TSTP Solution File: NUM537+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM537+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:10:21 EDT 2022
% Result : Theorem 4.93s 3.26s
% Output : Proof 5.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : NUM537+1 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.31 % Computer : n012.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri Sep 2 11:32:49 EDT 2022
% 0.16/0.31 % CPUTime :
% 0.16/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.31 Usage: tptp [options] [-file:]file
% 0.16/0.31 -h, -? prints this message.
% 0.16/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.31 -m, -model generate model.
% 0.16/0.31 -p, -proof generate proof.
% 0.16/0.31 -c, -core generate unsat core of named formulas.
% 0.16/0.31 -st, -statistics display statistics.
% 0.16/0.31 -t:timeout set timeout (in second).
% 0.16/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.31 -<param>:<value> configuration parameter and value.
% 0.16/0.31 -o:<output-file> file to place output in.
% 4.93/3.26 % SZS status Theorem
% 4.93/3.26 % SZS output start Proof
% 4.93/3.26 tff(aElementOf0_type, type, (
% 4.93/3.26 aElementOf0: ( $i * $i ) > $o)).
% 4.93/3.26 tff(xS_type, type, (
% 4.93/3.26 xS: $i)).
% 4.93/3.26 tff(tptp_fun_W2_1_type, type, (
% 4.93/3.26 tptp_fun_W2_1: ( $i * $i ) > $i)).
% 4.93/3.26 tff(sdtmndt0_type, type, (
% 4.93/3.26 sdtmndt0: ( $i * $i ) > $i)).
% 4.93/3.26 tff(xx_type, type, (
% 4.93/3.26 xx: $i)).
% 4.93/3.26 tff(sdtpldt0_type, type, (
% 4.93/3.26 sdtpldt0: ( $i * $i ) > $i)).
% 4.93/3.26 tff(aElement0_type, type, (
% 4.93/3.26 aElement0: $i > $o)).
% 4.93/3.26 tff(aSet0_type, type, (
% 4.93/3.26 aSet0: $i > $o)).
% 4.93/3.26 tff(tptp_fun_W3_3_type, type, (
% 4.93/3.26 tptp_fun_W3_3: ( $i * $i * $i ) > $i)).
% 4.93/3.26 tff(tptp_fun_W3_2_type, type, (
% 4.93/3.26 tptp_fun_W3_2: ( $i * $i * $i ) > $i)).
% 4.93/3.26 tff(aSubsetOf0_type, type, (
% 4.93/3.26 aSubsetOf0: ( $i * $i ) > $o)).
% 4.93/3.26 tff(1,assumption,((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))), introduced(assumption)).
% 4.93/3.26 tff(2,assumption,((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))), introduced(assumption)).
% 4.93/3.26 tff(3,plain,
% 4.93/3.26 (aSet0(xS) <=> aSet0(xS)),
% 4.93/3.26 inference(rewrite,[status(thm)],[])).
% 4.93/3.26 tff(4,axiom,(aElement0(xx) & aSet0(xS)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__679')).
% 4.93/3.26 tff(5,plain,
% 4.93/3.26 (aSet0(xS)),
% 4.93/3.26 inference(and_elim,[status(thm)],[4])).
% 4.93/3.26 tff(6,plain,
% 4.93/3.26 (aSet0(xS)),
% 4.93/3.26 inference(modus_ponens,[status(thm)],[5, 3])).
% 4.93/3.26 tff(7,plain,
% 4.93/3.26 (aElement0(xx) <=> aElement0(xx)),
% 4.93/3.26 inference(rewrite,[status(thm)],[])).
% 4.93/3.26 tff(8,plain,
% 4.93/3.26 (aElement0(xx)),
% 4.93/3.26 inference(and_elim,[status(thm)],[4])).
% 4.93/3.26 tff(9,plain,
% 4.93/3.26 (aElement0(xx)),
% 4.93/3.26 inference(modus_ponens,[status(thm)],[8, 7])).
% 4.93/3.26 tff(10,plain,
% 4.93/3.26 (^[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))))))))))))))))),
% 4.93/3.27 inference(bind,[status(th)],[])).
% 4.93/3.27 tff(11,plain,
% 4.93/3.27 (![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))))))))))))))),
% 4.93/3.27 inference(quant_intro,[status(thm)],[10])).
% 4.93/3.27 tff(12,plain,
% 4.93/3.27 (^[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)))))))))))),
% 4.93/3.27 inference(bind,[status(th)],[])).
% 4.93/3.27 tff(13,plain,
% 4.93/3.27 (![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))))))))))),
% 4.93/3.27 inference(quant_intro,[status(thm)],[12])).
% 4.93/3.27 tff(14,plain,
% 4.93/3.27 (^[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)))))))))))),
% 4.93/3.27 inference(bind,[status(th)],[])).
% 4.93/3.27 tff(15,plain,
% 4.93/3.27 (![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))))))))))),
% 4.93/3.27 inference(quant_intro,[status(thm)],[14])).
% 4.93/3.27 tff(16,plain,
% 4.93/3.27 (![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))))))))))),
% 4.93/3.27 inference(transitivity,[status(thm)],[15, 13])).
% 4.93/3.27 tff(17,plain,
% 4.93/3.27 (^[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))))))))))))),
% 4.93/3.27 inference(bind,[status(th)],[])).
% 4.93/3.27 tff(18,plain,
% 4.93/3.27 (![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))))))))))),
% 4.93/3.27 inference(quant_intro,[status(thm)],[17])).
% 4.93/3.27 tff(19,plain,
% 4.93/3.27 (^[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))))))))),
% 4.93/3.27 inference(bind,[status(th)],[])).
% 4.93/3.27 tff(20,plain,
% 4.93/3.27 (![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)))))))),
% 4.93/3.27 inference(quant_intro,[status(thm)],[19])).
% 4.93/3.27 tff(21,plain,
% 4.93/3.27 (![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)))))))),
% 4.93/3.27 inference(rewrite,[status(thm)],[])).
% 4.93/3.27 tff(22,plain,
% 4.93/3.27 (^[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)))))))))),
% 4.93/3.27 inference(bind,[status(th)],[])).
% 4.93/3.27 tff(23,plain,
% 4.93/3.27 (![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)))))))),
% 4.93/3.27 inference(quant_intro,[status(thm)],[22])).
% 4.93/3.27 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/sandbox2/benchmark/theBenchmark.p','mDefCons')).
% 4.93/3.27 tff(25,plain,
% 4.93/3.27 (![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)))))))),
% 4.93/3.27 inference(modus_ponens,[status(thm)],[24, 23])).
% 4.93/3.27 tff(26,plain,
% 4.93/3.27 (![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)))))))),
% 4.93/3.27 inference(modus_ponens,[status(thm)],[25, 21])).
% 4.93/3.27 tff(27,plain,(
% 4.93/3.27 ![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)))))))))),
% 4.93/3.27 inference(skolemize,[status(sab)],[26])).
% 4.93/3.27 tff(28,plain,
% 4.93/3.27 (![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)))))))),
% 4.93/3.27 inference(modus_ponens,[status(thm)],[27, 20])).
% 4.93/3.27 tff(29,plain,
% 4.93/3.27 (![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))))))))))),
% 4.93/3.27 inference(modus_ponens,[status(thm)],[28, 18])).
% 4.93/3.27 tff(30,plain,
% 4.93/3.27 (![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))))))))))),
% 4.93/3.27 inference(modus_ponens,[status(thm)],[29, 16])).
% 4.93/3.27 tff(31,plain,
% 4.93/3.27 (![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))))))))))))))),
% 4.93/3.27 inference(modus_ponens,[status(thm)],[30, 11])).
