%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG114+4 : TPTP v9.0.0. Released v4.0.0.
% 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 05:24:14 AM UTC 2025
% Result : Theorem 1.17s 1.37s
% Output : Proof 1.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : RNG114+4 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n004.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 03:24:23 EDT 2025
% 0.13/0.35 % CPUTime :
% 1.17/1.37 % SZS status Theorem
% 1.17/1.37 % SZS output start Proof
% 1.17/1.37 tff(sdtpldt0_type, type, (
% 1.17/1.37 sdtpldt0: ( $i * $i ) > $i)).
% 1.17/1.37 tff(sdtasdt0_type, type, (
% 1.17/1.37 sdtasdt0: ( $i * $i ) > $i)).
% 1.17/1.37 tff(tptp_fun_W1_24_type, type, (
% 1.17/1.37 tptp_fun_W1_24: $i > $i)).
% 1.17/1.37 tff(tptp_fun_W1_36_type, type, (
% 1.17/1.37 tptp_fun_W1_36: $i)).
% 1.17/1.37 tff(xb_type, type, (
% 1.17/1.37 xb: $i)).
% 1.17/1.37 tff(tptp_fun_W1_23_type, type, (
% 1.17/1.37 tptp_fun_W1_23: $i > $i)).
% 1.17/1.37 tff(tptp_fun_W0_37_type, type, (
% 1.17/1.37 tptp_fun_W0_37: $i)).
% 1.17/1.37 tff(xa_type, type, (
% 1.17/1.37 xa: $i)).
% 1.17/1.37 tff(xu_type, type, (
% 1.17/1.37 xu: $i)).
% 1.17/1.37 tff(aElement0_type, type, (
% 1.17/1.37 aElement0: $i > $o)).
% 1.17/1.37 tff(aElementOf0_type, type, (
% 1.17/1.37 aElementOf0: ( $i * $i ) > $o)).
% 1.17/1.37 tff(slsdtgt0_type, type, (
% 1.17/1.37 slsdtgt0: $i > $i)).
% 1.17/1.37 tff(aIdeal0_type, type, (
% 1.17/1.37 aIdeal0: $i > $o)).
% 1.17/1.37 tff(xI_type, type, (
% 1.17/1.37 xI: $i)).
% 1.17/1.37 tff(aSet0_type, type, (
% 1.17/1.37 aSet0: $i > $o)).
% 1.17/1.37 tff(sdtpldt1_type, type, (
% 1.17/1.37 sdtpldt1: ( $i * $i ) > $i)).
% 1.17/1.37 tff(sz00_type, type, (
% 1.17/1.37 sz00: $i)).
% 1.17/1.37 tff(iLess0_type, type, (
% 1.17/1.37 iLess0: ( $i * $i ) > $o)).
% 1.17/1.37 tff(sbrdtbr0_type, type, (
% 1.17/1.37 sbrdtbr0: $i > $i)).
% 1.17/1.37 tff(1,plain,
% 1.17/1.37 (^[W0: $i] : refl((~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0))))))) <=> (~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0))))))))),
% 1.17/1.37 inference(bind,[status(th)],[])).
% 1.17/1.37 tff(2,plain,
% 1.17/1.37 (![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0)))))))),
% 1.17/1.37 inference(quant_intro,[status(thm)],[1])).
% 1.17/1.37 tff(3,plain,
% 1.17/1.37 (^[W0: $i] : rewrite((~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0))))))) <=> (~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0))))))))),
% 1.17/1.37 inference(bind,[status(th)],[])).
% 1.17/1.37 tff(4,plain,
% 1.17/1.37 (![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0)))))))),
% 1.17/1.37 inference(quant_intro,[status(thm)],[3])).
% 1.17/1.37 tff(5,plain,
% 1.17/1.37 (![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0)))))))),
% 1.17/1.37 inference(transitivity,[status(thm)],[4, 2])).
% 1.17/1.37 tff(6,plain,
% 1.17/1.37 (^[W0: $i] : trans(monotonicity(rewrite(((~aElementOf0(W0, slsdtgt0(xb))) | (aElement0(tptp_fun_W1_24(W0)) & (sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0))) <=> ((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))), rewrite((aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : (~(aElement0(W1) & (sdtasdt0(xb, W1) = W0)))) <=> (aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0))))), ((((~aElementOf0(W0, slsdtgt0(xb))) | (aElement0(tptp_fun_W1_24(W0)) & (sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0))) & (aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : (~(aElement0(W1) & (sdtasdt0(xb, W1) = W0))))) <=> (((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0))))) & (aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0))))))), rewrite((((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0))))) & (aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0))))) <=> (~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0)))))))), ((((~aElementOf0(W0, slsdtgt0(xb))) | (aElement0(tptp_fun_W1_24(W0)) & (sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0))) & (aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : (~(aElement0(W1) & (sdtasdt0(xb, W1) = W0))))) <=> (~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0)))))))))),
% 1.17/1.37 inference(bind,[status(th)],[])).
