TSTP Solution File: ALG029+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG029+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 16:07:14 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG029+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 29 13:07:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(op2_type, type, (
% 0.20/0.40 op2: ( $i * $i ) > $i)).
% 0.20/0.40 tff(tptp_fun_U_0_type, type, (
% 0.20/0.40 tptp_fun_U_0: $i)).
% 0.20/0.40 tff(tptp_fun_V_1_type, type, (
% 0.20/0.40 tptp_fun_V_1: $i)).
% 0.20/0.40 tff(h_type, type, (
% 0.20/0.40 h: $i > $i)).
% 0.20/0.40 tff(j_type, type, (
% 0.20/0.40 j: $i > $i)).
% 0.20/0.40 tff(sorti2_type, type, (
% 0.20/0.40 sorti2: $i > $o)).
% 0.20/0.40 tff(sorti1_type, type, (
% 0.20/0.40 sorti1: $i > $o)).
% 0.20/0.40 tff(op1_type, type, (
% 0.20/0.40 op1: ( $i * $i ) > $i)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[X1: $i] : refl(((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ((~sorti2(X1)) | (h(j(X1)) = X1)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1)) <=> ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 ((~((![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))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 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/sandbox/benchmark/theBenchmark.p','co1')).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (~((~(![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)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![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))),
% 0.20/0.40 inference(or_elim,[status(thm)],[6])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.20/0.40 inference(and_elim,[status(thm)],[7])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.20/0.40 tff(10,plain,(
% 0.20/0.40 ![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.20/0.40 inference(skolemize,[status(sab)],[9])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (((~(~sorti2(U!0))) & (~((~sorti2(V!1)) | (op2(U!0, V!1) = op2(V!1, U!0))))) <=> (sorti2(U!0) & (~((~sorti2(V!1)) | (op2(U!0, V!1) = op2(V!1, U!0)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 ((~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, V) = op2(V, U))))) <=> (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, V) = op2(V, U)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 ((~![U: $i] : (sorti2(U) => ![V: $i] : (sorti2(V) => (op2(U, V) = op2(V, U))))) <=> (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, V) = op2(V, U)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(15,axiom,(~![U: $i] : (sorti2(U) => ![V: $i] : (sorti2(V) => (op2(U, V) = op2(V, U))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax4')).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, V) = op2(V, U))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, V) = op2(V, U))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, V) = op2(V, U))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, V) = op2(V, U))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, V) = op2(V, U))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, V) = op2(V, U))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (~![U: $i] : ((~sorti2(U)) | ![V: $i] : ((~sorti2(V)) | (op2(U, V) = op2(V, U))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[21, 13])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (sorti2(U!0) & (~((~sorti2(V!1)) | (op2(U!0, V!1) = op2(V!1, U!0))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (sorti2(U!0)),
% 0.20/0.40 inference(and_elim,[status(thm)],[23])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (((~![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))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(U!0)) | (h(j(U!0)) = U!0))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(U!0)) | (h(j(U!0)) = U!0)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (h(j(U!0)) = U!0),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[27, 24, 11])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (~((~sorti2(V!1)) | (op2(U!0, V!1) = op2(V!1, U!0)))),
% 0.20/0.40 inference(and_elim,[status(thm)],[23])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (sorti2(V!1)),
% 0.20/0.40 inference(or_elim,[status(thm)],[29])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(V!1)) | (h(j(V!1)) = V!1))) <=> ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(V!1)) | (h(j(V!1)) = V!1))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | ((~sorti2(V!1)) | (h(j(V!1)) = V!1))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 ((~![X1: $i] : ((~sorti2(X1)) | (h(j(X1)) = X1))) | (~sorti2(V!1)) | (h(j(V!1)) = V!1)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (h(j(V!1)) = V!1),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[33, 30, 11])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (op2(h(j(V!1)), h(j(U!0))) = op2(V!1, U!0)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[34, 28])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (^[V: $i] : refl(((~sorti2(V)) | sorti1(j(V))) <=> ((~sorti2(V)) | sorti1(j(V))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) & ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.20/0.40 inference(or_elim,[status(thm)],[6])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.20/0.40 inference(and_elim,[status(thm)],[39])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[40, 38])).
