 929])).
% 31.98/32.15 tff(933,plain,
% 31.98/32.15 (lazy_impl(true, impl(impl(impl(Q!7, true), impl(false, true)), true)) = lazy_impl(prop(true), impl(impl(impl(Q!7, true), impl(false, true)), true))),
% 31.98/32.15 inference(monotonicity,[status(thm)],[317])).
% 31.98/32.15 tff(934,plain,
% 31.98/32.15 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, impl(impl(impl(Q!7, true), impl(false, true)), true)) = phi(impl(impl(impl(Q!7, true), impl(false, true)), true)))),
% 31.98/32.15 inference(quant_inst,[status(thm)],[])).
% 31.98/32.15 tff(935,plain,
% 31.98/32.15 (lazy_impl(true, impl(impl(impl(Q!7, true), impl(false, true)), true)) = phi(impl(impl(impl(Q!7, true), impl(false, true)), true))),
% 31.98/32.15 inference(unit_resolution,[status(thm)],[934, 325])).
% 31.98/32.15 tff(936,plain,
% 31.98/32.15 (phi(impl(impl(impl(Q!7, true), impl(false, true)), true)) = lazy_impl(true, impl(impl(impl(Q!7, true), impl(false, true)), true))),
% 31.98/32.15 inference(symmetry,[status(thm)],[935])).
% 31.98/32.15 tff(937,plain,
% 31.98/32.15 (phi(impl(impl(impl(Q!7, true), impl(false, true)), true)) = impl(impl(impl(Q!7, true), impl(false, true)), true)),
% 31.98/32.15 inference(transitivity,[status(thm)],[936, 933, 932, 926, 925, 923, 898, 892])).
% 31.98/32.15 tff(938,plain,
% 31.98/32.15 ((impl(impl(impl(Q!7, true), impl(false, true)), true) = phi(impl(impl(impl(Q!7, true), impl(false, true)), true))) <=> (phi(impl(impl(impl(Q!7, true), impl(false, true)), true)) = impl(impl(impl(Q!7, true), impl(false, true)), true))),
% 31.98/32.15 inference(commutativity,[status(thm)],[])).
% 31.98/32.15 tff(939,plain,
% 31.98/32.16 (lazy_impl(prop(true), impl(impl(impl(Q!7, true), impl(false, true)), true)) = lazy_impl(true, impl(impl(impl(Q!7, true), impl(false, true)), true))),
% 31.98/32.16 inference(symmetry,[status(thm)],[933])).
% 31.98/32.16 tff(940,plain,
% 31.98/32.16 (lazy_impl(prop(false), impl(impl(impl(Q!7, true), impl(false, false)), false)) = lazy_impl(prop(true), impl(impl(impl(Q!7, true), impl(false, true)), true))),
% 31.98/32.16 inference(symmetry,[status(thm)],[932])).
% 31.98/32.16 tff(941,plain,
% 31.98/32.16 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = impl(impl(impl(Q!7, true), impl(false, false)), false)),
% 31.98/32.16 inference(transitivity,[status(thm)],[901, 830, 928, 927])).
% 31.98/32.16 tff(942,plain,
% 31.98/32.16 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = lazy_impl(prop(false), impl(impl(impl(Q!7, true), impl(false, false)), false))),
% 31.98/32.16 inference(monotonicity,[status(thm)],[931, 941])).
% 31.98/32.16 tff(943,plain,
% 31.98/32.16 (err = phi(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.16 inference(symmetry,[status(thm)],[904])).
% 31.98/32.16 tff(944,plain,
% 31.98/32.16 (err = phi(impl(impl(impl(Q!7, true), impl(false, true)), true))),
% 31.98/32.16 inference(transitivity,[status(thm)],[943, 328, 318, 942, 940, 939, 935])).
% 31.98/32.16 tff(945,plain,
% 31.98/32.16 (phi(impl(impl(Q!7, true), true)) = impl(impl(impl(Q!7, true), impl(false, true)), true)),
% 31.98/32.16 inference(transitivity,[status(thm)],[898, 892])).
% 31.98/32.16 tff(946,plain,
% 31.98/32.16 ((phi(impl(impl(Q!7, true), true)) = err) <=> (impl(impl(impl(Q!7, true), impl(false, true)), true) = phi(impl(impl(impl(Q!7, true), impl(false, true)), true)))),
% 31.98/32.16 inference(monotonicity,[status(thm)],[945, 944])).
% 31.98/32.16 tff(947,plain,
% 31.98/32.16 ((phi(impl(impl(Q!7, true), true)) = err) <=> (phi(impl(impl(impl(Q!7, true), impl(false, true)), true)) = impl(impl(impl(Q!7, true), impl(false, true)), true))),
% 31.98/32.16 inference(transitivity,[status(thm)],[946, 938])).
% 31.98/32.16 tff(948,plain,
% 31.98/32.16 ((~(phi(impl(impl(Q!7, true), true)) = err)) <=> (~(phi(impl(impl(impl(Q!7, true), impl(false, true)), true)) = impl(impl(impl(Q!7, true), impl(false, true)), true)))),
% 31.98/32.16 inference(monotonicity,[status(thm)],[947])).
% 31.98/32.16 tff(949,plain,
% 31.98/32.16 (~(phi(impl(impl(impl(Q!7, true), impl(false, true)), true)) = impl(impl(impl(Q!7, true), impl(false, true)), true))),
% 31.98/32.16 inference(modus_ponens,[status(thm)],[908, 948])).
% 31.98/32.16 tff(950,plain,
% 31.98/32.16 ($false),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[949, 937])).
% 31.98/32.16 tff(951,plain,(bool(impl(impl(Q!7, true), true)) | (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true))) | (~bool(impl(P!8, true)))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.16 tff(952,plain,
% 31.98/32.16 (bool(impl(impl(Q!7, true), true))),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[951, 852, 889])).
% 31.98/32.16 tff(953,plain,
% 31.98/32.16 ((~((prop(impl(impl(Q!7, true), true)) = true) <=> bool(impl(impl(Q!7, true), true)))) | (prop(impl(impl(Q!7, true), true)) = true) | (~bool(impl(impl(Q!7, true), true)))),
% 31.98/32.16 inference(tautology,[status(thm)],[])).
% 31.98/32.16 tff(954,plain,
% 31.98/32.16 ((~((prop(impl(impl(Q!7, true), true)) = true) <=> bool(impl(impl(Q!7, true), true)))) | (prop(impl(impl(Q!7, true), true)) = true)),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[953, 952])).
% 31.98/32.16 tff(955,plain,
% 31.98/32.16 (prop(impl(impl(Q!7, true), true)) = true),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[954, 888])).
% 31.98/32.16 tff(956,plain,
% 31.98/32.16 (prop(impl(impl(Q!7, true), true)) = prop(true)),
% 31.98/32.16 inference(transitivity,[status(thm)],[955, 317])).
% 31.98/32.16 tff(957,plain,
% 31.98/32.16 (lazy_impl(prop(impl(impl(Q!7, true), true)), impl(impl(Q!7, true), true)) = lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))),
% 31.98/32.16 inference(monotonicity,[status(thm)],[956, 703])).
% 31.98/32.16 tff(958,plain,
% 31.98/32.16 (lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = lazy_impl(prop(impl(impl(Q!7, true), true)), impl(impl(Q!7, true), true))),
% 31.98/32.16 inference(symmetry,[status(thm)],[957])).
% 31.98/32.16 tff(959,plain,
% 31.98/32.16 (impl(true, impl(impl(Q!7, true), true)) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.16 inference(symmetry,[status(thm)],[876])).
% 31.98/32.16 tff(960,plain,
% 31.98/32.16 (impl(true, impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[874, 952])).
% 31.98/32.16 tff(961,plain,
% 31.98/32.16 (impl(impl(Q!7, true), true) = impl(true, impl(impl(Q!7, true), true))),
% 31.98/32.16 inference(symmetry,[status(thm)],[960])).
% 31.98/32.16 tff(962,plain,
% 31.98/32.16 (impl(impl(Q!7, impl(false, true)), true) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.16 inference(transitivity,[status(thm)],[701, 961, 959])).
% 31.98/32.16 tff(963,plain,
% 31.98/32.16 (lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.16 inference(monotonicity,[status(thm)],[962])).
% 31.98/32.16 tff(964,plain,
% 31.98/32.16 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))),
% 31.98/32.16 inference(symmetry,[status(thm)],[963])).
% 31.98/32.16 tff(965,plain,
% 31.98/32.16 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = lazy_impl(true, impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.16 inference(monotonicity,[status(thm)],[316])).
% 31.98/32.16 tff(966,plain,
% 31.98/32.16 (lazy_impl(true, impl(impl(P!8, true), impl(impl(Q!7, true), true))) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.16 inference(symmetry,[status(thm)],[965])).
% 31.98/32.16 tff(967,plain,
% 31.98/32.16 (err = f7(impl(impl(Q!7, true), true))),
% 31.98/32.16 inference(transitivity,[status(thm)],[943, 328, 966, 964, 958, 886])).
% 31.98/32.16 tff(968,plain,
% 31.98/32.16 (forallprefers(err, false) <=> forallprefers(f7(impl(impl(Q!7, true), true)), f7(P!6))),
% 31.98/32.16 inference(monotonicity,[status(thm)],[967, 883])).
% 31.98/32.16 tff(969,plain,
% 31.98/32.16 (forallprefers(f7(impl(impl(Q!7, true), true)), f7(P!6)) <=> forallprefers(err, false)),
% 31.98/32.16 inference(symmetry,[status(thm)],[968])).
% 31.98/32.16 tff(970,plain,
% 31.98/32.16 ((~forallprefers(f7(impl(impl(Q!7, true), true)), f7(P!6))) <=> (~forallprefers(err, false))),
% 31.98/32.16 inference(monotonicity,[status(thm)],[969])).
% 31.98/32.16 tff(971,plain,
% 31.98/32.16 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(impl(impl(Q!7, true), true)), f7(P!6)))),
% 31.98/32.16 inference(quant_inst,[status(thm)],[])).
% 31.98/32.16 tff(972,plain,
% 31.98/32.16 (~forallprefers(f7(impl(impl(Q!7, true), true)), f7(P!6))),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[971, 778])).
% 31.98/32.16 tff(973,plain,
% 31.98/32.16 (~forallprefers(err, false)),
% 31.98/32.16 inference(modus_ponens,[status(thm)],[972, 970])).
% 31.98/32.16 tff(974,plain,
% 31.98/32.16 (((~![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)))))))),
% 31.98/32.16 inference(rewrite,[status(thm)],[])).
% 31.98/32.16 tff(975,plain,
% 31.98/32.16 ((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))))))),
% 31.98/32.16 inference(rewrite,[status(thm)],[])).
% 31.98/32.16 tff(976,plain,
% 31.98/32.16 (((~![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)))))))),
% 31.98/32.16 inference(monotonicity,[status(thm)],[975])).
% 31.98/32.16 tff(977,plain,
% 31.98/32.16 (((~![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)))))))),
% 31.98/32.16 inference(transitivity,[status(thm)],[976, 974])).
% 31.98/32.16 tff(978,plain,
% 31.98/32.16 ((~![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))))))),
% 31.98/32.16 inference(quant_inst,[status(thm)],[])).
% 31.98/32.16 tff(979,plain,
% 31.98/32.16 ((~![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))))))),
% 31.98/32.16 inference(modus_ponens,[status(thm)],[978, 977])).
% 31.98/32.16 tff(980,plain,
% 31.98/32.16 (forallprefers(err, false) <=> ((~((~(err = false)) | (~(false = true)))) | (~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))))),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[979, 25])).
% 31.98/32.16 tff(981,assumption,(~(bool(err) <=> ((err = false) | (err = true)))), introduced(assumption)).
% 31.98/32.16 tff(982,plain,
% 31.98/32.16 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(err) <=> ((err = false) | (err = true)))),
% 31.98/32.16 inference(quant_inst,[status(thm)],[])).
% 31.98/32.16 tff(983,plain,
% 31.98/32.16 ($false),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[982, 69, 981])).
% 31.98/32.16 tff(984,plain,(bool(err) <=> ((err = false) | (err = true))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.16 tff(985,assumption,((err = false) | (err = true)), introduced(assumption)).
% 31.98/32.16 tff(986,plain,
% 31.98/32.16 ((err = false) <=> (false = err)),
% 31.98/32.16 inference(commutativity,[status(thm)],[])).
% 31.98/32.16 tff(987,plain,
% 31.98/32.16 ((false = err) <=> (err = false)),
% 31.98/32.16 inference(symmetry,[status(thm)],[986])).
% 31.98/32.16 tff(988,plain,
% 31.98/32.16 ((~(false = err)) <=> (~(err = false))),
% 31.98/32.16 inference(monotonicity,[status(thm)],[987])).
% 31.98/32.16 tff(989,plain,
% 31.98/32.16 (~(err = false)),
% 31.98/32.16 inference(modus_ponens,[status(thm)],[114, 988])).
% 31.98/32.16 tff(990,plain,
% 31.98/32.16 ((err = true) <=> (true = err)),
% 31.98/32.16 inference(commutativity,[status(thm)],[])).
% 31.98/32.16 tff(991,plain,
% 31.98/32.16 ((true = err) <=> (err = true)),
% 31.98/32.16 inference(symmetry,[status(thm)],[990])).
% 31.98/32.16 tff(992,plain,
% 31.98/32.16 ((~(true = err)) <=> (~(err = true))),
% 31.98/32.16 inference(monotonicity,[status(thm)],[991])).
% 31.98/32.16 tff(993,plain,
% 31.98/32.16 (~(err = true)),
% 31.98/32.16 inference(modus_ponens,[status(thm)],[153, 992])).
% 31.98/32.16 tff(994,plain,
% 31.98/32.16 ((~((err = false) | (err = true))) | (err = false) | (err = true)),
% 31.98/32.16 inference(tautology,[status(thm)],[])).
% 31.98/32.16 tff(995,plain,
% 31.98/32.16 ($false),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[994, 993, 989, 985])).
% 31.98/32.16 tff(996,plain,(~((err = false) | (err = true))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.16 tff(997,plain,
% 31.98/32.16 ((~(bool(err) <=> ((err = false) | (err = true)))) | (~bool(err)) | ((err = false) | (err = true))),
% 31.98/32.16 inference(tautology,[status(thm)],[])).
% 31.98/32.16 tff(998,plain,
% 31.98/32.16 ((~(bool(err) <=> ((err = false) | (err = true)))) | (~bool(err))),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[997, 996])).
% 31.98/32.16 tff(999,plain,
% 31.98/32.16 (~bool(err)),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[998, 984])).
% 31.98/32.16 tff(1000,plain,
% 31.98/32.16 ((~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))) | (~d(false)) | (~d(err)) | bool(err) | (~bool(false))),
% 31.98/32.16 inference(tautology,[status(thm)],[])).
% 31.98/32.16 tff(1001,plain,
% 31.98/32.16 (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[1000, 736, 559, 756, 999])).
% 31.98/32.16 tff(1002,plain,
% 31.98/32.16 (((~((~(err = false)) | (~(false = true)))) | (~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false))))) | ((~d(false)) | (~d(err)) | bool(err) | (~bool(false)))),
% 31.98/32.16 inference(tautology,[status(thm)],[])).
% 31.98/32.16 tff(1003,plain,
% 31.98/32.16 ((~((~(err = false)) | (~(false = true)))) | (~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false))))),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[1002, 1001])).
% 31.98/32.16 tff(1004,plain,
% 31.98/32.16 ((~(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))))))),
% 31.98/32.16 inference(tautology,[status(thm)],[])).
% 31.98/32.16 tff(1005,plain,
% 31.98/32.16 ((~(forallprefers(err, false) <=> ((~((~(err = false)) | (~(false = true)))) | (~(d(err) | (~d(false)))) | (~((~d(false)) | (~d(err)) | bool(err) | (~bool(false))))))) | forallprefers(err, false)),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[1004, 1003])).
% 31.98/32.16 tff(1006,plain,
% 31.98/32.16 (forallprefers(err, false)),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[1005, 980])).
% 31.98/32.16 tff(1007,plain,
% 31.98/32.16 ($false),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[1006, 973])).
% 31.98/32.16 tff(1008,plain,((~(P!8 = true)) | (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true)))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.16 tff(1009,plain,
% 31.98/32.16 (~(P!8 = true)),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[1008, 889])).
% 31.98/32.16 tff(1010,plain,
% 31.98/32.16 (P!8 = false),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[677, 1009])).
% 31.98/32.16 tff(1011,plain,
% 31.98/32.16 (impl(P!8, true) = impl(false, true)),
% 31.98/32.16 inference(monotonicity,[status(thm)],[1010])).
% 31.98/32.16 tff(1012,plain,
% 31.98/32.16 (impl(P!8, true) = true),
% 31.98/32.16 inference(transitivity,[status(thm)],[1011, 699])).
% 31.98/32.16 tff(1013,plain,
% 31.98/32.16 (bool(impl(P!8, true)) <=> bool(true)),
% 31.98/32.16 inference(monotonicity,[status(thm)],[1012])).
% 31.98/32.16 tff(1014,plain,
% 31.98/32.16 (bool(true) <=> bool(impl(P!8, true))),
% 31.98/32.16 inference(symmetry,[status(thm)],[1013])).
% 31.98/32.16 tff(1015,plain,
% 31.98/32.16 (bool(impl(P!8, true))),
% 31.98/32.16 inference(modus_ponens,[status(thm)],[247, 1014])).
% 31.98/32.16 tff(1016,plain,
% 31.98/32.16 (bool(impl(impl(Q!7, true), true))),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[951, 1015, 889])).
% 31.98/32.16 tff(1017,plain,
% 31.98/32.16 ((~((prop(impl(impl(Q!7, true), true)) = true) <=> bool(impl(impl(Q!7, true), true)))) | (prop(impl(impl(Q!7, true), true)) = true)),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[953, 1016])).
% 31.98/32.16 tff(1018,plain,
% 31.98/32.16 (prop(impl(impl(Q!7, true), true)) = true),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[1017, 888])).
% 31.98/32.16 tff(1019,plain,
% 31.98/32.16 (prop(impl(impl(Q!7, true), true)) = prop(true)),
% 31.98/32.16 inference(transitivity,[status(thm)],[1018, 317])).
% 31.98/32.16 tff(1020,plain,
% 31.98/32.16 (lazy_impl(prop(impl(impl(Q!7, true), true)), impl(impl(Q!7, true), true)) = lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))),
% 31.98/32.16 inference(monotonicity,[status(thm)],[1019, 703])).
% 31.98/32.16 tff(1021,plain,
% 31.98/32.16 (lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = lazy_impl(prop(impl(impl(Q!7, true), true)), impl(impl(Q!7, true), true))),
% 31.98/32.16 inference(symmetry,[status(thm)],[1020])).
% 31.98/32.16 tff(1022,plain,
% 31.98/32.16 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = impl(true, impl(impl(Q!7, true), true))),
% 31.98/32.16 inference(monotonicity,[status(thm)],[1012])).
% 31.98/32.16 tff(1023,plain,
% 31.98/32.16 (impl(true, impl(impl(Q!7, true), true)) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.16 inference(symmetry,[status(thm)],[1022])).
% 31.98/32.16 tff(1024,plain,
% 31.98/32.16 (impl(true, impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[874, 1016])).
% 31.98/32.16 tff(1025,plain,
% 31.98/32.16 (impl(impl(Q!7, true), true) = impl(true, impl(impl(Q!7, true), true))),
% 31.98/32.16 inference(symmetry,[status(thm)],[1024])).
% 31.98/32.16 tff(1026,plain,
% 31.98/32.16 (impl(impl(Q!7, impl(false, true)), true) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.16 inference(transitivity,[status(thm)],[701, 1025, 1023])).
% 31.98/32.16 tff(1027,plain,
% 31.98/32.16 (lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.16 inference(monotonicity,[status(thm)],[1026])).
% 31.98/32.16 tff(1028,plain,
% 31.98/32.16 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))),
% 31.98/32.16 inference(symmetry,[status(thm)],[1027])).
% 31.98/32.16 tff(1029,plain,
% 31.98/32.16 (err = f7(impl(impl(Q!7, true), true))),
% 31.98/32.16 inference(transitivity,[status(thm)],[943, 328, 966, 1028, 1021, 886])).
% 31.98/32.16 tff(1030,plain,
% 31.98/32.16 (forallprefers(err, false) <=> forallprefers(f7(impl(impl(Q!7, true), true)), f7(P!6))),
% 31.98/32.16 inference(monotonicity,[status(thm)],[1029, 883])).
% 31.98/32.16 tff(1031,plain,
% 31.98/32.16 (forallprefers(f7(impl(impl(Q!7, true), true)), f7(P!6)) <=> forallprefers(err, false)),
% 31.98/32.16 inference(symmetry,[status(thm)],[1030])).
% 31.98/32.16 tff(1032,plain,
% 31.98/32.16 ((~forallprefers(f7(impl(impl(Q!7, true), true)), f7(P!6))) <=> (~forallprefers(err, false))),
% 31.98/32.16 inference(monotonicity,[status(thm)],[1031])).
% 31.98/32.16 tff(1033,plain,
% 31.98/32.16 (~forallprefers(err, false)),
% 31.98/32.16 inference(modus_ponens,[status(thm)],[972, 1032])).
% 31.98/32.16 tff(1034,plain,
% 31.98/32.16 ($false),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[1006, 1033])).
% 31.98/32.16 tff(1035,plain,(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.16 tff(1036,plain,
% 31.98/32.16 (impl(impl(Q!7, true), true) = impl(true, impl(impl(Q!7, true), true))),
% 31.98/32.16 inference(symmetry,[status(thm)],[875])).
% 31.98/32.16 tff(1037,plain,
% 31.98/32.16 (impl(impl(Q!7, impl(false, true)), true) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.16 inference(transitivity,[status(thm)],[701, 1036, 959])).
% 31.98/32.16 tff(1038,plain,
% 31.98/32.16 (lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.16 inference(monotonicity,[status(thm)],[1037])).
% 31.98/32.16 tff(1039,plain,
% 31.98/32.16 (lazy_impl(true, impl(impl(Q!7, true), true)) = lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))),
% 31.98/32.16 inference(monotonicity,[status(thm)],[317, 703])).
% 31.98/32.16 tff(1040,plain,
% 31.98/32.16 (phi(impl(impl(Q!7, true), true)) = lazy_impl(true, impl(impl(Q!7, true), true))),
% 31.98/32.16 inference(symmetry,[status(thm)],[685])).
% 31.98/32.16 tff(1041,plain,
% 31.98/32.16 (phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)),
% 31.98/32.16 inference(transitivity,[status(thm)],[1040, 1039, 1038, 965, 327, 1035, 876, 875])).
% 31.98/32.16 tff(1042,plain,
% 31.98/32.16 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.16 inference(modus_ponens,[status(thm)],[1041, 880])).
% 31.98/32.16 tff(1043,plain,
% 31.98/32.16 ($false),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[831, 1042])).
% 31.98/32.16 tff(1044,plain,((impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true))) | (~(P!8 = true))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.16 tff(1045,plain,
% 31.98/32.16 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[1044, 667])).
% 31.98/32.16 tff(1046,assumption,(~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true)), introduced(assumption)).
% 31.98/32.16 tff(1047,plain,
% 31.98/32.16 (impl(true, impl(false, true)) = impl(true, true)),
% 31.98/32.16 inference(monotonicity,[status(thm)],[699])).
% 31.98/32.16 tff(1048,plain,
% 31.98/32.16 (impl(true, impl(false, true)) = true),
% 31.98/32.16 inference(transitivity,[status(thm)],[1047, 847])).
% 31.98/32.16 tff(1049,plain,
% 31.98/32.16 (impl(impl(true, impl(false, true)), true) = impl(true, true)),
% 31.98/32.16 inference(monotonicity,[status(thm)],[1048])).
% 31.98/32.16 tff(1050,plain,
% 31.98/32.16 (impl(true, true) = impl(impl(true, impl(false, true)), true)),
% 31.98/32.16 inference(symmetry,[status(thm)],[1049])).
% 31.98/32.16 tff(1051,plain,
% 31.98/32.16 (true = impl(true, true)),
% 31.98/32.16 inference(symmetry,[status(thm)],[847])).
% 31.98/32.16 tff(1052,plain,
% 31.98/32.16 (true = impl(impl(true, impl(false, true)), true)),
% 31.98/32.16 inference(transitivity,[status(thm)],[1051, 1050])).
% 31.98/32.16 tff(1053,plain,
% 31.98/32.16 (lazy_impl(true, true) = lazy_impl(prop(true), impl(impl(true, impl(false, true)), true))),
% 31.98/32.16 inference(monotonicity,[status(thm)],[317, 1052])).
% 31.98/32.16 tff(1054,plain,
% 31.98/32.16 (lazy_impl(prop(true), impl(impl(true, impl(false, true)), true)) = lazy_impl(true, true)),
% 31.98/32.16 inference(symmetry,[status(thm)],[1053])).
% 31.98/32.16 tff(1055,plain,
% 31.98/32.16 (^[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))))),
% 31.98/32.16 inference(bind,[status(th)],[])).
% 31.98/32.16 tff(1056,plain,
% 31.98/32.16 (![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)))),
% 31.98/32.16 inference(quant_intro,[status(thm)],[1055])).
% 31.98/32.16 tff(1057,plain,
% 31.98/32.16 (![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)))),
% 31.98/32.16 inference(rewrite,[status(thm)],[])).
% 31.98/32.16 tff(1058,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/sandbox/benchmark/Axioms/SWV012+0.ax','def_f1')).
% 31.98/32.16 tff(1059,plain,
% 31.98/32.16 (![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))),
% 31.98/32.16 inference(modus_ponens,[status(thm)],[1058, 1057])).
% 31.98/32.16 tff(1060,plain,(
% 31.98/32.16 ![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))),
% 31.98/32.16 inference(skolemize,[status(sab)],[1059])).
% 31.98/32.16 tff(1061,plain,
% 31.98/32.16 (![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))),
% 31.98/32.16 inference(modus_ponens,[status(thm)],[1060, 1056])).
% 31.98/32.16 tff(1062,plain,
% 31.98/32.16 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(true, false, true) = lazy_impl(prop(true), impl(impl(true, impl(false, true)), true)))),
% 31.98/32.16 inference(quant_inst,[status(thm)],[])).
% 31.98/32.16 tff(1063,plain,
% 31.98/32.16 (f1(true, false, true) = lazy_impl(prop(true), impl(impl(true, impl(false, true)), true))),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[1062, 1061])).
% 31.98/32.16 tff(1064,assumption,(Q!7 = true), introduced(assumption)).
% 31.98/32.16 tff(1065,plain,
% 31.98/32.16 (true = Q!7),
% 31.98/32.16 inference(symmetry,[status(thm)],[1064])).
% 31.98/32.16 tff(1066,plain,
% 31.98/32.16 (f1(true, false, true) = f1(Q!7, false, true)),
% 31.98/32.16 inference(monotonicity,[status(thm)],[1065])).
% 31.98/32.16 tff(1067,plain,
% 31.98/32.16 (f1(Q!7, false, true) = f1(true, false, true)),
% 31.98/32.16 inference(symmetry,[status(thm)],[1066])).
% 31.98/32.16 tff(1068,plain,
% 31.98/32.16 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(Q!7, false, true) = lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))),
% 31.98/32.16 inference(quant_inst,[status(thm)],[])).
% 31.98/32.16 tff(1069,plain,
% 31.98/32.16 (f1(Q!7, false, true) = lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[1068, 1061])).
% 31.98/32.16 tff(1070,plain,
% 31.98/32.16 (lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = f1(Q!7, false, true)),
% 31.98/32.16 inference(symmetry,[status(thm)],[1069])).
% 31.98/32.16 tff(1071,plain,
% 31.98/32.16 (lazy_impl(true, impl(impl(Q!7, true), true)) = lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))),
% 31.98/32.16 inference(symmetry,[status(thm)],[702])).
% 31.98/32.16 tff(1072,assumption,(impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true))), introduced(assumption)).
% 31.98/32.16 tff(1073,plain,
% 31.98/32.16 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true),
% 31.98/32.16 inference(transitivity,[status(thm)],[965, 327, 1035, 1072, 1040, 1071, 1070, 1067, 1063, 1054, 705, 221])).
% 31.98/32.16 tff(1074,plain,
% 31.98/32.16 ($false),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[1046, 1073])).
% 31.98/32.16 tff(1075,plain,((~(Q!7 = true)) | (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true) | (~(impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true))))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.16 tff(1076,plain,
% 31.98/32.16 (~(Q!7 = true)),
% 31.98/32.16 inference(unit_resolution,[status(thm)],[1075, 1046, 1045])).
% 31.98/32.16 tff(1077,plain,
% 31.98/32.16 (impl(false, impl(false, true)) = impl(false, true)),
% 31.98/32.16 inference(monotonicity,[status(thm)],[699])).
% 31.98/32.16 tff(1078,plain,
% 31.98/32.16 (impl(false, impl(false, true)) = true),
% 31.98/32.16 inference(transitivity,[status(thm)],[1077, 699])).
% 31.98/32.16 tff(1079,plain,
% 31.98/32.16 (impl(impl(false, impl(false, true)), true) = impl(true, true)),
% 31.98/32.17 inference(monotonicity,[status(thm)],[1078])).
% 31.98/32.17 tff(1080,plain,
% 31.98/32.17 (impl(true, true) = impl(impl(false, impl(false, true)), true)),
% 31.98/32.17 inference(symmetry,[status(thm)],[1079])).
% 31.98/32.17 tff(1081,plain,
% 31.98/32.17 (true = impl(impl(false, impl(false, true)), true)),
% 31.98/32.17 inference(transitivity,[status(thm)],[1051, 1080])).
% 31.98/32.17 tff(1082,plain,
% 31.98/32.17 (lazy_impl(true, true) = lazy_impl(prop(true), impl(impl(false, impl(false, true)), true))),
% 31.98/32.17 inference(monotonicity,[status(thm)],[317, 1081])).
% 31.98/32.17 tff(1083,plain,
% 31.98/32.17 (lazy_impl(prop(true), impl(impl(false, impl(false, true)), true)) = lazy_impl(true, true)),
% 31.98/32.17 inference(symmetry,[status(thm)],[1082])).
% 31.98/32.17 tff(1084,plain,
% 31.98/32.17 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(false, false, true) = lazy_impl(prop(true), impl(impl(false, impl(false, true)), true)))),
% 31.98/32.17 inference(quant_inst,[status(thm)],[])).
% 31.98/32.17 tff(1085,plain,
% 31.98/32.17 (f1(false, false, true) = lazy_impl(prop(true), impl(impl(false, impl(false, true)), true))),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1084, 1061])).
% 31.98/32.17 tff(1086,assumption,(Q!7 = false), introduced(assumption)).
% 31.98/32.17 tff(1087,plain,
% 31.98/32.17 (false = Q!7),
% 31.98/32.17 inference(symmetry,[status(thm)],[1086])).
% 31.98/32.17 tff(1088,plain,
% 31.98/32.17 (f1(false, false, true) = f1(Q!7, false, true)),
% 31.98/32.17 inference(monotonicity,[status(thm)],[1087])).
% 31.98/32.17 tff(1089,plain,
% 31.98/32.17 (f1(Q!7, false, true) = f1(false, false, true)),
% 31.98/32.17 inference(symmetry,[status(thm)],[1088])).
% 31.98/32.17 tff(1090,plain,
% 31.98/32.17 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true),
% 31.98/32.17 inference(transitivity,[status(thm)],[965, 327, 1035, 1072, 1040, 1071, 1070, 1089, 1085, 1083, 705, 221])).
% 31.98/32.17 tff(1091,plain,
% 31.98/32.17 ($false),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1046, 1090])).
% 31.98/32.17 tff(1092,plain,((~(Q!7 = false)) | (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true) | (~(impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true))))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.17 tff(1093,plain,
% 31.98/32.17 (~(Q!7 = false)),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1092, 1046, 1045])).
% 31.98/32.17 tff(1094,plain,
% 31.98/32.17 (~((Q!7 = false) | (Q!7 = true))),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[633, 1093, 1076])).
% 31.98/32.17 tff(1095,plain,
% 31.98/32.17 (~bool(Q!7)),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[631, 1094])).
% 31.98/32.17 tff(1096,plain,
% 31.98/32.17 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(Q!7) | (impl(Q!7, true) = phi(Q!7)))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(Q!7) | (impl(Q!7, true) = phi(Q!7)))),
% 31.98/32.17 inference(rewrite,[status(thm)],[])).
% 31.98/32.17 tff(1097,plain,
% 31.98/32.17 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(Q!7) | (impl(Q!7, true) = phi(Q!7)))),
% 31.98/32.17 inference(quant_inst,[status(thm)],[])).
% 31.98/32.17 tff(1098,plain,
% 31.98/32.17 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(Q!7) | (impl(Q!7, true) = phi(Q!7))),
% 31.98/32.17 inference(modus_ponens,[status(thm)],[1097, 1096])).
% 31.98/32.17 tff(1099,plain,
% 31.98/32.17 (bool(Q!7) | (impl(Q!7, true) = phi(Q!7))),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1098, 81])).
% 31.98/32.17 tff(1100,plain,
% 31.98/32.17 (impl(Q!7, true) = phi(Q!7)),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1099, 1095])).
% 31.98/32.17 tff(1101,plain,
% 31.98/32.17 (phi(Q!7) = impl(Q!7, true)),
% 31.98/32.17 inference(symmetry,[status(thm)],[1100])).
% 31.98/32.17 tff(1102,plain,
% 31.98/32.17 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(Q!7) | (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = phi(Q!7)))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(Q!7) | (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = phi(Q!7)))),
% 31.98/32.17 inference(rewrite,[status(thm)],[])).
% 31.98/32.17 tff(1103,plain,
% 31.98/32.17 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(Q!7) | (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = phi(Q!7)))),
% 31.98/32.17 inference(quant_inst,[status(thm)],[])).
