TSTP Solution File: NUM535+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM535+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 : Sun Sep 18 13:10:20 EDT 2022
% Result : Theorem 0.67s 0.71s
% Output : Proof 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM535+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 11:54:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.67/0.71 % SZS status Theorem
% 0.67/0.71 % SZS output start Proof
% 0.67/0.71 tff(xx_type, type, (
% 0.67/0.71 xx: $i)).
% 0.67/0.71 tff(tptp_fun_W3_2_type, type, (
% 0.67/0.71 tptp_fun_W3_2: ( $i * $i * $i ) > $i)).
% 0.67/0.71 tff(sdtmndt0_type, type, (
% 0.67/0.71 sdtmndt0: ( $i * $i ) > $i)).
% 0.67/0.71 tff(xS_type, type, (
% 0.67/0.71 xS: $i)).
% 0.67/0.71 tff(aElementOf0_type, type, (
% 0.67/0.71 aElementOf0: ( $i * $i ) > $o)).
% 0.67/0.71 tff(aElement0_type, type, (
% 0.67/0.71 aElement0: $i > $o)).
% 0.67/0.71 tff(tptp_fun_W2_1_type, type, (
% 0.67/0.71 tptp_fun_W2_1: ( $i * $i ) > $i)).
% 0.67/0.71 tff(sdtpldt0_type, type, (
% 0.67/0.71 sdtpldt0: ( $i * $i ) > $i)).
% 0.67/0.71 tff(aSet0_type, type, (
% 0.67/0.71 aSet0: $i > $o)).
% 0.67/0.71 tff(aSubsetOf0_type, type, (
% 0.67/0.71 aSubsetOf0: ( $i * $i ) > $o)).
% 0.67/0.71 tff(tptp_fun_W3_3_type, type, (
% 0.67/0.71 tptp_fun_W3_3: ( $i * $i * $i ) > $i)).
% 0.67/0.71 tff(1,assumption,(~(aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))))), introduced(assumption)).
% 0.67/0.71 tff(2,assumption,((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))), introduced(assumption)).
% 0.67/0.71 tff(3,plain,
% 0.67/0.71 (aSet0(xS) <=> aSet0(xS)),
% 0.67/0.71 inference(rewrite,[status(thm)],[])).
% 0.67/0.71 tff(4,axiom,(aSet0(xS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__617')).
% 0.67/0.71 tff(5,plain,
% 0.67/0.71 (aSet0(xS)),
% 0.67/0.71 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.67/0.71 tff(6,plain,
% 0.67/0.71 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.67/0.71 inference(bind,[status(th)],[])).
% 0.67/0.71 tff(7,plain,
% 0.67/0.71 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.67/0.71 inference(quant_intro,[status(thm)],[6])).
% 0.67/0.71 tff(8,plain,
% 0.67/0.71 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.67/0.71 inference(bind,[status(th)],[])).
% 0.67/0.71 tff(9,plain,
% 0.67/0.71 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.67/0.71 inference(quant_intro,[status(thm)],[8])).
% 0.67/0.71 tff(10,plain,
% 0.67/0.71 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.67/0.71 inference(transitivity,[status(thm)],[9, 7])).
% 0.67/0.71 tff(11,plain,
% 0.67/0.71 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.67/0.71 inference(rewrite,[status(thm)],[])).
% 0.67/0.71 tff(12,plain,
% 0.67/0.71 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, W0) => aElement0(W1)) <=> (aElement0(W1) | (~aElementOf0(W1, W0))))), (![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)) <=> ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))), ((aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> (aSet0(W0) => ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))), rewrite((aSet0(W0) => ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))), ((aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))))),
% 0.67/0.71 inference(bind,[status(th)],[])).
% 0.67/0.71 tff(13,plain,
% 0.67/0.71 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.67/0.71 inference(quant_intro,[status(thm)],[12])).
% 0.67/0.71 tff(14,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mEOfElem')).
% 0.67/0.71 tff(15,plain,
% 0.67/0.71 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.67/0.71 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.67/0.71 tff(16,plain,
% 0.67/0.71 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.67/0.71 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.67/0.71 tff(17,plain,(
% 0.67/0.71 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.67/0.71 inference(skolemize,[status(sab)],[16])).
% 0.67/0.71 tff(18,plain,
% 0.67/0.71 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.67/0.71 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.67/0.71 tff(19,plain,
% 0.67/0.71 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))),
% 0.67/0.71 inference(rewrite,[status(thm)],[])).
% 0.67/0.71 tff(20,plain,
% 0.67/0.71 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))),
% 0.67/0.71 inference(quant_inst,[status(thm)],[])).
% 0.67/0.71 tff(21,plain,
% 0.67/0.71 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 0.67/0.71 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.67/0.71 tff(22,plain,
% 0.67/0.71 (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 0.67/0.71 inference(unit_resolution,[status(thm)],[21, 18, 5])).
% 0.67/0.71 tff(23,plain,
% 0.67/0.71 (aElementOf0(xx, xS) <=> aElementOf0(xx, xS)),
% 0.67/0.71 inference(rewrite,[status(thm)],[])).
% 0.67/0.71 tff(24,axiom,(aElementOf0(xx, xS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__617_02')).
% 0.67/0.71 tff(25,plain,
% 0.67/0.71 (aElementOf0(xx, xS)),
% 0.67/0.71 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.67/0.71 tff(26,plain,
% 0.67/0.71 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(xx) | (~aElementOf0(xx, xS)))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(xx) | (~aElementOf0(xx, xS)))),
% 0.67/0.71 inference(rewrite,[status(thm)],[])).
% 0.67/0.71 tff(27,plain,
% 0.67/0.71 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(xx) | (~aElementOf0(xx, xS)))),
% 0.67/0.71 inference(quant_inst,[status(thm)],[])).
% 0.67/0.71 tff(28,plain,
% 0.67/0.71 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(xx) | (~aElementOf0(xx, xS))),
% 0.67/0.71 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.67/0.71 tff(29,plain,
% 0.67/0.71 (aElement0(xx)),
% 0.67/0.71 inference(unit_resolution,[status(thm)],[28, 25, 22])).
% 0.67/0.71 tff(30,plain,
% 0.67/0.71 (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite((~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))) <=> (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))), (![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))) <=> ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))), (((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)))))))))))))), rewrite(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)))))))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))), (((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))))),
% 0.67/0.71 inference(bind,[status(th)],[])).
% 0.67/0.71 tff(31,plain,
% 0.67/0.71 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))),
% 0.67/0.71 inference(quant_intro,[status(thm)],[30])).
% 0.67/0.71 tff(32,plain,
% 0.67/0.71 (^[W0: $i, W1: $i] : refl(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))))),
% 0.67/0.71 inference(bind,[status(th)],[])).
% 0.67/0.71 tff(33,plain,
% 0.67/0.71 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))))),
% 0.67/0.71 inference(quant_intro,[status(thm)],[32])).
% 0.67/0.71 tff(34,plain,
% 0.67/0.71 (^[W0: $i, W1: $i] : rewrite(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))))),
% 0.67/0.71 inference(bind,[status(th)],[])).
