TSTP Solution File: ALG069+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG069+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 16:07:45 EDT 2022
% Result : Theorem 0.12s 0.41s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG069+1 : TPTP v8.1.0. Released v2.7.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.35 % Computer : n021.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Mon Aug 29 13:16:10 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.12/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.36 Usage: tptp [options] [-file:]file
% 0.12/0.36 -h, -? prints this message.
% 0.12/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.36 -m, -model generate model.
% 0.12/0.36 -p, -proof generate proof.
% 0.12/0.36 -c, -core generate unsat core of named formulas.
% 0.12/0.36 -st, -statistics display statistics.
% 0.12/0.36 -t:timeout set timeout (in second).
% 0.12/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.36 -<param>:<value> configuration parameter and value.
% 0.12/0.36 -o:<output-file> file to place output in.
% 0.12/0.41 % SZS status Theorem
% 0.12/0.41 % SZS output start Proof
% 0.12/0.41 tff(tptp_fun_U_1_type, type, (
% 0.12/0.41 tptp_fun_U_1: $i)).
% 0.12/0.41 tff(op2_type, type, (
% 0.12/0.41 op2: ( $i * $i ) > $i)).
% 0.12/0.41 tff(h_type, type, (
% 0.12/0.41 h: $i > $i)).
% 0.12/0.41 tff(tptp_fun_V_0_type, type, (
% 0.12/0.41 tptp_fun_V_0: $i > $i)).
% 0.12/0.41 tff(j_type, type, (
% 0.12/0.41 j: $i > $i)).
% 0.12/0.41 tff(sorti2_type, type, (
% 0.12/0.41 sorti2: $i > $o)).
% 0.12/0.41 tff(sorti1_type, type, (
% 0.12/0.41 sorti1: $i > $o)).
% 0.12/0.41 tff(op1_type, type, (
% 0.12/0.41 op1: ( $i * $i ) > $i)).
% 0.12/0.41 tff(1,plain,
% 0.12/0.41 (^[X1: $i] : refl(((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ((~sorti2(X1)) | (h(j(X1)) = X1)))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(2,plain,
% 0.12/0.41 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.41 tff(3,plain,
% 0.12/0.41 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(4,plain,
% 0.12/0.41 ((~((![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))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 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/sandbox/benchmark/theBenchmark.p','co1')).
% 0.12/0.41 tff(6,plain,
% 0.12/0.41 (~((~(![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)))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.41 tff(7,plain,
% 0.12/0.41 (![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))),
% 0.12/0.41 inference(or_elim,[status(thm)],[6])).
% 0.12/0.41 tff(8,plain,
% 0.12/0.41 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.12/0.41 inference(and_elim,[status(thm)],[7])).
% 0.12/0.41 tff(9,plain,
% 0.12/0.41 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.12/0.41 tff(10,plain,(
% 0.12/0.41 ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.12/0.41 inference(skolemize,[status(sab)],[9])).
% 0.12/0.41 tff(11,plain,
% 0.12/0.41 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.12/0.41 tff(12,plain,
% 0.12/0.41 (((~(~sorti2(U!1))) & ![V: $i] : (~(sorti2(V) & (op2(V, V) = U!1)))) <=> (sorti2(U!1) & ![V: $i] : (~(sorti2(V) & (op2(V, V) = U!1))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(13,plain,
% 0.12/0.41 ((~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (op2(V, V) = U)))) <=> (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (op2(V, V) = U))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(14,plain,
% 0.12/0.41 ((~![U: $i] : (sorti2(U) => ?[V: $i] : (sorti2(V) & (op2(V, V) = U)))) <=> (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (op2(V, V) = U))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(15,axiom,(~![U: $i] : (sorti2(U) => ?[V: $i] : (sorti2(V) & (op2(V, V) = U)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax4')).
% 0.12/0.41 tff(16,plain,
% 0.12/0.41 (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (op2(V, V) = U)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.12/0.41 tff(17,plain,
% 0.12/0.41 (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (op2(V, V) = U)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.12/0.41 tff(18,plain,
% 0.12/0.41 (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (op2(V, V) = U)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.12/0.41 tff(19,plain,
% 0.12/0.41 (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (op2(V, V) = U)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.12/0.41 tff(20,plain,
% 0.12/0.41 (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (op2(V, V) = U)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.12/0.41 tff(21,plain,
% 0.12/0.41 (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (op2(V, V) = U)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.12/0.41 tff(22,plain,
% 0.12/0.41 (~![U: $i] : ((~sorti2(U)) | ?[V: $i] : (sorti2(V) & (op2(V, V) = U)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[21, 13])).