% 31.98/32.17 tff(1104,plain,
% 31.98/32.17 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(Q!7) | (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = phi(Q!7))),
% 31.98/32.17 inference(modus_ponens,[status(thm)],[1103, 1102])).
% 31.98/32.17 tff(1105,plain,
% 31.98/32.17 (bool(Q!7) | (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = phi(Q!7))),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1104, 81])).
% 31.98/32.17 tff(1106,plain,
% 31.98/32.17 (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = phi(Q!7)),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1105, 1095])).
% 31.98/32.17 tff(1107,plain,
% 31.98/32.17 (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = impl(Q!7, true)),
% 31.98/32.17 inference(transitivity,[status(thm)],[1106, 1101])).
% 31.98/32.17 tff(1108,plain,
% 31.98/32.17 (phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = phi(impl(Q!7, true))),
% 31.98/32.17 inference(monotonicity,[status(thm)],[1107])).
% 31.98/32.17 tff(1109,plain,
% 31.98/32.17 (phi(impl(Q!7, true)) = phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.17 inference(symmetry,[status(thm)],[1108])).
% 31.98/32.17 tff(1110,assumption,(~bool(Q!7)), introduced(assumption)).
% 31.98/32.17 tff(1111,plain,
% 31.98/32.17 (impl(Q!7, true) = phi(Q!7)),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1099, 1110])).
% 31.98/32.17 tff(1112,plain,
% 31.98/32.17 (phi(Q!7) = impl(Q!7, true)),
% 31.98/32.17 inference(symmetry,[status(thm)],[1111])).
% 31.98/32.17 tff(1113,assumption,(bool(impl(Q!7, true))), introduced(assumption)).
% 31.98/32.17 tff(1114,assumption,(phi(Q!7) = err), introduced(assumption)).
% 31.98/32.17 tff(1115,assumption,(impl(Q!7, true) = phi(Q!7)), introduced(assumption)).
% 31.98/32.17 tff(1116,plain,
% 31.98/32.17 (impl(Q!7, true) = err),
% 31.98/32.17 inference(transitivity,[status(thm)],[1115, 1114])).
% 31.98/32.17 tff(1117,plain,
% 31.98/32.17 (bool(impl(Q!7, true)) <=> bool(err)),
% 31.98/32.17 inference(monotonicity,[status(thm)],[1116])).
% 31.98/32.17 tff(1118,plain,
% 31.98/32.17 (bool(err) <=> bool(impl(Q!7, true))),
% 31.98/32.17 inference(symmetry,[status(thm)],[1117])).
% 31.98/32.17 tff(1119,plain,
% 31.98/32.17 ((~bool(err)) <=> (~bool(impl(Q!7, true)))),
% 31.98/32.17 inference(monotonicity,[status(thm)],[1118])).
% 31.98/32.17 tff(1120,plain,
% 31.98/32.17 (~bool(impl(Q!7, true))),
% 31.98/32.17 inference(modus_ponens,[status(thm)],[999, 1119])).
% 31.98/32.17 tff(1121,plain,
% 31.98/32.17 ($false),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1113, 1120])).
% 31.98/32.17 tff(1122,plain,((~(phi(Q!7) = err)) | (~bool(impl(Q!7, true))) | (~(impl(Q!7, true) = phi(Q!7)))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.17 tff(1123,plain,
% 31.98/32.17 (~(phi(Q!7) = err)),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1122, 1113, 1111])).
% 31.98/32.17 tff(1124,plain,
% 31.98/32.17 ((d(Q!7) | (~(phi(Q!7) = err))) | (phi(Q!7) = err)),
% 31.98/32.17 inference(tautology,[status(thm)],[])).
% 31.98/32.17 tff(1125,plain,
% 31.98/32.17 (d(Q!7) | (~(phi(Q!7) = err))),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1124, 1123])).
% 31.98/32.17 tff(1126,plain,
% 31.98/32.17 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(Q!7)) | (~(phi(Q!7) = Q!7)))) | (~(d(Q!7) | (~(phi(Q!7) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(Q!7)) | (~(phi(Q!7) = Q!7)))) | (~(d(Q!7) | (~(phi(Q!7) = err)))))),
% 31.98/32.17 inference(rewrite,[status(thm)],[])).
% 31.98/32.17 tff(1127,plain,
% 31.98/32.17 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(Q!7)) | (~(phi(Q!7) = Q!7)))) | (~(d(Q!7) | (~(phi(Q!7) = err)))))),
% 31.98/32.17 inference(quant_inst,[status(thm)],[])).
% 31.98/32.17 tff(1128,plain,
% 31.98/32.17 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(Q!7)) | (~(phi(Q!7) = Q!7)))) | (~(d(Q!7) | (~(phi(Q!7) = err))))),
% 31.98/32.17 inference(modus_ponens,[status(thm)],[1127, 1126])).
% 31.98/32.17 tff(1129,plain,
% 31.98/32.17 ((~((~d(Q!7)) | (~(phi(Q!7) = Q!7)))) | (~(d(Q!7) | (~(phi(Q!7) = err))))),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1128, 127])).
% 31.98/32.17 tff(1130,plain,
% 31.98/32.17 (~((~d(Q!7)) | (~(phi(Q!7) = Q!7)))),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1129, 1125])).
% 31.98/32.17 tff(1131,plain,
% 31.98/32.17 (((~d(Q!7)) | (~(phi(Q!7) = Q!7))) | (phi(Q!7) = Q!7)),
% 31.98/32.17 inference(tautology,[status(thm)],[])).
% 31.98/32.17 tff(1132,plain,
% 31.98/32.17 (phi(Q!7) = Q!7),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1131, 1130])).
% 31.98/32.17 tff(1133,plain,
% 31.98/32.17 (Q!7 = phi(Q!7)),
% 31.98/32.17 inference(symmetry,[status(thm)],[1132])).
% 31.98/32.17 tff(1134,plain,
% 31.98/32.17 (Q!7 = impl(Q!7, true)),
% 31.98/32.17 inference(transitivity,[status(thm)],[1133, 1112])).
% 31.98/32.17 tff(1135,plain,
% 31.98/32.17 (bool(Q!7) <=> bool(impl(Q!7, true))),
% 31.98/32.17 inference(monotonicity,[status(thm)],[1134])).
% 31.98/32.17 tff(1136,plain,
% 31.98/32.17 (bool(impl(Q!7, true)) <=> bool(Q!7)),
% 31.98/32.17 inference(symmetry,[status(thm)],[1135])).
% 31.98/32.17 tff(1137,plain,
% 31.98/32.17 (bool(Q!7)),
% 31.98/32.17 inference(modus_ponens,[status(thm)],[1113, 1136])).
% 31.98/32.17 tff(1138,plain,
% 31.98/32.17 ($false),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1110, 1137])).
% 31.98/32.17 tff(1139,plain,((~bool(impl(Q!7, true))) | bool(Q!7)), inference(lemma,lemma(discharge,[]))).
% 31.98/32.17 tff(1140,plain,
% 31.98/32.17 (~bool(impl(Q!7, true))),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1139, 1095])).
% 31.98/32.17 tff(1141,plain,
% 31.98/32.17 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(Q!7, true)) | (impl(impl(Q!7, true), true) = phi(impl(Q!7, true))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(Q!7, true)) | (impl(impl(Q!7, true), true) = phi(impl(Q!7, true))))),
% 31.98/32.17 inference(rewrite,[status(thm)],[])).
% 31.98/32.17 tff(1142,plain,
% 31.98/32.17 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(Q!7, true)) | (impl(impl(Q!7, true), true) = phi(impl(Q!7, true))))),
% 31.98/32.17 inference(quant_inst,[status(thm)],[])).
% 31.98/32.17 tff(1143,plain,
% 31.98/32.17 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(Q!7, true)) | (impl(impl(Q!7, true), true) = phi(impl(Q!7, true)))),
% 31.98/32.17 inference(modus_ponens,[status(thm)],[1142, 1141])).
% 31.98/32.17 tff(1144,plain,
% 31.98/32.17 (bool(impl(Q!7, true)) | (impl(impl(Q!7, true), true) = phi(impl(Q!7, true)))),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1143, 81])).
% 31.98/32.17 tff(1145,plain,
% 31.98/32.17 (impl(impl(Q!7, true), true) = phi(impl(Q!7, true))),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1144, 1140])).
% 31.98/32.17 tff(1146,plain,
% 31.98/32.17 (impl(impl(Q!7, true), true) = impl(impl(Q!7, true), impl(false, true))),
% 31.98/32.17 inference(symmetry,[status(thm)],[890])).
% 31.98/32.17 tff(1147,assumption,(impl(impl(Q!7, true), true) = phi(impl(Q!7, true))), introduced(assumption)).
% 31.98/32.17 tff(1148,plain,
% 31.98/32.17 (phi(impl(Q!7, true)) = impl(impl(Q!7, true), true)),
% 31.98/32.17 inference(symmetry,[status(thm)],[1147])).
% 31.98/32.17 tff(1149,assumption,(~(phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))), introduced(assumption)).
% 31.98/32.17 tff(1150,plain,
% 31.98/32.17 ((~d(impl(impl(Q!7, true), true))) | (~(phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)))),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[916, 1149])).
% 31.98/32.17 tff(1151,plain,
% 31.98/32.17 (~(d(impl(impl(Q!7, true), true)) | (~(phi(impl(impl(Q!7, true), true)) = err)))),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[914, 1150])).
% 31.98/32.17 tff(1152,plain,
% 31.98/32.17 (phi(impl(impl(Q!7, true), true)) = err),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[909, 1151])).
% 31.98/32.17 tff(1153,plain,
% 31.98/32.17 (err = phi(impl(impl(Q!7, true), true))),
% 31.98/32.17 inference(symmetry,[status(thm)],[1152])).
% 31.98/32.17 tff(1154,plain,
% 31.98/32.17 ((phi(impl(Q!7, true)) = err) <=> (impl(impl(Q!7, true), true) = phi(impl(impl(Q!7, true), true)))),
% 31.98/32.17 inference(monotonicity,[status(thm)],[1148, 1153])).
% 31.98/32.17 tff(1155,plain,
% 31.98/32.17 ((phi(impl(Q!7, true)) = err) <=> (phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))),
% 31.98/32.17 inference(transitivity,[status(thm)],[1154, 833])).
% 31.98/32.17 tff(1156,plain,
% 31.98/32.17 ((phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)) <=> (phi(impl(Q!7, true)) = err)),
% 31.98/32.17 inference(symmetry,[status(thm)],[1155])).
% 31.98/32.17 tff(1157,plain,
% 31.98/32.17 ((~(phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))) <=> (~(phi(impl(Q!7, true)) = err))),
% 31.98/32.17 inference(monotonicity,[status(thm)],[1156])).
% 31.98/32.17 tff(1158,plain,
% 31.98/32.17 (~(phi(impl(Q!7, true)) = err)),
% 31.98/32.17 inference(modus_ponens,[status(thm)],[1149, 1157])).
% 31.98/32.17 tff(1159,plain,
% 31.98/32.17 ((d(impl(Q!7, true)) | (~(phi(impl(Q!7, true)) = err))) | (phi(impl(Q!7, true)) = err)),
% 31.98/32.17 inference(tautology,[status(thm)],[])).
% 31.98/32.17 tff(1160,plain,
% 31.98/32.17 (d(impl(Q!7, true)) | (~(phi(impl(Q!7, true)) = err))),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1159, 1158])).
% 31.98/32.17 tff(1161,plain,
% 31.98/32.17 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(Q!7, true))) | (~(phi(impl(Q!7, true)) = impl(Q!7, true))))) | (~(d(impl(Q!7, true)) | (~(phi(impl(Q!7, true)) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(Q!7, true))) | (~(phi(impl(Q!7, true)) = impl(Q!7, true))))) | (~(d(impl(Q!7, true)) | (~(phi(impl(Q!7, true)) = err)))))),
% 31.98/32.17 inference(rewrite,[status(thm)],[])).
% 31.98/32.17 tff(1162,plain,
% 31.98/32.17 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(Q!7, true))) | (~(phi(impl(Q!7, true)) = impl(Q!7, true))))) | (~(d(impl(Q!7, true)) | (~(phi(impl(Q!7, true)) = err)))))),
% 31.98/32.17 inference(quant_inst,[status(thm)],[])).
% 31.98/32.17 tff(1163,plain,
% 31.98/32.17 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(Q!7, true))) | (~(phi(impl(Q!7, true)) = impl(Q!7, true))))) | (~(d(impl(Q!7, true)) | (~(phi(impl(Q!7, true)) = err))))),
% 31.98/32.17 inference(modus_ponens,[status(thm)],[1162, 1161])).
% 31.98/32.17 tff(1164,plain,
% 31.98/32.17 ((~((~d(impl(Q!7, true))) | (~(phi(impl(Q!7, true)) = impl(Q!7, true))))) | (~(d(impl(Q!7, true)) | (~(phi(impl(Q!7, true)) = err))))),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1163, 127])).
% 31.98/32.17 tff(1165,plain,
% 31.98/32.17 (~((~d(impl(Q!7, true))) | (~(phi(impl(Q!7, true)) = impl(Q!7, true))))),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1164, 1160])).
% 31.98/32.17 tff(1166,plain,
% 31.98/32.17 (((~d(impl(Q!7, true))) | (~(phi(impl(Q!7, true)) = impl(Q!7, true)))) | (phi(impl(Q!7, true)) = impl(Q!7, true))),
% 31.98/32.17 inference(tautology,[status(thm)],[])).
% 31.98/32.17 tff(1167,plain,
% 31.98/32.17 (phi(impl(Q!7, true)) = impl(Q!7, true)),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1166, 1165])).
% 31.98/32.17 tff(1168,plain,
% 31.98/32.17 (impl(Q!7, true) = phi(impl(Q!7, true))),
% 31.98/32.17 inference(symmetry,[status(thm)],[1167])).
% 31.98/32.17 tff(1169,plain,
% 31.98/32.17 (impl(Q!7, true) = impl(impl(Q!7, true), impl(false, true))),
% 31.98/32.17 inference(transitivity,[status(thm)],[1168, 1148, 1146])).
% 31.98/32.17 tff(1170,plain,
% 31.98/32.17 (impl(impl(Q!7, true), true) = impl(impl(impl(Q!7, true), impl(false, true)), true)),
% 31.98/32.17 inference(monotonicity,[status(thm)],[1169])).
% 31.98/32.17 tff(1171,plain,
% 31.98/32.17 (impl(impl(impl(Q!7, true), impl(false, true)), true) = impl(impl(Q!7, true), true)),
% 31.98/32.17 inference(symmetry,[status(thm)],[1170])).
% 31.98/32.17 tff(1172,assumption,(impl(impl(impl(Q!7, true), true), true) = phi(impl(impl(Q!7, true), true))), introduced(assumption)).
% 31.98/32.17 tff(1173,plain,
% 31.98/32.17 (phi(impl(impl(Q!7, true), true)) = impl(impl(impl(Q!7, true), true), true)),
% 31.98/32.17 inference(symmetry,[status(thm)],[1172])).
% 31.98/32.17 tff(1174,plain,
% 31.98/32.17 (phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)),
% 31.98/32.17 inference(transitivity,[status(thm)],[1173, 892, 1171])).
% 31.98/32.17 tff(1175,plain,
% 31.98/32.17 ($false),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1149, 1174])).
% 31.98/32.17 tff(1176,plain,((phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)) | (~(impl(impl(impl(Q!7, true), true), true) = phi(impl(impl(Q!7, true), true)))) | (~(impl(impl(Q!7, true), true) = phi(impl(Q!7, true))))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.17 tff(1177,plain,
% 31.98/32.17 (phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1176, 1145, 897])).
% 31.98/32.17 tff(1178,plain,
% 31.98/32.17 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)),
% 31.98/32.17 inference(transitivity,[status(thm)],[1045, 1177])).
% 31.98/32.17 tff(1179,plain,
% 31.98/32.17 (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.17 inference(monotonicity,[status(thm)],[1178])).
% 31.98/32.17 tff(1180,plain,
% 31.98/32.17 (phi(impl(impl(Q!7, true), true)) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.17 inference(symmetry,[status(thm)],[1045])).
% 31.98/32.17 tff(1181,plain,
% 31.98/32.17 (phi(impl(Q!7, true)) = impl(impl(Q!7, true), true)),
% 31.98/32.17 inference(symmetry,[status(thm)],[1145])).
% 31.98/32.17 tff(1182,plain,
% 31.98/32.17 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(Q!7, true)) | (impl(impl(Q!7, true), tptp_fun_R_2(Q!7, P!8)) = phi(impl(Q!7, true))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(Q!7, true)) | (impl(impl(Q!7, true), tptp_fun_R_2(Q!7, P!8)) = phi(impl(Q!7, true))))),
% 31.98/32.17 inference(rewrite,[status(thm)],[])).
% 31.98/32.17 tff(1183,plain,
% 31.98/32.17 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(Q!7, true)) | (impl(impl(Q!7, true), tptp_fun_R_2(Q!7, P!8)) = phi(impl(Q!7, true))))),
% 31.98/32.17 inference(quant_inst,[status(thm)],[])).
% 31.98/32.17 tff(1184,plain,
% 31.98/32.17 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(Q!7, true)) | (impl(impl(Q!7, true), tptp_fun_R_2(Q!7, P!8)) = phi(impl(Q!7, true)))),
% 31.98/32.17 inference(modus_ponens,[status(thm)],[1183, 1182])).
% 31.98/32.17 tff(1185,plain,
% 31.98/32.17 (impl(impl(Q!7, true), tptp_fun_R_2(Q!7, P!8)) = phi(impl(Q!7, true))),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1184, 81, 1140])).
% 31.98/32.17 tff(1186,plain,
% 31.98/32.17 (impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = impl(impl(Q!7, true), tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.17 inference(monotonicity,[status(thm)],[1107])).
% 31.98/32.17 tff(1187,plain,
% 31.98/32.17 (impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = impl(impl(Q!7, true), true)),
% 31.98/32.17 inference(transitivity,[status(thm)],[1186, 1185, 1181])).
% 31.98/32.17 tff(1188,plain,
% 31.98/32.17 (phi(impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.17 inference(monotonicity,[status(thm)],[1187])).
% 31.98/32.17 tff(1189,plain,
% 31.98/32.17 (bool(impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) <=> bool(impl(impl(Q!7, true), true))),
% 31.98/32.17 inference(monotonicity,[status(thm)],[1187])).
% 31.98/32.17 tff(1190,plain,
% 31.98/32.17 (bool(impl(impl(Q!7, true), true)) <=> bool(impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.17 inference(symmetry,[status(thm)],[1189])).
% 31.98/32.17 tff(1191,plain,
% 31.98/32.17 ((~bool(impl(impl(Q!7, true), true))) <=> (~bool(impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))),
% 31.98/32.17 inference(monotonicity,[status(thm)],[1190])).
% 31.98/32.17 tff(1192,plain,
% 31.98/32.17 (~bool(impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.17 inference(modus_ponens,[status(thm)],[824, 1191])).
% 31.98/32.17 tff(1193,plain,
% 31.98/32.17 (impl(P!8, tptp_fun_R_2(Q!7, P!8)) = impl(true, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.17 inference(monotonicity,[status(thm)],[667])).
% 31.98/32.17 tff(1194,plain,
% 31.98/32.17 (impl(true, tptp_fun_R_2(Q!7, P!8)) = impl(P!8, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.17 inference(symmetry,[status(thm)],[1193])).
% 31.98/32.17 tff(1195,plain,
% 31.98/32.17 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.17 inference(transitivity,[status(thm)],[965, 327, 1179, 1180])).
% 31.98/32.17 tff(1196,plain,
% 31.98/32.17 (d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) <=> d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.17 inference(monotonicity,[status(thm)],[1195])).
% 31.98/32.17 tff(1197,plain,
% 31.98/32.17 (d(impl(impl(P!8, true), impl(impl(Q!7, true), true))) <=> d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.98/32.17 inference(symmetry,[status(thm)],[1196])).
% 31.98/32.17 tff(1198,plain,
% 31.98/32.17 (or1(P!8, Q!7) = phi(Q!7)),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[682, 1093])).
% 31.98/32.17 tff(1199,plain,
% 31.98/32.17 (phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1176, 1147, 1172])).
% 31.98/32.17 tff(1200,plain,
% 31.98/32.17 (impl(impl(Q!7, true), true) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.17 inference(symmetry,[status(thm)],[1199])).
% 31.98/32.17 tff(1201,plain,
% 31.98/32.17 (phi(impl(Q!7, true)) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.17 inference(transitivity,[status(thm)],[1148, 1200])).
% 31.98/32.17 tff(1202,plain,
% 31.98/32.17 ((phi(impl(Q!7, true)) = err) <=> (phi(impl(impl(Q!7, true), true)) = err)),
% 31.98/32.17 inference(monotonicity,[status(thm)],[1201])).
% 31.98/32.17 tff(1203,assumption,(impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = phi(Q!7)), introduced(assumption)).
% 31.98/32.17 tff(1204,plain,
% 31.98/32.17 (phi(Q!7) = impl(Q!7, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.17 inference(symmetry,[status(thm)],[1203])).
% 31.98/32.17 tff(1205,plain,
% 31.98/32.17 (impl(Q!7, true) = impl(Q!7, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.17 inference(transitivity,[status(thm)],[1115, 1204])).
% 31.98/32.17 tff(1206,plain,
% 31.98/32.17 (phi(Q!7) = impl(Q!7, true)),
% 31.98/32.17 inference(symmetry,[status(thm)],[1115])).
% 31.98/32.17 tff(1207,plain,
% 31.98/32.17 (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = impl(Q!7, true)),
% 31.98/32.17 inference(transitivity,[status(thm)],[1203, 1206])).
% 31.98/32.17 tff(1208,plain,
% 31.98/32.17 (phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = phi(impl(Q!7, true))),
% 31.98/32.17 inference(monotonicity,[status(thm)],[1207])).
% 31.98/32.17 tff(1209,plain,
% 31.98/32.17 (phi(impl(Q!7, true)) = phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.17 inference(symmetry,[status(thm)],[1208])).
% 31.98/32.17 tff(1210,plain,
% 31.98/32.17 ((phi(impl(Q!7, true)) = impl(Q!7, true)) <=> (phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.17 inference(monotonicity,[status(thm)],[1209, 1205])).
% 31.98/32.17 tff(1211,plain,
% 31.98/32.17 ((phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8))) <=> (phi(impl(Q!7, true)) = impl(Q!7, true))),
% 31.98/32.17 inference(symmetry,[status(thm)],[1210])).
% 31.98/32.17 tff(1212,plain,
% 31.98/32.17 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)),
% 31.98/32.17 inference(transitivity,[status(thm)],[1045, 1199])).
% 31.98/32.17 tff(1213,plain,
% 31.98/32.17 (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.17 inference(monotonicity,[status(thm)],[1212])).
% 31.98/32.17 tff(1214,assumption,(impl(impl(Q!7, true), tptp_fun_R_2(Q!7, P!8)) = phi(impl(Q!7, true))), introduced(assumption)).
% 31.98/32.17 tff(1215,plain,
% 31.98/32.17 (impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = impl(impl(Q!7, true), tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.17 inference(monotonicity,[status(thm)],[1207])).
% 31.98/32.17 tff(1216,plain,
% 31.98/32.17 (impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = impl(impl(Q!7, true), true)),
% 31.98/32.17 inference(transitivity,[status(thm)],[1215, 1214, 1148])).
% 31.98/32.17 tff(1217,plain,
% 31.98/32.17 (phi(impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.17 inference(monotonicity,[status(thm)],[1216])).
% 31.98/32.17 tff(1218,assumption,(~bool(impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))), introduced(assumption)).
% 31.98/32.17 tff(1219,plain,
% 31.98/32.17 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.17 inference(transitivity,[status(thm)],[965, 327, 1213, 1180])).
% 31.98/32.17 tff(1220,plain,
% 31.98/32.17 (d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) <=> d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.17 inference(monotonicity,[status(thm)],[1219])).
% 31.98/32.17 tff(1221,plain,
% 31.98/32.17 (d(impl(impl(P!8, true), impl(impl(Q!7, true), true))) <=> d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.98/32.17 inference(symmetry,[status(thm)],[1220])).
% 31.98/32.17 tff(1222,assumption,(~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)), introduced(assumption)).
% 31.98/32.17 tff(1223,plain,
% 31.98/32.17 (d(impl(impl(P!8, true), impl(impl(Q!7, true), true))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err))),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[334, 1222])).
% 31.98/32.17 tff(1224,plain,
% 31.98/32.17 (~((~d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true)))))),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[342, 1223])).
% 31.98/32.17 tff(1225,plain,
% 31.98/32.17 (((~d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.17 inference(tautology,[status(thm)],[])).
% 31.98/32.17 tff(1226,plain,
% 31.98/32.17 (d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1225, 1224])).
% 31.98/32.17 tff(1227,plain,
% 31.98/32.17 (d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.98/32.17 inference(modus_ponens,[status(thm)],[1226, 1221])).
% 31.98/32.17 tff(1228,plain,
% 31.98/32.17 ((true = impl(Q!7, true)) <=> (impl(Q!7, true) = true)),
% 31.98/32.17 inference(commutativity,[status(thm)],[])).
% 31.98/32.17 tff(1229,assumption,(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err), introduced(assumption)).
% 31.98/32.17 tff(1230,plain,
% 31.98/32.17 (phi(true) = phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.17 inference(symmetry,[status(thm)],[363])).
% 31.98/32.17 tff(1231,plain,
% 31.98/32.17 (true = err),
% 31.98/32.17 inference(transitivity,[status(thm)],[637, 1230, 1229])).
% 31.98/32.17 tff(1232,plain,
% 31.98/32.17 ($false),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[153, 1231])).
% 31.98/32.17 tff(1233,plain,((~(prop(tptp_fun_R_2(Q!7, P!8)) = false)) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.17 tff(1234,plain,
% 31.98/32.17 (~(prop(tptp_fun_R_2(Q!7, P!8)) = false)),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[1233, 484])).
% 31.98/32.17 tff(1235,plain,
% 31.98/32.17 (bool(tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[447, 1234])).
% 31.98/32.17 tff(1236,plain,
% 31.98/32.17 (prop(tptp_fun_R_2(Q!7, P!8)) = true),
% 31.98/32.17 inference(unit_resolution,[status(thm)],[452, 1235])).
% 31.98/32.17 tff(1237,plain,
% 31.98/32.17 (true = prop(tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.17 inference(symmetry,[status(thm)],[1236])).
% 31.98/32.17 tff(1238,plain,
% 31.98/32.17 (lazy_impl(true, impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))),
% 31.98/32.18 inference(monotonicity,[status(thm)],[1237])).
% 31.98/32.18 tff(1239,plain,
% 31.98/32.18 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))),
% 31.98/32.18 inference(quant_inst,[status(thm)],[])).
% 31.98/32.18 tff(1240,plain,
% 31.98/32.18 (lazy_impl(true, impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[1239, 325])).
% 31.98/32.18 tff(1241,plain,
% 31.98/32.18 (phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = lazy_impl(true, impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))),
% 31.98/32.18 inference(symmetry,[status(thm)],[1240])).
% 31.98/32.18 tff(1242,plain,
% 31.98/32.18 ((f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)) = phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))) <=> (phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.18 inference(commutativity,[status(thm)],[])).
% 31.98/32.18 tff(1243,plain,
% 31.98/32.18 (err = phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.18 inference(symmetry,[status(thm)],[484])).
% 31.98/32.18 tff(1244,plain,
% 31.98/32.18 (phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.18 inference(transitivity,[status(thm)],[1241, 1238, 42])).
% 31.98/32.18 tff(1245,plain,
% 31.98/32.18 ((phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = err) <=> (f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)) = phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))))),
% 31.98/32.18 inference(monotonicity,[status(thm)],[1244, 1243])).
% 31.98/32.18 tff(1246,plain,
% 31.98/32.18 ((phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = err) <=> (phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.18 inference(transitivity,[status(thm)],[1245, 1242])).
% 31.98/32.18 tff(1247,plain,
% 31.98/32.18 ((phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) <=> (phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = err)),
% 31.98/32.18 inference(symmetry,[status(thm)],[1246])).
% 31.98/32.18 tff(1248,plain,
% 31.98/32.18 ((~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))) <=> (~(phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = err))),
% 31.98/32.18 inference(monotonicity,[status(thm)],[1247])).
% 31.98/32.18 tff(1249,plain,
% 31.98/32.18 (~(phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = err)),
% 31.98/32.18 inference(modus_ponens,[status(thm)],[475, 1248])).
% 31.98/32.18 tff(1250,plain,
% 31.98/32.18 ((d(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) | (~(phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = err))) | (phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = err)),
% 31.98/32.18 inference(tautology,[status(thm)],[])).
% 31.98/32.18 tff(1251,plain,
% 31.98/32.18 (d(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) | (~(phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = err))),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[1250, 1249])).
% 31.98/32.18 tff(1252,plain,
% 31.98/32.18 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) | (~(phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))) | (~(d(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) | (~(phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) | (~(phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))) | (~(d(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) | (~(phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = err)))))),
% 31.98/32.18 inference(rewrite,[status(thm)],[])).
% 31.98/32.18 tff(1253,plain,
% 31.98/32.18 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) | (~(phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))) | (~(d(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) | (~(phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = err)))))),
% 31.98/32.18 inference(quant_inst,[status(thm)],[])).
% 31.98/32.18 tff(1254,plain,
% 31.98/32.18 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) | (~(phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))) | (~(d(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) | (~(phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = err))))),
% 31.98/32.18 inference(modus_ponens,[status(thm)],[1253, 1252])).
% 31.98/32.18 tff(1255,plain,
% 31.98/32.18 ((~((~d(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) | (~(phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))) | (~(d(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) | (~(phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = err))))),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[1254, 127])).
% 31.98/32.18 tff(1256,plain,
% 31.98/32.18 (~((~d(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) | (~(phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[1255, 1251])).
% 31.98/32.18 tff(1257,plain,
% 31.98/32.18 (((~d(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) | (~(phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))),
% 31.98/32.18 inference(tautology,[status(thm)],[])).
% 31.98/32.18 tff(1258,plain,
% 31.98/32.18 (phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[1257, 1256])).
% 31.98/32.18 tff(1259,plain,
% 31.98/32.18 (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))),
% 31.98/32.18 inference(symmetry,[status(thm)],[1258])).
% 31.98/32.18 tff(1260,plain,
% 31.98/32.18 (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.18 inference(transitivity,[status(thm)],[1259, 1241, 1238, 42])).
% 31.98/32.18 tff(1261,plain,
% 31.98/32.18 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = lazy_impl(true, f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.18 inference(monotonicity,[status(thm)],[1236, 1260])).
% 31.98/32.18 tff(1262,plain,
% 31.98/32.18 (lazy_impl(true, f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))),
% 31.98/32.18 inference(symmetry,[status(thm)],[1261])).
% 31.98/32.18 tff(1263,plain,
% 31.98/32.18 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))))),
% 31.98/32.18 inference(quant_inst,[status(thm)],[])).
% 31.98/32.18 tff(1264,plain,
% 31.98/32.18 (lazy_impl(true, f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[1263, 325])).
% 31.98/32.18 tff(1265,plain,
% 31.98/32.18 (phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = lazy_impl(true, f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.18 inference(symmetry,[status(thm)],[1264])).
% 31.98/32.18 tff(1266,plain,
% 31.98/32.18 (phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.18 inference(transitivity,[status(thm)],[1265, 1262, 42])).
% 31.98/32.18 tff(1267,plain,
% 31.98/32.18 ($false),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[475, 1266])).
% 31.98/32.18 tff(1268,plain,(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.18 tff(1269,plain,
% 31.98/32.18 (or2(P!8, Q!7) = true),
% 31.98/32.18 inference(transitivity,[status(thm)],[365, 1268, 41, 11, 9])).
% 31.98/32.18 tff(1270,plain,
% 31.98/32.18 (true = P!8),
% 31.98/32.18 inference(symmetry,[status(thm)],[667])).
% 31.98/32.18 tff(1271,plain,
% 31.98/32.18 (or1(true, Q!7) = or1(P!8, Q!7)),
% 31.98/32.18 inference(monotonicity,[status(thm)],[1270])).
% 31.98/32.18 tff(1272,plain,
% 31.98/32.18 (or1(P!8, Q!7) = or1(true, Q!7)),
% 31.98/32.18 inference(symmetry,[status(thm)],[1271])).
% 31.98/32.18 tff(1273,plain,
% 31.98/32.18 ((or1(P!8, Q!7) = or2(P!8, Q!7)) <=> (or1(true, Q!7) = true)),
% 31.98/32.18 inference(monotonicity,[status(thm)],[1272, 1269])).
% 31.98/32.18 tff(1274,plain,
% 31.98/32.18 ((~(or1(P!8, Q!7) = or2(P!8, Q!7))) <=> (~(or1(true, Q!7) = true))),
% 31.98/32.18 inference(monotonicity,[status(thm)],[1273])).
% 31.98/32.18 tff(1275,plain,
% 31.98/32.18 (~(or1(true, Q!7) = true)),
% 31.98/32.18 inference(modus_ponens,[status(thm)],[377, 1274])).
% 31.98/32.18 tff(1276,plain,
% 31.98/32.18 (~bool(Q!7)),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[665, 1275])).
% 31.98/32.18 tff(1277,plain,
% 31.98/32.18 (impl(Q!7, true) = phi(Q!7)),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[1099, 1276])).
% 31.98/32.18 tff(1278,plain,
% 31.98/32.18 (phi(Q!7) = impl(Q!7, true)),
% 31.98/32.18 inference(symmetry,[status(thm)],[1277])).
% 31.98/32.18 tff(1279,plain,
% 31.98/32.18 (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = phi(Q!7)),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[1105, 1276])).