% 4.93/3.27 tff(32,plain,
% 4.93/3.27 (((~![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))))))))))))))),
% 4.93/3.27 inference(rewrite,[status(thm)],[])).
% 4.93/3.27 tff(33,plain,
% 4.93/3.27 (((~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))))))))))))))),
% 4.93/3.27 inference(rewrite,[status(thm)],[])).
% 4.93/3.27 tff(34,plain,
% 4.93/3.27 (^[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))))))))))))))),
% 4.93/3.28 inference(bind,[status(th)],[])).
% 4.93/3.28 tff(35,plain,
% 4.93/3.28 (![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)))))))))))))),
% 4.93/3.28 inference(quant_intro,[status(thm)],[34])).
% 4.93/3.28 tff(36,plain,
% 4.93/3.28 (((~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))))))))))))))),
% 4.93/3.28 inference(monotonicity,[status(thm)],[35])).
% 4.93/3.28 tff(37,plain,
% 4.93/3.28 (((~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))))))))))))))),
% 4.93/3.28 inference(transitivity,[status(thm)],[36, 33])).
% 4.93/3.28 tff(38,plain,
% 4.93/3.28 (((~![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)))))))))))))))),
% 4.93/3.28 inference(monotonicity,[status(thm)],[37])).
% 4.93/3.28 tff(39,plain,
% 4.93/3.28 (((~![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))))))))))))))),
% 4.93/3.28 inference(transitivity,[status(thm)],[38, 32])).
% 4.93/3.28 tff(40,plain,
% 4.93/3.28 ((~![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))))))))))))))),
% 4.93/3.28 inference(quant_inst,[status(thm)],[])).
% 4.93/3.28 tff(41,plain,
% 4.93/3.28 ((~![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)))))))))))))),
% 4.93/3.28 inference(modus_ponens,[status(thm)],[40, 39])).
% 4.93/3.28 tff(42,plain,
% 4.93/3.28 (![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)))))))))))))),
% 4.93/3.28 inference(unit_resolution,[status(thm)],[41, 31, 9, 6])).
% 4.93/3.28 tff(43,plain,
% 4.93/3.28 (((~![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))))))))))),
% 4.93/3.28 inference(rewrite,[status(thm)],[])).
% 4.93/3.28 tff(44,plain,
% 4.93/3.28 ((~((~((~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)))))))))),
% 4.93/3.28 inference(rewrite,[status(thm)],[])).
% 4.93/3.28 tff(45,plain,
% 4.93/3.28 (((~![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))))))))))),
% 4.93/3.29 inference(monotonicity,[status(thm)],[44])).
% 4.93/3.29 tff(46,plain,
% 4.93/3.29 (((~![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))))))))))),
% 4.93/3.29 inference(transitivity,[status(thm)],[45, 43])).
% 4.93/3.29 tff(47,plain,
% 4.93/3.29 ((~![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)))))))))))))),
% 4.93/3.29 inference(quant_inst,[status(thm)],[])).
% 4.93/3.29 tff(48,plain,
% 4.93/3.29 ((~![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: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))),
% 4.93/3.29 inference(modus_ponens,[status(thm)],[47, 46])).
% 4.93/3.29 tff(49,plain,
% 4.93/3.29 ($false),
% 4.93/3.29 inference(unit_resolution,[status(thm)],[48, 42, 2])).
% 4.93/3.29 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,[]))).
% 4.93/3.29 tff(51,plain,
% 4.93/3.29 (((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))) | aSet0(sdtpldt0(xS, xx))),
% 4.93/3.29 inference(tautology,[status(thm)],[])).
% 4.93/3.29 tff(52,plain,
% 4.93/3.29 (aSet0(sdtpldt0(xS, xx))),
% 4.93/3.29 inference(unit_resolution,[status(thm)],[51, 50])).
% 4.93/3.29 tff(53,plain,
% 4.93/3.29 (^[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))))))))))))))),
% 4.93/3.29 inference(bind,[status(th)],[])).
% 4.93/3.29 tff(54,plain,
% 4.93/3.29 (![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))))))))))))),
% 4.93/3.29 inference(quant_intro,[status(thm)],[53])).
% 4.93/3.29 tff(55,plain,
% 4.93/3.29 (^[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)))))))))),
% 4.93/3.29 inference(bind,[status(th)],[])).
% 4.93/3.29 tff(56,plain,
% 4.93/3.29 (![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))))))))),
% 4.93/3.29 inference(quant_intro,[status(thm)],[55])).
% 4.93/3.29 tff(57,plain,
% 4.93/3.29 (^[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)))))))))),
% 4.93/3.29 inference(bind,[status(th)],[])).
% 4.93/3.29 tff(58,plain,
% 4.93/3.29 (![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))))))))),
% 4.93/3.29 inference(quant_intro,[status(thm)],[57])).
% 4.93/3.29 tff(59,plain,
% 4.93/3.29 (![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))))))))),
% 4.93/3.29 inference(transitivity,[status(thm)],[58, 56])).
% 4.93/3.29 tff(60,plain,
% 4.93/3.29 (^[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))))))))))),
% 4.93/3.29 inference(bind,[status(th)],[])).
% 4.93/3.29 tff(61,plain,
% 4.93/3.29 (![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))))))))),
% 4.93/3.30 inference(quant_intro,[status(thm)],[60])).
% 4.93/3.30 tff(62,plain,
% 4.93/3.30 (^[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))))))))),
% 4.93/3.30 inference(bind,[status(th)],[])).
% 4.93/3.30 tff(63,plain,
% 4.93/3.30 (![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)))))))),
% 4.93/3.30 inference(quant_intro,[status(thm)],[62])).
% 4.93/3.30 tff(64,plain,
% 4.93/3.30 (![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)))))))),
% 4.93/3.30 inference(rewrite,[status(thm)],[])).
% 4.93/3.30 tff(65,plain,
% 4.93/3.30 (^[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)))))))))),
% 4.93/3.30 inference(bind,[status(th)],[])).
% 4.93/3.30 tff(66,plain,
% 4.93/3.30 (![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)))))))),
% 4.93/3.30 inference(quant_intro,[status(thm)],[65])).
% 4.93/3.30 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/sandbox2/benchmark/theBenchmark.p','mDefDiff')).
% 4.93/3.30 tff(68,plain,
% 4.93/3.30 (![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)))))))),
% 4.93/3.30 inference(modus_ponens,[status(thm)],[67, 66])).
% 4.93/3.30 tff(69,plain,
% 4.93/3.30 (![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)))))))),
% 4.93/3.30 inference(modus_ponens,[status(thm)],[68, 64])).
% 4.93/3.30 tff(70,plain,(
% 4.93/3.30 ![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)))))))))),
% 4.93/3.30 inference(skolemize,[status(sab)],[69])).
% 4.93/3.30 tff(71,plain,
% 4.93/3.30 (![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)))))))),
% 4.93/3.30 inference(modus_ponens,[status(thm)],[70, 63])).
% 4.93/3.30 tff(72,plain,
% 4.93/3.30 (![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))))))))),
% 4.93/3.30 inference(modus_ponens,[status(thm)],[71, 61])).
% 4.93/3.30 tff(73,plain,
% 4.93/3.30 (![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))))))))),
% 4.93/3.30 inference(modus_ponens,[status(thm)],[72, 59])).
% 4.93/3.30 tff(74,plain,
% 4.93/3.30 (![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))))))))))))),
% 4.93/3.30 inference(modus_ponens,[status(thm)],[73, 54])).
% 4.93/3.30 tff(75,plain,
% 4.93/3.30 (((~![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] : (~((~((~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))))))))))))) | (~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))))))))))))),
% 4.93/3.30 inference(rewrite,[status(thm)],[])).
