%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG071+1 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 04:58:05 AM UTC 2025
% Result : Theorem 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG071+1 : TPTP v9.0.0. Released v2.7.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 10:49:11 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.37 % SZS status Theorem
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(j_type, type, (
% 0.18/0.37 j: $i > $i)).
% 0.18/0.37 tff(tptp_fun_U_1_type, type, (
% 0.18/0.37 tptp_fun_U_1: $i)).
% 0.18/0.37 tff(op1_type, type, (
% 0.18/0.37 op1: ( $i * $i ) > $i)).
% 0.18/0.37 tff(tptp_fun_V_0_type, type, (
% 0.18/0.37 tptp_fun_V_0: $i > $i)).
% 0.18/0.37 tff(h_type, type, (
% 0.18/0.37 h: $i > $i)).
% 0.18/0.37 tff(op2_type, type, (
% 0.18/0.37 op2: ( $i * $i ) > $i)).
% 0.18/0.37 tff(sorti1_type, type, (
% 0.18/0.37 sorti1: $i > $o)).
% 0.18/0.37 tff(sorti2_type, type, (
% 0.18/0.37 sorti2: $i > $o)).
% 0.18/0.37 tff(1,plain,
% 0.18/0.37 (^[V: $i] : refl(((~sorti2(V)) | sorti1(j(V))) <=> ((~sorti2(V)) | sorti1(j(V))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 ((~((![U: $i] : (sorti1(U) => sorti2(h(U))) & ![V: $i] : (sorti2(V) => sorti1(j(V)))) => (~(((![W: $i] : (sorti1(W) => ![X: $i] : (sorti1(X) => (h(op1(W, X)) = op2(h(W), h(X))))) & ![Y: $i] : (sorti2(Y) => ![Z: $i] : (sorti2(Z) => (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) & ![X1: $i] : (sorti2(X1) => (h(j(X1)) = X1))) & ![X2: $i] : (sorti1(X2) => (j(h(X2)) = X2)))))) <=> (~((~(![U: $i] : ((~sorti1(U)) | sorti2(h(U))) & ![V: $i] : ((~sorti2(V)) | sorti1(j(V))))) | (~(![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) & ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) & ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) & ![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(5,axiom,(~((![U: $i] : (sorti1(U) => sorti2(h(U))) & ![V: $i] : (sorti2(V) => sorti1(j(V)))) => (~(((![W: $i] : (sorti1(W) => ![X: $i] : (sorti1(X) => (h(op1(W, X)) = op2(h(W), h(X))))) & ![Y: $i] : (sorti2(Y) => ![Z: $i] : (sorti2(Z) => (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) & ![X1: $i] : (sorti2(X1) => (h(j(X1)) = X1))) & ![X2: $i] : (sorti1(X2) => (j(h(X2)) = X2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 0.18/0.37 tff(6,plain,
% 0.18/0.37 (~((~(![U: $i] : ((~sorti1(U)) | sorti2(h(U))) & ![V: $i] : ((~sorti2(V)) | sorti1(j(V))))) | (~(![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) & ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) & ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) & ![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2)))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.37 tff(7,plain,
% 0.18/0.37 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) & ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.18/0.37 inference(or_elim,[status(thm)],[6])).
% 0.18/0.37 tff(8,plain,
% 0.18/0.37 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.18/0.37 inference(and_elim,[status(thm)],[7])).
% 0.18/0.37 tff(9,plain,
% 0.18/0.37 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.18/0.37 tff(10,plain,(
% 0.18/0.37 ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.18/0.37 inference(skolemize,[status(sab)],[9])).
% 0.18/0.37 tff(11,plain,
% 0.18/0.37 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.18/0.37 tff(12,plain,
% 0.18/0.37 ((sorti2(U!1) & ![V: $i] : (~(sorti2(V) & (~(op2(V, op2(V, U!1)) = U!1)) & (op2(U!1, op2(V, U!1)) = V)))) <=> (sorti2(U!1) & ![V: $i] : (~(sorti2(V) & (~(op2(V, op2(V, U!1)) = U!1)) & (op2(U!1, op2(V, U!1)) = V))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 ((~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (~(op2(V, op2(V, U)) = U)) & (op2(U, op2(V, U)) = V)))) <=> (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (~(op2(V, op2(V, U)) = U)) & (op2(U, op2(V, U)) = V))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(14,plain,
% 0.18/0.37 ((~![U: $i] : (sorti2(U) => ?[V: $i] : ((sorti2(V) & (~(op2(V, op2(V, U)) = U))) & (op2(U, op2(V, U)) = V)))) <=> (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (~(op2(V, op2(V, U)) = U)) & (op2(U, op2(V, U)) = V))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(15,axiom,(~![U: $i] : (sorti2(U) => ?[V: $i] : ((sorti2(V) & (~(op2(V, op2(V, U)) = U))) & (op2(U, op2(V, U)) = V)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax4')).