% 31.98/32.18 tff(1280,plain,
% 31.98/32.18 (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = impl(Q!7, true)),
% 31.98/32.18 inference(transitivity,[status(thm)],[1279, 1278])).
% 31.98/32.18 tff(1281,assumption,(d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))), introduced(assumption)).
% 31.98/32.18 tff(1282,plain,
% 31.98/32.18 (bool(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.18 inference(modus_ponens,[status(thm)],[247, 211])).
% 31.98/32.18 tff(1283,plain,
% 31.98/32.18 ((~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) <=> (~bool(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))))),
% 31.98/32.18 inference(monotonicity,[status(thm)],[207])).
% 31.98/32.18 tff(1284,assumption,(~bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))), introduced(assumption)).
% 31.98/32.18 tff(1285,plain,
% 31.98/32.18 (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err)),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[1233, 10])).
% 31.98/32.18 tff(1286,plain,
% 31.98/32.18 (d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err))),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[483, 1285])).
% 31.98/32.18 tff(1287,plain,
% 31.98/32.18 (~((~d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))))),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[481, 1286])).
% 31.98/32.18 tff(1288,plain,
% 31.98/32.18 (((~d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))))) | d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.18 inference(tautology,[status(thm)],[])).
% 31.98/32.18 tff(1289,plain,
% 31.98/32.18 (d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[1288, 1287])).
% 31.98/32.18 tff(1290,plain,
% 31.98/32.18 (d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))),
% 31.98/32.18 inference(modus_ponens,[status(thm)],[1289, 195])).
% 31.98/32.18 tff(1291,plain,
% 31.98/32.18 (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[292, 1290, 1281, 1284])).
% 31.98/32.18 tff(1292,plain,
% 31.98/32.18 (~bool(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.18 inference(modus_ponens,[status(thm)],[1291, 1283])).
% 31.98/32.18 tff(1293,plain,
% 31.98/32.18 ($false),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[1292, 1282])).
% 31.98/32.18 tff(1294,plain,((~(prop(tptp_fun_R_2(Q!7, P!8)) = false)) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.18 tff(1295,plain,
% 31.98/32.18 (bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[1294, 10, 1281])).
% 31.98/32.18 tff(1296,assumption,(~(bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) <=> ((lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false) | (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true)))), introduced(assumption)).
% 31.98/32.18 tff(1297,plain,
% 31.98/32.18 ($false),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[192, 69, 1296])).
% 31.98/32.18 tff(1298,plain,(bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) <=> ((lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false) | (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.18 tff(1299,plain,
% 31.98/32.18 ((~bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))) | ((lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false) | (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true))),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[294, 1298])).
% 31.98/32.18 tff(1300,plain,
% 31.98/32.18 ((lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false) | (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true)),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[1299, 1295])).
% 31.98/32.18 tff(1301,plain,
% 31.98/32.18 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[302, 301, 1300])).
% 31.98/32.18 tff(1302,plain,
% 31.98/32.18 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.18 inference(symmetry,[status(thm)],[1035])).
% 31.98/32.18 tff(1303,assumption,(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true), introduced(assumption)).
% 31.98/32.18 tff(1304,plain,
% 31.98/32.18 (impl(true, true) = impl(P!8, true)),
% 31.98/32.18 inference(symmetry,[status(thm)],[848])).
% 31.98/32.18 tff(1305,plain,
% 31.98/32.18 (true = impl(P!8, true)),
% 31.98/32.18 inference(transitivity,[status(thm)],[1051, 1304])).
% 31.98/32.18 tff(1306,plain,
% 31.98/32.18 (impl(true, impl(impl(Q!7, true), true)) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.18 inference(monotonicity,[status(thm)],[1305])).
% 31.98/32.18 tff(1307,plain,
% 31.98/32.18 (impl(impl(Q!7, true), true) = true),
% 31.98/32.18 inference(transitivity,[status(thm)],[1036, 1306, 1302, 328, 318, 1303])).
% 31.98/32.18 tff(1308,plain,
% 31.98/32.18 (phi(impl(impl(Q!7, true), true)) = phi(true)),
% 31.98/32.18 inference(monotonicity,[status(thm)],[1307])).
% 31.98/32.18 tff(1309,plain,
% 31.98/32.18 (phi(true) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.18 inference(symmetry,[status(thm)],[1308])).
% 31.98/32.18 tff(1310,plain,
% 31.98/32.18 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.18 inference(transitivity,[status(thm)],[1302, 328, 318, 1303, 637, 1309])).
% 31.98/32.18 tff(1311,plain,
% 31.98/32.18 ($false),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[831, 1310])).
% 31.98/32.18 tff(1312,plain,((impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true))) | (~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true)) | (~(P!8 = true))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.18 tff(1313,plain,
% 31.98/32.18 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[1312, 1301, 667])).
% 31.98/32.18 tff(1314,plain,
% 31.98/32.18 (phi(impl(impl(Q!7, true), true)) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.18 inference(symmetry,[status(thm)],[1313])).
% 31.98/32.18 tff(1315,plain,
% 31.98/32.18 (phi(impl(impl(Q!7, true), true)) = true),
% 31.98/32.18 inference(transitivity,[status(thm)],[1314, 1302, 328, 318, 1301])).
% 31.98/32.18 tff(1316,plain,
% 31.98/32.18 ((phi(impl(impl(Q!7, true), true)) = err) <=> (true = err)),
% 31.98/32.18 inference(monotonicity,[status(thm)],[1315])).
% 31.98/32.18 tff(1317,plain,
% 31.98/32.18 ((true = err) <=> (phi(impl(impl(Q!7, true), true)) = err)),
% 31.98/32.18 inference(symmetry,[status(thm)],[1316])).
% 31.98/32.18 tff(1318,plain,
% 31.98/32.18 ((~(true = err)) <=> (~(phi(impl(impl(Q!7, true), true)) = err))),
% 31.98/32.18 inference(monotonicity,[status(thm)],[1317])).
% 31.98/32.18 tff(1319,plain,
% 31.98/32.18 (~(phi(impl(impl(Q!7, true), true)) = err)),
% 31.98/32.18 inference(modus_ponens,[status(thm)],[153, 1318])).
% 31.98/32.18 tff(1320,plain,
% 31.98/32.18 (d(impl(impl(Q!7, true), true)) | (~(phi(impl(impl(Q!7, true), true)) = err))),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[909, 1319])).
% 31.98/32.18 tff(1321,plain,
% 31.98/32.18 (~((~d(impl(impl(Q!7, true), true))) | (~(phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))))),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[914, 1320])).
% 31.98/32.18 tff(1322,plain,
% 31.98/32.18 (phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[916, 1321])).
% 31.98/32.18 tff(1323,plain,
% 31.98/32.18 (impl(impl(Q!7, true), true) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.18 inference(symmetry,[status(thm)],[1322])).
% 31.98/32.18 tff(1324,plain,
% 31.98/32.18 (~bool(impl(Q!7, true))),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[1139, 1276])).
% 31.98/32.18 tff(1325,plain,
% 31.98/32.18 (impl(impl(Q!7, true), true) = phi(impl(Q!7, true))),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[1144, 1324])).
% 31.98/32.18 tff(1326,plain,
% 31.98/32.18 (phi(impl(Q!7, true)) = impl(impl(Q!7, true), true)),
% 31.98/32.18 inference(symmetry,[status(thm)],[1325])).
% 31.98/32.18 tff(1327,plain,
% 31.98/32.18 (phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = phi(impl(Q!7, true))),
% 31.98/32.18 inference(monotonicity,[status(thm)],[1280])).
% 31.98/32.18 tff(1328,plain,
% 31.98/32.18 (phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = true),
% 31.98/32.18 inference(transitivity,[status(thm)],[1327, 1326, 1323, 1314, 1302, 328, 318, 1301])).
% 31.98/32.18 tff(1329,plain,
% 31.98/32.18 ((phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8))) <=> (true = impl(Q!7, true))),
% 31.98/32.18 inference(monotonicity,[status(thm)],[1328, 1280])).
% 31.98/32.18 tff(1330,plain,
% 31.98/32.18 ((phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8))) <=> (impl(Q!7, true) = true)),
% 31.98/32.18 inference(transitivity,[status(thm)],[1329, 1228])).
% 31.98/32.18 tff(1331,plain,
% 31.98/32.18 ((impl(Q!7, true) = true) <=> (phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.18 inference(symmetry,[status(thm)],[1330])).
% 31.98/32.18 tff(1332,plain,
% 31.98/32.18 ((~(impl(Q!7, true) = true)) <=> (~(phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8))))),
% 31.98/32.18 inference(monotonicity,[status(thm)],[1331])).
% 31.98/32.18 tff(1333,assumption,(~(bool(impl(Q!7, true)) <=> ((impl(Q!7, true) = false) | (impl(Q!7, true) = true)))), introduced(assumption)).
% 31.98/32.18 tff(1334,plain,
% 31.98/32.18 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(impl(Q!7, true)) <=> ((impl(Q!7, true) = false) | (impl(Q!7, true) = true)))),
% 31.98/32.18 inference(quant_inst,[status(thm)],[])).
% 31.98/32.18 tff(1335,plain,
% 31.98/32.18 ($false),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[1334, 69, 1333])).
% 31.98/32.18 tff(1336,plain,(bool(impl(Q!7, true)) <=> ((impl(Q!7, true) = false) | (impl(Q!7, true) = true))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.18 tff(1337,plain,
% 31.98/32.18 ((~(bool(impl(Q!7, true)) <=> ((impl(Q!7, true) = false) | (impl(Q!7, true) = true)))) | bool(impl(Q!7, true)) | (~((impl(Q!7, true) = false) | (impl(Q!7, true) = true)))),
% 31.98/32.18 inference(tautology,[status(thm)],[])).
% 31.98/32.18 tff(1338,plain,
% 31.98/32.18 (bool(impl(Q!7, true)) | (~((impl(Q!7, true) = false) | (impl(Q!7, true) = true)))),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[1337, 1336])).
% 31.98/32.18 tff(1339,plain,
% 31.98/32.18 (~((impl(Q!7, true) = false) | (impl(Q!7, true) = true))),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[1338, 1324])).
% 31.98/32.18 tff(1340,plain,
% 31.98/32.18 (((impl(Q!7, true) = false) | (impl(Q!7, true) = true)) | (~(impl(Q!7, true) = true))),
% 31.98/32.18 inference(tautology,[status(thm)],[])).
% 31.98/32.18 tff(1341,plain,
% 31.98/32.18 (~(impl(Q!7, true) = true)),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[1340, 1339])).
% 31.98/32.18 tff(1342,plain,
% 31.98/32.18 (~(phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.18 inference(modus_ponens,[status(thm)],[1341, 1332])).
% 31.98/32.18 tff(1343,plain,
% 31.98/32.18 (((~d(impl(Q!7, tptp_fun_R_2(Q!7, P!8)))) | (~(phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8))))) | (phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.18 inference(tautology,[status(thm)],[])).
% 31.98/32.18 tff(1344,plain,
% 31.98/32.18 ((~d(impl(Q!7, tptp_fun_R_2(Q!7, P!8)))) | (~(phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8))))),
% 31.98/32.18 inference(unit_resolution,[status(thm)],[1343, 1342])).
% 31.98/32.18 tff(1345,plain,
% 31.98/32.18 ((phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = err) <=> (true = err)),
% 31.98/32.18 inference(monotonicity,[status(thm)],[1328])).
% 31.98/32.18 tff(1346,plain,
% 31.98/32.18 ((true = err) <=> (phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = err)),
% 31.98/32.18 inference(symmetry,[status(thm)],[1345])).
% 31.98/32.18 tff(1347,plain,
% 31.98/32.18 ((~(true = err)) <=> (~(phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = err))),
% 31.98/32.18 inference(monotonicity,[status(thm)],[1346])).
% 31.98/32.18 tff(1348,plain,
% 31.98/32.18 (~(phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = err)),
% 31.98/32.18 inference(modus_ponens,[status(thm)],[153, 1347])).
% 31.98/32.18 tff(1349,plain,
% 31.98/32.18 ((d(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) | (~(phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = err))) | (phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = err)),
% 31.98/32.19 inference(tautology,[status(thm)],[])).
% 31.98/32.19 tff(1350,plain,
% 31.98/32.19 (d(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) | (~(phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = err))),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[1349, 1348])).
% 31.98/32.19 tff(1351,plain,
% 31.98/32.19 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(Q!7, tptp_fun_R_2(Q!7, P!8)))) | (~(phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8)))))) | (~(d(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) | (~(phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(Q!7, tptp_fun_R_2(Q!7, P!8)))) | (~(phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8)))))) | (~(d(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) | (~(phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = err)))))),
% 31.98/32.19 inference(rewrite,[status(thm)],[])).
% 31.98/32.19 tff(1352,plain,
% 31.98/32.19 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(impl(Q!7, tptp_fun_R_2(Q!7, P!8)))) | (~(phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8)))))) | (~(d(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) | (~(phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = err)))))),
% 31.98/32.19 inference(quant_inst,[status(thm)],[])).
% 31.98/32.19 tff(1353,plain,
% 31.98/32.19 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(impl(Q!7, tptp_fun_R_2(Q!7, P!8)))) | (~(phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8)))))) | (~(d(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) | (~(phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = err))))),
% 31.98/32.19 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 31.98/32.19 tff(1354,plain,
% 31.98/32.19 ((~((~d(impl(Q!7, tptp_fun_R_2(Q!7, P!8)))) | (~(phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8)))))) | (~(d(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) | (~(phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = err))))),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[1353, 127])).
% 31.98/32.19 tff(1355,plain,
% 31.98/32.19 ($false),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[1354, 1350, 1344])).
% 31.98/32.19 tff(1356,plain,((~(prop(tptp_fun_R_2(Q!7, P!8)) = false)) | (~(P!8 = true)) | (~d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.19 tff(1357,plain,
% 31.98/32.19 (~(prop(tptp_fun_R_2(Q!7, P!8)) = false)),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[1356, 1227, 667])).
% 31.98/32.19 tff(1358,plain,
% 31.98/32.19 (bool(tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[447, 1357])).
% 31.98/32.19 tff(1359,plain,
% 31.98/32.19 (((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | ((~bool(tptp_fun_R_2(Q!7, P!8))) | (impl(true, tptp_fun_R_2(Q!7, P!8)) = tptp_fun_R_2(Q!7, P!8)))) <=> ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | (~bool(tptp_fun_R_2(Q!7, P!8))) | (impl(true, tptp_fun_R_2(Q!7, P!8)) = tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.19 inference(rewrite,[status(thm)],[])).
% 31.98/32.19 tff(1360,plain,
% 31.98/32.19 ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | ((~bool(tptp_fun_R_2(Q!7, P!8))) | (impl(true, tptp_fun_R_2(Q!7, P!8)) = tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.19 inference(quant_inst,[status(thm)],[])).
% 31.98/32.19 tff(1361,plain,
% 31.98/32.19 ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | (~bool(tptp_fun_R_2(Q!7, P!8))) | (impl(true, tptp_fun_R_2(Q!7, P!8)) = tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.19 inference(modus_ponens,[status(thm)],[1360, 1359])).
% 31.98/32.19 tff(1362,plain,
% 31.98/32.19 ((~bool(tptp_fun_R_2(Q!7, P!8))) | (impl(true, tptp_fun_R_2(Q!7, P!8)) = tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[1361, 843])).
% 31.98/32.19 tff(1363,plain,
% 31.98/32.19 (impl(true, tptp_fun_R_2(Q!7, P!8)) = tptp_fun_R_2(Q!7, P!8)),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[1362, 1358])).
% 31.98/32.19 tff(1364,plain,
% 31.98/32.19 (tptp_fun_R_2(Q!7, P!8) = impl(true, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.19 inference(symmetry,[status(thm)],[1363])).
% 31.98/32.19 tff(1365,plain,
% 31.98/32.19 (tptp_fun_R_2(Q!7, P!8) = impl(P!8, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.19 inference(transitivity,[status(thm)],[1364, 1194])).
% 31.98/32.19 tff(1366,plain,
% 31.98/32.19 (bool(tptp_fun_R_2(Q!7, P!8)) <=> bool(impl(P!8, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1365])).
% 31.98/32.19 tff(1367,plain,
% 31.98/32.19 (bool(impl(P!8, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.19 inference(modus_ponens,[status(thm)],[1358, 1366])).
% 31.98/32.19 tff(1368,plain,
% 31.98/32.19 (((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (bool(impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~bool(impl(P!8, tptp_fun_R_2(Q!7, P!8)))) | (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = phi(impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) <=> ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | bool(impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~bool(impl(P!8, tptp_fun_R_2(Q!7, P!8)))) | (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = phi(impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))),
% 31.98/32.19 inference(rewrite,[status(thm)],[])).
% 31.98/32.19 tff(1369,plain,
% 31.98/32.19 ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | (bool(impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~bool(impl(P!8, tptp_fun_R_2(Q!7, P!8)))) | (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = phi(impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))),
% 31.98/32.19 inference(quant_inst,[status(thm)],[])).
% 31.98/32.19 tff(1370,plain,
% 31.98/32.19 ((~![A: $i, B: $i] : (bool(B) | (~bool(A)) | (impl(A, B) = phi(B)))) | bool(impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~bool(impl(P!8, tptp_fun_R_2(Q!7, P!8)))) | (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = phi(impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))),
% 31.98/32.19 inference(modus_ponens,[status(thm)],[1369, 1368])).
% 31.98/32.19 tff(1371,plain,
% 31.98/32.19 (bool(impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~bool(impl(P!8, tptp_fun_R_2(Q!7, P!8)))) | (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = phi(impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[1370, 865])).
% 31.98/32.19 tff(1372,plain,
% 31.98/32.19 (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = phi(impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[1371, 1367, 1218])).
% 31.98/32.19 tff(1373,plain,
% 31.98/32.19 (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.19 inference(transitivity,[status(thm)],[1372, 1217, 1180])).
% 31.98/32.19 tff(1374,plain,
% 31.98/32.19 (prop(tptp_fun_R_2(Q!7, P!8)) = true),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[452, 1358])).
% 31.98/32.19 tff(1375,plain,
% 31.98/32.19 (prop(tptp_fun_R_2(Q!7, P!8)) = prop(true)),
% 31.98/32.19 inference(transitivity,[status(thm)],[1374, 317])).
% 31.98/32.19 tff(1376,plain,
% 31.98/32.19 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1375, 1373])).
% 31.98/32.19 tff(1377,plain,
% 31.98/32.19 (f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.19 inference(transitivity,[status(thm)],[41, 1376, 965, 327, 1213, 1180])).
% 31.98/32.19 tff(1378,plain,
% 31.98/32.19 (phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = phi(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1377])).
% 31.98/32.19 tff(1379,plain,
% 31.98/32.19 (or2(P!8, Q!7) = phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.19 inference(transitivity,[status(thm)],[365, 1378, 1213, 1199, 1147, 1209])).
% 31.98/32.19 tff(1380,assumption,(or1(P!8, Q!7) = phi(Q!7)), introduced(assumption)).
% 31.98/32.19 tff(1381,plain,
% 31.98/32.19 (or1(P!8, Q!7) = impl(Q!7, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.19 inference(transitivity,[status(thm)],[1380, 1204])).
% 31.98/32.19 tff(1382,plain,
% 31.98/32.19 ((or1(P!8, Q!7) = or2(P!8, Q!7)) <=> (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))))),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1381, 1379])).
% 31.98/32.19 tff(1383,plain,
% 31.98/32.19 ((or1(P!8, Q!7) = or2(P!8, Q!7)) <=> (phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.19 inference(transitivity,[status(thm)],[1382, 832])).
% 31.98/32.19 tff(1384,plain,
% 31.98/32.19 ((or1(P!8, Q!7) = or2(P!8, Q!7)) <=> (phi(impl(Q!7, true)) = impl(Q!7, true))),
% 31.98/32.19 inference(transitivity,[status(thm)],[1383, 1211])).
% 31.98/32.19 tff(1385,plain,
% 31.98/32.19 ((~(or1(P!8, Q!7) = or2(P!8, Q!7))) <=> (~(phi(impl(Q!7, true)) = impl(Q!7, true)))),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1384])).
% 31.98/32.19 tff(1386,plain,
% 31.98/32.19 (~(phi(impl(Q!7, true)) = impl(Q!7, true))),
% 31.98/32.19 inference(modus_ponens,[status(thm)],[377, 1385])).
% 31.98/32.19 tff(1387,plain,
% 31.98/32.19 ((~d(impl(Q!7, true))) | (~(phi(impl(Q!7, true)) = impl(Q!7, true)))),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[1166, 1386])).
% 31.98/32.19 tff(1388,plain,
% 31.98/32.19 (~(d(impl(Q!7, true)) | (~(phi(impl(Q!7, true)) = err)))),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[1164, 1387])).
% 31.98/32.19 tff(1389,plain,
% 31.98/32.19 (phi(impl(Q!7, true)) = err),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[1159, 1388])).
% 31.98/32.19 tff(1390,plain,
% 31.98/32.19 (phi(impl(impl(Q!7, true), true)) = err),
% 31.98/32.19 inference(modus_ponens,[status(thm)],[1389, 1202])).
% 31.98/32.19 tff(1391,assumption,(impl(impl(impl(Q!7, true), true), P!6) = phi(impl(impl(Q!7, true), true))), introduced(assumption)).
% 31.98/32.19 tff(1392,plain,
% 31.98/32.19 (lazy_impl(true, impl(impl(impl(Q!7, true), impl(false, false)), false)) = lazy_impl(prop(false), impl(impl(impl(Q!7, true), impl(false, false)), false))),
% 31.98/32.19 inference(monotonicity,[status(thm)],[930])).
% 31.98/32.19 tff(1393,plain,
% 31.98/32.19 (lazy_impl(prop(false), impl(impl(impl(Q!7, true), impl(false, false)), false)) = lazy_impl(true, impl(impl(impl(Q!7, true), impl(false, false)), false))),
% 31.98/32.19 inference(symmetry,[status(thm)],[1392])).
% 31.98/32.19 tff(1394,plain,
% 31.98/32.19 (phi(impl(impl(Q!7, true), true)) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.19 inference(symmetry,[status(thm)],[1072])).
% 31.98/32.19 tff(1395,plain,
% 31.98/32.19 (impl(impl(impl(Q!7, true), impl(false, false)), false) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.19 inference(transitivity,[status(thm)],[921, 918, 1391, 1394])).
% 31.98/32.19 tff(1396,plain,
% 31.98/32.19 (prop(false) = prop(true)),
% 31.98/32.19 inference(transitivity,[status(thm)],[759, 317])).
% 31.98/32.19 tff(1397,plain,
% 31.98/32.19 (lazy_impl(prop(false), impl(impl(impl(Q!7, true), impl(false, false)), false)) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1396, 1395])).
% 31.98/32.19 tff(1398,plain,
% 31.98/32.19 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = lazy_impl(prop(false), impl(impl(impl(Q!7, true), impl(false, false)), false))),
% 31.98/32.19 inference(symmetry,[status(thm)],[1397])).
% 31.98/32.19 tff(1399,plain,
% 31.98/32.19 (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = phi(impl(impl(impl(Q!7, true), impl(false, false)), false))),
% 31.98/32.19 inference(transitivity,[status(thm)],[328, 966, 1398, 1393, 925])).
% 31.98/32.19 tff(1400,plain,
% 31.98/32.19 ((phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err) <=> (phi(impl(impl(impl(Q!7, true), impl(false, false)), false)) = err)),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1399])).
% 31.98/32.19 tff(1401,plain,
% 31.98/32.19 ((phi(impl(impl(impl(Q!7, true), impl(false, false)), false)) = err) <=> (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)),
% 31.98/32.19 inference(symmetry,[status(thm)],[1400])).
% 31.98/32.19 tff(1402,plain,
% 31.98/32.19 (impl(impl(impl(Q!7, true), impl(false, true)), true) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.19 inference(transitivity,[status(thm)],[891, 1172, 1394])).
% 31.98/32.19 tff(1403,plain,
% 31.98/32.19 (lazy_impl(prop(true), impl(impl(impl(Q!7, true), impl(false, true)), true)) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1402])).
% 31.98/32.19 tff(1404,plain,
% 31.98/32.19 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = lazy_impl(prop(true), impl(impl(impl(Q!7, true), impl(false, true)), true))),
% 31.98/32.19 inference(symmetry,[status(thm)],[1403])).
% 31.98/32.19 tff(1405,plain,
% 31.98/32.19 (phi(impl(impl(impl(Q!7, true), impl(false, false)), false)) = lazy_impl(true, impl(impl(impl(Q!7, true), impl(false, false)), false))),
% 31.98/32.19 inference(symmetry,[status(thm)],[925])).
% 31.98/32.19 tff(1406,plain,
% 31.98/32.19 (phi(impl(impl(impl(Q!7, true), impl(false, false)), false)) = phi(impl(impl(impl(Q!7, true), impl(false, true)), true))),
% 31.98/32.19 inference(transitivity,[status(thm)],[1405, 1392, 1397, 1404, 939, 935])).
% 31.98/32.19 tff(1407,plain,
% 31.98/32.19 ((phi(impl(impl(impl(Q!7, true), impl(false, false)), false)) = err) <=> (phi(impl(impl(impl(Q!7, true), impl(false, true)), true)) = err)),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1406])).
% 31.98/32.19 tff(1408,plain,
% 31.98/32.19 ((phi(impl(impl(impl(Q!7, true), impl(false, true)), true)) = err) <=> (phi(impl(impl(impl(Q!7, true), impl(false, false)), false)) = err)),
% 31.98/32.19 inference(symmetry,[status(thm)],[1407])).
% 31.98/32.19 tff(1409,plain,
% 31.98/32.19 (phi(impl(impl(Q!7, true), true)) = phi(impl(impl(impl(Q!7, true), impl(false, true)), true))),
% 31.98/32.19 inference(transitivity,[status(thm)],[1394, 1302, 328, 966, 1404, 939, 935])).
% 31.98/32.19 tff(1410,plain,
% 31.98/32.19 ((phi(impl(impl(Q!7, true), true)) = err) <=> (phi(impl(impl(impl(Q!7, true), impl(false, true)), true)) = err)),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1409])).
% 31.98/32.19 tff(1411,plain,
% 31.98/32.19 ((phi(impl(impl(Q!7, true), true)) = err) <=> (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)),
% 31.98/32.19 inference(transitivity,[status(thm)],[1410, 1408, 1401])).
% 31.98/32.19 tff(1412,assumption,(phi(impl(impl(Q!7, true), true)) = err), introduced(assumption)).
% 31.98/32.19 tff(1413,plain,
% 31.98/32.19 (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err),
% 31.98/32.19 inference(modus_ponens,[status(thm)],[1412, 1411])).
% 31.98/32.19 tff(1414,plain,
% 31.98/32.19 ($false),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[1222, 1413])).
% 31.98/32.19 tff(1415,plain,((~(phi(impl(impl(Q!7, true), true)) = err)) | (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err) | (~(impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true)))) | (~(impl(impl(impl(Q!7, true), true), true) = phi(impl(impl(Q!7, true), true)))) | (~(impl(impl(impl(Q!7, true), true), P!6) = phi(impl(impl(Q!7, true), true))))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.19 tff(1416,plain,
% 31.98/32.19 (~(phi(impl(impl(Q!7, true), true)) = err)),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[1415, 1222, 1045, 1172, 1391])).
% 31.98/32.19 tff(1417,plain,
% 31.98/32.19 ($false),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[1416, 1390])).
% 31.98/32.19 tff(1418,plain,((phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err) | (~(impl(impl(Q!7, true), true) = phi(impl(Q!7, true)))) | (~(impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = phi(Q!7))) | (~(impl(Q!7, true) = phi(Q!7))) | (~(impl(impl(Q!7, true), tptp_fun_R_2(Q!7, P!8)) = phi(impl(Q!7, true)))) | (~(or1(P!8, Q!7) = phi(Q!7))) | bool(impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~(P!8 = true)) | (~(impl(impl(impl(Q!7, true), true), true) = phi(impl(impl(Q!7, true), true)))) | (~(impl(impl(impl(Q!7, true), true), P!6) = phi(impl(impl(Q!7, true), true))))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.19 tff(1419,plain,
% 31.98/32.19 (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[1418, 1145, 1106, 1100, 1185, 1198, 1192, 667, 897, 829])).
% 31.98/32.19 tff(1420,plain,
% 31.98/32.19 (err = phi(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.19 inference(symmetry,[status(thm)],[1419])).
% 31.98/32.19 tff(1421,plain,
% 31.98/32.19 (err = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.19 inference(transitivity,[status(thm)],[1420, 1179, 1180])).
% 31.98/32.19 tff(1422,plain,
% 31.98/32.19 (d(err) <=> d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1421])).
% 31.98/32.19 tff(1423,plain,
% 31.98/32.19 (d(err) <=> d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.98/32.19 inference(transitivity,[status(thm)],[1422, 1197])).
% 31.98/32.19 tff(1424,plain,
% 31.98/32.19 (d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.98/32.19 inference(modus_ponens,[status(thm)],[559, 1423])).
% 31.98/32.19 tff(1425,plain,
% 31.98/32.19 (~(prop(tptp_fun_R_2(Q!7, P!8)) = false)),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[1356, 1424, 667])).
% 31.98/32.19 tff(1426,plain,
% 31.98/32.19 (bool(tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[447, 1425])).
% 31.98/32.19 tff(1427,plain,
% 31.98/32.19 (impl(true, tptp_fun_R_2(Q!7, P!8)) = tptp_fun_R_2(Q!7, P!8)),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[1362, 1426])).
% 31.98/32.19 tff(1428,plain,
% 31.98/32.19 (tptp_fun_R_2(Q!7, P!8) = impl(true, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.19 inference(symmetry,[status(thm)],[1427])).
% 31.98/32.19 tff(1429,plain,
% 31.98/32.19 (tptp_fun_R_2(Q!7, P!8) = impl(P!8, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.19 inference(transitivity,[status(thm)],[1428, 1194])).
% 31.98/32.19 tff(1430,plain,
% 31.98/32.19 (bool(tptp_fun_R_2(Q!7, P!8)) <=> bool(impl(P!8, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1429])).
% 31.98/32.19 tff(1431,plain,
% 31.98/32.19 (bool(impl(P!8, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.19 inference(modus_ponens,[status(thm)],[1426, 1430])).
% 31.98/32.19 tff(1432,plain,
% 31.98/32.19 (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = phi(impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[1371, 1431, 1192])).
% 31.98/32.19 tff(1433,plain,
% 31.98/32.19 (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.19 inference(transitivity,[status(thm)],[1432, 1188, 1180])).
% 31.98/32.19 tff(1434,plain,
% 31.98/32.19 (prop(tptp_fun_R_2(Q!7, P!8)) = true),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[452, 1426])).
% 31.98/32.19 tff(1435,plain,
% 31.98/32.19 (prop(tptp_fun_R_2(Q!7, P!8)) = prop(true)),
% 31.98/32.19 inference(transitivity,[status(thm)],[1434, 317])).
% 31.98/32.19 tff(1436,plain,
% 31.98/32.19 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1435, 1433])).
% 31.98/32.19 tff(1437,plain,
% 31.98/32.19 (f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.19 inference(transitivity,[status(thm)],[41, 1436, 965, 327, 1179, 1180])).
% 31.98/32.19 tff(1438,plain,
% 31.98/32.19 (phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = phi(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1437])).
% 31.98/32.19 tff(1439,plain,
% 31.98/32.19 (or2(P!8, Q!7) = phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.19 inference(transitivity,[status(thm)],[365, 1438, 1179, 1177, 1145, 1109])).
% 31.98/32.19 tff(1440,plain,
% 31.98/32.19 (phi(Q!7) = impl(Q!7, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.19 inference(symmetry,[status(thm)],[1106])).
% 31.98/32.19 tff(1441,plain,
% 31.98/32.19 (or1(P!8, Q!7) = impl(Q!7, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.19 inference(transitivity,[status(thm)],[1198, 1440])).
% 31.98/32.19 tff(1442,plain,
% 31.98/32.19 ((or1(P!8, Q!7) = or2(P!8, Q!7)) <=> (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))))),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1441, 1439])).
% 31.98/32.19 tff(1443,plain,
% 31.98/32.19 ((or1(P!8, Q!7) = or2(P!8, Q!7)) <=> (phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.19 inference(transitivity,[status(thm)],[1442, 832])).
% 31.98/32.19 tff(1444,plain,
% 31.98/32.19 ((phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8))) <=> (or1(P!8, Q!7) = or2(P!8, Q!7))),
% 31.98/32.19 inference(symmetry,[status(thm)],[1443])).
% 31.98/32.19 tff(1445,plain,
% 31.98/32.19 (err = phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.19 inference(transitivity,[status(thm)],[1420, 1179, 1177, 1145, 1109])).
% 31.98/32.19 tff(1446,plain,
% 31.98/32.19 ((phi(Q!7) = err) <=> (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))))),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1440, 1445])).
% 31.98/32.19 tff(1447,plain,
% 31.98/32.19 ((phi(Q!7) = err) <=> (phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.19 inference(transitivity,[status(thm)],[1446, 832])).
% 31.98/32.19 tff(1448,assumption,(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err), introduced(assumption)).
% 31.98/32.19 tff(1449,plain,
% 31.98/32.19 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = lazy_impl(true, impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.19 inference(symmetry,[status(thm)],[318])).
% 31.98/32.19 tff(1450,assumption,(~(phi(Q!7) = err)), introduced(assumption)).
% 31.98/32.19 tff(1451,plain,
% 31.98/32.19 (d(Q!7) | (~(phi(Q!7) = err))),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[1124, 1450])).
% 31.98/32.19 tff(1452,plain,
% 31.98/32.19 (~((~d(Q!7)) | (~(phi(Q!7) = Q!7)))),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[1129, 1451])).
% 31.98/32.19 tff(1453,plain,
% 31.98/32.19 (phi(Q!7) = Q!7),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[1131, 1452])).
