%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM456+6 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:21:02 AM UTC 2025
% Result : Theorem 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM456+6 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 01:14:41 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(smndt0_type, type, (
% 0.19/0.44 smndt0: $i > $i)).
% 0.19/0.44 tff(sz10_type, type, (
% 0.19/0.44 sz10: $i)).
% 0.19/0.44 tff(tptp_fun_W0_22_type, type, (
% 0.19/0.44 tptp_fun_W0_22: $i)).
% 0.19/0.44 tff(aElementOf0_type, type, (
% 0.19/0.44 aElementOf0: ( $i * $i ) > $o)).
% 0.19/0.44 tff(stldt0_type, type, (
% 0.19/0.44 stldt0: $i > $i)).
% 0.19/0.44 tff(sbsmnsldt0_type, type, (
% 0.19/0.44 sbsmnsldt0: $i > $i)).
% 0.19/0.44 tff(xS_type, type, (
% 0.19/0.44 xS: $i)).
% 0.19/0.44 tff(cS2200_type, type, (
% 0.19/0.44 cS2200: $i)).
% 0.19/0.44 tff(szAzrzSzezqlpdtcmdtrp0_type, type, (
% 0.19/0.44 szAzrzSzezqlpdtcmdtrp0: ( $i * $i ) > $i)).
% 0.19/0.44 tff(xp_type, type, (
% 0.19/0.44 xp: $i)).
% 0.19/0.44 tff(sdteqdtlpzmzozddtrp0_type, type, (
% 0.19/0.44 sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o)).
% 0.19/0.44 tff(aDivisorOf0_type, type, (
% 0.19/0.44 aDivisorOf0: ( $i * $i ) > $o)).
% 0.19/0.44 tff(sdtpldt0_type, type, (
% 0.19/0.44 sdtpldt0: ( $i * $i ) > $i)).
% 0.19/0.44 tff(sdtasdt0_type, type, (
% 0.19/0.44 sdtasdt0: ( $i * $i ) > $i)).
% 0.19/0.44 tff(tptp_fun_W1_23_type, type, (
% 0.19/0.44 tptp_fun_W1_23: $i)).
% 0.19/0.44 tff(aInteger0_type, type, (
% 0.19/0.44 aInteger0: $i > $o)).
% 0.19/0.44 tff(aSet0_type, type, (
% 0.19/0.44 aSet0: $i > $o)).
% 0.19/0.44 tff(sz00_type, type, (
% 0.19/0.44 sz00: $i)).
% 0.19/0.44 tff(aSubsetOf0_type, type, (
% 0.19/0.44 aSubsetOf0: ( $i * $i ) > $o)).
% 0.19/0.44 tff(cS2076_type, type, (
% 0.19/0.44 cS2076: $i)).
% 0.19/0.44 tff(1,plain,
% 0.19/0.44 ((aInteger0(W0!22) & (aInteger0(W1!23) & (sdtasdt0(xp, W1!23) = sdtpldt0(W0!22, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0!22, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0!22, sz10, xp) & aElementOf0(W0!22, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) & (~((W0!22 = smndt0(sz10)) | aElementOf0(W0!22, cS2200) | (W0!22 = sz10)))) <=> (aInteger0(W0!22) & aInteger0(W1!23) & (sdtasdt0(xp, W1!23) = sdtpldt0(W0!22, smndt0(sz10))) & aDivisorOf0(xp, sdtpldt0(W0!22, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0!22, sz10, xp) & aElementOf0(W0!22, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) & (~((W0!22 = smndt0(sz10)) | aElementOf0(W0!22, cS2200) | (W0!22 = sz10))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(2,plain,
% 0.19/0.44 ((~((W0!22 = smndt0(sz10)) | (W0!22 = sz10) | aElementOf0(W0!22, cS2200))) <=> (~((W0!22 = smndt0(sz10)) | aElementOf0(W0!22, cS2200) | (W0!22 = sz10)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(3,plain,
% 0.19/0.44 ((aInteger0(W0!22) & (aInteger0(W1!23) & (sdtasdt0(xp, W1!23) = sdtpldt0(W0!22, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0!22, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0!22, sz10, xp) & aElementOf0(W0!22, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) & (~((W0!22 = smndt0(sz10)) | (W0!22 = sz10) | aElementOf0(W0!22, cS2200)))) <=> (aInteger0(W0!22) & (aInteger0(W1!23) & (sdtasdt0(xp, W1!23) = sdtpldt0(W0!22, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0!22, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0!22, sz10, xp) & aElementOf0(W0!22, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) & (~((W0!22 = smndt0(sz10)) | aElementOf0(W0!22, cS2200) | (W0!22 = sz10))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[2])).