% 0.18/0.38 tff(16,plain,
% 0.18/0.38 (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (~(op2(V, op2(V, U)) = U)) & (op2(U, op2(V, U)) = V)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.18/0.38 tff(17,plain,
% 0.18/0.38 (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (~(op2(V, op2(V, U)) = U)) & (op2(U, op2(V, U)) = V)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.18/0.38 tff(18,plain,
% 0.18/0.38 (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (~(op2(V, op2(V, U)) = U)) & (op2(U, op2(V, U)) = V)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.18/0.38 tff(19,plain,
% 0.18/0.38 (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (~(op2(V, op2(V, U)) = U)) & (op2(U, op2(V, U)) = V)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.18/0.38 tff(20,plain,
% 0.18/0.38 (sorti2(U!1) & ![V: $i] : (~(sorti2(V) & (~(op2(V, op2(V, U!1)) = U!1)) & (op2(U!1, op2(V, U!1)) = V)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.18/0.38 tff(21,plain,
% 0.18/0.38 (sorti2(U!1)),
% 0.18/0.38 inference(and_elim,[status(thm)],[20])).
% 0.18/0.38 tff(22,plain,
% 0.18/0.38 (((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(U!1)) | sorti1(j(U!1)))) <=> ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(U!1)) | sorti1(j(U!1)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(23,plain,
% 0.18/0.38 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(U!1)) | sorti1(j(U!1)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(24,plain,
% 0.18/0.38 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(U!1)) | sorti1(j(U!1))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.18/0.38 tff(25,plain,
% 0.18/0.38 (sorti1(j(U!1))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 0.18/0.38 tff(26,plain,
% 0.18/0.38 (^[U: $i] : refl(((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U)))))) <=> ((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U)))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(27,plain,
% 0.18/0.38 (![U: $i] : ((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U)))))) <=> ![U: $i] : ((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U))))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[26])).
% 0.18/0.38 tff(28,plain,
% 0.18/0.38 (^[U: $i] : rewrite(((~sorti1(U)) | (sorti1(tptp_fun_V_0(U)) & (~(op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U)) & (op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U)))) <=> ((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U)))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(29,plain,
% 0.18/0.38 (![U: $i] : ((~sorti1(U)) | (sorti1(tptp_fun_V_0(U)) & (~(op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U)) & (op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U)))) <=> ![U: $i] : ((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U))))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[28])).
% 0.18/0.38 tff(30,plain,
% 0.18/0.38 (![U: $i] : ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (~(op1(V, op1(V, U)) = U)) & (op1(U, op1(V, U)) = V))) <=> ![U: $i] : ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (~(op1(V, op1(V, U)) = U)) & (op1(U, op1(V, U)) = V)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(31,plain,
% 0.18/0.38 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite(((sorti1(V) & (~(op1(V, op1(V, U)) = U))) & (op1(U, op1(V, U)) = V)) <=> (sorti1(V) & (~(op1(V, op1(V, U)) = U)) & (op1(U, op1(V, U)) = V)))), (?[V: $i] : ((sorti1(V) & (~(op1(V, op1(V, U)) = U))) & (op1(U, op1(V, U)) = V)) <=> ?[V: $i] : (sorti1(V) & (~(op1(V, op1(V, U)) = U)) & (op1(U, op1(V, U)) = V)))), ((sorti1(U) => ?[V: $i] : ((sorti1(V) & (~(op1(V, op1(V, U)) = U))) & (op1(U, op1(V, U)) = V))) <=> (sorti1(U) => ?[V: $i] : (sorti1(V) & (~(op1(V, op1(V, U)) = U)) & (op1(U, op1(V, U)) = V))))), rewrite((sorti1(U) => ?[V: $i] : (sorti1(V) & (~(op1(V, op1(V, U)) = U)) & (op1(U, op1(V, U)) = V))) <=> ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (~(op1(V, op1(V, U)) = U)) & (op1(U, op1(V, U)) = V)))), ((sorti1(U) => ?[V: $i] : ((sorti1(V) & (~(op1(V, op1(V, U)) = U))) & (op1(U, op1(V, U)) = V))) <=> ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (~(op1(V, op1(V, U)) = U)) & (op1(U, op1(V, U)) = V)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(32,plain,
% 0.18/0.38 (![U: $i] : (sorti1(U) => ?[V: $i] : ((sorti1(V) & (~(op1(V, op1(V, U)) = U))) & (op1(U, op1(V, U)) = V))) <=> ![U: $i] : ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (~(op1(V, op1(V, U)) = U)) & (op1(U, op1(V, U)) = V)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[31])).