% 31.98/32.19 tff(1454,plain,
% 31.98/32.19 (impl(Q!7, true) = Q!7),
% 31.98/32.19 inference(transitivity,[status(thm)],[1111, 1453])).
% 31.98/32.19 tff(1455,plain,
% 31.98/32.19 (impl(impl(Q!7, true), true) = impl(Q!7, true)),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1454])).
% 31.98/32.19 tff(1456,plain,
% 31.98/32.19 (impl(Q!7, true) = impl(impl(Q!7, true), true)),
% 31.98/32.19 inference(symmetry,[status(thm)],[1455])).
% 31.98/32.19 tff(1457,plain,
% 31.98/32.19 (Q!7 = phi(Q!7)),
% 31.98/32.19 inference(symmetry,[status(thm)],[1453])).
% 31.98/32.19 tff(1458,plain,
% 31.98/32.19 (Q!7 = impl(Q!7, true)),
% 31.98/32.19 inference(transitivity,[status(thm)],[1457, 1112])).
% 31.98/32.19 tff(1459,plain,
% 31.98/32.19 (phi(Q!7) = phi(impl(Q!7, true))),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1458])).
% 31.98/32.19 tff(1460,plain,
% 31.98/32.19 (phi(impl(Q!7, true)) = phi(Q!7)),
% 31.98/32.19 inference(symmetry,[status(thm)],[1459])).
% 31.98/32.19 tff(1461,plain,
% 31.98/32.19 (phi(impl(Q!7, true)) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1456])).
% 31.98/32.19 tff(1462,plain,
% 31.98/32.19 (phi(impl(impl(Q!7, true), true)) = phi(impl(Q!7, true))),
% 31.98/32.19 inference(symmetry,[status(thm)],[1461])).
% 31.98/32.19 tff(1463,plain,
% 31.98/32.19 (bool(impl(Q!7, true)) <=> bool(impl(impl(Q!7, true), true))),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1456])).
% 31.98/32.19 tff(1464,plain,
% 31.98/32.19 ((~bool(impl(Q!7, true))) <=> (~bool(impl(impl(Q!7, true), true)))),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1463])).
% 31.98/32.19 tff(1465,plain,
% 31.98/32.19 (bool(Q!7) <=> bool(impl(Q!7, true))),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1458])).
% 31.98/32.19 tff(1466,plain,
% 31.98/32.19 ((~bool(Q!7)) <=> (~bool(impl(Q!7, true)))),
% 31.98/32.19 inference(monotonicity,[status(thm)],[1465])).
% 31.98/32.19 tff(1467,plain,
% 31.98/32.19 (~bool(impl(Q!7, true))),
% 31.98/32.19 inference(modus_ponens,[status(thm)],[1110, 1466])).
% 31.98/32.19 tff(1468,plain,
% 31.98/32.19 (~bool(impl(impl(Q!7, true), true))),
% 31.98/32.19 inference(modus_ponens,[status(thm)],[1467, 1464])).
% 31.98/32.19 tff(1469,plain,
% 31.98/32.19 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.19 inference(unit_resolution,[status(thm)],[869, 1468, 900])).
% 31.98/32.19 tff(1470,plain,
% 31.98/32.19 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = impl(impl(Q!7, impl(false, true)), true)),
% 31.98/32.20 inference(transitivity,[status(thm)],[1469, 1462, 1460, 1112, 1456, 703])).
% 31.98/32.20 tff(1471,plain,
% 31.98/32.20 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))),
% 31.98/32.20 inference(monotonicity,[status(thm)],[1470])).
% 31.98/32.20 tff(1472,plain,
% 31.98/32.20 (lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.20 inference(symmetry,[status(thm)],[1471])).
% 31.98/32.20 tff(1473,plain,
% 31.98/32.20 (f1(Q!7, false, true) = f1(impl(Q!7, true), false, true)),
% 31.98/32.20 inference(monotonicity,[status(thm)],[1458])).
% 31.98/32.20 tff(1474,plain,
% 31.98/32.20 (f1(impl(Q!7, true), false, true) = f1(Q!7, false, true)),
% 31.98/32.20 inference(symmetry,[status(thm)],[1473])).
% 31.98/32.20 tff(1475,plain,
% 31.98/32.20 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(impl(Q!7, true), false, true) = lazy_impl(prop(true), impl(impl(impl(Q!7, true), impl(false, true)), true)))),
% 31.98/32.20 inference(quant_inst,[status(thm)],[])).
% 31.98/32.20 tff(1476,plain,
% 31.98/32.20 (f1(impl(Q!7, true), false, true) = lazy_impl(prop(true), impl(impl(impl(Q!7, true), impl(false, true)), true))),
% 31.98/32.20 inference(unit_resolution,[status(thm)],[1475, 1061])).
% 31.98/32.20 tff(1477,plain,
% 31.98/32.20 (lazy_impl(prop(true), impl(impl(impl(Q!7, true), impl(false, true)), true)) = f1(impl(Q!7, true), false, true)),
% 31.98/32.20 inference(symmetry,[status(thm)],[1476])).
% 31.98/32.20 tff(1478,plain,
% 31.98/32.20 (phi(impl(impl(impl(Q!7, true), impl(false, true)), true)) = err),
% 31.98/32.20 inference(transitivity,[status(thm)],[936, 933, 1477, 1474, 1069, 1472, 1449, 327, 1448])).
% 31.98/32.20 tff(1479,plain,
% 31.98/32.20 (phi(Q!7) = phi(impl(impl(impl(Q!7, true), impl(false, true)), true))),
% 31.98/32.20 inference(transitivity,[status(thm)],[1459, 1461, 1040, 1039, 1070, 1473, 1476, 939, 935])).
% 31.98/32.20 tff(1480,plain,
% 31.98/32.20 ((phi(Q!7) = err) <=> (phi(impl(impl(impl(Q!7, true), impl(false, true)), true)) = err)),
% 31.98/32.20 inference(monotonicity,[status(thm)],[1479])).
% 31.98/32.20 tff(1481,plain,
% 31.98/32.20 ((~(phi(Q!7) = err)) <=> (~(phi(impl(impl(impl(Q!7, true), impl(false, true)), true)) = err))),
% 31.98/32.20 inference(monotonicity,[status(thm)],[1480])).
% 31.98/32.20 tff(1482,plain,
% 31.98/32.20 (~(phi(impl(impl(impl(Q!7, true), impl(false, true)), true)) = err)),
% 31.98/32.20 inference(modus_ponens,[status(thm)],[1450, 1481])).
% 31.98/32.20 tff(1483,plain,
% 31.98/32.20 ($false),
% 31.98/32.20 inference(unit_resolution,[status(thm)],[1482, 1478])).
% 31.98/32.20 tff(1484,plain,((phi(Q!7) = err) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)) | (~bool(impl(P!8, true))) | bool(Q!7)), inference(lemma,lemma(discharge,[]))).
% 31.98/32.20 tff(1485,plain,
% 31.98/32.20 (phi(Q!7) = err),
% 31.98/32.20 inference(unit_resolution,[status(thm)],[1484, 1419, 852, 1095])).
% 31.98/32.20 tff(1486,plain,
% 31.98/32.20 (phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.20 inference(modus_ponens,[status(thm)],[1485, 1447])).
% 31.98/32.20 tff(1487,plain,
% 31.98/32.20 (or1(P!8, Q!7) = or2(P!8, Q!7)),
% 31.98/32.20 inference(modus_ponens,[status(thm)],[1486, 1444])).
% 31.98/32.20 tff(1488,plain,
% 31.98/32.20 ($false),
% 31.98/32.20 inference(unit_resolution,[status(thm)],[377, 1487])).
% 31.98/32.20 tff(1489,plain,((lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true) | (~(P!8 = true)) | bool(impl(impl(Q!7, true), true))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.20 tff(1490,plain,
% 31.98/32.20 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true),
% 31.98/32.20 inference(unit_resolution,[status(thm)],[1489, 824, 667])).
% 31.98/32.20 tff(1491,plain,
% 31.98/32.20 (impl(impl(impl(Q!7, true), true), true) = impl(impl(impl(Q!7, true), impl(false, true)), true)),
% 31.98/32.20 inference(monotonicity,[status(thm)],[1146])).
% 31.98/32.20 tff(1492,plain,
% 31.98/32.20 (impl(impl(impl(Q!7, true), impl(false, true)), true) = impl(impl(impl(Q!7, true), true), true)),
% 31.98/32.20 inference(symmetry,[status(thm)],[1491])).
% 31.98/32.20 tff(1493,plain,
% 31.98/32.20 (impl(impl(impl(Q!7, true), impl(false, true)), true) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.20 inference(transitivity,[status(thm)],[1492, 897, 1180])).
% 31.98/32.20 tff(1494,plain,
% 31.98/32.20 (lazy_impl(prop(true), impl(impl(impl(Q!7, true), impl(false, true)), true)) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.20 inference(monotonicity,[status(thm)],[1493])).
% 31.98/32.20 tff(1495,plain,
% 31.98/32.20 (impl(impl(impl(Q!7, true), impl(false, false)), false) = impl(impl(impl(Q!7, true), impl(false, true)), true)),
% 31.98/32.20 inference(transitivity,[status(thm)],[921, 918, 829, 898, 1491])).
% 31.98/32.20 tff(1496,plain,
% 31.98/32.20 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = lazy_impl(prop(true), impl(impl(impl(Q!7, true), impl(false, true)), true))),
% 31.98/32.20 inference(symmetry,[status(thm)],[1494])).
% 31.98/32.20 tff(1497,plain,
% 31.98/32.20 (impl(impl(impl(Q!7, true), impl(false, false)), false) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.20 inference(transitivity,[status(thm)],[921, 918, 829, 1180])).
% 31.98/32.20 tff(1498,plain,
% 31.98/32.20 (lazy_impl(prop(false), impl(impl(impl(Q!7, true), impl(false, false)), false)) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.20 inference(monotonicity,[status(thm)],[1396, 1497])).
% 31.98/32.20 tff(1499,plain,
% 31.98/32.20 (phi(impl(impl(impl(Q!7, true), impl(false, false)), false)) = phi(impl(impl(impl(Q!7, true), impl(false, true)), true))),
% 31.98/32.20 inference(transitivity,[status(thm)],[1405, 1392, 1498, 1496, 939, 935])).
% 31.98/32.20 tff(1500,plain,
% 31.98/32.20 ((phi(impl(impl(impl(Q!7, true), impl(false, false)), false)) = impl(impl(impl(Q!7, true), impl(false, false)), false)) <=> (phi(impl(impl(impl(Q!7, true), impl(false, true)), true)) = impl(impl(impl(Q!7, true), impl(false, true)), true))),
% 31.98/32.20 inference(monotonicity,[status(thm)],[1499, 1495])).
% 31.98/32.20 tff(1501,plain,
% 31.98/32.20 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = impl(impl(impl(Q!7, true), impl(false, false)), false)),
% 31.98/32.20 inference(transitivity,[status(thm)],[1045, 830, 928, 927])).
% 31.98/32.20 tff(1502,plain,
% 31.98/32.20 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = lazy_impl(prop(false), impl(impl(impl(Q!7, true), impl(false, false)), false))),
% 31.98/32.20 inference(symmetry,[status(thm)],[1498])).
% 31.98/32.20 tff(1503,plain,
% 31.98/32.20 (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = phi(impl(impl(impl(Q!7, true), impl(false, false)), false))),
% 31.98/32.20 inference(transitivity,[status(thm)],[328, 318, 1502, 1393, 925])).
% 31.98/32.20 tff(1504,plain,
% 31.98/32.20 ((phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true))) <=> (phi(impl(impl(impl(Q!7, true), impl(false, false)), false)) = impl(impl(impl(Q!7, true), impl(false, false)), false))),
% 31.98/32.20 inference(monotonicity,[status(thm)],[1503, 1501])).
% 31.98/32.20 tff(1505,plain,
% 31.98/32.20 (phi(impl(impl(impl(Q!7, true), impl(false, false)), false)) = impl(impl(impl(Q!7, true), impl(false, false)), false)),
% 31.98/32.20 inference(modus_ponens,[status(thm)],[1035, 1504])).
% 31.98/32.20 tff(1506,plain,
% 31.98/32.20 (phi(impl(impl(impl(Q!7, true), impl(false, true)), true)) = impl(impl(impl(Q!7, true), impl(false, true)), true)),
% 31.98/32.20 inference(modus_ponens,[status(thm)],[1505, 1500])).
% 31.98/32.20 tff(1507,plain,
% 31.98/32.20 (impl(impl(impl(Q!7, true), impl(false, true)), true) = phi(impl(impl(impl(Q!7, true), impl(false, true)), true))),
% 31.98/32.20 inference(symmetry,[status(thm)],[1506])).
% 31.98/32.20 tff(1508,plain,
% 31.98/32.20 ((phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err) <=> (phi(impl(impl(impl(Q!7, true), impl(false, false)), false)) = err)),
% 31.98/32.20 inference(monotonicity,[status(thm)],[1503])).
% 31.98/32.20 tff(1509,plain,
% 31.98/32.20 ((phi(impl(impl(impl(Q!7, true), impl(false, false)), false)) = err) <=> (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)),
% 31.98/32.20 inference(symmetry,[status(thm)],[1508])).
% 31.98/32.20 tff(1510,plain,
% 31.98/32.20 ((phi(impl(impl(impl(Q!7, true), impl(false, false)), false)) = err) <=> (phi(impl(impl(impl(Q!7, true), impl(false, true)), true)) = err)),
% 31.98/32.20 inference(monotonicity,[status(thm)],[1499])).
% 31.98/32.20 tff(1511,plain,
% 31.98/32.20 ((phi(impl(impl(impl(Q!7, true), impl(false, true)), true)) = err) <=> (phi(impl(impl(impl(Q!7, true), impl(false, false)), false)) = err)),
% 31.98/32.20 inference(symmetry,[status(thm)],[1510])).
% 31.98/32.20 tff(1512,plain,
% 31.98/32.20 (phi(impl(impl(impl(Q!7, true), impl(false, true)), true)) = true),
% 31.98/32.20 inference(transitivity,[status(thm)],[936, 933, 1494, 1490])).
% 31.98/32.20 tff(1513,plain,
% 31.98/32.20 ((phi(impl(impl(impl(Q!7, true), impl(false, true)), true)) = err) <=> (true = err)),
% 31.98/32.20 inference(monotonicity,[status(thm)],[1512])).
% 31.98/32.20 tff(1514,plain,
% 31.98/32.20 ((true = err) <=> (phi(impl(impl(impl(Q!7, true), impl(false, true)), true)) = err)),
% 31.98/32.20 inference(symmetry,[status(thm)],[1513])).
% 31.98/32.20 tff(1515,plain,
% 31.98/32.20 ((true = err) <=> (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)),
% 31.98/32.20 inference(transitivity,[status(thm)],[1514, 1511, 1509])).
% 31.98/32.20 tff(1516,plain,
% 31.98/32.20 ((~(true = err)) <=> (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err))),
% 31.98/32.20 inference(monotonicity,[status(thm)],[1515])).
% 31.98/32.20 tff(1517,plain,
% 31.98/32.20 (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)),
% 31.98/32.20 inference(modus_ponens,[status(thm)],[153, 1516])).
% 31.98/32.20 tff(1518,plain,
% 31.98/32.20 (~(phi(impl(impl(Q!7, true), true)) = err)),
% 31.98/32.20 inference(unit_resolution,[status(thm)],[1415, 1517, 1045, 897, 829])).
% 31.98/32.20 tff(1519,plain,
% 31.98/32.20 (d(impl(impl(Q!7, true), true)) | (~(phi(impl(impl(Q!7, true), true)) = err))),
% 31.98/32.20 inference(unit_resolution,[status(thm)],[909, 1518])).
% 31.98/32.20 tff(1520,plain,
% 31.98/32.20 (~((~d(impl(impl(Q!7, true), true))) | (~(phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))))),
% 31.98/32.20 inference(unit_resolution,[status(thm)],[914, 1519])).
% 31.98/32.20 tff(1521,plain,
% 31.98/32.20 (phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)),
% 31.98/32.20 inference(unit_resolution,[status(thm)],[916, 1520])).
% 31.98/32.20 tff(1522,plain,
% 31.98/32.20 (impl(impl(Q!7, true), true) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.20 inference(symmetry,[status(thm)],[1521])).
% 31.98/32.20 tff(1523,plain,
% 31.98/32.20 (impl(impl(Q!7, true), true) = true),
% 31.98/32.20 inference(transitivity,[status(thm)],[1522, 898, 1491, 1507, 936, 933, 1494, 1490])).
% 31.98/32.20 tff(1524,plain,
% 31.98/32.20 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(impl(impl(Q!7, true), true)) <=> ((impl(impl(Q!7, true), true) = false) | (impl(impl(Q!7, true), true) = true)))),
% 31.98/32.20 inference(quant_inst,[status(thm)],[])).
% 31.98/32.20 tff(1525,plain,
% 31.98/32.20 (bool(impl(impl(Q!7, true), true)) <=> ((impl(impl(Q!7, true), true) = false) | (impl(impl(Q!7, true), true) = true))),
% 31.98/32.20 inference(unit_resolution,[status(thm)],[1524, 69])).
% 31.98/32.20 tff(1526,plain,
% 31.98/32.20 ((~(bool(impl(impl(Q!7, true), true)) <=> ((impl(impl(Q!7, true), true) = false) | (impl(impl(Q!7, true), true) = true)))) | bool(impl(impl(Q!7, true), true)) | (~((impl(impl(Q!7, true), true) = false) | (impl(impl(Q!7, true), true) = true)))),
% 31.98/32.20 inference(tautology,[status(thm)],[])).
% 31.98/32.20 tff(1527,plain,
% 31.98/32.20 ((~(bool(impl(impl(Q!7, true), true)) <=> ((impl(impl(Q!7, true), true) = false) | (impl(impl(Q!7, true), true) = true)))) | (~((impl(impl(Q!7, true), true) = false) | (impl(impl(Q!7, true), true) = true)))),
% 31.98/32.20 inference(unit_resolution,[status(thm)],[1526, 824])).
% 31.98/32.20 tff(1528,plain,
% 31.98/32.20 (~((impl(impl(Q!7, true), true) = false) | (impl(impl(Q!7, true), true) = true))),
% 31.98/32.20 inference(unit_resolution,[status(thm)],[1527, 1525])).
% 31.98/32.20 tff(1529,plain,
% 31.98/32.20 (((impl(impl(Q!7, true), true) = false) | (impl(impl(Q!7, true), true) = true)) | (~(impl(impl(Q!7, true), true) = true))),
% 31.98/32.20 inference(tautology,[status(thm)],[])).
% 31.98/32.20 tff(1530,plain,
% 31.98/32.20 (~(impl(impl(Q!7, true), true) = true)),
% 31.98/32.20 inference(unit_resolution,[status(thm)],[1529, 1528])).
% 31.98/32.20 tff(1531,plain,
% 31.98/32.20 ($false),
% 31.98/32.20 inference(unit_resolution,[status(thm)],[1530, 1523])).
% 31.98/32.20 tff(1532,plain,(bool(impl(impl(Q!7, true), true)) | (~(P!8 = true))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.20 tff(1533,plain,
% 31.98/32.20 (bool(impl(impl(Q!7, true), true))),
% 31.98/32.20 inference(unit_resolution,[status(thm)],[1532, 667])).
% 31.98/32.20 tff(1534,plain,
% 31.98/32.20 (impl(true, impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)),
% 31.98/32.20 inference(unit_resolution,[status(thm)],[874, 1533])).
% 31.98/32.20 tff(1535,plain,
% 31.98/32.20 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = impl(true, impl(impl(Q!7, true), true))),
% 31.98/32.20 inference(symmetry,[status(thm)],[1306])).
% 31.98/32.20 tff(1536,plain,
% 31.98/32.20 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)),
% 31.98/32.20 inference(transitivity,[status(thm)],[1535, 1534])).
% 31.98/32.20 tff(1537,plain,
% 31.98/32.20 (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.20 inference(monotonicity,[status(thm)],[1536])).
% 31.98/32.20 tff(1538,plain,
% 31.98/32.20 (impl(impl(Q!7, true), true) = impl(true, impl(impl(Q!7, true), true))),
% 31.98/32.20 inference(symmetry,[status(thm)],[1534])).
% 31.98/32.20 tff(1539,plain,
% 31.98/32.20 (((~![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))),
% 31.98/32.20 inference(rewrite,[status(thm)],[])).
% 31.98/32.20 tff(1540,plain,
% 31.98/32.20 ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | ((~bool(false)) | (impl(true, false) = false))),
% 31.98/32.20 inference(quant_inst,[status(thm)],[])).
% 31.98/32.20 tff(1541,plain,
% 31.98/32.20 ((~![B: $i] : ((~bool(B)) | (impl(true, B) = B))) | (~bool(false)) | (impl(true, false) = false)),
% 31.98/32.20 inference(modus_ponens,[status(thm)],[1540, 1539])).
% 31.98/32.20 tff(1542,plain,
% 31.98/32.20 (impl(true, false) = false),
% 31.98/32.20 inference(unit_resolution,[status(thm)],[1541, 843, 756])).
% 31.98/32.20 tff(1543,plain,
% 31.98/32.20 (impl(true, impl(true, false)) = impl(true, false)),
% 31.98/32.20 inference(monotonicity,[status(thm)],[1542])).
% 31.98/32.20 tff(1544,plain,
% 31.98/32.20 (impl(true, impl(true, false)) = false),
% 31.98/32.20 inference(transitivity,[status(thm)],[1543, 1542])).
% 31.98/32.20 tff(1545,plain,
% 31.98/32.20 (impl(impl(true, impl(true, false)), false) = impl(false, false)),
% 31.98/32.20 inference(monotonicity,[status(thm)],[1544])).
% 31.98/32.20 tff(1546,plain,
% 31.98/32.20 (impl(impl(true, impl(true, false)), false) = true),
% 31.98/32.20 inference(transitivity,[status(thm)],[1545, 811])).
% 31.98/32.20 tff(1547,plain,
% 31.98/32.20 (lazy_impl(prop(false), impl(impl(true, impl(true, false)), false)) = lazy_impl(true, true)),
% 31.98/32.20 inference(monotonicity,[status(thm)],[759, 1546])).
% 31.98/32.20 tff(1548,plain,
% 31.98/32.20 ((~![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)))),
% 31.98/32.20 inference(quant_inst,[status(thm)],[])).
% 31.98/32.20 tff(1549,plain,
% 31.98/32.20 (f1(true, true, false) = lazy_impl(prop(false), impl(impl(true, impl(true, false)), false))),
% 31.98/32.20 inference(unit_resolution,[status(thm)],[1548, 1061])).
% 31.98/32.20 tff(1550,plain,
% 31.98/32.20 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.20 inference(transitivity,[status(thm)],[965, 327, 1537, 1180])).
% 31.98/32.20 tff(1551,plain,
% 31.98/32.20 (d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) <=> d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.20 inference(monotonicity,[status(thm)],[1550])).
% 31.98/32.20 tff(1552,plain,
% 31.98/32.20 (d(impl(impl(P!8, true), impl(impl(Q!7, true), true))) <=> d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.98/32.20 inference(symmetry,[status(thm)],[1551])).
% 31.98/32.20 tff(1553,plain,
% 31.98/32.20 (lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = lazy_impl(true, impl(impl(Q!7, true), true))),
% 31.98/32.20 inference(symmetry,[status(thm)],[1039])).
% 31.98/32.20 tff(1554,plain,
% 31.98/32.20 (lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.20 inference(transitivity,[status(thm)],[1553, 685, 1180])).
% 31.98/32.20 tff(1555,plain,
% 31.98/32.20 (d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) <=> d(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.20 inference(monotonicity,[status(thm)],[1554])).
% 31.98/32.20 tff(1556,plain,
% 31.98/32.20 (d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) <=> d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.98/32.20 inference(transitivity,[status(thm)],[1555, 1552])).
% 31.98/32.20 tff(1557,plain,
% 31.98/32.20 (((~![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(true), impl(impl(Q!7, impl(false, true)), true)), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) | (~d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(true), impl(impl(Q!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(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) | (~d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))))))))),
% 31.98/32.20 inference(rewrite,[status(thm)],[])).
% 31.98/32.20 tff(1558,plain,
% 31.98/32.20 ((forallprefers(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)), false) <=> ((~((~(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = false)) | (~(false = true)))) | (~(d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) | (~d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))))))) <=> (forallprefers(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) | (~d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))))))),
% 31.98/32.20 inference(rewrite,[status(thm)],[])).
% 31.98/32.20 tff(1559,plain,
% 31.98/32.20 (((~![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(true), impl(impl(Q!7, impl(false, true)), true)), false) <=> ((~((~(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = false)) | (~(false = true)))) | (~(d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) | (~d(lazy_impl(prop(true), impl(impl(Q!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(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) | (~d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))))))))),
% 31.98/32.20 inference(monotonicity,[status(thm)],[1558])).
% 31.98/32.20 tff(1560,plain,
% 31.98/32.20 (((~![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(true), impl(impl(Q!7, impl(false, true)), true)), false) <=> ((~((~(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = false)) | (~(false = true)))) | (~(d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) | (~d(lazy_impl(prop(true), impl(impl(Q!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(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) | (~d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))))))))),
% 31.98/32.20 inference(transitivity,[status(thm)],[1559, 1557])).
% 31.98/32.20 tff(1561,plain,
% 31.98/32.20 ((~![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(true), impl(impl(Q!7, impl(false, true)), true)), false) <=> ((~((~(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = false)) | (~(false = true)))) | (~(d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) | (~d(false)))) | (~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) | (~d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))))))))),
% 31.98/32.20 inference(quant_inst,[status(thm)],[])).
% 31.98/32.20 tff(1562,plain,
% 31.98/32.20 ((~![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(true), impl(impl(Q!7, impl(false, true)), true)), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) | (~d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))))))),
% 31.98/32.20 inference(modus_ponens,[status(thm)],[1561, 1560])).
% 31.98/32.20 tff(1563,plain,
% 31.98/32.20 (forallprefers(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) | (~d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))))))),
% 31.98/32.20 inference(unit_resolution,[status(thm)],[1562, 25])).
% 31.98/32.20 tff(1564,plain,
% 31.98/32.20 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) = lazy_impl(prop(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))), lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))))),
% 31.98/32.20 inference(quant_inst,[status(thm)],[])).
% 31.98/32.20 tff(1565,plain,
% 31.98/32.20 (f7(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) = lazy_impl(prop(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))), lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))),
% 31.98/32.20 inference(unit_resolution,[status(thm)],[1564, 713])).
% 31.98/32.20 tff(1566,plain,
% 31.98/32.20 (lazy_impl(prop(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))), lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) = f7(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))),
% 31.98/32.20 inference(symmetry,[status(thm)],[1565])).
% 31.98/32.20 tff(1567,plain,
% 31.98/32.20 ((~![X: $i] : ((prop(X) = true) <=> bool(X))) | ((prop(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) = true) <=> bool(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))))),
% 31.98/32.21 inference(quant_inst,[status(thm)],[])).
% 31.98/32.21 tff(1568,plain,
% 31.98/32.21 ((prop(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) = true) <=> bool(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1567, 311])).
% 31.98/32.21 tff(1569,plain,
% 31.98/32.21 (bool(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) <=> bool(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1554])).
% 31.98/32.21 tff(1570,plain,
% 31.98/32.21 (bool(impl(impl(P!8, true), impl(impl(Q!7, true), true))) <=> bool(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))),
% 31.98/32.21 inference(symmetry,[status(thm)],[1569])).
% 31.98/32.21 tff(1571,plain,
% 31.98/32.21 (impl(impl(Q!7, true), true) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.21 inference(transitivity,[status(thm)],[1538, 1306])).
% 31.98/32.21 tff(1572,plain,
% 31.98/32.21 (bool(impl(impl(Q!7, true), true)) <=> bool(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1571])).
% 31.98/32.21 tff(1573,plain,
% 31.98/32.21 (bool(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.21 inference(modus_ponens,[status(thm)],[1533, 1572])).
% 31.98/32.21 tff(1574,plain,
% 31.98/32.21 (bool(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))),
% 31.98/32.21 inference(modus_ponens,[status(thm)],[1573, 1570])).
% 31.98/32.21 tff(1575,plain,
% 31.98/32.21 ((~((prop(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) = true) <=> bool(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))))) | (prop(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) = true) | (~bool(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))))),
% 31.98/32.21 inference(tautology,[status(thm)],[])).
% 31.98/32.21 tff(1576,plain,
% 31.98/32.21 (prop(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) = true),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1575, 1574, 1568])).
% 31.98/32.21 tff(1577,plain,
% 31.98/32.21 (prop(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) = prop(true)),
% 31.98/32.21 inference(transitivity,[status(thm)],[1576, 317])).
% 31.98/32.21 tff(1578,plain,
% 31.98/32.21 (lazy_impl(prop(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))), lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1577, 1554])).
% 31.98/32.21 tff(1579,plain,
% 31.98/32.21 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = lazy_impl(prop(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))), lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))),
% 31.98/32.21 inference(symmetry,[status(thm)],[1578])).
% 31.98/32.21 tff(1580,plain,
% 31.98/32.21 (phi(impl(impl(Q!7, true), true)) = phi(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.21 inference(symmetry,[status(thm)],[1537])).
% 31.98/32.21 tff(1581,plain,
% 31.98/32.21 (lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = f7(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))),
% 31.98/32.21 inference(transitivity,[status(thm)],[1553, 685, 1580, 328, 966, 1579, 1566])).
% 31.98/32.21 tff(1582,plain,
% 31.98/32.21 (forallprefers(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)), false) <=> forallprefers(f7(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))), f7(P!6))),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1581, 883])).
% 31.98/32.21 tff(1583,plain,
% 31.98/32.21 (forallprefers(f7(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))), f7(P!6)) <=> forallprefers(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)), false)),
% 31.98/32.21 inference(symmetry,[status(thm)],[1582])).
% 31.98/32.21 tff(1584,plain,
% 31.98/32.21 ((~forallprefers(f7(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))), f7(P!6))) <=> (~forallprefers(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)), false))),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1583])).
% 31.98/32.21 tff(1585,plain,
% 31.98/32.21 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))), f7(P!6)))),
% 31.98/32.21 inference(quant_inst,[status(thm)],[])).
% 31.98/32.21 tff(1586,plain,
% 31.98/32.21 (~forallprefers(f7(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))), f7(P!6))),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1585, 778])).
% 31.98/32.21 tff(1587,plain,
% 31.98/32.21 (~forallprefers(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)), false)),
% 31.98/32.21 inference(modus_ponens,[status(thm)],[1586, 1584])).
% 31.98/32.21 tff(1588,plain,
% 31.98/32.21 ((~(forallprefers(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)), false) <=> ((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) | (~d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))))))) | forallprefers(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)), false) | (~((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) | (~d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))))))),
% 31.98/32.21 inference(tautology,[status(thm)],[])).
% 31.98/32.21 tff(1589,plain,
% 31.98/32.21 (~((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) | (~d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))))))),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1588, 1587, 1563])).
% 31.98/32.21 tff(1590,plain,
% 31.98/32.21 (((~((~d(false)) | (~bool(false)) | bool(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))) | (~d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))))) | (~((~(false = true)) | (~(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = false)))) | (~((~d(false)) | d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))))) | ((~d(false)) | d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))))),
% 31.98/32.21 inference(tautology,[status(thm)],[])).
% 31.98/32.21 tff(1591,plain,
% 31.98/32.21 ((~d(false)) | d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1590, 1589])).
% 31.98/32.21 tff(1592,plain,
% 31.98/32.21 ((~((~d(false)) | d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))))) | (~d(false)) | d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))),
% 31.98/32.21 inference(tautology,[status(thm)],[])).
% 31.98/32.21 tff(1593,plain,
% 31.98/32.21 ((~((~d(false)) | d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))))) | d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1592, 736])).
% 31.98/32.21 tff(1594,plain,
% 31.98/32.21 (d(lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)))),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1593, 1591])).
% 31.98/32.21 tff(1595,plain,
% 31.98/32.21 (d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.98/32.21 inference(modus_ponens,[status(thm)],[1594, 1556])).
% 31.98/32.21 tff(1596,plain,
% 31.98/32.21 (~(prop(tptp_fun_R_2(Q!7, P!8)) = false)),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1356, 1595, 667])).
% 31.98/32.21 tff(1597,plain,
% 31.98/32.21 (bool(tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[447, 1596])).
% 31.98/32.21 tff(1598,plain,
% 31.98/32.21 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(tptp_fun_R_2(Q!7, P!8)) <=> ((tptp_fun_R_2(Q!7, P!8) = false) | (tptp_fun_R_2(Q!7, P!8) = true)))),
% 31.98/32.21 inference(quant_inst,[status(thm)],[])).
% 31.98/32.21 tff(1599,plain,
% 31.98/32.21 (bool(tptp_fun_R_2(Q!7, P!8)) <=> ((tptp_fun_R_2(Q!7, P!8) = false) | (tptp_fun_R_2(Q!7, P!8) = true))),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1598, 69])).
% 31.98/32.21 tff(1600,plain,
% 31.98/32.21 ((~(bool(tptp_fun_R_2(Q!7, P!8)) <=> ((tptp_fun_R_2(Q!7, P!8) = false) | (tptp_fun_R_2(Q!7, P!8) = true)))) | (~bool(tptp_fun_R_2(Q!7, P!8))) | ((tptp_fun_R_2(Q!7, P!8) = false) | (tptp_fun_R_2(Q!7, P!8) = true))),
% 31.98/32.21 inference(tautology,[status(thm)],[])).
% 31.98/32.21 tff(1601,plain,
% 31.98/32.21 ((~bool(tptp_fun_R_2(Q!7, P!8))) | ((tptp_fun_R_2(Q!7, P!8) = false) | (tptp_fun_R_2(Q!7, P!8) = true))),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1600, 1599])).