% 0.67/0.71 tff(35,plain,
% 0.67/0.71 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))))),
% 0.67/0.71 inference(quant_intro,[status(thm)],[34])).
% 0.67/0.71 tff(36,plain,
% 0.67/0.71 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))))),
% 0.67/0.71 inference(transitivity,[status(thm)],[35, 33])).
% 0.67/0.71 tff(37,plain,
% 0.67/0.71 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aSet0(W0) & aElement0(W1)) <=> (~((~aSet0(W0)) | (~aElement0(W1))))), ((~(aSet0(W0) & aElement0(W1))) <=> (~(~((~aSet0(W0)) | (~aElement0(W1))))))), rewrite((~(~((~aSet0(W0)) | (~aElement0(W1))))) <=> ((~aSet0(W0)) | (~aElement0(W1)))), ((~(aSet0(W0) & aElement0(W1))) <=> ((~aSet0(W0)) | (~aElement0(W1))))), quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(rewrite(((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) <=> ((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))), trans(monotonicity(trans(monotonicity(rewrite((aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))) <=> (~((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))), (((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))) <=> ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (~((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))), rewrite(((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (~((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))) <=> (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))), (((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))) <=> (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))), (((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))) <=> ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))), rewrite(((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))) <=> ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))), (((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))) <=> ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))), ((((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))) <=> (((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)))))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))), rewrite((((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)))))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) <=> (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))), ((((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))) <=> (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))))), (![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))) <=> ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))))), (((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))) <=> (((~aSet0(W0)) | (~aElement0(W1))) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))))), rewrite((((~aSet0(W0)) | (~aElement0(W1))) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))))), (((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))))))),
% 0.67/0.71 inference(bind,[status(th)],[])).
% 0.67/0.71 tff(38,plain,
% 0.67/0.71 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))))),
% 0.67/0.71 inference(quant_intro,[status(thm)],[37])).
% 0.67/0.71 tff(39,plain,
% 0.67/0.71 (^[W0: $i, W1: $i] : rewrite(((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))))),
% 0.67/0.71 inference(bind,[status(th)],[])).
% 0.67/0.71 tff(40,plain,
% 0.67/0.71 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))))),
% 0.67/0.71 inference(quant_intro,[status(thm)],[39])).
% 0.67/0.71 tff(41,plain,
% 0.67/0.71 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))),
% 0.67/0.71 inference(rewrite,[status(thm)],[])).
% 0.67/0.71 tff(42,plain,
% 0.67/0.71 (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite(((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1)))))) <=> ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))), (![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1)))))) <=> ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))), (((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1))))))) <=> ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1))))))))), rewrite(((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))), (((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))))),
% 0.67/0.71 inference(bind,[status(th)],[])).
% 0.67/0.71 tff(43,plain,
% 0.67/0.71 (![W0: $i, W1: $i] : ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))),
% 0.67/0.71 inference(quant_intro,[status(thm)],[42])).
% 0.67/0.71 tff(44,axiom,(![W0: $i, W1: $i] : ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefDiff')).
% 0.67/0.71 tff(45,plain,
% 0.67/0.71 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))),
% 0.67/0.71 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.67/0.71 tff(46,plain,
% 0.67/0.71 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))),
% 0.67/0.71 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.67/0.71 tff(47,plain,(
% 0.67/0.71 ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))))))),
% 0.67/0.71 inference(skolemize,[status(sab)],[46])).
% 0.67/0.71 tff(48,plain,
% 0.67/0.71 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))))),
% 0.67/0.71 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.67/0.71 tff(49,plain,
% 0.67/0.71 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))))),
% 0.67/0.71 inference(modus_ponens,[status(thm)],[48, 38])).
% 0.67/0.71 tff(50,plain,
% 0.67/0.71 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))))),
% 0.67/0.71 inference(modus_ponens,[status(thm)],[49, 36])).
% 0.67/0.71 tff(51,plain,
% 0.67/0.71 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))),
% 0.67/0.71 inference(modus_ponens,[status(thm)],[50, 31])).
% 0.67/0.71 tff(52,plain,
% 0.67/0.71 (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))) | (~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))))),
% 0.67/0.71 inference(rewrite,[status(thm)],[])).
% 0.67/0.71 tff(53,plain,
% 0.67/0.71 (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(54,plain,
% 0.67/0.72 (^[W2: $i] : rewrite((~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))) <=> (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))))),
% 0.67/0.72 inference(bind,[status(th)],[])).
% 0.67/0.72 tff(55,plain,
% 0.67/0.72 (![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))) <=> ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))),
% 0.67/0.72 inference(quant_intro,[status(thm)],[54])).
% 0.67/0.72 tff(56,plain,
% 0.67/0.72 (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))))),
% 0.67/0.72 inference(monotonicity,[status(thm)],[55])).
% 0.67/0.72 tff(57,plain,
% 0.67/0.72 (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))))),
% 0.67/0.72 inference(transitivity,[status(thm)],[56, 53])).
% 0.67/0.72 tff(58,plain,
% 0.67/0.72 (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))))),
% 0.67/0.72 inference(monotonicity,[status(thm)],[57])).
% 0.67/0.72 tff(59,plain,
% 0.67/0.72 (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))) | (~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))))),
% 0.67/0.72 inference(transitivity,[status(thm)],[58, 52])).
% 0.67/0.72 tff(60,plain,
% 0.67/0.72 ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))))),
% 0.67/0.72 inference(quant_inst,[status(thm)],[])).
% 0.67/0.72 tff(61,plain,
% 0.67/0.72 ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))) | (~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.67/0.72 tff(62,plain,
% 0.67/0.72 (![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))),
% 0.67/0.72 inference(unit_resolution,[status(thm)],[61, 51, 5, 29])).
% 0.67/0.72 tff(63,plain,
% 0.67/0.72 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(64,plain,
% 0.67/0.72 ((~((~((~aSet0(sdtmndt0(xS, xx))) | (sdtmndt0(xS, xx) = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), sdtmndt0(xS, xx)) <=> ((~aElement0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), xS)) | (tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS) = xx))))) | (~((~(sdtmndt0(xS, xx) = sdtmndt0(xS, xx))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))))) <=> (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(65,plain,
% 0.67/0.72 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) | (~((~((~aSet0(sdtmndt0(xS, xx))) | (sdtmndt0(xS, xx) = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), sdtmndt0(xS, xx)) <=> ((~aElement0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), xS)) | (tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS) = xx))))) | (~((~(sdtmndt0(xS, xx) = sdtmndt0(xS, xx))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))),
% 0.67/0.72 inference(monotonicity,[status(thm)],[64])).
% 0.67/0.72 tff(66,plain,
% 0.67/0.72 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) | (~((~((~aSet0(sdtmndt0(xS, xx))) | (sdtmndt0(xS, xx) = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), sdtmndt0(xS, xx)) <=> ((~aElement0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), xS)) | (tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS) = xx))))) | (~((~(sdtmndt0(xS, xx) = sdtmndt0(xS, xx))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))))),
% 0.67/0.72 inference(transitivity,[status(thm)],[65, 63])).
