%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG112+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:24:14 AM UTC 2025
% Result : Theorem 6.96s 7.12s
% Output : Proof 7.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : RNG112+1 : TPTP v9.0.0. Released v4.0.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n012.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Jun 20 03:23:55 EDT 2025
% 0.15/0.36 % CPUTime :
% 6.96/7.12 % SZS status Theorem
% 6.96/7.12 % SZS output start Proof
% 6.96/7.12 tff(aElementOf0_type, type, (
% 6.96/7.12 aElementOf0: ( $i * $i ) > $o)).
% 6.96/7.12 tff(xI_type, type, (
% 6.96/7.12 xI: $i)).
% 6.96/7.12 tff(tptp_fun_W1_22_type, type, (
% 6.96/7.12 tptp_fun_W1_22: $i > $i)).
% 6.96/7.12 tff(tptp_fun_W1_21_type, type, (
% 6.96/7.12 tptp_fun_W1_21: $i)).
% 6.96/7.12 tff(sz00_type, type, (
% 6.96/7.12 sz00: $i)).
% 6.96/7.12 tff(iLess0_type, type, (
% 6.96/7.12 iLess0: ( $i * $i ) > $o)).
% 6.96/7.12 tff(sbrdtbr0_type, type, (
% 6.96/7.12 sbrdtbr0: $i > $i)).
% 6.96/7.12 tff(tptp_fun_W0_20_type, type, (
% 6.96/7.12 tptp_fun_W0_20: $i)).
% 6.96/7.12 tff(sdtpldt1_type, type, (
% 6.96/7.12 sdtpldt1: ( $i * $i ) > $i)).
% 6.96/7.12 tff(slsdtgt0_type, type, (
% 6.96/7.12 slsdtgt0: $i > $i)).
% 6.96/7.12 tff(xb_type, type, (
% 6.96/7.12 xb: $i)).
% 6.96/7.12 tff(xa_type, type, (
% 6.96/7.12 xa: $i)).
% 6.96/7.12 tff(aIdeal0_type, type, (
% 6.96/7.12 aIdeal0: $i > $o)).
% 6.96/7.12 tff(1,plain,
% 6.96/7.12 ((xI = sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) <=> (xI = sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))),
% 6.96/7.12 inference(rewrite,[status(thm)],[])).
% 6.96/7.12 tff(2,axiom,(aIdeal0(xI) & (xI = sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2174')).
% 6.96/7.12 tff(3,plain,
% 6.96/7.12 (xI = sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))),
% 6.96/7.12 inference(and_elim,[status(thm)],[2])).
% 6.96/7.12 tff(4,plain,
% 6.96/7.12 (xI = sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))),
% 6.96/7.12 inference(modus_ponens,[status(thm)],[3, 1])).
% 6.96/7.12 tff(5,plain,
% 6.96/7.12 (aElementOf0(W0!20, xI) <=> aElementOf0(W0!20, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))),
% 6.96/7.12 inference(monotonicity,[status(thm)],[4])).
% 6.96/7.12 tff(6,plain,
% 6.96/7.12 (aElementOf0(W0!20, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) <=> aElementOf0(W0!20, xI)),
% 6.96/7.12 inference(symmetry,[status(thm)],[5])).
% 6.96/7.12 tff(7,plain,
% 6.96/7.12 (?[W0: $i] : (aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00))) <=> ?[W0: $i] : (aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)))),
% 6.96/7.12 inference(rewrite,[status(thm)],[])).
% 6.96/7.12 tff(8,axiom,(?[W0: $i] : (aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2228')).
% 6.96/7.12 tff(9,plain,
% 6.96/7.12 (?[W0: $i] : (aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)))),
% 6.96/7.12 inference(modus_ponens,[status(thm)],[8, 7])).
% 6.96/7.12 tff(10,plain,(
% 6.96/7.12 aElementOf0(W0!20, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0!20 = sz00))),
% 6.96/7.12 inference(skolemize,[status(sab)],[9])).