% 31.98/32.21 tff(1602,plain,
% 31.98/32.21 ((tptp_fun_R_2(Q!7, P!8) = false) | (tptp_fun_R_2(Q!7, P!8) = true)),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1601, 1597])).
% 31.98/32.21 tff(1603,plain,
% 31.98/32.21 (phi(P!8) = phi(true)),
% 31.98/32.21 inference(monotonicity,[status(thm)],[667])).
% 31.98/32.21 tff(1604,plain,
% 31.98/32.21 (phi(P!8) = true),
% 31.98/32.21 inference(transitivity,[status(thm)],[1603, 221])).
% 31.98/32.21 tff(1605,plain,
% 31.98/32.21 ((or1(P!8, Q!7) = phi(P!8)) <=> (or1(true, Q!7) = true)),
% 31.98/32.21 inference(monotonicity,[status(thm)],[668, 1604])).
% 31.98/32.21 tff(1606,plain,
% 31.98/32.21 ((or1(true, Q!7) = true) <=> (or1(P!8, Q!7) = phi(P!8))),
% 31.98/32.21 inference(symmetry,[status(thm)],[1605])).
% 31.98/32.21 tff(1607,assumption,(bool(Q!7)), introduced(assumption)).
% 31.98/32.21 tff(1608,plain,
% 31.98/32.21 (or1(true, Q!7) = true),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[665, 1607])).
% 31.98/32.21 tff(1609,plain,
% 31.98/32.21 (or1(P!8, Q!7) = phi(P!8)),
% 31.98/32.21 inference(modus_ponens,[status(thm)],[1608, 1606])).
% 31.98/32.21 tff(1610,plain,
% 31.98/32.21 (phi(true) = phi(P!8)),
% 31.98/32.21 inference(symmetry,[status(thm)],[1603])).
% 31.98/32.21 tff(1611,plain,
% 31.98/32.21 (impl(P!8, true) = phi(P!8)),
% 31.98/32.21 inference(transitivity,[status(thm)],[848, 847, 637, 1610])).
% 31.98/32.21 tff(1612,plain,
% 31.98/32.21 (phi(impl(P!8, true)) = phi(true)),
% 31.98/32.21 inference(monotonicity,[status(thm)],[849])).
% 31.98/32.21 tff(1613,plain,
% 31.98/32.21 (phi(true) = phi(impl(P!8, true))),
% 31.98/32.21 inference(symmetry,[status(thm)],[1612])).
% 31.98/32.21 tff(1614,plain,
% 31.98/32.21 (impl(impl(false, impl(false, true)), true) = true),
% 31.98/32.21 inference(transitivity,[status(thm)],[1079, 847])).
% 31.98/32.21 tff(1615,plain,
% 31.98/32.21 (lazy_impl(prop(true), impl(impl(false, impl(false, true)), true)) = lazy_impl(true, true)),
% 31.98/32.21 inference(monotonicity,[status(thm)],[316, 1614])).
% 31.98/32.21 tff(1616,plain,
% 31.98/32.21 ((Q!7 = false) | (Q!7 = true)),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[631, 1607])).
% 31.98/32.21 tff(1617,assumption,(or1(true, Q!7) = true), introduced(assumption)).
% 31.98/32.21 tff(1618,plain,
% 31.98/32.21 (or1(P!8, Q!7) = phi(P!8)),
% 31.98/32.21 inference(modus_ponens,[status(thm)],[1617, 1606])).
% 31.98/32.21 tff(1619,plain,
% 31.98/32.21 (impl(impl(true, impl(false, true)), true) = true),
% 31.98/32.21 inference(transitivity,[status(thm)],[1049, 847])).
% 31.98/32.21 tff(1620,plain,
% 31.98/32.21 (lazy_impl(prop(true), impl(impl(true, impl(false, true)), true)) = lazy_impl(true, true)),
% 31.98/32.21 inference(monotonicity,[status(thm)],[316, 1619])).
% 31.98/32.21 tff(1621,plain,
% 31.98/32.21 (f1(Q!7, false, true) = f1(true, false, true)),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1064])).
% 31.98/32.21 tff(1622,plain,
% 31.98/32.21 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(P!8, true))),
% 31.98/32.21 inference(transitivity,[status(thm)],[1045, 1040, 1039, 1070, 1621, 1063, 1620, 705, 1613])).
% 31.98/32.21 tff(1623,assumption,(phi(P!8) = err), introduced(assumption)).
% 31.98/32.21 tff(1624,plain,
% 31.98/32.21 (err = phi(P!8)),
% 31.98/32.21 inference(symmetry,[status(thm)],[1623])).
% 31.98/32.21 tff(1625,plain,
% 31.98/32.21 (phi(phi(P!8)) = phi(err)),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1623])).
% 31.98/32.21 tff(1626,plain,
% 31.98/32.21 (phi(phi(P!8)) = phi(P!8)),
% 31.98/32.21 inference(transitivity,[status(thm)],[1625, 567, 1624])).
% 31.98/32.21 tff(1627,plain,
% 31.98/32.21 ($false),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[402, 1626])).
% 31.98/32.21 tff(1628,plain,((~(phi(P!8) = err)) | (phi(phi(P!8)) = phi(P!8))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.21 tff(1629,plain,
% 31.98/32.21 (~(phi(P!8) = err)),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1628, 402])).
% 31.98/32.21 tff(1630,plain,
% 31.98/32.21 (d(P!8) | (~(phi(P!8) = err))),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[116, 1629])).
% 31.98/32.21 tff(1631,plain,
% 31.98/32.21 (~((~d(P!8)) | (~(phi(P!8) = P!8)))),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[131, 1630])).
% 31.98/32.21 tff(1632,plain,
% 31.98/32.21 (phi(P!8) = P!8),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[106, 1631])).
% 31.98/32.21 tff(1633,plain,
% 31.98/32.21 (phi(phi(P!8)) = phi(P!8)),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1632])).
% 31.98/32.21 tff(1634,plain,
% 31.98/32.21 ($false),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[402, 1633])).
% 31.98/32.21 tff(1635,plain,(phi(phi(P!8)) = phi(P!8)), inference(lemma,lemma(discharge,[]))).
% 31.98/32.21 tff(1636,assumption,(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true))), introduced(assumption)).
% 31.98/32.21 tff(1637,assumption,(tptp_fun_R_2(Q!7, P!8) = true), introduced(assumption)).
% 31.98/32.21 tff(1638,plain,
% 31.98/32.21 (f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)) = f3(P!8, Q!7, true)),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1637])).
% 31.98/32.21 tff(1639,plain,
% 31.98/32.21 (or2(P!8, Q!7) = phi(phi(P!8))),
% 31.98/32.21 inference(transitivity,[status(thm)],[365, 524, 1638, 257, 965, 327, 1636, 500, 499])).
% 31.98/32.21 tff(1640,plain,
% 31.98/32.21 ((or1(P!8, Q!7) = or2(P!8, Q!7)) <=> (phi(P!8) = phi(phi(P!8)))),
% 31.98/32.21 inference(monotonicity,[status(thm)],[529, 1639])).
% 31.98/32.21 tff(1641,plain,
% 31.98/32.21 ((or1(P!8, Q!7) = or2(P!8, Q!7)) <=> (phi(phi(P!8)) = phi(P!8))),
% 31.98/32.21 inference(transitivity,[status(thm)],[1640, 401])).
% 31.98/32.21 tff(1642,plain,
% 31.98/32.21 ((phi(phi(P!8)) = phi(P!8)) <=> (or1(P!8, Q!7) = or2(P!8, Q!7))),
% 31.98/32.21 inference(symmetry,[status(thm)],[1641])).
% 31.98/32.21 tff(1643,assumption,(phi(phi(P!8)) = phi(P!8)), introduced(assumption)).
% 31.98/32.21 tff(1644,plain,
% 31.98/32.21 (or1(P!8, Q!7) = or2(P!8, Q!7)),
% 31.98/32.21 inference(modus_ponens,[status(thm)],[1643, 1642])).
% 31.98/32.21 tff(1645,plain,
% 31.98/32.21 ($false),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[377, 1644])).
% 31.98/32.21 tff(1646,plain,((~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~(phi(phi(P!8)) = phi(P!8))) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))) | (~(impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(P!8, true)))) | (~(impl(P!8, true) = phi(P!8))) | (~(tptp_fun_R_2(Q!7, P!8) = true)) | (~(or1(P!8, Q!7) = phi(P!8)))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.21 tff(1647,plain,
% 31.98/32.21 ((~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~(phi(phi(P!8)) = phi(P!8))) | (~(impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(P!8, true)))) | (~(impl(P!8, true) = phi(P!8))) | (~(tptp_fun_R_2(Q!7, P!8) = true)) | (~(or1(P!8, Q!7) = phi(P!8)))),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1646, 1268])).
% 31.98/32.21 tff(1648,plain,
% 31.98/32.21 ((~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true)))) | (~(impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(P!8, true)))) | (~(impl(P!8, true) = phi(P!8))) | (~(tptp_fun_R_2(Q!7, P!8) = true)) | (~(or1(P!8, Q!7) = phi(P!8)))),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1647, 1635])).
% 31.98/32.21 tff(1649,plain,
% 31.98/32.21 ((~(impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(P!8, true)))) | (~(impl(P!8, true) = phi(P!8))) | (~(tptp_fun_R_2(Q!7, P!8) = true)) | (~(or1(P!8, Q!7) = phi(P!8)))),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1648, 1035])).
% 31.98/32.21 tff(1650,plain,
% 31.98/32.21 (~(tptp_fun_R_2(Q!7, P!8) = true)),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1649, 1622, 1611, 1618])).
% 31.98/32.21 tff(1651,plain,
% 31.98/32.21 ((~((tptp_fun_R_2(Q!7, P!8) = false) | (tptp_fun_R_2(Q!7, P!8) = true))) | (tptp_fun_R_2(Q!7, P!8) = false) | (tptp_fun_R_2(Q!7, P!8) = true)),
% 31.98/32.21 inference(tautology,[status(thm)],[])).
% 31.98/32.21 tff(1652,plain,
% 31.98/32.21 (tptp_fun_R_2(Q!7, P!8) = false),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1651, 1650, 1602])).
% 31.98/32.21 tff(1653,plain,
% 31.98/32.21 (impl(true, tptp_fun_R_2(Q!7, P!8)) = tptp_fun_R_2(Q!7, P!8)),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1362, 1597])).
% 31.98/32.21 tff(1654,plain,
% 31.98/32.21 (impl(true, impl(true, tptp_fun_R_2(Q!7, P!8))) = impl(true, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1653])).
% 31.98/32.21 tff(1655,plain,
% 31.98/32.21 (impl(true, impl(true, tptp_fun_R_2(Q!7, P!8))) = false),
% 31.98/32.21 inference(transitivity,[status(thm)],[1654, 1653, 1652])).
% 31.98/32.21 tff(1656,plain,
% 31.98/32.21 (impl(impl(true, impl(true, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)) = impl(false, false)),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1655, 1652])).
% 31.98/32.21 tff(1657,plain,
% 31.98/32.21 (impl(true, tptp_fun_R_2(Q!7, P!8)) = impl(true, impl(true, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.21 inference(symmetry,[status(thm)],[1654])).
% 31.98/32.21 tff(1658,plain,
% 31.98/32.21 (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = impl(true, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1064])).
% 31.98/32.21 tff(1659,plain,
% 31.98/32.21 (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = impl(true, impl(true, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.21 inference(transitivity,[status(thm)],[1658, 1657])).
% 31.98/32.21 tff(1660,plain,
% 31.98/32.21 (impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = impl(impl(true, impl(true, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1659])).
% 31.98/32.21 tff(1661,plain,
% 31.98/32.21 (impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = true),
% 31.98/32.21 inference(transitivity,[status(thm)],[1660, 1656, 811])).
% 31.98/32.21 tff(1662,plain,
% 31.98/32.21 (impl(P!8, tptp_fun_R_2(Q!7, P!8)) = false),
% 31.98/32.21 inference(transitivity,[status(thm)],[1193, 1653, 1652])).
% 31.98/32.21 tff(1663,plain,
% 31.98/32.21 (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = impl(false, true)),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1662, 1661])).
% 31.98/32.21 tff(1664,plain,
% 31.98/32.21 (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = true),
% 31.98/32.21 inference(transitivity,[status(thm)],[1663, 699])).
% 31.98/32.21 tff(1665,plain,
% 31.98/32.21 (prop(tptp_fun_R_2(Q!7, P!8)) = true),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[452, 1597])).
% 31.98/32.21 tff(1666,plain,
% 31.98/32.21 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = lazy_impl(true, true)),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1665, 1664])).
% 31.98/32.21 tff(1667,plain,
% 31.98/32.21 (f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)) = true),
% 31.98/32.21 inference(transitivity,[status(thm)],[41, 1666, 705, 221])).
% 31.98/32.21 tff(1668,plain,
% 31.98/32.21 (phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = phi(true)),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1667])).
% 31.98/32.21 tff(1669,plain,
% 31.98/32.21 (phi(true) = phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.21 inference(symmetry,[status(thm)],[1668])).
% 31.98/32.21 tff(1670,plain,
% 31.98/32.21 (or1(P!8, Q!7) = or2(P!8, Q!7)),
% 31.98/32.21 inference(transitivity,[status(thm)],[668, 1617, 637, 1669, 576])).
% 31.98/32.21 tff(1671,plain,
% 31.98/32.21 ($false),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[377, 1670])).
% 31.98/32.21 tff(1672,plain,((~(Q!7 = true)) | (~(or1(true, Q!7) = true)) | (~(P!8 = true))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.21 tff(1673,plain,
% 31.98/32.21 (~(Q!7 = true)),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1672, 1608, 667])).
% 31.98/32.21 tff(1674,plain,
% 31.98/32.21 (Q!7 = false),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[633, 1673, 1616])).
% 31.98/32.21 tff(1675,plain,
% 31.98/32.21 (f1(Q!7, false, true) = f1(false, false, true)),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1674])).
% 31.98/32.21 tff(1676,plain,
% 31.98/32.21 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(P!8, true))),
% 31.98/32.21 inference(transitivity,[status(thm)],[1045, 1040, 1039, 1070, 1675, 1085, 1615, 705, 1613])).
% 31.98/32.21 tff(1677,plain,
% 31.98/32.21 (~(tptp_fun_R_2(Q!7, P!8) = true)),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1649, 1676, 1611, 1609])).
% 31.98/32.21 tff(1678,plain,
% 31.98/32.21 (tptp_fun_R_2(Q!7, P!8) = false),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1651, 1677, 1602])).
% 31.98/32.21 tff(1679,plain,
% 31.98/32.21 (f1(true, true, tptp_fun_R_2(Q!7, P!8)) = f1(true, true, false)),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1678])).
% 31.98/32.21 tff(1680,plain,
% 31.98/32.21 ((~![P: $i, Q: $i, R: $i] : (f1(P, Q, R) = lazy_impl(prop(R), impl(impl(P, impl(Q, R)), R)))) | (f1(true, true, tptp_fun_R_2(Q!7, P!8)) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(true, impl(true, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))))),
% 31.98/32.21 inference(quant_inst,[status(thm)],[])).
% 31.98/32.21 tff(1681,plain,
% 31.98/32.21 (f1(true, true, tptp_fun_R_2(Q!7, P!8)) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(true, impl(true, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1680, 1061])).
% 31.98/32.21 tff(1682,plain,
% 31.98/32.21 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(true, impl(true, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))) = f1(true, true, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.21 inference(symmetry,[status(thm)],[1681])).
% 31.98/32.21 tff(1683,plain,
% 31.98/32.21 (((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | ((~bool(tptp_fun_R_2(Q!7, P!8))) | (impl(false, tptp_fun_R_2(Q!7, P!8)) = true))) <=> ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | (~bool(tptp_fun_R_2(Q!7, P!8))) | (impl(false, tptp_fun_R_2(Q!7, P!8)) = true))),
% 31.98/32.21 inference(rewrite,[status(thm)],[])).
% 31.98/32.21 tff(1684,plain,
% 31.98/32.21 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | ((~bool(tptp_fun_R_2(Q!7, P!8))) | (impl(false, tptp_fun_R_2(Q!7, P!8)) = true))),
% 31.98/32.21 inference(quant_inst,[status(thm)],[])).
% 31.98/32.21 tff(1685,plain,
% 31.98/32.21 ((~![B: $i] : ((~bool(B)) | (impl(false, B) = true))) | (~bool(tptp_fun_R_2(Q!7, P!8))) | (impl(false, tptp_fun_R_2(Q!7, P!8)) = true)),
% 31.98/32.21 inference(modus_ponens,[status(thm)],[1684, 1683])).
% 31.98/32.21 tff(1686,plain,
% 31.98/32.21 ((~bool(tptp_fun_R_2(Q!7, P!8))) | (impl(false, tptp_fun_R_2(Q!7, P!8)) = true)),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1685, 695])).
% 31.98/32.21 tff(1687,plain,
% 31.98/32.21 (impl(false, tptp_fun_R_2(Q!7, P!8)) = true),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1686, 1597])).
% 31.98/32.21 tff(1688,plain,
% 31.98/32.21 (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = impl(false, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1674])).
% 31.98/32.21 tff(1689,plain,
% 31.98/32.21 (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = true),
% 31.98/32.21 inference(transitivity,[status(thm)],[1688, 1687])).
% 31.98/32.21 tff(1690,plain,
% 31.98/32.21 (impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = impl(true, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1689])).
% 31.98/32.21 tff(1691,plain,
% 31.98/32.21 (impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = tptp_fun_R_2(Q!7, P!8)),
% 31.98/32.21 inference(transitivity,[status(thm)],[1690, 1653])).
% 31.98/32.21 tff(1692,plain,
% 31.98/32.21 (impl(P!8, tptp_fun_R_2(Q!7, P!8)) = impl(true, impl(true, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.21 inference(transitivity,[status(thm)],[1193, 1657])).
% 31.98/32.21 tff(1693,plain,
% 31.98/32.21 (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = impl(impl(true, impl(true, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1692, 1691])).
% 31.98/32.21 tff(1694,plain,
% 31.98/32.21 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(true, impl(true, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1693])).
% 31.98/32.21 tff(1695,plain,
% 31.98/32.21 (f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)) = true),
% 31.98/32.21 inference(transitivity,[status(thm)],[41, 1694, 1682, 1679, 1549, 1547, 705, 221])).
% 31.98/32.21 tff(1696,plain,
% 31.98/32.21 (phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = phi(true)),
% 31.98/32.21 inference(monotonicity,[status(thm)],[1695])).
% 31.98/32.21 tff(1697,plain,
% 31.98/32.21 (phi(true) = phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.21 inference(symmetry,[status(thm)],[1696])).
% 31.98/32.21 tff(1698,plain,
% 31.98/32.21 (or1(P!8, Q!7) = or2(P!8, Q!7)),
% 31.98/32.21 inference(transitivity,[status(thm)],[668, 1608, 637, 1697, 576])).
% 31.98/32.21 tff(1699,plain,
% 31.98/32.21 ($false),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[377, 1698])).
% 31.98/32.21 tff(1700,plain,((~bool(Q!7)) | (~(P!8 = true))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.21 tff(1701,plain,
% 31.98/32.21 (~bool(Q!7)),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1700, 667])).
% 31.98/32.21 tff(1702,plain,
% 31.98/32.21 (~bool(impl(Q!7, true))),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1139, 1701])).
% 31.98/32.21 tff(1703,plain,
% 31.98/32.21 (impl(impl(Q!7, true), true) = phi(impl(Q!7, true))),
% 31.98/32.21 inference(unit_resolution,[status(thm)],[1144, 1702])).
% 31.98/32.21 tff(1704,plain,
% 31.98/32.21 (phi(impl(Q!7, true)) = impl(impl(Q!7, true), true)),
% 31.98/32.21 inference(symmetry,[status(thm)],[1703])).
% 31.98/32.21 tff(1705,plain,
% 31.98/32.21 (((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(Q!7, true)) | (impl(impl(Q!7, true), P!6) = phi(impl(Q!7, true))))) <=> ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(Q!7, true)) | (impl(impl(Q!7, true), P!6) = phi(impl(Q!7, true))))),
% 31.98/32.21 inference(rewrite,[status(thm)],[])).
% 31.98/32.21 tff(1706,plain,
% 31.98/32.21 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | (bool(impl(Q!7, true)) | (impl(impl(Q!7, true), P!6) = phi(impl(Q!7, true))))),
% 31.98/32.21 inference(quant_inst,[status(thm)],[])).
% 31.98/32.21 tff(1707,plain,
% 31.98/32.21 ((~![A: $i, B: $i] : (bool(A) | (impl(A, B) = phi(A)))) | bool(impl(Q!7, true)) | (impl(impl(Q!7, true), P!6) = phi(impl(Q!7, true)))),
% 31.98/32.21 inference(modus_ponens,[status(thm)],[1706, 1705])).
% 31.98/32.21 tff(1708,plain,
% 31.98/32.21 (bool(impl(Q!7, true)) | (impl(impl(Q!7, true), P!6) = phi(impl(Q!7, true)))),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[1707, 81])).
% 31.98/32.22 tff(1709,plain,
% 31.98/32.22 (impl(impl(Q!7, true), P!6) = phi(impl(Q!7, true))),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[1708, 1702])).
% 31.98/32.22 tff(1710,plain,
% 31.98/32.22 (impl(Q!7, impl(false, P!6)) = impl(Q!7, true)),
% 31.98/32.22 inference(monotonicity,[status(thm)],[818])).
% 31.98/32.22 tff(1711,plain,
% 31.98/32.22 (impl(impl(Q!7, impl(false, P!6)), P!6) = impl(impl(Q!7, true), P!6)),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1710])).
% 31.98/32.22 tff(1712,plain,
% 31.98/32.22 (impl(Q!7, true) = impl(Q!7, impl(false, P!6))),
% 31.98/32.22 inference(symmetry,[status(thm)],[1710])).
% 31.98/32.22 tff(1713,plain,
% 31.98/32.22 (impl(Q!7, impl(false, false)) = impl(Q!7, true)),
% 31.98/32.22 inference(monotonicity,[status(thm)],[811])).
% 31.98/32.22 tff(1714,plain,
% 31.98/32.22 (impl(Q!7, impl(false, false)) = impl(Q!7, impl(false, P!6))),
% 31.98/32.22 inference(transitivity,[status(thm)],[1713, 1712])).
% 31.98/32.22 tff(1715,plain,
% 31.98/32.22 (impl(impl(Q!7, impl(false, false)), false) = impl(impl(Q!7, impl(false, P!6)), P!6)),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1714, 919])).
% 31.98/32.22 tff(1716,plain,
% 31.98/32.22 (impl(impl(Q!7, impl(false, false)), false) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.22 inference(transitivity,[status(thm)],[1715, 1711, 1709, 1704, 1538, 1306])).
% 31.98/32.22 tff(1717,plain,
% 31.98/32.22 (lazy_impl(prop(false), impl(impl(Q!7, impl(false, false)), false)) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1396, 1716])).
% 31.98/32.22 tff(1718,plain,
% 31.98/32.22 (lazy_impl(true, impl(impl(Q!7, impl(false, false)), false)) = lazy_impl(prop(false), impl(impl(Q!7, impl(false, false)), false))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[930])).
% 31.98/32.22 tff(1719,plain,
% 31.98/32.22 ((~![B: $i] : (lazy_impl(true, B) = phi(B))) | (lazy_impl(true, impl(impl(Q!7, impl(false, false)), false)) = phi(impl(impl(Q!7, impl(false, false)), false)))),
% 31.98/32.22 inference(quant_inst,[status(thm)],[])).
% 31.98/32.22 tff(1720,plain,
% 31.98/32.22 (lazy_impl(true, impl(impl(Q!7, impl(false, false)), false)) = phi(impl(impl(Q!7, impl(false, false)), false))),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[1719, 325])).
% 31.98/32.22 tff(1721,plain,
% 31.98/32.22 (phi(impl(impl(Q!7, impl(false, false)), false)) = lazy_impl(true, impl(impl(Q!7, impl(false, false)), false))),
% 31.98/32.22 inference(symmetry,[status(thm)],[1720])).
% 31.98/32.22 tff(1722,plain,
% 31.98/32.22 (phi(impl(impl(Q!7, impl(false, false)), false)) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.22 inference(transitivity,[status(thm)],[1721, 1718, 1717, 965, 327, 1537])).
% 31.98/32.22 tff(1723,plain,
% 31.98/32.22 ((phi(impl(impl(Q!7, impl(false, false)), false)) = err) <=> (phi(impl(impl(Q!7, true), true)) = err)),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1722])).
% 31.98/32.22 tff(1724,plain,
% 31.98/32.22 ((phi(impl(impl(Q!7, true), true)) = err) <=> (phi(impl(impl(Q!7, impl(false, false)), false)) = err)),
% 31.98/32.22 inference(symmetry,[status(thm)],[1723])).
% 31.98/32.22 tff(1725,assumption,(~bool(impl(Q!7, true))), introduced(assumption)).
% 31.98/32.22 tff(1726,plain,
% 31.98/32.22 (impl(impl(Q!7, true), true) = phi(impl(Q!7, true))),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[1144, 1725])).
% 31.98/32.22 tff(1727,plain,
% 31.98/32.22 (phi(impl(Q!7, true)) = impl(impl(Q!7, true), true)),
% 31.98/32.22 inference(symmetry,[status(thm)],[1726])).
% 31.98/32.22 tff(1728,plain,
% 31.98/32.22 (phi(impl(Q!7, true)) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.22 inference(transitivity,[status(thm)],[1727, 1538, 1306, 1045])).
% 31.98/32.22 tff(1729,plain,
% 31.98/32.22 ((phi(impl(Q!7, true)) = err) <=> (phi(impl(impl(Q!7, true), true)) = err)),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1728])).
% 31.98/32.22 tff(1730,plain,
% 31.98/32.22 ((phi(impl(impl(Q!7, true), true)) = err) <=> (phi(impl(Q!7, true)) = err)),
% 31.98/32.22 inference(symmetry,[status(thm)],[1729])).
% 31.98/32.22 tff(1731,plain,
% 31.98/32.22 ((~(phi(impl(impl(Q!7, true), true)) = err)) <=> (~(phi(impl(Q!7, true)) = err))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1730])).
% 31.98/32.22 tff(1732,assumption,(~(phi(impl(impl(Q!7, true), true)) = err)), introduced(assumption)).
% 31.98/32.22 tff(1733,plain,
% 31.98/32.22 (~(phi(impl(Q!7, true)) = err)),
% 31.98/32.22 inference(modus_ponens,[status(thm)],[1732, 1731])).
% 31.98/32.22 tff(1734,plain,
% 31.98/32.22 (d(impl(Q!7, true)) | (~(phi(impl(Q!7, true)) = err))),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[1159, 1733])).
% 31.98/32.22 tff(1735,plain,
% 31.98/32.22 (~((~d(impl(Q!7, true))) | (~(phi(impl(Q!7, true)) = impl(Q!7, true))))),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[1164, 1734])).
% 31.98/32.22 tff(1736,plain,
% 31.98/32.22 (phi(impl(Q!7, true)) = impl(Q!7, true)),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[1166, 1735])).
% 31.98/32.22 tff(1737,plain,
% 31.98/32.22 (impl(Q!7, true) = phi(impl(Q!7, true))),
% 31.98/32.22 inference(symmetry,[status(thm)],[1736])).
% 31.98/32.22 tff(1738,plain,
% 31.98/32.22 (impl(Q!7, true) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.22 inference(transitivity,[status(thm)],[1737, 1727, 1538, 1306])).
% 31.98/32.22 tff(1739,plain,
% 31.98/32.22 (bool(impl(Q!7, true)) <=> bool(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1738])).
% 31.98/32.22 tff(1740,plain,
% 31.98/32.22 (bool(impl(impl(P!8, true), impl(impl(Q!7, true), true))) <=> bool(impl(Q!7, true))),
% 31.98/32.22 inference(symmetry,[status(thm)],[1739])).
% 31.98/32.22 tff(1741,plain,
% 31.98/32.22 (bool(impl(impl(P!8, true), impl(impl(Q!7, true), true))) <=> bool(impl(impl(Q!7, true), true))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1536])).
% 31.98/32.22 tff(1742,plain,
% 31.98/32.22 (bool(impl(impl(Q!7, true), true)) <=> bool(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.22 inference(symmetry,[status(thm)],[1741])).
% 31.98/32.22 tff(1743,plain,
% 31.98/32.22 (bool(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.22 inference(modus_ponens,[status(thm)],[1533, 1742])).
% 31.98/32.22 tff(1744,plain,
% 31.98/32.22 (bool(impl(Q!7, true))),
% 31.98/32.22 inference(modus_ponens,[status(thm)],[1743, 1740])).
% 31.98/32.22 tff(1745,plain,
% 31.98/32.22 ($false),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[1725, 1744])).
% 31.98/32.22 tff(1746,plain,(bool(impl(Q!7, true)) | (~(P!8 = true)) | (phi(impl(impl(Q!7, true), true)) = err)), inference(lemma,lemma(discharge,[]))).
% 31.98/32.22 tff(1747,plain,
% 31.98/32.22 (phi(impl(impl(Q!7, true), true)) = err),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[1746, 1702, 667])).
% 31.98/32.22 tff(1748,plain,
% 31.98/32.22 (phi(impl(impl(Q!7, impl(false, false)), false)) = err),
% 31.98/32.22 inference(modus_ponens,[status(thm)],[1747, 1724])).
% 31.98/32.22 tff(1749,plain,
% 31.98/32.22 (lazy_impl(prop(false), impl(impl(Q!7, impl(false, false)), false)) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.22 inference(transitivity,[status(thm)],[1717, 965, 327, 1537, 1180])).
% 31.98/32.22 tff(1750,plain,
% 31.98/32.22 (bool(lazy_impl(prop(false), impl(impl(Q!7, impl(false, false)), false))) <=> bool(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1749])).
% 31.98/32.22 tff(1751,plain,
% 31.98/32.22 (bool(impl(impl(P!8, true), impl(impl(Q!7, true), true))) <=> bool(lazy_impl(prop(false), impl(impl(Q!7, impl(false, false)), false)))),
% 31.98/32.22 inference(symmetry,[status(thm)],[1750])).
% 31.98/32.22 tff(1752,plain,
% 31.98/32.22 (bool(lazy_impl(prop(false), impl(impl(Q!7, impl(false, false)), false)))),
% 31.98/32.22 inference(modus_ponens,[status(thm)],[1743, 1751])).
% 31.98/32.22 tff(1753,assumption,(phi(impl(impl(Q!7, impl(false, false)), false)) = err), introduced(assumption)).
% 31.98/32.22 tff(1754,plain,
% 31.98/32.22 (lazy_impl(prop(false), impl(impl(Q!7, impl(false, false)), false)) = lazy_impl(true, impl(impl(Q!7, impl(false, false)), false))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[759])).
% 31.98/32.22 tff(1755,plain,
% 31.98/32.22 (lazy_impl(prop(false), impl(impl(Q!7, impl(false, false)), false)) = err),
% 31.98/32.22 inference(transitivity,[status(thm)],[1754, 1720, 1753])).
% 31.98/32.22 tff(1756,plain,
% 31.98/32.22 (bool(lazy_impl(prop(false), impl(impl(Q!7, impl(false, false)), false))) <=> bool(err)),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1755])).
% 31.98/32.22 tff(1757,plain,
% 31.98/32.22 (bool(err) <=> bool(lazy_impl(prop(false), impl(impl(Q!7, impl(false, false)), false)))),
% 31.98/32.22 inference(symmetry,[status(thm)],[1756])).
% 31.98/32.22 tff(1758,plain,
% 31.98/32.22 ((~bool(err)) <=> (~bool(lazy_impl(prop(false), impl(impl(Q!7, impl(false, false)), false))))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1757])).
% 31.98/32.22 tff(1759,plain,
% 31.98/32.22 (~bool(lazy_impl(prop(false), impl(impl(Q!7, impl(false, false)), false)))),
% 31.98/32.22 inference(modus_ponens,[status(thm)],[999, 1758])).
% 31.98/32.22 tff(1760,assumption,(bool(lazy_impl(prop(false), impl(impl(Q!7, impl(false, false)), false)))), introduced(assumption)).
% 31.98/32.22 tff(1761,plain,
% 31.98/32.22 ($false),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[1760, 1759])).
% 31.98/32.22 tff(1762,plain,((~(phi(impl(impl(Q!7, impl(false, false)), false)) = err)) | (~bool(lazy_impl(prop(false), impl(impl(Q!7, impl(false, false)), false))))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.22 tff(1763,plain,
% 31.98/32.22 ($false),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[1762, 1752, 1748])).
% 31.98/32.22 tff(1764,plain,(~(P!8 = true)), inference(lemma,lemma(discharge,[]))).
% 31.98/32.22 tff(1765,plain,
% 31.98/32.22 (P!8 = false),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[677, 1764])).
% 31.98/32.22 tff(1766,plain,
% 31.98/32.22 (impl(P!8, true) = impl(false, true)),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1765])).
% 31.98/32.22 tff(1767,plain,
% 31.98/32.22 (impl(P!8, true) = true),
% 31.98/32.22 inference(transitivity,[status(thm)],[1766, 699])).
% 31.98/32.22 tff(1768,plain,
% 31.98/32.22 (bool(impl(P!8, true)) <=> bool(true)),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1767])).
% 31.98/32.22 tff(1769,plain,
% 31.98/32.22 (bool(true) <=> bool(impl(P!8, true))),
% 31.98/32.22 inference(symmetry,[status(thm)],[1768])).
% 31.98/32.22 tff(1770,plain,
% 31.98/32.22 (bool(impl(P!8, true))),
% 31.98/32.22 inference(modus_ponens,[status(thm)],[247, 1769])).
% 31.98/32.22 tff(1771,plain,
% 31.98/32.22 (bool(impl(impl(Q!7, true), true)) | (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true)))),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[869, 1770])).