% 0.18/0.38 tff(33,axiom,(![U: $i] : (sorti1(U) => ?[V: $i] : ((sorti1(V) & (~(op1(V, op1(V, U)) = U))) & (op1(U, op1(V, U)) = V)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax3')).
% 0.18/0.38 tff(34,plain,
% 0.18/0.38 (![U: $i] : ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (~(op1(V, op1(V, U)) = U)) & (op1(U, op1(V, U)) = V)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.18/0.38 tff(35,plain,
% 0.18/0.38 (![U: $i] : ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (~(op1(V, op1(V, U)) = U)) & (op1(U, op1(V, U)) = V)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.18/0.38 tff(36,plain,(
% 0.18/0.38 ![U: $i] : ((~sorti1(U)) | (sorti1(tptp_fun_V_0(U)) & (~(op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U)) & (op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[35])).
% 0.18/0.38 tff(37,plain,
% 0.18/0.38 (![U: $i] : ((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.18/0.38 tff(38,plain,
% 0.18/0.38 (![U: $i] : ((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.18/0.38 tff(39,plain,
% 0.18/0.38 (((~![U: $i] : ((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U))))))) | ((~sorti1(j(U!1))) | (~((op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(U!1)) | (~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = tptp_fun_V_0(j(U!1)))))))) <=> ((~![U: $i] : ((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U))))))) | (~sorti1(j(U!1))) | (~((op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(U!1)) | (~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = tptp_fun_V_0(j(U!1)))))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(40,plain,
% 0.18/0.38 ((~![U: $i] : ((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U))))))) | ((~sorti1(j(U!1))) | (~((op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(U!1)) | (~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = tptp_fun_V_0(j(U!1)))))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(41,plain,
% 0.18/0.38 ((~![U: $i] : ((~sorti1(U)) | (~((op1(tptp_fun_V_0(U), op1(tptp_fun_V_0(U), U)) = U) | (~sorti1(tptp_fun_V_0(U))) | (~(op1(U, op1(tptp_fun_V_0(U), U)) = tptp_fun_V_0(U))))))) | (~sorti1(j(U!1))) | (~((op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(U!1)) | (~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = tptp_fun_V_0(j(U!1))))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 (~((op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(U!1)) | (~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = tptp_fun_V_0(j(U!1)))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[41, 38, 25])).
% 0.18/0.38 tff(43,plain,
% 0.18/0.38 (((op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(U!1)) | (~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = tptp_fun_V_0(j(U!1))))) | sorti1(tptp_fun_V_0(j(U!1)))),
% 0.18/0.38 inference(tautology,[status(thm)],[])).
% 0.18/0.38 tff(44,plain,
% 0.18/0.38 (sorti1(tptp_fun_V_0(j(U!1)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.18/0.38 tff(45,plain,
% 0.18/0.38 (^[U: $i] : refl(((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(46,plain,
% 0.18/0.38 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[45])).
% 0.18/0.38 tff(47,plain,
% 0.18/0.38 (^[U: $i] : rewrite(((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(48,plain,
% 0.18/0.38 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[47])).
% 0.18/0.38 tff(49,plain,
% 0.18/0.38 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[48, 46])).
% 0.18/0.38 tff(50,plain,
% 0.18/0.38 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(51,plain,
% 0.18/0.38 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((sorti1(V) => sorti1(op1(U, V))) <=> ((~sorti1(V)) | sorti1(op1(U, V))))), (![V: $i] : (sorti1(V) => sorti1(op1(U, V))) <=> ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))), ((sorti1(U) => ![V: $i] : (sorti1(V) => sorti1(op1(U, V)))) <=> (sorti1(U) => ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))))), rewrite((sorti1(U) => ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V)))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))), ((sorti1(U) => ![V: $i] : (sorti1(V) => sorti1(op1(U, V)))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(52,plain,
% 0.18/0.38 (![U: $i] : (sorti1(U) => ![V: $i] : (sorti1(V) => sorti1(op1(U, V)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[51])).
