TSTP Solution File: NUM536+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM536+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:10:21 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM536+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Sep 2 11:33:18 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(aElementOf0_type, type, (
% 0.20/0.40 aElementOf0: ( $i * $i ) > $o)).
% 0.20/0.40 tff(xS_type, type, (
% 0.20/0.40 xS: $i)).
% 0.20/0.40 tff(tptp_fun_W3_3_type, type, (
% 0.20/0.40 tptp_fun_W3_3: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(sdtpldt0_type, type, (
% 0.20/0.40 sdtpldt0: ( $i * $i ) > $i)).
% 0.20/0.40 tff(xx_type, type, (
% 0.20/0.40 xx: $i)).
% 0.20/0.40 tff(aElement0_type, type, (
% 0.20/0.40 aElement0: $i > $o)).
% 0.20/0.40 tff(sdtmndt0_type, type, (
% 0.20/0.40 sdtmndt0: ( $i * $i ) > $i)).
% 0.20/0.40 tff(aSet0_type, type, (
% 0.20/0.40 aSet0: $i > $o)).
% 0.20/0.40 tff(tptp_fun_W3_2_type, type, (
% 0.20/0.40 tptp_fun_W3_2: ( $i * $i * $i ) > $i)).
% 0.20/0.40 tff(1,assumption,(~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))), introduced(assumption)).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (aSet0(sdtmndt0(sdtpldt0(xS, xx), xx)) <=> aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 ((~((aSet0(sdtpldt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (aElement0(W0) & (aElementOf0(W0, xS) | (W0 = xx))))) => ((aSet0(sdtmndt0(sdtpldt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> ((aElement0(W0) & aElementOf0(W0, sdtpldt0(xS, xx))) & (~(W0 = xx))))) => (sdtmndt0(sdtpldt0(xS, xx), xx) = xS)))) <=> (~((sdtmndt0(sdtpldt0(xS, xx), xx) = xS) | (~(aSet0(sdtmndt0(sdtpldt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (aElement0(W0) & aElementOf0(W0, sdtpldt0(xS, xx)) & (~(W0 = xx)))))) | (~(aSet0(sdtpldt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, xS))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(4,axiom,(~((aSet0(sdtpldt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (aElement0(W0) & (aElementOf0(W0, xS) | (W0 = xx))))) => ((aSet0(sdtmndt0(sdtpldt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> ((aElement0(W0) & aElementOf0(W0, sdtpldt0(xS, xx))) & (~(W0 = xx))))) => (sdtmndt0(sdtpldt0(xS, xx), xx) = xS)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (~((sdtmndt0(sdtpldt0(xS, xx), xx) = xS) | (~(aSet0(sdtmndt0(sdtpldt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (aElement0(W0) & aElementOf0(W0, sdtpldt0(xS, xx)) & (~(W0 = xx)))))) | (~(aSet0(sdtpldt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, xS)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (aSet0(sdtmndt0(sdtpldt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (aElement0(W0) & aElementOf0(W0, sdtpldt0(xS, xx)) & (~(W0 = xx))))),
% 0.20/0.40 inference(or_elim,[status(thm)],[5])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.20/0.40 inference(and_elim,[status(thm)],[6])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (aElement0(xx) <=> aElement0(xx)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(10,axiom,(aElement0(xx) & aSet0(xS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__679')).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (aElement0(xx)),
% 0.20/0.40 inference(and_elim,[status(thm)],[10])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (aElement0(xx)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[11, 9])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite((~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))) <=> (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))), (![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))) <=> ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))), (((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))))))))))))))), rewrite(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))))))))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))), (((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (^[W0: $i, W1: $i] : refl(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (^[W0: $i, W1: $i] : rewrite(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[18, 16])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aSet0(W0) & aElement0(W1)) <=> (~((~aSet0(W0)) | (~aElement0(W1))))), ((~(aSet0(W0) & aElement0(W1))) <=> (~(~((~aSet0(W0)) | (~aElement0(W1))))))), rewrite((~(~((~aSet0(W0)) | (~aElement0(W1))))) <=> ((~aSet0(W0)) | (~aElement0(W1)))), ((~(aSet0(W0) & aElement0(W1))) <=> ((~aSet0(W0)) | (~aElement0(W1))))), quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(rewrite(((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) <=> ((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))), trans(monotonicity(trans(monotonicity(rewrite((aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))) <=> (~((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))), (((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (~((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))), rewrite(((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (~((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))) <=> (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))), (((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))), (((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))) <=> ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))), rewrite(((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))) <=> ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))), (((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))) <=> ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))), ((((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))) <=> (((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))))))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))), rewrite((((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))))))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) <=> (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))), ((((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))) <=> (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))))), (![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))) <=> ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))))), (((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) <=> (((~aSet0(W0)) | (~aElement0(W1))) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))))), rewrite((((~aSet0(W0)) | (~aElement0(W1))) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))))), (((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (^[W0: $i, W1: $i] : rewrite(((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite(((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1)))))) <=> ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))), (![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1)))))) <=> ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))), (((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1))))))) <=> ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0))))))))), rewrite(((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))), (((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (![W0: $i, W1: $i] : ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.41 tff(27,axiom,(![W0: $i, W1: $i] : ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefCons')).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.41 tff(30,plain,(