% 1.17/1.37 tff(7,plain,
% 1.17/1.37 (![W0: $i] : (((~aElementOf0(W0, slsdtgt0(xb))) | (aElement0(tptp_fun_W1_24(W0)) & (sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0))) & (aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : (~(aElement0(W1) & (sdtasdt0(xb, W1) = W0))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0)))))))),
% 1.17/1.37 inference(quant_intro,[status(thm)],[6])).
% 1.17/1.37 tff(8,plain,
% 1.17/1.37 (![W0: $i] : (aElementOf0(W0, slsdtgt0(xb)) <=> ?[W1: $i] : (aElement0(W1) & (sdtasdt0(xb, W1) = W0))) <=> ![W0: $i] : (aElementOf0(W0, slsdtgt0(xb)) <=> ?[W1: $i] : (aElement0(W1) & (sdtasdt0(xb, W1) = W0)))),
% 1.17/1.37 inference(rewrite,[status(thm)],[])).
% 1.17/1.37 tff(9,axiom,((((((aSet0(xI) & ![W0: $i] : (aElementOf0(W0, xI) => (![W1: $i] : (aElementOf0(W1, xI) => aElementOf0(sdtpldt0(W0, W1), xI)) & ![W1: $i] : (aElement0(W1) => aElementOf0(sdtasdt0(W1, W0), xI))))) & aIdeal0(xI)) & ![W0: $i] : (aElementOf0(W0, slsdtgt0(xa)) <=> ?[W1: $i] : (aElement0(W1) & (sdtasdt0(xa, W1) = W0)))) & ![W0: $i] : (aElementOf0(W0, slsdtgt0(xb)) <=> ?[W1: $i] : (aElement0(W1) & (sdtasdt0(xb, W1) = W0)))) & ![W0: $i] : (aElementOf0(W0, xI) <=> ?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0)))) & (xI = sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2174')).
% 1.17/1.37 tff(10,plain,
% 1.17/1.37 (((((aSet0(xI) & ![W0: $i] : (aElementOf0(W0, xI) => (![W1: $i] : (aElementOf0(W1, xI) => aElementOf0(sdtpldt0(W0, W1), xI)) & ![W1: $i] : (aElement0(W1) => aElementOf0(sdtasdt0(W1, W0), xI))))) & aIdeal0(xI)) & ![W0: $i] : (aElementOf0(W0, slsdtgt0(xa)) <=> ?[W1: $i] : (aElement0(W1) & (sdtasdt0(xa, W1) = W0)))) & ![W0: $i] : (aElementOf0(W0, slsdtgt0(xb)) <=> ?[W1: $i] : (aElement0(W1) & (sdtasdt0(xb, W1) = W0)))) & ![W0: $i] : (aElementOf0(W0, xI) <=> ?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0)))),
% 1.17/1.37 inference(and_elim,[status(thm)],[9])).
% 1.17/1.37 tff(11,plain,
% 1.17/1.37 ((((aSet0(xI) & ![W0: $i] : (aElementOf0(W0, xI) => (![W1: $i] : (aElementOf0(W1, xI) => aElementOf0(sdtpldt0(W0, W1), xI)) & ![W1: $i] : (aElement0(W1) => aElementOf0(sdtasdt0(W1, W0), xI))))) & aIdeal0(xI)) & ![W0: $i] : (aElementOf0(W0, slsdtgt0(xa)) <=> ?[W1: $i] : (aElement0(W1) & (sdtasdt0(xa, W1) = W0)))) & ![W0: $i] : (aElementOf0(W0, slsdtgt0(xb)) <=> ?[W1: $i] : (aElement0(W1) & (sdtasdt0(xb, W1) = W0)))),
% 1.17/1.37 inference(and_elim,[status(thm)],[10])).
% 1.17/1.37 tff(12,plain,
% 1.17/1.37 (![W0: $i] : (aElementOf0(W0, slsdtgt0(xb)) <=> ?[W1: $i] : (aElement0(W1) & (sdtasdt0(xb, W1) = W0)))),
% 1.17/1.37 inference(and_elim,[status(thm)],[11])).