% 31.98/32.22 tff(1772,plain,
% 31.98/32.22 (bool(impl(impl(Q!7, true), true))),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[1771, 831])).
% 31.98/32.22 tff(1773,plain,
% 31.98/32.22 (impl(true, impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[874, 1772])).
% 31.98/32.22 tff(1774,plain,
% 31.98/32.22 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = impl(true, impl(impl(Q!7, true), true))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1767])).
% 31.98/32.22 tff(1775,plain,
% 31.98/32.22 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)),
% 31.98/32.22 inference(transitivity,[status(thm)],[1774, 1773])).
% 31.98/32.22 tff(1776,plain,
% 31.98/32.22 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = impl(impl(Q!7, impl(false, true)), true)),
% 31.98/32.22 inference(transitivity,[status(thm)],[1774, 1773, 703])).
% 31.98/32.22 tff(1777,plain,
% 31.98/32.22 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1776])).
% 31.98/32.22 tff(1778,plain,
% 31.98/32.22 (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.22 inference(transitivity,[status(thm)],[328, 318, 1777, 1553, 685])).
% 31.98/32.22 tff(1779,plain,
% 31.98/32.22 ((phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true))) <=> (phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1778, 1775])).
% 31.98/32.22 tff(1780,plain,
% 31.98/32.22 ((phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)) <=> (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.22 inference(symmetry,[status(thm)],[1779])).
% 31.98/32.22 tff(1781,plain,
% 31.98/32.22 ((~(phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))) <=> (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1780])).
% 31.98/32.22 tff(1782,plain,
% 31.98/32.22 ((phi(impl(impl(Q!7, true), true)) = impl(impl(P!8, true), impl(impl(Q!7, true), true))) <=> (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true)))),
% 31.98/32.22 inference(commutativity,[status(thm)],[])).
% 31.98/32.22 tff(1783,plain,
% 31.98/32.22 (impl(true, impl(impl(Q!7, true), true)) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.22 inference(symmetry,[status(thm)],[1774])).
% 31.98/32.22 tff(1784,plain,
% 31.98/32.22 (impl(impl(Q!7, true), true) = impl(true, impl(impl(Q!7, true), true))),
% 31.98/32.22 inference(symmetry,[status(thm)],[1773])).
% 31.98/32.22 tff(1785,plain,
% 31.98/32.22 (impl(impl(Q!7, true), true) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.22 inference(transitivity,[status(thm)],[1784, 1783])).
% 31.98/32.22 tff(1786,plain,
% 31.98/32.22 ((phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)) <=> (phi(impl(impl(Q!7, true), true)) = impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1785])).
% 31.98/32.22 tff(1787,plain,
% 31.98/32.22 ((phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)) <=> (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true)))),
% 31.98/32.22 inference(transitivity,[status(thm)],[1786, 1782])).
% 31.98/32.22 tff(1788,plain,
% 31.98/32.22 ((impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true))) <=> (phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))),
% 31.98/32.22 inference(symmetry,[status(thm)],[1787])).
% 31.98/32.22 tff(1789,plain,
% 31.98/32.22 ((~(impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true)))) <=> (~(phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1788])).
% 31.98/32.22 tff(1790,plain,
% 31.98/32.22 (~(phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))),
% 31.98/32.22 inference(modus_ponens,[status(thm)],[831, 1789])).
% 31.98/32.22 tff(1791,plain,
% 31.98/32.22 (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.22 inference(modus_ponens,[status(thm)],[1790, 1781])).
% 31.98/32.22 tff(1792,plain,
% 31.98/32.22 ($false),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[1035, 1791])).
% 31.98/32.22 tff(1793,plain,(impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.22 tff(1794,plain,
% 31.98/32.22 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = impl(impl(impl(Q!7, true), impl(false, false)), false)),
% 31.98/32.22 inference(transitivity,[status(thm)],[1793, 830, 823, 821])).
% 31.98/32.22 tff(1795,plain,
% 31.98/32.22 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = lazy_impl(prop(false), impl(impl(impl(Q!7, true), impl(false, false)), false))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[931, 1794])).
% 31.98/32.22 tff(1796,plain,
% 31.98/32.22 (lazy_impl(prop(false), impl(impl(impl(Q!7, true), impl(false, false)), false)) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.22 inference(symmetry,[status(thm)],[1795])).
% 31.98/32.22 tff(1797,plain,
% 31.98/32.22 ((lazy_impl(prop(false), impl(impl(impl(Q!7, true), impl(false, false)), false)) = true) <=> (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true)),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1796])).
% 31.98/32.22 tff(1798,plain,
% 31.98/32.22 ((lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true) <=> (lazy_impl(prop(false), impl(impl(impl(Q!7, true), impl(false, false)), false)) = true)),
% 31.98/32.22 inference(symmetry,[status(thm)],[1797])).
% 31.98/32.22 tff(1799,assumption,(P!8 = false), introduced(assumption)).
% 31.98/32.22 tff(1800,plain,
% 31.98/32.22 (impl(P!8, true) = impl(false, true)),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1799])).
% 31.98/32.22 tff(1801,plain,
% 31.98/32.22 (impl(P!8, true) = true),
% 31.98/32.22 inference(transitivity,[status(thm)],[1800, 699])).
% 31.98/32.22 tff(1802,plain,
% 31.98/32.22 (bool(impl(P!8, true)) <=> bool(true)),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1801])).
% 31.98/32.22 tff(1803,plain,
% 31.98/32.22 (bool(true) <=> bool(impl(P!8, true))),
% 31.98/32.22 inference(symmetry,[status(thm)],[1802])).
% 31.98/32.22 tff(1804,plain,
% 31.98/32.22 (bool(impl(P!8, true))),
% 31.98/32.22 inference(modus_ponens,[status(thm)],[247, 1803])).
% 31.98/32.22 tff(1805,plain,
% 31.98/32.22 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[869, 824, 1804])).
% 31.98/32.22 tff(1806,plain,
% 31.98/32.22 (phi(impl(impl(Q!7, true), true)) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.22 inference(symmetry,[status(thm)],[1805])).
% 31.98/32.22 tff(1807,plain,
% 31.98/32.22 (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.22 inference(transitivity,[status(thm)],[1035, 1805])).
% 31.98/32.22 tff(1808,plain,
% 31.98/32.22 ((phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err) <=> (phi(impl(impl(Q!7, true), true)) = err)),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1807])).
% 31.98/32.22 tff(1809,plain,
% 31.98/32.22 ((~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)) <=> (~(phi(impl(impl(Q!7, true), true)) = err))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1808])).
% 31.98/32.22 tff(1810,plain,
% 31.98/32.22 (~(phi(impl(impl(Q!7, true), true)) = err)),
% 31.98/32.22 inference(modus_ponens,[status(thm)],[1222, 1809])).
% 31.98/32.22 tff(1811,plain,
% 31.98/32.22 (d(impl(impl(Q!7, true), true)) | (~(phi(impl(impl(Q!7, true), true)) = err))),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[909, 1810])).
% 31.98/32.22 tff(1812,plain,
% 31.98/32.22 (~((~d(impl(impl(Q!7, true), true))) | (~(phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))))),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[914, 1811])).
% 31.98/32.22 tff(1813,plain,
% 31.98/32.22 (phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[916, 1812])).
% 31.98/32.22 tff(1814,plain,
% 31.98/32.22 (impl(impl(Q!7, true), true) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.22 inference(symmetry,[status(thm)],[1813])).
% 31.98/32.22 tff(1815,plain,
% 31.98/32.22 (impl(impl(Q!7, true), true) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.22 inference(transitivity,[status(thm)],[1814, 1806, 1302, 328, 966])).
% 31.98/32.22 tff(1816,plain,
% 31.98/32.22 ((impl(impl(Q!7, true), true) = true) <=> (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true)),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1815])).
% 31.98/32.22 tff(1817,plain,
% 31.98/32.22 ((~(impl(impl(Q!7, true), true) = true)) <=> (~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1816])).
% 31.98/32.22 tff(1818,plain,
% 31.98/32.22 (~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true)),
% 31.98/32.22 inference(modus_ponens,[status(thm)],[1530, 1817])).
% 31.98/32.22 tff(1819,plain,
% 31.98/32.22 (~(Q!7 = true)),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[1075, 1818, 1805])).
% 31.98/32.22 tff(1820,plain,
% 31.98/32.22 (~(Q!7 = false)),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[1092, 1818, 1805])).
% 31.98/32.22 tff(1821,plain,
% 31.98/32.22 (~((Q!7 = false) | (Q!7 = true))),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[633, 1820, 1819])).
% 31.98/32.22 tff(1822,plain,
% 31.98/32.22 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.22 inference(transitivity,[status(thm)],[1302, 328, 966])).
% 31.98/32.22 tff(1823,plain,
% 31.98/32.22 (d(impl(impl(P!8, true), impl(impl(Q!7, true), true))) <=> d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1822])).
% 31.98/32.22 tff(1824,plain,
% 31.98/32.22 (d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.98/32.22 inference(modus_ponens,[status(thm)],[1226, 1823])).
% 31.98/32.22 tff(1825,plain,
% 31.98/32.22 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = impl(impl(impl(Q!7, true), impl(false, false)), false)),
% 31.98/32.22 inference(transitivity,[status(thm)],[965, 327, 1035, 1805, 830, 823, 821])).
% 31.98/32.22 tff(1826,plain,
% 31.98/32.22 (bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))) <=> bool(impl(impl(impl(Q!7, true), impl(false, false)), false))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1825])).
% 31.98/32.22 tff(1827,plain,
% 31.98/32.22 (bool(impl(impl(impl(Q!7, true), impl(false, false)), false)) <=> bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.98/32.22 inference(symmetry,[status(thm)],[1826])).
% 31.98/32.22 tff(1828,plain,
% 31.98/32.22 (impl(impl(Q!7, true), true) = impl(impl(impl(Q!7, true), impl(false, false)), false)),
% 31.98/32.22 inference(transitivity,[status(thm)],[1814, 830, 823, 821])).
% 31.98/32.22 tff(1829,plain,
% 31.98/32.22 (bool(impl(impl(Q!7, true), true)) <=> bool(impl(impl(impl(Q!7, true), impl(false, false)), false))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1828])).
% 31.98/32.22 tff(1830,plain,
% 31.98/32.22 (bool(impl(impl(Q!7, true), true)) <=> bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.98/32.22 inference(transitivity,[status(thm)],[1829, 1827])).
% 31.98/32.22 tff(1831,plain,
% 31.98/32.22 ((~bool(impl(impl(Q!7, true), true))) <=> (~bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1830])).
% 31.98/32.22 tff(1832,plain,
% 31.98/32.22 (~bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 31.98/32.22 inference(modus_ponens,[status(thm)],[824, 1831])).
% 31.98/32.22 tff(1833,plain,
% 31.98/32.22 (~(prop(tptp_fun_R_2(Q!7, P!8)) = false)),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[1294, 1832, 1824])).
% 31.98/32.22 tff(1834,plain,
% 31.98/32.22 (bool(tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[447, 1833])).
% 31.98/32.22 tff(1835,plain,
% 31.98/32.22 (prop(tptp_fun_R_2(Q!7, P!8)) = true),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[452, 1834])).
% 31.98/32.22 tff(1836,plain,
% 31.98/32.22 (impl(false, tptp_fun_R_2(Q!7, P!8)) = true),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[1686, 1834])).
% 31.98/32.22 tff(1837,plain,
% 31.98/32.22 (or1(P!8, Q!7) = phi(Q!7)),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[682, 1820])).
% 31.98/32.22 tff(1838,plain,
% 31.98/32.22 (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = phi(Q!7)),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[1105, 1110])).
% 31.98/32.22 tff(1839,plain,
% 31.98/32.22 (phi(Q!7) = impl(Q!7, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.22 inference(symmetry,[status(thm)],[1838])).
% 31.98/32.22 tff(1840,plain,
% 31.98/32.22 (impl(Q!7, true) = impl(Q!7, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.22 inference(transitivity,[status(thm)],[1111, 1839])).
% 31.98/32.22 tff(1841,plain,
% 31.98/32.22 (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = impl(Q!7, true)),
% 31.98/32.22 inference(transitivity,[status(thm)],[1838, 1112])).
% 31.98/32.22 tff(1842,plain,
% 31.98/32.22 (phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = phi(impl(Q!7, true))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1841])).
% 31.98/32.22 tff(1843,plain,
% 31.98/32.22 (phi(impl(Q!7, true)) = phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.22 inference(symmetry,[status(thm)],[1842])).
% 31.98/32.22 tff(1844,plain,
% 31.98/32.22 ((phi(impl(Q!7, true)) = impl(Q!7, true)) <=> (phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1843, 1840])).
% 31.98/32.22 tff(1845,plain,
% 31.98/32.22 ((phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8))) <=> (phi(impl(Q!7, true)) = impl(Q!7, true))),
% 31.98/32.22 inference(symmetry,[status(thm)],[1844])).
% 31.98/32.22 tff(1846,plain,
% 31.98/32.22 ((~(phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8)))) <=> (~(phi(impl(Q!7, true)) = impl(Q!7, true)))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1845])).
% 31.98/32.22 tff(1847,plain,
% 31.98/32.22 (~bool(impl(Q!7, true))),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[1139, 1110])).
% 31.98/32.22 tff(1848,plain,
% 31.98/32.22 (impl(impl(Q!7, true), true) = phi(impl(Q!7, true))),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[1144, 1847])).
% 31.98/32.22 tff(1849,plain,
% 31.98/32.22 (d(impl(impl(Q!7, true), true)) | (~(phi(impl(impl(Q!7, true), true)) = err))),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[909, 1732])).
% 31.98/32.22 tff(1850,plain,
% 31.98/32.22 (~((~d(impl(impl(Q!7, true), true))) | (~(phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))))),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[914, 1849])).
% 31.98/32.22 tff(1851,plain,
% 31.98/32.22 (phi(impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[916, 1850])).
% 31.98/32.22 tff(1852,plain,
% 31.98/32.22 (impl(impl(impl(Q!7, true), impl(false, P!6)), P!6) = impl(impl(impl(Q!7, true), true), P!6)),
% 31.98/32.22 inference(symmetry,[status(thm)],[823])).
% 31.98/32.22 tff(1853,plain,
% 31.98/32.22 (impl(impl(impl(Q!7, true), impl(false, false)), false) = impl(impl(impl(Q!7, true), impl(false, P!6)), P!6)),
% 31.98/32.22 inference(symmetry,[status(thm)],[821])).
% 31.98/32.22 tff(1854,plain,
% 31.98/32.22 (impl(impl(impl(Q!7, true), impl(false, false)), false) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.22 inference(transitivity,[status(thm)],[1853, 1852, 1391, 1394])).
% 31.98/32.22 tff(1855,plain,
% 31.98/32.22 (lazy_impl(prop(false), impl(impl(impl(Q!7, true), impl(false, false)), false)) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1396, 1854])).
% 31.98/32.22 tff(1856,plain,
% 31.98/32.22 (phi(impl(impl(Q!7, true), true)) = impl(impl(impl(Q!7, true), true), P!6)),
% 31.98/32.22 inference(symmetry,[status(thm)],[1391])).
% 31.98/32.22 tff(1857,plain,
% 31.98/32.22 (impl(false, true) = impl(P!8, true)),
% 31.98/32.22 inference(symmetry,[status(thm)],[1800])).
% 31.98/32.22 tff(1858,plain,
% 31.98/32.22 (true = impl(false, true)),
% 31.98/32.22 inference(symmetry,[status(thm)],[699])).
% 31.98/32.22 tff(1859,plain,
% 31.98/32.22 (true = impl(P!8, true)),
% 31.98/32.22 inference(transitivity,[status(thm)],[1858, 1857])).
% 31.98/32.22 tff(1860,plain,
% 31.98/32.22 (impl(true, impl(impl(Q!7, true), true)) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 31.98/32.22 inference(monotonicity,[status(thm)],[1859])).
% 31.98/32.22 tff(1861,plain,
% 31.98/32.22 (phi(impl(Q!7, true)) = impl(impl(Q!7, true), true)),
% 31.98/32.22 inference(symmetry,[status(thm)],[1848])).
% 31.98/32.22 tff(1862,plain,
% 31.98/32.22 (bool(impl(Q!7, true)) | (impl(impl(Q!7, true), tptp_fun_R_2(Q!7, P!8)) = phi(impl(Q!7, true)))),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[1184, 81])).
% 31.98/32.22 tff(1863,plain,
% 31.98/32.22 (impl(impl(Q!7, true), tptp_fun_R_2(Q!7, P!8)) = phi(impl(Q!7, true))),
% 31.98/32.22 inference(unit_resolution,[status(thm)],[1862, 1847])).
% 31.98/32.23 tff(1864,plain,
% 31.98/32.23 (impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = impl(impl(Q!7, true), tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.23 inference(monotonicity,[status(thm)],[1841])).
% 31.98/32.23 tff(1865,plain,
% 31.98/32.23 (impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = impl(impl(Q!7, true), true)),
% 31.98/32.23 inference(transitivity,[status(thm)],[1864, 1863, 1861])).
% 31.98/32.23 tff(1866,assumption,(impl(false, tptp_fun_R_2(Q!7, P!8)) = true), introduced(assumption)).
% 31.98/32.23 tff(1867,plain,
% 31.98/32.23 (impl(P!8, tptp_fun_R_2(Q!7, P!8)) = impl(false, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.23 inference(monotonicity,[status(thm)],[1799])).
% 31.98/32.23 tff(1868,plain,
% 31.98/32.23 (impl(P!8, tptp_fun_R_2(Q!7, P!8)) = true),
% 31.98/32.23 inference(transitivity,[status(thm)],[1867, 1866])).
% 31.98/32.23 tff(1869,plain,
% 31.98/32.23 (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = impl(true, impl(impl(Q!7, true), true))),
% 31.98/32.23 inference(monotonicity,[status(thm)],[1868, 1865])).
% 31.98/32.23 tff(1870,plain,
% 31.98/32.23 (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = impl(impl(impl(Q!7, true), impl(false, false)), false)),
% 31.98/32.23 inference(transitivity,[status(thm)],[1869, 1860, 1072, 1856, 823, 821])).
% 31.98/32.23 tff(1871,plain,
% 31.98/32.23 (prop(tptp_fun_R_2(Q!7, P!8)) = prop(false)),
% 31.98/32.23 inference(transitivity,[status(thm)],[459, 930])).
% 31.98/32.23 tff(1872,plain,
% 31.98/32.23 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = lazy_impl(prop(false), impl(impl(impl(Q!7, true), impl(false, false)), false))),
% 31.98/32.23 inference(monotonicity,[status(thm)],[1871, 1870])).
% 31.98/32.23 tff(1873,plain,
% 31.98/32.23 (f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)) = impl(impl(impl(Q!7, true), impl(false, false)), false)),
% 31.98/32.23 inference(transitivity,[status(thm)],[41, 1872, 1855, 965, 327, 1035, 1072, 1856, 823, 821])).
% 31.98/32.23 tff(1874,plain,
% 31.98/32.23 (phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = phi(impl(impl(impl(Q!7, true), impl(false, false)), false))),
% 31.98/32.23 inference(monotonicity,[status(thm)],[1873])).
% 31.98/32.23 tff(1875,plain,
% 31.98/32.23 (or2(P!8, Q!7) = phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.23 inference(transitivity,[status(thm)],[365, 1874, 1405, 1392, 1855, 965, 327, 1035, 1072, 1851, 1848, 1843])).
% 31.98/32.23 tff(1876,plain,
% 31.98/32.23 (or1(P!8, Q!7) = impl(Q!7, tptp_fun_R_2(Q!7, P!8))),
% 31.98/32.23 inference(transitivity,[status(thm)],[1380, 1839])).
% 31.98/32.23 tff(1877,plain,
% 31.98/32.23 ((or1(P!8, Q!7) = or2(P!8, Q!7)) <=> (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))))),
% 31.98/32.23 inference(monotonicity,[status(thm)],[1876, 1875])).
% 31.98/32.23 tff(1878,plain,
% 31.98/32.23 ((or1(P!8, Q!7) = or2(P!8, Q!7)) <=> (phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.23 inference(transitivity,[status(thm)],[1877, 832])).
% 31.98/32.23 tff(1879,plain,
% 31.98/32.23 ((~(or1(P!8, Q!7) = or2(P!8, Q!7))) <=> (~(phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8))))),
% 31.98/32.23 inference(monotonicity,[status(thm)],[1878])).
% 31.98/32.23 tff(1880,plain,
% 31.98/32.23 (~(phi(impl(Q!7, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 31.98/32.23 inference(modus_ponens,[status(thm)],[377, 1879])).
% 31.98/32.23 tff(1881,plain,
% 31.98/32.23 (~(phi(impl(Q!7, true)) = impl(Q!7, true))),
% 31.98/32.23 inference(modus_ponens,[status(thm)],[1880, 1846])).
% 31.98/32.23 tff(1882,plain,
% 31.98/32.23 ((~d(impl(Q!7, true))) | (~(phi(impl(Q!7, true)) = impl(Q!7, true)))),
% 31.98/32.23 inference(unit_resolution,[status(thm)],[1166, 1881])).
% 31.98/32.23 tff(1883,plain,
% 31.98/32.23 (impl(impl(Q!7, true), true) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.23 inference(symmetry,[status(thm)],[1851])).
% 31.98/32.23 tff(1884,plain,
% 31.98/32.23 (phi(impl(Q!7, true)) = phi(impl(impl(Q!7, true), true))),
% 31.98/32.23 inference(transitivity,[status(thm)],[1861, 1883])).
% 31.98/32.23 tff(1885,plain,
% 31.98/32.23 ((phi(impl(Q!7, true)) = err) <=> (phi(impl(impl(Q!7, true), true)) = err)),
% 31.98/32.23 inference(monotonicity,[status(thm)],[1884])).
% 31.98/32.23 tff(1886,plain,
% 31.98/32.23 ((phi(impl(impl(Q!7, true), true)) = err) <=> (phi(impl(Q!7, true)) = err)),
% 31.98/32.23 inference(symmetry,[status(thm)],[1885])).
% 31.98/32.23 tff(1887,plain,
% 31.98/32.23 ((~(phi(impl(impl(Q!7, true), true)) = err)) <=> (~(phi(impl(Q!7, true)) = err))),
% 31.98/32.23 inference(monotonicity,[status(thm)],[1886])).
% 31.98/32.23 tff(1888,plain,
% 31.98/32.23 (~(phi(impl(Q!7, true)) = err)),
% 31.98/32.23 inference(modus_ponens,[status(thm)],[1732, 1887])).
% 31.98/32.23 tff(1889,plain,
% 31.98/32.23 (d(impl(Q!7, true)) | (~(phi(impl(Q!7, true)) = err))),
% 31.98/32.23 inference(unit_resolution,[status(thm)],[1159, 1888])).
% 31.98/32.23 tff(1890,plain,
% 31.98/32.23 ($false),
% 31.98/32.23 inference(unit_resolution,[status(thm)],[1164, 1889, 1882])).
% 31.98/32.23 tff(1891,plain,(bool(Q!7) | (phi(impl(impl(Q!7, true), true)) = err) | (~(impl(impl(P!8, true), impl(impl(Q!7, true), true)) = phi(impl(impl(Q!7, true), true)))) | (~(impl(impl(impl(Q!7, true), true), P!6) = phi(impl(impl(Q!7, true), true)))) | (~(P!8 = false)) | (~(impl(false, tptp_fun_R_2(Q!7, P!8)) = true)) | (~(prop(tptp_fun_R_2(Q!7, P!8)) = true)) | (~(or1(P!8, Q!7) = phi(Q!7)))), inference(lemma,lemma(discharge,[]))).
% 31.98/32.23 tff(1892,plain,
% 31.98/32.23 (bool(Q!7)),
% 31.98/32.23 inference(unit_resolution,[status(thm)],[1891, 1837, 1805, 829, 1799, 1836, 1835, 1810])).
% 31.98/32.23 tff(1893,plain,
% 31.98/32.23 ($false),
% 31.98/32.23 inference(unit_resolution,[status(thm)],[631, 1892, 1821])).
% 31.98/32.23 tff(1894,plain,(bool(impl(impl(Q!7, true), true)) | (~(P!8 = false)) | (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)), inference(lemma,lemma(discharge,[]))).
% 31.98/32.23 tff(1895,plain,
% 31.98/32.23 (bool(impl(impl(Q!7, true), true)) | (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)),
% 31.98/32.23 inference(unit_resolution,[status(thm)],[1894, 1765])).
% 31.98/32.23 tff(1896,plain,
% 31.98/32.23 (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err),
% 31.98/32.23 inference(unit_resolution,[status(thm)],[1895, 824])).
% 31.98/32.23 tff(1897,plain,
% 31.98/32.23 (impl(Q!7, true) = impl(false, true)),
% 31.98/32.23 inference(monotonicity,[status(thm)],[1086])).
% 31.98/32.23 tff(1898,plain,
% 31.98/32.23 (impl(Q!7, true) = true),
% 31.98/32.23 inference(transitivity,[status(thm)],[1897, 699])).
% 31.98/32.23 tff(1899,plain,
% 31.98/32.23 (impl(impl(Q!7, true), true) = impl(true, true)),
% 31.98/32.23 inference(monotonicity,[status(thm)],[1898])).
% 31.98/32.23 tff(1900,plain,
% 31.98/32.23 (impl(impl(Q!7, true), true) = true),
% 31.98/32.23 inference(transitivity,[status(thm)],[1899, 847])).
% 31.98/32.23 tff(1901,assumption,(~(impl(impl(Q!7, true), true) = true)), introduced(assumption)).
% 31.98/32.23 tff(1902,plain,
% 31.98/32.23 ($false),
% 31.98/32.23 inference(unit_resolution,[status(thm)],[1901, 1900])).
% 31.98/32.23 tff(1903,plain,((~(Q!7 = false)) | (impl(impl(Q!7, true), true) = true)), inference(lemma,lemma(discharge,[]))).
% 31.98/32.23 tff(1904,plain,
% 31.98/32.23 (~(Q!7 = false)),
% 31.98/32.23 inference(unit_resolution,[status(thm)],[1903, 1530])).
% 31.98/32.23 tff(1905,plain,
% 31.98/32.23 (or1(P!8, Q!7) = phi(Q!7)),
% 31.98/32.23 inference(unit_resolution,[status(thm)],[682, 1904])).
% 31.98/32.23 tff(1906,plain,
% 31.98/32.23 (impl(Q!7, true) = impl(true, true)),
% 31.98/32.23 inference(monotonicity,[status(thm)],[1064])).
% 31.98/32.23 tff(1907,plain,
% 31.98/32.23 (impl(Q!7, true) = true),
% 31.98/32.23 inference(transitivity,[status(thm)],[1906, 847])).
% 31.98/32.23 tff(1908,plain,
% 31.98/32.23 (impl(impl(Q!7, true), true) = impl(true, true)),
% 31.98/32.23 inference(monotonicity,[status(thm)],[1907])).
% 31.98/32.23 tff(1909,plain,
% 31.98/32.23 (impl(impl(Q!7, true), true) = true),
% 31.98/32.23 inference(transitivity,[status(thm)],[1908, 847])).
% 31.98/32.23 tff(1910,plain,
% 31.98/32.23 (impl(true, impl(impl(Q!7, true), true)) = impl(true, true)),
% 31.98/32.23 inference(monotonicity,[status(thm)],[1909])).
% 31.98/32.23 tff(1911,plain,
% 31.98/32.23 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = impl(true, impl(impl(Q!7, true), true))),
% 31.98/32.23 inference(monotonicity,[status(thm)],[1801])).
% 31.98/32.23 tff(1912,plain,
% 31.98/32.23 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = true),
% 31.98/32.23 inference(transitivity,[status(thm)],[1911, 1910, 847])).
% 31.98/32.23 tff(1913,plain,
% 31.98/32.23 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = lazy_impl(true, true)),
% 31.98/32.23 inference(monotonicity,[status(thm)],[316, 1912])).
% 31.98/32.23 tff(1914,plain,
% 31.98/32.23 (lazy_impl(true, true) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 31.98/32.23 inference(symmetry,[status(thm)],[1913])).
% 31.98/32.23 tff(1915,plain,
% 31.98/32.23 (phi(true) = lazy_impl(true, true)),
% 31.98/32.23 inference(symmetry,[status(thm)],[705])).
% 31.98/32.23 tff(1916,plain,
% 31.98/32.23 (true = err),
% 31.98/32.23 inference(transitivity,[status(thm)],[637, 1915, 1914, 1449, 327, 1448])).
% 31.98/32.23 tff(1917,plain,
% 31.98/32.23 ($false),
% 31.98/32.23 inference(unit_resolution,[status(thm)],[153, 1916])).
% 31.98/32.23 tff(1918,plain,((~(Q!7 = true)) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)) | (~(P!8 = false))), inference(lemma,lemma(discharge,[]))).
% 32.07/32.23 tff(1919,plain,
% 32.07/32.23 ((~(Q!7 = true)) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err))),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[1918, 1765])).
% 32.07/32.23 tff(1920,plain,
% 32.07/32.23 (~(Q!7 = true)),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[1919, 1896])).
% 32.07/32.23 tff(1921,plain,
% 32.07/32.23 (~((Q!7 = false) | (Q!7 = true))),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[633, 1904, 1920])).
% 32.07/32.23 tff(1922,plain,
% 32.07/32.23 (~bool(Q!7)),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[631, 1921])).
% 32.07/32.23 tff(1923,assumption,(bool(tptp_fun_R_2(Q!7, P!8))), introduced(assumption)).
% 32.07/32.23 tff(1924,plain,
% 32.07/32.23 (prop(tptp_fun_R_2(Q!7, P!8)) = true),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[452, 1923])).
% 32.07/32.23 tff(1925,plain,
% 32.07/32.23 (impl(false, tptp_fun_R_2(Q!7, P!8)) = true),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[1686, 1923])).
% 32.07/32.23 tff(1926,plain,
% 32.07/32.23 (impl(true, impl(impl(Q!7, true), true)) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 32.07/32.23 inference(symmetry,[status(thm)],[1911])).
% 32.07/32.23 tff(1927,plain,
% 32.07/32.23 (phi(Q!7) = err),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[1484, 1110, 1804, 1448])).
% 32.07/32.23 tff(1928,plain,
% 32.07/32.23 (impl(Q!7, true) = err),
% 32.07/32.23 inference(transitivity,[status(thm)],[1111, 1927])).
% 32.07/32.23 tff(1929,plain,
% 32.07/32.23 (bool(impl(Q!7, true)) <=> bool(err)),
% 32.07/32.23 inference(monotonicity,[status(thm)],[1928])).
% 32.07/32.23 tff(1930,plain,
% 32.07/32.23 (bool(err) <=> bool(impl(Q!7, true))),
% 32.07/32.23 inference(symmetry,[status(thm)],[1929])).
% 32.07/32.23 tff(1931,plain,
% 32.07/32.23 ((~bool(err)) <=> (~bool(impl(Q!7, true)))),
% 32.07/32.23 inference(monotonicity,[status(thm)],[1930])).
% 32.07/32.23 tff(1932,plain,
% 32.07/32.23 (~bool(impl(Q!7, true))),
% 32.07/32.23 inference(modus_ponens,[status(thm)],[999, 1931])).
% 32.07/32.23 tff(1933,plain,
% 32.07/32.23 (impl(impl(Q!7, true), true) = phi(impl(Q!7, true))),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[1144, 1932])).
% 32.07/32.23 tff(1934,plain,
% 32.07/32.23 (phi(impl(Q!7, true)) = impl(impl(Q!7, true), true)),
% 32.07/32.23 inference(symmetry,[status(thm)],[1933])).
% 32.07/32.23 tff(1935,plain,
% 32.07/32.23 (impl(impl(Q!7, true), tptp_fun_R_2(Q!7, P!8)) = phi(impl(Q!7, true))),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[1862, 1932])).
% 32.07/32.23 tff(1936,plain,
% 32.07/32.23 (impl(Q!7, impl(false, tptp_fun_R_2(Q!7, P!8))) = impl(Q!7, true)),
% 32.07/32.23 inference(monotonicity,[status(thm)],[1866])).
% 32.07/32.23 tff(1937,plain,
% 32.07/32.23 (impl(impl(Q!7, impl(false, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8)) = impl(impl(Q!7, true), tptp_fun_R_2(Q!7, P!8))),
% 32.07/32.23 inference(monotonicity,[status(thm)],[1936])).
% 32.07/32.23 tff(1938,plain,
% 32.07/32.23 (impl(Q!7, true) = impl(Q!7, impl(false, tptp_fun_R_2(Q!7, P!8)))),
% 32.07/32.23 inference(symmetry,[status(thm)],[1936])).
% 32.07/32.23 tff(1939,plain,
% 32.07/32.23 (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = impl(Q!7, impl(false, tptp_fun_R_2(Q!7, P!8)))),
% 32.07/32.23 inference(transitivity,[status(thm)],[1838, 1112, 1938])).
% 32.07/32.23 tff(1940,plain,
% 32.07/32.23 (impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = impl(impl(Q!7, impl(false, tptp_fun_R_2(Q!7, P!8))), tptp_fun_R_2(Q!7, P!8))),
% 32.07/32.23 inference(monotonicity,[status(thm)],[1939])).
% 32.07/32.23 tff(1941,plain,
% 32.07/32.23 (impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = impl(impl(Q!7, true), true)),
% 32.07/32.23 inference(transitivity,[status(thm)],[1940, 1937, 1935, 1934])).
% 32.07/32.23 tff(1942,plain,
% 32.07/32.23 (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = impl(true, impl(impl(Q!7, true), true))),
% 32.07/32.23 inference(monotonicity,[status(thm)],[1868, 1941])).
% 32.07/32.23 tff(1943,plain,
% 32.07/32.23 (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 32.07/32.23 inference(transitivity,[status(thm)],[1942, 1926])).
