TSTP Solution File: SYN062+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN062+1 : TPTP v8.1.0. Released v2.0.0.
% 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 : Thu Sep 29 23:53:27 EDT 2022
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN062+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Sep 5 01:29:56 EDT 2022
% 0.13/0.33 % 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.
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(big_h_type, type, (
% 0.19/0.38 big_h: $i > $o)).
% 0.19/0.38 tff(tptp_fun_X_0_type, type, (
% 0.19/0.38 tptp_fun_X_0: $i)).
% 0.19/0.38 tff(big_g_type, type, (
% 0.19/0.38 big_g: $i > $o)).
% 0.19/0.38 tff(big_k_type, type, (
% 0.19/0.38 big_k: $i > $o)).
% 0.19/0.38 tff(big_f_type, type, (
% 0.19/0.38 big_f: $i > $o)).
% 0.19/0.38 tff(big_j_type, type, (
% 0.19/0.38 big_j: $i > $o)).
% 0.19/0.38 tff(big_i_type, type, (
% 0.19/0.38 big_i: $i > $o)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 ((~![X: $i] : (big_j(X) | (~(big_f(X) & big_k(X))))) <=> (~![X: $i] : (big_j(X) | (~(big_f(X) & big_k(X)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 ((~![X: $i] : ((big_f(X) & big_k(X)) => big_j(X))) <=> (~![X: $i] : (big_j(X) | (~(big_f(X) & big_k(X)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(3,axiom,(~![X: $i] : ((big_f(X) & big_k(X)) => big_j(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel32')).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (~![X: $i] : (big_j(X) | (~(big_f(X) & big_k(X))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (~![X: $i] : (big_j(X) | (~(big_f(X) & big_k(X))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (~![X: $i] : (big_j(X) | (~(big_f(X) & big_k(X))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (~![X: $i] : (big_j(X) | (~(big_f(X) & big_k(X))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 (~![X: $i] : (big_j(X) | (~(big_f(X) & big_k(X))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (~![X: $i] : (big_j(X) | (~(big_f(X) & big_k(X))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (~![X: $i] : (big_j(X) | (~(big_f(X) & big_k(X))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.19/0.38 tff(11,plain,(
% 0.19/0.38 ~(big_j(X!0) | (~(big_f(X!0) & big_k(X!0))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[10])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (big_f(X!0) & big_k(X!0)),
% 0.19/0.38 inference(or_elim,[status(thm)],[11])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (big_k(X!0)),
% 0.19/0.38 inference(and_elim,[status(thm)],[12])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (^[X: $i] : refl((big_h(X) | (~big_k(X))) <=> (big_h(X) | (~big_k(X))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (![X: $i] : (big_h(X) | (~big_k(X))) <=> ![X: $i] : (big_h(X) | (~big_k(X)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (![X: $i] : (big_h(X) | (~big_k(X))) <=> ![X: $i] : (big_h(X) | (~big_k(X)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 (^[X: $i] : rewrite((big_k(X) => big_h(X)) <=> (big_h(X) | (~big_k(X))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (![X: $i] : (big_k(X) => big_h(X)) <=> ![X: $i] : (big_h(X) | (~big_k(X)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.38 tff(19,axiom,(![X: $i] : (big_k(X) => big_h(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel32_3')).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (![X: $i] : (big_h(X) | (~big_k(X)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (![X: $i] : (big_h(X) | (~big_k(X)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.19/0.38 tff(22,plain,(
