TSTP Solution File: ALG177+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG177+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 : Tue Sep 6 16:08:55 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG177+1 : TPTP v8.1.0. Released v2.7.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 29 13:42:54 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(sorti1_type, type, (
% 0.14/0.40 sorti1: $i > $o)).
% 0.14/0.40 tff(op1_type, type, (
% 0.14/0.40 op1: ( $i * $i ) > $i)).
% 0.14/0.40 tff(j_type, type, (
% 0.14/0.40 j: $i > $i)).
% 0.14/0.40 tff(tptp_fun_V_1_type, type, (
% 0.14/0.40 tptp_fun_V_1: $i > $i)).
% 0.14/0.40 tff(h_type, type, (
% 0.14/0.40 h: $i > $i)).
% 0.14/0.40 tff(tptp_fun_U_0_type, type, (
% 0.14/0.40 tptp_fun_U_0: $i)).
% 0.14/0.40 tff(op2_type, type, (
% 0.14/0.40 op2: ( $i * $i ) > $i)).
% 0.14/0.40 tff(sorti2_type, type, (
% 0.14/0.40 sorti2: $i > $o)).
% 0.14/0.40 tff(1,plain,
% 0.14/0.40 (^[U: $i] : refl(((~sorti1(U)) | sorti2(h(U))) <=> ((~sorti1(U)) | sorti2(h(U))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) <=> ![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.40 tff(3,plain,
% 0.14/0.40 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) <=> ![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(4,plain,
% 0.14/0.40 ((~((![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))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 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')).
% 0.14/0.40 tff(6,plain,
% 0.14/0.40 (~((~(![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)))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.14/0.40 tff(7,plain,
% 0.14/0.40 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) & ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.14/0.40 inference(or_elim,[status(thm)],[6])).
% 0.14/0.40 tff(8,plain,
% 0.14/0.40 (![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.14/0.40 inference(and_elim,[status(thm)],[7])).
% 0.14/0.40 tff(9,plain,
% 0.14/0.40 (![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.14/0.40 tff(10,plain,(
% 0.14/0.40 ![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[9])).
% 0.14/0.40 tff(11,plain,
% 0.14/0.40 (![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.14/0.40 tff(12,plain,
% 0.14/0.40 ((sorti1(U!0) & ![V: $i] : ((~sorti1(V)) | (~(op1(U!0, V) = V)))) <=> (sorti1(U!0) & ![V: $i] : ((~sorti1(V)) | (~(op1(U!0, V) = V))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(13,plain,
% 0.14/0.40 (?[U: $i] : (sorti1(U) & ![V: $i] : ((~sorti1(V)) | (~(op1(U, V) = V)))) <=> ?[U: $i] : (sorti1(U) & ![V: $i] : ((~sorti1(V)) | (~(op1(U, V) = V))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(14,plain,
% 0.14/0.40 (^[U: $i] : rewrite((sorti1(U) & ![V: $i] : (sorti1(V) => (~(op1(U, V) = V)))) <=> (sorti1(U) & ![V: $i] : ((~sorti1(V)) | (~(op1(U, V) = V)))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(15,plain,
% 0.14/0.40 (?[U: $i] : (sorti1(U) & ![V: $i] : (sorti1(V) => (~(op1(U, V) = V)))) <=> ?[U: $i] : (sorti1(U) & ![V: $i] : ((~sorti1(V)) | (~(op1(U, V) = V))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.14/0.40 tff(16,axiom,(?[U: $i] : (sorti1(U) & ![V: $i] : (sorti1(V) => (~(op1(U, V) = V))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax3')).
