%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG086+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 : Sat Jun 21 05:24:09 AM UTC 2025
% Result : Theorem 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : RNG086+2 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 03:21:01 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(sdtpldt0_type, type, (
% 0.21/0.41 sdtpldt0: ( $i * $i ) > $i)).
% 0.21/0.41 tff(tptp_fun_W1_11_type, type, (
% 0.21/0.41 tptp_fun_W1_11: $i)).
% 0.21/0.41 tff(tptp_fun_W0_12_type, type, (
% 0.21/0.41 tptp_fun_W0_12: $i)).
% 0.21/0.41 tff(xx_type, type, (
% 0.21/0.41 xx: $i)).
% 0.21/0.41 tff(aElementOf0_type, type, (
% 0.21/0.41 aElementOf0: ( $i * $i ) > $o)).
% 0.21/0.41 tff(xJ_type, type, (
% 0.21/0.41 xJ: $i)).
% 0.21/0.41 tff(xI_type, type, (
% 0.21/0.41 xI: $i)).
% 0.21/0.41 tff(sdtpldt1_type, type, (
% 0.21/0.41 sdtpldt1: ( $i * $i ) > $i)).
% 0.21/0.41 tff(xy_type, type, (
% 0.21/0.41 xy: $i)).
% 0.21/0.41 tff(aElement0_type, type, (
% 0.21/0.41 aElement0: $i > $o)).
% 0.21/0.41 tff(xz_type, type, (
% 0.21/0.41 xz: $i)).
% 0.21/0.41 tff(1,plain,
% 0.21/0.41 (?[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))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(2,plain,
% 0.21/0.41 (^[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)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(3,plain,
% 0.21/0.41 (?[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))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.41 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/sandbox/benchmark/theBenchmark.p','m__901')).
% 0.21/0.41 tff(5,plain,
% 0.21/0.41 (((?[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))),
% 0.21/0.41 inference(and_elim,[status(thm)],[4])).
% 0.21/0.41 tff(6,plain,
% 0.21/0.41 ((?[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))),
% 0.21/0.41 inference(and_elim,[status(thm)],[5])).
% 0.21/0.41 tff(7,plain,
% 0.21/0.41 (?[W0: $i, W1: $i] : ((aElementOf0(W0, xI) & aElementOf0(W1, xJ)) & (sdtpldt0(W0, W1) = xx)) & aElementOf0(xx, sdtpldt1(xI, xJ))),
% 0.21/0.41 inference(and_elim,[status(thm)],[6])).
% 0.21/0.41 tff(8,plain,
% 0.21/0.41 (?[W0: $i, W1: $i] : ((aElementOf0(W0, xI) & aElementOf0(W1, xJ)) & (sdtpldt0(W0, W1) = xx))),
% 0.21/0.41 inference(and_elim,[status(thm)],[7])).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 (?[W0: $i, W1: $i] : (aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (sdtpldt0(W0, W1) = xx))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.21/0.41 tff(10,plain,
% 0.21/0.41 (?[W0: $i, W1: $i] : (aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (sdtpldt0(W0, W1) = xx))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.21/0.41 tff(11,plain,(
% 0.21/0.41 aElementOf0(W0!12, xI) & aElementOf0(W1!11, xJ) & (sdtpldt0(W0!12, W1!11) = xx)),
% 0.21/0.41 inference(skolemize,[status(sab)],[10])).
% 0.21/0.41 tff(12,plain,
% 0.21/0.41 (sdtpldt0(W0!12, W1!11) = xx),
% 0.21/0.41 inference(and_elim,[status(thm)],[11])).
% 0.21/0.41 tff(13,plain,
% 0.21/0.41 (xx = sdtpldt0(W0!12, W1!11)),
% 0.21/0.41 inference(symmetry,[status(thm)],[12])).
% 0.21/0.41 tff(14,plain,
% 0.21/0.41 (^[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)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 (![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))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[14])).
% 0.21/0.41 tff(16,plain,
% 0.21/0.41 (^[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))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 (![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))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 ((~?[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))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 ((~?[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))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(20,axiom,(~?[W0: $i, W1: $i] : ((aElementOf0(W0, xI) & aElementOf0(W1, xJ)) & (xx = sdtpldt0(W0, W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 (~?[W0: $i, W1: $i] : (aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (xx = sdtpldt0(W0, W1)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 (~?[W0: $i, W1: $i] : (aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (xx = sdtpldt0(W0, W1)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 (~?[W0: $i, W1: $i] : (aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (xx = sdtpldt0(W0, W1)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (~?[W0: $i, W1: $i] : (aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (xx = sdtpldt0(W0, W1)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (^[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))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(26,plain,(
% 0.21/0.41 ![W0: $i, W1: $i] : (~(aElementOf0(W0, xI) & aElementOf0(W1, xJ) & (xx = sdtpldt0(W0, W1))))),
% 0.21/0.41 inference(nnf-neg,[status(sab)],[24, 25])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 (![W0: $i, W1: $i] : ((~aElementOf0(W1, xJ)) | (~aElementOf0(W0, xI)) | (~(xx = sdtpldt0(W0, W1))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[26, 17])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (![W0: $i, W1: $i] : ((~aElementOf0(W1, xJ)) | (~aElementOf0(W0, xI)) | (~(xx = sdtpldt0(W0, W1))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[27, 15])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 (aElementOf0(W1!11, xJ)),
% 0.21/0.41 inference(and_elim,[status(thm)],[11])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 (aElementOf0(W0!12, xI)),
% 0.21/0.41 inference(and_elim,[status(thm)],[11])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (((~![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))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 ((~![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))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, xJ)) | (~aElementOf0(W0, xI)) | (~(xx = sdtpldt0(W0, W1))))) | (~aElementOf0(W1!11, xJ)) | (~aElementOf0(W0!12, xI)) | (~(xx = sdtpldt0(W0!12, W1!11)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[33, 30, 29, 28, 13])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------