% 0.20/0.41 ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[29])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[32, 19])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[33, 14])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (((~![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)) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)) | (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)) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)) | (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)))))))))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)) | (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)) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)) | (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)))))))))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (^[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)) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)) | (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)))))))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (![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)) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)) | (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))))))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (((~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)) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)) | (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)))))))))))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[38])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (((~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)) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)) | (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)))))))))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[39, 36])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (((~![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)) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)) | (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))))))))))))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[40])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (((~![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)) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)) | (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)))))))))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[41, 35])).
% 0.20/0.43 tff(43,plain,
% 0.20/0.43 ((~![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)))))))))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(44,plain,
% 0.20/0.43 ((~![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)) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)) | (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))))))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.43 tff(45,plain,
% 0.20/0.43 (![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)) | (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))))))))))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[44, 34, 12, 8])).
% 0.20/0.43 tff(46,plain,
% 0.20/0.43 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)) | (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(sdtpldt0(xS, xx))) | (sdtpldt0(xS, xx) = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), 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))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(47,plain,
% 0.20/0.43 (~((~((~aSet0(sdtpldt0(xS, xx))) | (sdtpldt0(xS, xx) = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), 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))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.43 tff(48,plain,
% 0.20/0.43 (((~((~aSet0(sdtpldt0(xS, xx))) | (sdtpldt0(xS, xx) = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), 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))) | (~((~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)))))))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 ((~(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))))))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.20/0.43 tff(50,plain,
% 0.20/0.43 (^[W0: $i] : refl((aElementOf0(W0, sdtpldt0(xS, xx)) <=> (~((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, xS)))))) <=> (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (~((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, xS)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 (![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (~((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, xS)))))) <=> ![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (~((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, xS))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 (^[W0: $i] : rewrite((aElementOf0(W0, sdtpldt0(xS, xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, xS)))) <=> (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (~((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, xS)))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(53,plain,
% 0.20/0.44 (![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, xS)))) <=> ![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (~((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, xS))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.44 tff(54,plain,
% 0.20/0.44 (![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, xS)))) <=> ![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, xS))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(55,plain,
% 0.20/0.44 (aSet0(sdtpldt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, xS))))),
% 0.20/0.44 inference(or_elim,[status(thm)],[5])).
% 0.20/0.44 tff(56,plain,
% 0.20/0.44 (![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, xS))))),
% 0.20/0.44 inference(and_elim,[status(thm)],[55])).
% 0.20/0.44 tff(57,plain,
% 0.20/0.44 (![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, xS))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[56, 54])).
% 0.20/0.44 tff(58,plain,(
% 0.20/0.44 ![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, xS))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[57])).
% 0.20/0.44 tff(59,plain,
% 0.20/0.44 (![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (~((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, xS))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[58, 53])).