% 0.14/0.40 tff(17,plain,
% 0.14/0.40 (?[U: $i] : (sorti1(U) & ![V: $i] : ((~sorti1(V)) | (~(op1(U, V) = V))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.14/0.40 tff(18,plain,
% 0.14/0.40 (?[U: $i] : (sorti1(U) & ![V: $i] : ((~sorti1(V)) | (~(op1(U, V) = V))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.14/0.40 tff(19,plain,
% 0.14/0.40 (sorti1(U!0) & ![V: $i] : ((~sorti1(V)) | (~(op1(U!0, V) = V)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.14/0.40 tff(20,plain,
% 0.14/0.40 (sorti1(U!0)),
% 0.14/0.40 inference(and_elim,[status(thm)],[19])).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 (((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | ((~sorti1(U!0)) | sorti2(h(U!0)))) <=> ((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | (~sorti1(U!0)) | sorti2(h(U!0)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(22,plain,
% 0.14/0.40 ((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | ((~sorti1(U!0)) | sorti2(h(U!0)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(23,plain,
% 0.14/0.40 ((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | (~sorti1(U!0)) | sorti2(h(U!0))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.14/0.40 tff(24,plain,
% 0.14/0.40 (sorti2(h(U!0))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[23, 20, 11])).
% 0.14/0.40 tff(25,plain,
% 0.14/0.40 (^[U: $i] : refl(((~sorti2(U)) | (~((~sorti2(tptp_fun_V_1(U))) | (~(op2(U, tptp_fun_V_1(U)) = tptp_fun_V_1(U)))))) <=> ((~sorti2(U)) | (~((~sorti2(tptp_fun_V_1(U))) | (~(op2(U, tptp_fun_V_1(U)) = tptp_fun_V_1(U)))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(26,plain,
% 0.14/0.40 (![U: $i] : ((~sorti2(U)) | (~((~sorti2(tptp_fun_V_1(U))) | (~(op2(U, tptp_fun_V_1(U)) = tptp_fun_V_1(U)))))) <=> ![U: $i] : ((~sorti2(U)) | (~((~sorti2(tptp_fun_V_1(U))) | (~(op2(U, tptp_fun_V_1(U)) = tptp_fun_V_1(U))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[25])).
% 0.14/0.40 tff(27,plain,
% 0.14/0.40 ((~?[U: $i] : (sorti2(U) & ![V: $i] : ((~sorti2(V)) | (~(op2(U, V) = V))))) <=> (~?[U: $i] : (sorti2(U) & ![V: $i] : ((~sorti2(V)) | (~(op2(U, V) = V)))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(28,plain,
% 0.14/0.40 ((~?[U: $i] : (sorti2(U) & ![V: $i] : (sorti2(V) => (~(op2(U, V) = V))))) <=> (~?[U: $i] : (sorti2(U) & ![V: $i] : ((~sorti2(V)) | (~(op2(U, V) = V)))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(29,axiom,(~?[U: $i] : (sorti2(U) & ![V: $i] : (sorti2(V) => (~(op2(U, V) = V))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax4')).
% 0.14/0.40 tff(30,plain,
% 0.14/0.40 (~?[U: $i] : (sorti2(U) & ![V: $i] : ((~sorti2(V)) | (~(op2(U, V) = V))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.14/0.40 tff(31,plain,
% 0.14/0.40 (~?[U: $i] : (sorti2(U) & ![V: $i] : ((~sorti2(V)) | (~(op2(U, V) = V))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.14/0.40 tff(32,plain,
% 0.14/0.40 (~?[U: $i] : (sorti2(U) & ![V: $i] : ((~sorti2(V)) | (~(op2(U, V) = V))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.14/0.40 tff(33,plain,
% 0.14/0.40 (~?[U: $i] : (sorti2(U) & ![V: $i] : ((~sorti2(V)) | (~(op2(U, V) = V))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[32, 27])).
% 0.14/0.40 tff(34,plain,
% 0.14/0.40 (~?[U: $i] : (sorti2(U) & ![V: $i] : ((~sorti2(V)) | (~(op2(U, V) = V))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[33, 27])).
% 0.14/0.40 tff(35,plain,
% 0.14/0.40 (~?[U: $i] : (sorti2(U) & ![V: $i] : ((~sorti2(V)) | (~(op2(U, V) = V))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.14/0.40 tff(36,plain,
% 0.14/0.40 (~?[U: $i] : (sorti2(U) & ![V: $i] : ((~sorti2(V)) | (~(op2(U, V) = V))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[35, 27])).
