TSTP Solution File: SYN066-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN066-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 23:53:29 EDT 2022
% Result : Unsatisfiable 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN066-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n022.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 01:32:39 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.
% 0.19/0.48 % SZS status Unsatisfiable
% 0.19/0.48 % SZS output start Proof
% 0.19/0.48 tff(big_r_type, type, (
% 0.19/0.48 big_r: ( $i * $i ) > $o)).
% 0.19/0.48 tff(a_type, type, (
% 0.19/0.48 a: $i)).
% 0.19/0.48 tff(big_q_type, type, (
% 0.19/0.48 big_q: ( $i * $i ) > $o)).
% 0.19/0.48 tff(g_type, type, (
% 0.19/0.48 g: $i > $i)).
% 0.19/0.48 tff(elem_0_type, type, (
% 0.19/0.48 elem_0: $i)).
% 0.19/0.48 tff(h_type, type, (
% 0.19/0.48 h: ( $i * $i ) > $i)).
% 0.19/0.48 tff(f_type, type, (
% 0.19/0.48 f: ( $i * $i ) > $i)).
% 0.19/0.48 tff(big_p_type, type, (
% 0.19/0.48 big_p: ( $i * $i ) > $o)).
% 0.19/0.48 tff(1,plain,
% 0.19/0.48 (^[Y: $i, X: $i] : refl(big_p(f(X, Y), X) <=> big_p(f(X, Y), X))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(2,plain,
% 0.19/0.48 (![Y: $i, X: $i] : big_p(f(X, Y), X) <=> ![Y: $i, X: $i] : big_p(f(X, Y), X)),
% 0.19/0.48 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.48 tff(3,plain,
% 0.19/0.48 (![Y: $i, X: $i] : big_p(f(X, Y), X) <=> ![Y: $i, X: $i] : big_p(f(X, Y), X)),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(4,axiom,(![Y: $i, X: $i] : big_p(f(X, Y), X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_2')).
% 0.19/0.48 tff(5,plain,
% 0.19/0.48 (![Y: $i, X: $i] : big_p(f(X, Y), X)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.49 tff(6,plain,(
% 0.19/0.49 ![Y: $i, X: $i] : big_p(f(X, Y), X)),
% 0.19/0.49 inference(skolemize,[status(sab)],[5])).
% 0.19/0.49 tff(7,plain,
% 0.19/0.49 (![Y: $i, X: $i] : big_p(f(X, Y), X)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.49 tff(8,plain,
% 0.19/0.49 ((~![Y: $i, X: $i] : big_p(f(X, Y), X)) | big_p(f(g(elem!0), elem!0), g(elem!0))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(9,plain,
% 0.19/0.49 (big_p(f(g(elem!0), elem!0), g(elem!0))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.49 tff(10,plain,
% 0.19/0.49 (^[Y: $i, X: $i] : refl(((~big_p(Y, X)) | big_p(f(X, Y), g(X))) <=> ((~big_p(Y, X)) | big_p(f(X, Y), g(X))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(11,plain,
% 0.19/0.49 (![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X))) <=> ![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.49 tff(12,plain,
% 0.19/0.49 (![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X))) <=> ![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(13,axiom,(![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_1')).
% 0.19/0.49 tff(14,plain,
% 0.19/0.49 (![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.49 tff(15,plain,(
% 0.19/0.49 ![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[14])).
% 0.19/0.49 tff(16,plain,
% 0.19/0.49 (![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.19/0.49 tff(17,plain,
% 0.19/0.49 (((~![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X)))) | ((~big_p(f(g(elem!0), elem!0), g(elem!0))) | big_p(f(g(elem!0), f(g(elem!0), elem!0)), g(g(elem!0))))) <=> ((~![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X)))) | (~big_p(f(g(elem!0), elem!0), g(elem!0))) | big_p(f(g(elem!0), f(g(elem!0), elem!0)), g(g(elem!0))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(18,plain,
% 0.19/0.49 ((~![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X)))) | ((~big_p(f(g(elem!0), elem!0), g(elem!0))) | big_p(f(g(elem!0), f(g(elem!0), elem!0)), g(g(elem!0))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(19,plain,
% 0.19/0.49 ((~![Y: $i, X: $i] : ((~big_p(Y, X)) | big_p(f(X, Y), g(X)))) | (~big_p(f(g(elem!0), elem!0), g(elem!0))) | big_p(f(g(elem!0), f(g(elem!0), elem!0)), g(g(elem!0)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.49 tff(20,plain,
% 0.19/0.49 (big_p(f(g(elem!0), f(g(elem!0), elem!0)), g(g(elem!0)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[19, 16, 9])).