% 0.20/0.44 tff(60,plain,
% 0.20/0.44 (![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (~((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, xS))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[59, 51])).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 (((~![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (~((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, xS))))))) | (aElementOf0(xx, sdtpldt0(xS, xx)) <=> aElement0(xx))) <=> ((~![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (~((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, xS))))))) | (aElementOf0(xx, sdtpldt0(xS, xx)) <=> aElement0(xx)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(62,plain,
% 0.20/0.44 ((aElementOf0(xx, sdtpldt0(xS, xx)) <=> (~((~aElement0(xx)) | (~((xx = xx) | aElementOf0(xx, xS)))))) <=> (aElementOf0(xx, sdtpldt0(xS, xx)) <=> aElement0(xx))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(63,plain,
% 0.20/0.44 (((~![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (~((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, xS))))))) | (aElementOf0(xx, sdtpldt0(xS, xx)) <=> (~((~aElement0(xx)) | (~((xx = xx) | aElementOf0(xx, xS))))))) <=> ((~![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (~((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, xS))))))) | (aElementOf0(xx, sdtpldt0(xS, xx)) <=> aElement0(xx)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[62])).
% 0.20/0.44 tff(64,plain,
% 0.20/0.44 (((~![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (~((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, xS))))))) | (aElementOf0(xx, sdtpldt0(xS, xx)) <=> (~((~aElement0(xx)) | (~((xx = xx) | aElementOf0(xx, xS))))))) <=> ((~![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (~((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, xS))))))) | (aElementOf0(xx, sdtpldt0(xS, xx)) <=> aElement0(xx)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[63, 61])).
% 0.20/0.44 tff(65,plain,
% 0.20/0.44 ((~![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (~((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, xS))))))) | (aElementOf0(xx, sdtpldt0(xS, xx)) <=> (~((~aElement0(xx)) | (~((xx = xx) | aElementOf0(xx, xS))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(66,plain,
% 0.20/0.44 ((~![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (~((~aElement0(W0)) | (~((W0 = xx) | aElementOf0(W0, xS))))))) | (aElementOf0(xx, sdtpldt0(xS, xx)) <=> aElement0(xx))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.44 tff(67,plain,
% 0.20/0.44 (aElementOf0(xx, sdtpldt0(xS, xx)) <=> aElement0(xx)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[66, 60])).
% 0.20/0.44 tff(68,plain,
% 0.20/0.44 ((~(aElementOf0(xx, sdtpldt0(xS, xx)) <=> aElement0(xx))) | aElementOf0(xx, sdtpldt0(xS, xx)) | (~aElement0(xx))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(69,plain,
% 0.20/0.44 ((~(aElementOf0(xx, sdtpldt0(xS, xx)) <=> aElement0(xx))) | aElementOf0(xx, sdtpldt0(xS, xx))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[68, 12])).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 (aElementOf0(xx, sdtpldt0(xS, xx))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[69, 67])).
% 0.20/0.44 tff(71,plain,
% 0.20/0.44 (aSet0(sdtpldt0(xS, xx)) <=> aSet0(sdtpldt0(xS, xx))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 (aSet0(sdtpldt0(xS, xx))),
% 0.20/0.44 inference(and_elim,[status(thm)],[55])).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 (aSet0(sdtpldt0(xS, xx))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.44 tff(74,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(77,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[77, 75])).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 (^[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)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.44 tff(82,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mConsDiff')).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.20/0.44 tff(85,plain,(
% 0.20/0.44 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[84])).
% 0.20/0.44 tff(86,plain,
% 0.20/0.44 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (sdtpldt0(sdtmndt0(W0, W1), W1) = W0)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 (((~![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))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(88,plain,
% 0.20/0.44 ((~![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))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 ((~![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)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 (![W1: $i] : ((~aElementOf0(W1, sdtpldt0(xS, xx))) | (sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), W1), W1) = sdtpldt0(xS, xx)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[89, 86, 73])).
% 0.20/0.44 tff(91,plain,
% 0.20/0.44 (((~![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(92,plain,
% 0.20/0.44 ((~![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)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 ((~![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))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 (sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx) = sdtpldt0(xS, xx)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[93, 90, 70])).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 (sdtpldt0(xS, xx) = sdtpldt0(sdtmndt0(sdtpldt0(xS, xx), xx), xx)),
% 0.20/0.44 inference(symmetry,[status(thm)],[94])).