% 6.96/7.12 tff(11,plain,
% 6.96/7.12 (aElementOf0(W0!20, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))),
% 6.96/7.12 inference(and_elim,[status(thm)],[10])).
% 6.96/7.12 tff(12,plain,
% 6.96/7.12 (aElementOf0(W0!20, xI)),
% 6.96/7.12 inference(modus_ponens,[status(thm)],[11, 6])).
% 6.96/7.12 tff(13,plain,
% 6.96/7.12 (^[W0: $i] : trans(monotonicity(rewrite((~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI)))) <=> (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI))))))), (((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI))))) <=> ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI))))))))), rewrite(((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI))))))) <=> ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))))), (((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI))))) <=> ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))))))),
% 6.96/7.12 inference(bind,[status(th)],[])).
% 6.96/7.12 tff(14,plain,
% 6.96/7.12 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI))))) <=> ![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))))),
% 6.96/7.13 inference(quant_intro,[status(thm)],[13])).
% 6.96/7.13 tff(15,plain,
% 6.96/7.13 (^[W0: $i] : refl(((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI))))) <=> ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI))))))),
% 6.96/7.13 inference(bind,[status(th)],[])).
% 6.96/7.13 tff(16,plain,
% 6.96/7.13 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI))))) <=> ![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI)))))),
% 6.96/7.13 inference(quant_intro,[status(thm)],[15])).
% 6.96/7.13 tff(17,plain,
% 6.96/7.13 (^[W0: $i] : rewrite(((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI))))) <=> ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI))))))),
% 6.96/7.13 inference(bind,[status(th)],[])).
% 6.96/7.13 tff(18,plain,
% 6.96/7.13 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI))))) <=> ![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI)))))),
% 6.96/7.13 inference(quant_intro,[status(thm)],[17])).
% 6.96/7.13 tff(19,plain,
% 6.96/7.13 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI))))) <=> ![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI)))))),
% 6.96/7.13 inference(transitivity,[status(thm)],[18, 16])).
% 6.96/7.13 tff(20,plain,
% 6.96/7.13 (^[W0: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElementOf0(W0, xI) & (~(W0 = sz00))) <=> (~((~aElementOf0(W0, xI)) | (W0 = sz00)))), ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) <=> (~(~((~aElementOf0(W0, xI)) | (W0 = sz00)))))), rewrite((~(~((~aElementOf0(W0, xI)) | (W0 = sz00)))) <=> ((~aElementOf0(W0, xI)) | (W0 = sz00))), ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) <=> ((~aElementOf0(W0, xI)) | (W0 = sz00)))), trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElementOf0(W2, xI) & (~(W2 = sz00))) <=> (~((~aElementOf0(W2, xI)) | (W2 = sz00)))), ((~(aElementOf0(W2, xI) & (~(W2 = sz00)))) <=> (~(~((~aElementOf0(W2, xI)) | (W2 = sz00)))))), rewrite((~(~((~aElementOf0(W2, xI)) | (W2 = sz00)))) <=> ((~aElementOf0(W2, xI)) | (W2 = sz00))), ((~(aElementOf0(W2, xI) & (~(W2 = sz00)))) <=> ((~aElementOf0(W2, xI)) | (W2 = sz00)))), (((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00))))) <=> ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | ((~aElementOf0(W2, xI)) | (W2 = sz00))))), rewrite(((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | ((~aElementOf0(W2, xI)) | (W2 = sz00))) <=> ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))), (((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00))))) <=> ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))), (![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00))))) <=> ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI))))), ((aElementOf0(W1!21, xI) & (~(W1!21 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))) <=> (aElementOf0(W1!21, xI) & (~(W1!21 = sz00)) & ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))), rewrite((aElementOf0(W1!21, xI) & (~(W1!21 = sz00)) & ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) <=> (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI))))), ((aElementOf0(W1!21, xI) & (~(W1!21 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))) <=> (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI)))))), (((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | (aElementOf0(W1!21, xI) & (~(W1!21 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00))))))) <=> (((~aElementOf0(W0, xI)) | (W0 = sz00)) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI))))))), rewrite((((~aElementOf0(W0, xI)) | (W0 = sz00)) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI))))) <=> ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI)))))), (((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | (aElementOf0(W1!21, xI) & (~(W1!21 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00))))))) <=> ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI)))))))),
% 6.96/7.13 inference(bind,[status(th)],[])).