% 0.67/0.72 tff(67,plain,
% 0.67/0.72 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) | (~((~((~aSet0(sdtmndt0(xS, xx))) | (sdtmndt0(xS, xx) = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), sdtmndt0(xS, xx)) <=> ((~aElement0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), xS)) | (tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS) = xx))))) | (~((~(sdtmndt0(xS, xx) = sdtmndt0(xS, xx))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))),
% 0.67/0.72 inference(quant_inst,[status(thm)],[])).
% 0.67/0.72 tff(68,plain,
% 0.67/0.72 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx))))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))))))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))))),
% 0.77/0.72 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.77/0.72 tff(69,plain,
% 0.77/0.72 ($false),
% 0.77/0.72 inference(unit_resolution,[status(thm)],[68, 62, 2])).
% 0.77/0.72 tff(70,plain,(~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.72 tff(71,plain,
% 0.77/0.72 (((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))) | aSet0(sdtmndt0(xS, xx))),
% 0.77/0.72 inference(tautology,[status(thm)],[])).
% 0.77/0.72 tff(72,plain,
% 0.77/0.72 (aSet0(sdtmndt0(xS, xx))),
% 0.77/0.72 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.77/0.72 tff(73,plain,
% 0.77/0.72 (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite((~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))) <=> (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))), (![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))) <=> ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))), (((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))))))))))))))), rewrite(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))))))))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))), (((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))))),
% 0.77/0.72 inference(bind,[status(th)],[])).
% 0.77/0.72 tff(74,plain,
% 0.77/0.72 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))),
% 0.77/0.72 inference(quant_intro,[status(thm)],[73])).
% 0.77/0.72 tff(75,plain,
% 0.77/0.72 (^[W0: $i, W1: $i] : refl(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))))),
% 0.77/0.72 inference(bind,[status(th)],[])).
% 0.77/0.72 tff(76,plain,
% 0.77/0.72 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))))),
% 0.77/0.72 inference(quant_intro,[status(thm)],[75])).
% 0.77/0.72 tff(77,plain,
% 0.77/0.72 (^[W0: $i, W1: $i] : rewrite(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))))),
% 0.77/0.72 inference(bind,[status(th)],[])).
% 0.77/0.72 tff(78,plain,
% 0.77/0.72 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))))),
% 0.77/0.72 inference(quant_intro,[status(thm)],[77])).
% 0.77/0.72 tff(79,plain,
% 0.77/0.72 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))))),
% 0.77/0.72 inference(transitivity,[status(thm)],[78, 76])).
% 0.77/0.72 tff(80,plain,
% 0.77/0.72 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aSet0(W0) & aElement0(W1)) <=> (~((~aSet0(W0)) | (~aElement0(W1))))), ((~(aSet0(W0) & aElement0(W1))) <=> (~(~((~aSet0(W0)) | (~aElement0(W1))))))), rewrite((~(~((~aSet0(W0)) | (~aElement0(W1))))) <=> ((~aSet0(W0)) | (~aElement0(W1)))), ((~(aSet0(W0) & aElement0(W1))) <=> ((~aSet0(W0)) | (~aElement0(W1))))), quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(rewrite(((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) <=> ((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))), trans(monotonicity(trans(monotonicity(rewrite((aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))) <=> (~((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))), (((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (~((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))), rewrite(((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (~((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))) <=> (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))), (((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))), (((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))) <=> ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))), rewrite(((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))) <=> ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))), (((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))) <=> ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))), ((((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))) <=> (((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))))))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))), rewrite((((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))))))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) <=> (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))), ((((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))) <=> (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))))), (![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))) <=> ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))))), (((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) <=> (((~aSet0(W0)) | (~aElement0(W1))) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))))), rewrite((((~aSet0(W0)) | (~aElement0(W1))) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))))), (((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))))))),
% 0.77/0.73 inference(bind,[status(th)],[])).
% 0.77/0.73 tff(81,plain,
% 0.77/0.73 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))))),
% 0.77/0.73 inference(quant_intro,[status(thm)],[80])).
% 0.77/0.73 tff(82,plain,
% 0.77/0.73 (^[W0: $i, W1: $i] : rewrite(((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))),
% 0.77/0.73 inference(bind,[status(th)],[])).
% 0.77/0.73 tff(83,plain,
% 0.77/0.73 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))),
% 0.77/0.73 inference(quant_intro,[status(thm)],[82])).
% 0.77/0.73 tff(84,plain,
% 0.77/0.73 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))),
% 0.77/0.73 inference(rewrite,[status(thm)],[])).
% 0.77/0.73 tff(85,plain,
% 0.77/0.73 (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite(((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1)))))) <=> ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))), (![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1)))))) <=> ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))), (((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1))))))) <=> ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0))))))))), rewrite(((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))), (((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))))),
% 0.77/0.73 inference(bind,[status(th)],[])).
% 0.77/0.73 tff(86,plain,
% 0.77/0.73 (![W0: $i, W1: $i] : ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))),
% 0.77/0.73 inference(quant_intro,[status(thm)],[85])).
% 0.77/0.73 tff(87,axiom,(![W0: $i, W1: $i] : ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefCons')).
% 0.77/0.73 tff(88,plain,
% 0.77/0.73 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.77/0.73 tff(89,plain,
% 0.77/0.73 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.77/0.73 tff(90,plain,(
% 0.77/0.73 ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))),
% 0.77/0.73 inference(skolemize,[status(sab)],[89])).
% 0.77/0.73 tff(91,plain,
% 0.77/0.73 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.77/0.73 tff(92,plain,
% 0.77/0.73 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[91, 81])).
% 0.77/0.73 tff(93,plain,
% 0.77/0.73 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[92, 79])).
% 0.77/0.73 tff(94,plain,
% 0.77/0.73 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))),
% 0.77/0.73 inference(modus_ponens,[status(thm)],[93, 74])).
% 0.77/0.73 tff(95,plain,
% 0.77/0.73 (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | (~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))))),
% 0.77/0.73 inference(rewrite,[status(thm)],[])).
% 0.77/0.73 tff(96,plain,
% 0.77/0.73 (((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))))))))))))) <=> ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))))),
% 0.77/0.73 inference(rewrite,[status(thm)],[])).
% 0.77/0.73 tff(97,plain,
% 0.77/0.73 (^[W2: $i] : rewrite((~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))) <=> (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))))),
% 0.77/0.73 inference(bind,[status(th)],[])).
% 0.77/0.73 tff(98,plain,
% 0.77/0.73 (![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))) <=> ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))))))))))))),
% 0.77/0.73 inference(quant_intro,[status(thm)],[97])).
% 0.77/0.73 tff(99,plain,
% 0.77/0.73 (((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))))))))))))) <=> ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))))),
% 0.77/0.73 inference(monotonicity,[status(thm)],[98])).
% 0.77/0.73 tff(100,plain,
% 0.77/0.73 (((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))))))))))))) <=> ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))))),
% 0.77/0.73 inference(transitivity,[status(thm)],[99, 96])).
% 0.77/0.73 tff(101,plain,
% 0.77/0.73 (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))))))))))))))),
% 0.77/0.73 inference(monotonicity,[status(thm)],[100])).
