%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM144+1 : TPTP v9.0.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:01:08 AM UTC 2025
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM144+1 : TPTP v9.0.0. Released v6.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 : Thu Jun 19 12:24:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(vsomeExp_type, type, (
% 0.19/0.40 vsomeExp: $i > $i)).
% 0.19/0.40 tff(tptp_fun_Veout_51_type, type, (
% 0.19/0.40 tptp_fun_Veout_51: $i)).
% 0.19/0.40 tff(vnoExp_type, type, (
% 0.19/0.40 vnoExp: $i)).
% 0.19/0.40 tff(vreduce_type, type, (
% 0.19/0.40 vreduce: $i > $i)).
% 0.19/0.40 tff(vabs_type, type, (
% 0.19/0.40 vabs: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(ve1_type, type, (
% 0.19/0.40 ve1: $i)).
% 0.19/0.40 tff(tptp_fun_VS_53_type, type, (
% 0.19/0.40 tptp_fun_VS_53: $i)).
% 0.19/0.40 tff(tptp_fun_Vx_54_type, type, (
% 0.19/0.40 tptp_fun_Vx_54: $i)).
% 0.19/0.40 tff(vtcheck_type, type, (
% 0.19/0.40 vtcheck: ( $i * $i * $i ) > $o)).
% 0.19/0.40 tff(tptp_fun_VT_50_type, type, (
% 0.19/0.40 tptp_fun_VT_50: $i)).
% 0.19/0.40 tff(tptp_fun_VC_52_type, type, (
% 0.19/0.40 tptp_fun_VC_52: $i)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 ((~![Vx: $i, VS: $i, VC: $i, Veout: $i, VT: $i] : ((~((vreduce(vabs(Vx, VS, ve1)) = vsomeExp(Veout)) & vtcheck(VC, vabs(Vx, VS, ve1), VT))) | vtcheck(VC, Veout, VT))) <=> (~![Vx: $i, VS: $i, VC: $i, Veout: $i, VT: $i] : ((~((vreduce(vabs(Vx, VS, ve1)) = vsomeExp(Veout)) & vtcheck(VC, vabs(Vx, VS, ve1), VT))) | vtcheck(VC, Veout, VT)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 ((~![Vx: $i, VS: $i, VC: $i, Veout: $i, VT: $i] : (((vreduce(vabs(Vx, VS, ve1)) = vsomeExp(Veout)) & vtcheck(VC, vabs(Vx, VS, ve1), VT)) => vtcheck(VC, Veout, VT))) <=> (~![Vx: $i, VS: $i, VC: $i, Veout: $i, VT: $i] : ((~((vreduce(vabs(Vx, VS, ve1)) = vsomeExp(Veout)) & vtcheck(VC, vabs(Vx, VS, ve1), VT))) | vtcheck(VC, Veout, VT)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(3,axiom,(~![Vx: $i, VS: $i, VC: $i, Veout: $i, VT: $i] : (((vreduce(vabs(Vx, VS, ve1)) = vsomeExp(Veout)) & vtcheck(VC, vabs(Vx, VS, ve1), VT)) => vtcheck(VC, Veout, VT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Preservation-T-abs'')).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (~![Vx: $i, VS: $i, VC: $i, Veout: $i, VT: $i] : ((~((vreduce(vabs(Vx, VS, ve1)) = vsomeExp(Veout)) & vtcheck(VC, vabs(Vx, VS, ve1), VT))) | vtcheck(VC, Veout, VT))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (~![Vx: $i, VS: $i, VC: $i, Veout: $i, VT: $i] : ((~((vreduce(vabs(Vx, VS, ve1)) = vsomeExp(Veout)) & vtcheck(VC, vabs(Vx, VS, ve1), VT))) | vtcheck(VC, Veout, VT))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (~![Vx: $i, VS: $i, VC: $i, Veout: $i, VT: $i] : ((~((vreduce(vabs(Vx, VS, ve1)) = vsomeExp(Veout)) & vtcheck(VC, vabs(Vx, VS, ve1), VT))) | vtcheck(VC, Veout, VT))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (~![Vx: $i, VS: $i, VC: $i, Veout: $i, VT: $i] : ((~((vreduce(vabs(Vx, VS, ve1)) = vsomeExp(Veout)) & vtcheck(VC, vabs(Vx, VS, ve1), VT))) | vtcheck(VC, Veout, VT))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.40 tff(8,plain,(
% 0.19/0.40 ~((~((vreduce(vabs(Vx!54, VS!53, ve1)) = vsomeExp(Veout!51)) & vtcheck(VC!52, vabs(Vx!54, VS!53, ve1), VT!50))) | vtcheck(VC!52, Veout!51, VT!50))),
% 0.19/0.40 inference(skolemize,[status(sab)],[7])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 ((vreduce(vabs(Vx!54, VS!53, ve1)) = vsomeExp(Veout!51)) & vtcheck(VC!52, vabs(Vx!54, VS!53, ve1), VT!50)),
% 0.19/0.40 inference(or_elim,[status(thm)],[8])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (vreduce(vabs(Vx!54, VS!53, ve1)) = vsomeExp(Veout!51)),
% 0.19/0.40 inference(and_elim,[status(thm)],[9])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (^[Vx: $i, VS: $i, Ve: $i] : refl((vreduce(vabs(Vx, VS, Ve)) = vnoExp) <=> (vreduce(vabs(Vx, VS, Ve)) = vnoExp))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (![Vx: $i, VS: $i, Ve: $i] : (vreduce(vabs(Vx, VS, Ve)) = vnoExp) <=> ![Vx: $i, VS: $i, Ve: $i] : (vreduce(vabs(Vx, VS, Ve)) = vnoExp)),
