TSTP Solution File: NUM556+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM556+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 13:10:29 EDT 2022
% Result : Theorem 4.45s 3.02s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : NUM556+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n015.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Sep 2 11:55:24 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 4.45/3.02 % SZS status Theorem
% 4.45/3.02 % SZS output start Proof
% 4.45/3.02 tff(aElementOf0_type, type, (
% 4.45/3.02 aElementOf0: ( $i * $i ) > $o)).
% 4.45/3.02 tff(xS_type, type, (
% 4.45/3.02 xS: $i)).
% 4.45/3.02 tff(tptp_fun_W0_14_type, type, (
% 4.45/3.02 tptp_fun_W0_14: $i)).
% 4.45/3.02 tff(xx_type, type, (
% 4.45/3.02 xx: $i)).
% 4.45/3.02 tff(sdtmndt0_type, type, (
% 4.45/3.02 sdtmndt0: ( $i * $i ) > $i)).
% 4.45/3.02 tff(xy_type, type, (
% 4.45/3.02 xy: $i)).
% 4.45/3.02 tff(xQ_type, type, (
% 4.45/3.02 xQ: $i)).
% 4.45/3.02 tff(aElement0_type, type, (
% 4.45/3.02 aElement0: $i > $o)).
% 4.45/3.02 tff(sdtpldt0_type, type, (
% 4.45/3.02 sdtpldt0: ( $i * $i ) > $i)).
% 4.45/3.02 tff(aSet0_type, type, (
% 4.45/3.02 aSet0: $i > $o)).
% 4.45/3.02 tff(tptp_fun_W3_2_type, type, (
% 4.45/3.02 tptp_fun_W3_2: ( $i * $i * $i ) > $i)).
% 4.45/3.02 tff(xT_type, type, (
% 4.45/3.02 xT: $i)).
% 4.45/3.02 tff(sz00_type, type, (
% 4.45/3.02 sz00: $i)).
% 4.45/3.02 tff(xk_type, type, (
% 4.45/3.02 xk: $i)).
% 4.45/3.02 tff(xP_type, type, (
% 4.45/3.02 xP: $i)).
% 4.45/3.02 tff(aSubsetOf0_type, type, (
% 4.45/3.02 aSubsetOf0: ( $i * $i ) > $o)).
% 4.45/3.02 tff(sbrdtbr0_type, type, (
% 4.45/3.02 sbrdtbr0: $i > $i)).
% 4.45/3.02 tff(szszuzczcdt0_type, type, (
% 4.45/3.02 szszuzczcdt0: $i > $i)).
% 4.45/3.02 tff(isFinite0_type, type, (
% 4.45/3.02 isFinite0: $i > $o)).
% 4.45/3.02 tff(slbdtsldtrb0_type, type, (
% 4.45/3.02 slbdtsldtrb0: ( $i * $i ) > $i)).
% 4.45/3.02 tff(tptp_fun_W3_3_type, type, (
% 4.45/3.02 tptp_fun_W3_3: ( $i * $i * $i ) > $i)).
% 4.45/3.02 tff(tptp_fun_W2_1_type, type, (
% 4.45/3.02 tptp_fun_W2_1: ( $i * $i ) > $i)).
% 4.45/3.02 tff(1,plain,
% 4.45/3.02 (aSet0(xS) <=> aSet0(xS)),
% 4.45/3.02 inference(rewrite,[status(thm)],[])).
% 4.45/3.02 tff(2,axiom,((aSet0(xS) & aSet0(xT)) & (~(xk = sz00))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2202_02')).
% 4.45/3.02 tff(3,plain,
% 4.45/3.02 (aSet0(xS) & aSet0(xT)),
% 4.45/3.02 inference(and_elim,[status(thm)],[2])).
% 4.45/3.02 tff(4,plain,
% 4.45/3.02 (aSet0(xS)),
% 4.45/3.02 inference(and_elim,[status(thm)],[3])).
% 4.45/3.02 tff(5,plain,
% 4.45/3.02 (aSet0(xS)),
% 4.45/3.02 inference(modus_ponens,[status(thm)],[4, 1])).
% 4.45/3.02 tff(6,plain,
% 4.45/3.02 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 4.45/3.02 inference(bind,[status(th)],[])).
% 4.45/3.02 tff(7,plain,
% 4.45/3.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.45/3.02 inference(quant_intro,[status(thm)],[6])).
