TSTP Solution File: NUM536+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM536+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 13:10:21 EDT 2022
% Result : Theorem 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM536+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 11:29:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 % SZS output start Proof
% 0.20/0.47 tff(aElementOf0_type, type, (
% 0.20/0.47 aElementOf0: ( $i * $i ) > $o)).
% 0.20/0.47 tff(xS_type, type, (
% 0.20/0.47 xS: $i)).
% 0.20/0.47 tff(tptp_fun_W3_3_type, type, (
% 0.20/0.47 tptp_fun_W3_3: ( $i * $i * $i ) > $i)).
% 0.20/0.47 tff(sdtpldt0_type, type, (
% 0.20/0.47 sdtpldt0: ( $i * $i ) > $i)).
% 0.20/0.47 tff(xx_type, type, (
% 0.20/0.47 xx: $i)).
% 0.20/0.47 tff(aElement0_type, type, (
% 0.20/0.47 aElement0: $i > $o)).
% 0.20/0.47 tff(sdtmndt0_type, type, (
% 0.20/0.47 sdtmndt0: ( $i * $i ) > $i)).
% 0.20/0.47 tff(aSet0_type, type, (
% 0.20/0.47 aSet0: $i > $o)).
% 0.20/0.47 tff(tptp_fun_W3_2_type, type, (
% 0.20/0.47 tptp_fun_W3_2: ( $i * $i * $i ) > $i)).
% 0.20/0.47 tff(1,assumption,(~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)), introduced(assumption)).
% 0.20/0.47 tff(2,assumption,((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))), introduced(assumption)).
% 0.20/0.47 tff(3,plain,
% 0.20/0.47 (aSet0(xS) <=> aSet0(xS)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(4,axiom,(aElement0(xx) & aSet0(xS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__679')).
% 0.20/0.47 tff(5,plain,
% 0.20/0.47 (aSet0(xS)),
% 0.20/0.47 inference(and_elim,[status(thm)],[4])).
% 0.20/0.47 tff(6,plain,
% 0.20/0.47 (aSet0(xS)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[5, 3])).
% 0.20/0.47 tff(7,plain,
% 0.20/0.47 (aElement0(xx) <=> aElement0(xx)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(8,plain,
% 0.20/0.47 (aElement0(xx)),
% 0.20/0.47 inference(and_elim,[status(thm)],[4])).
% 0.20/0.47 tff(9,plain,
% 0.20/0.47 (aElement0(xx)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.47 tff(10,plain,
% 0.20/0.47 (^[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))))))))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(11,plain,
% 0.20/0.47 (![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))))))))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.47 tff(12,plain,
% 0.20/0.47 (^[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)))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(13,plain,
% 0.20/0.47 (![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))))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.47 tff(14,plain,
% 0.20/0.47 (^[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)))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(15,plain,
% 0.20/0.47 (![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))))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.47 tff(16,plain,
% 0.20/0.47 (![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))))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[15, 13])).
% 0.20/0.47 tff(17,plain,
% 0.20/0.47 (^[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))))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(18,plain,
% 0.20/0.48 (![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))))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.48 tff(19,plain,
% 0.20/0.48 (^[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))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(20,plain,
% 0.20/0.48 (![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)))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.48 tff(21,plain,
% 0.20/0.48 (![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)))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(22,plain,
% 0.20/0.48 (^[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)))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(23,plain,
% 0.20/0.48 (![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)))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.48 tff(24,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')).
% 0.20/0.48 tff(25,plain,
% 0.20/0.48 (![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)))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.48 tff(26,plain,
% 0.20/0.48 (![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)))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.48 tff(27,plain,(
% 0.20/0.48 ![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)))))))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[26])).
% 0.20/0.48 tff(28,plain,
% 0.20/0.48 (![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)))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.20/0.48 tff(29,plain,
% 0.20/0.48 (![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))))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.20/0.48 tff(30,plain,
% 0.20/0.48 (![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))))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[29, 16])).
% 0.20/0.48 tff(31,plain,
% 0.20/0.48 (![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))))))))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[30, 11])).
% 0.20/0.48 tff(32,plain,
% 0.20/0.48 (((~![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(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = 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(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(34,plain,
% 0.20/0.48 (^[W2: $i] : rewrite((~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))) <=> (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(35,plain,
% 0.20/0.48 (![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))) <=> ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.48 tff(36,plain,
% 0.20/0.48 (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[35])).