% 0.77/0.73 tff(102,plain,
% 0.77/0.73 (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | (~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))))),
% 0.77/0.73 inference(transitivity,[status(thm)],[101, 95])).
% 0.77/0.73 tff(103,plain,
% 0.77/0.73 ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))))),
% 0.77/0.74 inference(quant_inst,[status(thm)],[])).
% 0.77/0.74 tff(104,plain,
% 0.77/0.74 ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | (~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))))))))))))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.77/0.74 tff(105,plain,
% 0.77/0.74 (![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))))))))))))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[104, 94, 29, 72])).
% 0.77/0.74 tff(106,plain,
% 0.77/0.74 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))))))))))))) | (~((~((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(xS = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W3: $i] : (aElementOf0(W3, xS) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))))))))))))),
% 0.77/0.74 inference(quant_inst,[status(thm)],[])).
% 0.77/0.74 tff(107,plain,
% 0.77/0.74 (~((~((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(xS = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W3: $i] : (aElementOf0(W3, xS) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx)))))))))))))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.77/0.74 tff(108,plain,
% 0.77/0.74 (((~((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(xS = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W3: $i] : (aElementOf0(W3, xS) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))))))))))) | ((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))),
% 0.77/0.74 inference(tautology,[status(thm)],[])).
% 0.77/0.74 tff(109,plain,
% 0.77/0.74 ((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.77/0.74 tff(110,plain,
% 0.77/0.74 ((~((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))))),
% 0.77/0.74 inference(tautology,[status(thm)],[])).
% 0.77/0.74 tff(111,plain,
% 0.77/0.74 ((~((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[110, 5, 1])).
% 0.77/0.74 tff(112,plain,
% 0.77/0.74 (xS = sdtpldt0(sdtmndt0(xS, xx), xx)),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[111, 109])).
% 0.77/0.74 tff(113,plain,
% 0.77/0.74 (sdtpldt0(sdtmndt0(xS, xx), xx) = xS),
% 0.77/0.74 inference(symmetry,[status(thm)],[112])).
% 0.77/0.74 tff(114,plain,
% 0.77/0.74 (aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) <=> aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx))),
% 0.77/0.74 inference(monotonicity,[status(thm)],[113, 112])).
% 0.77/0.74 tff(115,plain,
% 0.77/0.74 (aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS)),
% 0.77/0.74 inference(symmetry,[status(thm)],[114])).
% 0.77/0.74 tff(116,assumption,(xS = sdtpldt0(sdtmndt0(xS, xx), xx)), introduced(assumption)).
% 0.77/0.74 tff(117,plain,
% 0.77/0.74 (aSubsetOf0(xS, xS) <=> aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx))),
% 0.77/0.74 inference(monotonicity,[status(thm)],[116])).
% 0.77/0.74 tff(118,plain,
% 0.77/0.74 (aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) <=> aSubsetOf0(xS, xS)),
% 0.77/0.74 inference(symmetry,[status(thm)],[117])).
% 0.77/0.74 tff(119,plain,
% 0.77/0.74 ((~aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx))) <=> (~aSubsetOf0(xS, xS))),
% 0.77/0.74 inference(monotonicity,[status(thm)],[118])).
% 0.77/0.74 tff(120,assumption,(~aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx))), introduced(assumption)).
% 0.77/0.74 tff(121,plain,
% 0.77/0.74 (~aSubsetOf0(xS, xS)),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.77/0.74 tff(122,plain,
% 0.77/0.74 (^[W0: $i] : refl(((~aSet0(W0)) | aSubsetOf0(W0, W0)) <=> ((~aSet0(W0)) | aSubsetOf0(W0, W0)))),
% 0.77/0.74 inference(bind,[status(th)],[])).
% 0.77/0.74 tff(123,plain,
% 0.77/0.74 (![W0: $i] : ((~aSet0(W0)) | aSubsetOf0(W0, W0)) <=> ![W0: $i] : ((~aSet0(W0)) | aSubsetOf0(W0, W0))),
% 0.77/0.74 inference(quant_intro,[status(thm)],[122])).
% 0.77/0.74 tff(124,plain,
% 0.77/0.74 (![W0: $i] : ((~aSet0(W0)) | aSubsetOf0(W0, W0)) <=> ![W0: $i] : ((~aSet0(W0)) | aSubsetOf0(W0, W0))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(125,plain,
% 0.77/0.74 (^[W0: $i] : rewrite((aSet0(W0) => aSubsetOf0(W0, W0)) <=> ((~aSet0(W0)) | aSubsetOf0(W0, W0)))),
% 0.77/0.74 inference(bind,[status(th)],[])).
% 0.77/0.74 tff(126,plain,
% 0.77/0.74 (![W0: $i] : (aSet0(W0) => aSubsetOf0(W0, W0)) <=> ![W0: $i] : ((~aSet0(W0)) | aSubsetOf0(W0, W0))),
% 0.77/0.74 inference(quant_intro,[status(thm)],[125])).
% 0.77/0.74 tff(127,axiom,(![W0: $i] : (aSet0(W0) => aSubsetOf0(W0, W0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSubRefl')).
% 0.77/0.74 tff(128,plain,
% 0.77/0.74 (![W0: $i] : ((~aSet0(W0)) | aSubsetOf0(W0, W0))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.77/0.74 tff(129,plain,
% 0.77/0.74 (![W0: $i] : ((~aSet0(W0)) | aSubsetOf0(W0, W0))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.77/0.74 tff(130,plain,(
% 0.77/0.74 ![W0: $i] : ((~aSet0(W0)) | aSubsetOf0(W0, W0))),
% 0.77/0.74 inference(skolemize,[status(sab)],[129])).
% 0.77/0.74 tff(131,plain,
% 0.77/0.74 (![W0: $i] : ((~aSet0(W0)) | aSubsetOf0(W0, W0))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.77/0.74 tff(132,plain,
% 0.77/0.74 (((~![W0: $i] : ((~aSet0(W0)) | aSubsetOf0(W0, W0))) | ((~aSet0(xS)) | aSubsetOf0(xS, xS))) <=> ((~![W0: $i] : ((~aSet0(W0)) | aSubsetOf0(W0, W0))) | (~aSet0(xS)) | aSubsetOf0(xS, xS))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(133,plain,
% 0.77/0.74 ((~![W0: $i] : ((~aSet0(W0)) | aSubsetOf0(W0, W0))) | ((~aSet0(xS)) | aSubsetOf0(xS, xS))),
% 0.77/0.74 inference(quant_inst,[status(thm)],[])).
% 0.77/0.74 tff(134,plain,
% 0.77/0.74 ((~![W0: $i] : ((~aSet0(W0)) | aSubsetOf0(W0, W0))) | (~aSet0(xS)) | aSubsetOf0(xS, xS)),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.77/0.74 tff(135,plain,
% 0.77/0.74 (aSubsetOf0(xS, xS)),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[134, 131, 5])).
% 0.77/0.74 tff(136,plain,
% 0.77/0.74 ($false),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[135, 121])).