% 0.12/0.41 tff(23,plain,
% 0.12/0.41 (sorti2(U!1) & ![V: $i] : (~(sorti2(V) & (op2(V, V) = U!1)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.12/0.41 tff(24,plain,
% 0.12/0.41 (sorti2(U!1)),
% 0.12/0.41 inference(and_elim,[status(thm)],[23])).
% 0.12/0.41 tff(25,plain,
% 0.12/0.41 (((~![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))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(26,plain,
% 0.12/0.41 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(U!1)) | (h(j(U!1)) = U!1))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(27,plain,
% 0.12/0.41 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(U!1)) | (h(j(U!1)) = U!1)),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.12/0.41 tff(28,plain,
% 0.12/0.41 (h(j(U!1)) = U!1),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[27, 24, 11])).
% 0.12/0.41 tff(29,plain,
% 0.12/0.41 (^[V: $i] : refl(((~sorti2(V)) | sorti1(j(V))) <=> ((~sorti2(V)) | sorti1(j(V))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(30,plain,
% 0.12/0.41 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[29])).
% 0.12/0.41 tff(31,plain,
% 0.12/0.41 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(32,plain,
% 0.12/0.41 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) & ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.12/0.41 inference(or_elim,[status(thm)],[6])).
% 0.12/0.41 tff(33,plain,
% 0.12/0.41 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.12/0.41 inference(and_elim,[status(thm)],[32])).
% 0.12/0.41 tff(34,plain,
% 0.12/0.41 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[33, 31])).
% 0.12/0.41 tff(35,plain,(
% 0.12/0.41 ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[34])).
% 0.12/0.41 tff(36,plain,
% 0.12/0.41 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[35, 30])).
% 0.12/0.41 tff(37,plain,
% 0.12/0.41 (((~![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)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(38,plain,
% 0.12/0.41 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(U!1)) | sorti1(j(U!1)))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(39,plain,
% 0.12/0.41 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(U!1)) | sorti1(j(U!1))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.12/0.41 tff(40,plain,
% 0.12/0.41 (sorti1(j(U!1))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[39, 24, 36])).
% 0.12/0.41 tff(41,plain,
% 0.12/0.41 (^[U: $i] : refl(((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U))))) <=> ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(42,plain,
% 0.12/0.41 (![U: $i] : ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U))))) <=> ![U: $i] : ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U)))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[41])).
% 0.12/0.41 tff(43,plain,
% 0.12/0.41 (^[U: $i] : rewrite(((~sorti1(U)) | (sorti1(tptp_fun_V_0(U)) & (op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U))) <=> ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(44,plain,
% 0.12/0.41 (![U: $i] : ((~sorti1(U)) | (sorti1(tptp_fun_V_0(U)) & (op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U))) <=> ![U: $i] : ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U)))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[43])).
% 0.12/0.41 tff(45,plain,
% 0.12/0.41 (![U: $i] : ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (op1(V, V) = U))) <=> ![U: $i] : ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (op1(V, V) = U)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(46,plain,
% 0.12/0.41 (^[U: $i] : rewrite((sorti1(U) => ?[V: $i] : (sorti1(V) & (op1(V, V) = U))) <=> ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (op1(V, V) = U))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(47,plain,
% 0.12/0.41 (![U: $i] : (sorti1(U) => ?[V: $i] : (sorti1(V) & (op1(V, V) = U))) <=> ![U: $i] : ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (op1(V, V) = U)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[46])).
% 0.12/0.41 tff(48,axiom,(![U: $i] : (sorti1(U) => ?[V: $i] : (sorti1(V) & (op1(V, V) = U)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax3')).
% 0.12/0.41 tff(49,plain,
% 0.12/0.41 (![U: $i] : ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (op1(V, V) = U)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.12/0.41 tff(50,plain,
% 0.12/0.41 (![U: $i] : ((~sorti1(U)) | ?[V: $i] : (sorti1(V) & (op1(V, V) = U)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.12/0.41 tff(51,plain,(
% 0.12/0.41 ![U: $i] : ((~sorti1(U)) | (sorti1(tptp_fun_V_0(U)) & (op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[50])).
% 0.12/0.41 tff(52,plain,
% 0.12/0.41 (![U: $i] : ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U)))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.12/0.41 tff(53,plain,
% 0.12/0.41 (![U: $i] : ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U)))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[52, 42])).
