%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG202+1 : TPTP v9.0.0. Released v2.7.0.
% 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 04:58:39 AM UTC 2025
% Result : Theorem 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG202+1 : TPTP v9.0.0. Released v2.7.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n015.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 10:48:41 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(tptp_fun_U_0_type, type, (
% 0.11/0.36 tptp_fun_U_0: $i)).
% 0.11/0.36 tff(op2_type, type, (
% 0.11/0.36 op2: ( $i * $i ) > $i)).
% 0.11/0.36 tff(h_type, type, (
% 0.11/0.36 h: $i > $i)).
% 0.11/0.36 tff(j_type, type, (
% 0.11/0.36 j: $i > $i)).
% 0.11/0.36 tff(sorti2_type, type, (
% 0.11/0.36 sorti2: $i > $o)).
% 0.11/0.36 tff(sorti1_type, type, (
% 0.11/0.36 sorti1: $i > $o)).
% 0.11/0.36 tff(op1_type, type, (
% 0.11/0.36 op1: ( $i * $i ) > $i)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 (^[X1: $i] : refl(((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ((~sorti2(X1)) | (h(j(X1)) = X1)))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 ((~((![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))))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 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')).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (~((~(![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)))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (![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))),
% 0.11/0.36 inference(or_elim,[status(thm)],[6])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.11/0.36 inference(and_elim,[status(thm)],[7])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.11/0.36 tff(10,plain,(
% 0.11/0.36 ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.11/0.36 inference(skolemize,[status(sab)],[9])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 ((~![U: $i] : ((~sorti2(U)) | (op2(U, U) = U))) <=> (~![U: $i] : ((~sorti2(U)) | (op2(U, U) = U)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 ((~![U: $i] : (sorti2(U) => (op2(U, U) = U))) <=> (~![U: $i] : ((~sorti2(U)) | (op2(U, U) = U)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(14,axiom,(~![U: $i] : (sorti2(U) => (op2(U, U) = U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax4')).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 (~![U: $i] : ((~sorti2(U)) | (op2(U, U) = U))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 (~![U: $i] : ((~sorti2(U)) | (op2(U, U) = U))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 (~![U: $i] : ((~sorti2(U)) | (op2(U, U) = U))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 (~![U: $i] : ((~sorti2(U)) | (op2(U, U) = U))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.11/0.36 tff(19,plain,(
% 0.11/0.36 ~((~sorti2(U!0)) | (op2(U!0, U!0) = U!0))),
% 0.11/0.36 inference(skolemize,[status(sab)],[18])).
% 0.11/0.36 tff(20,plain,
% 0.11/0.36 (sorti2(U!0)),
% 0.11/0.36 inference(or_elim,[status(thm)],[19])).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 (((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(U!0)) | (h(j(U!0)) = U!0))) <=> ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(U!0)) | (h(j(U!0)) = U!0))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(U!0)) | (h(j(U!0)) = U!0))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(U!0)) | (h(j(U!0)) = U!0)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.11/0.36 tff(24,plain,
% 0.11/0.36 (h(j(U!0)) = U!0),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[23, 20, 11])).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 (^[V: $i] : refl(((~sorti2(V)) | sorti1(j(V))) <=> ((~sorti2(V)) | sorti1(j(V))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(26,plain,
% 0.11/0.36 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[25])).
% 0.11/0.36 tff(27,plain,
% 0.11/0.36 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(28,plain,
% 0.11/0.36 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) & ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.11/0.36 inference(or_elim,[status(thm)],[6])).
% 0.11/0.36 tff(29,plain,
% 0.11/0.36 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.11/0.36 inference(and_elim,[status(thm)],[28])).
% 0.11/0.36 tff(30,plain,
% 0.11/0.36 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[29, 27])).
% 0.11/0.36 tff(31,plain,(
% 0.11/0.36 ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[30])).