% 4.93/3.30 tff(76,plain,
% 4.93/3.30 (((~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)))))))))))) <=> ((~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))))))))))))),
% 4.93/3.30 inference(rewrite,[status(thm)],[])).
% 4.93/3.30 tff(77,plain,
% 4.93/3.30 (^[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))))))))))))),
% 4.93/3.31 inference(bind,[status(th)],[])).
% 4.93/3.31 tff(78,plain,
% 4.93/3.31 (![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)))))))))))),
% 4.93/3.31 inference(quant_intro,[status(thm)],[77])).
% 4.93/3.31 tff(79,plain,
% 4.93/3.31 (((~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))))))))))))),
% 4.93/3.31 inference(monotonicity,[status(thm)],[78])).
% 4.93/3.31 tff(80,plain,
% 4.93/3.31 (((~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))))))))))))),
% 4.93/3.31 inference(transitivity,[status(thm)],[79, 76])).
% 4.93/3.31 tff(81,plain,
% 4.93/3.31 (((~![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))))))))))))) | ((~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)))))))))))))),
% 4.93/3.31 inference(monotonicity,[status(thm)],[80])).
% 4.93/3.31 tff(82,plain,
% 4.93/3.31 (((~![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))))))))))))) | (~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))))))))))))),
% 4.93/3.31 inference(transitivity,[status(thm)],[81, 75])).
% 4.93/3.31 tff(83,plain,
% 4.93/3.31 ((~![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))))))))))))),
% 4.93/3.31 inference(quant_inst,[status(thm)],[])).
% 4.93/3.31 tff(84,plain,
% 4.93/3.31 ((~![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] : (~((~((~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)))))))))))),
% 4.93/3.31 inference(modus_ponens,[status(thm)],[83, 82])).
% 4.93/3.31 tff(85,plain,
% 4.93/3.31 (![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)))))))))))),
% 4.93/3.31 inference(unit_resolution,[status(thm)],[84, 74, 9, 52])).
% 4.93/3.31 tff(86,plain,
% 4.93/3.31 (((~![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(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~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)))))))))))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))))))),
% 4.93/3.31 inference(rewrite,[status(thm)],[])).
% 4.93/3.31 tff(87,plain,
% 4.93/3.31 ((~((~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx)) <=> ((~aElement0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))))))))) <=> (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))))),
% 4.93/3.32 inference(rewrite,[status(thm)],[])).
% 4.93/3.32 tff(88,plain,
% 4.93/3.32 (((~![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(sdtmndt0(sdtpldt0(xS, xx), xx))) | (sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx)) <=> ((~aElement0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~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)))))))))))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))))))),
% 4.93/3.32 inference(monotonicity,[status(thm)],[87])).
% 4.93/3.32 tff(89,plain,
% 4.93/3.32 (((~![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(sdtmndt0(sdtpldt0(xS, xx), xx))) | (sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx)) <=> ((~aElement0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~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)))))))))))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))))))),
% 4.93/3.32 inference(transitivity,[status(thm)],[88, 86])).
% 4.93/3.32 tff(90,plain,
% 4.93/3.32 ((~![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(sdtmndt0(sdtpldt0(xS, xx), xx))) | (sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx)) <=> ((~aElement0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))))))))),
% 4.93/3.32 inference(quant_inst,[status(thm)],[])).
% 4.93/3.32 tff(91,plain,
% 4.93/3.32 ((~![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(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))))),
% 4.93/3.32 inference(modus_ponens,[status(thm)],[90, 89])).
% 4.93/3.32 tff(92,plain,
% 4.93/3.32 ($false),
% 4.93/3.32 inference(unit_resolution,[status(thm)],[91, 85, 1])).
% 4.93/3.32 tff(93,plain,(~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))))), inference(lemma,lemma(discharge,[]))).
% 4.93/3.32 tff(94,plain,
% 4.93/3.32 (((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))) | ![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))),
% 4.93/3.32 inference(tautology,[status(thm)],[])).
% 4.93/3.32 tff(95,plain,
% 4.93/3.32 (![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))),
% 4.93/3.32 inference(unit_resolution,[status(thm)],[94, 93])).
% 4.93/3.32 tff(96,plain,
% 4.93/3.32 ((~![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))) | (aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx))))),
% 4.93/3.32 inference(quant_inst,[status(thm)],[])).
% 4.93/3.32 tff(97,plain,
% 4.93/3.32 (aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx)))),
% 4.93/3.32 inference(unit_resolution,[status(thm)],[96, 95])).
% 4.93/3.32 tff(98,plain,
% 4.93/3.32 (((~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))))))),
% 4.93/3.32 inference(tautology,[status(thm)],[])).
% 4.93/3.32 tff(99,plain,
% 4.93/3.32 (![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))),
% 4.93/3.32 inference(unit_resolution,[status(thm)],[98, 50])).
% 4.93/3.32 tff(100,plain,
% 4.93/3.32 ((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))) | (aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))))),
% 4.93/3.32 inference(quant_inst,[status(thm)],[])).
% 4.93/3.32 tff(101,plain,
% 4.93/3.32 (aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))))),
% 4.93/3.32 inference(unit_resolution,[status(thm)],[100, 99])).
% 4.93/3.32 tff(102,plain,
% 4.93/3.32 (((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))) | aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))),
% 4.93/3.32 inference(tautology,[status(thm)],[])).
% 4.93/3.32 tff(103,plain,
% 4.93/3.32 (aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))),
% 4.93/3.32 inference(unit_resolution,[status(thm)],[102, 93])).
% 4.93/3.32 tff(104,plain,
% 4.93/3.32 (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)))) | (~((~(W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)))) | (~((~(W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))))))),
% 4.93/3.33 inference(rewrite,[status(thm)],[])).
% 4.93/3.33 tff(105,plain,
% 4.93/3.33 (((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)))) | (~((~(W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))))))) <=> ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)))) | (~((~(W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))))))),
% 4.93/3.33 inference(rewrite,[status(thm)],[])).
% 4.93/3.33 tff(106,plain,
% 4.93/3.33 (^[W2: $i] : rewrite((~((~((W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))))) <=> (~((~((~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)))) | (~((~(W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))))))),
% 4.93/3.33 inference(bind,[status(th)],[])).
% 4.93/3.33 tff(107,plain,
% 4.93/3.33 (![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))))) <=> ![W2: $i] : (~((~((~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)))) | (~((~(W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))))))),
% 4.93/3.33 inference(quant_intro,[status(thm)],[106])).
% 4.93/3.33 tff(108,plain,
% 4.93/3.33 (((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))))))) <=> ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)))) | (~((~(W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))))))),
% 4.93/3.33 inference(monotonicity,[status(thm)],[107])).
% 4.93/3.33 tff(109,plain,
% 4.93/3.33 (((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))))))) <=> ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)))) | (~((~(W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))))))),
% 4.93/3.33 inference(transitivity,[status(thm)],[108, 105])).
% 4.93/3.33 tff(110,plain,
% 4.93/3.33 (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)))) | (~((~(W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))))))))),
% 4.93/3.34 inference(monotonicity,[status(thm)],[109])).
% 4.93/3.34 tff(111,plain,
% 4.93/3.34 (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)))) | (~((~(W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))))))),
% 4.93/3.34 inference(transitivity,[status(thm)],[110, 104])).
% 4.93/3.34 tff(112,plain,
% 4.93/3.34 ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))))))),
% 4.93/3.34 inference(quant_inst,[status(thm)],[])).
% 4.93/3.34 tff(113,plain,
% 4.93/3.34 ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)))) | (~((~(W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))))))),
% 4.93/3.34 inference(modus_ponens,[status(thm)],[112, 111])).