% 0.77/0.74 tff(137,plain,((~(xS = sdtpldt0(sdtmndt0(xS, xx), xx))) | aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.74 tff(138,plain,
% 0.77/0.74 (aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[137, 112])).
% 0.77/0.74 tff(139,plain,
% 0.77/0.74 (aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS)),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[138, 115])).
% 0.77/0.74 tff(140,assumption,(~aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS)), introduced(assumption)).
% 0.77/0.74 tff(141,plain,
% 0.77/0.74 ($false),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.77/0.74 tff(142,plain,(aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS) | (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.74 tff(143,plain,
% 0.77/0.74 (aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS)),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[142, 1])).
% 0.77/0.74 tff(144,plain,
% 0.77/0.74 ((~(~((~aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx))) | (~aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS))))) <=> ((~aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx))) | (~aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS)))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(145,plain,
% 0.77/0.74 ((aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) & aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS)) <=> (~((~aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx))) | (~aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS))))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(146,plain,
% 0.77/0.74 ((~(aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) & aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS))) <=> (~(~((~aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx))) | (~aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS)))))),
% 0.77/0.74 inference(monotonicity,[status(thm)],[145])).
% 0.77/0.74 tff(147,plain,
% 0.77/0.74 ((~(aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) & aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS))) <=> ((~aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx))) | (~aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS)))),
% 0.77/0.74 inference(transitivity,[status(thm)],[146, 144])).
% 0.77/0.74 tff(148,plain,
% 0.77/0.74 ((~(aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) & aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS))) <=> (~(aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) & aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS)))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(149,axiom,(~(aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) & aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.77/0.74 tff(150,plain,
% 0.77/0.74 (~(aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx)) & aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.77/0.74 tff(151,plain,
% 0.77/0.74 ((~aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx))) | (~aSubsetOf0(sdtpldt0(sdtmndt0(xS, xx), xx), xS))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[150, 147])).
% 0.77/0.74 tff(152,plain,
% 0.77/0.74 (~aSubsetOf0(xS, sdtpldt0(sdtmndt0(xS, xx), xx))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[151, 143])).
% 0.77/0.74 tff(153,plain,
% 0.77/0.74 (~(xS = sdtpldt0(sdtmndt0(xS, xx), xx))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[137, 152])).
% 0.77/0.74 tff(154,plain,
% 0.77/0.74 (~((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[110, 5, 1, 153])).
% 0.77/0.74 tff(155,plain,
% 0.77/0.74 ((~((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))) | (~((~(xS = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W3: $i] : (aElementOf0(W3, xS) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))))))))))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[108, 154])).
% 0.77/0.74 tff(156,plain,
% 0.77/0.74 ($false),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[106, 105, 155])).
% 0.77/0.74 tff(157,plain,(aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.74 tff(158,assumption,(aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))), introduced(assumption)).
% 0.77/0.74 tff(159,assumption,(~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))), introduced(assumption)).
% 0.77/0.74 tff(160,plain,
% 0.77/0.74 (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) | aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))),
% 0.77/0.74 inference(tautology,[status(thm)],[])).
% 0.77/0.74 tff(161,plain,
% 0.77/0.74 ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.77/0.74 tff(162,plain,
% 0.77/0.74 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)))),
% 0.77/0.74 inference(rewrite,[status(thm)],[])).
% 0.77/0.74 tff(163,plain,
% 0.77/0.74 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)))),
% 0.77/0.74 inference(quant_inst,[status(thm)],[])).
% 0.77/0.74 tff(164,plain,
% 0.77/0.74 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))),
% 0.77/0.74 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.77/0.74 tff(165,plain,
% 0.77/0.74 (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[164, 22])).
% 0.77/0.74 tff(166,plain,
% 0.77/0.74 (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[165, 159])).
% 0.77/0.74 tff(167,plain,
% 0.77/0.74 ((~(aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))))) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) | (~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))))),
% 0.77/0.74 inference(tautology,[status(thm)],[])).
% 0.77/0.74 tff(168,plain,
% 0.77/0.74 ($false),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[167, 166, 161, 158])).
% 0.77/0.74 tff(169,plain,(aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~(aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.74 tff(170,plain,
% 0.77/0.74 (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))),
% 0.77/0.74 inference(unit_resolution,[status(thm)],[169, 157])).
% 0.77/0.74 tff(171,plain,
% 0.77/0.74 (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(xS)) | (~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | (~aSet0(xS)) | (~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))))))))))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(172,plain,
% 0.77/0.75 (((~aSet0(xS)) | (~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(W3, xS)))))))))))))) <=> ((~aSet0(xS)) | (~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))))))))))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(173,plain,
% 0.77/0.75 (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(xS)) | (~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(W3, xS))))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(xS)) | (~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))))))))))))))),
% 0.77/0.75 inference(monotonicity,[status(thm)],[172])).
% 0.77/0.75 tff(174,plain,
% 0.77/0.75 (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(xS)) | (~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(W3, xS))))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | (~aSet0(xS)) | (~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))))))))))),
% 0.77/0.75 inference(transitivity,[status(thm)],[173, 171])).
% 0.77/0.75 tff(175,plain,
% 0.77/0.75 ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(xS)) | (~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(W3, xS))))))))))))))),
% 0.77/0.75 inference(quant_inst,[status(thm)],[])).
% 0.77/0.75 tff(176,plain,
% 0.77/0.75 ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | (~aSet0(xS)) | (~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))))))))))))),
% 0.77/0.75 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.77/0.75 tff(177,plain,
% 0.77/0.75 ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))))))))))))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[176, 94, 5])).
% 0.77/0.75 tff(178,plain,
% 0.77/0.75 (![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))))))))))))),
% 0.77/0.75 inference(unit_resolution,[status(thm)],[177, 170])).
% 0.77/0.75 tff(179,plain,
% 0.77/0.75 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))))))))))))) | (~((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))) | (~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))))))))))))) | (~((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))) | (~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(180,plain,
% 0.77/0.75 ((~((~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> ((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))))))))) <=> (~((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))) | (~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))))),
% 0.77/0.75 inference(rewrite,[status(thm)],[])).
% 0.77/0.75 tff(181,plain,
% 0.77/0.75 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))))))))))))) | (~((~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> ((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))))))))))))) | (~((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))) | (~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))),
% 0.77/0.76 inference(monotonicity,[status(thm)],[180])).
% 0.77/0.76 tff(182,plain,
% 0.77/0.76 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))))))))))))) | (~((~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> ((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))))))))))))) | (~((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))) | (~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))),
% 0.77/0.76 inference(transitivity,[status(thm)],[181, 179])).
% 0.77/0.76 tff(183,plain,
% 0.77/0.76 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))))))))))))) | (~((~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> ((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))))))))))))),
% 0.77/0.76 inference(quant_inst,[status(thm)],[])).
% 0.77/0.76 tff(184,plain,
% 0.77/0.76 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | aElementOf0(tptp_fun_W3_2(W2, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))))))))))))) | (~((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))) | (~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.77/0.76 tff(185,plain,
% 0.77/0.76 (~((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))) | (~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[184, 178])).
% 0.77/0.76 tff(186,plain,
% 0.77/0.76 (((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))) | (~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))) | ![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))),
% 0.77/0.76 inference(tautology,[status(thm)],[])).