% 0.19/0.44 tff(4,plain,
% 0.19/0.44 ((aInteger0(W0!22) & (aInteger0(W1!23) & (sdtasdt0(xp, W1!23) = sdtpldt0(W0!22, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0!22, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0!22, sz10, xp) & aElementOf0(W0!22, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) & (~((W0!22 = smndt0(sz10)) | (W0!22 = sz10) | aElementOf0(W0!22, cS2200)))) <=> (aInteger0(W0!22) & aInteger0(W1!23) & (sdtasdt0(xp, W1!23) = sdtpldt0(W0!22, smndt0(sz10))) & aDivisorOf0(xp, sdtpldt0(W0!22, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0!22, sz10, xp) & aElementOf0(W0!22, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) & (~((W0!22 = smndt0(sz10)) | aElementOf0(W0!22, cS2200) | (W0!22 = sz10))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[3, 1])).
% 0.19/0.44 tff(5,plain,
% 0.19/0.44 (?[W0: $i] : (aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp) & aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) & (~((W0 = smndt0(sz10)) | (W0 = sz10) | aElementOf0(W0, cS2200)))) <=> ?[W0: $i] : (aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp) & aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) & (~((W0 = smndt0(sz10)) | (W0 = sz10) | aElementOf0(W0, cS2200))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(6,plain,
% 0.19/0.44 (^[W0: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10))))) <=> (aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))))), (((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) <=> ((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))))), rewrite(((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) <=> (aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10))))), (((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) <=> (aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))))), ((((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp)) <=> ((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp)))), rewrite(((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp)) <=> (aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp))), ((((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp)) <=> (aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp)))), (((((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp)) & aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) <=> ((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp)) & aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))))), rewrite(((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp)) & aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) <=> (aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp) & aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)))), (((((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp)) & aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) <=> (aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp) & aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))))), rewrite((~(((W0 = sz10) | (W0 = smndt0(sz10))) | aElementOf0(W0, cS2200))) <=> (~((W0 = smndt0(sz10)) | (W0 = sz10) | aElementOf0(W0, cS2200)))), ((((((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp)) & aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) & (~(((W0 = sz10) | (W0 = smndt0(sz10))) | aElementOf0(W0, cS2200)))) <=> ((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp) & aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) & (~((W0 = smndt0(sz10)) | (W0 = sz10) | aElementOf0(W0, cS2200)))))), rewrite(((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp) & aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) & (~((W0 = smndt0(sz10)) | (W0 = sz10) | aElementOf0(W0, cS2200)))) <=> (aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp) & aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) & (~((W0 = smndt0(sz10)) | (W0 = sz10) | aElementOf0(W0, cS2200))))), ((((((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp)) & aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) & (~(((W0 = sz10) | (W0 = smndt0(sz10))) | aElementOf0(W0, cS2200)))) <=> (aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp) & aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) & (~((W0 = smndt0(sz10)) | (W0 = sz10) | aElementOf0(W0, cS2200))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(7,plain,
% 0.19/0.45 (?[W0: $i] : (((((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp)) & aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) & (~(((W0 = sz10) | (W0 = smndt0(sz10))) | aElementOf0(W0, cS2200)))) <=> ?[W0: $i] : (aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp) & aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) & (~((W0 = smndt0(sz10)) | (W0 = sz10) | aElementOf0(W0, cS2200))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.45 tff(8,axiom,(?[W0: $i] : (((((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp)) & aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) & (~(((W0 = sz10) | (W0 = smndt0(sz10))) | aElementOf0(W0, cS2200))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2203')).