% 0.18/0.38 tff(53,axiom,(![U: $i] : (sorti1(U) => ![V: $i] : (sorti1(V) => sorti1(op1(U, V))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax1')).
% 0.18/0.38 tff(54,plain,
% 0.18/0.38 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.18/0.38 tff(55,plain,
% 0.18/0.38 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.18/0.38 tff(56,plain,(
% 0.18/0.38 ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[55])).
% 0.18/0.38 tff(57,plain,
% 0.18/0.38 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.18/0.38 tff(58,plain,
% 0.18/0.38 (((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))) | ((~sorti1(tptp_fun_V_0(j(U!1)))) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V))))) <=> ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(59,plain,
% 0.18/0.38 ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))) | ((~sorti1(tptp_fun_V_0(j(U!1)))) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(60,plain,
% 0.18/0.38 ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(U, V))))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | ![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.18/0.38 tff(61,plain,
% 0.18/0.38 (![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[60, 57, 44])).
% 0.18/0.38 tff(62,plain,
% 0.18/0.38 (((~![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V)))) | ((~sorti1(j(U!1))) | sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1))))) <=> ((~![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V)))) | (~sorti1(j(U!1))) | sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(63,plain,
% 0.18/0.38 ((~![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V)))) | ((~sorti1(j(U!1))) | sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(64,plain,
% 0.18/0.38 ((~![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V)))) | (~sorti1(j(U!1))) | sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.18/0.38 tff(65,plain,
% 0.18/0.38 (sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[64, 25, 61])).
% 0.18/0.38 tff(66,plain,
% 0.18/0.38 (^[W: $i] : refl(((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) <=> ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(67,plain,
% 0.18/0.38 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) <=> ![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[66])).
% 0.18/0.38 tff(68,plain,
% 0.18/0.38 (^[W: $i] : rewrite(((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) <=> ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(69,plain,
% 0.18/0.38 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) <=> ![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[68])).
% 0.18/0.38 tff(70,plain,
% 0.18/0.38 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) <=> ![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[69, 67])).
% 0.18/0.38 tff(71,plain,
% 0.18/0.38 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) <=> ![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(72,plain,
% 0.18/0.38 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X))))) & ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) & ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) & ![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.18/0.38 inference(or_elim,[status(thm)],[6])).
% 0.18/0.38 tff(73,plain,
% 0.18/0.38 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.18/0.38 inference(and_elim,[status(thm)],[72])).
% 0.18/0.38 tff(74,plain,
% 0.18/0.38 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[73, 71])).
% 0.18/0.38 tff(75,plain,(
% 0.18/0.38 ![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[74])).
% 0.18/0.38 tff(76,plain,
% 0.18/0.38 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[75, 70])).
% 0.18/0.38 tff(77,plain,
% 0.18/0.38 (((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | ((~sorti1(tptp_fun_V_0(j(U!1)))) | ![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X)))))) <=> ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | ![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(78,plain,
% 0.18/0.39 ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | ((~sorti1(tptp_fun_V_0(j(U!1)))) | ![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X)))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(79,plain,
% 0.18/0.39 ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | ![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.18/0.39 tff(80,plain,
% 0.18/0.39 (![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[79, 76, 44])).
% 0.18/0.39 tff(81,plain,
% 0.18/0.39 (((~![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))) | ((~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | (h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = op2(h(tptp_fun_V_0(j(U!1))), h(op1(tptp_fun_V_0(j(U!1)), j(U!1))))))) <=> ((~![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))) | (~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | (h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = op2(h(tptp_fun_V_0(j(U!1))), h(op1(tptp_fun_V_0(j(U!1)), j(U!1))))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(82,plain,
% 0.18/0.39 ((~![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))) | ((~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | (h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = op2(h(tptp_fun_V_0(j(U!1))), h(op1(tptp_fun_V_0(j(U!1)), j(U!1))))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(83,plain,
% 0.18/0.39 ((~![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))) | (~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | (h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = op2(h(tptp_fun_V_0(j(U!1))), h(op1(tptp_fun_V_0(j(U!1)), j(U!1)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.18/0.39 tff(84,plain,
% 0.18/0.39 (h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = op2(h(tptp_fun_V_0(j(U!1))), h(op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[83, 80, 65])).
