TSTP Solution File: ALG201+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG201+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 16:09:07 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG201+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n003.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 13:50:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(j_type, type, (
% 0.13/0.39 j: $i > $i)).
% 0.13/0.39 tff(tptp_fun_U_0_type, type, (
% 0.13/0.39 tptp_fun_U_0: $i)).
% 0.13/0.39 tff(op1_type, type, (
% 0.13/0.39 op1: ( $i * $i ) > $i)).
% 0.13/0.39 tff(op2_type, type, (
% 0.13/0.39 op2: ( $i * $i ) > $i)).
% 0.13/0.39 tff(sorti2_type, type, (
% 0.13/0.39 sorti2: $i > $o)).
% 0.13/0.39 tff(h_type, type, (
% 0.13/0.39 h: $i > $i)).
% 0.13/0.39 tff(sorti1_type, type, (
% 0.13/0.39 sorti1: $i > $o)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 ((~![U: $i] : ((~sorti2(U)) | (~(op2(U, U) = U)))) <=> (~![U: $i] : ((~sorti2(U)) | (~(op2(U, U) = U))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 ((~![U: $i] : (sorti2(U) => (~(op2(U, U) = U)))) <=> (~![U: $i] : ((~sorti2(U)) | (~(op2(U, U) = U))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(3,axiom,(~![U: $i] : (sorti2(U) => (~(op2(U, U) = U)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax4')).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (~![U: $i] : ((~sorti2(U)) | (~(op2(U, U) = U)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (~![U: $i] : ((~sorti2(U)) | (~(op2(U, U) = U)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (~![U: $i] : ((~sorti2(U)) | (~(op2(U, U) = U)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (~![U: $i] : ((~sorti2(U)) | (~(op2(U, U) = U)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (~![U: $i] : ((~sorti2(U)) | (~(op2(U, U) = U)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (~![U: $i] : ((~sorti2(U)) | (~(op2(U, U) = U)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (~![U: $i] : ((~sorti2(U)) | (~(op2(U, U) = U)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.13/0.39 tff(11,plain,(
% 0.13/0.39 ~((~sorti2(U!0)) | (~(op2(U!0, U!0) = U!0)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[10])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (op2(U!0, U!0) = U!0),
% 0.13/0.39 inference(or_elim,[status(thm)],[11])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (U!0 = op2(U!0, U!0)),
% 0.13/0.39 inference(symmetry,[status(thm)],[12])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (j(U!0) = j(op2(U!0, U!0))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[13])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (j(op2(U!0, U!0)) = j(U!0)),
% 0.13/0.39 inference(symmetry,[status(thm)],[14])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (^[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))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (![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)))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[16])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (^[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))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (![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)))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[18])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (![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)))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[19, 17])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (![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)))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 ((~((![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))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(23,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')).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (~((~(![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)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (![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))),
% 0.13/0.39 inference(or_elim,[status(thm)],[24])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.13/0.39 inference(and_elim,[status(thm)],[25])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.13/0.39 tff(28,plain,(
% 0.13/0.39 ![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.13/0.39 inference(skolemize,[status(sab)],[27])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[28, 20])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (sorti2(U!0)),
% 0.13/0.39 inference(or_elim,[status(thm)],[11])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | ((~sorti2(U!0)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z)))))) <=> ((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | (~sorti2(U!0)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z)))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 ((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | ((~sorti2(U!0)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z)))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 ((~![Y: $i] : ((~sorti2(Y)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(Y, Z)) = op1(j(Y), j(Z)))))) | (~sorti2(U!0)) | ![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[33, 30, 29])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (((~![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))) | ((~sorti2(U!0)) | (j(op2(U!0, U!0)) = op1(j(U!0), j(U!0))))) <=> ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))) | (~sorti2(U!0)) | (j(op2(U!0, U!0)) = op1(j(U!0), j(U!0))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))) | ((~sorti2(U!0)) | (j(op2(U!0, U!0)) = op1(j(U!0), j(U!0))))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 ((~![Z: $i] : ((~sorti2(Z)) | (j(op2(U!0, Z)) = op1(j(U!0), j(Z))))) | (~sorti2(U!0)) | (j(op2(U!0, U!0)) = op1(j(U!0), j(U!0)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (j(op2(U!0, U!0)) = op1(j(U!0), j(U!0))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[37, 30, 34])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (op1(j(U!0), j(U!0)) = j(op2(U!0, U!0))),
% 0.13/0.40 inference(symmetry,[status(thm)],[38])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 (op1(j(U!0), j(U!0)) = j(U!0)),
% 0.13/0.40 inference(transitivity,[status(thm)],[39, 15])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 (^[V: $i] : refl(((~sorti2(V)) | sorti1(j(V))) <=> ((~sorti2(V)) | sorti1(j(V))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[41])).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 (![V: $i] : ((~sorti2(V)) | sorti1(j(V))) <=> ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(44,plain,
% 0.13/0.40 (![U: $i] : ((~sorti1(U)) | sorti2(h(U))) & ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.13/0.40 inference(or_elim,[status(thm)],[24])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.13/0.40 inference(and_elim,[status(thm)],[44])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[45, 43])).