% 6.96/7.13 tff(21,plain,
% 6.96/7.13 (![W0: $i] : ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | (aElementOf0(W1!21, xI) & (~(W1!21 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00))))))) <=> ![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI)))))),
% 6.96/7.13 inference(quant_intro,[status(thm)],[20])).
% 6.96/7.13 tff(22,plain,
% 6.96/7.13 (![W0: $i] : ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00))))))) <=> ![W0: $i] : ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))))),
% 6.96/7.13 inference(rewrite,[status(thm)],[])).
% 6.96/7.13 tff(23,plain,
% 6.96/7.13 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite(((aElementOf0(W2, xI) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1)))) <=> ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00))))))), (![W2: $i] : ((aElementOf0(W2, xI) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1)))) <=> ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00))))))), (((aElementOf0(W1, xI) & (~(W1 = sz00))) & ![W2: $i] : ((aElementOf0(W2, xI) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))))) <=> ((aElementOf0(W1, xI) & (~(W1 = sz00))) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))))), rewrite(((aElementOf0(W1, xI) & (~(W1 = sz00))) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))) <=> (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00))))))), (((aElementOf0(W1, xI) & (~(W1 = sz00))) & ![W2: $i] : ((aElementOf0(W2, xI) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))))) <=> (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00))))))))), (?[W1: $i] : ((aElementOf0(W1, xI) & (~(W1 = sz00))) & ![W2: $i] : ((aElementOf0(W2, xI) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))))) <=> ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))))), (((aElementOf0(W0, xI) & (~(W0 = sz00))) => ?[W1: $i] : ((aElementOf0(W1, xI) & (~(W1 = sz00))) & ![W2: $i] : ((aElementOf0(W2, xI) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1)))))) <=> ((aElementOf0(W0, xI) & (~(W0 = sz00))) => ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00))))))))), rewrite(((aElementOf0(W0, xI) & (~(W0 = sz00))) => ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00))))))) <=> ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))))), (((aElementOf0(W0, xI) & (~(W0 = sz00))) => ?[W1: $i] : ((aElementOf0(W1, xI) & (~(W1 = sz00))) & ![W2: $i] : ((aElementOf0(W2, xI) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1)))))) <=> ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))))))),
% 6.96/7.13 inference(bind,[status(th)],[])).
% 6.96/7.13 tff(24,plain,
% 6.96/7.13 (![W0: $i] : ((aElementOf0(W0, xI) & (~(W0 = sz00))) => ?[W1: $i] : ((aElementOf0(W1, xI) & (~(W1 = sz00))) & ![W2: $i] : ((aElementOf0(W2, xI) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1)))))) <=> ![W0: $i] : ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))))),
% 6.96/7.13 inference(quant_intro,[status(thm)],[23])).
% 6.96/7.13 tff(25,axiom,(![W0: $i] : ((aElementOf0(W0, xI) & (~(W0 = sz00))) => ?[W1: $i] : ((aElementOf0(W1, xI) & (~(W1 = sz00))) & ![W2: $i] : ((aElementOf0(W2, xI) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2351')).
% 6.96/7.13 tff(26,plain,
% 6.96/7.13 (![W0: $i] : ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))))),
% 6.96/7.13 inference(modus_ponens,[status(thm)],[25, 24])).
% 6.96/7.13 tff(27,plain,
% 6.96/7.13 (![W0: $i] : ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))))),
% 6.96/7.13 inference(modus_ponens,[status(thm)],[26, 22])).