% 1.17/1.37 tff(13,plain,
% 1.17/1.37 (![W0: $i] : (aElementOf0(W0, slsdtgt0(xb)) <=> ?[W1: $i] : (aElement0(W1) & (sdtasdt0(xb, W1) = W0)))),
% 1.17/1.37 inference(modus_ponens,[status(thm)],[12, 8])).
% 1.17/1.37 tff(14,plain,(
% 1.17/1.37 ![W0: $i] : (((~aElementOf0(W0, slsdtgt0(xb))) | (aElement0(tptp_fun_W1_24(W0)) & (sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0))) & (aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : (~(aElement0(W1) & (sdtasdt0(xb, W1) = W0)))))),
% 1.17/1.37 inference(skolemize,[status(sab)],[13])).
% 1.17/1.37 tff(15,plain,
% 1.17/1.37 (![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0)))))))),
% 1.17/1.37 inference(modus_ponens,[status(thm)],[14, 7])).
% 1.17/1.37 tff(16,plain,
% 1.17/1.37 (![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0)))))))),
% 1.17/1.37 inference(modus_ponens,[status(thm)],[15, 5])).
% 1.17/1.37 tff(17,plain,
% 1.17/1.37 (((~![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0)))))))) | (~((~(aElementOf0(W1!36, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W1!36))))) | (~((~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36))))))))) <=> ((~![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0)))))))) | (~((~(aElementOf0(W1!36, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W1!36))))) | (~((~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36)))))))))),
% 1.17/1.37 inference(rewrite,[status(thm)],[])).
% 1.17/1.37 tff(18,plain,
% 1.17/1.37 ((~((~((~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36)))))) | (~(aElementOf0(W1!36, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W1!36))))))) <=> (~((~(aElementOf0(W1!36, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W1!36))))) | (~((~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36))))))))),
% 1.17/1.37 inference(rewrite,[status(thm)],[])).
% 1.17/1.37 tff(19,plain,
% 1.17/1.37 (((~![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0)))))))) | (~((~((~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36)))))) | (~(aElementOf0(W1!36, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W1!36)))))))) <=> ((~![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0)))))))) | (~((~(aElementOf0(W1!36, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W1!36))))) | (~((~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36)))))))))),
% 1.17/1.37 inference(monotonicity,[status(thm)],[18])).
% 1.17/1.37 tff(20,plain,
% 1.17/1.37 (((~![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0)))))))) | (~((~((~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36)))))) | (~(aElementOf0(W1!36, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W1!36)))))))) <=> ((~![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0)))))))) | (~((~(aElementOf0(W1!36, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W1!36))))) | (~((~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36)))))))))),
% 1.17/1.38 inference(transitivity,[status(thm)],[19, 17])).
% 1.17/1.38 tff(21,plain,
% 1.17/1.38 ((~![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0)))))))) | (~((~((~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36)))))) | (~(aElementOf0(W1!36, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W1!36)))))))),
% 1.17/1.38 inference(quant_inst,[status(thm)],[])).
% 1.17/1.38 tff(22,plain,
% 1.17/1.38 ((~![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W0))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W0)))))))) | (~((~(aElementOf0(W1!36, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W1!36))))) | (~((~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36))))))))),
% 1.17/1.38 inference(modus_ponens,[status(thm)],[21, 20])).
% 1.17/1.38 tff(23,plain,
% 1.17/1.38 (~((~(aElementOf0(W1!36, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W1!36))))) | (~((~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36)))))))),
% 1.17/1.38 inference(unit_resolution,[status(thm)],[22, 16])).
% 1.17/1.38 tff(24,plain,
% 1.17/1.38 (((~(aElementOf0(W1!36, slsdtgt0(xb)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xb, W1) = W1!36))))) | (~((~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36))))))) | ((~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36)))))),
% 1.17/1.38 inference(tautology,[status(thm)],[])).
% 1.17/1.38 tff(25,plain,
% 1.17/1.38 ((~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36))))),
% 1.17/1.38 inference(unit_resolution,[status(thm)],[24, 23])).
% 1.17/1.38 tff(26,plain,
% 1.17/1.38 (?[W0: $i, W1: $i] : (aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb)) & (sdtpldt0(W0, W1) = xu)) <=> ?[W0: $i, W1: $i] : (aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb)) & (sdtpldt0(W0, W1) = xu))),
% 1.17/1.38 inference(rewrite,[status(thm)],[])).
