TSTP Solution File: RNG086+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG086+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 20 03:18:19 EDT 2022
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : RNG086+2 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n029.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 : Fri Sep 2 22:32:14 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.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(sdtpldt0_type, type, (
% 0.20/0.42 sdtpldt0: ( $i * $i ) > $i)).
% 0.20/0.42 tff(tptp_fun_W1_11_type, type, (
% 0.20/0.42 tptp_fun_W1_11: $i)).
% 0.20/0.42 tff(tptp_fun_W0_12_type, type, (
% 0.20/0.42 tptp_fun_W0_12: $i)).
% 0.20/0.42 tff(xx_type, type, (
% 0.20/0.42 xx: $i)).
% 0.20/0.42 tff(aElementOf0_type, type, (
% 0.20/0.42 aElementOf0: ( $i * $i ) > $o)).
% 0.20/0.42 tff(xJ_type, type, (
% 0.20/0.42 xJ: $i)).
% 0.20/0.42 tff(xI_type, type, (
% 0.20/0.42 xI: $i)).
% 0.20/0.42 tff(sdtpldt1_type, type, (
% 0.20/0.42 sdtpldt1: ( $i * $i ) > $i)).
% 0.20/0.42 tff(xy_type, type, (
% 0.20/0.42 xy: $i)).
% 0.20/0.42 tff(aElement0_type, type, (
% 0.20/0.42 aElement0: $i > $o)).
% 0.20/0.42 tff(xz_type, type, (
% 0.20/0.42 xz: $i)).
% 0.20/0.42 tff(1,plain,
% 0.20/0.42 (?[W0: $i, W1: $i] : (aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (sdtpldt0(W0, W1) = xx)) <=> ?[W0: $i, W1: $i] : (aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (sdtpldt0(W0, W1) = xx))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 (^[W0: $i, W1: $i] : rewrite(((aElementOf0(W0, xI) & aElementOf0(W1, xJ)) & (sdtpldt0(W0, W1) = xx)) <=> (aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (sdtpldt0(W0, W1) = xx)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 (?[W0: $i, W1: $i] : ((aElementOf0(W0, xI) & aElementOf0(W1, xJ)) & (sdtpldt0(W0, W1) = xx)) <=> ?[W0: $i, W1: $i] : (aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (sdtpldt0(W0, W1) = xx))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.42 tff(4,axiom,((((?[W0: $i, W1: $i] : ((aElementOf0(W0, xI) & aElementOf0(W1, xJ)) & (sdtpldt0(W0, W1) = xx)) & aElementOf0(xx, sdtpldt1(xI, xJ))) & ?[W0: $i, W1: $i] : ((aElementOf0(W0, xI) & aElementOf0(W1, xJ)) & (sdtpldt0(W0, W1) = xy))) & aElementOf0(xy, sdtpldt1(xI, xJ))) & aElement0(xz)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__901')).
% 0.20/0.42 tff(5,plain,
% 0.20/0.42 (((?[W0: $i, W1: $i] : ((aElementOf0(W0, xI) & aElementOf0(W1, xJ)) & (sdtpldt0(W0, W1) = xx)) & aElementOf0(xx, sdtpldt1(xI, xJ))) & ?[W0: $i, W1: $i] : ((aElementOf0(W0, xI) & aElementOf0(W1, xJ)) & (sdtpldt0(W0, W1) = xy))) & aElementOf0(xy, sdtpldt1(xI, xJ))),
% 0.20/0.42 inference(and_elim,[status(thm)],[4])).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 ((?[W0: $i, W1: $i] : ((aElementOf0(W0, xI) & aElementOf0(W1, xJ)) & (sdtpldt0(W0, W1) = xx)) & aElementOf0(xx, sdtpldt1(xI, xJ))) & ?[W0: $i, W1: $i] : ((aElementOf0(W0, xI) & aElementOf0(W1, xJ)) & (sdtpldt0(W0, W1) = xy))),
% 0.20/0.42 inference(and_elim,[status(thm)],[5])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (?[W0: $i, W1: $i] : ((aElementOf0(W0, xI) & aElementOf0(W1, xJ)) & (sdtpldt0(W0, W1) = xx)) & aElementOf0(xx, sdtpldt1(xI, xJ))),
% 0.20/0.42 inference(and_elim,[status(thm)],[6])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (?[W0: $i, W1: $i] : ((aElementOf0(W0, xI) & aElementOf0(W1, xJ)) & (sdtpldt0(W0, W1) = xx))),
% 0.20/0.42 inference(and_elim,[status(thm)],[7])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (?[W0: $i, W1: $i] : (aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (sdtpldt0(W0, W1) = xx))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 (?[W0: $i, W1: $i] : (aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (sdtpldt0(W0, W1) = xx))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.20/0.42 tff(11,plain,(
% 0.20/0.42 aElementOf0(W0!12, xI) & aElementOf0(W1!11, xJ) & (sdtpldt0(W0!12, W1!11) = xx)),
% 0.20/0.42 inference(skolemize,[status(sab)],[10])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (sdtpldt0(W0!12, W1!11) = xx),
% 0.20/0.42 inference(and_elim,[status(thm)],[11])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (xx = sdtpldt0(W0!12, W1!11)),