% 0.77/0.76 tff(187,plain,
% 0.77/0.76 (![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.77/0.76 tff(188,plain,
% 0.77/0.76 ((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))) | (aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~(aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS) | (tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))),
% 0.77/0.76 inference(quant_inst,[status(thm)],[])).
% 0.77/0.76 tff(189,plain,
% 0.77/0.76 (aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~(aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS) | (tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))))),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[188, 187])).
% 0.77/0.76 tff(190,assumption,(~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)), introduced(assumption)).
% 0.77/0.76 tff(191,plain,
% 0.77/0.76 (((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))) | (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) <=> ((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))) | (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))),
% 0.77/0.76 inference(rewrite,[status(thm)],[])).
% 0.77/0.76 tff(192,plain,
% 0.77/0.76 ((aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~(aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))))) <=> (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))),
% 0.77/0.76 inference(rewrite,[status(thm)],[])).
% 0.77/0.76 tff(193,plain,
% 0.77/0.76 (((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))) | (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~(aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))) <=> ((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))) | (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))),
% 0.77/0.76 inference(monotonicity,[status(thm)],[192])).
% 0.77/0.76 tff(194,plain,
% 0.77/0.76 (((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))) | (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~(aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))) <=> ((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))) | (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))),
% 0.77/0.77 inference(transitivity,[status(thm)],[193, 191])).
% 0.77/0.77 tff(195,plain,
% 0.77/0.77 ((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))) | (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~(aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))),
% 0.77/0.77 inference(quant_inst,[status(thm)],[])).
% 0.77/0.77 tff(196,plain,
% 0.77/0.77 ((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))) | (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))),
% 0.77/0.77 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.77/0.77 tff(197,plain,
% 0.77/0.77 (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[196, 187])).
% 0.77/0.77 tff(198,plain,
% 0.77/0.77 ((~(aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))),
% 0.77/0.77 inference(tautology,[status(thm)],[])).
% 0.77/0.77 tff(199,plain,
% 0.77/0.77 ((~(aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[198, 170])).
% 0.77/0.77 tff(200,plain,
% 0.77/0.77 (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[199, 197])).
% 0.77/0.77 tff(201,assumption,(![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS))), introduced(assumption)).
% 0.77/0.77 tff(202,plain,
% 0.77/0.77 (((~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS))) | ((~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) <=> ((~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))),
% 0.77/0.77 inference(rewrite,[status(thm)],[])).
% 0.77/0.77 tff(203,plain,
% 0.77/0.77 ((~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS))) | ((~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))),
% 0.77/0.77 inference(quant_inst,[status(thm)],[])).
% 0.77/0.77 tff(204,plain,
% 0.77/0.77 ((~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.77/0.77 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.77/0.77 tff(205,plain,
% 0.77/0.77 ($false),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[204, 190, 201, 200])).
% 0.77/0.77 tff(206,plain,((~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS))) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.77 tff(207,plain,
% 0.77/0.77 (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[206, 190])).
% 0.77/0.77 tff(208,plain,
% 0.77/0.77 (((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS)))) | ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS))),
% 0.77/0.77 inference(tautology,[status(thm)],[])).
% 0.77/0.77 tff(209,plain,
% 0.77/0.77 ((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS)))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[208, 207])).
% 0.77/0.77 tff(210,plain,
% 0.77/0.77 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))))))))),
% 0.77/0.77 inference(bind,[status(th)],[])).
% 0.77/0.77 tff(211,plain,
% 0.77/0.77 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 0.77/0.77 inference(quant_intro,[status(thm)],[210])).
% 0.77/0.77 tff(212,plain,
% 0.77/0.77 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 0.77/0.77 inference(bind,[status(th)],[])).
% 0.77/0.77 tff(213,plain,
% 0.77/0.77 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.82/0.77 inference(quant_intro,[status(thm)],[212])).
% 0.82/0.77 tff(214,plain,
% 0.82/0.77 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 0.82/0.77 inference(bind,[status(th)],[])).
% 0.82/0.77 tff(215,plain,
% 0.82/0.77 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.82/0.77 inference(quant_intro,[status(thm)],[214])).
% 0.82/0.77 tff(216,plain,
% 0.82/0.77 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.82/0.77 inference(transitivity,[status(thm)],[215, 213])).
% 0.82/0.77 tff(217,plain,
% 0.82/0.77 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 0.82/0.77 inference(bind,[status(th)],[])).
% 0.82/0.77 tff(218,plain,
% 0.82/0.77 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.82/0.77 inference(quant_intro,[status(thm)],[217])).
% 0.82/0.77 tff(219,plain,
% 0.82/0.77 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))),
% 0.82/0.77 inference(bind,[status(th)],[])).
% 0.82/0.77 tff(220,plain,
% 0.82/0.77 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))),
% 0.82/0.77 inference(quant_intro,[status(thm)],[219])).
% 0.82/0.77 tff(221,plain,
% 0.82/0.77 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.82/0.77 inference(rewrite,[status(thm)],[])).
% 0.82/0.77 tff(222,plain,
% 0.82/0.77 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))) <=> (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), (![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))) <=> ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), ((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))), rewrite((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))) <=> ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), ((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))))),
% 0.82/0.77 inference(bind,[status(th)],[])).
% 0.82/0.77 tff(223,plain,
% 0.82/0.77 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.82/0.77 inference(quant_intro,[status(thm)],[222])).
% 0.82/0.77 tff(224,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefSub')).
% 0.82/0.77 tff(225,plain,
% 0.82/0.77 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.82/0.77 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.82/0.77 tff(226,plain,
% 0.82/0.77 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.82/0.77 inference(modus_ponens,[status(thm)],[225, 221])).
% 0.82/0.77 tff(227,plain,(
% 0.82/0.77 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))),
% 0.82/0.77 inference(skolemize,[status(sab)],[226])).
% 0.82/0.77 tff(228,plain,
% 0.82/0.77 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))),
% 0.82/0.77 inference(modus_ponens,[status(thm)],[227, 220])).
% 0.82/0.77 tff(229,plain,
% 0.82/0.77 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.82/0.77 inference(modus_ponens,[status(thm)],[228, 218])).
% 0.82/0.77 tff(230,plain,
% 0.82/0.77 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.82/0.77 inference(modus_ponens,[status(thm)],[229, 216])).
% 0.82/0.77 tff(231,plain,
% 0.82/0.77 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 0.82/0.77 inference(modus_ponens,[status(thm)],[230, 211])).
% 0.82/0.77 tff(232,plain,
% 0.82/0.77 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))),
% 0.82/0.77 inference(rewrite,[status(thm)],[])).
% 0.82/0.77 tff(233,plain,
% 0.82/0.77 (((~aSet0(xS)) | ![W1: $i] : (~((~(aSubsetOf0(W1, xS) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) <=> ((~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))),
% 0.82/0.77 inference(rewrite,[status(thm)],[])).
% 0.82/0.77 tff(234,plain,
% 0.82/0.77 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~(aSubsetOf0(W1, xS) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))))),
% 0.82/0.77 inference(monotonicity,[status(thm)],[233])).