% 0.19/0.38 ![X: $i] : (big_h(X) | (~big_k(X)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[21])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 (![X: $i] : (big_h(X) | (~big_k(X)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (((~![X: $i] : (big_h(X) | (~big_k(X)))) | (big_h(X!0) | (~big_k(X!0)))) <=> ((~![X: $i] : (big_h(X) | (~big_k(X)))) | big_h(X!0) | (~big_k(X!0)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 ((~![X: $i] : (big_h(X) | (~big_k(X)))) | (big_h(X!0) | (~big_k(X!0)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 ((~![X: $i] : (big_h(X) | (~big_k(X)))) | big_h(X!0) | (~big_k(X!0))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (big_h(X!0)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[26, 23, 13])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 ((big_g(X!0) | big_h(X!0)) | (~big_h(X!0))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (big_g(X!0) | big_h(X!0)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (~big_j(X!0)),
% 0.19/0.38 inference(or_elim,[status(thm)],[11])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 (^[X: $i] : refl((big_j(X) | (~big_i(X)) | (~big_h(X))) <=> (big_j(X) | (~big_i(X)) | (~big_h(X))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 (![X: $i] : (big_j(X) | (~big_i(X)) | (~big_h(X))) <=> ![X: $i] : (big_j(X) | (~big_i(X)) | (~big_h(X)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((big_i(X) & big_h(X)) <=> (~((~big_i(X)) | (~big_h(X))))), ((~(big_i(X) & big_h(X))) <=> (~(~((~big_i(X)) | (~big_h(X))))))), rewrite((~(~((~big_i(X)) | (~big_h(X))))) <=> ((~big_i(X)) | (~big_h(X)))), ((~(big_i(X) & big_h(X))) <=> ((~big_i(X)) | (~big_h(X))))), ((big_j(X) | (~(big_i(X) & big_h(X)))) <=> (big_j(X) | ((~big_i(X)) | (~big_h(X)))))), rewrite((big_j(X) | ((~big_i(X)) | (~big_h(X)))) <=> (big_j(X) | (~big_i(X)) | (~big_h(X)))), ((big_j(X) | (~(big_i(X) & big_h(X)))) <=> (big_j(X) | (~big_i(X)) | (~big_h(X)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 (![X: $i] : (big_j(X) | (~(big_i(X) & big_h(X)))) <=> ![X: $i] : (big_j(X) | (~big_i(X)) | (~big_h(X)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 (![X: $i] : (big_j(X) | (~(big_i(X) & big_h(X)))) <=> ![X: $i] : (big_j(X) | (~(big_i(X) & big_h(X))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 (^[X: $i] : rewrite(((big_i(X) & big_h(X)) => big_j(X)) <=> (big_j(X) | (~(big_i(X) & big_h(X)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 (![X: $i] : ((big_i(X) & big_h(X)) => big_j(X)) <=> ![X: $i] : (big_j(X) | (~(big_i(X) & big_h(X))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.38 tff(38,axiom,(![X: $i] : ((big_i(X) & big_h(X)) => big_j(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel32_2')).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 (![X: $i] : (big_j(X) | (~(big_i(X) & big_h(X))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 (![X: $i] : (big_j(X) | (~(big_i(X) & big_h(X))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.19/0.38 tff(41,plain,(
% 0.19/0.38 ![X: $i] : (big_j(X) | (~(big_i(X) & big_h(X))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[40])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 (![X: $i] : (big_j(X) | (~big_i(X)) | (~big_h(X)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 (![X: $i] : (big_j(X) | (~big_i(X)) | (~big_h(X)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 (((~![X: $i] : (big_j(X) | (~big_i(X)) | (~big_h(X)))) | (big_j(X!0) | (~big_i(X!0)) | (~big_h(X!0)))) <=> ((~![X: $i] : (big_j(X) | (~big_i(X)) | (~big_h(X)))) | big_j(X!0) | (~big_i(X!0)) | (~big_h(X!0)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 ((~![X: $i] : (big_j(X) | (~big_i(X)) | (~big_h(X)))) | (big_j(X!0) | (~big_i(X!0)) | (~big_h(X!0)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 ((~![X: $i] : (big_j(X) | (~big_i(X)) | (~big_h(X)))) | big_j(X!0) | (~big_i(X!0)) | (~big_h(X!0))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 ((~big_i(X!0)) | (~big_h(X!0))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[46, 43, 30])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (~big_i(X!0)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[47, 27])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 (big_f(X!0)),