% 6.96/7.13 tff(28,plain,(
% 6.96/7.13 ![W0: $i] : ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | (aElementOf0(W1!21, xI) & (~(W1!21 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))))),
% 6.96/7.13 inference(skolemize,[status(sab)],[27])).
% 6.96/7.13 tff(29,plain,
% 6.96/7.13 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI)))))),
% 6.96/7.13 inference(modus_ponens,[status(thm)],[28, 21])).
% 6.96/7.13 tff(30,plain,
% 6.96/7.13 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~aElementOf0(W1!21, xI)))))),
% 6.96/7.13 inference(modus_ponens,[status(thm)],[29, 19])).
% 6.96/7.13 tff(31,plain,
% 6.96/7.13 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))))),
% 6.96/7.13 inference(modus_ponens,[status(thm)],[30, 14])).
% 6.96/7.13 tff(32,plain,
% 6.96/7.13 (~(W0!20 = sz00)),
% 6.96/7.13 inference(and_elim,[status(thm)],[10])).
% 6.96/7.13 tff(33,plain,
% 6.96/7.13 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))))) | ((W0!20 = sz00) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))) | (~aElementOf0(W0!20, xI)))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))))) | (W0!20 = sz00) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))) | (~aElementOf0(W0!20, xI)))),
% 6.96/7.13 inference(rewrite,[status(thm)],[])).
% 6.96/7.13 tff(34,plain,
% 6.96/7.13 (((W0!20 = sz00) | (~aElementOf0(W0!20, xI)) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI))))))) <=> ((W0!20 = sz00) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))) | (~aElementOf0(W0!20, xI)))),
% 6.96/7.13 inference(rewrite,[status(thm)],[])).
% 6.96/7.13 tff(35,plain,
% 6.96/7.13 ((~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))) <=> (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI))))))),
% 6.96/7.13 inference(rewrite,[status(thm)],[])).
% 6.96/7.13 tff(36,plain,
% 6.96/7.13 (((W0!20 = sz00) | (~aElementOf0(W0!20, xI)) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI))))))) <=> ((W0!20 = sz00) | (~aElementOf0(W0!20, xI)) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))))),
% 6.96/7.13 inference(monotonicity,[status(thm)],[35])).
% 6.96/7.13 tff(37,plain,
% 6.96/7.13 (((W0!20 = sz00) | (~aElementOf0(W0!20, xI)) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI))))))) <=> ((W0!20 = sz00) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))) | (~aElementOf0(W0!20, xI)))),
% 6.96/7.13 inference(transitivity,[status(thm)],[36, 34])).
% 6.96/7.13 tff(38,plain,
% 6.96/7.13 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))))) | ((W0!20 = sz00) | (~aElementOf0(W0!20, xI)) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))))) | ((W0!20 = sz00) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))) | (~aElementOf0(W0!20, xI))))),
% 6.96/7.13 inference(monotonicity,[status(thm)],[37])).
% 6.96/7.13 tff(39,plain,
% 6.96/7.13 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))))) | ((W0!20 = sz00) | (~aElementOf0(W0!20, xI)) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))))) | (W0!20 = sz00) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))) | (~aElementOf0(W0!20, xI)))),
% 6.96/7.13 inference(transitivity,[status(thm)],[38, 33])).
% 6.96/7.13 tff(40,plain,
% 6.96/7.13 ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))))) | ((W0!20 = sz00) | (~aElementOf0(W0!20, xI)) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))))),
% 6.96/7.13 inference(quant_inst,[status(thm)],[])).
% 6.96/7.13 tff(41,plain,
% 6.96/7.13 ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))))) | (W0!20 = sz00) | (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))) | (~aElementOf0(W0!20, xI))),
% 6.96/7.13 inference(modus_ponens,[status(thm)],[40, 39])).
% 6.96/7.13 tff(42,plain,
% 6.96/7.13 ((~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))) | (~aElementOf0(W0!20, xI))),
% 6.96/7.13 inference(unit_resolution,[status(thm)],[41, 32, 31])).
