TSTP Solution File: SYN732+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN732+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 23:57:09 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN732+1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Sep 5 07:10:17 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(p_type, type, (
% 0.21/0.39 p: ( $i * $i ) > $o)).
% 0.21/0.39 tff(tptp_fun_V_1_type, type, (
% 0.21/0.39 tptp_fun_V_1: $i > $i)).
% 0.21/0.39 tff(elem_2_type, type, (
% 0.21/0.39 elem_2: $i)).
% 0.21/0.39 tff(q_type, type, (
% 0.21/0.39 q: ( $i * $i ) > $o)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 (^[Z: $i, W: $i] : rewrite((~((~p(tptp_fun_V_1(Z), Z)) | (~(~(p(Z, W) | q(W, Z)))))) <=> (~(p(Z, W) | q(W, Z) | (~p(tptp_fun_V_1(Z), Z)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (![Z: $i, W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~(~(p(Z, W) | q(W, Z)))))) <=> ![Z: $i, W: $i] : (~(p(Z, W) | q(W, Z) | (~p(tptp_fun_V_1(Z), Z))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (^[Z: $i, W: $i] : refl((~((~p(tptp_fun_V_1(Z), Z)) | (~(~(p(Z, W) | q(W, Z)))))) <=> (~((~p(tptp_fun_V_1(Z), Z)) | (~(~(p(Z, W) | q(W, Z)))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (![Z: $i, W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~(~(p(Z, W) | q(W, Z)))))) <=> ![Z: $i, W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~(~(p(Z, W) | q(W, Z))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (![Z: $i] : ![W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~(~(p(Z, W) | q(W, Z)))))) <=> ![Z: $i, W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~(~(p(Z, W) | q(W, Z))))))),
% 0.21/0.39 inference(pull_quant,[status(thm)],[])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (^[Z: $i] : trans(monotonicity(trans(monotonicity(pull_quant((~![W: $i] : (~(p(Z, W) | q(W, Z)))) <=> ?[W: $i] : (~(~(p(Z, W) | q(W, Z))))), (((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z))))) <=> ((~p(tptp_fun_V_1(Z), Z)) | ?[W: $i] : (~(~(p(Z, W) | q(W, Z))))))), pull_quant(((~p(tptp_fun_V_1(Z), Z)) | ?[W: $i] : (~(~(p(Z, W) | q(W, Z))))) <=> ?[W: $i] : ((~p(tptp_fun_V_1(Z), Z)) | (~(~(p(Z, W) | q(W, Z)))))), (((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z))))) <=> ?[W: $i] : ((~p(tptp_fun_V_1(Z), Z)) | (~(~(p(Z, W) | q(W, Z))))))), ((~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z)))))) <=> (~?[W: $i] : ((~p(tptp_fun_V_1(Z), Z)) | (~(~(p(Z, W) | q(W, Z)))))))), pull_quant((~?[W: $i] : ((~p(tptp_fun_V_1(Z), Z)) | (~(~(p(Z, W) | q(W, Z)))))) <=> ![W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~(~(p(Z, W) | q(W, Z))))))), ((~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z)))))) <=> ![W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~(~(p(Z, W) | q(W, Z))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (![Z: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z)))))) <=> ![Z: $i] : ![W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~(~(p(Z, W) | q(W, Z))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 (![Z: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z)))))) <=> ![Z: $i, W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~(~(p(Z, W) | q(W, Z))))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[7, 5])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 (![Z: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z)))))) <=> ![Z: $i, W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~(~(p(Z, W) | q(W, Z))))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[8, 4])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (^[Z: $i] : rewrite((~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z)))))) <=> (~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z)))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (![Z: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z)))))) <=> ![Z: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (![Z: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z)))))) <=> ![Z: $i, W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~(~(p(Z, W) | q(W, Z))))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[11, 9])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (^[Z: $i] : rewrite((p(tptp_fun_V_1(Z), Z) & ![W: $i] : (~(p(Z, W) | q(W, Z)))) <=> (~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z)))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (![Z: $i] : (p(tptp_fun_V_1(Z), Z) & ![W: $i] : (~(p(Z, W) | q(W, Z)))) <=> ![Z: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 ((~?[Z: $i] : ((~?[V: $i] : p(V, Z)) | ?[W: $i] : (p(Z, W) | q(W, Z)))) <=> (~?[Z: $i] : ((~?[V: $i] : p(V, Z)) | ?