% 0.20/0.40 tff(42,plain,(
% 0.20/0.40 ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[41])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[42, 37])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(V!1)) | sorti1(j(V!1)))) <=> ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(V!1)) | sorti1(j(V!1)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(V!1)) | sorti1(j(V!1)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(V!1)) | sorti1(j(V!1))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 (sorti1(j(V!1))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[46, 30, 43])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 (^[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))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 (![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)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 (^[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))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 (![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)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 (![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)))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[51, 49])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 (![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)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.20/0.40 inference(and_elim,[status(thm)],[7])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.40 tff(56,plain,(
% 0.20/0.40 ![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[55])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 (![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 (((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | ((~sorti1(j(V!1))) | ![X: $i] : ((~sorti1(X)) | (h(op1(j(V!1), X)) = op2(h(j(V!1)), h(X)))))) <=> ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | (~sorti1(j(V!1))) | ![X: $i] : ((~sorti1(X)) | (h(op1(j(V!1), X)) = op2(h(j(V!1)), h(X)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | ((~sorti1(j(V!1))) | ![X: $i] : ((~sorti1(X)) | (h(op1(j(V!1), X)) = op2(h(j(V!1)), h(X)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 ((~![W: $i] : ((~sorti1(W)) | ![X: $i] : ((~sorti1(X)) | (h(op1(W, X)) = op2(h(W), h(X)))))) | (~sorti1(j(V!1))) | ![X: $i] : ((~sorti1(X)) | (h(op1(j(V!1), X)) = op2(h(j(V!1)), h(X))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (![X: $i] : ((~sorti1(X)) | (h(op1(j(V!1), X)) = op2(h(j(V!1)), h(X))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[60, 57, 47])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (((~![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)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(U!0)) | sorti1(j(U!0)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(U!0)) | sorti1(j(U!0))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 (sorti1(j(U!0))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[64, 24, 43])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (((~![X: $i] : ((~sorti1(X)) | (h(op1(j(V!1), X)) = op2(h(j(V!1)), h(X))))) | ((~sorti1(j(U!0))) | (h(op1(j(V!1), j(U!0))) = op2(h(j(V!1)), h(j(U!0)))))) <=> ((~![X: $i] : ((~sorti1(X)) | (h(op1(j(V!1), X)) = op2(h(j(V!1)), h(X))))) | (~sorti1(j(U!0))) | (h(op1(j(V!1), j(U!0))) = op2(h(j(V!1)), h(j(U!0)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 ((~![X: $i] : ((~sorti1(X)) | (h(op1(j(V!1), X)) = op2(h(j(V!1)), h(X))))) | ((~sorti1(j(U!0))) | (h(op1(j(V!1), j(U!0))) = op2(h(j(V!1)), h(j(U!0)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 ((~![X: $i] : ((~sorti1(X)) | (h(op1(j(V!1), X)) = op2(h(j(V!1)), h(X))))) | (~sorti1(j(U!0))) | (h(op1(j(V!1), j(U!0))) = op2(h(j(V!1)), h(j(U!0))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 (h(op1(j(V!1), j(U!0))) = op2(h(j(V!1)), h(j(U!0)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[68, 65, 61])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (^[U: $i] : refl(((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U)))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (^[U: $i] : rewrite(((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U)))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[73, 71])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((sorti1(V) => (op1(U, V) = op1(V, U))) <=> ((~sorti1(V)) | (op1(U, V) = op1(V, U))))), (![V: $i] : (sorti1(V) => (op1(U, V) = op1(V, U))) <=> ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))), ((sorti1(U) => ![V: $i] : (sorti1(V) => (op1(U, V) = op1(V, U)))) <=> (sorti1(U) => ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U)))))), rewrite((sorti1(U) => ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U)))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))), ((sorti1(U) => ![V: $i] : (sorti1(V) => (op1(U, V) = op1(V, U)))) <=> ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 (![U: $i] : (sorti1(U) => ![V: $i] : (sorti1(V) => (op1(U, V) = op1(V, U)))) <=> ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.40 tff(78,axiom,(![U: $i] : (sorti1(U) => ![V: $i] : (sorti1(V) => (op1(U, V) = op1(V, U))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax3')).