% 0.19/0.45 tff(9,plain,
% 0.19/0.45 (?[W0: $i] : (aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp) & aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) & (~((W0 = smndt0(sz10)) | (W0 = sz10) | aElementOf0(W0, cS2200))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.45 tff(10,plain,
% 0.19/0.45 (?[W0: $i] : (aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp) & aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) & (~((W0 = smndt0(sz10)) | (W0 = sz10) | aElementOf0(W0, cS2200))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.45 tff(11,plain,
% 0.19/0.45 (aInteger0(W0!22) & aInteger0(W1!23) & (sdtasdt0(xp, W1!23) = sdtpldt0(W0!22, smndt0(sz10))) & aDivisorOf0(xp, sdtpldt0(W0!22, smndt0(sz10))) & sdteqdtlpzmzozddtrp0(W0!22, sz10, xp) & aElementOf0(W0!22, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) & (~((W0!22 = smndt0(sz10)) | aElementOf0(W0!22, cS2200) | (W0!22 = sz10)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.19/0.45 tff(12,plain,
% 0.19/0.45 (~((W0!22 = smndt0(sz10)) | aElementOf0(W0!22, cS2200) | (W0!22 = sz10))),
% 0.19/0.45 inference(and_elim,[status(thm)],[11])).
% 0.19/0.45 tff(13,plain,
% 0.19/0.45 (~(W0!22 = sz10)),
% 0.19/0.45 inference(or_elim,[status(thm)],[12])).
% 0.19/0.45 tff(14,plain,
% 0.19/0.45 (~(W0!22 = smndt0(sz10))),
% 0.19/0.45 inference(or_elim,[status(thm)],[12])).
% 0.19/0.45 tff(15,plain,
% 0.19/0.45 ((~((W0!22 = sz10) | (W0!22 = smndt0(sz10)))) | (W0!22 = sz10) | (W0!22 = smndt0(sz10))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(16,plain,
% 0.19/0.45 (~((W0!22 = sz10) | (W0!22 = smndt0(sz10)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[15, 14, 13])).
% 0.19/0.45 tff(17,plain,
% 0.19/0.45 (aElementOf0(W0!22, szAzrzSzezqlpdtcmdtrp0(sz10, xp))),
% 0.19/0.45 inference(and_elim,[status(thm)],[11])).
% 0.19/0.45 tff(18,plain,
% 0.19/0.45 (^[W0: $i] : refl(((~aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) | aElementOf0(W0, stldt0(sbsmnsldt0(xS)))) <=> ((~aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) | aElementOf0(W0, stldt0(sbsmnsldt0(xS)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(19,plain,
% 0.19/0.45 (![W0: $i] : ((~aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) | aElementOf0(W0, stldt0(sbsmnsldt0(xS)))) <=> ![W0: $i] : ((~aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) | aElementOf0(W0, stldt0(sbsmnsldt0(xS))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.45 tff(20,plain,
% 0.19/0.45 (![W0: $i] : ((~aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) | aElementOf0(W0, stldt0(sbsmnsldt0(xS)))) <=> ![W0: $i] : ((~aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) | aElementOf0(W0, stldt0(sbsmnsldt0(xS))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(21,plain,
% 0.19/0.45 (^[W0: $i] : rewrite((aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) => aElementOf0(W0, stldt0(sbsmnsldt0(xS)))) <=> ((~aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) | aElementOf0(W0, stldt0(sbsmnsldt0(xS)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(22,plain,
% 0.19/0.45 (![W0: $i] : (aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) => aElementOf0(W0, stldt0(sbsmnsldt0(xS)))) <=> ![W0: $i] : ((~aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) | aElementOf0(W0, stldt0(sbsmnsldt0(xS))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.45 tff(23,axiom,((((((((aInteger0(xp) & (~(xp = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(sz10, xp))) & ![W0: $i] : ((aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) => (((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp))) & ((aInteger0(W0) & ((?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) | aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) | sdteqdtlpzmzozddtrp0(W0, sz10, xp))) => aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))))) & aSet0(sbsmnsldt0(xS))) & ![W0: $i] : (aElementOf0(W0, sbsmnsldt0(xS)) <=> (aInteger0(W0) & ?[W1: $i] : (aElementOf0(W1, xS) & aElementOf0(W0, W1))))) & ![W0: $i] : (aElementOf0(W0, stldt0(sbsmnsldt0(xS))) <=> (aInteger0(W0) & (~aElementOf0(W0, sbsmnsldt0(xS)))))) & ![W0: $i] : (aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) => aElementOf0(W0, stldt0(sbsmnsldt0(xS))))) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10, xp), stldt0(sbsmnsldt0(xS)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2171')).