% 6.96/7.13 tff(43,plain,
% 6.96/7.13 (~((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))))),
% 6.96/7.13 inference(unit_resolution,[status(thm)],[42, 12])).
% 6.96/7.13 tff(44,plain,
% 6.96/7.13 (((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI))))) | aElementOf0(W1!21, xI)),
% 6.96/7.13 inference(tautology,[status(thm)],[])).
% 6.96/7.13 tff(45,plain,
% 6.96/7.13 (aElementOf0(W1!21, xI)),
% 6.96/7.13 inference(unit_resolution,[status(thm)],[44, 43])).
% 6.96/7.13 tff(46,plain,
% 6.96/7.13 (((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI))))) | (~(W1!21 = sz00))),
% 6.96/7.13 inference(tautology,[status(thm)],[])).
% 6.96/7.13 tff(47,plain,
% 6.96/7.13 (~(W1!21 = sz00)),
% 6.96/7.13 inference(unit_resolution,[status(thm)],[46, 43])).
% 6.96/7.13 tff(48,plain,
% 6.96/7.13 (^[W0: $i] : refl(((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), xI))))) <=> ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), xI))))))),
% 6.96/7.13 inference(bind,[status(th)],[])).
% 6.96/7.13 tff(49,plain,
% 6.96/7.13 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), xI))))) <=> ![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), xI)))))),
% 6.96/7.13 inference(quant_intro,[status(thm)],[48])).
% 6.96/7.13 tff(50,plain,
% 6.96/7.13 (^[W0: $i] : trans(monotonicity(rewrite((~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), xI) & (~(tptp_fun_W1_22(W0) = sz00)))))) <=> (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), xI))))), (((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), xI) & (~(tptp_fun_W1_22(W0) = sz00))))))) <=> ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), xI))))))), rewrite(((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), xI))))) <=> ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), xI)))))), (((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), xI) & (~(tptp_fun_W1_22(W0) = sz00))))))) <=> ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), xI)))))))),
% 6.96/7.13 inference(bind,[status(th)],[])).
% 6.96/7.13 tff(51,plain,
% 6.96/7.13 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), xI) & (~(tptp_fun_W1_22(W0) = sz00))))))) <=> ![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), xI)))))),
% 6.96/7.13 inference(quant_intro,[status(thm)],[50])).
% 6.96/7.13 tff(52,plain,
% 6.96/7.13 (^[W0: $i] : rewrite(((~aElementOf0(W0, xI)) | (W0 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), xI) & (~(tptp_fun_W1_22(W0) = sz00))))))) <=> ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), xI) & (~(tptp_fun_W1_22(W0) = sz00))))))))),
% 6.96/7.13 inference(bind,[status(th)],[])).
% 6.96/7.13 tff(53,plain,
% 6.96/7.13 (![W0: $i] : ((~aElementOf0(W0, xI)) | (W0 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), xI) & (~(tptp_fun_W1_22(W0) = sz00))))))) <=> ![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), xI) & (~(tptp_fun_W1_22(W0) = sz00)))))))),
% 6.96/7.13 inference(quant_intro,[status(thm)],[52])).
% 6.96/7.13 tff(54,plain,
% 6.96/7.13 ((~?[W0: $i] : (aElementOf0(W0, xI) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00))))))) <=> (~?[W0: $i] : (aElementOf0(W0, xI) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))))))),
% 6.96/7.13 inference(rewrite,[status(thm)],[])).
% 6.96/7.13 tff(55,plain,
% 6.96/7.13 ((~?[W0: $i] : ((aElementOf0(W0, xI) & (~(W0 = sz00))) & ![W1: $i] : ((aElementOf0(W1, xI) & (~(W1 = sz00))) => (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0)))))) <=> (~?[W0: $i] : (aElementOf0(W0, xI) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))))))),
% 6.96/7.13 inference(rewrite,[status(thm)],[])).