% 0.20/0.44 tff(96,plain,
% 0.20/0.44 ((~((~(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))))))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(97,plain,
% 0.20/0.44 ((~((~(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))))))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.20/0.45 tff(98,plain,
% 0.20/0.45 (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[97, 49])).
% 0.20/0.45 tff(99,plain,
% 0.20/0.45 (((~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)))))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(100,plain,
% 0.20/0.45 (![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.20/0.45 tff(101,plain,
% 0.20/0.45 ((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))) | (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(102,plain,
% 0.20/0.45 (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.20/0.45 tff(103,plain,
% 0.20/0.45 ((~(aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))))) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx)) | ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(104,plain,
% 0.20/0.45 (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx)) | ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.20/0.45 tff(105,plain,
% 0.20/0.45 (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[104, 1])).
% 0.20/0.45 tff(106,plain,
% 0.20/0.45 (((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx))))) | aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(107,plain,
% 0.20/0.45 (aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[106, 1])).
% 0.20/0.45 tff(108,plain,
% 0.20/0.45 (aSet0(xS) <=> aSet0(xS)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(109,plain,
% 0.20/0.45 (aSet0(xS)),
% 0.20/0.45 inference(and_elim,[status(thm)],[10])).
% 0.20/0.45 tff(110,plain,
% 0.20/0.45 (aSet0(xS)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.45 tff(111,plain,
% 0.20/0.45 (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | (~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(112,plain,
% 0.20/0.45 (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(113,plain,
% 0.20/0.45 (^[W2: $i] : rewrite((~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))) <=> (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(114,plain,
% 0.20/0.45 (![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))) <=> ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[113])).
% 0.20/0.45 tff(115,plain,
% 0.20/0.45 (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[114])).
% 0.20/0.45 tff(116,plain,
% 0.20/0.45 (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[115, 112])).
% 0.20/0.45 tff(117,plain,
% 0.20/0.45 (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[116])).
% 0.20/0.45 tff(118,plain,
% 0.20/0.45 (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | (~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[117, 111])).
% 0.20/0.45 tff(119,plain,
% 0.20/0.45 ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(120,plain,
% 0.20/0.45 ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0))))))))))))))) | (~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.45 tff(121,plain,
% 0.20/0.45 (![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[120, 34, 12, 110])).
% 0.20/0.45 tff(122,plain,
% 0.20/0.45 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(123,plain,
% 0.20/0.46 ((~((~((~aSet0(sdtpldt0(xS, xx))) | (sdtpldt0(xS, xx) = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), sdtpldt0(xS, xx)) <=> ((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS))) | (~((tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), xS))))))) | (~((~(sdtpldt0(xS, xx) = sdtpldt0(xS, xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))))) <=> (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(124,plain,
% 0.20/0.46 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) | (~((~((~aSet0(sdtpldt0(xS, xx))) | (sdtpldt0(xS, xx) = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), sdtpldt0(xS, xx)) <=> ((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS))) | (~((tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), xS))))))) | (~((~(sdtpldt0(xS, xx) = sdtpldt0(xS, xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[123])).
% 0.20/0.46 tff(125,plain,
% 0.20/0.46 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) | (~((~((~aSet0(sdtpldt0(xS, xx))) | (sdtpldt0(xS, xx) = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), sdtpldt0(xS, xx)) <=> ((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS))) | (~((tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), xS))))))) | (~((~(sdtpldt0(xS, xx) = sdtpldt0(xS, xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[124, 122])).
% 0.20/0.46 tff(126,plain,
% 0.20/0.46 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) | (~((~((~aSet0(sdtpldt0(xS, xx))) | (sdtpldt0(xS, xx) = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), sdtpldt0(xS, xx)) <=> ((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS))) | (~((tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), xS))))))) | (~((~(sdtpldt0(xS, xx) = sdtpldt0(xS, xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(127,plain,
% 0.20/0.46 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS))))))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))))))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.20/0.46 tff(128,plain,
% 0.20/0.46 (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[127, 121])).