% 0.19/0.45 tff(24,plain,
% 0.19/0.45 (((((((aInteger0(xp) & (~(xp = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(sz10, xp))) & ![W0: $i] : ((aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) => (((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp))) & ((aInteger0(W0) & ((?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) | aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) | sdteqdtlpzmzozddtrp0(W0, sz10, xp))) => aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))))) & aSet0(sbsmnsldt0(xS))) & ![W0: $i] : (aElementOf0(W0, sbsmnsldt0(xS)) <=> (aInteger0(W0) & ?[W1: $i] : (aElementOf0(W1, xS) & aElementOf0(W0, W1))))) & ![W0: $i] : (aElementOf0(W0, stldt0(sbsmnsldt0(xS))) <=> (aInteger0(W0) & (~aElementOf0(W0, sbsmnsldt0(xS)))))) & ![W0: $i] : (aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) => aElementOf0(W0, stldt0(sbsmnsldt0(xS))))),
% 0.19/0.45 inference(and_elim,[status(thm)],[23])).
% 0.19/0.45 tff(25,plain,
% 0.19/0.45 (![W0: $i] : (aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) => aElementOf0(W0, stldt0(sbsmnsldt0(xS))))),
% 0.19/0.45 inference(and_elim,[status(thm)],[24])).
% 0.19/0.45 tff(26,plain,
% 0.19/0.45 (![W0: $i] : ((~aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) | aElementOf0(W0, stldt0(sbsmnsldt0(xS))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.19/0.45 tff(27,plain,
% 0.19/0.45 (![W0: $i] : ((~aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) | aElementOf0(W0, stldt0(sbsmnsldt0(xS))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[26, 20])).
% 0.19/0.45 tff(28,plain,(
% 0.19/0.45 ![W0: $i] : ((~aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) | aElementOf0(W0, stldt0(sbsmnsldt0(xS))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[27])).
% 0.19/0.45 tff(29,plain,
% 0.19/0.45 (![W0: $i] : ((~aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) | aElementOf0(W0, stldt0(sbsmnsldt0(xS))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[28, 19])).
% 0.19/0.45 tff(30,plain,
% 0.19/0.45 (((~![W0: $i] : ((~aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) | aElementOf0(W0, stldt0(sbsmnsldt0(xS))))) | ((~aElementOf0(W0!22, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) | aElementOf0(W0!22, stldt0(sbsmnsldt0(xS))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) | aElementOf0(W0, stldt0(sbsmnsldt0(xS))))) | (~aElementOf0(W0!22, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) | aElementOf0(W0!22, stldt0(sbsmnsldt0(xS))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(31,plain,
% 0.19/0.45 ((~![W0: $i] : ((~aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) | aElementOf0(W0, stldt0(sbsmnsldt0(xS))))) | ((~aElementOf0(W0!22, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) | aElementOf0(W0!22, stldt0(sbsmnsldt0(xS))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(32,plain,
% 0.19/0.45 ((~![W0: $i] : ((~aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) | aElementOf0(W0, stldt0(sbsmnsldt0(xS))))) | (~aElementOf0(W0!22, szAzrzSzezqlpdtcmdtrp0(sz10, xp))) | aElementOf0(W0!22, stldt0(sbsmnsldt0(xS)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.45 tff(33,plain,
% 0.19/0.45 (aElementOf0(W0!22, stldt0(sbsmnsldt0(xS)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[32, 29, 17])).
% 0.19/0.45 tff(34,plain,
% 0.19/0.45 ((~(aElementOf0(W0!22, stldt0(sbsmnsldt0(xS))) <=> ((W0!22 = sz10) | (W0!22 = smndt0(sz10))))) | (~aElementOf0(W0!22, stldt0(sbsmnsldt0(xS)))) | ((W0!22 = sz10) | (W0!22 = smndt0(sz10)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(35,plain,
% 0.19/0.45 (~(aElementOf0(W0!22, stldt0(sbsmnsldt0(xS))) <=> ((W0!22 = sz10) | (W0!22 = smndt0(sz10))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[34, 33, 16])).