% 0.11/0.36 tff(32,plain,
% 0.11/0.36 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.11/0.36 tff(33,plain,
% 0.11/0.36 (((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(U!0)) | sorti1(j(U!0)))) <=> ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(U!0)) | sorti1(j(U!0)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(34,plain,
% 0.11/0.36 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(U!0)) | sorti1(j(U!0)))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(35,plain,
% 0.11/0.36 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(U!0)) | sorti1(j(U!0))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.11/0.36 tff(36,plain,
% 0.11/0.36 (sorti1(j(U!0))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[35, 20, 32])).
% 0.11/0.36 tff(37,plain,
% 0.11/0.36 (^[U: $i] : refl(((~sorti1(U)) | (op1(U, U) = U)) <=> ((~sorti1(U)) | (op1(U, U) = U)))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(38,plain,
% 0.11/0.36 (![U: $i] : ((~sorti1(U)) | (op1(U, U) = U)) <=> ![U: $i] : ((~sorti1(U)) | (op1(U, U) = U))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[37])).
% 0.11/0.36 tff(39,plain,
% 0.11/0.36 (![U: $i] : ((~sorti1(U)) | (op1(U, U) = U)) <=> ![U: $i] : ((~sorti1(U)) | (op1(U, U) = U))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(40,plain,
% 0.11/0.36 (^[U: $i] : rewrite((sorti1(U) => (op1(U, U) = U)) <=> ((~sorti1(U)) | (op1(U, U) = U)))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(41,plain,
% 0.11/0.36 (![U: $i] : (sorti1(U) => (op1(U, U) = U)) <=> ![U: $i] : ((~sorti1(U)) | (op1(U, U) = U))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[40])).
% 0.11/0.36 tff(42,axiom,(![U: $i] : (sorti1(U) => (op1(U, U) = U))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax3')).
% 0.11/0.36 tff(43,plain,
% 0.11/0.36 (![U: $i] : ((~sorti1(U)) | (op1(U, U) = U))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.11/0.36 tff(44,plain,
% 0.11/0.36 (![U: $i] : ((~sorti1(U)) | (op1(U, U) = U))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.11/0.36 tff(45,plain,(
% 0.11/0.36 ![U: $i] : ((~sorti1(U)) | (op1(U, U) = U))),
% 0.11/0.36 inference(skolemize,[status(sab)],[44])).
% 0.11/0.36 tff(46,plain,
% 0.11/0.36 (![U: $i] : ((~sorti1(U)) | (op1(U, U) = U))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.11/0.36 tff(47,plain,
% 0.11/0.36 (((~![U: $i] : ((~sorti1(U)) | (op1(U, U) = U))) | ((~sorti1(j(U!0))) | (op1(j(U!0), j(U!0)) = j(U!0)))) <=> ((~![U: $i] : ((~sorti1(U)) | (op1(U, U) = U))) | (~sorti1(j(U!0))) | (op1(j(U!0), j(U!0)) = j(U!0)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(48,plain,
% 0.11/0.37 ((~![U: $i] : ((~sorti1(U)) | (op1(U, U) = U))) | ((~sorti1(j(U!0))) | (op1(j(U!0), j(U!0)) = j(U!0)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(49,plain,
% 0.11/0.37 ((~![U: $i] : ((~sorti1(U)) | (op1(U, U) = U))) | (~sorti1(j(U!0))) | (op1(j(U!0), j(U!0)) = j(U!0))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.11/0.37 tff(50,plain,
% 0.11/0.37 (op1(j(U!0), j(U!0)) = j(U!0)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[49, 46, 36])).
% 0.11/0.37 tff(51,plain,
% 0.11/0.37 (h(op1(j(U!0), j(U!0))) = h(j(U!0))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[50])).
% 0.11/0.37 tff(52,plain,
% 0.11/0.37 (^[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))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(53,plain,
% 0.11/0.37 (![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)))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[52])).
% 0.11/0.37 tff(54,plain,
% 0.11/0.37 (^[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))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(55,plain,
% 0.11/0.37 (![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)))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[54])).
% 0.11/0.37 tff(56,plain,
% 0.11/0.37 (![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)))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[55, 53])).
% 0.11/0.37 tff(57,plain,
% 0.11/0.37 (![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)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(58,plain,
% 0.11/0.37 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.11/0.37 inference(and_elim,[status(thm)],[7])).