% 0.18/0.39 tff(85,plain,
% 0.18/0.39 (op2(h(tptp_fun_V_0(j(U!1))), h(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.18/0.39 inference(symmetry,[status(thm)],[84])).
% 0.18/0.39 tff(86,plain,
% 0.18/0.39 (((~![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))) | ((~sorti1(j(U!1))) | (h(op1(tptp_fun_V_0(j(U!1)), j(U!1))) = op2(h(tptp_fun_V_0(j(U!1))), h(j(U!1)))))) <=> ((~![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))) | (~sorti1(j(U!1))) | (h(op1(tptp_fun_V_0(j(U!1)), j(U!1))) = op2(h(tptp_fun_V_0(j(U!1))), h(j(U!1)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(87,plain,
% 0.18/0.39 ((~![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))) | ((~sorti1(j(U!1))) | (h(op1(tptp_fun_V_0(j(U!1)), j(U!1))) = op2(h(tptp_fun_V_0(j(U!1))), h(j(U!1)))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(88,plain,
% 0.18/0.39 ((~![X: $i] : ((~sorti1(X)) | (h(op1(tptp_fun_V_0(j(U!1)), X)) = op2(h(tptp_fun_V_0(j(U!1))), h(X))))) | (~sorti1(j(U!1))) | (h(op1(tptp_fun_V_0(j(U!1)), j(U!1))) = op2(h(tptp_fun_V_0(j(U!1))), h(j(U!1))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.18/0.39 tff(89,plain,
% 0.18/0.39 (h(op1(tptp_fun_V_0(j(U!1)), j(U!1))) = op2(h(tptp_fun_V_0(j(U!1))), h(j(U!1)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[88, 25, 80])).
% 0.18/0.39 tff(90,plain,
% 0.18/0.39 (op2(h(tptp_fun_V_0(j(U!1))), h(j(U!1))) = h(op1(tptp_fun_V_0(j(U!1)), j(U!1)))),
% 0.18/0.39 inference(symmetry,[status(thm)],[89])).
% 0.18/0.39 tff(91,plain,
% 0.18/0.39 (^[X1: $i] : refl(((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ((~sorti2(X1)) | (h(j(X1)) = X1)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(92,plain,
% 0.18/0.39 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[91])).
% 0.18/0.39 tff(93,plain,
% 0.18/0.39 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(94,plain,
% 0.18/0.39 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.18/0.39 inference(and_elim,[status(thm)],[72])).
% 0.18/0.39 tff(95,plain,
% 0.18/0.39 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.18/0.39 tff(96,plain,(
% 0.18/0.39 ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.18/0.39 inference(skolemize,[status(sab)],[95])).
% 0.18/0.39 tff(97,plain,
% 0.18/0.39 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.18/0.39 tff(98,plain,
% 0.18/0.39 (((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(U!1)) | (h(j(U!1)) = U!1))) <=> ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(U!1)) | (h(j(U!1)) = U!1))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(99,plain,
% 0.18/0.39 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(U!1)) | (h(j(U!1)) = U!1))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(100,plain,
% 0.18/0.39 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(U!1)) | (h(j(U!1)) = U!1)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.18/0.39 tff(101,plain,
% 0.18/0.39 (h(j(U!1)) = U!1),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[100, 21, 97])).
% 0.18/0.39 tff(102,plain,
% 0.18/0.39 (U!1 = h(j(U!1))),
% 0.18/0.39 inference(symmetry,[status(thm)],[101])).
% 0.18/0.39 tff(103,plain,
% 0.18/0.39 (op2(h(tptp_fun_V_0(j(U!1))), U!1) = op2(h(tptp_fun_V_0(j(U!1))), h(j(U!1)))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[102])).
% 0.18/0.39 tff(104,plain,
% 0.18/0.39 (op2(h(tptp_fun_V_0(j(U!1))), U!1) = h(op1(tptp_fun_V_0(j(U!1)), j(U!1)))),
% 0.18/0.39 inference(transitivity,[status(thm)],[103, 90])).
% 0.18/0.39 tff(105,plain,
% 0.18/0.39 (op2(h(tptp_fun_V_0(j(U!1))), op2(h(tptp_fun_V_0(j(U!1))), U!1)) = op2(h(tptp_fun_V_0(j(U!1))), h(op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[104])).
% 0.18/0.39 tff(106,plain,
% 0.18/0.39 (((op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(U!1)) | (~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = tptp_fun_V_0(j(U!1))))) | (op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = tptp_fun_V_0(j(U!1)))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(107,plain,
% 0.18/0.39 (op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = tptp_fun_V_0(j(U!1))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[106, 42])).