% 0.20/0.46 tff(129,plain,
% 0.20/0.46 (((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))))))) | ![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(130,plain,
% 0.20/0.46 (![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.20/0.46 tff(131,plain,
% 0.20/0.46 ((~![W3: $i] : (aElementOf0(W3, sdtpldt0(xS, xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS))))))) | (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(132,plain,
% 0.20/0.46 (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.20/0.46 tff(133,plain,
% 0.20/0.46 ((~(aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))))))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(134,plain,
% 0.20/0.46 ((~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.20/0.46 tff(135,plain,
% 0.20/0.46 (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[134, 105])).
% 0.20/0.46 tff(136,plain,
% 0.20/0.46 (((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))) | ((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(137,plain,
% 0.20/0.46 ((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.20/0.46 tff(138,assumption,(~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)), introduced(assumption)).
% 0.20/0.46 tff(139,plain,
% 0.20/0.46 (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite((~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))) <=> (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))), (![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))) <=> ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))), (((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)))))))))))))), rewrite(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)))))))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))), (((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(140,plain,
% 0.20/0.46 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[139])).
% 0.20/0.46 tff(141,plain,
% 0.20/0.46 (^[W0: $i, W1: $i] : refl(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(142,plain,
% 0.20/0.46 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[141])).
% 0.20/0.47 tff(143,plain,
% 0.20/0.47 (^[W0: $i, W1: $i] : rewrite(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(144,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[143])).
% 0.20/0.47 tff(145,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[144, 142])).
% 0.20/0.47 tff(146,plain,
% 0.20/0.47 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aSet0(W0) & aElement0(W1)) <=> (~((~aSet0(W0)) | (~aElement0(W1))))), ((~(aSet0(W0) & aElement0(W1))) <=> (~(~((~aSet0(W0)) | (~aElement0(W1))))))), rewrite((~(~((~aSet0(W0)) | (~aElement0(W1))))) <=> ((~aSet0(W0)) | (~aElement0(W1)))), ((~(aSet0(W0) & aElement0(W1))) <=> ((~aSet0(W0)) | (~aElement0(W1))))), quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(rewrite(((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) <=> ((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))), trans(monotonicity(trans(monotonicity(rewrite((aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))) <=> (~((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))), (((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))) <=> ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (~((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))), rewrite(((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (~((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))) <=> (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))), (((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))) <=> (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))), (((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))) <=> ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))), rewrite(((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))) <=> ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))), (((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))) <=> ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))), ((((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))) <=> (((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)))))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))), rewrite((((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)))))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) <=> (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))), ((((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))) <=> (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))))), (![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))) <=> ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))))), (((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))) <=> (((~aSet0(W0)) | (~aElement0(W1))) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))))), rewrite((((~aSet0(W0)) | (~aElement0(W1))) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))))), (((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(147,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[146])).
% 0.20/0.47 tff(148,plain,
% 0.20/0.47 (^[W0: $i, W1: $i] : rewrite(((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(149,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[148])).
% 0.20/0.47 tff(150,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(151,plain,
% 0.20/0.47 (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite(((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1)))))) <=> ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))), (![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1)))))) <=> ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))), (((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1))))))) <=> ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1))))))))), rewrite(((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))), (((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(152,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[151])).
% 0.20/0.47 tff(153,axiom,(![W0: $i, W1: $i] : ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefDiff')).
% 0.20/0.47 tff(154,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.47 tff(155,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.20/0.47 tff(156,plain,(
% 0.20/0.47 ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[155])).
% 0.20/0.47 tff(157,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[156, 149])).
% 0.20/0.47 tff(158,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[157, 147])).
% 0.20/0.47 tff(159,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[158, 145])).
% 0.20/0.47 tff(160,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[159, 140])).
% 0.20/0.47 tff(161,plain,
% 0.20/0.47 (((~![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))))))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(162,plain,
% 0.20/0.47 (((~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))))))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(163,plain,
% 0.20/0.47 (^[W2: $i] : rewrite((~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))))))))) <=> (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(164,plain,
% 0.20/0.47 (![W2: $i] : (~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))))))))) <=> ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[163])).
% 0.20/0.47 tff(165,plain,
% 0.20/0.47 (((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))))))))) <=> ((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))))))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[164])).