% 1.17/1.38 tff(27,plain,
% 1.17/1.38 (^[W0: $i, W1: $i] : rewrite(((aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb))) & (sdtpldt0(W0, W1) = xu)) <=> (aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb)) & (sdtpldt0(W0, W1) = xu)))),
% 1.17/1.38 inference(bind,[status(th)],[])).
% 1.17/1.38 tff(28,plain,
% 1.17/1.38 (?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb))) & (sdtpldt0(W0, W1) = xu)) <=> ?[W0: $i, W1: $i] : (aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb)) & (sdtpldt0(W0, W1) = xu))),
% 1.17/1.38 inference(quant_intro,[status(thm)],[27])).
% 1.17/1.38 tff(29,axiom,(((?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb))) & (sdtpldt0(W0, W1) = xu)) & aElementOf0(xu, xI)) & (~(xu = sz00))) & ![W0: $i] : (((?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0)) | aElementOf0(W0, xI)) & (~(W0 = sz00))) => (~iLess0(sbrdtbr0(W0), sbrdtbr0(xu))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2273')).
% 1.17/1.38 tff(30,plain,
% 1.17/1.38 ((?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb))) & (sdtpldt0(W0, W1) = xu)) & aElementOf0(xu, xI)) & (~(xu = sz00))),
% 1.17/1.38 inference(and_elim,[status(thm)],[29])).
% 1.17/1.38 tff(31,plain,
% 1.17/1.38 (?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb))) & (sdtpldt0(W0, W1) = xu)) & aElementOf0(xu, xI)),
% 1.17/1.38 inference(and_elim,[status(thm)],[30])).
% 1.17/1.38 tff(32,plain,
% 1.17/1.38 (?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb))) & (sdtpldt0(W0, W1) = xu))),
% 1.17/1.38 inference(and_elim,[status(thm)],[31])).
% 1.17/1.38 tff(33,plain,
% 1.17/1.38 (?[W0: $i, W1: $i] : (aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb)) & (sdtpldt0(W0, W1) = xu))),
% 1.17/1.38 inference(modus_ponens,[status(thm)],[32, 28])).
% 1.17/1.38 tff(34,plain,
% 1.17/1.38 (?[W0: $i, W1: $i] : (aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb)) & (sdtpldt0(W0, W1) = xu))),
% 1.17/1.38 inference(modus_ponens,[status(thm)],[33, 26])).
% 1.17/1.38 tff(35,plain,(
% 1.17/1.38 aElementOf0(W0!37, slsdtgt0(xa)) & aElementOf0(W1!36, slsdtgt0(xb)) & (sdtpldt0(W0!37, W1!36) = xu)),
% 1.17/1.38 inference(skolemize,[status(sab)],[34])).
% 1.17/1.38 tff(36,plain,
% 1.17/1.38 (aElementOf0(W1!36, slsdtgt0(xb))),
% 1.17/1.38 inference(and_elim,[status(thm)],[35])).
% 1.17/1.38 tff(37,plain,
% 1.17/1.38 ((~((~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36)))))) | (~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36))))),
% 1.17/1.38 inference(tautology,[status(thm)],[])).
% 1.17/1.38 tff(38,plain,
% 1.17/1.38 ((~((~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W1_24(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36)))))) | (~((~aElement0(tptp_fun_W1_24(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36))))),
% 1.17/1.38 inference(unit_resolution,[status(thm)],[37, 36])).
% 1.17/1.38 tff(39,plain,
% 1.17/1.38 (~((~aElement0(tptp_fun_W1_24(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36)))),
% 1.17/1.38 inference(unit_resolution,[status(thm)],[38, 25])).
% 1.17/1.38 tff(40,plain,
% 1.17/1.38 (((~aElement0(tptp_fun_W1_24(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36))) | (sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36)),
% 1.17/1.38 inference(tautology,[status(thm)],[])).
% 1.17/1.38 tff(41,plain,
% 1.17/1.38 (sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36),
% 1.17/1.38 inference(unit_resolution,[status(thm)],[40, 39])).
% 1.17/1.38 tff(42,plain,
% 1.17/1.38 (^[W0: $i] : refl((~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0))))))) <=> (~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0))))))))),
% 1.17/1.38 inference(bind,[status(th)],[])).
% 1.17/1.38 tff(43,plain,
% 1.17/1.38 (![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0)))))))),
% 1.17/1.38 inference(quant_intro,[status(thm)],[42])).
% 1.17/1.38 tff(44,plain,
% 1.17/1.38 (^[W0: $i] : rewrite((~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0))))))) <=> (~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0))))))))),
% 1.17/1.38 inference(bind,[status(th)],[])).