% 6.96/7.13 tff(56,axiom,(~?[W0: $i] : ((aElementOf0(W0, xI) & (~(W0 = sz00))) & ![W1: $i] : ((aElementOf0(W1, xI) & (~(W1 = sz00))) => (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 6.96/7.13 tff(57,plain,
% 6.96/7.13 (~?[W0: $i] : (aElementOf0(W0, xI) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00))))))),
% 6.96/7.13 inference(modus_ponens,[status(thm)],[56, 55])).
% 6.96/7.13 tff(58,plain,
% 6.96/7.13 (~?[W0: $i] : (aElementOf0(W0, xI) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00))))))),
% 6.96/7.13 inference(modus_ponens,[status(thm)],[57, 54])).
% 6.96/7.13 tff(59,plain,
% 6.96/7.13 (~?[W0: $i] : (aElementOf0(W0, xI) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00))))))),
% 6.96/7.13 inference(modus_ponens,[status(thm)],[58, 54])).
% 6.96/7.13 tff(60,plain,
% 6.96/7.13 (~?[W0: $i] : (aElementOf0(W0, xI) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00))))))),
% 6.96/7.13 inference(modus_ponens,[status(thm)],[59, 54])).
% 6.96/7.13 tff(61,plain,
% 6.96/7.13 (^[W0: $i] : nnf_neg(refl($oeq((~aElementOf0(W0, xI)), (~aElementOf0(W0, xI)))), refl($oeq((W0 = sz00), (W0 = sz00))), sk($oeq((~![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))))), (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), xI) & (~(tptp_fun_W1_22(W0) = sz00)))))))), $oeq((~(aElementOf0(W0, xI) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00))))))), ((~aElementOf0(W0, xI)) | (W0 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), xI) & (~(tptp_fun_W1_22(W0) = sz00)))))))))),
% 6.96/7.13 inference(bind,[status(th)],[])).
% 6.96/7.13 tff(62,plain,(
% 6.96/7.13 ![W0: $i] : ((~aElementOf0(W0, xI)) | (W0 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), xI) & (~(tptp_fun_W1_22(W0) = sz00)))))))),
% 6.96/7.13 inference(nnf-neg,[status(sab)],[60, 61])).
% 6.96/7.13 tff(63,plain,
% 6.96/7.13 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (~(aElementOf0(tptp_fun_W1_22(W0), xI) & (~(tptp_fun_W1_22(W0) = sz00)))))))),
% 6.96/7.13 inference(modus_ponens,[status(thm)],[62, 53])).
% 6.96/7.13 tff(64,plain,
% 6.96/7.13 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), xI)))))),
% 6.96/7.13 inference(modus_ponens,[status(thm)],[63, 51])).
% 6.96/7.13 tff(65,plain,
% 6.96/7.13 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), xI)))))),
% 6.96/7.13 inference(modus_ponens,[status(thm)],[64, 49])).
% 6.96/7.13 tff(66,plain,
% 6.96/7.13 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), xI)))))) | ((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), xI)))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), xI)))))) | (W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), xI)))))),
% 6.96/7.13 inference(rewrite,[status(thm)],[])).
% 6.96/7.13 tff(67,plain,
% 6.96/7.13 ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), xI)))))) | ((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), xI)))))),
% 6.96/7.13 inference(quant_inst,[status(thm)],[])).
% 6.96/7.13 tff(68,plain,
% 6.96/7.13 ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_22(W0) = sz00) | (~aElementOf0(tptp_fun_W1_22(W0), xI)))))) | (W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), xI))))),
% 6.96/7.13 inference(modus_ponens,[status(thm)],[67, 66])).
% 6.96/7.13 tff(69,plain,
% 6.96/7.13 (~((~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), xI)))),
% 6.96/7.13 inference(unit_resolution,[status(thm)],[68, 65, 47, 45])).
% 6.96/7.13 tff(70,plain,
% 6.96/7.13 (((~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), xI))) | aElementOf0(tptp_fun_W1_22(W1!21), xI)),
% 6.96/7.14 inference(tautology,[status(thm)],[])).