% 0.12/0.41 tff(54,plain,
% 0.12/0.41 (((~![U: $i] : ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U)))))) | ((~sorti1(j(U!1))) | (~((~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = j(U!1))))))) <=> ((~![U: $i] : ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U)))))) | (~sorti1(j(U!1))) | (~((~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = j(U!1))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(55,plain,
% 0.12/0.41 ((~![U: $i] : ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U)))))) | ((~sorti1(j(U!1))) | (~((~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = j(U!1))))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(56,plain,
% 0.12/0.41 ((~![U: $i] : ((~sorti1(U)) | (~((~sorti1(tptp_fun_V_0(U))) | (~(op1(tptp_fun_V_0(U), tptp_fun_V_0(U)) = U)))))) | (~sorti1(j(U!1))) | (~((~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = j(U!1)))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.12/0.41 tff(57,plain,
% 0.12/0.41 (~((~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = j(U!1))))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[56, 53, 40])).
% 0.12/0.41 tff(58,plain,
% 0.12/0.41 (((~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = j(U!1)))) | (op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = j(U!1))),
% 0.12/0.41 inference(tautology,[status(thm)],[])).
% 0.12/0.41 tff(59,plain,
% 0.12/0.41 (op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = j(U!1)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.12/0.41 tff(60,plain,
% 0.12/0.41 (h(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1)))) = h(j(U!1))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[59])).
% 0.12/0.41 tff(61,plain,
% 0.12/0.41 (((~sorti1(tptp_fun_V_0(j(U!1)))) | (~(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))) = j(U!1)))) | sorti1(tptp_fun_V_0(j(U!1)))),
% 0.12/0.41 inference(tautology,[status(thm)],[])).
% 0.12/0.41 tff(62,plain,
% 0.12/0.41 (sorti1(tptp_fun_V_0(j(U!1)))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[61, 57])).
% 0.12/0.41 tff(63,plain,
% 0.12/0.41 (^[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))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(64,plain,
% 0.12/0.41 (![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)))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[63])).
% 0.12/0.41 tff(65,plain,
% 0.12/0.41 (^[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))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(66,plain,
% 0.12/0.41 (![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)))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[65])).
% 0.12/0.41 tff(67,plain,
% 0.12/0.41 (![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)))))),
% 0.12/0.41 inference(transitivity,[status(thm)],[66, 64])).
% 0.12/0.41 tff(68,plain,
% 0.12/0.41 (![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)))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(69,plain,
% 0.12/0.41 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.12/0.41 inference(and_elim,[status(thm)],[7])).
% 0.12/0.41 tff(70,plain,
% 0.12/0.41 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.12/0.41 tff(71,plain,(
% 0.12/0.41 ![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.12/0.41 inference(skolemize,[status(sab)],[70])).
% 0.12/0.41 tff(72,plain,
% 0.12/0.41 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.12/0.41 tff(73,plain,
% 0.12/0.41 (((~![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)))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(74,plain,
% 0.12/0.41 ((~![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)))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(75,plain,
% 0.12/0.41 ((~![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))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.12/0.41 tff(76,plain,
% 0.12/0.41 (![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))))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[75, 72, 62])).
% 0.12/0.41 tff(77,plain,
% 0.12/0.41 (((~![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(tptp_fun_V_0(j(U!1)))) | (h(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1)))) = op2(h(tptp_fun_V_0(j(U!1))), h(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))))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | (h(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1)))) = op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(78,plain,
% 0.12/0.41 ((~![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(tptp_fun_V_0(j(U!1)))) | (h(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1)))) = op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1))))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(79,plain,
% 0.12/0.41 ((~![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(tptp_fun_V_0(j(U!1)))) | (h(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1)))) = op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1)))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.12/0.41 tff(80,plain,
% 0.12/0.41 (h(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1)))) = op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1))))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[79, 62, 76])).
% 0.12/0.41 tff(81,plain,
% 0.12/0.41 (op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1)))) = h(op1(tptp_fun_V_0(j(U!1)), tptp_fun_V_0(j(U!1))))),
% 0.12/0.41 inference(symmetry,[status(thm)],[80])).
% 0.12/0.41 tff(82,plain,
% 0.12/0.41 (op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1)))) = U!1),
% 0.12/0.41 inference(transitivity,[status(thm)],[81, 60, 28])).
% 0.12/0.41 tff(83,plain,
% 0.12/0.41 (^[U: $i] : refl(((~sorti1(U)) | sorti2(h(U))) <=> ((~sorti1(U)) | sorti2(h(U))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(84,plain,
% 0.12/0.41 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) <=> ![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[83])).
% 0.12/0.41 tff(85,plain,
% 0.12/0.41 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) <=> ![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(86,plain,
% 0.12/0.41 (![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.12/0.41 inference(and_elim,[status(thm)],[32])).