% 0.20/0.48 tff(37,plain,
% 0.20/0.48 (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[36, 33])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 (((~![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(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = 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(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 (((~![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(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = 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(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[38, 32])).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 ((~![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(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 ((~![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(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 (![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[41, 31, 9, 6])).
% 0.20/0.48 tff(43,plain,
% 0.20/0.48 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 ((~((~((~aSet0(sdtpldt0(xS, xx))) | (sdtpldt0(xS, xx) = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), sdtpldt0(xS, xx)) <=> ((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS))) | (~((tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), xS))))))) | (~((~(sdtpldt0(xS, xx) = sdtpldt0(xS, xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))) <=> (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) | (~((~((~aSet0(sdtpldt0(xS, xx))) | (sdtpldt0(xS, xx) = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), sdtpldt0(xS, xx)) <=> ((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS))) | (~((tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), xS))))))) | (~((~(sdtpldt0(xS, xx) = sdtpldt0(xS, xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[44])).
% 0.20/0.49 tff(46,plain,
% 0.20/0.49 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) | (~((~((~aSet0(sdtpldt0(xS, xx))) | (sdtpldt0(xS, xx) = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), sdtpldt0(xS, xx)) <=> ((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS))) | (~((tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), xS))))))) | (~((~(sdtpldt0(xS, xx) = sdtpldt0(xS, xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[45, 43])).
% 0.20/0.49 tff(47,plain,
% 0.20/0.49 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) | (~((~((~aSet0(sdtpldt0(xS, xx))) | (sdtpldt0(xS, xx) = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), sdtpldt0(xS, xx)) <=> ((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS))) | (~((tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), xS))))))) | (~((~(sdtpldt0(xS, xx) = sdtpldt0(xS, xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(48,plain,
% 0.20/0.49 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.49 tff(49,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[48, 42, 2])).
% 0.20/0.49 tff(50,plain,(~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(51,plain,
% 0.20/0.49 (((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))) | aSet0(sdtpldt0(xS, xx))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(52,plain,
% 0.20/0.49 (aSet0(sdtpldt0(xS, xx))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.49 tff(53,plain,
% 0.20/0.49 (^[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))))))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(54,plain,
% 0.20/0.49 (![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))))))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.49 tff(55,plain,
% 0.20/0.49 (^[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)))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(56,plain,
% 0.20/0.49 (![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))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.49 tff(57,plain,
% 0.20/0.49 (^[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)))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(58,plain,
% 0.20/0.49 (![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))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.49 tff(59,plain,
% 0.20/0.49 (![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))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[58, 56])).
% 0.20/0.49 tff(60,plain,
% 0.20/0.49 (^[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))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(61,plain,
% 0.20/0.49 (![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))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.49 tff(62,plain,
% 0.20/0.49 (^[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))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(63,plain,
% 0.20/0.49 (![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)))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.49 tff(64,plain,
% 0.20/0.49 (![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)))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(65,plain,
% 0.20/0.49 (^[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)))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(66,plain,
% 0.20/0.49 (![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)))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.49 tff(67,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')).
% 0.20/0.49 tff(68,plain,
% 0.20/0.49 (![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)))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.49 tff(69,plain,
% 0.20/0.49 (![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)))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.20/0.49 tff(70,plain,(
% 0.20/0.49 ![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)))))))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[69])).
% 0.20/0.49 tff(71,plain,
% 0.20/0.49 (![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)))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.20/0.49 tff(72,plain,
% 0.20/0.49 (![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))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[71, 61])).
% 0.20/0.49 tff(73,plain,
% 0.20/0.49 (![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))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[72, 59])).
% 0.20/0.49 tff(74,plain,
% 0.20/0.49 (![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))))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[73, 54])).
% 0.20/0.49 tff(75,plain,
% 0.20/0.49 (((~![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))))))))))))) | ((~aElement0(xx)) | (~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (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))))))))))))) | (~aElement0(xx)) | (~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(76,plain,
% 0.20/0.49 (((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))))))))) <=> ((~aElement0(xx)) | (~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(77,plain,
% 0.20/0.49 (^[W2: $i] : rewrite((~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))))))))) <=> (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(78,plain,
% 0.20/0.50 (![W2: $i] : (~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))))))))) <=> ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.50 tff(79,plain,
% 0.20/0.50 (((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))))))))) <=> ((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))))))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[78])).