% 0.82/0.77 tff(235,plain,
% 0.82/0.77 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~(aSubsetOf0(W1, xS) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))),
% 0.82/0.77 inference(transitivity,[status(thm)],[234, 232])).
% 0.82/0.77 tff(236,plain,
% 0.82/0.77 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~(aSubsetOf0(W1, xS) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))),
% 0.82/0.77 inference(quant_inst,[status(thm)],[])).
% 0.82/0.77 tff(237,plain,
% 0.82/0.77 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))),
% 0.82/0.77 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.82/0.77 tff(238,plain,
% 0.82/0.77 (![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))),
% 0.82/0.77 inference(unit_resolution,[status(thm)],[237, 231, 5])).
% 0.82/0.77 tff(239,plain,
% 0.82/0.77 (((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS))) | aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~((~aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)) | (~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS)))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS))) | aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~((~aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)) | (~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS))))))))))),
% 0.82/0.77 inference(rewrite,[status(thm)],[])).
% 0.82/0.77 tff(240,plain,
% 0.82/0.77 ((~((~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS))))) | (~((~aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)) | (~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS))))))))) <=> (~((~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS))) | aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~((~aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)) | (~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS)))))))))),
% 0.82/0.77 inference(rewrite,[status(thm)],[])).
% 0.82/0.77 tff(241,plain,
% 0.82/0.77 (((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS))))) | (~((~aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)) | (~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS)))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS))) | aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~((~aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)) | (~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS))))))))))),
% 0.82/0.77 inference(monotonicity,[status(thm)],[240])).
% 0.82/0.77 tff(242,plain,
% 0.82/0.77 (((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS))))) | (~((~aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)) | (~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS)))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS))) | aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~((~aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)) | (~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS))))))))))),
% 0.82/0.78 inference(transitivity,[status(thm)],[241, 239])).
% 0.82/0.78 tff(243,plain,
% 0.82/0.78 ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS))))) | (~((~aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)) | (~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS)))))))))),
% 0.82/0.78 inference(quant_inst,[status(thm)],[])).
% 0.82/0.78 tff(244,plain,
% 0.82/0.78 ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS))) | aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~((~aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)) | (~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS)))))))))),
% 0.82/0.78 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.82/0.78 tff(245,plain,
% 0.82/0.78 (~((~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS))) | aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~((~aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)) | (~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS))))))))),
% 0.82/0.78 inference(unit_resolution,[status(thm)],[244, 238])).
% 0.82/0.78 tff(246,plain,
% 0.82/0.78 (((~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS))) | aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~((~aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)) | (~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS)))))))) | ((~aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)) | (~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS))))))),
% 0.82/0.78 inference(tautology,[status(thm)],[])).
% 0.82/0.78 tff(247,plain,
% 0.82/0.78 ((~aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)) | (~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS)))))),
% 0.82/0.78 inference(unit_resolution,[status(thm)],[246, 245])).
% 0.82/0.78 tff(248,plain,
% 0.82/0.78 ((~((~aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)) | (~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS))))))) | (~aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)) | (~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS)))))),
% 0.82/0.78 inference(tautology,[status(thm)],[])).
% 0.82/0.78 tff(249,plain,
% 0.82/0.78 ((~aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)) | (~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS)))))),
% 0.82/0.78 inference(unit_resolution,[status(thm)],[248, 247])).
% 0.82/0.78 tff(250,plain,
% 0.82/0.78 (~aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)),
% 0.82/0.78 inference(unit_resolution,[status(thm)],[249, 209])).
% 0.82/0.78 tff(251,plain,
% 0.82/0.78 (((~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS))) | aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~((~aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)) | (~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(W2, xS)))))))) | ((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS))) | aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))),
% 0.82/0.78 inference(tautology,[status(thm)],[])).
% 0.82/0.78 tff(252,plain,
% 0.82/0.78 ((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS))) | aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)),
% 0.82/0.78 inference(unit_resolution,[status(thm)],[251, 245])).
% 0.82/0.78 tff(253,plain,
% 0.82/0.78 (((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(W3)) | (~(aElementOf0(W3, xS) | (W3 = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))) | (~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))) | aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))),
% 0.82/0.78 inference(tautology,[status(thm)],[])).
% 0.82/0.78 tff(254,plain,
% 0.82/0.78 (aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))),
% 0.82/0.78 inference(unit_resolution,[status(thm)],[253, 185])).
% 0.82/0.78 tff(255,plain,
% 0.82/0.78 ((~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS))) | aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS))) | aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)),
% 0.82/0.78 inference(tautology,[status(thm)],[])).
% 0.82/0.78 tff(256,plain,
% 0.82/0.78 ((~((~aSet0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS))) | aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS))) | aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)),
% 0.82/0.78 inference(unit_resolution,[status(thm)],[255, 254])).
% 0.82/0.78 tff(257,plain,
% 0.82/0.78 ((~((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS))) | aSubsetOf0(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS)),
% 0.82/0.78 inference(unit_resolution,[status(thm)],[256, 252])).
% 0.82/0.78 tff(258,plain,
% 0.82/0.78 (~((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS))),
% 0.82/0.78 inference(unit_resolution,[status(thm)],[257, 250])).
% 0.82/0.78 tff(259,plain,
% 0.82/0.78 (((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS)) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))),
% 0.82/0.78 inference(tautology,[status(thm)],[])).
% 0.82/0.78 tff(260,plain,
% 0.82/0.78 (aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))),
% 0.82/0.78 inference(unit_resolution,[status(thm)],[259, 258])).
% 0.82/0.78 tff(261,plain,
% 0.82/0.78 ((~(aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~(aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS) | (tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))) | (~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (~((~aElement0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~(aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS) | (tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))))),
% 0.82/0.78 inference(tautology,[status(thm)],[])).
% 0.82/0.78 tff(262,plain,
% 0.82/0.78 ((~(aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) <=> (~((~aElement0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~(aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS) | (tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))))) | (~((~aElement0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~(aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS) | (tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))))),
% 0.82/0.78 inference(unit_resolution,[status(thm)],[261, 260])).
% 0.82/0.78 tff(263,plain,
% 0.82/0.78 (~((~aElement0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~(aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS) | (tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))))),
% 0.82/0.78 inference(unit_resolution,[status(thm)],[262, 189])).
% 0.82/0.78 tff(264,plain,
% 0.82/0.78 (((~aElement0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~(aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS) | (tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))))) | (aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS) | (tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))),
% 0.82/0.78 inference(tautology,[status(thm)],[])).
% 0.82/0.78 tff(265,plain,
% 0.82/0.78 (aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS) | (tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))),
% 0.82/0.78 inference(unit_resolution,[status(thm)],[264, 263])).
% 0.82/0.78 tff(266,plain,
% 0.82/0.78 (((~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS)) | (~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS))),
% 0.82/0.78 inference(tautology,[status(thm)],[])).
% 0.82/0.78 tff(267,plain,
% 0.82/0.78 (~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS)),
% 0.82/0.78 inference(unit_resolution,[status(thm)],[266, 258])).