% 32.07/32.23 tff(1944,plain,
% 32.07/32.23 (prop(tptp_fun_R_2(Q!7, P!8)) = prop(true)),
% 32.07/32.23 inference(transitivity,[status(thm)],[459, 317])).
% 32.07/32.23 tff(1945,plain,
% 32.07/32.23 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 32.07/32.23 inference(monotonicity,[status(thm)],[1944, 1943])).
% 32.07/32.23 tff(1946,plain,
% 32.07/32.23 (lazy_impl(true, impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))),
% 32.07/32.23 inference(monotonicity,[status(thm)],[502])).
% 32.07/32.23 tff(1947,plain,
% 32.07/32.23 (phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = err),
% 32.07/32.23 inference(transitivity,[status(thm)],[1241, 1946, 1945, 965, 327, 1448])).
% 32.07/32.23 tff(1948,plain,
% 32.07/32.23 (f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)) = phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 32.07/32.23 inference(symmetry,[status(thm)],[1268])).
% 32.07/32.23 tff(1949,plain,
% 32.07/32.23 (phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 32.07/32.23 inference(transitivity,[status(thm)],[1241, 1946, 42, 1948])).
% 32.07/32.23 tff(1950,plain,
% 32.07/32.23 ((phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = err) <=> (phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err)),
% 32.07/32.23 inference(monotonicity,[status(thm)],[1949])).
% 32.07/32.23 tff(1951,plain,
% 32.07/32.23 ((phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err) <=> (phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = err)),
% 32.07/32.23 inference(symmetry,[status(thm)],[1950])).
% 32.07/32.23 tff(1952,plain,
% 32.07/32.23 ((~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err)) <=> (~(phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = err))),
% 32.07/32.23 inference(monotonicity,[status(thm)],[1951])).
% 32.07/32.23 tff(1953,plain,
% 32.07/32.23 ((err = phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))) <=> (phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err)),
% 32.07/32.23 inference(commutativity,[status(thm)],[])).
% 32.07/32.23 tff(1954,plain,
% 32.07/32.23 (or1(P!8, Q!7) = err),
% 32.07/32.23 inference(transitivity,[status(thm)],[1380, 1927])).
% 32.07/32.23 tff(1955,plain,
% 32.07/32.23 ((or1(P!8, Q!7) = or2(P!8, Q!7)) <=> (err = phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))))),
% 32.07/32.23 inference(monotonicity,[status(thm)],[1954, 365])).
% 32.07/32.23 tff(1956,plain,
% 32.07/32.23 ((or1(P!8, Q!7) = or2(P!8, Q!7)) <=> (phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err)),
% 32.07/32.23 inference(transitivity,[status(thm)],[1955, 1953])).
% 32.07/32.23 tff(1957,plain,
% 32.07/32.23 ((~(or1(P!8, Q!7) = or2(P!8, Q!7))) <=> (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err))),
% 32.07/32.23 inference(monotonicity,[status(thm)],[1956])).
% 32.07/32.23 tff(1958,plain,
% 32.07/32.23 (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err)),
% 32.07/32.23 inference(modus_ponens,[status(thm)],[377, 1957])).
% 32.07/32.23 tff(1959,plain,
% 32.07/32.23 (~(phi(impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = err)),
% 32.07/32.23 inference(modus_ponens,[status(thm)],[1958, 1952])).
% 32.07/32.23 tff(1960,plain,
% 32.07/32.23 ($false),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[1959, 1947])).
% 32.07/32.23 tff(1961,plain,(bool(Q!7) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)) | (~(P!8 = false)) | (~(impl(false, tptp_fun_R_2(Q!7, P!8)) = true)) | (~(prop(tptp_fun_R_2(Q!7, P!8)) = true)) | (~(or1(P!8, Q!7) = phi(Q!7)))), inference(lemma,lemma(discharge,[]))).
% 32.07/32.23 tff(1962,plain,
% 32.07/32.23 ($false),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[1961, 1925, 1924, 1799, 1448, 1110, 1380])).
% 32.07/32.23 tff(1963,plain,((~bool(tptp_fun_R_2(Q!7, P!8))) | (~(P!8 = false)) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)) | bool(Q!7) | (~(or1(P!8, Q!7) = phi(Q!7)))), inference(lemma,lemma(discharge,[]))).
% 32.07/32.23 tff(1964,plain,
% 32.07/32.23 ((~bool(tptp_fun_R_2(Q!7, P!8))) | (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)) | bool(Q!7) | (~(or1(P!8, Q!7) = phi(Q!7)))),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[1963, 1765])).
% 32.07/32.23 tff(1965,plain,
% 32.07/32.23 (~bool(tptp_fun_R_2(Q!7, P!8))),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[1964, 1922, 1905, 1896])).
% 32.07/32.23 tff(1966,plain,
% 32.07/32.23 (prop(tptp_fun_R_2(Q!7, P!8)) = false),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[447, 1965])).
% 32.07/32.23 tff(1967,plain,
% 32.07/32.23 (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err)),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[1233, 1966])).
% 32.07/32.23 tff(1968,plain,
% 32.07/32.23 (d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = err))),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[483, 1967])).
% 32.07/32.23 tff(1969,plain,
% 32.07/32.23 (~((~d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))) | (~(phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))))),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[481, 1968])).
% 32.07/32.23 tff(1970,plain,
% 32.07/32.23 (d(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[1288, 1969])).
% 32.07/32.23 tff(1971,plain,
% 32.07/32.23 (d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))),
% 32.07/32.23 inference(modus_ponens,[status(thm)],[1970, 195])).
% 32.07/32.23 tff(1972,plain,
% 32.07/32.23 (d(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[287, 1971])).
% 32.07/32.23 tff(1973,plain,
% 32.07/32.23 (bool(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))))),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[1294, 1972, 1966])).
% 32.07/32.23 tff(1974,plain,
% 32.07/32.23 ((lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false) | (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true)),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[1299, 1973])).
% 32.07/32.23 tff(1975,plain,
% 32.07/32.23 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = lazy_impl(false, impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))),
% 32.07/32.23 inference(monotonicity,[status(thm)],[1966])).
% 32.07/32.23 tff(1976,plain,
% 32.07/32.23 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true),
% 32.07/32.23 inference(transitivity,[status(thm)],[1975, 9])).
% 32.07/32.23 tff(1977,plain,
% 32.07/32.23 (~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[300, 1976])).
% 32.07/32.23 tff(1978,plain,
% 32.07/32.23 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = true),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[302, 1977, 1974])).
% 32.07/32.23 tff(1979,plain,
% 32.07/32.23 (lazy_impl(prop(false), impl(impl(impl(Q!7, true), impl(false, false)), false)) = true),
% 32.07/32.23 inference(modus_ponens,[status(thm)],[1978, 1798])).
% 32.07/32.23 tff(1980,plain,
% 32.07/32.23 (phi(impl(impl(impl(Q!7, true), impl(false, false)), false)) = true),
% 32.07/32.23 inference(transitivity,[status(thm)],[1405, 1392, 1979])).
% 32.07/32.23 tff(1981,plain,
% 32.07/32.23 ((phi(impl(impl(impl(Q!7, true), impl(false, false)), false)) = err) <=> (true = err)),
% 32.07/32.23 inference(monotonicity,[status(thm)],[1980])).
% 32.07/32.23 tff(1982,plain,
% 32.07/32.23 ((true = err) <=> (phi(impl(impl(impl(Q!7, true), impl(false, false)), false)) = err)),
% 32.07/32.23 inference(symmetry,[status(thm)],[1981])).
% 32.07/32.23 tff(1983,plain,
% 32.07/32.23 ((~(true = err)) <=> (~(phi(impl(impl(impl(Q!7, true), impl(false, false)), false)) = err))),
% 32.07/32.23 inference(monotonicity,[status(thm)],[1982])).
% 32.07/32.23 tff(1984,plain,
% 32.07/32.23 (~(phi(impl(impl(impl(Q!7, true), impl(false, false)), false)) = err)),
% 32.07/32.23 inference(modus_ponens,[status(thm)],[153, 1983])).
% 32.07/32.23 tff(1985,plain,
% 32.07/32.23 (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = phi(impl(impl(impl(Q!7, true), impl(false, false)), false))),
% 32.07/32.23 inference(transitivity,[status(thm)],[328, 318, 1795, 1393, 925])).
% 32.07/32.23 tff(1986,plain,
% 32.07/32.23 ((phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err) <=> (phi(impl(impl(impl(Q!7, true), impl(false, false)), false)) = err)),
% 32.07/32.23 inference(monotonicity,[status(thm)],[1985])).
% 32.07/32.23 tff(1987,plain,
% 32.07/32.23 (phi(impl(impl(impl(Q!7, true), impl(false, false)), false)) = err),
% 32.07/32.23 inference(modus_ponens,[status(thm)],[1896, 1986])).
% 32.07/32.23 tff(1988,plain,
% 32.07/32.23 ($false),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[1987, 1984])).
% 32.07/32.23 tff(1989,plain,(bool(impl(impl(Q!7, true), true))), inference(lemma,lemma(discharge,[]))).
% 32.07/32.23 tff(1990,plain,
% 32.07/32.23 (impl(true, impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[874, 1989])).
% 32.07/32.23 tff(1991,plain,
% 32.07/32.23 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = impl(impl(Q!7, impl(false, true)), true)),
% 32.07/32.23 inference(transitivity,[status(thm)],[1774, 1990, 703])).
% 32.07/32.23 tff(1992,plain,
% 32.07/32.23 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))),
% 32.07/32.23 inference(monotonicity,[status(thm)],[1991])).
% 32.07/32.23 tff(1993,plain,
% 32.07/32.23 (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = phi(impl(impl(Q!7, true), true))),
% 32.07/32.23 inference(transitivity,[status(thm)],[328, 318, 1992, 702, 685])).
% 32.07/32.23 tff(1994,plain,
% 32.07/32.23 ((phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err) <=> (phi(impl(impl(Q!7, true), true)) = err)),
% 32.07/32.23 inference(monotonicity,[status(thm)],[1993])).
% 32.07/32.23 tff(1995,plain,
% 32.07/32.23 ((phi(impl(impl(Q!7, true), true)) = err) <=> (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)),
% 32.07/32.23 inference(symmetry,[status(thm)],[1994])).
% 32.07/32.23 tff(1996,plain,
% 32.07/32.23 ((~(bool(impl(impl(Q!7, true), true)) <=> ((impl(impl(Q!7, true), true) = false) | (impl(impl(Q!7, true), true) = true)))) | (~bool(impl(impl(Q!7, true), true))) | ((impl(impl(Q!7, true), true) = false) | (impl(impl(Q!7, true), true) = true))),
% 32.07/32.23 inference(tautology,[status(thm)],[])).
% 32.07/32.23 tff(1997,plain,
% 32.07/32.23 ((~(bool(impl(impl(Q!7, true), true)) <=> ((impl(impl(Q!7, true), true) = false) | (impl(impl(Q!7, true), true) = true)))) | ((impl(impl(Q!7, true), true) = false) | (impl(impl(Q!7, true), true) = true))),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[1996, 1989])).
% 32.07/32.23 tff(1998,plain,
% 32.07/32.23 ((impl(impl(Q!7, true), true) = false) | (impl(impl(Q!7, true), true) = true)),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[1997, 1525])).
% 32.07/32.23 tff(1999,plain,
% 32.07/32.23 (lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true)) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 32.07/32.23 inference(symmetry,[status(thm)],[1992])).
% 32.07/32.23 tff(2000,plain,
% 32.07/32.23 (impl(impl(Q!7, true), true) = impl(true, impl(impl(Q!7, true), true))),
% 32.07/32.23 inference(symmetry,[status(thm)],[1990])).
% 32.07/32.23 tff(2001,plain,
% 32.07/32.23 (impl(impl(Q!7, true), true) = lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 32.07/32.23 inference(transitivity,[status(thm)],[2000, 1783, 1793, 1040, 1071, 1999])).
% 32.07/32.23 tff(2002,plain,
% 32.07/32.23 ((impl(impl(Q!7, true), true) = false) <=> (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)),
% 32.07/32.23 inference(monotonicity,[status(thm)],[2001])).
% 32.07/32.23 tff(2003,plain,
% 32.07/32.23 ((lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false) <=> (impl(impl(Q!7, true), true) = false)),
% 32.07/32.23 inference(symmetry,[status(thm)],[2002])).
% 32.07/32.23 tff(2004,plain,
% 32.07/32.23 ((~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)) <=> (~(impl(impl(Q!7, true), true) = false))),
% 32.07/32.23 inference(monotonicity,[status(thm)],[2003])).
% 32.07/32.23 tff(2005,plain,
% 32.07/32.23 (bool(impl(impl(Q!7, true), true))),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[1894, 1799, 1222])).
% 32.07/32.23 tff(2006,plain,
% 32.07/32.23 (impl(true, impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[874, 2005])).
% 32.07/32.23 tff(2007,plain,
% 32.07/32.23 (impl(impl(Q!7, true), true) = impl(true, impl(impl(Q!7, true), true))),
% 32.07/32.23 inference(symmetry,[status(thm)],[2006])).
% 32.07/32.23 tff(2008,plain,
% 32.07/32.23 (phi(impl(Q!7, true)) = phi(impl(impl(P!8, true), impl(impl(Q!7, true), true)))),
% 32.07/32.23 inference(transitivity,[status(thm)],[1727, 2007, 1926, 1302])).
% 32.07/32.23 tff(2009,plain,
% 32.07/32.23 ((phi(impl(Q!7, true)) = err) <=> (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)),
% 32.07/32.23 inference(monotonicity,[status(thm)],[2008])).
% 32.07/32.23 tff(2010,plain,
% 32.07/32.23 ((phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err) <=> (phi(impl(Q!7, true)) = err)),
% 32.07/32.23 inference(symmetry,[status(thm)],[2009])).
% 32.07/32.23 tff(2011,plain,
% 32.07/32.23 ((~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)) <=> (~(phi(impl(Q!7, true)) = err))),
% 32.07/32.23 inference(monotonicity,[status(thm)],[2010])).
% 32.07/32.23 tff(2012,plain,
% 32.07/32.23 (~(phi(impl(Q!7, true)) = err)),
% 32.07/32.23 inference(modus_ponens,[status(thm)],[1222, 2011])).
% 32.07/32.23 tff(2013,plain,
% 32.07/32.23 (d(impl(Q!7, true)) | (~(phi(impl(Q!7, true)) = err))),
% 32.07/32.23 inference(unit_resolution,[status(thm)],[1159, 2012])).
% 32.07/32.23 tff(2014,plain,
% 32.07/32.24 (~((~d(impl(Q!7, true))) | (~(phi(impl(Q!7, true)) = impl(Q!7, true))))),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[1164, 2013])).
% 32.07/32.24 tff(2015,plain,
% 32.07/32.24 (phi(impl(Q!7, true)) = impl(Q!7, true)),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[1166, 2014])).
% 32.07/32.24 tff(2016,plain,
% 32.07/32.24 (impl(Q!7, true) = phi(impl(Q!7, true))),
% 32.07/32.24 inference(symmetry,[status(thm)],[2015])).
% 32.07/32.24 tff(2017,plain,
% 32.07/32.24 (impl(Q!7, true) = impl(impl(Q!7, true), true)),
% 32.07/32.24 inference(transitivity,[status(thm)],[2016, 1727])).
% 32.07/32.24 tff(2018,plain,
% 32.07/32.24 (bool(impl(Q!7, true)) <=> bool(impl(impl(Q!7, true), true))),
% 32.07/32.24 inference(monotonicity,[status(thm)],[2017])).
% 32.07/32.24 tff(2019,plain,
% 32.07/32.24 (bool(impl(impl(Q!7, true), true)) <=> bool(impl(Q!7, true))),
% 32.07/32.24 inference(symmetry,[status(thm)],[2018])).
% 32.07/32.24 tff(2020,plain,
% 32.07/32.24 (bool(impl(Q!7, true))),
% 32.07/32.24 inference(modus_ponens,[status(thm)],[2005, 2019])).
% 32.07/32.24 tff(2021,plain,
% 32.07/32.24 ($false),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[1725, 2020])).
% 32.07/32.24 tff(2022,plain,(bool(impl(Q!7, true)) | (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err) | (~(P!8 = false))), inference(lemma,lemma(discharge,[]))).
% 32.07/32.24 tff(2023,plain,
% 32.07/32.24 (bool(impl(Q!7, true)) | (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[2022, 1765])).
% 32.07/32.24 tff(2024,plain,
% 32.07/32.24 (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[2023, 1847])).
% 32.07/32.24 tff(2025,plain,
% 32.07/32.24 (~bool(tptp_fun_R_2(Q!7, P!8))),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[1964, 2024, 1380, 1110])).
% 32.07/32.24 tff(2026,plain,
% 32.07/32.24 (prop(tptp_fun_R_2(Q!7, P!8)) = false),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[447, 2025])).
% 32.07/32.24 tff(2027,plain,
% 32.07/32.24 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = lazy_impl(false, impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))),
% 32.07/32.24 inference(monotonicity,[status(thm)],[2026])).
% 32.07/32.24 tff(2028,plain,
% 32.07/32.24 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true),
% 32.07/32.24 inference(transitivity,[status(thm)],[2027, 9])).
% 32.07/32.24 tff(2029,plain,
% 32.07/32.24 (~(lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = false)),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[300, 2028])).
% 32.07/32.24 tff(2030,plain,
% 32.07/32.24 (~(impl(impl(Q!7, true), true) = false)),
% 32.07/32.24 inference(modus_ponens,[status(thm)],[2029, 2004])).
% 32.07/32.24 tff(2031,plain,
% 32.07/32.24 ((~((impl(impl(Q!7, true), true) = false) | (impl(impl(Q!7, true), true) = true))) | (impl(impl(Q!7, true), true) = false) | (impl(impl(Q!7, true), true) = true)),
% 32.07/32.24 inference(tautology,[status(thm)],[])).
% 32.07/32.24 tff(2032,plain,
% 32.07/32.24 (impl(impl(Q!7, true), true) = true),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[2031, 2030, 1998])).
% 32.07/32.24 tff(2033,plain,
% 32.07/32.24 (phi(impl(impl(Q!7, true), true)) = impl(impl(P!8, true), impl(impl(Q!7, true), true))),
% 32.07/32.24 inference(symmetry,[status(thm)],[1793])).
% 32.07/32.24 tff(2034,plain,
% 32.07/32.24 (phi(impl(impl(Q!7, true), true)) = true),
% 32.07/32.24 inference(transitivity,[status(thm)],[2033, 1774, 1990, 2032])).
% 32.07/32.24 tff(2035,plain,
% 32.07/32.24 ((phi(impl(impl(Q!7, true), true)) = err) <=> (true = err)),
% 32.07/32.24 inference(monotonicity,[status(thm)],[2034])).
% 32.07/32.24 tff(2036,plain,
% 32.07/32.24 ((true = err) <=> (phi(impl(impl(Q!7, true), true)) = err)),
% 32.07/32.24 inference(symmetry,[status(thm)],[2035])).
% 32.07/32.24 tff(2037,plain,
% 32.07/32.24 ((true = err) <=> (phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)),
% 32.07/32.24 inference(transitivity,[status(thm)],[2036, 1995])).
% 32.07/32.24 tff(2038,plain,
% 32.07/32.24 ((~(true = err)) <=> (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err))),
% 32.07/32.24 inference(monotonicity,[status(thm)],[2037])).
% 32.07/32.24 tff(2039,plain,
% 32.07/32.24 (~(phi(impl(impl(P!8, true), impl(impl(Q!7, true), true))) = err)),
% 32.07/32.24 inference(modus_ponens,[status(thm)],[153, 2038])).
% 32.07/32.24 tff(2040,plain,
% 32.07/32.24 ($false),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[2024, 2039])).
% 32.07/32.24 tff(2041,plain,(bool(Q!7) | (~(or1(P!8, Q!7) = phi(Q!7)))), inference(lemma,lemma(discharge,[]))).
% 32.07/32.24 tff(2042,plain,
% 32.07/32.24 (bool(Q!7)),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[2041, 683])).
% 32.07/32.24 tff(2043,plain,
% 32.07/32.24 ((Q!7 = false) | (Q!7 = true)),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[631, 2042])).
% 32.07/32.24 tff(2044,plain,
% 32.07/32.24 (((~![B: $i] : ((~bool(B)) | (or1(false, B) = B))) | ((~bool(Q!7)) | (or1(false, Q!7) = Q!7))) <=> ((~![B: $i] : ((~bool(B)) | (or1(false, B) = B))) | (~bool(Q!7)) | (or1(false, Q!7) = Q!7))),
% 32.07/32.24 inference(rewrite,[status(thm)],[])).
% 32.07/32.24 tff(2045,plain,
% 32.07/32.24 ((~![B: $i] : ((~bool(B)) | (or1(false, B) = B))) | ((~bool(Q!7)) | (or1(false, Q!7) = Q!7))),
% 32.07/32.24 inference(quant_inst,[status(thm)],[])).
% 32.07/32.24 tff(2046,plain,
% 32.07/32.24 ((~![B: $i] : ((~bool(B)) | (or1(false, B) = B))) | (~bool(Q!7)) | (or1(false, Q!7) = Q!7)),
% 32.07/32.24 inference(modus_ponens,[status(thm)],[2045, 2044])).
% 32.07/32.24 tff(2047,plain,
% 32.07/32.24 ((~bool(Q!7)) | (or1(false, Q!7) = Q!7)),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[2046, 647])).
% 32.07/32.24 tff(2048,plain,
% 32.07/32.24 (or1(false, Q!7) = Q!7),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[2047, 2042])).
% 32.07/32.24 tff(2049,assumption,(impl(true, impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)), introduced(assumption)).
% 32.07/32.24 tff(2050,plain,
% 32.07/32.24 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = impl(true, impl(impl(Q!7, true), true))),
% 32.07/32.24 inference(symmetry,[status(thm)],[1860])).
% 32.07/32.24 tff(2051,plain,
% 32.07/32.24 (impl(impl(P!8, true), impl(impl(Q!7, true), true)) = impl(impl(Q!7, impl(false, true)), true)),
% 32.07/32.24 inference(transitivity,[status(thm)],[2050, 2049, 703])).
% 32.07/32.24 tff(2052,plain,
% 32.07/32.24 (lazy_impl(prop(true), impl(impl(P!8, true), impl(impl(Q!7, true), true))) = lazy_impl(prop(true), impl(impl(Q!7, impl(false, true)), true))),
% 32.07/32.24 inference(monotonicity,[status(thm)],[2051])).
% 32.07/32.24 tff(2053,plain,
% 32.07/32.24 (((~![B: $i] : ((~bool(B)) | (or1(true, B) = true))) | ((~bool(true)) | (or1(true, true) = true))) <=> ((~![B: $i] : ((~bool(B)) | (or1(true, B) = true))) | (~bool(true)) | (or1(true, true) = true))),
% 32.07/32.24 inference(rewrite,[status(thm)],[])).
% 32.07/32.24 tff(2054,plain,
% 32.07/32.24 ((~![B: $i] : ((~bool(B)) | (or1(true, B) = true))) | ((~bool(true)) | (or1(true, true) = true))),
% 32.07/32.24 inference(quant_inst,[status(thm)],[])).
% 32.07/32.24 tff(2055,plain,
% 32.07/32.24 ((~![B: $i] : ((~bool(B)) | (or1(true, B) = true))) | (~bool(true)) | (or1(true, true) = true)),
% 32.07/32.24 inference(modus_ponens,[status(thm)],[2054, 2053])).
% 32.07/32.24 tff(2056,plain,
% 32.07/32.24 (or1(true, true) = true),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[2055, 661, 247])).
% 32.07/32.24 tff(2057,plain,
% 32.07/32.24 (or1(P!8, Q!7) = or1(true, true)),
% 32.07/32.24 inference(monotonicity,[status(thm)],[667, 1064])).
% 32.07/32.24 tff(2058,plain,
% 32.07/32.24 (or1(P!8, Q!7) = or2(P!8, Q!7)),
% 32.07/32.24 inference(transitivity,[status(thm)],[2057, 2056, 197, 196, 42, 1948, 576])).
% 32.07/32.24 tff(2059,plain,
% 32.07/32.24 ($false),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[377, 2058])).
% 32.07/32.24 tff(2060,plain,((~(P!8 = true)) | (~(prop(tptp_fun_R_2(Q!7, P!8)) = false)) | (~(Q!7 = true))), inference(lemma,lemma(discharge,[]))).
% 32.07/32.24 tff(2061,plain,
% 32.07/32.24 (~(P!8 = true)),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[2060, 1064, 10])).
% 32.07/32.24 tff(2062,plain,
% 32.07/32.24 (P!8 = false),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[677, 2061])).
% 32.07/32.24 tff(2063,plain,
% 32.07/32.24 (or1(P!8, Q!7) = or1(false, true)),
% 32.07/32.24 inference(monotonicity,[status(thm)],[2062, 1064])).
% 32.07/32.24 tff(2064,plain,
% 32.07/32.24 (or1(P!8, Q!7) = or2(P!8, Q!7)),
% 32.07/32.24 inference(transitivity,[status(thm)],[2063, 651, 197, 196, 42, 1948, 576])).
% 32.07/32.24 tff(2065,plain,
% 32.07/32.24 ($false),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[377, 2064])).
% 32.07/32.24 tff(2066,plain,((~(Q!7 = true)) | (~(prop(tptp_fun_R_2(Q!7, P!8)) = false))), inference(lemma,lemma(discharge,[]))).
% 32.07/32.24 tff(2067,plain,
% 32.07/32.24 (~(prop(tptp_fun_R_2(Q!7, P!8)) = false)),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[2066, 1064])).
% 32.07/32.24 tff(2068,plain,
% 32.07/32.24 (bool(tptp_fun_R_2(Q!7, P!8))),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[447, 2067])).
% 32.07/32.24 tff(2069,plain,
% 32.07/32.24 ((tptp_fun_R_2(Q!7, P!8) = false) | (tptp_fun_R_2(Q!7, P!8) = true)),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[1601, 2068])).
% 32.07/32.24 tff(2070,assumption,(or1(false, Q!7) = Q!7), introduced(assumption)).
% 32.07/32.24 tff(2071,assumption,(tptp_fun_R_2(Q!7, P!8) = false), introduced(assumption)).
% 32.07/32.24 tff(2072,plain,
% 32.07/32.24 (impl(true, tptp_fun_R_2(Q!7, P!8)) = tptp_fun_R_2(Q!7, P!8)),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[1362, 2068])).
% 32.07/32.24 tff(2073,plain,
% 32.07/32.24 (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = false),
% 32.07/32.24 inference(transitivity,[status(thm)],[1658, 2072, 2071])).
% 32.07/32.24 tff(2074,plain,
% 32.07/32.24 (impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = impl(false, false)),
% 32.07/32.24 inference(monotonicity,[status(thm)],[2073, 2071])).
% 32.07/32.24 tff(2075,plain,
% 32.07/32.24 (impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = true),
% 32.07/32.24 inference(transitivity,[status(thm)],[2074, 811])).
% 32.07/32.24 tff(2076,plain,
% 32.07/32.24 (impl(false, tptp_fun_R_2(Q!7, P!8)) = true),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[1686, 2068])).
% 32.07/32.24 tff(2077,plain,
% 32.07/32.24 (impl(P!8, tptp_fun_R_2(Q!7, P!8)) = true),
% 32.07/32.24 inference(transitivity,[status(thm)],[1867, 2076])).
% 32.07/32.24 tff(2078,plain,
% 32.07/32.24 (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = impl(true, true)),
% 32.07/32.24 inference(monotonicity,[status(thm)],[2077, 2075])).
% 32.07/32.24 tff(2079,plain,
% 32.07/32.24 (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = true),
% 32.07/32.24 inference(transitivity,[status(thm)],[2078, 847])).
% 32.07/32.24 tff(2080,plain,
% 32.07/32.24 (prop(tptp_fun_R_2(Q!7, P!8)) = true),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[452, 2068])).
% 32.07/32.24 tff(2081,plain,
% 32.07/32.24 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = lazy_impl(true, true)),
% 32.07/32.24 inference(monotonicity,[status(thm)],[2080, 2079])).
% 32.07/32.24 tff(2082,plain,
% 32.07/32.24 (f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)) = true),
% 32.07/32.24 inference(transitivity,[status(thm)],[41, 2081, 705, 221])).
% 32.07/32.24 tff(2083,plain,
% 32.07/32.24 (phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = phi(true)),
% 32.07/32.24 inference(monotonicity,[status(thm)],[2082])).
% 32.07/32.24 tff(2084,plain,
% 32.07/32.24 (phi(true) = phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 32.07/32.24 inference(symmetry,[status(thm)],[2083])).
% 32.07/32.24 tff(2085,plain,
% 32.07/32.24 (or1(P!8, Q!7) = or1(false, Q!7)),
% 32.07/32.24 inference(monotonicity,[status(thm)],[1799])).
% 32.07/32.24 tff(2086,plain,
% 32.07/32.24 (or1(P!8, Q!7) = or2(P!8, Q!7)),
% 32.07/32.24 inference(transitivity,[status(thm)],[2085, 2070, 1064, 637, 2084, 576])).
% 32.07/32.24 tff(2087,plain,
% 32.07/32.24 ($false),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[377, 2086])).
% 32.07/32.24 tff(2088,plain,((~(tptp_fun_R_2(Q!7, P!8) = false)) | (~(or1(false, Q!7) = Q!7)) | (~(Q!7 = true)) | (~(P!8 = false))), inference(lemma,lemma(discharge,[]))).
% 32.07/32.24 tff(2089,plain,
% 32.07/32.24 (~(tptp_fun_R_2(Q!7, P!8) = false)),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[2088, 1064, 2070, 1799])).
% 32.07/32.24 tff(2090,plain,
% 32.07/32.24 (tptp_fun_R_2(Q!7, P!8) = true),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[1651, 2089, 2069])).
% 32.07/32.24 tff(2091,plain,
% 32.07/32.24 (f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)) = f3(P!8, Q!7, true)),
% 32.07/32.24 inference(monotonicity,[status(thm)],[2090])).
% 32.07/32.24 tff(2092,plain,
% 32.07/32.24 (f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)) = true),
% 32.07/32.24 inference(transitivity,[status(thm)],[2091, 257, 2052, 1070, 1621, 1063, 1620, 705, 221])).
% 32.07/32.24 tff(2093,plain,
% 32.07/32.24 (phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = phi(true)),
% 32.07/32.24 inference(monotonicity,[status(thm)],[2092])).
% 32.07/32.24 tff(2094,plain,
% 32.07/32.24 (phi(true) = phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 32.07/32.24 inference(symmetry,[status(thm)],[2093])).
% 32.07/32.24 tff(2095,plain,
% 32.07/32.24 (or1(P!8, Q!7) = or2(P!8, Q!7)),
% 32.07/32.24 inference(transitivity,[status(thm)],[2085, 2070, 1064, 637, 2094, 576])).
% 32.07/32.24 tff(2096,plain,
% 32.07/32.24 ($false),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[377, 2095])).
% 32.07/32.24 tff(2097,plain,((~(Q!7 = true)) | (~(or1(false, Q!7) = Q!7)) | (~(impl(true, impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true))) | (~(P!8 = false))), inference(lemma,lemma(discharge,[]))).
% 32.07/32.24 tff(2098,plain,
% 32.07/32.24 ((~(Q!7 = true)) | (~(or1(false, Q!7) = Q!7)) | (~(impl(true, impl(impl(Q!7, true), true)) = impl(impl(Q!7, true), true)))),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[2097, 1765])).
% 32.07/32.24 tff(2099,plain,
% 32.07/32.24 (~(Q!7 = true)),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[2098, 2048, 1990])).
% 32.07/32.24 tff(2100,plain,
% 32.07/32.24 ($false),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[633, 2099, 2043, 43])).
% 32.07/32.24 tff(2101,plain,(Q!7 = false), inference(lemma,lemma(discharge,[]))).
% 32.07/32.24 tff(2102,plain,
% 32.07/32.24 (f3(P!8, Q!7, false) = f3(false, false, false)),
% 32.07/32.24 inference(monotonicity,[status(thm)],[1765, 2101])).
% 32.07/32.24 tff(2103,plain,
% 32.07/32.24 (f3(false, false, false) = f3(P!8, Q!7, false)),
% 32.07/32.24 inference(symmetry,[status(thm)],[2102])).
% 32.07/32.24 tff(2104,assumption,(~(f3(false, false, false) = lazy_impl(prop(false), impl(impl(false, false), impl(impl(false, false), false))))), introduced(assumption)).
% 32.07/32.24 tff(2105,plain,
% 32.07/32.24 ((~![P: $i, Q: $i, R: $i] : (f3(P, Q, R) = lazy_impl(prop(R), impl(impl(P, R), impl(impl(Q, R), R))))) | (f3(false, false, false) = lazy_impl(prop(false), impl(impl(false, false), impl(impl(false, false), false))))),
% 32.07/32.24 inference(quant_inst,[status(thm)],[])).
% 32.07/32.24 tff(2106,plain,
% 32.07/32.24 ($false),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[2105, 39, 2104])).
% 32.07/32.24 tff(2107,plain,(f3(false, false, false) = lazy_impl(prop(false), impl(impl(false, false), impl(impl(false, false), false)))), inference(lemma,lemma(discharge,[]))).
% 32.07/32.24 tff(2108,plain,
% 32.07/32.24 (lazy_impl(prop(false), impl(impl(false, false), impl(impl(false, false), false))) = f3(false, false, false)),
% 32.07/32.24 inference(symmetry,[status(thm)],[2107])).
% 32.07/32.24 tff(2109,plain,
% 32.07/32.24 (impl(impl(false, false), false) = impl(true, false)),
% 32.07/32.24 inference(monotonicity,[status(thm)],[811])).
% 32.07/32.24 tff(2110,plain,
% 32.07/32.24 (impl(impl(false, false), false) = false),
% 32.07/32.24 inference(transitivity,[status(thm)],[2109, 1542])).