% 0.18/0.39 tff(108,plain,
% 0.18/0.39 (h(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = h(tptp_fun_V_0(j(U!1)))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[107])).
% 0.18/0.39 tff(109,plain,
% 0.18/0.39 (((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | ((~sorti1(j(U!1))) | ![X: $i] : ((~sorti1(X)) | (h(op1(j(U!1), X)) = op2(h(j(U!1)), h(X)))))) <=> ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | (~sorti1(j(U!1))) | ![X: $i] : ((~sorti1(X)) | (h(op1(j(U!1), X)) = op2(h(j(U!1)), h(X)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(110,plain,
% 0.18/0.39 ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | ((~sorti1(j(U!1))) | ![X: $i] : ((~sorti1(X)) | (h(op1(j(U!1), X)) = op2(h(j(U!1)), h(X)))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(111,plain,
% 0.18/0.39 ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | (~sorti1(j(U!1))) | ![X: $i] : ((~sorti1(X)) | (h(op1(j(U!1), X)) = op2(h(j(U!1)), h(X))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.18/0.39 tff(112,plain,
% 0.18/0.39 (![X: $i] : ((~sorti1(X)) | (h(op1(j(U!1), X)) = op2(h(j(U!1)), h(X))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[111, 76, 25])).
% 0.18/0.39 tff(113,plain,
% 0.18/0.39 (((~![X: $i] : ((~sorti1(X)) | (h(op1(j(U!1), X)) = op2(h(j(U!1)), h(X))))) | ((~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | (h(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = op2(h(j(U!1)), h(op1(tptp_fun_V_0(j(U!1)), j(U!1))))))) <=> ((~![X: $i] : ((~sorti1(X)) | (h(op1(j(U!1), X)) = op2(h(j(U!1)), h(X))))) | (~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | (h(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = op2(h(j(U!1)), h(op1(tptp_fun_V_0(j(U!1)), j(U!1))))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(114,plain,
% 0.18/0.39 ((~![X: $i] : ((~sorti1(X)) | (h(op1(j(U!1), X)) = op2(h(j(U!1)), h(X))))) | ((~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | (h(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = op2(h(j(U!1)), h(op1(tptp_fun_V_0(j(U!1)), j(U!1))))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(115,plain,
% 0.18/0.39 ((~![X: $i] : ((~sorti1(X)) | (h(op1(j(U!1), X)) = op2(h(j(U!1)), h(X))))) | (~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | (h(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = op2(h(j(U!1)), h(op1(tptp_fun_V_0(j(U!1)), j(U!1)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.18/0.39 tff(116,plain,
% 0.18/0.39 ((~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | (h(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = op2(h(j(U!1)), h(op1(tptp_fun_V_0(j(U!1)), j(U!1)))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[115, 112])).
% 0.18/0.39 tff(117,plain,
% 0.18/0.39 (h(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = op2(h(j(U!1)), h(op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[116, 65])).
% 0.18/0.39 tff(118,plain,
% 0.18/0.39 (op2(h(j(U!1)), h(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) = h(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.18/0.39 inference(symmetry,[status(thm)],[117])).
% 0.18/0.39 tff(119,plain,
% 0.18/0.39 (op2(U!1, op2(h(tptp_fun_V_0(j(U!1))), U!1)) = op2(h(j(U!1)), h(op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[102, 104])).
% 0.18/0.39 tff(120,plain,
% 0.18/0.39 (op2(U!1, op2(h(tptp_fun_V_0(j(U!1))), U!1)) = h(tptp_fun_V_0(j(U!1)))),
% 0.18/0.39 inference(transitivity,[status(thm)],[119, 118, 108])).
% 0.18/0.39 tff(121,plain,
% 0.18/0.39 (^[U: $i] : refl(((~sorti1(U)) | sorti2(h(U))) <=> ((~sorti1(U)) | sorti2(h(U))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(122,plain,
% 0.18/0.39 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) <=> ![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[121])).
% 0.18/0.39 tff(123,plain,
% 0.18/0.39 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) <=> ![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(124,plain,
% 0.18/0.39 (![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.18/0.39 inference(and_elim,[status(thm)],[7])).
% 0.18/0.39 tff(125,plain,
% 0.18/0.39 (![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.18/0.39 tff(126,plain,(
% 0.18/0.39 ![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[125])).