% 0.20/0.50 tff(80,plain,
% 0.20/0.50 (((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))))))))) <=> ((~aElement0(xx)) | (~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))))))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[79, 76])).
% 0.20/0.50 tff(81,plain,
% 0.20/0.50 (((~![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(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (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))))))))))))) | ((~aElement0(xx)) | (~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))))))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[80])).
% 0.20/0.50 tff(82,plain,
% 0.20/0.50 (((~![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(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (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))))))))))))) | (~aElement0(xx)) | (~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))))))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[81, 75])).
% 0.20/0.50 tff(83,plain,
% 0.20/0.50 ((~![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(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))))))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(84,plain,
% 0.20/0.50 ((~![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))))))))))))) | (~aElement0(xx)) | (~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.50 tff(85,plain,
% 0.20/0.50 ((~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[84, 74, 9])).
% 0.20/0.50 tff(86,plain,
% 0.20/0.50 (![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[85, 52])).
% 0.20/0.50 tff(87,plain,
% 0.20/0.50 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))))))))) | (~((~((~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(xS = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W3: $i] : (aElementOf0(W3, xS) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(88,plain,
% 0.20/0.50 (~((~((~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(xS = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W3: $i] : (aElementOf0(W3, xS) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.20/0.50 tff(89,plain,
% 0.20/0.50 (((~((~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(xS = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W3: $i] : (aElementOf0(W3, xS) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))))))) | ((~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(90,plain,
% 0.20/0.50 ((~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.20/0.50 tff(91,plain,
% 0.20/0.50 ((xS = sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (sdtmndt0(sdtpldt0(xS, xx), xx) = xS)),
% 0.20/0.50 inference(commutativity,[status(thm)],[])).
% 0.20/0.50 tff(92,plain,
% 0.20/0.50 ((sdtmndt0(sdtpldt0(xS, xx), xx) = xS) <=> (xS = sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.20/0.50 inference(symmetry,[status(thm)],[91])).
% 0.20/0.50 tff(93,plain,
% 0.20/0.50 ((~(sdtmndt0(sdtpldt0(xS, xx), xx) = xS)) <=> (~(xS = sdtmndt0(sdtpldt0(xS, xx), xx)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[92])).
% 0.20/0.50 tff(94,plain,
% 0.20/0.50 ((~(sdtmndt0(sdtpldt0(xS, xx), xx) = xS)) <=> (~(sdtmndt0(sdtpldt0(xS, xx), xx) = xS))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(95,axiom,(~(sdtmndt0(sdtpldt0(xS, xx), xx) = xS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.20/0.50 tff(96,plain,
% 0.20/0.50 (~(sdtmndt0(sdtpldt0(xS, xx), xx) = xS)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.50 tff(97,plain,
% 0.20/0.50 (~(xS = sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[96, 93])).
% 0.20/0.50 tff(98,plain,
% 0.20/0.50 ((~((~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))))) | (~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(99,plain,
% 0.20/0.50 ((~((~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))))) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[98, 6])).
% 0.20/0.50 tff(100,plain,
% 0.20/0.50 (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[99, 97, 90])).
% 0.20/0.51 tff(101,plain,
% 0.20/0.51 ((~(aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)))) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) | (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(102,plain,
% 0.20/0.51 (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) | (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.20/0.51 tff(103,plain,
% 0.20/0.51 (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[102, 1])).
% 0.20/0.51 tff(104,plain,
% 0.20/0.51 (((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(105,plain,
% 0.20/0.51 (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.20/0.51 tff(106,plain,
% 0.20/0.51 (((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))) | ![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(107,plain,
% 0.20/0.51 (![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[106, 50])).
% 0.20/0.51 tff(108,plain,
% 0.20/0.51 ((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))) | (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(109,plain,
% 0.20/0.51 (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.20/0.51 tff(110,plain,
% 0.20/0.51 ((~(aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))))))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(111,plain,
% 0.20/0.51 ((~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.20/0.51 tff(112,plain,
% 0.20/0.51 (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[111, 105])).