% 4.93/3.34 tff(114,plain,
% 4.93/3.34 (![W2: $i] : (~((~((~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)))) | (~((~(W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))))))),
% 4.93/3.34 inference(unit_resolution,[status(thm)],[113, 31, 9, 103])).
% 4.93/3.34 tff(115,plain,
% 4.93/3.34 ((~![W2: $i] : (~((~((~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)))) | (~((~(W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))))))) | (~((~((~aSet0(sdtpldt0(xS, xx))) | (aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx)) <=> ((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(sdtpldt0(xS, xx), xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (sdtpldt0(xS, xx) = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)))) | (~((~(sdtpldt0(xS, xx) = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))))))),
% 4.93/3.34 inference(quant_inst,[status(thm)],[])).
% 4.93/3.34 tff(116,plain,
% 4.93/3.34 (~((~((~aSet0(sdtpldt0(xS, xx))) | (aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx)) <=> ((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(sdtpldt0(xS, xx), xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (sdtpldt0(xS, xx) = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)))) | (~((~(sdtpldt0(xS, xx) = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))))),
% 4.93/3.34 inference(unit_resolution,[status(thm)],[115, 114])).
% 4.93/3.34 tff(117,plain,
% 4.93/3.34 (((~((~aSet0(sdtpldt0(xS, xx))) | (aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx)) <=> ((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W3_2(sdtpldt0(xS, xx), xx, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (sdtpldt0(xS, xx) = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)))) | (~((~(sdtpldt0(xS, xx) = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))))) | ((~(sdtpldt0(xS, xx) = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))),
% 4.93/3.34 inference(tautology,[status(thm)],[])).
% 4.93/3.34 tff(118,plain,
% 4.93/3.34 ((~(sdtpldt0(xS, xx) = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))),
% 4.93/3.34 inference(unit_resolution,[status(thm)],[117, 116])).
% 4.93/3.34 tff(119,plain,
% 4.93/3.34 (((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))) | (aElementOf0(xx, sdtpldt0(xS, xx)) <=> aElement0(xx))) <=> ((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))) | (aElementOf0(xx, sdtpldt0(xS, xx)) <=> aElement0(xx)))),
% 4.93/3.34 inference(rewrite,[status(thm)],[])).
% 4.93/3.34 tff(120,plain,
% 4.93/3.34 ((aElementOf0(xx, sdtpldt0(xS, xx)) <=> (~((~aElement0(xx)) | (~((xx = xx) | aElementOf0(xx, xS)))))) <=> (aElementOf0(xx, sdtpldt0(xS, xx)) <=> aElement0(xx))),
% 4.93/3.34 inference(rewrite,[status(thm)],[])).
% 4.93/3.34 tff(121,plain,
% 4.93/3.34 (((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))) | (aElementOf0(xx, sdtpldt0(xS, xx)) <=> (~((~aElement0(xx)) | (~((xx = xx) | aElementOf0(xx, xS))))))) <=> ((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))) | (aElementOf0(xx, sdtpldt0(xS, xx)) <=> aElement0(xx)))),
% 4.93/3.34 inference(monotonicity,[status(thm)],[120])).
% 4.93/3.34 tff(122,plain,
% 4.93/3.34 (((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))) | (aElementOf0(xx, sdtpldt0(xS, xx)) <=> (~((~aElement0(xx)) | (~((xx = xx) | aElementOf0(xx, xS))))))) <=> ((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))) | (aElementOf0(xx, sdtpldt0(xS, xx)) <=> aElement0(xx)))),
% 4.93/3.35 inference(transitivity,[status(thm)],[121, 119])).
% 4.93/3.35 tff(123,plain,
% 4.93/3.35 ((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))) | (aElementOf0(xx, sdtpldt0(xS, xx)) <=> (~((~aElement0(xx)) | (~((xx = xx) | aElementOf0(xx, xS))))))),
% 4.93/3.35 inference(quant_inst,[status(thm)],[])).
% 4.93/3.35 tff(124,plain,
% 4.93/3.35 ((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))) | (aElementOf0(xx, sdtpldt0(xS, xx)) <=> aElement0(xx))),
% 4.93/3.35 inference(modus_ponens,[status(thm)],[123, 122])).
% 4.93/3.35 tff(125,plain,
% 4.93/3.35 (aElementOf0(xx, sdtpldt0(xS, xx)) <=> aElement0(xx)),
% 4.93/3.35 inference(unit_resolution,[status(thm)],[124, 99])).
% 4.93/3.35 tff(126,plain,
% 4.93/3.35 ((~(aElementOf0(xx, sdtpldt0(xS, xx)) <=> aElement0(xx))) | aElementOf0(xx, sdtpldt0(xS, xx)) | (~aElement0(xx))),
% 4.93/3.35 inference(tautology,[status(thm)],[])).
% 4.93/3.35 tff(127,plain,
% 4.93/3.35 ((~(aElementOf0(xx, sdtpldt0(xS, xx)) <=> aElement0(xx))) | aElementOf0(xx, sdtpldt0(xS, xx))),
% 4.93/3.35 inference(unit_resolution,[status(thm)],[126, 9])).
% 4.93/3.35 tff(128,plain,
% 4.93/3.35 (aElementOf0(xx, sdtpldt0(xS, xx))),
% 4.93/3.35 inference(unit_resolution,[status(thm)],[127, 125])).
% 4.93/3.35 tff(129,plain,
% 4.93/3.35 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0))) <=> ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0))))),
% 4.93/3.35 inference(bind,[status(th)],[])).
% 4.93/3.35 tff(130,plain,
% 4.93/3.35 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))),
% 4.93/3.35 inference(quant_intro,[status(thm)],[129])).
% 4.93/3.35 tff(131,plain,
% 4.93/3.35 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0))) <=> ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0))))),
% 4.93/3.35 inference(bind,[status(th)],[])).
% 4.93/3.35 tff(132,plain,
% 4.93/3.35 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))),
% 4.93/3.35 inference(quant_intro,[status(thm)],[131])).
% 4.93/3.35 tff(133,plain,
% 4.93/3.35 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))),
% 4.93/3.35 inference(transitivity,[status(thm)],[132, 130])).
% 4.93/3.35 tff(134,plain,
% 4.93/3.35 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))),
% 4.93/3.35 inference(rewrite,[status(thm)],[])).
% 4.93/3.35 tff(135,plain,
% 4.93/3.35 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, W0) => (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)) <=> ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))), (![W1: $i] : (aElementOf0(W1, W0) => (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)) <=> ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))), ((aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => (sdtpldt0(sdtmndt0(W0, W1), W1) = W0))) <=> (aSet0(W0) => ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0))))), rewrite((aSet0(W0) => ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0))) <=> ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))), ((aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => (sdtpldt0(sdtmndt0(W0, W1), W1) = W0))) <=> ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))))),
% 4.93/3.35 inference(bind,[status(th)],[])).
% 4.93/3.35 tff(136,plain,
% 4.93/3.35 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => (sdtpldt0(sdtmndt0(W0, W1), W1) = W0))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))),
% 4.93/3.35 inference(quant_intro,[status(thm)],[135])).
% 4.93/3.35 tff(137,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mConsDiff')).
% 4.93/3.35 tff(138,plain,
% 4.93/3.35 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))),
% 4.93/3.35 inference(modus_ponens,[status(thm)],[137, 136])).
% 4.93/3.35 tff(139,plain,
% 4.93/3.35 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))),
% 4.93/3.35 inference(modus_ponens,[status(thm)],[138, 134])).
% 4.93/3.35 tff(140,plain,(
% 4.93/3.35 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))),
% 4.93/3.35 inference(skolemize,[status(sab)],[139])).
% 4.93/3.35 tff(141,plain,
% 4.93/3.35 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))),
% 4.93/3.35 inference(modus_ponens,[status(thm)],[140, 133])).