% 1.17/1.38 tff(45,plain,
% 1.17/1.38 (![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0)))))))),
% 1.17/1.38 inference(quant_intro,[status(thm)],[44])).
% 1.17/1.38 tff(46,plain,
% 1.17/1.38 (![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0)))))))),
% 1.17/1.38 inference(transitivity,[status(thm)],[45, 43])).
% 1.17/1.38 tff(47,plain,
% 1.17/1.38 (^[W0: $i] : trans(monotonicity(rewrite(((~aElementOf0(W0, slsdtgt0(xa))) | (aElement0(tptp_fun_W1_23(W0)) & (sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0))) <=> ((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))), rewrite((aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : (~(aElement0(W1) & (sdtasdt0(xa, W1) = W0)))) <=> (aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0))))), ((((~aElementOf0(W0, slsdtgt0(xa))) | (aElement0(tptp_fun_W1_23(W0)) & (sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0))) & (aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : (~(aElement0(W1) & (sdtasdt0(xa, W1) = W0))))) <=> (((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0))))) & (aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0))))))), rewrite((((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0))))) & (aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0))))) <=> (~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0)))))))), ((((~aElementOf0(W0, slsdtgt0(xa))) | (aElement0(tptp_fun_W1_23(W0)) & (sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0))) & (aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : (~(aElement0(W1) & (sdtasdt0(xa, W1) = W0))))) <=> (~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0)))))))))),
% 1.17/1.38 inference(bind,[status(th)],[])).
% 1.17/1.38 tff(48,plain,
% 1.17/1.38 (![W0: $i] : (((~aElementOf0(W0, slsdtgt0(xa))) | (aElement0(tptp_fun_W1_23(W0)) & (sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0))) & (aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : (~(aElement0(W1) & (sdtasdt0(xa, W1) = W0))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0)))))))),
% 1.17/1.38 inference(quant_intro,[status(thm)],[47])).
% 1.17/1.38 tff(49,plain,
% 1.17/1.38 (![W0: $i] : (aElementOf0(W0, slsdtgt0(xa)) <=> ?[W1: $i] : (aElement0(W1) & (sdtasdt0(xa, W1) = W0))) <=> ![W0: $i] : (aElementOf0(W0, slsdtgt0(xa)) <=> ?[W1: $i] : (aElement0(W1) & (sdtasdt0(xa, W1) = W0)))),
% 1.17/1.38 inference(rewrite,[status(thm)],[])).
% 1.17/1.38 tff(50,plain,
% 1.17/1.38 (((aSet0(xI) & ![W0: $i] : (aElementOf0(W0, xI) => (![W1: $i] : (aElementOf0(W1, xI) => aElementOf0(sdtpldt0(W0, W1), xI)) & ![W1: $i] : (aElement0(W1) => aElementOf0(sdtasdt0(W1, W0), xI))))) & aIdeal0(xI)) & ![W0: $i] : (aElementOf0(W0, slsdtgt0(xa)) <=> ?[W1: $i] : (aElement0(W1) & (sdtasdt0(xa, W1) = W0)))),
% 1.17/1.38 inference(and_elim,[status(thm)],[11])).
% 1.17/1.38 tff(51,plain,
% 1.17/1.38 (![W0: $i] : (aElementOf0(W0, slsdtgt0(xa)) <=> ?[W1: $i] : (aElement0(W1) & (sdtasdt0(xa, W1) = W0)))),
% 1.17/1.38 inference(and_elim,[status(thm)],[50])).
% 1.17/1.38 tff(52,plain,
% 1.17/1.38 (![W0: $i] : (aElementOf0(W0, slsdtgt0(xa)) <=> ?[W1: $i] : (aElement0(W1) & (sdtasdt0(xa, W1) = W0)))),
% 1.17/1.38 inference(modus_ponens,[status(thm)],[51, 49])).
% 1.17/1.38 tff(53,plain,(
% 1.17/1.38 ![W0: $i] : (((~aElementOf0(W0, slsdtgt0(xa))) | (aElement0(tptp_fun_W1_23(W0)) & (sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0))) & (aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : (~(aElement0(W1) & (sdtasdt0(xa, W1) = W0)))))),
% 1.17/1.38 inference(skolemize,[status(sab)],[52])).
% 1.17/1.38 tff(54,plain,
% 1.17/1.38 (![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0)))))))),
% 1.17/1.38 inference(modus_ponens,[status(thm)],[53, 48])).
% 1.17/1.38 tff(55,plain,
% 1.17/1.38 (![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0)))))))),
% 1.17/1.38 inference(modus_ponens,[status(thm)],[54, 46])).