% 0.20/0.51 tff(113,plain,
% 0.20/0.51 (((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)) | (~(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(114,plain,
% 0.20/0.51 (~(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[113, 103])).
% 0.20/0.51 tff(115,plain,
% 0.20/0.51 ((~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(116,plain,
% 0.20/0.51 (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[115, 114, 1])).
% 0.20/0.51 tff(117,plain,
% 0.20/0.51 (((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))) | ((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(118,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[117, 116, 112])).
% 0.20/0.51 tff(119,plain,(aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(120,plain,
% 0.20/0.51 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(121,plain,
% 0.20/0.51 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[120])).
% 0.20/0.51 tff(122,plain,
% 0.20/0.51 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(123,plain,
% 0.20/0.51 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[122])).
% 0.20/0.51 tff(124,plain,
% 0.20/0.51 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[123, 121])).
% 0.20/0.51 tff(125,plain,
% 0.20/0.51 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(126,plain,
% 0.20/0.51 (^[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))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(127,plain,
% 0.20/0.51 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[126])).
% 0.20/0.51 tff(128,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mEOfElem')).
% 0.20/0.51 tff(129,plain,
% 0.20/0.51 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.20/0.51 tff(130,plain,
% 0.20/0.51 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.20/0.51 tff(131,plain,(
% 0.20/0.51 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.51 inference(skolemize,[status(sab)],[130])).
% 0.20/0.51 tff(132,plain,
% 0.20/0.51 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.20/0.51 tff(133,plain,
% 0.20/0.51 (((~![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))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(134,plain,
% 0.20/0.51 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(135,plain,
% 0.20/0.51 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.51 tff(136,plain,
% 0.20/0.51 (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[135, 132, 6])).
% 0.20/0.51 tff(137,plain,
% 0.20/0.51 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(138,plain,
% 0.20/0.51 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(139,plain,
% 0.20/0.51 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.51 tff(140,plain,
% 0.20/0.51 (aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[139, 136])).
% 0.20/0.51 tff(141,plain,
% 0.20/0.51 (aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[140, 119])).
% 0.20/0.51 tff(142,plain,
% 0.20/0.51 ((~(aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)) | ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(143,plain,
% 0.20/0.51 ((~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)) | ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[142, 100])).
% 0.20/0.51 tff(144,plain,
% 0.20/0.51 ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[143, 119])).
% 0.20/0.51 tff(145,plain,
% 0.20/0.51 (((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(146,plain,
% 0.20/0.51 ((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[145, 119])).
% 0.20/0.51 tff(147,plain,
% 0.20/0.51 ((~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))))) | (~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(148,plain,
% 0.20/0.51 (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[147, 146, 141])).
% 0.20/0.51 tff(149,plain,
% 0.20/0.51 ((~(aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))))))) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx)) | ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(150,plain,
% 0.20/0.51 (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx)) | ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[149, 109])).
% 0.20/0.51 tff(151,plain,
% 0.20/0.51 (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[150, 148])).
% 0.20/0.51 tff(152,plain,
% 0.20/0.51 ((~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))) | (~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(153,plain,
% 0.20/0.51 (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[152, 151, 144, 141])).
% 0.20/0.51 tff(154,plain,
% 0.20/0.51 (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> aElementOf0(xx, xS)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[153])).
% 0.20/0.51 tff(155,plain,
% 0.20/0.51 (aElementOf0(xx, xS) <=> aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)),
% 0.20/0.51 inference(symmetry,[status(thm)],[154])).
% 0.20/0.51 tff(156,plain,
% 0.20/0.51 ((~aElementOf0(xx, xS)) <=> (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[155])).
% 0.20/0.51 tff(157,plain,
% 0.20/0.51 ((~aElementOf0(xx, xS)) <=> (~aElementOf0(xx, xS))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(158,axiom,(~aElementOf0(xx, xS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__679_02')).
% 0.20/0.51 tff(159,plain,
% 0.20/0.51 (~aElementOf0(xx, xS)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.20/0.51 tff(160,plain,
% 0.20/0.51 (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[159, 156])).
% 0.20/0.51 tff(161,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[119, 160])).
% 0.20/0.51 % SZS output end Proof
%------------------------------------------------------------------------------