% 4.93/3.35 tff(142,plain,
% 4.93/3.35 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))) | ((~aSet0(sdtpldt0(xS, xx))) | ![W1: $i] : ((~aElementOf0(W1, sdtpldt0(xS, xx))) | (sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), W1), W1) = sdtpldt0(xS, xx))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))) | (~aSet0(sdtpldt0(xS, xx))) | ![W1: $i] : ((~aElementOf0(W1, sdtpldt0(xS, xx))) | (sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), W1), W1) = sdtpldt0(xS, xx))))),
% 4.93/3.35 inference(rewrite,[status(thm)],[])).
% 4.93/3.35 tff(143,plain,
% 4.93/3.35 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))) | ((~aSet0(sdtpldt0(xS, xx))) | ![W1: $i] : ((~aElementOf0(W1, sdtpldt0(xS, xx))) | (sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), W1), W1) = sdtpldt0(xS, xx))))),
% 4.93/3.35 inference(quant_inst,[status(thm)],[])).
% 4.93/3.35 tff(144,plain,
% 4.93/3.35 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))) | (~aSet0(sdtpldt0(xS, xx))) | ![W1: $i] : ((~aElementOf0(W1, sdtpldt0(xS, xx))) | (sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), W1), W1) = sdtpldt0(xS, xx)))),
% 4.93/3.35 inference(modus_ponens,[status(thm)],[143, 142])).
% 4.93/3.35 tff(145,plain,
% 4.93/3.35 (![W1: $i] : ((~aElementOf0(W1, sdtpldt0(xS, xx))) | (sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), W1), W1) = sdtpldt0(xS, xx)))),
% 4.93/3.35 inference(unit_resolution,[status(thm)],[144, 141, 52])).
% 4.93/3.35 tff(146,plain,
% 4.93/3.35 (((~![W1: $i] : ((~aElementOf0(W1, sdtpldt0(xS, xx))) | (sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), W1), W1) = sdtpldt0(xS, xx)))) | ((~aElementOf0(xx, sdtpldt0(xS, xx))) | (sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx) = sdtpldt0(xS, xx)))) <=> ((~![W1: $i] : ((~aElementOf0(W1, sdtpldt0(xS, xx))) | (sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), W1), W1) = sdtpldt0(xS, xx)))) | (~aElementOf0(xx, sdtpldt0(xS, xx))) | (sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx) = sdtpldt0(xS, xx)))),
% 4.93/3.35 inference(rewrite,[status(thm)],[])).
% 4.93/3.35 tff(147,plain,
% 4.93/3.35 ((~![W1: $i] : ((~aElementOf0(W1, sdtpldt0(xS, xx))) | (sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), W1), W1) = sdtpldt0(xS, xx)))) | ((~aElementOf0(xx, sdtpldt0(xS, xx))) | (sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx) = sdtpldt0(xS, xx)))),
% 4.93/3.35 inference(quant_inst,[status(thm)],[])).
% 4.93/3.35 tff(148,plain,
% 4.93/3.35 ((~![W1: $i] : ((~aElementOf0(W1, sdtpldt0(xS, xx))) | (sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), W1), W1) = sdtpldt0(xS, xx)))) | (~aElementOf0(xx, sdtpldt0(xS, xx))) | (sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx) = sdtpldt0(xS, xx))),
% 4.93/3.35 inference(modus_ponens,[status(thm)],[147, 146])).
% 4.93/3.35 tff(149,plain,
% 4.93/3.35 (sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx) = sdtpldt0(xS, xx)),
% 4.93/3.35 inference(unit_resolution,[status(thm)],[148, 145, 128])).
% 4.93/3.35 tff(150,plain,
% 4.93/3.35 (sdtpldt0(xS, xx) = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)),
% 4.93/3.35 inference(symmetry,[status(thm)],[149])).
% 4.93/3.35 tff(151,plain,
% 4.93/3.35 ((~((~(sdtpldt0(xS, xx) = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))) | (~(sdtpldt0(xS, xx) = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))),
% 4.93/3.35 inference(tautology,[status(thm)],[])).
% 4.93/3.35 tff(152,plain,
% 4.93/3.35 ((~((~(sdtpldt0(xS, xx) = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))),
% 4.93/3.35 inference(unit_resolution,[status(thm)],[151, 150])).
% 4.93/3.35 tff(153,plain,
% 4.93/3.35 (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))),
% 4.93/3.35 inference(unit_resolution,[status(thm)],[152, 118])).
% 4.93/3.35 tff(154,plain,
% 4.93/3.35 (((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))) | ![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))),
% 4.93/3.35 inference(tautology,[status(thm)],[])).
% 4.93/3.35 tff(155,plain,
% 4.93/3.35 (![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))),
% 4.93/3.35 inference(unit_resolution,[status(thm)],[154, 153])).
% 4.93/3.35 tff(156,plain,
% 4.93/3.35 ((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))) | (aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx)))))))),
% 4.93/3.35 inference(quant_inst,[status(thm)],[])).
% 4.93/3.35 tff(157,plain,
% 4.93/3.35 (aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))))))),
% 4.93/3.35 inference(unit_resolution,[status(thm)],[156, 155])).
% 4.93/3.35 tff(158,plain,
% 4.93/3.35 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 4.93/3.35 inference(bind,[status(th)],[])).
% 4.93/3.35 tff(159,plain,
% 4.93/3.35 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.93/3.35 inference(quant_intro,[status(thm)],[158])).
% 4.93/3.35 tff(160,plain,
% 4.93/3.35 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 4.93/3.35 inference(bind,[status(th)],[])).
% 4.93/3.35 tff(161,plain,
% 4.93/3.35 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.93/3.35 inference(quant_intro,[status(thm)],[160])).
% 4.93/3.35 tff(162,plain,
% 4.93/3.35 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.93/3.35 inference(transitivity,[status(thm)],[161, 159])).
% 4.93/3.35 tff(163,plain,
% 4.93/3.35 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.93/3.35 inference(rewrite,[status(thm)],[])).
% 4.93/3.35 tff(164,plain,
% 4.93/3.35 (^[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))))))),
% 4.93/3.35 inference(bind,[status(th)],[])).
% 4.93/3.35 tff(165,plain,
% 4.93/3.35 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.93/3.35 inference(quant_intro,[status(thm)],[164])).
% 4.93/3.35 tff(166,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mEOfElem')).
% 4.93/3.35 tff(167,plain,
% 4.93/3.35 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.93/3.35 inference(modus_ponens,[status(thm)],[166, 165])).
% 4.93/3.35 tff(168,plain,
% 4.93/3.35 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.93/3.35 inference(modus_ponens,[status(thm)],[167, 163])).
% 4.93/3.35 tff(169,plain,(
% 4.93/3.35 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.93/3.35 inference(skolemize,[status(sab)],[168])).
% 4.93/3.35 tff(170,plain,
% 4.93/3.35 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.93/3.35 inference(modus_ponens,[status(thm)],[169, 162])).
% 4.93/3.35 tff(171,plain,
% 4.93/3.35 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)))))),
% 4.93/3.35 inference(rewrite,[status(thm)],[])).
% 4.93/3.35 tff(172,plain,
% 4.93/3.35 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)))))),
% 4.93/3.35 inference(quant_inst,[status(thm)],[])).
% 4.93/3.35 tff(173,plain,
% 4.93/3.35 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))))),
% 4.93/3.35 inference(modus_ponens,[status(thm)],[172, 171])).
% 4.93/3.35 tff(174,plain,
% 4.93/3.35 (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))))),
% 4.93/3.35 inference(unit_resolution,[status(thm)],[173, 170, 103])).