% 0.20/0.42 inference(symmetry,[status(thm)],[12])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (^[W0: $i, W1: $i] : refl(((~aElementOf0(W1, xJ)) | (~aElementOf0(W0, xI)) | (~(xx = sdtpldt0(W0, W1)))) <=> ((~aElementOf0(W1, xJ)) | (~aElementOf0(W0, xI)) | (~(xx = sdtpldt0(W0, W1)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (![W0: $i, W1: $i] : ((~aElementOf0(W1, xJ)) | (~aElementOf0(W0, xI)) | (~(xx = sdtpldt0(W0, W1)))) <=> ![W0: $i, W1: $i] : ((~aElementOf0(W1, xJ)) | (~aElementOf0(W0, xI)) | (~(xx = sdtpldt0(W0, W1))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite((aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (xx = sdtpldt0(W0, W1))) <=> (~((~aElementOf0(W1, xJ)) | (~aElementOf0(W0, xI)) | (~(xx = sdtpldt0(W0, W1)))))), ((~(aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (xx = sdtpldt0(W0, W1)))) <=> (~(~((~aElementOf0(W1, xJ)) | (~aElementOf0(W0, xI)) | (~(xx = sdtpldt0(W0, W1)))))))), rewrite((~(~((~aElementOf0(W1, xJ)) | (~aElementOf0(W0, xI)) | (~(xx = sdtpldt0(W0, W1)))))) <=> ((~aElementOf0(W1, xJ)) | (~aElementOf0(W0, xI)) | (~(xx = sdtpldt0(W0, W1))))), ((~(aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (xx = sdtpldt0(W0, W1)))) <=> ((~aElementOf0(W1, xJ)) | (~aElementOf0(W0, xI)) | (~(xx = sdtpldt0(W0, W1))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (![W0: $i, W1: $i] : (~(aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (xx = sdtpldt0(W0, W1)))) <=> ![W0: $i, W1: $i] : ((~aElementOf0(W1, xJ)) | (~aElementOf0(W0, xI)) | (~(xx = sdtpldt0(W0, W1))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 ((~?[W0: $i, W1: $i] : (aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (xx = sdtpldt0(W0, W1)))) <=> (~?[W0: $i, W1: $i] : (aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (xx = sdtpldt0(W0, W1))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 ((~?[W0: $i, W1: $i] : ((aElementOf0(W0, xI) & aElementOf0(W1, xJ)) & (xx = sdtpldt0(W0, W1)))) <=> (~?[W0: $i, W1: $i] : (aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (xx = sdtpldt0(W0, W1))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(20,axiom,(~?[W0: $i, W1: $i] : ((aElementOf0(W0, xI) & aElementOf0(W1, xJ)) & (xx = sdtpldt0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (~?[W0: $i, W1: $i] : (aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (xx = sdtpldt0(W0, W1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (~?[W0: $i, W1: $i] : (aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (xx = sdtpldt0(W0, W1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (~?[W0: $i, W1: $i] : (aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (xx = sdtpldt0(W0, W1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (~?[W0: $i, W1: $i] : (aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (xx = sdtpldt0(W0, W1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (~?[W0: $i, W1: $i] : (aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (xx = sdtpldt0(W0, W1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (~?[W0: $i, W1: $i] : (aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (xx = sdtpldt0(W0, W1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (~?[W0: $i, W1: $i] : (aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (xx = sdtpldt0(W0, W1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[26, 18])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (^[W0: $i, W1: $i] : refl($oeq((~(aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (xx = sdtpldt0(W0, W1)))), (~(aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (xx = sdtpldt0(W0, W1))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(29,plain,(
% 0.20/0.42 ![W0: $i, W1: $i] : (~(aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (xx = sdtpldt0(W0, W1))))),
% 0.20/0.42 inference(nnf-neg,[status(sab)],[27, 28])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (![W0: $i, W1: $i] : ((~aElementOf0(W1, xJ)) | (~aElementOf0(W0, xI)) | (~(xx = sdtpldt0(W0, W1))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[29, 17])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (![W0: $i, W1: $i] : ((~aElementOf0(W1, xJ)) | (~aElementOf0(W0, xI)) | (~(xx = sdtpldt0(W0, W1))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[30, 15])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (aElementOf0(W1!11, xJ)),
% 0.20/0.42 inference(and_elim,[status(thm)],[11])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (aElementOf0(W0!12, xI)),
% 0.20/0.42 inference(and_elim,[status(thm)],[11])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (((~![W0: $i, W1: $i] : ((~aElementOf0(W1, xJ)) | (~aElementOf0(W0, xI)) | (~(xx = sdtpldt0(W0, W1))))) | ((~aElementOf0(W1!11, xJ)) | (~aElementOf0(W0!12, xI)) | (~(xx = sdtpldt0(W0!12, W1!11))))) <=> ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, xJ)) | (~aElementOf0(W0, xI)) | (~(xx = sdtpldt0(W0, W1))))) | (~aElementOf0(W1!11, xJ)) | (~aElementOf0(W0!12, xI)) | (~(xx = sdtpldt0(W0!12, W1!11))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, xJ)) | (~aElementOf0(W0, xI)) | (~(xx = sdtpldt0(W0, W1))))) | ((~aElementOf0(W1!11, xJ)) | (~aElementOf0(W0!12, xI)) | (~(xx = sdtpldt0(W0!12, W1!11))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(36,plain,
% 0.20/0.43 ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, xJ)) | (~aElementOf0(W0, xI)) | (~(xx = sdtpldt0(W0, W1))))) | (~aElementOf0(W1!11, xJ)) | (~aElementOf0(W0!12, xI)) | (~(xx = sdtpldt0(W0!12, W1!11)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.43 tff(37,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[36, 33, 32, 31, 13])).
% 0.20/0.43 % SZS output end Proof
%------------------------------------------------------------------------------