% 1.17/1.38 tff(56,plain,
% 1.17/1.38 (((~![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0)))))))) | (~((~(aElementOf0(W0!37, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0!37))))) | (~((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37))))))))) <=> ((~![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0)))))))) | (~((~(aElementOf0(W0!37, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0!37))))) | (~((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37)))))))))),
% 1.17/1.38 inference(rewrite,[status(thm)],[])).
% 1.17/1.38 tff(57,plain,
% 1.17/1.38 ((~((~((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37)))))) | (~(aElementOf0(W0!37, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0!37))))))) <=> (~((~(aElementOf0(W0!37, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0!37))))) | (~((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37))))))))),
% 1.17/1.38 inference(rewrite,[status(thm)],[])).
% 1.17/1.38 tff(58,plain,
% 1.17/1.38 (((~![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0)))))))) | (~((~((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37)))))) | (~(aElementOf0(W0!37, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0!37)))))))) <=> ((~![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0)))))))) | (~((~(aElementOf0(W0!37, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0!37))))) | (~((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37)))))))))),
% 1.17/1.38 inference(monotonicity,[status(thm)],[57])).
% 1.17/1.38 tff(59,plain,
% 1.17/1.38 (((~![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0)))))))) | (~((~((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37)))))) | (~(aElementOf0(W0!37, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0!37)))))))) <=> ((~![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0)))))))) | (~((~(aElementOf0(W0!37, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0!37))))) | (~((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37)))))))))),
% 1.17/1.38 inference(transitivity,[status(thm)],[58, 56])).
% 1.17/1.38 tff(60,plain,
% 1.17/1.38 ((~![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0)))))))) | (~((~((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37)))))) | (~(aElementOf0(W0!37, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0!37)))))))),
% 1.17/1.38 inference(quant_inst,[status(thm)],[])).
% 1.17/1.38 tff(61,plain,
% 1.17/1.38 ((~![W0: $i] : (~((~((~aElementOf0(W0, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0)) = W0)))))) | (~(aElementOf0(W0, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0)))))))) | (~((~(aElementOf0(W0!37, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0!37))))) | (~((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37))))))))),
% 1.17/1.38 inference(modus_ponens,[status(thm)],[60, 59])).
% 1.17/1.38 tff(62,plain,
% 1.17/1.38 (~((~(aElementOf0(W0!37, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0!37))))) | (~((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37)))))))),
% 1.17/1.38 inference(unit_resolution,[status(thm)],[61, 55])).
% 1.17/1.38 tff(63,plain,
% 1.17/1.38 (((~(aElementOf0(W0!37, slsdtgt0(xa)) | ![W1: $i] : ((~aElement0(W1)) | (~(sdtasdt0(xa, W1) = W0!37))))) | (~((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37))))))) | ((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37)))))),
% 1.17/1.38 inference(tautology,[status(thm)],[])).
% 1.17/1.38 tff(64,plain,
% 1.17/1.38 ((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37))))),
% 1.17/1.38 inference(unit_resolution,[status(thm)],[63, 62])).
% 1.17/1.38 tff(65,plain,
% 1.17/1.38 (aElementOf0(W0!37, slsdtgt0(xa))),
% 1.17/1.38 inference(and_elim,[status(thm)],[35])).
% 1.17/1.38 tff(66,plain,
% 1.17/1.38 ((~((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37)))))) | (~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37))))),
% 1.17/1.38 inference(tautology,[status(thm)],[])).
% 1.17/1.38 tff(67,plain,
% 1.17/1.38 ((~((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W1_23(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37)))))) | (~((~aElement0(tptp_fun_W1_23(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37))))),
% 1.17/1.38 inference(unit_resolution,[status(thm)],[66, 65])).
% 1.17/1.38 tff(68,plain,
% 1.17/1.38 (~((~aElement0(tptp_fun_W1_23(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37)))),
% 1.17/1.38 inference(unit_resolution,[status(thm)],[67, 64])).
% 1.17/1.38 tff(69,plain,
% 1.17/1.38 (((~aElement0(tptp_fun_W1_23(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37))) | (sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37)),
% 1.17/1.38 inference(tautology,[status(thm)],[])).
% 1.17/1.38 tff(70,plain,
% 1.17/1.38 (sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37),
% 1.17/1.38 inference(unit_resolution,[status(thm)],[69, 68])).
% 1.17/1.38 tff(71,plain,
% 1.17/1.38 (sdtpldt0(sdtasdt0(xa, tptp_fun_W1_23(W0!37)), sdtasdt0(xb, tptp_fun_W1_24(W1!36))) = sdtpldt0(W0!37, W1!36)),
% 1.17/1.38 inference(monotonicity,[status(thm)],[70, 41])).