% 0.19/0.49 tff(21,plain,
% 0.19/0.49 (^[Y: $i, X: $i] : refl(((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X))) <=> ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(22,plain,
% 0.19/0.49 (![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X))) <=> ![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.49 tff(23,plain,
% 0.19/0.49 (![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X))) <=> ![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(24,axiom,(![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_3')).
% 0.19/0.49 tff(25,plain,
% 0.19/0.49 (![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.49 tff(26,plain,(
% 0.19/0.49 ![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[25])).
% 0.19/0.49 tff(27,plain,
% 0.19/0.49 (![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.19/0.49 tff(28,plain,
% 0.19/0.49 (((~![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X)))) | ((~big_p(f(g(elem!0), f(g(elem!0), elem!0)), g(g(elem!0)))) | big_q(h(g(elem!0), f(g(elem!0), elem!0)), g(g(elem!0))))) <=> ((~![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X)))) | (~big_p(f(g(elem!0), f(g(elem!0), elem!0)), g(g(elem!0)))) | big_q(h(g(elem!0), f(g(elem!0), elem!0)), g(g(elem!0))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(29,plain,
% 0.19/0.49 ((~![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X)))) | ((~big_p(f(g(elem!0), f(g(elem!0), elem!0)), g(g(elem!0)))) | big_q(h(g(elem!0), f(g(elem!0), elem!0)), g(g(elem!0))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(30,plain,
% 0.19/0.49 ((~![Y: $i, X: $i] : ((~big_p(f(X, Y), g(X))) | big_q(h(X, Y), g(X)))) | (~big_p(f(g(elem!0), f(g(elem!0), elem!0)), g(g(elem!0)))) | big_q(h(g(elem!0), f(g(elem!0), elem!0)), g(g(elem!0)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.49 tff(31,plain,
% 0.19/0.49 (big_q(h(g(elem!0), f(g(elem!0), elem!0)), g(g(elem!0)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[30, 27, 20])).
% 0.19/0.49 tff(32,plain,
% 0.19/0.49 (^[Z: $i, Y: $i, X: $i] : refl(((~big_q(X, Y)) | big_r(Z, Z)) <=> ((~big_q(X, Y)) | big_r(Z, Z)))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(33,plain,
% 0.19/0.49 (![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.49 tff(34,plain,
% 0.19/0.49 (![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(35,axiom,(![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_5')).
% 0.19/0.49 tff(36,plain,
% 0.19/0.49 (![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.49 tff(37,plain,(
% 0.19/0.49 ![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z))),
% 0.19/0.49 inference(skolemize,[status(sab)],[36])).
% 0.19/0.49 tff(38,plain,
% 0.19/0.49 (![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.19/0.49 tff(39,plain,
% 0.19/0.49 (((~![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z))) | ((~big_q(h(g(elem!0), f(g(elem!0), elem!0)), g(g(elem!0)))) | big_r(a, a))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z))) | (~big_q(h(g(elem!0), f(g(elem!0), elem!0)), g(g(elem!0)))) | big_r(a, a))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(40,plain,
% 0.19/0.49 ((~![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z))) | ((~big_q(h(g(elem!0), f(g(elem!0), elem!0)), g(g(elem!0)))) | big_r(a, a))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(41,plain,
% 0.19/0.49 ((~![Z: $i, Y: $i, X: $i] : ((~big_q(X, Y)) | big_r(Z, Z))) | (~big_q(h(g(elem!0), f(g(elem!0), elem!0)), g(g(elem!0)))) | big_r(a, a)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.49 tff(42,plain,
% 0.19/0.49 (big_r(a, a)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[41, 38, 31])).
% 0.19/0.49 tff(43,plain,
% 0.19/0.49 (^[Z: $i] : refl((~big_r(a, Z)) <=> (~big_r(a, Z)))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(44,plain,
% 0.19/0.49 (![Z: $i] : (~big_r(a, Z)) <=> ![Z: $i] : (~big_r(a, Z))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.49 tff(45,plain,
% 0.19/0.49 (![Z: $i] : (~big_r(a, Z)) <=> ![Z: $i] : (~big_r(a, Z))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(46,axiom,(![Z: $i] : (~big_r(a, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_6')).
% 0.19/0.49 tff(47,plain,
% 0.19/0.49 (![Z: $i] : (~big_r(a, Z))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.49 tff(48,plain,(
% 0.19/0.49 ![Z: $i] : (~big_r(a, Z))),
% 0.19/0.49 inference(skolemize,[status(sab)],[47])).
% 0.19/0.49 tff(49,plain,
% 0.19/0.49 (![Z: $i] : (~big_r(a, Z))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.19/0.49 tff(50,plain,
% 0.19/0.49 ((~![Z: $i] : (~big_r(a, Z))) | (~big_r(a, a))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(51,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[50, 49, 42])).
% 0.19/0.49 % SZS output end Proof
%------------------------------------------------------------------------------