% 0.82/0.78 tff(268,plain,
% 0.82/0.78 ((~(aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS) | (tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS) | (tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))),
% 0.82/0.78 inference(tautology,[status(thm)],[])).
% 0.82/0.78 tff(269,plain,
% 0.82/0.78 ((~(aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS) | (tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))))) | (tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))),
% 0.82/0.78 inference(unit_resolution,[status(thm)],[268, 267])).
% 0.82/0.78 tff(270,plain,
% 0.82/0.78 (tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) = tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[269, 265])).
% 0.82/0.79 tff(271,plain,
% 0.82/0.79 (aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtmndt0(xS, xx)) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))),
% 0.82/0.79 inference(monotonicity,[status(thm)],[270])).
% 0.82/0.79 tff(272,plain,
% 0.82/0.79 (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)) <=> aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtmndt0(xS, xx))),
% 0.82/0.79 inference(symmetry,[status(thm)],[271])).
% 0.82/0.79 tff(273,assumption,(~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))), introduced(assumption)).
% 0.82/0.79 tff(274,plain,
% 0.82/0.79 (~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[167, 190, 158])).
% 0.82/0.79 tff(275,plain,
% 0.82/0.79 (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) | ((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))),
% 0.82/0.79 inference(tautology,[status(thm)],[])).
% 0.82/0.79 tff(276,plain,
% 0.82/0.79 ((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[275, 274])).
% 0.82/0.79 tff(277,plain,
% 0.82/0.79 ((~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))),
% 0.82/0.79 inference(tautology,[status(thm)],[])).
% 0.82/0.79 tff(278,plain,
% 0.82/0.79 (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[277, 276, 273])).
% 0.82/0.79 tff(279,plain,
% 0.82/0.79 (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) <=> aElementOf0(xx, xS)),
% 0.82/0.79 inference(monotonicity,[status(thm)],[278])).
% 0.82/0.79 tff(280,plain,
% 0.82/0.79 (aElementOf0(xx, xS) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.82/0.79 inference(symmetry,[status(thm)],[279])).
% 0.82/0.79 tff(281,plain,
% 0.82/0.79 (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.82/0.79 inference(modus_ponens,[status(thm)],[25, 280])).
% 0.82/0.79 tff(282,plain,
% 0.82/0.79 ($false),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[190, 281])).
% 0.82/0.79 tff(283,plain,(aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)) | (~(aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))))), inference(lemma,lemma(discharge,[]))).
% 0.82/0.79 tff(284,plain,
% 0.82/0.79 (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[283, 157])).
% 0.82/0.79 tff(285,plain,
% 0.82/0.79 (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[284, 190])).
% 0.82/0.79 tff(286,plain,
% 0.82/0.79 (aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtmndt0(xS, xx))),
% 0.82/0.79 inference(modus_ponens,[status(thm)],[285, 272])).
% 0.82/0.79 tff(287,plain,
% 0.82/0.79 (((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)))))) | ![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))),
% 0.82/0.79 inference(tautology,[status(thm)],[])).
% 0.82/0.79 tff(288,plain,
% 0.82/0.79 (![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[287, 70])).
% 0.82/0.79 tff(289,plain,
% 0.82/0.79 ((~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))) | (aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtmndt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS)) | (tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) = xx))))),
% 0.82/0.79 inference(quant_inst,[status(thm)],[])).
% 0.82/0.79 tff(290,plain,
% 0.82/0.79 (aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtmndt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS)) | (tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) = xx)))),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[289, 288])).
% 0.82/0.79 tff(291,plain,
% 0.82/0.79 (((~aElement0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS)) | (tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) = xx)) | aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS)),
% 0.82/0.79 inference(tautology,[status(thm)],[])).
% 0.82/0.79 tff(292,plain,
% 0.82/0.79 ((~aElement0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS)) | (tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) = xx)),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[291, 267])).
% 0.82/0.79 tff(293,plain,
% 0.82/0.79 ((~(aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtmndt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS)) | (tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) = xx))))) | (~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtmndt0(xS, xx))) | (~((~aElement0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS)) | (tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) = xx)))),
% 0.82/0.79 inference(tautology,[status(thm)],[])).
% 0.82/0.79 tff(294,plain,
% 0.82/0.79 ((~(aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtmndt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), xS)) | (tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS) = xx))))) | (~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtmndt0(xS, xx)))),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[293, 292])).
% 0.82/0.79 tff(295,plain,
% 0.82/0.79 (~aElementOf0(tptp_fun_W2_1(sdtpldt0(xS, tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))), xS), sdtmndt0(xS, xx))),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[294, 290])).
% 0.82/0.79 tff(296,plain,
% 0.82/0.79 ($false),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[295, 286])).
% 0.82/0.79 tff(297,plain,(aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)), inference(lemma,lemma(discharge,[]))).
% 0.82/0.79 tff(298,plain,
% 0.82/0.79 ((~(aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))),
% 0.82/0.79 inference(tautology,[status(thm)],[])).
% 0.82/0.79 tff(299,plain,
% 0.82/0.79 ((~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[298, 157])).
% 0.82/0.79 tff(300,plain,
% 0.82/0.79 ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[299, 297])).
% 0.82/0.79 tff(301,plain,
% 0.82/0.79 ((~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))) | (~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))),
% 0.82/0.79 inference(tautology,[status(thm)],[])).
% 0.82/0.79 tff(302,plain,
% 0.82/0.79 ((~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[301, 170])).
% 0.82/0.79 tff(303,plain,
% 0.82/0.79 (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[302, 300])).
% 0.82/0.79 tff(304,plain,
% 0.82/0.79 (((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))) | (~(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx))),
% 0.82/0.79 inference(tautology,[status(thm)],[])).
% 0.82/0.79 tff(305,plain,
% 0.82/0.79 (~(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[304, 303])).
% 0.82/0.79 tff(306,plain,
% 0.82/0.79 ((~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx))) | (~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)),
% 0.82/0.79 inference(tautology,[status(thm)],[])).
% 0.82/0.79 tff(307,plain,
% 0.82/0.79 (~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx))),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[306, 297, 170, 305])).
% 0.82/0.79 tff(308,plain,
% 0.82/0.79 (((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))),
% 0.82/0.79 inference(tautology,[status(thm)],[])).
% 0.82/0.79 tff(309,plain,
% 0.82/0.79 (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[308, 303])).
% 0.82/0.79 tff(310,plain,
% 0.82/0.79 ((~(aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx))))) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)) | ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx))),
% 0.82/0.79 inference(tautology,[status(thm)],[])).
% 0.82/0.79 tff(311,plain,
% 0.82/0.79 (~(aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx))))),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[310, 309, 307])).
% 0.82/0.79 tff(312,plain,
% 0.82/0.79 ((~![W3: $i] : (aElementOf0(W3, sdtmndt0(xS, xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx))))) | (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx))))),
% 0.82/0.79 inference(quant_inst,[status(thm)],[])).
% 0.82/0.79 tff(313,plain,
% 0.82/0.79 ($false),
% 0.82/0.79 inference(unit_resolution,[status(thm)],[312, 288, 311])).
% 0.82/0.79 % SZS output end Proof
%------------------------------------------------------------------------------