% 0.12/0.41 tff(87,plain,
% 0.12/0.41 (![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.12/0.41 tff(88,plain,(
% 0.12/0.41 ![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[87])).
% 0.12/0.41 tff(89,plain,
% 0.12/0.41 (![U: $i] : ((~sorti1(U)) | sorti2(h(U)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.12/0.42 tff(90,plain,
% 0.12/0.42 (((~![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)))))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(91,plain,
% 0.12/0.42 ((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | ((~sorti1(tptp_fun_V_0(j(U!1)))) | sorti2(h(tptp_fun_V_0(j(U!1)))))),
% 0.12/0.42 inference(quant_inst,[status(thm)],[])).
% 0.12/0.42 tff(92,plain,
% 0.12/0.42 ((~![U: $i] : ((~sorti1(U)) | sorti2(h(U)))) | (~sorti1(tptp_fun_V_0(j(U!1)))) | sorti2(h(tptp_fun_V_0(j(U!1))))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.12/0.42 tff(93,plain,
% 0.12/0.42 (sorti2(h(tptp_fun_V_0(j(U!1))))),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[92, 89, 62])).
% 0.12/0.42 tff(94,plain,
% 0.12/0.42 (^[V: $i] : refl(((~sorti2(V)) | (~(op2(V, V) = U!1))) <=> ((~sorti2(V)) | (~(op2(V, V) = U!1))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(95,plain,
% 0.12/0.42 (![V: $i] : ((~sorti2(V)) | (~(op2(V, V) = U!1))) <=> ![V: $i] : ((~sorti2(V)) | (~(op2(V, V) = U!1)))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[94])).
% 0.12/0.42 tff(96,plain,
% 0.12/0.42 (^[V: $i] : trans(monotonicity(rewrite((sorti2(V) & (op2(V, V) = U!1)) <=> (~((~sorti2(V)) | (~(op2(V, V) = U!1))))), ((~(sorti2(V) & (op2(V, V) = U!1))) <=> (~(~((~sorti2(V)) | (~(op2(V, V) = U!1))))))), rewrite((~(~((~sorti2(V)) | (~(op2(V, V) = U!1))))) <=> ((~sorti2(V)) | (~(op2(V, V) = U!1)))), ((~(sorti2(V) & (op2(V, V) = U!1))) <=> ((~sorti2(V)) | (~(op2(V, V) = U!1)))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(97,plain,
% 0.12/0.42 (![V: $i] : (~(sorti2(V) & (op2(V, V) = U!1))) <=> ![V: $i] : ((~sorti2(V)) | (~(op2(V, V) = U!1)))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[96])).
% 0.12/0.42 tff(98,plain,
% 0.12/0.42 (![V: $i] : (~(sorti2(V) & (op2(V, V) = U!1)))),
% 0.12/0.42 inference(and_elim,[status(thm)],[23])).
% 0.12/0.42 tff(99,plain,
% 0.12/0.42 (![V: $i] : ((~sorti2(V)) | (~(op2(V, V) = U!1)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.12/0.42 tff(100,plain,
% 0.12/0.42 (![V: $i] : ((~sorti2(V)) | (~(op2(V, V) = U!1)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.12/0.42 tff(101,plain,
% 0.12/0.42 (((~![V: $i] : ((~sorti2(V)) | (~(op2(V, V) = U!1)))) | ((~sorti2(h(tptp_fun_V_0(j(U!1))))) | (~(op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1)))) = U!1)))) <=> ((~![V: $i] : ((~sorti2(V)) | (~(op2(V, V) = U!1)))) | (~sorti2(h(tptp_fun_V_0(j(U!1))))) | (~(op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1)))) = U!1)))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(102,plain,
% 0.12/0.42 ((~![V: $i] : ((~sorti2(V)) | (~(op2(V, V) = U!1)))) | ((~sorti2(h(tptp_fun_V_0(j(U!1))))) | (~(op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1)))) = U!1)))),
% 0.12/0.42 inference(quant_inst,[status(thm)],[])).
% 0.12/0.42 tff(103,plain,
% 0.12/0.42 ((~![V: $i] : ((~sorti2(V)) | (~(op2(V, V) = U!1)))) | (~sorti2(h(tptp_fun_V_0(j(U!1))))) | (~(op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1)))) = U!1))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.12/0.42 tff(104,plain,
% 0.12/0.42 (~(op2(h(tptp_fun_V_0(j(U!1))), h(tptp_fun_V_0(j(U!1)))) = U!1)),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[103, 100, 93])).
% 0.12/0.42 tff(105,plain,
% 0.12/0.42 ($false),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[104, 82])).
% 0.12/0.42 % SZS output end Proof
%------------------------------------------------------------------------------