% 0.14/0.40 tff(37,plain,
% 0.14/0.40 (^[U: $i] : nnf_neg(refl($oeq((~sorti2(U)), (~sorti2(U)))), sk($oeq((~![V: $i] : ((~sorti2(V)) | (~(op2(U, V) = V)))), (~((~sorti2(tptp_fun_V_1(U))) | (~(op2(U, tptp_fun_V_1(U)) = tptp_fun_V_1(U))))))), $oeq((~(sorti2(U) & ![V: $i] : ((~sorti2(V)) | (~(op2(U, V) = V))))), ((~sorti2(U)) | (~((~sorti2(tptp_fun_V_1(U))) | (~(op2(U, tptp_fun_V_1(U)) = tptp_fun_V_1(U))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(38,plain,(
% 0.14/0.40 ![U: $i] : ((~sorti2(U)) | (~((~sorti2(tptp_fun_V_1(U))) | (~(op2(U, tptp_fun_V_1(U)) = tptp_fun_V_1(U))))))),
% 0.14/0.40 inference(nnf-neg,[status(sab)],[36, 37])).
% 0.14/0.40 tff(39,plain,
% 0.14/0.40 (![U: $i] : ((~sorti2(U)) | (~((~sorti2(tptp_fun_V_1(U))) | (~(op2(U, tptp_fun_V_1(U)) = tptp_fun_V_1(U))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[38, 26])).
% 0.14/0.40 tff(40,plain,
% 0.14/0.40 (((~![U: $i] : ((~sorti2(U)) | (~((~sorti2(tptp_fun_V_1(U))) | (~(op2(U, tptp_fun_V_1(U)) = tptp_fun_V_1(U))))))) | ((~sorti2(h(U!0))) | (~((~sorti2(tptp_fun_V_1(h(U!0)))) | (~(op2(h(U!0), tptp_fun_V_1(h(U!0))) = tptp_fun_V_1(h(U!0)))))))) <=> ((~![U: $i] : ((~sorti2(U)) | (~((~sorti2(tptp_fun_V_1(U))) | (~(op2(U, tptp_fun_V_1(U)) = tptp_fun_V_1(U))))))) | (~sorti2(h(U!0))) | (~((~sorti2(tptp_fun_V_1(h(U!0)))) | (~(op2(h(U!0), tptp_fun_V_1(h(U!0))) = tptp_fun_V_1(h(U!0)))))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(41,plain,
% 0.14/0.40 ((~![U: $i] : ((~sorti2(U)) | (~((~sorti2(tptp_fun_V_1(U))) | (~(op2(U, tptp_fun_V_1(U)) = tptp_fun_V_1(U))))))) | ((~sorti2(h(U!0))) | (~((~sorti2(tptp_fun_V_1(h(U!0)))) | (~(op2(h(U!0), tptp_fun_V_1(h(U!0))) = tptp_fun_V_1(h(U!0)))))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(42,plain,
% 0.14/0.40 ((~![U: $i] : ((~sorti2(U)) | (~((~sorti2(tptp_fun_V_1(U))) | (~(op2(U, tptp_fun_V_1(U)) = tptp_fun_V_1(U))))))) | (~sorti2(h(U!0))) | (~((~sorti2(tptp_fun_V_1(h(U!0)))) | (~(op2(h(U!0), tptp_fun_V_1(h(U!0))) = tptp_fun_V_1(h(U!0))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.14/0.40 tff(43,plain,
% 0.14/0.40 (~((~sorti2(tptp_fun_V_1(h(U!0)))) | (~(op2(h(U!0), tptp_fun_V_1(h(U!0))) = tptp_fun_V_1(h(U!0)))))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[42, 39, 24])).