% 0.20/0.40 tff(79,plain,
% 0.20/0.40 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.20/0.41 tff(81,plain,(
% 0.20/0.41 ![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[80])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 (((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))) | ((~sorti1(j(U!0))) | ![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = op1(V, j(U!0)))))) <=> ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))) | (~sorti1(j(U!0))) | ![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = op1(V, j(U!0)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))) | ((~sorti1(j(U!0))) | ![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = op1(V, j(U!0)))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 ((~![U: $i] : ((~sorti1(U)) | ![V: $i] : ((~sorti1(V)) | (op1(U, V) = op1(V, U))))) | (~sorti1(j(U!0))) | ![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = op1(V, j(U!0))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 (![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = op1(V, j(U!0))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[85, 82, 65])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 (((~![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = op1(V, j(U!0))))) | ((~sorti1(j(V!1))) | (op1(j(U!0), j(V!1)) = op1(j(V!1), j(U!0))))) <=> ((~![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = op1(V, j(U!0))))) | (~sorti1(j(V!1))) | (op1(j(U!0), j(V!1)) = op1(j(V!1), j(U!0))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 ((~![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = op1(V, j(U!0))))) | ((~sorti1(j(V!1))) | (op1(j(U!0), j(V!1)) = op1(j(V!1), j(U!0))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 ((~![V: $i] : ((~sorti1(V)) | (op1(j(U!0), V) = op1(V, j(U!0))))) | (~sorti1(j(V!1))) | (op1(j(U!0), j(V!1)) = op1(j(V!1), j(U!0)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 (op1(j(U!0), j(V!1)) = op1(j(V!1), j(U!0))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[89, 47, 86])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (h(op1(j(U!0), j(V!1))) = h(op1(j(V!1), j(U!0)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[90])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (((~![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)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 ((~![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)))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 ((~![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))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 (![X: $i] : ((~sorti1(X)) | (h(op1(j(U!0), X)) = op2(h(j(U!0)), h(X))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[94, 57, 65])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 (((~![X: $i] : ((~sorti1(X)) | (h(op1(j(U!0), X)) = op2(h(j(U!0)), h(X))))) | ((~sorti1(j(V!1))) | (h(op1(j(U!0), j(V!1))) = op2(h(j(U!0)), h(j(V!1)))))) <=> ((~![X: $i] : ((~sorti1(X)) | (h(op1(j(U!0), X)) = op2(h(j(U!0)), h(X))))) | (~sorti1(j(V!1))) | (h(op1(j(U!0), j(V!1))) = op2(h(j(U!0)), h(j(V!1)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 ((~![X: $i] : ((~sorti1(X)) | (h(op1(j(U!0), X)) = op2(h(j(U!0)), h(X))))) | ((~sorti1(j(V!1))) | (h(op1(j(U!0), j(V!1))) = op2(h(j(U!0)), h(j(V!1)))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 ((~![X: $i] : ((~sorti1(X)) | (h(op1(j(U!0), X)) = op2(h(j(U!0)), h(X))))) | (~sorti1(j(V!1))) | (h(op1(j(U!0), j(V!1))) = op2(h(j(U!0)), h(j(V!1))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 (h(op1(j(U!0), j(V!1))) = op2(h(j(U!0)), h(j(V!1)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[98, 47, 95])).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 (op2(h(j(U!0)), h(j(V!1))) = h(op1(j(U!0), j(V!1)))),
% 0.20/0.41 inference(symmetry,[status(thm)],[99])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 (V!1 = h(j(V!1))),
% 0.20/0.41 inference(symmetry,[status(thm)],[34])).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 (U!0 = h(j(U!0))),
% 0.20/0.41 inference(symmetry,[status(thm)],[28])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (op2(U!0, V!1) = op2(h(j(U!0)), h(j(V!1)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[102, 101])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 (op2(U!0, V!1) = op2(V!1, U!0)),
% 0.20/0.41 inference(transitivity,[status(thm)],[103, 100, 91, 69, 35])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 (~(op2(U!0, V!1) = op2(V!1, U!0))),
% 0.20/0.41 inference(or_elim,[status(thm)],[29])).
% 0.20/0.41 tff(106,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.20/0.41 % SZS output end Proof
%------------------------------------------------------------------------------