% 0.19/0.38 inference(and_elim,[status(thm)],[12])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 (^[X: $i] : refl((big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X)))) <=> (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 (![X: $i] : (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X)))) <=> ![X: $i] : (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((big_f(X) & (big_g(X) | big_h(X))) <=> (~((~big_f(X)) | (~(big_g(X) | big_h(X)))))), ((~(big_f(X) & (big_g(X) | big_h(X)))) <=> (~(~((~big_f(X)) | (~(big_g(X) | big_h(X)))))))), rewrite((~(~((~big_f(X)) | (~(big_g(X) | big_h(X)))))) <=> ((~big_f(X)) | (~(big_g(X) | big_h(X))))), ((~(big_f(X) & (big_g(X) | big_h(X)))) <=> ((~big_f(X)) | (~(big_g(X) | big_h(X)))))), ((big_i(X) | (~(big_f(X) & (big_g(X) | big_h(X))))) <=> (big_i(X) | ((~big_f(X)) | (~(big_g(X) | big_h(X))))))), rewrite((big_i(X) | ((~big_f(X)) | (~(big_g(X) | big_h(X))))) <=> (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X))))), ((big_i(X) | (~(big_f(X) & (big_g(X) | big_h(X))))) <=> (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(53,plain,
% 0.19/0.38 (![X: $i] : (big_i(X) | (~(big_f(X) & (big_g(X) | big_h(X))))) <=> ![X: $i] : (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.38 tff(54,plain,
% 0.19/0.38 (![X: $i] : (big_i(X) | (~(big_f(X) & (big_g(X) | big_h(X))))) <=> ![X: $i] : (big_i(X) | (~(big_f(X) & (big_g(X) | big_h(X)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(55,plain,
% 0.19/0.38 (^[X: $i] : rewrite(((big_f(X) & (big_g(X) | big_h(X))) => big_i(X)) <=> (big_i(X) | (~(big_f(X) & (big_g(X) | big_h(X))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(56,plain,
% 0.19/0.38 (![X: $i] : ((big_f(X) & (big_g(X) | big_h(X))) => big_i(X)) <=> ![X: $i] : (big_i(X) | (~(big_f(X) & (big_g(X) | big_h(X)))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.38 tff(57,axiom,(![X: $i] : ((big_f(X) & (big_g(X) | big_h(X))) => big_i(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel32_1')).
% 0.19/0.38 tff(58,plain,
% 0.19/0.38 (![X: $i] : (big_i(X) | (~(big_f(X) & (big_g(X) | big_h(X)))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.38 tff(59,plain,
% 0.19/0.38 (![X: $i] : (big_i(X) | (~(big_f(X) & (big_g(X) | big_h(X)))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.19/0.38 tff(60,plain,(
% 0.19/0.38 ![X: $i] : (big_i(X) | (~(big_f(X) & (big_g(X) | big_h(X)))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[59])).
% 0.19/0.38 tff(61,plain,
% 0.19/0.38 (![X: $i] : (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.19/0.38 tff(62,plain,
% 0.19/0.38 (![X: $i] : (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.19/0.38 tff(63,plain,
% 0.19/0.38 (((~![X: $i] : (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X))))) | (big_i(X!0) | (~big_f(X!0)) | (~(big_g(X!0) | big_h(X!0))))) <=> ((~![X: $i] : (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X))))) | big_i(X!0) | (~big_f(X!0)) | (~(big_g(X!0) | big_h(X!0))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(64,plain,
% 0.19/0.38 ((~![X: $i] : (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X))))) | (big_i(X!0) | (~big_f(X!0)) | (~(big_g(X!0) | big_h(X!0))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(65,plain,
% 0.19/0.38 ((~![X: $i] : (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X))))) | big_i(X!0) | (~big_f(X!0)) | (~(big_g(X!0) | big_h(X!0)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.38 tff(66,plain,
% 0.19/0.38 (big_i(X!0) | (~(big_g(X!0) | big_h(X!0)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[65, 62, 49])).
% 0.19/0.38 tff(67,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[66, 48, 29])).
% 0.19/0.38 % SZS output end Proof
%------------------------------------------------------------------------------