% 0.14/0.40 tff(44,plain,
% 0.14/0.40 (((~sorti2(tptp_fun_V_1(h(U!0)))) | (~(op2(h(U!0), tptp_fun_V_1(h(U!0))) = tptp_fun_V_1(h(U!0))))) | (op2(h(U!0), tptp_fun_V_1(h(U!0))) = tptp_fun_V_1(h(U!0)))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(45,plain,
% 0.14/0.40 (op2(h(U!0), tptp_fun_V_1(h(U!0))) = tptp_fun_V_1(h(U!0))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.14/0.40 tff(46,plain,
% 0.14/0.40 (tptp_fun_V_1(h(U!0)) = op2(h(U!0), tptp_fun_V_1(h(U!0)))),
% 0.14/0.40 inference(symmetry,[status(thm)],[45])).
% 0.14/0.40 tff(47,plain,
% 0.14/0.40 (j(tptp_fun_V_1(h(U!0))) = j(op2(h(U!0), tptp_fun_V_1(h(U!0))))),
% 0.14/0.40 inference(monotonicity,[status(thm)],[46])).
% 0.14/0.40 tff(48,plain,
% 0.14/0.40 (j(op2(h(U!0), tptp_fun_V_1(h(U!0)))) = j(tptp_fun_V_1(h(U!0)))),
% 0.14/0.40 inference(symmetry,[status(thm)],[47])).
% 0.14/0.40 tff(49,plain,
% 0.14/0.40 (((~sorti2(tptp_fun_V_1(h(U!0)))) | (~(op2(h(U!0), tptp_fun_V_1(h(U!0))) = tptp_fun_V_1(h(U!0))))) | sorti2(tptp_fun_V_1(h(U!0)))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(50,plain,
% 0.14/0.40 (sorti2(tptp_fun_V_1(h(U!0)))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[49, 43])).
% 0.14/0.40 tff(51,plain,
% 0.14/0.40 (^[Y: $i] : refl(((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) <=> ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(52,plain,
% 0.14/0.40 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) <=> ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.14/0.40 tff(53,plain,
% 0.14/0.40 (^[Y: $i] : rewrite(((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) <=> ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(54,plain,
% 0.14/0.40 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) <=> ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[53])).
% 0.14/0.40 tff(55,plain,
% 0.14/0.40 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) <=> ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[54, 52])).
% 0.14/0.40 tff(56,plain,
% 0.14/0.40 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z))))) <=> ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(57,plain,
% 0.14/0.40 (![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))),
% 0.14/0.41 inference(or_elim,[status(thm)],[6])).
% 0.14/0.41 tff(58,plain,
% 0.14/0.41 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.14/0.41 inference(and_elim,[status(thm)],[57])).
% 0.14/0.41 tff(59,plain,
% 0.14/0.41 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[58, 56])).
% 0.14/0.41 tff(60,plain,(
% 0.14/0.41 ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.14/0.41 inference(skolemize,[status(sab)],[59])).
% 0.14/0.41 tff(61,plain,
% 0.14/0.41 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[60, 55])).
% 0.14/0.41 tff(62,plain,
% 0.14/0.41 (((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | ((~sorti2(h(U!0))) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(h(U!0), Z)) = op1(j(h(U!0)), j(Z)))))) <=> ((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | (~sorti2(h(U!0))) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(h(U!0), Z)) = op1(j(h(U!0)), j(Z)))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(63,plain,
% 0.14/0.41 ((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | ((~sorti2(h(U!0))) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(h(U!0), Z)) = op1(j(h(U!0)), j(Z)))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(64,plain,
% 0.14/0.41 ((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | (~sorti2(h(U!0))) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(h(U!0), Z)) = op1(j(h(U!0)), j(Z))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.14/0.41 tff(65,plain,
% 0.14/0.41 (![Z: $i] : ((~sorti2(Z)) | (j(op2(h(U!0), Z)) = op1(j(h(U!0)), j(Z))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[64, 61, 24])).
