%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM557+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:21:23 AM UTC 2025
% Result : Theorem 0.21s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM557+3 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n006.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 : Fri Jun 20 01:26:05 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(aElementOf0_type, type, (
% 0.21/0.41 aElementOf0: ( $i * $i ) > $o)).
% 0.21/0.41 tff(xS_type, type, (
% 0.21/0.41 xS: $i)).
% 0.21/0.41 tff(tptp_fun_W0_14_type, type, (
% 0.21/0.41 tptp_fun_W0_14: $i)).
% 0.21/0.41 tff(xP_type, type, (
% 0.21/0.41 xP: $i)).
% 0.21/0.41 tff(aSubsetOf0_type, type, (
% 0.21/0.41 aSubsetOf0: ( $i * $i ) > $o)).
% 0.21/0.41 tff(xk_type, type, (
% 0.21/0.41 xk: $i)).
% 0.21/0.41 tff(sbrdtbr0_type, type, (
% 0.21/0.41 sbrdtbr0: $i > $i)).
% 0.21/0.41 tff(slbdtsldtrb0_type, type, (
% 0.21/0.41 slbdtsldtrb0: ( $i * $i ) > $i)).
% 0.21/0.41 tff(1,plain,
% 0.21/0.41 (aSubsetOf0(xP, xS) <=> aSubsetOf0(xP, xS)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(2,axiom,((![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xS)) & aSubsetOf0(xP, xS)) & (sbrdtbr0(xP) = xk)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2431')).
% 0.21/0.41 tff(3,plain,
% 0.21/0.41 (![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xS)) & aSubsetOf0(xP, xS)),
% 0.21/0.41 inference(and_elim,[status(thm)],[2])).
% 0.21/0.41 tff(4,plain,
% 0.21/0.41 (aSubsetOf0(xP, xS)),
% 0.21/0.41 inference(and_elim,[status(thm)],[3])).
% 0.21/0.41 tff(5,plain,
% 0.21/0.41 (aSubsetOf0(xP, xS)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.41 tff(6,plain,
% 0.21/0.41 ((aSubsetOf0(xP, xS) | (~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS)) | (~aSubsetOf0(xP, xS))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(7,plain,
% 0.21/0.41 (aSubsetOf0(xP, xS) | (~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[6, 5])).
% 0.21/0.41 tff(8,plain,
% 0.21/0.41 ((sbrdtbr0(xP) = xk) <=> (sbrdtbr0(xP) = xk)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 (sbrdtbr0(xP) = xk),
% 0.21/0.41 inference(and_elim,[status(thm)],[2])).
% 0.21/0.41 tff(10,plain,
% 0.21/0.41 (sbrdtbr0(xP) = xk),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.21/0.41 tff(11,plain,
% 0.21/0.41 (((~(aSubsetOf0(xP, xS) | (~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS))) | (~(sbrdtbr0(xP) = xk))) <=> ((~(sbrdtbr0(xP) = xk)) | (~(aSubsetOf0(xP, xS) | (~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(12,plain,
% 0.21/0.41 (((~aSubsetOf0(xP, xS)) & (~((~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS)))) <=> (~(aSubsetOf0(xP, xS) | (~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(13,plain,
% 0.21/0.41 ((((~aSubsetOf0(xP, xS)) & (~((~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS)))) | (~(sbrdtbr0(xP) = xk))) <=> ((~(aSubsetOf0(xP, xS) | (~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS))) | (~(sbrdtbr0(xP) = xk)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[12])).
% 0.21/0.41 tff(14,plain,
% 0.21/0.41 ((((~aSubsetOf0(xP, xS)) & (~((~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS)))) | (~(sbrdtbr0(xP) = xk))) <=> ((~(sbrdtbr0(xP) = xk)) | (~(aSubsetOf0(xP, xS) | (~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[13, 11])).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 ((((~aSubsetOf0(xP, xS)) & (~((~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS)))) | (~(sbrdtbr0(xP) = xk))) <=> (((~aSubsetOf0(xP, xS)) & (~((~aElementOf0(W0!14, xP)) | aElementOf0(W0!14, xS)))) | (~(sbrdtbr0(xP) = xk)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(16,plain,
% 0.21/0.41 ((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) <=> (aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 (((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk)) <=> ((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[16])).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 ((~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))) <=> (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[17])).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 ((~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))) <=> (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 ((~((![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xS)) | aSubsetOf0(xP, xS)) & (sbrdtbr0(xP) = xk))) <=> (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(21,axiom,(~(((![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xS)) | aSubsetOf0(xP, xS)) & (sbrdtbr0(xP) = xk)) | aElementOf0(xP, slbdtsldtrb0(xS, xk)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 (~((![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xS)) | aSubsetOf0(xP, xS)) & (sbrdtbr0(xP) = xk))),
% 0.21/0.41 inference(or_elim,[status(thm)],[21])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[22, 20])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.21/0.41 unexpected number of arguments: (let ((a!1 (refl (~ (not (aSubsetOf0 xP xS)) (not (aSubsetOf0 xP xS)))))
% 0.21/0.41 (a!2 (forall ((W0 $i)) (or (not (aElementOf0 W0 xP)) (aElementOf0 W0 xS))))
% 0.21/0.41 (a!3 (not (or (not (aElementOf0 W0!14 xP)) (aElementOf0 W0!14 xS))))
% 0.21/0.41 (a!6 (~ (not (= (sbrdtbr0 xP) xk)) (not (= (sbrdtbr0 xP) xk)))))
% 0.21/0.41 (let ((a!4 (~ (not (or (aSubsetOf0 xP xS) a!2))
% 0.21/0.41 (and (not (aSubsetOf0 xP xS)) a!3)))
% 0.21/0.41 (a!7 (not (and (or (aSubsetOf0 xP xS) a!2) (= (sbrdtbr0 xP) xk))))
% 0.21/0.41 (a!8 (or (and (not (aSubsetOf0 xP xS)) a!3) (not (= (sbrdtbr0 xP) xk)))))
% 0.21/0.41 (let ((a!5 (nnf-neg a!1 (sk (~ (not a!2) a!3)) a!4)))
% 0.21/0.41 (nnf-neg a!5 (refl a!6) (~ a!7 a!8)))))
% 0.21/0.41 Proof display could not be completed: unexpected number of arguments
% 0.21/0.42 % E exiting
%------------------------------------------------------------------------------