% 0.18/0.39 tff(127,plain,
% 0.18/0.39 (![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.18/0.39 tff(128,plain,
% 0.18/0.39 (((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | ((~sorti1(tptp_fun_V_0(j(U!1)))) | sorti2(h(tptp_fun_V_0(j(U!1)))))) <=> ((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | sorti2(h(tptp_fun_V_0(j(U!1)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(129,plain,
% 0.18/0.39 ((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | ((~sorti1(tptp_fun_V_0(j(U!1)))) | sorti2(h(tptp_fun_V_0(j(U!1)))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(130,plain,
% 0.18/0.39 ((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | sorti2(h(tptp_fun_V_0(j(U!1))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.18/0.39 tff(131,plain,
% 0.18/0.39 (sorti2(h(tptp_fun_V_0(j(U!1))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[130, 127, 44])).
% 0.18/0.39 tff(132,plain,
% 0.18/0.39 (^[V: $i] : refl(((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V))) <=> ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(133,plain,
% 0.18/0.39 (![V: $i] : ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V))) <=> ![V: $i] : ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[132])).
% 0.18/0.39 tff(134,plain,
% 0.18/0.39 (^[V: $i] : trans(monotonicity(rewrite((sorti2(V) & (~(op2(V, op2(V, U!1)) = U!1)) & (op2(U!1, op2(V, U!1)) = V)) <=> (~((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V))))), ((~(sorti2(V) & (~(op2(V, op2(V, U!1)) = U!1)) & (op2(U!1, op2(V, U!1)) = V))) <=> (~(~((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V))))))), rewrite((~(~((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V))))) <=> ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V)))), ((~(sorti2(V) & (~(op2(V, op2(V, U!1)) = U!1)) & (op2(U!1, op2(V, U!1)) = V))) <=> ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(135,plain,
% 0.18/0.39 (![V: $i] : (~(sorti2(V) & (~(op2(V, op2(V, U!1)) = U!1)) & (op2(U!1, op2(V, U!1)) = V))) <=> ![V: $i] : ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[134])).
% 0.18/0.39 tff(136,plain,
% 0.18/0.39 (![V: $i] : (~(sorti2(V) & (~(op2(V, op2(V, U!1)) = U!1)) & (op2(U!1, op2(V, U!1)) = V)))),
% 0.18/0.39 inference(and_elim,[status(thm)],[20])).
% 0.18/0.39 tff(137,plain,
% 0.18/0.39 (![V: $i] : ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.18/0.40 tff(138,plain,
% 0.18/0.40 (![V: $i] : ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.18/0.40 tff(139,plain,
% 0.18/0.40 (((~![V: $i] : ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V)))) | ((~sorti2(h(tptp_fun_V_0(j(U!1))))) | (op2(h(tptp_fun_V_0(j(U!1))), op2(h(tptp_fun_V_0(j(U!1))), U!1)) = U!1) | (~(op2(U!1, op2(h(tptp_fun_V_0(j(U!1))), U!1)) = h(tptp_fun_V_0(j(U!1))))))) <=> ((~![V: $i] : ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V)))) | (~sorti2(h(tptp_fun_V_0(j(U!1))))) | (op2(h(tptp_fun_V_0(j(U!1))), op2(h(tptp_fun_V_0(j(U!1))), U!1)) = U!1) | (~(op2(U!1, op2(h(tptp_fun_V_0(j(U!1))), U!1)) = h(tptp_fun_V_0(j(U!1))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(140,plain,
% 0.18/0.40 ((~![V: $i] : ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V)))) | ((~sorti2(h(tptp_fun_V_0(j(U!1))))) | (op2(h(tptp_fun_V_0(j(U!1))), op2(h(tptp_fun_V_0(j(U!1))), U!1)) = U!1) | (~(op2(U!1, op2(h(tptp_fun_V_0(j(U!1))), U!1)) = h(tptp_fun_V_0(j(U!1))))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(141,plain,
% 0.18/0.40 ((~![V: $i] : ((~sorti2(V)) | (op2(V, op2(V, U!1)) = U!1) | (~(op2(U!1, op2(V, U!1)) = V)))) | (~sorti2(h(tptp_fun_V_0(j(U!1))))) | (op2(h(tptp_fun_V_0(j(U!1))), op2(h(tptp_fun_V_0(j(U!1))), U!1)) = U!1) | (~(op2(U!1, op2(h(tptp_fun_V_0(j(U!1))), U!1)) = h(tptp_fun_V_0(j(U!1)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.18/0.40 tff(142,plain,
% 0.18/0.40 ((op2(h(tptp_fun_V_0(j(U!1))), op2(h(tptp_fun_V_0(j(U!1))), U!1)) = U!1) | (~(op2(U!1, op2(h(tptp_fun_V_0(j(U!1))), U!1)) = h(tptp_fun_V_0(j(U!1)))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[141, 138, 131])).