% 32.07/32.24 tff(2111,plain,
% 32.07/32.24 (impl(impl(false, false), impl(impl(false, false), false)) = impl(true, false)),
% 32.07/32.24 inference(monotonicity,[status(thm)],[811, 2110])).
% 32.07/32.24 tff(2112,plain,
% 32.07/32.24 (impl(impl(false, false), impl(impl(false, false), false)) = false),
% 32.07/32.24 inference(transitivity,[status(thm)],[2111, 1542])).
% 32.07/32.24 tff(2113,plain,
% 32.07/32.24 (lazy_impl(prop(false), impl(impl(false, false), impl(impl(false, false), false))) = lazy_impl(true, false)),
% 32.07/32.24 inference(monotonicity,[status(thm)],[759, 2112])).
% 32.07/32.24 tff(2114,plain,
% 32.07/32.24 (lazy_impl(true, false) = lazy_impl(prop(false), impl(impl(false, false), impl(impl(false, false), false)))),
% 32.07/32.24 inference(symmetry,[status(thm)],[2113])).
% 32.07/32.24 tff(2115,plain,
% 32.07/32.24 (false = f3(P!8, Q!7, false)),
% 32.07/32.24 inference(transitivity,[status(thm)],[765, 764, 2114, 2108, 2103])).
% 32.07/32.24 tff(2116,plain,
% 32.07/32.24 (forallprefers(false, lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> forallprefers(f3(P!8, Q!7, false), f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 32.07/32.24 inference(monotonicity,[status(thm)],[2115, 42])).
% 32.07/32.24 tff(2117,plain,
% 32.07/32.24 (forallprefers(f3(P!8, Q!7, false), f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) <=> forallprefers(false, lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))),
% 32.07/32.24 inference(symmetry,[status(thm)],[2116])).
% 32.07/32.24 tff(2118,plain,
% 32.07/32.24 ((~forallprefers(f3(P!8, Q!7, false), f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))) <=> (~forallprefers(false, lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))),
% 32.07/32.24 inference(monotonicity,[status(thm)],[2117])).
% 32.07/32.24 tff(2119,plain,
% 32.07/32.24 ((~![R1: $i] : (~forallprefers(f3(P!8, Q!7, R1), f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))))) | (~forallprefers(f3(P!8, Q!7, false), f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))))),
% 32.07/32.24 inference(quant_inst,[status(thm)],[])).
% 32.07/32.24 tff(2120,plain,
% 32.07/32.24 (~forallprefers(f3(P!8, Q!7, false), f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[2119, 278])).
% 32.07/32.24 tff(2121,plain,
% 32.07/32.24 (~forallprefers(false, lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))),
% 32.07/32.24 inference(modus_ponens,[status(thm)],[2120, 2118])).
% 32.07/32.24 tff(2122,plain,
% 32.07/32.24 ((~(forallprefers(false, lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) <=> ((lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))))))) | forallprefers(false, lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) | (~((lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))))))),
% 32.07/32.24 inference(tautology,[status(thm)],[])).
% 32.07/32.24 tff(2123,plain,
% 32.07/32.24 (~((lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))))),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[2122, 2121, 32])).
% 32.07/32.24 tff(2124,plain,
% 32.07/32.24 (((lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true) | (~((~d(false)) | bool(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))) | (~(d(false) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))))) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true))),
% 32.07/32.24 inference(tautology,[status(thm)],[])).
% 32.07/32.24 tff(2125,plain,
% 32.07/32.24 (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = true)),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[2124, 2123])).
% 32.07/32.24 tff(2126,plain,
% 32.07/32.24 ($false),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[2125, 12])).
% 32.07/32.24 tff(2127,plain,(~(prop(tptp_fun_R_2(Q!7, P!8)) = false)), inference(lemma,lemma(discharge,[]))).
% 32.07/32.24 tff(2128,plain,
% 32.07/32.24 (bool(tptp_fun_R_2(Q!7, P!8))),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[447, 2127])).
% 32.07/32.24 tff(2129,plain,
% 32.07/32.24 (impl(true, tptp_fun_R_2(Q!7, P!8)) = tptp_fun_R_2(Q!7, P!8)),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[1362, 2128])).
% 32.07/32.24 tff(2130,plain,
% 32.07/32.24 (impl(false, tptp_fun_R_2(Q!7, P!8)) = true),
% 32.07/32.24 inference(unit_resolution,[status(thm)],[1686, 2128])).
% 32.07/32.24 tff(2131,assumption,(impl(true, tptp_fun_R_2(Q!7, P!8)) = tptp_fun_R_2(Q!7, P!8)), introduced(assumption)).
% 32.07/32.24 tff(2132,plain,
% 32.07/32.24 (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = impl(false, tptp_fun_R_2(Q!7, P!8))),
% 32.07/32.24 inference(monotonicity,[status(thm)],[2101])).
% 32.07/32.24 tff(2133,plain,
% 32.07/32.24 (impl(Q!7, tptp_fun_R_2(Q!7, P!8)) = true),
% 32.07/32.24 inference(transitivity,[status(thm)],[2132, 1866])).
% 32.07/32.24 tff(2134,plain,
% 32.07/32.24 (impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = impl(true, tptp_fun_R_2(Q!7, P!8))),
% 32.07/32.24 inference(monotonicity,[status(thm)],[2133])).
% 32.07/32.24 tff(2135,plain,
% 32.07/32.24 (impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = tptp_fun_R_2(Q!7, P!8)),
% 32.07/32.24 inference(transitivity,[status(thm)],[2134, 2131])).
% 32.07/32.24 tff(2136,plain,
% 32.07/32.24 (impl(P!8, tptp_fun_R_2(Q!7, P!8)) = impl(false, tptp_fun_R_2(Q!7, P!8))),
% 32.07/32.24 inference(monotonicity,[status(thm)],[1765])).
% 32.07/32.24 tff(2137,plain,
% 32.07/32.24 (impl(P!8, tptp_fun_R_2(Q!7, P!8)) = true),
% 32.07/32.24 inference(transitivity,[status(thm)],[2136, 1866])).
% 32.07/32.24 tff(2138,plain,
% 32.07/32.24 (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = impl(true, tptp_fun_R_2(Q!7, P!8))),
% 32.07/32.24 inference(monotonicity,[status(thm)],[2137, 2135])).
% 32.07/32.24 tff(2139,plain,
% 32.07/32.24 (impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = tptp_fun_R_2(Q!7, P!8)),
% 32.07/32.24 inference(transitivity,[status(thm)],[2138, 2131])).
% 32.07/32.24 tff(2140,plain,
% 32.07/32.24 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))),
% 32.07/32.24 inference(monotonicity,[status(thm)],[2139])).
% 32.07/32.24 tff(2141,plain,
% 32.07/32.24 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), impl(impl(P!8, tptp_fun_R_2(Q!7, P!8)), impl(impl(Q!7, tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))),
% 32.07/32.24 inference(symmetry,[status(thm)],[2140])).
% 32.07/32.24 tff(2142,plain,
% 32.07/32.24 ((false = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) <=> (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false)),
% 32.07/32.24 inference(commutativity,[status(thm)],[])).
% 32.07/32.24 tff(2143,plain,
% 32.07/32.24 (d(lazy_impl(prop(P!6), P!6)) <=> d(f7(P!6))),
% 32.07/32.24 inference(monotonicity,[status(thm)],[720])).
% 32.07/32.24 tff(2144,plain,
% 32.07/32.24 (d(f7(P!6)) <=> d(lazy_impl(prop(P!6), P!6))),
% 32.07/32.24 inference(symmetry,[status(thm)],[2143])).
% 32.07/32.24 tff(2145,plain,
% 32.07/32.24 (f7(P!6) = false),
% 32.07/32.24 inference(transitivity,[status(thm)],[881, 730, 760, 763, 744])).
% 32.07/32.24 tff(2146,plain,
% 32.07/32.24 (d(f7(P!6)) <=> d(false)),
% 32.07/32.24 inference(monotonicity,[status(thm)],[2145])).
% 32.07/32.24 tff(2147,plain,
% 32.07/32.24 (d(false) <=> d(f7(P!6))),
% 32.07/32.24 inference(symmetry,[status(thm)],[2146])).
% 32.07/32.24 tff(2148,plain,
% 32.07/32.24 (d(false) <=> d(lazy_impl(prop(P!6), P!6))),
% 32.07/32.24 inference(transitivity,[status(thm)],[2147, 2144])).
% 32.07/32.24 tff(2149,plain,
% 32.07/32.24 (d(lazy_impl(prop(P!6), P!6))),
% 32.07/32.24 inference(modus_ponens,[status(thm)],[736, 2148])).
% 32.07/32.24 tff(2150,plain,
% 32.07/32.24 (((~![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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = 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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false)))))))),
% 32.07/32.25 inference(rewrite,[status(thm)],[])).
% 32.07/32.25 tff(2151,plain,
% 32.07/32.25 ((forallprefers(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~((~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false)) | (~(lazy_impl(prop(P!6), P!6) = true)))) | (~(d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))))) <=> (forallprefers(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false))))))),
% 32.07/32.25 inference(rewrite,[status(thm)],[])).
% 32.07/32.25 tff(2152,plain,
% 32.07/32.25 (((~![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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~((~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false)) | (~(lazy_impl(prop(P!6), P!6) = true)))) | (~(d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))))) <=> ((~![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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false)))))))),
% 32.07/32.25 inference(monotonicity,[status(thm)],[2151])).
% 32.07/32.25 tff(2153,plain,
% 32.07/32.25 (((~![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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~((~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false)) | (~(lazy_impl(prop(P!6), P!6) = true)))) | (~(d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))))) <=> ((~![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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false)))))))),
% 32.07/32.25 inference(transitivity,[status(thm)],[2152, 2150])).
% 32.07/32.25 tff(2154,plain,
% 32.07/32.25 ((~![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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~((~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false)) | (~(lazy_impl(prop(P!6), P!6) = true)))) | (~(d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))))))),
% 32.07/32.25 inference(quant_inst,[status(thm)],[])).
% 32.07/32.25 tff(2155,plain,
% 32.07/32.25 ((~![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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false))))))),
% 32.07/32.25 inference(modus_ponens,[status(thm)],[2154, 2153])).
% 32.07/32.25 tff(2156,plain,
% 32.07/32.25 (forallprefers(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false)))))),
% 32.07/32.25 inference(unit_resolution,[status(thm)],[2155, 25])).
% 32.07/32.25 tff(2157,plain,
% 32.07/32.25 ((~![P: $i] : (f7(P) = lazy_impl(prop(P), P))) | (f7(tptp_fun_R_2(Q!7, P!8)) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))),
% 32.07/32.25 inference(quant_inst,[status(thm)],[])).
% 32.07/32.25 tff(2158,plain,
% 32.07/32.25 (f7(tptp_fun_R_2(Q!7, P!8)) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))),
% 32.07/32.25 inference(unit_resolution,[status(thm)],[2157, 713])).
% 32.07/32.25 tff(2159,plain,
% 32.07/32.25 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = f7(tptp_fun_R_2(Q!7, P!8))),
% 32.07/32.25 inference(symmetry,[status(thm)],[2158])).
% 32.07/32.25 tff(2160,plain,
% 32.07/32.25 (forallprefers(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> forallprefers(f7(tptp_fun_R_2(Q!7, P!8)), f7(P!6))),
% 32.07/32.25 inference(monotonicity,[status(thm)],[2159, 720])).
% 32.07/32.25 tff(2161,plain,
% 32.07/32.25 (forallprefers(f7(tptp_fun_R_2(Q!7, P!8)), f7(P!6)) <=> forallprefers(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)), lazy_impl(prop(P!6), P!6))),
% 32.07/32.25 inference(symmetry,[status(thm)],[2160])).
% 32.07/32.25 tff(2162,plain,
% 32.07/32.25 ((~forallprefers(f7(tptp_fun_R_2(Q!7, P!8)), f7(P!6))) <=> (~forallprefers(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)), lazy_impl(prop(P!6), P!6)))),
% 32.07/32.25 inference(monotonicity,[status(thm)],[2161])).
% 32.07/32.25 tff(2163,plain,
% 32.07/32.25 ((~![P1: $i] : (~forallprefers(f7(P1), f7(P!6)))) | (~forallprefers(f7(tptp_fun_R_2(Q!7, P!8)), f7(P!6)))),
% 32.07/32.25 inference(quant_inst,[status(thm)],[])).
% 32.07/32.25 tff(2164,plain,
% 32.07/32.25 (~forallprefers(f7(tptp_fun_R_2(Q!7, P!8)), f7(P!6))),
% 32.07/32.25 inference(unit_resolution,[status(thm)],[2163, 778])).
% 32.07/32.25 tff(2165,plain,
% 32.07/32.25 (~forallprefers(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)), lazy_impl(prop(P!6), P!6))),
% 32.07/32.25 inference(modus_ponens,[status(thm)],[2164, 2162])).
% 32.07/32.25 tff(2166,plain,
% 32.07/32.25 ((~(forallprefers(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) <=> ((~(d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false))))))) | forallprefers(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)), lazy_impl(prop(P!6), P!6)) | (~((~(d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false))))))),
% 32.07/32.25 inference(tautology,[status(thm)],[])).
% 32.07/32.25 tff(2167,plain,
% 32.07/32.25 (~((~(d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false)))))),
% 32.07/32.25 inference(unit_resolution,[status(thm)],[2166, 2165, 2156])).
% 32.07/32.25 tff(2168,plain,
% 32.07/32.25 (((~(d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false))))) | (d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(P!6), P!6))))),
% 32.07/32.25 inference(tautology,[status(thm)],[])).
% 32.07/32.25 tff(2169,plain,
% 32.07/32.25 (d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(P!6), P!6)))),
% 32.07/32.25 inference(unit_resolution,[status(thm)],[2168, 2167])).
% 32.07/32.25 tff(2170,plain,
% 32.07/32.25 ((~(d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(P!6), P!6))))) | d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(P!6), P!6)))),
% 32.07/32.25 inference(tautology,[status(thm)],[])).
% 32.07/32.25 tff(2171,plain,
% 32.07/32.25 (d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(P!6), P!6)))),
% 32.07/32.25 inference(unit_resolution,[status(thm)],[2170, 2169])).
% 32.07/32.25 tff(2172,plain,
% 32.07/32.25 (d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))),
% 32.07/32.25 inference(unit_resolution,[status(thm)],[2171, 2149])).
% 32.07/32.25 tff(2173,plain,
% 32.07/32.25 ((d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~(phi(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = err))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))),
% 32.07/32.25 inference(tautology,[status(thm)],[])).
% 32.07/32.25 tff(2174,plain,
% 32.07/32.25 (d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~(phi(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = err))),
% 32.07/32.25 inference(unit_resolution,[status(thm)],[2173, 2172])).
% 32.07/32.25 tff(2175,plain,
% 32.07/32.25 (((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) | (~(phi(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~(d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~(phi(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = err)))))) <=> ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) | (~(phi(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~(d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~(phi(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = err)))))),
% 32.07/32.25 inference(rewrite,[status(thm)],[])).
% 32.07/32.25 tff(2176,plain,
% 32.07/32.25 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | ((~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) | (~(phi(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~(d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~(phi(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = err)))))),
% 32.07/32.25 inference(quant_inst,[status(thm)],[])).
% 32.07/32.25 tff(2177,plain,
% 32.07/32.25 ((~![X: $i] : ((~((~d(X)) | (~(phi(X) = X)))) | (~(d(X) | (~(phi(X) = err)))))) | (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) | (~(phi(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~(d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~(phi(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = err))))),
% 32.07/32.25 inference(modus_ponens,[status(thm)],[2176, 2175])).
% 32.07/32.25 tff(2178,plain,
% 32.07/32.25 (~((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) | (~(phi(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))),
% 32.07/32.25 inference(unit_resolution,[status(thm)],[2177, 127, 2174])).
% 32.07/32.25 tff(2179,plain,
% 32.07/32.25 (((~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) | (~(phi(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))) | (phi(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))),
% 32.07/32.25 inference(tautology,[status(thm)],[])).
% 32.07/32.25 tff(2180,plain,
% 32.07/32.25 (phi(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))),
% 32.07/32.25 inference(unit_resolution,[status(thm)],[2179, 2178])).
% 32.07/32.25 tff(2181,plain,
% 32.07/32.25 (f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))),
% 32.07/32.25 inference(transitivity,[status(thm)],[41, 2140])).
% 32.07/32.25 tff(2182,plain,
% 32.07/32.25 (phi(f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) = phi(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))),
% 32.07/32.25 inference(monotonicity,[status(thm)],[2181])).
% 32.07/32.25 tff(2183,plain,
% 32.07/32.25 (or2(P!8, Q!7) = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))),
% 32.07/32.25 inference(transitivity,[status(thm)],[365, 2182, 2180])).
% 32.07/32.25 tff(2184,plain,
% 32.07/32.25 (((Q!7 = false) | (Q!7 = true)) | (~(Q!7 = false))),
% 32.07/32.25 inference(tautology,[status(thm)],[])).
% 32.07/32.25 tff(2185,plain,
% 32.07/32.25 ((Q!7 = false) | (Q!7 = true)),
% 32.07/32.25 inference(unit_resolution,[status(thm)],[2184, 2101])).
% 32.07/32.25 tff(2186,plain,
% 32.07/32.25 ((~(bool(Q!7) <=> ((Q!7 = false) | (Q!7 = true)))) | bool(Q!7) | (~((Q!7 = false) | (Q!7 = true)))),
% 32.07/32.25 inference(tautology,[status(thm)],[])).
% 32.07/32.25 tff(2187,plain,
% 32.07/32.25 (bool(Q!7) | (~((Q!7 = false) | (Q!7 = true)))),
% 32.07/32.25 inference(unit_resolution,[status(thm)],[2186, 629])).
% 32.07/32.25 tff(2188,plain,
% 32.07/32.25 (bool(Q!7)),
% 32.07/32.25 inference(unit_resolution,[status(thm)],[2187, 2185])).
% 32.07/32.25 tff(2189,plain,
% 32.07/32.25 (or1(false, Q!7) = Q!7),
% 32.07/32.25 inference(unit_resolution,[status(thm)],[2047, 2188])).
% 32.07/32.25 tff(2190,plain,
% 32.07/32.25 (or1(P!8, Q!7) = or1(false, Q!7)),
% 32.07/32.25 inference(monotonicity,[status(thm)],[1765])).
% 32.07/32.25 tff(2191,plain,
% 32.07/32.25 (or1(P!8, Q!7) = false),
% 32.07/32.25 inference(transitivity,[status(thm)],[2190, 2189, 2101])).
% 32.07/32.25 tff(2192,plain,
% 32.07/32.25 ((or1(P!8, Q!7) = or2(P!8, Q!7)) <=> (false = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))),
% 32.07/32.25 inference(monotonicity,[status(thm)],[2191, 2183])).
% 32.07/32.25 tff(2193,plain,
% 32.07/32.25 ((or1(P!8, Q!7) = or2(P!8, Q!7)) <=> (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false)),
% 32.07/32.25 inference(transitivity,[status(thm)],[2192, 2142])).
% 32.07/32.25 tff(2194,plain,
% 32.07/32.25 ((~(or1(P!8, Q!7) = or2(P!8, Q!7))) <=> (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false))),
% 32.07/32.25 inference(monotonicity,[status(thm)],[2193])).
% 32.07/32.25 tff(2195,plain,
% 32.07/32.25 (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false)),
% 32.07/32.25 inference(modus_ponens,[status(thm)],[377, 2194])).
% 32.07/32.25 tff(2196,plain,
% 32.07/32.25 ((~![X: $i] : (bool(X) <=> ((X = false) | (X = true)))) | (bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) <=> ((lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false) | (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = true)))),
% 32.07/32.25 inference(quant_inst,[status(thm)],[])).
% 32.07/32.25 tff(2197,plain,
% 32.07/32.25 (bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) <=> ((lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false) | (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = true))),
% 32.07/32.25 inference(unit_resolution,[status(thm)],[2196, 69])).
% 32.07/32.25 tff(2198,plain,
% 32.07/32.25 (bool(lazy_impl(prop(P!6), P!6)) <=> bool(f7(P!6))),
% 32.07/32.25 inference(monotonicity,[status(thm)],[720])).
% 32.07/32.25 tff(2199,plain,
% 32.07/32.25 (bool(f7(P!6)) <=> bool(lazy_impl(prop(P!6), P!6))),
% 32.07/32.25 inference(symmetry,[status(thm)],[2198])).
% 32.07/32.25 tff(2200,plain,
% 32.07/32.25 (bool(f7(P!6)) <=> bool(false)),
% 32.07/32.25 inference(monotonicity,[status(thm)],[2145])).
% 32.07/32.25 tff(2201,plain,
% 32.07/32.25 (bool(false) <=> bool(f7(P!6))),
% 32.07/32.25 inference(symmetry,[status(thm)],[2200])).
% 32.07/32.25 tff(2202,plain,
% 32.07/32.25 (bool(false) <=> bool(lazy_impl(prop(P!6), P!6))),
% 32.07/32.25 inference(transitivity,[status(thm)],[2201, 2199])).
% 32.07/32.25 tff(2203,plain,
% 32.07/32.25 (bool(lazy_impl(prop(P!6), P!6))),
% 32.07/32.25 inference(modus_ponens,[status(thm)],[756, 2202])).
% 32.07/32.25 tff(2204,plain,
% 32.07/32.25 (((~(d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~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_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~((~(lazy_impl(prop(P!6), P!6) = true)) | (~(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false))))) | ((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))),
% 32.07/32.25 inference(tautology,[status(thm)],[])).
% 32.07/32.25 tff(2205,plain,
% 32.07/32.25 ((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))),
% 32.07/32.25 inference(unit_resolution,[status(thm)],[2204, 2167])).
% 32.07/32.25 tff(2206,plain,
% 32.07/32.25 ((~((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))))) | (~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))),
% 32.07/32.25 inference(tautology,[status(thm)],[])).
% 32.07/32.25 tff(2207,plain,
% 32.07/32.25 ((~d(lazy_impl(prop(P!6), P!6))) | (~bool(lazy_impl(prop(P!6), P!6))) | bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) | (~d(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))))),
% 32.07/32.25 inference(unit_resolution,[status(thm)],[2206, 2205])).
% 32.07/32.25 tff(2208,plain,
% 32.07/32.25 (bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))),
% 32.07/32.25 inference(unit_resolution,[status(thm)],[2207, 2172, 2203, 2149])).
% 32.07/32.25 tff(2209,plain,
% 32.07/32.25 ((~(bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) <=> ((lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false) | (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = true)))) | (~bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)))) | ((lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false) | (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = true))),
% 32.07/32.25 inference(tautology,[status(thm)],[])).
% 32.07/32.25 tff(2210,plain,
% 32.07/32.25 ((~(bool(lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))) <=> ((lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false) | (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = true)))) | ((lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false) | (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = true))),
% 32.07/32.25 inference(unit_resolution,[status(thm)],[2209, 2208])).
% 32.07/32.25 tff(2211,plain,
% 32.07/32.25 ((lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false) | (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = true)),
% 32.07/32.25 inference(unit_resolution,[status(thm)],[2210, 2197])).
% 32.07/32.25 tff(2212,plain,
% 32.07/32.25 ((~((lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false) | (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = true))) | (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false) | (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = true)),
% 32.07/32.25 inference(tautology,[status(thm)],[])).
% 32.07/32.25 tff(2213,plain,
% 32.07/32.25 ((lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = false) | (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = true)),
% 32.07/32.25 inference(unit_resolution,[status(thm)],[2212, 2211])).
% 32.07/32.25 tff(2214,plain,
% 32.07/32.25 (lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8)) = true),
% 32.07/32.25 inference(unit_resolution,[status(thm)],[2213, 2195])).
% 32.07/32.25 tff(2215,plain,
% 32.07/32.25 (true = lazy_impl(prop(tptp_fun_R_2(Q!7, P!8)), tptp_fun_R_2(Q!7, P!8))),
% 32.07/32.25 inference(symmetry,[status(thm)],[2214])).
% 32.07/32.25 tff(2216,plain,
% 32.07/32.25 (true = f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))),
% 32.07/32.25 inference(transitivity,[status(thm)],[2215, 2141, 42])).
% 32.07/32.25 tff(2217,assumption,(f3(false, false, false) = lazy_impl(prop(false), impl(impl(false, false), impl(impl(false, false), false)))), introduced(assumption)).
% 32.07/32.25 tff(2218,plain,
% 32.07/32.25 (lazy_impl(prop(false), impl(impl(false, false), impl(impl(false, false), false))) = f3(false, false, false)),
% 32.07/32.25 inference(symmetry,[status(thm)],[2217])).
% 32.07/32.25 tff(2219,plain,
% 32.07/32.25 (false = f3(P!8, Q!7, false)),
% 32.07/32.25 inference(transitivity,[status(thm)],[765, 764, 2114, 2218, 2103])).
% 32.07/32.25 tff(2220,plain,
% 32.07/32.25 (forallprefers(false, true) <=> forallprefers(f3(P!8, Q!7, false), f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))),
% 32.07/32.25 inference(monotonicity,[status(thm)],[2219, 2216])).
% 32.07/32.25 tff(2221,plain,
% 32.07/32.25 (forallprefers(f3(P!8, Q!7, false), f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8))) <=> forallprefers(false, true)),
% 32.07/32.25 inference(symmetry,[status(thm)],[2220])).
% 32.07/32.25 tff(2222,plain,
% 32.07/32.25 ((~forallprefers(f3(P!8, Q!7, false), f3(P!8, Q!7, tptp_fun_R_2(Q!7, P!8)))) <=> (~forallprefers(false, true))),
% 32.07/32.25 inference(monotonicity,[status(thm)],[2221])).
% 32.07/32.25 tff(2223,plain,
% 32.07/32.25 (~forallprefers(false, true)),
% 32.07/32.25 inference(modus_ponens,[status(thm)],[2120, 2222])).
% 32.07/32.25 tff(2224,plain,
% 32.07/32.25 (((~![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, 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, true))),
% 32.07/32.25 inference(rewrite,[status(thm)],[])).
% 32.07/32.25 tff(2225,plain,
% 32.07/32.25 ((forallprefers(false, true) <=> $true) <=> forallprefers(false, true)),
% 32.07/32.25 inference(rewrite,[status(thm)],[])).
% 32.07/32.25 tff(2226,plain,
% 32.07/32.26 (($true | (~(d(false) | (~d(true)))) | (~((~d(true)) | (~d(false)) | bool(false) | (~bool(true))))) <=> $true),
% 32.07/32.26 inference(rewrite,[status(thm)],[])).
% 32.07/32.26 tff(2227,plain,
% 32.07/32.26 ((~((~d(true)) | (~bool(true)) | bool(false) | (~d(false)))) <=> (~((~d(true)) | (~d(false)) | bool(false) | (~bool(true))))),
% 32.07/32.26 inference(rewrite,[status(thm)],[])).
% 32.07/32.26 tff(2228,plain,
% 32.07/32.26 ((~$false) <=> $true),
% 32.07/32.26 inference(rewrite,[status(thm)],[])).
% 32.07/32.26 tff(2229,plain,
% 32.07/32.26 (($false | $false) <=> $false),
% 32.07/32.26 inference(rewrite,[status(thm)],[])).
% 32.07/32.26 tff(2230,plain,
% 32.07/32.26 ((~$true) <=> $false),
% 32.07/32.26 inference(rewrite,[status(thm)],[])).
% 32.07/32.26 tff(2231,plain,
% 32.07/32.26 ((true = true) <=> $true),
% 32.07/32.26 inference(rewrite,[status(thm)],[])).
% 32.07/32.26 tff(2232,plain,
% 32.07/32.26 ((~(true = true)) <=> (~$true)),
% 32.07/32.26 inference(monotonicity,[status(thm)],[2231])).
% 32.07/32.26 tff(2233,plain,
% 32.07/32.26 ((~(true = true)) <=> $false),
% 32.07/32.26 inference(transitivity,[status(thm)],[2232, 2230])).
% 32.07/32.26 tff(2234,plain,
% 32.07/32.26 ((false = false) <=> $true),
% 32.07/32.26 inference(rewrite,[status(thm)],[])).
% 32.07/32.26 tff(2235,plain,
% 32.07/32.26 ((~(false = false)) <=> (~$true)),
% 32.07/32.26 inference(monotonicity,[status(thm)],[2234])).
% 32.07/32.26 tff(2236,plain,
% 32.07/32.26 ((~(false = false)) <=> $false),
% 32.07/32.26 inference(transitivity,[status(thm)],[2235, 2230])).
% 32.07/32.26 tff(2237,plain,
% 32.07/32.26 (((~(false = false)) | (~(true = true))) <=> ($false | $false)),
% 32.07/32.26 inference(monotonicity,[status(thm)],[2236, 2233])).
% 32.07/32.26 tff(2238,plain,
% 32.07/32.26 (((~(false = false)) | (~(true = true))) <=> $false),
% 32.07/32.26 inference(transitivity,[status(thm)],[2237, 2229])).
% 32.07/32.26 tff(2239,plain,
% 32.07/32.26 ((~((~(false = false)) | (~(true = true)))) <=> (~$false)),
% 32.07/32.26 inference(monotonicity,[status(thm)],[2238])).
% 32.07/32.26 tff(2240,plain,
% 32.07/32.26 ((~((~(false = false)) | (~(true = true)))) <=> $true),
% 32.07/32.26 inference(transitivity,[status(thm)],[2239, 2228])).
% 32.07/32.26 tff(2241,plain,
% 32.07/32.26 (((~((~(false = false)) | (~(true = true)))) | (~(d(false) | (~d(true)))) | (~((~d(true)) | (~bool(true)) | bool(false) | (~d(false))))) <=> ($true | (~(d(false) | (~d(true)))) | (~((~d(true)) | (~d(false)) | bool(false) | (~bool(true)))))),
% 32.07/32.26 inference(monotonicity,[status(thm)],[2240, 2227])).
% 32.07/32.26 tff(2242,plain,
% 32.07/32.26 (((~((~(false = false)) | (~(true = true)))) | (~(d(false) | (~d(true)))) | (~((~d(true)) | (~bool(true)) | bool(false) | (~d(false))))) <=> $true),
% 32.07/32.26 inference(transitivity,[status(thm)],[2241, 2226])).
% 32.07/32.26 tff(2243,plain,
% 32.07/32.26 ((forallprefers(false, true) <=> ((~((~(false = false)) | (~(true = true)))) | (~(d(false) | (~d(true)))) | (~((~d(true)) | (~bool(true)) | bool(false) | (~d(false)))))) <=> (forallprefers(false, true) <=> $true)),
% 32.07/32.26 inference(monotonicity,[status(thm)],[2242])).
% 32.07/32.26 tff(2244,plain,
% 32.07/32.26 ((forallprefers(false, true) <=> ((~((~(false = false)) | (~(true = true)))) | (~(d(false) | (~d(true)))) | (~((~d(true)) | (~bool(true)) | bool(false) | (~d(false)))))) <=> forallprefers(false, true)),
% 32.07/32.26 inference(transitivity,[status(thm)],[2243, 2225])).
% 32.07/32.26 tff(2245,plain,
% 32.07/32.26 (((~![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, true) <=> ((~((~(false = false)) | (~(true = true)))) | (~(d(false) | (~d(true)))) | (~((~d(true)) | (~bool(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, true))),
% 32.07/32.26 inference(monotonicity,[status(thm)],[2244])).
% 32.07/32.26 tff(2246,plain,
% 32.07/32.26 (((~![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, true) <=> ((~((~(false = false)) | (~(true = true)))) | (~(d(false) | (~d(true)))) | (~((~d(true)) | (~bool(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, true))),
% 32.07/32.26 inference(transitivity,[status(thm)],[2245, 2224])).
% 32.07/32.26 tff(2247,plain,
% 32.07/32.26 ((~![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, true) <=> ((~((~(false = false)) | (~(true = true)))) | (~(d(false) | (~d(true)))) | (~((~d(true)) | (~bool(true)) | bool(false) | (~d(false))))))),
% 32.07/32.27 inference(quant_inst,[status(thm)],[])).
% 32.07/32.27 tff(2248,plain,
% 32.07/32.27 ((~![X: $i, Y: $i] : (forallprefers(X, Y) <=> ((~((~(X = false)) | (~(Y = true)))) | (~(d(X) | (~d(Y)))) | (~((~d(Y)) | (~bool(Y)) | bool(X) | (~d(X))))))) | forallprefers(false, true)),
% 32.07/32.27 inference(modus_ponens,[status(thm)],[2247, 2246])).
% 32.07/32.27 tff(2249,plain,
% 32.07/32.27 (forallprefers(false, true)),
% 32.07/32.27 inference(unit_resolution,[status(thm)],[2248, 25])).
% 32.07/32.27 tff(2250,plain,
% 32.07/32.27 ($false),
% 32.07/32.27 inference(unit_resolution,[status(thm)],[2249, 2223])).
% 32.07/32.27 tff(2251,plain,((~(f3(false, false, false) = lazy_impl(prop(false), impl(impl(false, false), impl(impl(false, false), false))))) | (~(impl(true, tptp_fun_R_2(Q!7, P!8)) = tptp_fun_R_2(Q!7, P!8))) | (~(impl(false, tptp_fun_R_2(Q!7, P!8)) = true))), inference(lemma,lemma(discharge,[]))).
% 32.07/32.27 tff(2252,plain,
% 32.07/32.27 ((~(impl(true, tptp_fun_R_2(Q!7, P!8)) = tptp_fun_R_2(Q!7, P!8))) | (~(impl(false, tptp_fun_R_2(Q!7, P!8)) = true))),
% 32.07/32.27 inference(unit_resolution,[status(thm)],[2251, 2107])).
% 32.07/32.27 tff(2253,plain,
% 32.07/32.27 ($false),
% 32.07/32.27 inference(unit_resolution,[status(thm)],[2252, 2130, 2129])).
% 32.07/32.27 % SZS output end Proof
% 32.07/32.27 % E exiting
%------------------------------------------------------------------------------