% 4.93/3.35 tff(175,assumption,(~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))), introduced(assumption)).
% 4.93/3.35 tff(176,plain,
% 4.93/3.35 (((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))),
% 4.93/3.35 inference(tautology,[status(thm)],[])).
% 4.93/3.35 tff(177,plain,
% 4.93/3.35 (aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))),
% 4.93/3.35 inference(unit_resolution,[status(thm)],[176, 175])).
% 4.93/3.35 tff(178,plain,
% 4.93/3.36 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))))) | (aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))))) | aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))))),
% 4.93/3.36 inference(rewrite,[status(thm)],[])).
% 4.93/3.36 tff(179,plain,
% 4.93/3.36 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))))) | (aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))))),
% 4.93/3.36 inference(quant_inst,[status(thm)],[])).
% 4.93/3.36 tff(180,plain,
% 4.93/3.36 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))))) | aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx)))),
% 4.93/3.36 inference(modus_ponens,[status(thm)],[179, 178])).
% 4.93/3.36 tff(181,plain,
% 4.93/3.36 (aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))),
% 4.93/3.36 inference(unit_resolution,[status(thm)],[180, 177, 174])).
% 4.93/3.36 tff(182,plain,
% 4.93/3.36 (((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx)))),
% 4.93/3.36 inference(tautology,[status(thm)],[])).
% 4.93/3.36 tff(183,plain,
% 4.93/3.36 ((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))),
% 4.93/3.36 inference(unit_resolution,[status(thm)],[182, 177])).
% 4.93/3.36 tff(184,plain,
% 4.93/3.36 ((~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))))),
% 4.93/3.36 inference(tautology,[status(thm)],[])).
% 4.93/3.36 tff(185,plain,
% 4.93/3.36 ((~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS)))),
% 4.93/3.36 inference(unit_resolution,[status(thm)],[184, 183])).
% 4.93/3.36 tff(186,plain,
% 4.93/3.36 (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx)))))),
% 4.93/3.36 inference(unit_resolution,[status(thm)],[185, 181])).
% 4.93/3.36 tff(187,plain,
% 4.93/3.36 ((~(aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx)))))))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx)) | ((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx)))))),
% 4.93/3.36 inference(tautology,[status(thm)],[])).
% 4.93/3.36 tff(188,plain,
% 4.93/3.36 (aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))),
% 4.93/3.36 inference(unit_resolution,[status(thm)],[187, 186, 157])).
% 4.93/3.36 tff(189,plain,
% 4.93/3.36 ((~(aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))))),
% 4.93/3.36 inference(tautology,[status(thm)],[])).
% 4.93/3.36 tff(190,plain,
% 4.93/3.36 (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))),
% 4.93/3.36 inference(unit_resolution,[status(thm)],[189, 188, 101])).
% 4.93/3.36 tff(191,plain,
% 4.93/3.36 ((~![W3: $i] : (aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))) | (aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx))))),
% 4.93/3.36 inference(quant_inst,[status(thm)],[])).
% 4.93/3.36 tff(192,plain,
% 4.93/3.36 (aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)))),
% 4.93/3.36 inference(unit_resolution,[status(thm)],[191, 95])).
% 4.93/3.36 tff(193,plain,
% 4.93/3.36 ((~(aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx))))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)))),
% 4.93/3.36 inference(tautology,[status(thm)],[])).
% 4.93/3.36 tff(194,plain,
% 4.93/3.36 ((~(aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx))))) | (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)))),
% 4.93/3.36 inference(unit_resolution,[status(thm)],[193, 177])).
% 4.93/3.36 tff(195,plain,
% 4.93/3.36 (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx))),
% 4.93/3.36 inference(unit_resolution,[status(thm)],[194, 192])).
% 4.93/3.36 tff(196,plain,
% 4.93/3.36 (((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)) | (~(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx))),
% 4.93/3.36 inference(tautology,[status(thm)],[])).
% 4.93/3.36 tff(197,plain,
% 4.93/3.36 (~(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)),
% 4.93/3.36 inference(unit_resolution,[status(thm)],[196, 195])).
% 4.93/3.36 tff(198,plain,
% 4.93/3.36 (((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))),
% 4.93/3.36 inference(tautology,[status(thm)],[])).
% 4.93/3.37 tff(199,plain,
% 4.93/3.37 (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)),
% 4.93/3.37 inference(unit_resolution,[status(thm)],[198, 175])).
% 4.93/3.37 tff(200,plain,
% 4.93/3.37 ((~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)),
% 4.93/3.37 inference(tautology,[status(thm)],[])).
% 4.93/3.37 tff(201,plain,
% 4.93/3.37 ((~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)),
% 4.93/3.37 inference(unit_resolution,[status(thm)],[200, 199])).
% 4.93/3.37 tff(202,plain,
% 4.93/3.37 (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))),
% 4.93/3.37 inference(unit_resolution,[status(thm)],[201, 197])).
% 4.93/3.37 tff(203,plain,
% 4.93/3.37 (((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))) | ((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))),
% 4.93/3.37 inference(tautology,[status(thm)],[])).
% 4.93/3.37 tff(204,plain,
% 4.93/3.37 ($false),
% 4.93/3.37 inference(unit_resolution,[status(thm)],[203, 202, 190])).
% 4.93/3.37 tff(205,plain,((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)), inference(lemma,lemma(discharge,[]))).
% 4.93/3.37 tff(206,plain,
% 4.93/3.37 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))))))))),
% 4.93/3.37 inference(bind,[status(th)],[])).
% 4.93/3.37 tff(207,plain,
% 4.93/3.37 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 4.93/3.37 inference(quant_intro,[status(thm)],[206])).
% 4.93/3.37 tff(208,plain,
% 4.93/3.37 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 4.93/3.37 inference(bind,[status(th)],[])).
% 4.93/3.37 tff(209,plain,
% 4.93/3.37 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 4.93/3.37 inference(quant_intro,[status(thm)],[208])).
% 4.93/3.37 tff(210,plain,
% 4.93/3.37 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 4.93/3.37 inference(bind,[status(th)],[])).
% 4.93/3.37 tff(211,plain,
% 4.93/3.37 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 4.93/3.37 inference(quant_intro,[status(thm)],[210])).
% 4.93/3.37 tff(212,plain,
% 4.93/3.37 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 4.93/3.37 inference(transitivity,[status(thm)],[211, 209])).
% 4.93/3.37 tff(213,plain,
% 4.93/3.37 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 4.93/3.37 inference(bind,[status(th)],[])).
% 4.93/3.37 tff(214,plain,
% 4.93/3.37 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 4.93/3.37 inference(quant_intro,[status(thm)],[213])).
% 4.93/3.37 tff(215,plain,
% 4.93/3.37 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))),
% 4.93/3.37 inference(bind,[status(th)],[])).
% 4.93/3.37 tff(216,plain,
% 4.93/3.37 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))),
% 4.93/3.37 inference(quant_intro,[status(thm)],[215])).
% 4.93/3.37 tff(217,plain,
% 4.93/3.37 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 4.93/3.37 inference(rewrite,[status(thm)],[])).
% 4.93/3.37 tff(218,plain,
% 4.93/3.37 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))) <=> (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), (![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))) <=> ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), ((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))), rewrite((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))) <=> ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), ((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))))),
% 4.93/3.37 inference(bind,[status(th)],[])).
% 4.93/3.37 tff(219,plain,
% 4.93/3.37 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 4.93/3.37 inference(quant_intro,[status(thm)],[218])).
% 4.93/3.37 tff(220,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mDefSub')).
% 4.93/3.37 tff(221,plain,
% 4.93/3.37 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 4.93/3.37 inference(modus_ponens,[status(thm)],[220, 219])).