% 0.20/0.47 tff(166,plain,
% 0.20/0.47 (((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))))))))) <=> ((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[165, 162])).
% 0.20/0.47 tff(167,plain,
% 0.20/0.47 (((~![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)))))))))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[166])).
% 0.20/0.47 tff(168,plain,
% 0.20/0.47 (((~![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))))))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[167, 161])).
% 0.20/0.48 tff(169,plain,
% 0.20/0.48 ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1))))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1))))))))))))) | ((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))))))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(170,plain,
% 0.20/0.48 ((~![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)))))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.20/0.48 tff(171,plain,
% 0.20/0.48 (![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[170, 160, 12, 73])).
% 0.20/0.48 tff(172,plain,
% 0.20/0.48 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2) <=> ((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))))))))) | (~((~((~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(xS = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W3: $i] : (aElementOf0(W3, xS) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(173,plain,
% 0.20/0.48 (~((~((~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(xS = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W3: $i] : (aElementOf0(W3, xS) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx))))))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.20/0.48 tff(174,plain,
% 0.20/0.48 (((~((~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))))) | (~((~(xS = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W3: $i] : (aElementOf0(W3, xS) <=> (~((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)))))))))) | ((~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(175,plain,
% 0.20/0.48 ((~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.20/0.48 tff(176,plain,
% 0.20/0.48 ((xS = sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (sdtmndt0(sdtpldt0(xS, xx), xx) = xS)),
% 0.20/0.48 inference(commutativity,[status(thm)],[])).
% 0.20/0.48 tff(177,plain,
% 0.20/0.48 ((sdtmndt0(sdtpldt0(xS, xx), xx) = xS) <=> (xS = sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.20/0.48 inference(symmetry,[status(thm)],[176])).
% 0.20/0.48 tff(178,plain,
% 0.20/0.48 ((~(sdtmndt0(sdtpldt0(xS, xx), xx) = xS)) <=> (~(xS = sdtmndt0(sdtpldt0(xS, xx), xx)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[177])).
% 0.20/0.48 tff(179,plain,
% 0.20/0.48 ((~(sdtmndt0(sdtpldt0(xS, xx), xx) = xS)) <=> (~(sdtmndt0(sdtpldt0(xS, xx), xx) = xS))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(180,plain,
% 0.20/0.48 (~(sdtmndt0(sdtpldt0(xS, xx), xx) = xS)),
% 0.20/0.48 inference(or_elim,[status(thm)],[5])).
% 0.20/0.48 tff(181,plain,
% 0.20/0.48 (~(sdtmndt0(sdtpldt0(xS, xx), xx) = xS)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.20/0.48 tff(182,plain,
% 0.20/0.48 (~(xS = sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[181, 178])).
% 0.20/0.48 tff(183,plain,
% 0.20/0.48 ((~((~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))))) | (~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(184,plain,
% 0.20/0.48 ((~((~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))))) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[183, 110])).
% 0.20/0.48 tff(185,plain,
% 0.20/0.48 (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[184, 182, 175])).
% 0.20/0.48 tff(186,plain,
% 0.20/0.48 ((~(aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)))) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) | (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(187,plain,
% 0.20/0.48 (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) | (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.20/0.48 tff(188,plain,
% 0.20/0.48 (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[187, 138])).
% 0.20/0.48 tff(189,assumption,((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)), introduced(assumption)).
% 0.20/0.48 tff(190,plain,
% 0.20/0.48 ((~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(191,plain,
% 0.20/0.48 (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[190, 138, 189])).
% 0.20/0.48 tff(192,plain,
% 0.20/0.48 (((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)) | (~(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(193,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[192, 191, 188])).
% 0.20/0.48 tff(194,plain,(aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(195,plain,
% 0.20/0.48 (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[194, 137])).
% 0.20/0.48 tff(196,plain,
% 0.20/0.48 ((~(aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)) | ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(197,plain,
% 0.20/0.48 ((~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)) | ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[196, 185])).
% 0.20/0.48 tff(198,plain,
% 0.20/0.48 ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[197, 195])).