% 0.13/0.40 tff(47,plain,(
% 0.13/0.40 ![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[46])).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 (![V: $i] : ((~sorti2(V)) | sorti1(j(V)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[47, 42])).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 (((~![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)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | ((~sorti2(U!0)) | sorti1(j(U!0)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 ((~![V: $i] : ((~sorti2(V)) | sorti1(j(V)))) | (~sorti2(U!0)) | sorti1(j(U!0))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.13/0.40 tff(52,plain,
% 0.13/0.40 (sorti1(j(U!0))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[51, 30, 48])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 (^[U: $i] : refl(((~sorti1(U)) | (~(op1(U, U) = U))) <=> ((~sorti1(U)) | (~(op1(U, U) = U))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 (![U: $i] : ((~sorti1(U)) | (~(op1(U, U) = U))) <=> ![U: $i] : ((~sorti1(U)) | (~(op1(U, U) = U)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[53])).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 (![U: $i] : ((~sorti1(U)) | (~(op1(U, U) = U))) <=> ![U: $i] : ((~sorti1(U)) | (~(op1(U, U) = U)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 (^[U: $i] : rewrite((sorti1(U) => (~(op1(U, U) = U))) <=> ((~sorti1(U)) | (~(op1(U, U) = U))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(57,plain,
% 0.13/0.40 (![U: $i] : (sorti1(U) => (~(op1(U, U) = U))) <=> ![U: $i] : ((~sorti1(U)) | (~(op1(U, U) = U)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[56])).
% 0.13/0.40 tff(58,axiom,(![U: $i] : (sorti1(U) => (~(op1(U, U) = U)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax3')).
% 0.13/0.40 tff(59,plain,
% 0.13/0.40 (![U: $i] : ((~sorti1(U)) | (~(op1(U, U) = U)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.13/0.40 tff(60,plain,
% 0.13/0.40 (![U: $i] : ((~sorti1(U)) | (~(op1(U, U) = U)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.13/0.40 tff(61,plain,(
% 0.13/0.40 ![U: $i] : ((~sorti1(U)) | (~(op1(U, U) = U)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[60])).
% 0.13/0.40 tff(62,plain,
% 0.13/0.40 (![U: $i] : ((~sorti1(U)) | (~(op1(U, U) = U)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.13/0.40 tff(63,plain,
% 0.13/0.40 (((~![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))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(64,plain,
% 0.13/0.40 ((~![U: $i] : ((~sorti1(U)) | (~(op1(U, U) = U)))) | ((~sorti1(j(U!0))) | (~(op1(j(U!0), j(U!0)) = j(U!0))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(65,plain,
% 0.13/0.40 ((~![U: $i] : ((~sorti1(U)) | (~(op1(U, U) = U)))) | (~sorti1(j(U!0))) | (~(op1(j(U!0), j(U!0)) = j(U!0)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.13/0.40 tff(66,plain,
% 0.13/0.40 (~(op1(j(U!0), j(U!0)) = j(U!0))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[65, 62, 52])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[66, 40])).
% 0.20/0.40 % SZS output end Proof
%------------------------------------------------------------------------------