% 4.93/3.37 tff(222,plain,
% 4.93/3.37 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 4.93/3.37 inference(modus_ponens,[status(thm)],[221, 217])).
% 4.93/3.37 tff(223,plain,(
% 4.93/3.37 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))),
% 4.93/3.37 inference(skolemize,[status(sab)],[222])).
% 4.93/3.37 tff(224,plain,
% 4.93/3.37 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))),
% 4.93/3.37 inference(modus_ponens,[status(thm)],[223, 216])).
% 4.93/3.37 tff(225,plain,
% 4.93/3.37 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 4.93/3.37 inference(modus_ponens,[status(thm)],[224, 214])).
% 4.93/3.37 tff(226,plain,
% 4.93/3.37 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 4.93/3.37 inference(modus_ponens,[status(thm)],[225, 212])).
% 4.93/3.37 tff(227,plain,
% 4.93/3.37 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 4.93/3.37 inference(modus_ponens,[status(thm)],[226, 207])).
% 4.93/3.37 tff(228,plain,
% 4.93/3.37 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))),
% 4.93/3.37 inference(rewrite,[status(thm)],[])).
% 4.93/3.37 tff(229,plain,
% 4.93/3.37 (((~aSet0(xS)) | ![W1: $i] : (~((~(aSubsetOf0(W1, xS) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) <=> ((~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))),
% 4.93/3.37 inference(rewrite,[status(thm)],[])).
% 4.93/3.37 tff(230,plain,
% 4.93/3.37 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~(aSubsetOf0(W1, xS) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))))),
% 4.93/3.37 inference(monotonicity,[status(thm)],[229])).
% 4.93/3.37 tff(231,plain,
% 4.93/3.37 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~(aSubsetOf0(W1, xS) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))),
% 5.04/3.37 inference(transitivity,[status(thm)],[230, 228])).
% 5.04/3.37 tff(232,plain,
% 5.04/3.37 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~(aSubsetOf0(W1, xS) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))),
% 5.04/3.37 inference(quant_inst,[status(thm)],[])).
% 5.04/3.37 tff(233,plain,
% 5.04/3.37 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))),
% 5.04/3.37 inference(modus_ponens,[status(thm)],[232, 231])).
% 5.04/3.37 tff(234,plain,
% 5.04/3.37 (![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))),
% 5.04/3.37 inference(unit_resolution,[status(thm)],[233, 227, 6])).
% 5.04/3.37 tff(235,plain,
% 5.04/3.37 (((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~(aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS)))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~(aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS))))))))))),
% 5.04/3.38 inference(rewrite,[status(thm)],[])).
% 5.04/3.38 tff(236,plain,
% 5.04/3.38 ((~((~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS))))))))) <=> (~((~(aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS)))))))))),
% 5.04/3.38 inference(rewrite,[status(thm)],[])).
% 5.04/3.38 tff(237,plain,
% 5.04/3.38 (((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS)))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~(aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS))))))))))),
% 5.04/3.38 inference(monotonicity,[status(thm)],[236])).
% 5.04/3.38 tff(238,plain,
% 5.04/3.38 (((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS)))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~(aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS))))))))))),
% 5.04/3.38 inference(transitivity,[status(thm)],[237, 235])).
% 5.04/3.38 tff(239,plain,
% 5.04/3.38 ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS)))))))))),
% 5.04/3.38 inference(quant_inst,[status(thm)],[])).
% 5.04/3.38 tff(240,plain,
% 5.04/3.38 ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~(aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS)))))))))),
% 5.04/3.38 inference(modus_ponens,[status(thm)],[239, 238])).
% 5.04/3.38 tff(241,plain,
% 5.04/3.38 (~((~(aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS))))))))),
% 5.04/3.38 inference(unit_resolution,[status(thm)],[240, 234])).
% 5.04/3.38 tff(242,plain,
% 5.04/3.38 (((~(aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS)))))))) | (aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))),
% 5.04/3.38 inference(tautology,[status(thm)],[])).
% 5.04/3.38 tff(243,plain,
% 5.04/3.38 (aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))),
% 5.04/3.38 inference(unit_resolution,[status(thm)],[242, 241])).
% 5.04/3.38 tff(244,plain,
% 5.04/3.38 ((~(aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))),
% 5.04/3.38 inference(tautology,[status(thm)],[])).
% 5.04/3.38 tff(245,plain,
% 5.04/3.38 ((~(aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))),
% 5.04/3.39 inference(unit_resolution,[status(thm)],[244, 103])).
% 5.04/3.39 tff(246,plain,
% 5.04/3.39 (aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))),
% 5.04/3.39 inference(unit_resolution,[status(thm)],[245, 243])).
% 5.04/3.39 tff(247,plain,
% 5.04/3.39 (aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)),
% 5.04/3.39 inference(unit_resolution,[status(thm)],[246, 205])).
% 5.04/3.39 tff(248,plain,
% 5.04/3.39 ((~(~((~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS))))) <=> ((~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)))),
% 5.04/3.39 inference(rewrite,[status(thm)],[])).
% 5.04/3.39 tff(249,plain,
% 5.04/3.39 ((aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) & aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) <=> (~((~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS))))),
% 5.04/3.39 inference(rewrite,[status(thm)],[])).
% 5.04/3.39 tff(250,plain,
% 5.04/3.39 ((~(aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) & aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) <=> (~(~((~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)))))),
% 5.04/3.39 inference(monotonicity,[status(thm)],[249])).
% 5.04/3.39 tff(251,plain,
% 5.04/3.39 ((~(aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) & aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) <=> ((~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)))),
% 5.04/3.39 inference(transitivity,[status(thm)],[250, 248])).
% 5.04/3.39 tff(252,plain,
% 5.04/3.39 ((~(aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) & aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) <=> (~(aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) & aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)))),
% 5.04/3.39 inference(rewrite,[status(thm)],[])).
% 5.04/3.39 tff(253,axiom,(~(aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) & aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 5.04/3.39 tff(254,plain,
% 5.04/3.39 (~(aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) & aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS))),
% 5.04/3.39 inference(modus_ponens,[status(thm)],[253, 252])).
% 5.04/3.39 tff(255,plain,
% 5.04/3.39 ((~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS))),
% 5.04/3.39 inference(modus_ponens,[status(thm)],[254, 251])).
% 5.04/3.39 tff(256,plain,
% 5.04/3.39 (~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))),
% 5.04/3.39 inference(unit_resolution,[status(thm)],[255, 247])).
% 5.04/3.39 tff(257,plain,
% 5.04/3.39 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))),
% 5.04/3.39 inference(rewrite,[status(thm)],[])).
% 5.04/3.39 tff(258,plain,
% 5.04/3.39 (((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))) <=> ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))),
% 5.04/3.39 inference(rewrite,[status(thm)],[])).
% 5.04/3.39 tff(259,plain,
% 5.04/3.39 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))))),
% 5.04/3.39 inference(monotonicity,[status(thm)],[258])).
% 5.04/3.39 tff(260,plain,
% 5.04/3.39 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))),
% 5.04/3.39 inference(transitivity,[status(thm)],[259, 257])).
% 5.04/3.39 tff(261,plain,
% 5.04/3.39 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))),
% 5.04/3.39 inference(quant_inst,[status(thm)],[])).
% 5.04/3.39 tff(262,plain,
% 5.04/3.39 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))),
% 5.04/3.39 inference(modus_ponens,[status(thm)],[261, 260])).
% 5.04/3.39 tff(263,plain,
% 5.04/3.39 (![W1: $i] : (~((~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))),
% 5.04/3.39 inference(unit_resolution,[status(thm)],[262, 227, 103])).
