%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM594+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:21:31 AM UTC 2025
% Result : Theorem 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM594+3 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n016.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 01:32:47 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.45 % SZS status Theorem
% 0.21/0.45 % SZS output start Proof
% 0.21/0.45 tff(aElementOf0_type, type, (
% 0.21/0.45 aElementOf0: ( $i * $i ) > $o)).
% 0.21/0.45 tff(szNzAzT0_type, type, (
% 0.21/0.45 szNzAzT0: $i)).
% 0.21/0.45 tff(tptp_fun_W0_41_type, type, (
% 0.21/0.45 tptp_fun_W0_41: $i)).
% 0.21/0.45 tff(szDzozmdt0_type, type, (
% 0.21/0.45 szDzozmdt0: $i > $i)).
% 0.21/0.45 tff(xd_type, type, (
% 0.21/0.45 xd: $i)).
% 0.21/0.45 tff(aFunction0_type, type, (
% 0.21/0.45 aFunction0: $i > $o)).
% 0.21/0.45 tff(sdtlpdtrp0_type, type, (
% 0.21/0.45 sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.21/0.45 tff(xC_type, type, (
% 0.21/0.45 xC: $i)).
% 0.21/0.45 tff(slbdtsldtrb0_type, type, (
% 0.21/0.45 slbdtsldtrb0: ( $i * $i ) > $i)).
% 0.21/0.45 tff(xk_type, type, (
% 0.21/0.45 xk: $i)).
% 0.21/0.45 tff(szszuzczcdt0_type, type, (
% 0.21/0.45 szszuzczcdt0: $i > $i)).
% 0.21/0.45 tff(xN_type, type, (
% 0.21/0.45 xN: $i)).
% 0.21/0.45 tff(sbrdtbr0_type, type, (
% 0.21/0.45 sbrdtbr0: $i > $i)).
% 0.21/0.45 tff(aSubsetOf0_type, type, (
% 0.21/0.45 aSubsetOf0: ( $i * $i ) > $o)).
% 0.21/0.45 tff(aSet0_type, type, (
% 0.21/0.45 aSet0: $i > $o)).
% 0.21/0.45 tff(xx_type, type, (
% 0.21/0.45 xx: $i)).
% 0.21/0.45 tff(sdtlcdtrc0_type, type, (
% 0.21/0.45 sdtlcdtrc0: ( $i * $i ) > $i)).
% 0.21/0.45 tff(1,plain,
% 0.21/0.45 ((szDzozmdt0(xd) = szNzAzT0) <=> (szDzozmdt0(xd) = szNzAzT0)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(2,axiom,((aFunction0(xd) & (szDzozmdt0(xd) = szNzAzT0)) & ![W0: $i] : (aElementOf0(W0, szNzAzT0) => ![W1: $i] : ((aSet0(W1) & (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)))) => (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4730')).
% 0.21/0.45 tff(3,plain,
% 0.21/0.45 (aFunction0(xd) & (szDzozmdt0(xd) = szNzAzT0)),
% 0.21/0.45 inference(and_elim,[status(thm)],[2])).
% 0.21/0.45 tff(4,plain,
% 0.21/0.45 (szDzozmdt0(xd) = szNzAzT0),
% 0.21/0.45 inference(and_elim,[status(thm)],[3])).
% 0.21/0.45 tff(5,plain,
% 0.21/0.45 (szDzozmdt0(xd) = szNzAzT0),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.45 tff(6,plain,
% 0.21/0.45 (szNzAzT0 = szDzozmdt0(xd)),
% 0.21/0.45 inference(symmetry,[status(thm)],[5])).
% 0.21/0.45 tff(7,plain,
% 0.21/0.45 (aElementOf0(W0!41, szNzAzT0) <=> aElementOf0(W0!41, szDzozmdt0(xd))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[6])).
% 0.21/0.45 tff(8,plain,
% 0.21/0.45 (aElementOf0(W0!41, szDzozmdt0(xd)) <=> aElementOf0(W0!41, szNzAzT0)),
% 0.21/0.45 inference(symmetry,[status(thm)],[7])).
% 0.21/0.45 tff(9,plain,
% 0.21/0.45 (?[W0: $i] : (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = xx)) <=> ?[W0: $i] : (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = xx))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(10,axiom,(?[W0: $i] : (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = xx)) & aElementOf0(xx, sdtlcdtrc0(xd, szDzozmdt0(xd)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4781')).
% 0.21/0.45 tff(11,plain,
% 0.21/0.45 (?[W0: $i] : (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = xx))),
% 0.21/0.45 inference(and_elim,[status(thm)],[10])).
% 0.21/0.45 tff(12,plain,
% 0.21/0.45 (?[W0: $i] : (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = xx))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[11, 9])).
% 0.21/0.45 tff(13,plain,(
% 0.21/0.45 aElementOf0(W0!41, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0!41) = xx)),
% 0.21/0.45 inference(skolemize,[status(sab)],[12])).
% 0.21/0.45 tff(14,plain,
% 0.21/0.45 (aElementOf0(W0!41, szDzozmdt0(xd))),
% 0.21/0.45 inference(and_elim,[status(thm)],[13])).