% 0.18/0.40 tff(143,plain,
% 0.18/0.40 (op2(h(tptp_fun_V_0(j(U!1))), op2(h(tptp_fun_V_0(j(U!1))), U!1)) = U!1),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[142, 120])).
% 0.18/0.40 tff(144,plain,
% 0.18/0.40 (U!1 = op2(h(tptp_fun_V_0(j(U!1))), op2(h(tptp_fun_V_0(j(U!1))), U!1))),
% 0.18/0.40 inference(symmetry,[status(thm)],[143])).
% 0.18/0.40 tff(145,plain,
% 0.18/0.40 (U!1 = h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[144, 105, 85])).
% 0.18/0.40 tff(146,plain,
% 0.18/0.40 (j(U!1) = j(h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[145])).
% 0.18/0.40 tff(147,plain,
% 0.18/0.40 (j(h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))) = j(U!1)),
% 0.18/0.40 inference(symmetry,[status(thm)],[146])).
% 0.18/0.40 tff(148,plain,
% 0.18/0.40 (((~![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V)))) | ((~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | sorti1(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))))) <=> ((~![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V)))) | (~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | sorti1(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(149,plain,
% 0.18/0.40 ((~![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V)))) | ((~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | sorti1(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(150,plain,
% 0.18/0.40 ((~![V: $i] : ((~sorti1(V)) | sorti1(op1(tptp_fun_V_0(j(U!1)), V)))) | (~sorti1(op1(tptp_fun_V_0(j(U!1)), j(U!1)))) | sorti1(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.18/0.40 tff(151,plain,
% 0.18/0.40 (sorti1(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[150, 61, 65])).
% 0.18/0.40 tff(152,plain,
% 0.18/0.40 (^[X2: $i] : refl(((~sorti1(X2)) | (j(h(X2)) = X2)) <=> ((~sorti1(X2)) | (j(h(X2)) = X2)))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(153,plain,
% 0.18/0.40 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2)) <=> ![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[152])).
% 0.18/0.40 tff(154,plain,
% 0.18/0.40 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2)) <=> ![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(155,plain,
% 0.18/0.40 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.18/0.40 inference(and_elim,[status(thm)],[72])).
% 0.18/0.40 tff(156,plain,
% 0.18/0.40 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.18/0.40 tff(157,plain,(
% 0.18/0.40 ![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.18/0.40 inference(skolemize,[status(sab)],[156])).
% 0.18/0.40 tff(158,plain,
% 0.18/0.40 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[157, 153])).
% 0.18/0.40 tff(159,plain,
% 0.18/0.40 (((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | ((~sorti1(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))) | (j(h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))) = op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))))) <=> ((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | (~sorti1(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))) | (j(h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))) = op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(160,plain,
% 0.18/0.40 ((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | ((~sorti1(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))) | (j(h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))) = op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(161,plain,
% 0.18/0.40 ((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | (~sorti1(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))) | (j(h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))) = op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.18/0.40 tff(162,plain,
% 0.18/0.40 (j(h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))))) = op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[161, 158, 151])).
% 0.18/0.40 tff(163,plain,
% 0.18/0.40 (op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(h(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1)))))),
% 0.18/0.40 inference(symmetry,[status(thm)],[162])).
% 0.18/0.40 tff(164,plain,
% 0.18/0.40 (op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(U!1)),
% 0.18/0.40 inference(transitivity,[status(thm)],[163, 147])).
% 0.18/0.40 tff(165,plain,
% 0.18/0.40 (((op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(U!1)) | (~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(j(U!1), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = tptp_fun_V_0(j(U!1))))) | (~(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(U!1)))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(166,plain,
% 0.18/0.40 (~(op1(tptp_fun_V_0(j(U!1)), op1(tptp_fun_V_0(j(U!1)), j(U!1))) = j(U!1))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[165, 42])).
% 0.18/0.40 tff(167,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[166, 164])).
% 0.18/0.40 % SZS output end Proof
% 0.18/0.40 % E exiting
%------------------------------------------------------------------------------