% 0.19/0.45 tff(36,plain,
% 0.19/0.45 (^[W0: $i] : refl((aElementOf0(W0, stldt0(sbsmnsldt0(xS))) <=> ((W0 = sz10) | (W0 = smndt0(sz10)))) <=> (aElementOf0(W0, stldt0(sbsmnsldt0(xS))) <=> ((W0 = sz10) | (W0 = smndt0(sz10)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(37,plain,
% 0.19/0.45 (![W0: $i] : (aElementOf0(W0, stldt0(sbsmnsldt0(xS))) <=> ((W0 = sz10) | (W0 = smndt0(sz10)))) <=> ![W0: $i] : (aElementOf0(W0, stldt0(sbsmnsldt0(xS))) <=> ((W0 = sz10) | (W0 = smndt0(sz10))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.45 tff(38,plain,
% 0.19/0.45 (![W0: $i] : (aElementOf0(W0, stldt0(sbsmnsldt0(xS))) <=> ((W0 = sz10) | (W0 = smndt0(sz10)))) <=> ![W0: $i] : (aElementOf0(W0, stldt0(sbsmnsldt0(xS))) <=> ((W0 = sz10) | (W0 = smndt0(sz10))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(39,axiom,(((((aSet0(sbsmnsldt0(xS)) & ![W0: $i] : (aElementOf0(W0, sbsmnsldt0(xS)) <=> (aInteger0(W0) & ?[W1: $i] : (aElementOf0(W1, xS) & aElementOf0(W0, W1))))) & aSet0(stldt0(sbsmnsldt0(xS)))) & ![W0: $i] : (aElementOf0(W0, stldt0(sbsmnsldt0(xS))) <=> (aInteger0(W0) & (~aElementOf0(W0, sbsmnsldt0(xS)))))) & ![W0: $i] : (aElementOf0(W0, stldt0(sbsmnsldt0(xS))) <=> ((W0 = sz10) | (W0 = smndt0(sz10))))) & (stldt0(sbsmnsldt0(xS)) = cS2076)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2079')).
% 0.19/0.45 tff(40,plain,
% 0.19/0.45 ((((aSet0(sbsmnsldt0(xS)) & ![W0: $i] : (aElementOf0(W0, sbsmnsldt0(xS)) <=> (aInteger0(W0) & ?[W1: $i] : (aElementOf0(W1, xS) & aElementOf0(W0, W1))))) & aSet0(stldt0(sbsmnsldt0(xS)))) & ![W0: $i] : (aElementOf0(W0, stldt0(sbsmnsldt0(xS))) <=> (aInteger0(W0) & (~aElementOf0(W0, sbsmnsldt0(xS)))))) & ![W0: $i] : (aElementOf0(W0, stldt0(sbsmnsldt0(xS))) <=> ((W0 = sz10) | (W0 = smndt0(sz10))))),
% 0.19/0.45 inference(and_elim,[status(thm)],[39])).
% 0.19/0.45 tff(41,plain,
% 0.19/0.45 (![W0: $i] : (aElementOf0(W0, stldt0(sbsmnsldt0(xS))) <=> ((W0 = sz10) | (W0 = smndt0(sz10))))),
% 0.19/0.45 inference(and_elim,[status(thm)],[40])).
% 0.19/0.45 tff(42,plain,
% 0.19/0.45 (![W0: $i] : (aElementOf0(W0, stldt0(sbsmnsldt0(xS))) <=> ((W0 = sz10) | (W0 = smndt0(sz10))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[41, 38])).
% 0.19/0.45 tff(43,plain,(
% 0.19/0.45 ![W0: $i] : (aElementOf0(W0, stldt0(sbsmnsldt0(xS))) <=> ((W0 = sz10) | (W0 = smndt0(sz10))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[42])).
% 0.19/0.45 tff(44,plain,
% 0.19/0.45 (![W0: $i] : (aElementOf0(W0, stldt0(sbsmnsldt0(xS))) <=> ((W0 = sz10) | (W0 = smndt0(sz10))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[43, 37])).
% 0.19/0.45 tff(45,plain,
% 0.19/0.45 ((~![W0: $i] : (aElementOf0(W0, stldt0(sbsmnsldt0(xS))) <=> ((W0 = sz10) | (W0 = smndt0(sz10))))) | (aElementOf0(W0!22, stldt0(sbsmnsldt0(xS))) <=> ((W0!22 = sz10) | (W0!22 = smndt0(sz10))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(46,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[45, 44, 35])).
% 0.19/0.45 % SZS output end Proof
% 0.19/0.46 % E exiting
%------------------------------------------------------------------------------