% 4.45/3.02 tff(8,plain,
% 4.45/3.02 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 4.45/3.02 inference(bind,[status(th)],[])).
% 4.45/3.02 tff(9,plain,
% 4.45/3.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.45/3.02 inference(quant_intro,[status(thm)],[8])).
% 4.45/3.02 tff(10,plain,
% 4.45/3.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.45/3.02 inference(transitivity,[status(thm)],[9, 7])).
% 4.45/3.02 tff(11,plain,
% 4.45/3.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.45/3.02 inference(rewrite,[status(thm)],[])).
% 4.45/3.02 tff(12,plain,
% 4.45/3.02 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, W0) => aElement0(W1)) <=> (aElement0(W1) | (~aElementOf0(W1, W0))))), (![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)) <=> ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))), ((aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> (aSet0(W0) => ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))), rewrite((aSet0(W0) => ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))), ((aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))))),
% 4.45/3.02 inference(bind,[status(th)],[])).
% 4.45/3.02 tff(13,plain,
% 4.45/3.02 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.45/3.02 inference(quant_intro,[status(thm)],[12])).
% 4.45/3.02 tff(14,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mEOfElem')).
% 4.45/3.02 tff(15,plain,
% 4.45/3.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.45/3.02 inference(modus_ponens,[status(thm)],[14, 13])).
% 4.45/3.02 tff(16,plain,
% 4.45/3.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.45/3.02 inference(modus_ponens,[status(thm)],[15, 11])).
% 4.45/3.02 tff(17,plain,(
% 4.45/3.02 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.45/3.02 inference(skolemize,[status(sab)],[16])).
% 4.45/3.02 tff(18,plain,
% 4.45/3.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.45/3.02 inference(modus_ponens,[status(thm)],[17, 10])).
% 4.45/3.02 tff(19,plain,
% 4.45/3.02 (((~![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))))),
% 4.45/3.02 inference(rewrite,[status(thm)],[])).
% 4.45/3.02 tff(20,plain,
% 4.45/3.02 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))),
% 4.45/3.02 inference(quant_inst,[status(thm)],[])).
% 4.45/3.02 tff(21,plain,
% 4.45/3.02 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 4.45/3.02 inference(modus_ponens,[status(thm)],[20, 19])).
% 4.45/3.02 tff(22,plain,
% 4.45/3.02 (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 4.45/3.02 inference(unit_resolution,[status(thm)],[21, 18, 5])).
% 4.45/3.02 tff(23,plain,
% 4.45/3.02 (aElementOf0(xx, xS) <=> aElementOf0(xx, xS)),
% 4.45/3.02 inference(rewrite,[status(thm)],[])).
% 4.45/3.02 tff(24,axiom,(aElementOf0(xx, xS)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2256')).
% 4.45/3.02 tff(25,plain,
% 4.45/3.02 (aElementOf0(xx, xS)),
% 4.45/3.02 inference(modus_ponens,[status(thm)],[24, 23])).
% 4.45/3.02 tff(26,plain,
% 4.45/3.02 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(xx) | (~aElementOf0(xx, xS)))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(xx) | (~aElementOf0(xx, xS)))),
% 4.45/3.02 inference(rewrite,[status(thm)],[])).
% 4.45/3.02 tff(27,plain,
% 4.45/3.02 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(xx) | (~aElementOf0(xx, xS)))),
% 4.45/3.02 inference(quant_inst,[status(thm)],[])).
% 4.45/3.02 tff(28,plain,
% 4.45/3.02 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(xx) | (~aElementOf0(xx, xS))),
% 4.45/3.02 inference(modus_ponens,[status(thm)],[27, 26])).
% 4.45/3.02 tff(29,plain,
% 4.45/3.02 (aElement0(xx)),
% 4.45/3.02 inference(unit_resolution,[status(thm)],[28, 25, 22])).
% 4.45/3.02 tff(30,plain,
% 4.45/3.02 (aSet0(sdtmndt0(xQ, xy)) <=> aSet0(sdtmndt0(xQ, xy))),
% 4.45/3.02 inference(rewrite,[status(thm)],[])).
% 4.45/3.02 tff(31,axiom,((((aSet0(sdtmndt0(xQ, xy)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = xy))))) & aSet0(xP)) & ![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx))))) & (xP = sdtpldt0(sdtmndt0(xQ, xy), xx))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2357')).