% 0.14/0.41 tff(66,plain,
% 0.14/0.41 (((~![Z: $i] : ((~sorti2(Z)) | (j(op2(h(U!0), Z)) = op1(j(h(U!0)), j(Z))))) | ((~sorti2(tptp_fun_V_1(h(U!0)))) | (j(op2(h(U!0), tptp_fun_V_1(h(U!0)))) = op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0))))))) <=> ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(h(U!0), Z)) = op1(j(h(U!0)), j(Z))))) | (~sorti2(tptp_fun_V_1(h(U!0)))) | (j(op2(h(U!0), tptp_fun_V_1(h(U!0)))) = op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0))))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(67,plain,
% 0.14/0.41 ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(h(U!0), Z)) = op1(j(h(U!0)), j(Z))))) | ((~sorti2(tptp_fun_V_1(h(U!0)))) | (j(op2(h(U!0), tptp_fun_V_1(h(U!0)))) = op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0))))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(68,plain,
% 0.14/0.41 ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(h(U!0), Z)) = op1(j(h(U!0)), j(Z))))) | (~sorti2(tptp_fun_V_1(h(U!0)))) | (j(op2(h(U!0), tptp_fun_V_1(h(U!0)))) = op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0)))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.14/0.41 tff(69,plain,
% 0.14/0.41 (j(op2(h(U!0), tptp_fun_V_1(h(U!0)))) = op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[68, 65, 50])).
% 0.14/0.41 tff(70,plain,
% 0.14/0.41 (op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0)))) = j(op2(h(U!0), tptp_fun_V_1(h(U!0))))),
% 0.14/0.41 inference(symmetry,[status(thm)],[69])).
% 0.14/0.41 tff(71,plain,
% 0.14/0.41 (op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0)))) = j(tptp_fun_V_1(h(U!0)))),
% 0.14/0.41 inference(transitivity,[status(thm)],[70, 48])).
% 0.14/0.41 tff(72,plain,
% 0.14/0.41 (sorti1(op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0))))) <=> sorti1(j(tptp_fun_V_1(h(U!0))))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[71])).
% 0.14/0.41 tff(73,plain,
% 0.14/0.41 (sorti1(j(tptp_fun_V_1(h(U!0)))) <=> sorti1(op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0)))))),
% 0.14/0.41 inference(symmetry,[status(thm)],[72])).
% 0.14/0.41 tff(74,plain,
% 0.14/0.41 (^[V: $i] : refl(((~sorti2(V)) | sorti1(j(V))) <=> ((~sorti2(V)) | sorti1(j(V))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(75,plain,
% 0.14/0.41 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[74])).
% 0.14/0.41 tff(76,plain,
% 0.14/0.41 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(77,plain,
% 0.14/0.41 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.14/0.41 inference(and_elim,[status(thm)],[7])).
% 0.14/0.41 tff(78,plain,
% 0.14/0.41 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.14/0.41 tff(79,plain,(
% 0.14/0.41 ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.14/0.41 inference(skolemize,[status(sab)],[78])).
% 0.14/0.41 tff(80,plain,
% 0.14/0.41 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.14/0.41 tff(81,plain,
% 0.14/0.41 (((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(tptp_fun_V_1(h(U!0)))) | sorti1(j(tptp_fun_V_1(h(U!0)))))) <=> ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(tptp_fun_V_1(h(U!0)))) | sorti1(j(tptp_fun_V_1(h(U!0)))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(82,plain,
% 0.14/0.41 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(tptp_fun_V_1(h(U!0)))) | sorti1(j(tptp_fun_V_1(h(U!0)))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(83,plain,
% 0.14/0.41 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(tptp_fun_V_1(h(U!0)))) | sorti1(j(tptp_fun_V_1(h(U!0))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.14/0.41 tff(84,plain,
% 0.14/0.41 (sorti1(j(tptp_fun_V_1(h(U!0))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[83, 80, 50])).
% 0.14/0.41 tff(85,plain,
% 0.14/0.41 (sorti1(op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0)))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[84, 73])).
% 0.14/0.41 tff(86,plain,
% 0.14/0.41 (^[X2: $i] : refl(((~sorti1(X2)) | (j(h(X2)) = X2)) <=> ((~sorti1(X2)) | (j(h(X2)) = X2)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(87,plain,
% 0.14/0.41 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2)) <=> ![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[86])).