[W: $i] : (p(Z, W) | q(W, Z))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 ((~(![Y: $i] : (![X: $i] : p(X, Y) => ![U: $i] : q(U, Y)) => ?[Z: $i] : (?[V: $i] : p(V, Z) => ?[W: $i] : (p(Z, W) | q(W, Z))))) <=> (~((~![Y: $i] : ((~![X: $i] : p(X, Y)) | ![U: $i] : q(U, Y))) | ?[Z: $i] : ((~?[V: $i] : p(V, Z)) | ?[W: $i] : (p(Z, W) | q(W, Z)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(17,axiom,(~(![Y: $i] : (![X: $i] : p(X, Y) => ![U: $i] : q(U, Y)) => ?[Z: $i] : (?[V: $i] : p(V, Z) => ?[W: $i] : (p(Z, W) | q(W, Z))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','x3411')).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (~((~![Y: $i] : ((~![X: $i] : p(X, Y)) | ![U: $i] : q(U, Y))) | ?[Z: $i] : ((~?[V: $i] : p(V, Z)) | ?[W: $i] : (p(Z, W) | q(W, Z))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (~?[Z: $i] : ((~?[V: $i] : p(V, Z)) | ?[W: $i] : (p(Z, W) | q(W, Z)))),
% 0.21/0.39 inference(or_elim,[status(thm)],[18])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 (~?[Z: $i] : ((~?[V: $i] : p(V, Z)) | ?[W: $i] : (p(Z, W) | q(W, Z)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 (~?[Z: $i] : ((~?[V: $i] : p(V, Z)) | ?[W: $i] : (p(Z, W) | q(W, Z)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 (~?[Z: $i] : ((~?[V: $i] : p(V, Z)) | ?[W: $i] : (p(Z, W) | q(W, Z)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[21, 15])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (~?[Z: $i] : ((~?[V: $i] : p(V, Z)) | ?[W: $i] : (p(Z, W) | q(W, Z)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 (~?[Z: $i] : ((~?[V: $i] : p(V, Z)) | ?[W: $i] : (p(Z, W) | q(W, Z)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[23, 15])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (~?[Z: $i] : ((~?[V: $i] : p(V, Z)) | ?[W: $i] : (p(Z, W) | q(W, Z)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[24, 15])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (^[Z: $i] : nnf_neg(nnf_neg(sk($oeq(?[V: $i] : p(V, Z), p(tptp_fun_V_1(Z), Z))), $oeq((~(~?[V: $i] : p(V, Z))), p(tptp_fun_V_1(Z), Z))), nnf_neg(proof_bind(^[W: $i] : refl($oeq((~(p(Z, W) | q(W, Z))), (~(p(Z, W) | q(W, Z)))))), $oeq((~?[W: $i] : (p(Z, W) | q(W, Z))), ![W: $i] : (~(p(Z, W) | q(W, Z))))), $oeq((~((~?[V: $i] : p(V, Z)) | ?[W: $i] : (p(Z, W) | q(W, Z)))), (p(tptp_fun_V_1(Z), Z) & ![W: $i] : (~(p(Z, W) | q(W, Z))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(27,plain,(
% 0.21/0.39 ![Z: $i] : (p(tptp_fun_V_1(Z), Z) & ![W: $i] : (~(p(Z, W) | q(W, Z))))),
% 0.21/0.39 inference(nnf-neg,[status(sab)],[25, 26])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 (![Z: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~![W: $i] : (~(p(Z, W) | q(W, Z))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[27, 14])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 (![Z: $i, W: $i] : (~((~p(tptp_fun_V_1(Z), Z)) | (~(~(p(Z, W) | q(W, Z))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[28, 12])).
% 0.21/0.39 tff(30,plain,
% 0.21/0.39 (![Z: $i, W: $i] : (~(p(Z, W) | q(W, Z) | (~p(tptp_fun_V_1(Z), Z))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[29, 2])).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 ((~![Z: $i, W: $i] : (~(p(Z, W) | q(W, Z) | (~p(tptp_fun_V_1(Z), Z))))) | (~(p(elem!2, elem!2) | q(elem!2, elem!2) | (~p(tptp_fun_V_1(elem!2), elem!2))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 (~(p(elem!2, elem!2) | q(elem!2, elem!2) | (~p(tptp_fun_V_1(elem!2), elem!2)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 ((p(elem!2, elem!2) | q(elem!2, elem!2) | (~p(tptp_fun_V_1(elem!2), elem!2))) | p(tptp_fun_V_1(elem!2), elem!2)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 (p(tptp_fun_V_1(elem!2), elem!2)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.21/0.39 tff(35,plain,
% 0.21/0.39 ((p(tptp_fun_V_1(elem!2), elem!2) | q(elem!2, tptp_fun_V_1(elem!2)) | (~p(tptp_fun_V_1(tptp_fun_V_1(elem!2)), tptp_fun_V_1(elem!2)))) | (~p(tptp_fun_V_1(elem!2), elem!2))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 (p(tptp_fun_V_1(elem!2), elem!2) | q(elem!2, tptp_fun_V_1(elem!2)) | (~p(tptp_fun_V_1(tptp_fun_V_1(elem!2)), tptp_fun_V_1(elem!2)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.21/0.39 tff(37,plain,
% 0.21/0.39 ((~![Z: $i, W: $i] : (~(p(Z, W) | q(W, Z) | (~p(tptp_fun_V_1(Z), Z))))) | (~(p(tptp_fun_V_1(elem!2), elem!2) | q(elem!2, tptp_fun_V_1(elem!2)) | (~p(tptp_fun_V_1(tptp_fun_V_1(elem!2)), tptp_fun_V_1(elem!2)))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(38,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[37, 30, 36])).
% 0.21/0.39 % SZS output end Proof
%------------------------------------------------------------------------------