% 0.20/0.48 tff(199,plain,
% 0.20/0.48 ((~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))) | (~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(200,plain,
% 0.20/0.48 (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[199, 198, 107, 105])).
% 0.20/0.48 tff(201,plain,
% 0.20/0.48 (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> aElementOf0(xx, xS)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[200])).
% 0.20/0.48 tff(202,plain,
% 0.20/0.48 (aElementOf0(xx, xS) <=> aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)),
% 0.20/0.48 inference(symmetry,[status(thm)],[201])).
% 0.20/0.48 tff(203,plain,
% 0.20/0.48 ((~aElementOf0(xx, xS)) <=> (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[202])).
% 0.20/0.48 tff(204,plain,
% 0.20/0.48 ((~aElementOf0(xx, xS)) <=> (~aElementOf0(xx, xS))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(205,axiom,(~aElementOf0(xx, xS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__679_02')).
% 0.20/0.48 tff(206,plain,
% 0.20/0.48 (~aElementOf0(xx, xS)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.20/0.48 tff(207,plain,
% 0.20/0.48 (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[206, 203])).
% 0.20/0.48 tff(208,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[195, 207])).
% 0.20/0.48 tff(209,plain,((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(210,plain,
% 0.20/0.48 ((~(aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx))))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(211,plain,
% 0.20/0.48 ((~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[210, 102])).
% 0.20/0.48 tff(212,plain,
% 0.20/0.48 (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[211, 209])).
% 0.20/0.48 tff(213,plain,
% 0.20/0.48 ((~(aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx)) <=> (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))))))) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx)) | ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(214,plain,
% 0.20/0.48 (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx)) | ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[213, 132])).
% 0.20/0.49 tff(215,plain,
% 0.20/0.49 ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[214, 212])).
% 0.20/0.49 tff(216,plain,
% 0.20/0.49 (((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(217,plain,
% 0.20/0.49 ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[216, 212])).
% 0.20/0.49 tff(218,plain,
% 0.20/0.49 (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[187, 217])).
% 0.20/0.49 tff(219,plain,
% 0.20/0.49 (((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(220,plain,
% 0.20/0.49 ((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[219, 218])).
% 0.20/0.49 tff(221,plain,
% 0.20/0.49 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(222,plain,
% 0.20/0.49 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[221])).
% 0.20/0.49 tff(223,plain,
% 0.20/0.49 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(224,plain,
% 0.20/0.49 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[223])).
% 0.20/0.49 tff(225,plain,
% 0.20/0.49 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[224, 222])).
% 0.20/0.49 tff(226,plain,
% 0.20/0.49 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(227,plain,
% 0.20/0.49 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, W0) => aElement0(W1)) <=> (aElement0(W1) | (~aElementOf0(W1, W0))))), (![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)) <=> ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))), ((aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> (aSet0(W0) => ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))), rewrite((aSet0(W0) => ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))), ((aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(228,plain,
% 0.20/0.49 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[227])).
% 0.20/0.49 tff(229,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mEOfElem')).
% 0.20/0.49 tff(230,plain,
% 0.20/0.49 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.20/0.49 tff(231,plain,
% 0.20/0.49 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[230, 226])).
% 0.20/0.49 tff(232,plain,(
% 0.20/0.49 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[231])).
% 0.20/0.49 tff(233,plain,
% 0.20/0.49 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[232, 225])).
% 0.20/0.49 tff(234,plain,
% 0.20/0.49 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(235,plain,
% 0.20/0.49 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(236,plain,
% 0.20/0.49 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.20/0.49 tff(237,plain,
% 0.20/0.49 (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[236, 233, 110])).
% 0.20/0.49 tff(238,plain,
% 0.20/0.49 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(239,plain,
% 0.20/0.49 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(240,plain,
% 0.20/0.49 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.20/0.49 tff(241,plain,
% 0.20/0.49 (aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[240, 237])).
% 0.20/0.49 tff(242,plain,
% 0.20/0.49 (aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[241, 218])).
% 0.20/0.49 tff(243,plain,
% 0.20/0.49 ((~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))))) | (~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(244,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[243, 242, 220, 215])).
% 0.20/0.49 % SZS output end Proof
%------------------------------------------------------------------------------