% 0.14/0.41 tff(88,plain,
% 0.14/0.41 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2)) <=> ![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(89,plain,
% 0.14/0.41 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.14/0.41 inference(and_elim,[status(thm)],[57])).
% 0.14/0.41 tff(90,plain,
% 0.14/0.41 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.14/0.41 tff(91,plain,(
% 0.14/0.41 ![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.14/0.41 inference(skolemize,[status(sab)],[90])).
% 0.14/0.41 tff(92,plain,
% 0.14/0.41 (![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.14/0.41 tff(93,plain,
% 0.14/0.41 (((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | ((~sorti1(U!0)) | (j(h(U!0)) = U!0))) <=> ((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | (~sorti1(U!0)) | (j(h(U!0)) = U!0))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(94,plain,
% 0.14/0.41 ((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | ((~sorti1(U!0)) | (j(h(U!0)) = U!0))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(95,plain,
% 0.14/0.41 ((~![X2: $i] : ((~sorti1(X2)) | (j(h(X2)) = X2))) | (~sorti1(U!0)) | (j(h(U!0)) = U!0)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.14/0.41 tff(96,plain,
% 0.14/0.41 (j(h(U!0)) = U!0),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[95, 20, 92])).
% 0.14/0.41 tff(97,plain,
% 0.14/0.41 (U!0 = j(h(U!0))),
% 0.14/0.41 inference(symmetry,[status(thm)],[96])).
% 0.14/0.41 tff(98,plain,
% 0.14/0.41 (op1(U!0, op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0))))) = op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0))))),
% 0.14/0.41 inference(monotonicity,[status(thm)],[97, 71])).
% 0.14/0.41 tff(99,plain,
% 0.14/0.41 (^[V: $i] : refl(((~sorti1(V)) | (~(op1(U!0, V) = V))) <=> ((~sorti1(V)) | (~(op1(U!0, V) = V))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(100,plain,
% 0.14/0.41 (![V: $i] : ((~sorti1(V)) | (~(op1(U!0, V) = V))) <=> ![V: $i] : ((~sorti1(V)) | (~(op1(U!0, V) = V)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[99])).
% 0.14/0.41 tff(101,plain,
% 0.14/0.41 (![V: $i] : ((~sorti1(V)) | (~(op1(U!0, V) = V)))),
% 0.14/0.41 inference(and_elim,[status(thm)],[19])).
% 0.14/0.41 tff(102,plain,
% 0.14/0.41 (![V: $i] : ((~sorti1(V)) | (~(op1(U!0, V) = V)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.14/0.41 tff(103,plain,
% 0.14/0.41 (((~![V: $i] : ((~sorti1(V)) | (~(op1(U!0, V) = V)))) | ((~sorti1(op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0)))))) | (~(op1(U!0, op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0))))) = op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0)))))))) <=> ((~![V: $i] : ((~sorti1(V)) | (~(op1(U!0, V) = V)))) | (~sorti1(op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0)))))) | (~(op1(U!0, op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0))))) = op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0)))))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(104,plain,
% 0.14/0.41 ((~![V: $i] : ((~sorti1(V)) | (~(op1(U!0, V) = V)))) | ((~sorti1(op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0)))))) | (~(op1(U!0, op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0))))) = op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0)))))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(105,plain,
% 0.14/0.41 ((~![V: $i] : ((~sorti1(V)) | (~(op1(U!0, V) = V)))) | (~sorti1(op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0)))))) | (~(op1(U!0, op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0))))) = op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0))))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.14/0.41 tff(106,plain,
% 0.14/0.41 ((~sorti1(op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0)))))) | (~(op1(U!0, op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0))))) = op1(j(h(U!0)), j(tptp_fun_V_1(h(U!0))))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[105, 102])).
% 0.14/0.41 tff(107,plain,
% 0.14/0.41 ($false),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[106, 98, 85])).
% 0.14/0.41 % SZS output end Proof
%------------------------------------------------------------------------------