% 1.17/1.38 tff(72,plain,
% 1.17/1.38 (sdtpldt0(W0!37, W1!36) = sdtpldt0(sdtasdt0(xa, tptp_fun_W1_23(W0!37)), sdtasdt0(xb, tptp_fun_W1_24(W1!36)))),
% 1.17/1.38 inference(symmetry,[status(thm)],[71])).
% 1.17/1.38 tff(73,plain,
% 1.17/1.38 (sdtpldt0(W0!37, W1!36) = xu),
% 1.17/1.38 inference(and_elim,[status(thm)],[35])).
% 1.17/1.38 tff(74,plain,
% 1.17/1.38 (xu = sdtpldt0(W0!37, W1!36)),
% 1.17/1.38 inference(symmetry,[status(thm)],[73])).
% 1.17/1.38 tff(75,plain,
% 1.17/1.38 (xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W1_23(W0!37)), sdtasdt0(xb, tptp_fun_W1_24(W1!36)))),
% 1.17/1.38 inference(transitivity,[status(thm)],[74, 72])).
% 1.17/1.38 tff(76,plain,
% 1.17/1.38 (((~aElement0(tptp_fun_W1_24(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W1_24(W1!36)) = W1!36))) | aElement0(tptp_fun_W1_24(W1!36))),
% 1.17/1.38 inference(tautology,[status(thm)],[])).
% 1.17/1.38 tff(77,plain,
% 1.17/1.38 (aElement0(tptp_fun_W1_24(W1!36))),
% 1.17/1.38 inference(unit_resolution,[status(thm)],[76, 39])).
% 1.17/1.38 tff(78,plain,
% 1.17/1.38 (((~aElement0(tptp_fun_W1_23(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W1_23(W0!37)) = W0!37))) | aElement0(tptp_fun_W1_23(W0!37))),
% 1.17/1.38 inference(tautology,[status(thm)],[])).
% 1.17/1.38 tff(79,plain,
% 1.17/1.38 (aElement0(tptp_fun_W1_23(W0!37))),
% 1.17/1.38 inference(unit_resolution,[status(thm)],[78, 68])).
% 1.17/1.38 tff(80,plain,
% 1.17/1.38 (^[W0: $i, W1: $i] : refl(((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))) <=> ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))))),
% 1.17/1.38 inference(bind,[status(th)],[])).
% 1.17/1.38 tff(81,plain,
% 1.17/1.38 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))) <=> ![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 1.17/1.38 inference(quant_intro,[status(thm)],[80])).
% 1.17/1.38 tff(82,plain,
% 1.17/1.38 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite((aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))) <=> (~((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))))), ((~(aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))) <=> (~(~((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))))))), rewrite((~(~((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))))) <=> ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))), ((~(aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))) <=> ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))))),
% 1.17/1.38 inference(bind,[status(th)],[])).
% 1.17/1.38 tff(83,plain,
% 1.17/1.38 (![W0: $i, W1: $i] : (~(aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))) <=> ![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 1.17/1.38 inference(quant_intro,[status(thm)],[82])).
% 1.17/1.38 tff(84,plain,
% 1.17/1.38 ((~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))) <=> (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 1.17/1.38 inference(rewrite,[status(thm)],[])).
% 1.17/1.38 tff(85,plain,
% 1.17/1.38 ((~?[W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))) <=> (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 1.17/1.38 inference(rewrite,[status(thm)],[])).
% 1.17/1.38 tff(86,axiom,(~?[W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 1.17/1.38 tff(87,plain,
% 1.17/1.38 (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 1.17/1.38 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.17/1.38 tff(88,plain,
% 1.17/1.38 (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 1.17/1.38 inference(modus_ponens,[status(thm)],[87, 84])).
% 1.17/1.38 tff(89,plain,
% 1.17/1.38 (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 1.17/1.38 inference(modus_ponens,[status(thm)],[88, 84])).
% 1.17/1.38 tff(90,plain,
% 1.17/1.38 (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 1.17/1.38 inference(modus_ponens,[status(thm)],[89, 84])).
% 1.17/1.38 tff(91,plain,
% 1.17/1.38 (^[W0: $i, W1: $i] : refl($oeq((~(aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))), (~(aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))))),
% 1.17/1.38 inference(bind,[status(th)],[])).