% 0.11/0.37 tff(59,plain,
% 0.11/0.37 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.11/0.37 tff(60,plain,(
% 0.11/0.37 ![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[59])).
% 0.11/0.37 tff(61,plain,
% 0.11/0.37 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.11/0.37 tff(62,plain,
% 0.11/0.37 (((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | ((~sorti1(j(U!0))) | ![X: $i] : ((~sorti1(X)) | (h(op1(j(U!0), X)) = op2(h(j(U!0)), h(X)))))) <=> ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | (~sorti1(j(U!0))) | ![X: $i] : ((~sorti1(X)) | (h(op1(j(U!0), X)) = op2(h(j(U!0)), h(X)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(63,plain,
% 0.11/0.37 ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | ((~sorti1(j(U!0))) | ![X: $i] : ((~sorti1(X)) | (h(op1(j(U!0), X)) = op2(h(j(U!0)), h(X)))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(64,plain,
% 0.11/0.37 ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | (~sorti1(j(U!0))) | ![X: $i] : ((~sorti1(X)) | (h(op1(j(U!0), X)) = op2(h(j(U!0)), h(X))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.11/0.37 tff(65,plain,
% 0.11/0.37 (![X: $i] : ((~sorti1(X)) | (h(op1(j(U!0), X)) = op2(h(j(U!0)), h(X))))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[64, 61, 36])).
% 0.11/0.37 tff(66,plain,
% 0.11/0.37 (((~![X: $i] : ((~sorti1(X)) | (h(op1(j(U!0), X)) = op2(h(j(U!0)), h(X))))) | ((~sorti1(j(U!0))) | (h(op1(j(U!0), j(U!0))) = op2(h(j(U!0)), h(j(U!0)))))) <=> ((~![X: $i] : ((~sorti1(X)) | (h(op1(j(U!0), X)) = op2(h(j(U!0)), h(X))))) | (~sorti1(j(U!0))) | (h(op1(j(U!0), j(U!0))) = op2(h(j(U!0)), h(j(U!0)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(67,plain,
% 0.11/0.37 ((~![X: $i] : ((~sorti1(X)) | (h(op1(j(U!0), X)) = op2(h(j(U!0)), h(X))))) | ((~sorti1(j(U!0))) | (h(op1(j(U!0), j(U!0))) = op2(h(j(U!0)), h(j(U!0)))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(68,plain,
% 0.11/0.37 ((~![X: $i] : ((~sorti1(X)) | (h(op1(j(U!0), X)) = op2(h(j(U!0)), h(X))))) | (~sorti1(j(U!0))) | (h(op1(j(U!0), j(U!0))) = op2(h(j(U!0)), h(j(U!0))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.11/0.37 tff(69,plain,
% 0.11/0.37 (h(op1(j(U!0), j(U!0))) = op2(h(j(U!0)), h(j(U!0)))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[68, 36, 65])).
% 0.11/0.37 tff(70,plain,
% 0.11/0.37 (op2(h(j(U!0)), h(j(U!0))) = h(op1(j(U!0), j(U!0)))),
% 0.11/0.37 inference(symmetry,[status(thm)],[69])).
% 0.11/0.37 tff(71,plain,
% 0.11/0.37 (U!0 = h(j(U!0))),
% 0.11/0.37 inference(symmetry,[status(thm)],[24])).
% 0.11/0.37 tff(72,plain,
% 0.11/0.37 (op2(U!0, U!0) = op2(h(j(U!0)), h(j(U!0)))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[71, 71])).
% 0.11/0.37 tff(73,plain,
% 0.11/0.37 (op2(U!0, U!0) = U!0),
% 0.11/0.37 inference(transitivity,[status(thm)],[72, 70, 51, 24])).
% 0.11/0.37 tff(74,plain,
% 0.11/0.37 (~(op2(U!0, U!0) = U!0)),
% 0.11/0.37 inference(or_elim,[status(thm)],[19])).
% 0.11/0.37 tff(75,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.11/0.37 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------