% 0.19/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (![Vx: $i, VS: $i, Ve: $i] : (vreduce(vabs(Vx, VS, Ve)) = vnoExp) <=> ![Vx: $i, VS: $i, Ve: $i] : (vreduce(vabs(Vx, VS, Ve)) = vnoExp)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : (vreduce(vabs(Vx, VS, Ve)) = vnoExp) <=> ![Vx: $i, VS: $i, Ve: $i] : (vreduce(vabs(Vx, VS, Ve)) = vnoExp)),
% 0.19/0.40 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vabs(Vx, VS, Ve)))) <=> ![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : (vreduce(vabs(Vx, VS, Ve)) = vnoExp)),
% 0.19/0.40 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vabs(Vx, VS, Ve)))) <=> ![Vx: $i, VS: $i, Ve: $i] : (vreduce(vabs(Vx, VS, Ve)) = vnoExp)),
% 0.19/0.40 inference(transitivity,[status(thm)],[15, 14])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (^[Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : trans(monotonicity(rewrite(((RESULT = vreduce(VExp0)) => (RESULT = vnoExp)) <=> ((~(RESULT = vreduce(VExp0))) | (RESULT = vnoExp))), (((VExp0 = vabs(Vx, VS, Ve)) => ((RESULT = vreduce(VExp0)) => (RESULT = vnoExp))) <=> ((VExp0 = vabs(Vx, VS, Ve)) => ((~(RESULT = vreduce(VExp0))) | (RESULT = vnoExp))))), rewrite(((VExp0 = vabs(Vx, VS, Ve)) => ((~(RESULT = vreduce(VExp0))) | (RESULT = vnoExp))) <=> ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vabs(Vx, VS, Ve))))), (((VExp0 = vabs(Vx, VS, Ve)) => ((RESULT = vreduce(VExp0)) => (RESULT = vnoExp))) <=> ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vabs(Vx, VS, Ve))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : ((VExp0 = vabs(Vx, VS, Ve)) => ((RESULT = vreduce(VExp0)) => (RESULT = vnoExp))) <=> ![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vabs(Vx, VS, Ve))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : ((VExp0 = vabs(Vx, VS, Ve)) => ((RESULT = vreduce(VExp0)) => (RESULT = vnoExp))) <=> ![Vx: $i, VS: $i, Ve: $i] : (vreduce(vabs(Vx, VS, Ve)) = vnoExp)),
% 0.19/0.40 inference(transitivity,[status(thm)],[18, 16])).
% 0.19/0.40 tff(20,axiom,(![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : ((VExp0 = vabs(Vx, VS, Ve)) => ((RESULT = vreduce(VExp0)) => (RESULT = vnoExp)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','reduce1')).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (![Vx: $i, VS: $i, Ve: $i] : (vreduce(vabs(Vx, VS, Ve)) = vnoExp)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (![Vx: $i, VS: $i, Ve: $i] : (vreduce(vabs(Vx, VS, Ve)) = vnoExp)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[21, 13])).
% 0.19/0.40 tff(23,plain,(
% 0.19/0.40 ![Vx: $i, VS: $i, Ve: $i] : (vreduce(vabs(Vx, VS, Ve)) = vnoExp)),
% 0.19/0.40 inference(skolemize,[status(sab)],[22])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (![Vx: $i, VS: $i, Ve: $i] : (vreduce(vabs(Vx, VS, Ve)) = vnoExp)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[23, 12])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 ((~![Vx: $i, VS: $i, Ve: $i] : (vreduce(vabs(Vx, VS, Ve)) = vnoExp)) | (vreduce(vabs(Vx!54, VS!53, ve1)) = vnoExp)),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (vreduce(vabs(Vx!54, VS!53, ve1)) = vnoExp),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (vnoExp = vreduce(vabs(Vx!54, VS!53, ve1))),
% 0.19/0.40 inference(symmetry,[status(thm)],[26])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (vnoExp = vsomeExp(Veout!51)),
% 0.19/0.40 inference(transitivity,[status(thm)],[27, 10])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (^[VExp0: $i] : refl((~(vnoExp = vsomeExp(VExp0))) <=> (~(vnoExp = vsomeExp(VExp0))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0))) <=> ![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0))) <=> ![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(32,axiom,(![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''DIFF-noExp-someExp'')).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.40 tff(34,plain,(
% 0.19/0.40 ![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[33])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 ((~![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0)))) | (~(vnoExp = vsomeExp(Veout!51)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (~(vnoExp = vsomeExp(Veout!51))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[37, 28])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------