% 5.04/3.39 tff(264,plain,
% 5.04/3.39 ((~![W1: $i] : (~((~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))) | (~((~((~aSet0(xS)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))),
% 5.04/3.39 inference(quant_inst,[status(thm)],[])).
% 5.04/3.39 tff(265,plain,
% 5.04/3.39 (~((~((~aSet0(xS)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))),
% 5.04/3.40 inference(unit_resolution,[status(thm)],[264, 263])).
% 5.04/3.40 tff(266,plain,
% 5.04/3.40 (((~((~aSet0(xS)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))))))))) | ((~aSet0(xS)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))),
% 5.04/3.40 inference(tautology,[status(thm)],[])).
% 5.04/3.40 tff(267,plain,
% 5.04/3.40 ((~aSet0(xS)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))),
% 5.04/3.40 inference(unit_resolution,[status(thm)],[266, 265])).
% 5.04/3.40 tff(268,plain,
% 5.04/3.40 ((~((~aSet0(xS)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aSet0(xS)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))),
% 5.04/3.40 inference(tautology,[status(thm)],[])).
% 5.04/3.40 tff(269,plain,
% 5.04/3.40 ((~((~aSet0(xS)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))),
% 5.04/3.40 inference(unit_resolution,[status(thm)],[268, 6])).
% 5.04/3.40 tff(270,plain,
% 5.04/3.40 ((~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))),
% 5.04/3.40 inference(unit_resolution,[status(thm)],[269, 267])).
% 5.04/3.40 tff(271,plain,
% 5.04/3.40 (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))),
% 5.04/3.40 inference(unit_resolution,[status(thm)],[270, 256])).
% 5.04/3.40 tff(272,plain,
% 5.04/3.40 (((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))),
% 5.04/3.40 inference(tautology,[status(thm)],[])).
% 5.04/3.40 tff(273,plain,
% 5.04/3.40 (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx))),
% 5.04/3.40 inference(unit_resolution,[status(thm)],[272, 271])).
% 5.04/3.40 tff(274,plain,
% 5.04/3.40 ((~(aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx))))) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)) | ((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx))),
% 5.04/3.40 inference(tautology,[status(thm)],[])).
% 5.04/3.40 tff(275,plain,
% 5.04/3.40 ((~(aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (~((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx))))) | ((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx))),
% 5.04/3.40 inference(unit_resolution,[status(thm)],[274, 273])).
% 5.04/3.40 tff(276,plain,
% 5.04/3.40 ((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx)),
% 5.04/3.40 inference(unit_resolution,[status(thm)],[275, 97])).
% 5.04/3.40 tff(277,plain,
% 5.04/3.40 (((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)),
% 5.04/3.40 inference(tautology,[status(thm)],[])).
% 5.04/3.40 tff(278,plain,
% 5.04/3.40 (aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)),
% 5.04/3.40 inference(unit_resolution,[status(thm)],[277, 271])).
% 5.04/3.40 tff(279,plain,
% 5.04/3.40 (((~![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))))),
% 5.04/3.40 inference(rewrite,[status(thm)],[])).
% 5.04/3.40 tff(280,plain,
% 5.04/3.40 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))),
% 5.04/3.40 inference(quant_inst,[status(thm)],[])).
% 5.04/3.40 tff(281,plain,
% 5.04/3.40 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 5.04/3.40 inference(modus_ponens,[status(thm)],[280, 279])).
% 5.04/3.40 tff(282,plain,
% 5.04/3.40 (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 5.04/3.40 inference(unit_resolution,[status(thm)],[281, 170, 6])).
% 5.04/3.40 tff(283,plain,
% 5.04/3.40 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)))),
% 5.04/3.40 inference(rewrite,[status(thm)],[])).
% 5.04/3.40 tff(284,plain,
% 5.04/3.40 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)))),
% 5.04/3.40 inference(quant_inst,[status(thm)],[])).
% 5.04/3.40 tff(285,plain,
% 5.04/3.40 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS))),
% 5.04/3.40 inference(modus_ponens,[status(thm)],[284, 283])).
% 5.04/3.40 tff(286,plain,
% 5.04/3.40 (aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))),
% 5.04/3.40 inference(unit_resolution,[status(thm)],[285, 282, 278])).
% 5.04/3.40 tff(287,plain,
% 5.04/3.40 ((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))) | (aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS))))))),
% 5.04/3.40 inference(quant_inst,[status(thm)],[])).
% 5.04/3.40 tff(288,plain,
% 5.04/3.40 (aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)))))),
% 5.04/3.41 inference(unit_resolution,[status(thm)],[287, 99])).
% 5.04/3.41 tff(289,plain,
% 5.04/3.41 (((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS))),
% 5.04/3.41 inference(tautology,[status(thm)],[])).
% 5.04/3.41 tff(290,plain,
% 5.04/3.41 ((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)),
% 5.04/3.41 inference(unit_resolution,[status(thm)],[289, 278])).
% 5.04/3.41 tff(291,plain,
% 5.04/3.41 ((~((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS))))) | (~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)))),
% 5.04/3.41 inference(tautology,[status(thm)],[])).
% 5.04/3.41 tff(292,plain,
% 5.04/3.41 ((~((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS))))) | (~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx))))),
% 5.04/3.41 inference(unit_resolution,[status(thm)],[291, 290])).
% 5.04/3.41 tff(293,plain,
% 5.04/3.41 (~((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS))))),
% 5.04/3.41 inference(unit_resolution,[status(thm)],[292, 286])).
% 5.04/3.41 tff(294,plain,
% 5.04/3.41 ((~(aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS))))))) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx)) | ((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS))))),
% 5.04/3.41 inference(tautology,[status(thm)],[])).
% 5.04/3.41 tff(295,plain,
% 5.04/3.41 (aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))),
% 5.04/3.41 inference(unit_resolution,[status(thm)],[294, 293, 288])).
% 5.04/3.41 tff(296,plain,
% 5.04/3.41 ((~((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx))) | (~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx)),
% 5.04/3.41 inference(tautology,[status(thm)],[])).
% 5.04/3.41 tff(297,plain,
% 5.04/3.41 (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx),
% 5.04/3.41 inference(unit_resolution,[status(thm)],[296, 295, 286, 276])).
% 5.04/3.41 tff(298,plain,
% 5.04/3.41 (aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS) <=> aElementOf0(xx, xS)),
% 5.04/3.41 inference(monotonicity,[status(thm)],[297])).
% 5.04/3.41 tff(299,plain,
% 5.04/3.41 (aElementOf0(xx, xS) <=> aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)),
% 5.04/3.41 inference(symmetry,[status(thm)],[298])).
% 5.04/3.41 tff(300,plain,
% 5.04/3.41 ((~aElementOf0(xx, xS)) <=> (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS))),
% 5.04/3.41 inference(monotonicity,[status(thm)],[299])).
% 5.04/3.41 tff(301,plain,
% 5.04/3.41 ((~aElementOf0(xx, xS)) <=> (~aElementOf0(xx, xS))),
% 5.04/3.41 inference(rewrite,[status(thm)],[])).
% 5.04/3.41 tff(302,axiom,(~aElementOf0(xx, xS)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__679_02')).
% 5.04/3.41 tff(303,plain,
% 5.04/3.41 (~aElementOf0(xx, xS)),
% 5.04/3.41 inference(modus_ponens,[status(thm)],[302, 301])).
% 5.04/3.41 tff(304,plain,
% 5.04/3.41 (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)),
% 5.04/3.41 inference(modus_ponens,[status(thm)],[303, 300])).
% 5.04/3.41 tff(305,plain,
% 5.07/3.41 ($false),
% 5.07/3.41 inference(unit_resolution,[status(thm)],[278, 304])).
% 5.07/3.41 % SZS output end Proof
%------------------------------------------------------------------------------