% 0.21/0.45 tff(15,plain,
% 0.21/0.45 (aElementOf0(W0!41, szNzAzT0)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[14, 8])).
% 0.21/0.45 tff(16,plain,
% 0.21/0.45 (^[W0: $i] : refl(((~aElementOf0(W0, szNzAzT0)) | (~(sdtlpdtrp0(xd, W0) = xx))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~(sdtlpdtrp0(xd, W0) = xx))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(17,plain,
% 0.21/0.45 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(sdtlpdtrp0(xd, W0) = xx))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(sdtlpdtrp0(xd, W0) = xx)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.45 tff(18,plain,
% 0.21/0.45 (^[W0: $i] : trans(monotonicity(rewrite((aElementOf0(W0, szNzAzT0) & (sdtlpdtrp0(xd, W0) = xx)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~(sdtlpdtrp0(xd, W0) = xx))))), ((~(aElementOf0(W0, szNzAzT0) & (sdtlpdtrp0(xd, W0) = xx))) <=> (~(~((~aElementOf0(W0, szNzAzT0)) | (~(sdtlpdtrp0(xd, W0) = xx))))))), rewrite((~(~((~aElementOf0(W0, szNzAzT0)) | (~(sdtlpdtrp0(xd, W0) = xx))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~(sdtlpdtrp0(xd, W0) = xx)))), ((~(aElementOf0(W0, szNzAzT0) & (sdtlpdtrp0(xd, W0) = xx))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~(sdtlpdtrp0(xd, W0) = xx)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(19,plain,
% 0.21/0.46 (![W0: $i] : (~(aElementOf0(W0, szNzAzT0) & (sdtlpdtrp0(xd, W0) = xx))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(sdtlpdtrp0(xd, W0) = xx)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.46 tff(20,plain,
% 0.21/0.46 ((~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & (sdtlpdtrp0(xd, W0) = xx))) <=> (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & (sdtlpdtrp0(xd, W0) = xx)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(21,axiom,(~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & (sdtlpdtrp0(xd, W0) = xx))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.21/0.46 tff(22,plain,
% 0.21/0.46 (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & (sdtlpdtrp0(xd, W0) = xx))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.46 tff(23,plain,
% 0.21/0.46 (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & (sdtlpdtrp0(xd, W0) = xx))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[22, 20])).
% 0.21/0.46 tff(24,plain,
% 0.21/0.46 (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & (sdtlpdtrp0(xd, W0) = xx))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[23, 20])).
% 0.21/0.46 tff(25,plain,
% 0.21/0.46 (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & (sdtlpdtrp0(xd, W0) = xx))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.21/0.46 tff(26,plain,
% 0.21/0.46 (^[W0: $i] : refl($oeq((~(aElementOf0(W0, szNzAzT0) & (sdtlpdtrp0(xd, W0) = xx))), (~(aElementOf0(W0, szNzAzT0) & (sdtlpdtrp0(xd, W0) = xx)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(27,plain,(
% 0.21/0.46 ![W0: $i] : (~(aElementOf0(W0, szNzAzT0) & (sdtlpdtrp0(xd, W0) = xx)))),
% 0.21/0.46 inference(nnf-neg,[status(sab)],[25, 26])).
% 0.21/0.46 tff(28,plain,
% 0.21/0.46 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(sdtlpdtrp0(xd, W0) = xx)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.21/0.46 tff(29,plain,
% 0.21/0.46 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(sdtlpdtrp0(xd, W0) = xx)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[28, 17])).
% 0.21/0.46 tff(30,plain,
% 0.21/0.46 (sdtlpdtrp0(xd, W0!41) = xx),
% 0.21/0.46 inference(and_elim,[status(thm)],[13])).
% 0.21/0.46 tff(31,plain,
% 0.21/0.46 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(sdtlpdtrp0(xd, W0) = xx)))) | ((~aElementOf0(W0!41, szNzAzT0)) | (~(sdtlpdtrp0(xd, W0!41) = xx)))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(sdtlpdtrp0(xd, W0) = xx)))) | (~aElementOf0(W0!41, szNzAzT0)) | (~(sdtlpdtrp0(xd, W0!41) = xx)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(32,plain,
% 0.21/0.46 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(sdtlpdtrp0(xd, W0) = xx)))) | ((~aElementOf0(W0!41, szNzAzT0)) | (~(sdtlpdtrp0(xd, W0!41) = xx)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(33,plain,
% 0.21/0.46 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(sdtlpdtrp0(xd, W0) = xx)))) | (~aElementOf0(W0!41, szNzAzT0)) | (~(sdtlpdtrp0(xd, W0!41) = xx))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.46 tff(34,plain,
% 0.21/0.46 (~aElementOf0(W0!41, szNzAzT0)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[33, 30, 29])).
% 0.21/0.46 tff(35,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[34, 15])).
% 0.21/0.46 % SZS output end Proof
% 0.21/0.46 % E exiting
%------------------------------------------------------------------------------