% 6.96/7.14 tff(71,plain,
% 6.96/7.14 (aElementOf0(tptp_fun_W1_22(W1!21), xI)),
% 6.96/7.14 inference(unit_resolution,[status(thm)],[70, 69])).
% 6.96/7.14 tff(72,plain,
% 6.96/7.14 (((~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), xI))) | (~(tptp_fun_W1_22(W1!21) = sz00))),
% 6.96/7.14 inference(tautology,[status(thm)],[])).
% 6.96/7.14 tff(73,plain,
% 6.96/7.14 (~(tptp_fun_W1_22(W1!21) = sz00)),
% 6.96/7.14 inference(unit_resolution,[status(thm)],[72, 69])).
% 6.96/7.14 tff(74,plain,
% 6.96/7.14 (((~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), xI))) | iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))),
% 6.96/7.14 inference(tautology,[status(thm)],[])).
% 6.96/7.14 tff(75,plain,
% 6.96/7.14 (iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))),
% 6.96/7.14 inference(unit_resolution,[status(thm)],[74, 69])).
% 6.96/7.14 tff(76,plain,
% 6.96/7.14 (((W1!21 = sz00) | (~aElementOf0(W1!21, xI)) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI))))) | ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))),
% 6.96/7.14 inference(tautology,[status(thm)],[])).
% 6.96/7.14 tff(77,plain,
% 6.96/7.14 (![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))),
% 6.96/7.14 inference(unit_resolution,[status(thm)],[76, 43])).
% 6.96/7.14 tff(78,plain,
% 6.96/7.14 (((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | ((~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), xI)))) <=> ((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), xI)))),
% 6.96/7.14 inference(rewrite,[status(thm)],[])).
% 6.96/7.14 tff(79,plain,
% 6.96/7.14 (((tptp_fun_W1_22(W1!21) = sz00) | (~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (~aElementOf0(tptp_fun_W1_22(W1!21), xI))) <=> ((~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), xI)))),
% 6.96/7.14 inference(rewrite,[status(thm)],[])).
% 6.96/7.14 tff(80,plain,
% 6.96/7.14 (((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | ((tptp_fun_W1_22(W1!21) = sz00) | (~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (~aElementOf0(tptp_fun_W1_22(W1!21), xI)))) <=> ((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | ((~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), xI))))),
% 6.96/7.14 inference(monotonicity,[status(thm)],[79])).
% 6.96/7.14 tff(81,plain,
% 6.96/7.14 (((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | ((tptp_fun_W1_22(W1!21) = sz00) | (~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (~aElementOf0(tptp_fun_W1_22(W1!21), xI)))) <=> ((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), xI)))),
% 6.96/7.14 inference(transitivity,[status(thm)],[80, 78])).
% 6.96/7.14 tff(82,plain,
% 6.96/7.14 ((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | ((tptp_fun_W1_22(W1!21) = sz00) | (~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (~aElementOf0(tptp_fun_W1_22(W1!21), xI)))),
% 6.96/7.14 inference(quant_inst,[status(thm)],[])).
% 6.96/7.14 tff(83,plain,
% 6.96/7.14 ((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!21))) | (~aElementOf0(W2, xI)))) | (~iLess0(sbrdtbr0(tptp_fun_W1_22(W1!21)), sbrdtbr0(W1!21))) | (tptp_fun_W1_22(W1!21) = sz00) | (~aElementOf0(tptp_fun_W1_22(W1!21), xI))),
% 6.96/7.14 inference(modus_ponens,[status(thm)],[82, 81])).
% 6.96/7.14 tff(84,plain,
% 6.96/7.14 ($false),
% 6.96/7.14 inference(unit_resolution,[status(thm)],[83, 77, 75, 73, 71])).
% 7.00/7.15 % SZS output end Proof
% 7.00/7.18 % E exiting
%------------------------------------------------------------------------------