% 1.17/1.38 tff(92,plain,(
% 1.17/1.38 ![W0: $i, W1: $i] : (~(aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 1.17/1.38 inference(nnf-neg,[status(sab)],[90, 91])).
% 1.17/1.38 tff(93,plain,
% 1.17/1.38 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 1.17/1.38 inference(modus_ponens,[status(thm)],[92, 83])).
% 1.17/1.38 tff(94,plain,
% 1.17/1.38 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 1.17/1.38 inference(modus_ponens,[status(thm)],[93, 81])).
% 1.17/1.38 tff(95,plain,
% 1.17/1.38 (((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | ((~aElement0(tptp_fun_W1_23(W0!37))) | (~aElement0(tptp_fun_W1_24(W1!36))) | (~(xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W1_23(W0!37)), sdtasdt0(xb, tptp_fun_W1_24(W1!36))))))) <=> ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | (~aElement0(tptp_fun_W1_23(W0!37))) | (~aElement0(tptp_fun_W1_24(W1!36))) | (~(xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W1_23(W0!37)), sdtasdt0(xb, tptp_fun_W1_24(W1!36))))))),
% 1.17/1.38 inference(rewrite,[status(thm)],[])).
% 1.17/1.38 tff(96,plain,
% 1.17/1.38 (((~aElement0(tptp_fun_W1_24(W1!36))) | (~aElement0(tptp_fun_W1_23(W0!37))) | (~(xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W1_23(W0!37)), sdtasdt0(xb, tptp_fun_W1_24(W1!36)))))) <=> ((~aElement0(tptp_fun_W1_23(W0!37))) | (~aElement0(tptp_fun_W1_24(W1!36))) | (~(xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W1_23(W0!37)), sdtasdt0(xb, tptp_fun_W1_24(W1!36))))))),
% 1.17/1.38 inference(rewrite,[status(thm)],[])).
% 1.17/1.38 tff(97,plain,
% 1.17/1.38 (((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | ((~aElement0(tptp_fun_W1_24(W1!36))) | (~aElement0(tptp_fun_W1_23(W0!37))) | (~(xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W1_23(W0!37)), sdtasdt0(xb, tptp_fun_W1_24(W1!36))))))) <=> ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | ((~aElement0(tptp_fun_W1_23(W0!37))) | (~aElement0(tptp_fun_W1_24(W1!36))) | (~(xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W1_23(W0!37)), sdtasdt0(xb, tptp_fun_W1_24(W1!36)))))))),
% 1.17/1.38 inference(monotonicity,[status(thm)],[96])).
% 1.17/1.38 tff(98,plain,
% 1.17/1.38 (((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | ((~aElement0(tptp_fun_W1_24(W1!36))) | (~aElement0(tptp_fun_W1_23(W0!37))) | (~(xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W1_23(W0!37)), sdtasdt0(xb, tptp_fun_W1_24(W1!36))))))) <=> ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | (~aElement0(tptp_fun_W1_23(W0!37))) | (~aElement0(tptp_fun_W1_24(W1!36))) | (~(xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W1_23(W0!37)), sdtasdt0(xb, tptp_fun_W1_24(W1!36))))))),
% 1.17/1.38 inference(transitivity,[status(thm)],[97, 95])).
% 1.17/1.38 tff(99,plain,
% 1.17/1.38 ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | ((~aElement0(tptp_fun_W1_24(W1!36))) | (~aElement0(tptp_fun_W1_23(W0!37))) | (~(xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W1_23(W0!37)), sdtasdt0(xb, tptp_fun_W1_24(W1!36))))))),
% 1.23/1.39 inference(quant_inst,[status(thm)],[])).
% 1.23/1.39 tff(100,plain,
% 1.23/1.39 ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | (~aElement0(tptp_fun_W1_23(W0!37))) | (~aElement0(tptp_fun_W1_24(W1!36))) | (~(xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W1_23(W0!37)), sdtasdt0(xb, tptp_fun_W1_24(W1!36)))))),
% 1.23/1.39 inference(modus_ponens,[status(thm)],[99, 98])).
% 1.23/1.39 tff(101,plain,
% 1.23/1.39 (~(xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W1_23(W0!37)), sdtasdt0(xb, tptp_fun_W1_24(W1!36))))),
% 1.23/1.39 inference(unit_resolution,[status(thm)],[100, 94, 79, 77])).
% 1.23/1.39 tff(102,plain,
% 1.23/1.39 ($false),
% 1.23/1.39 inference(unit_resolution,[status(thm)],[101, 75])).
% 1.23/1.39 % SZS output end Proof
% 1.23/1.39 % E exiting
%------------------------------------------------------------------------------