% 4.45/3.02 tff(32,plain,
% 4.45/3.02 (((aSet0(sdtmndt0(xQ, xy)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = xy))))) & aSet0(xP)) & ![W0: $i] : (aElementOf0(W0, xP) <=> (aElement0(W0) & (aElementOf0(W0, sdtmndt0(xQ, xy)) | (W0 = xx))))),
% 4.45/3.02 inference(and_elim,[status(thm)],[31])).
% 4.45/3.02 tff(33,plain,
% 4.45/3.02 ((aSet0(sdtmndt0(xQ, xy)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = xy))))) & aSet0(xP)),
% 4.45/3.02 inference(and_elim,[status(thm)],[32])).
% 4.45/3.02 tff(34,plain,
% 4.45/3.02 (aSet0(sdtmndt0(xQ, xy)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = xy))))),
% 4.45/3.02 inference(and_elim,[status(thm)],[33])).
% 4.45/3.02 tff(35,plain,
% 4.45/3.02 (aSet0(sdtmndt0(xQ, xy))),
% 4.45/3.02 inference(and_elim,[status(thm)],[34])).
% 4.45/3.02 tff(36,plain,
% 4.45/3.02 (aSet0(sdtmndt0(xQ, xy))),
% 4.45/3.02 inference(modus_ponens,[status(thm)],[35, 30])).
% 4.45/3.02 tff(37,plain,
% 4.45/3.02 (^[W0: $i, W1: $i] : rewrite(((~aElement0(W1)) | (~aSet0(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)))))))))) <=> ((~aElement0(W1)) | (~aSet0(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)))))))))))))))),
% 4.45/3.02 inference(bind,[status(th)],[])).
% 4.45/3.02 tff(38,plain,
% 4.45/3.02 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aSet0(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)))))))))) <=> ![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aSet0(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))))))))))))))),
% 4.45/3.02 inference(quant_intro,[status(thm)],[37])).
% 4.45/3.02 tff(39,plain,
% 4.45/3.02 (^[W0: $i, W1: $i] : refl(((~aElement0(W1)) | (~aSet0(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)))))))))) <=> ((~aElement0(W1)) | (~aSet0(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)))))))))))),
% 4.45/3.02 inference(bind,[status(th)],[])).
% 4.45/3.02 tff(40,plain,
% 4.45/3.02 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aSet0(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)))))))))) <=> ![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aSet0(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))))))))))),
% 4.45/3.02 inference(quant_intro,[status(thm)],[39])).
% 4.45/3.02 tff(41,plain,
% 4.45/3.02 (^[W0: $i, W1: $i] : rewrite(((~aElement0(W1)) | (~aSet0(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)))))))))) <=> ((~aElement0(W1)) | (~aSet0(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)))))))))))),
% 4.45/3.02 inference(bind,[status(th)],[])).
% 4.45/3.02 tff(42,plain,
% 4.45/3.02 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aSet0(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)))))))))) <=> ![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aSet0(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))))))))))),
% 4.45/3.02 inference(quant_intro,[status(thm)],[41])).
% 4.45/3.02 tff(43,plain,
% 4.45/3.02 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aSet0(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)))))))))) <=> ![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aSet0(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))))))))))),
% 4.45/3.02 inference(transitivity,[status(thm)],[42, 40])).
% 4.45/3.02 tff(44,plain,
% 4.45/3.02 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aSet0(W0) & aElement0(W1)) <=> (~((~aElement0(W1)) | (~aSet0(W0))))), ((~(aSet0(W0) & aElement0(W1))) <=> (~(~((~aElement0(W1)) | (~aSet0(W0))))))), rewrite((~(~((~aElement0(W1)) | (~aSet0(W0))))) <=> ((~aElement0(W1)) | (~aSet0(W0)))), ((~(aSet0(W0) & aElement0(W1))) <=> ((~aElement0(W1)) | (~aSet0(W0))))), 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))))))) <=> (((~aElement0(W1)) | (~aSet0(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)))))))))))), rewrite((((~aElement0(W1)) | (~aSet0(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)))))))))) <=> ((~aElement0(W1)) | (~aSet0(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))))))) <=> ((~aElement0(W1)) | (~aSet0(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))))))))))))),
% 4.45/3.03 inference(bind,[status(th)],[])).
% 4.45/3.03 tff(45,plain,
% 4.45/3.03 (![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] : ((~aElement0(W1)) | (~aSet0(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))))))))))),
% 4.45/3.03 inference(quant_intro,[status(thm)],[44])).
% 4.45/3.03 tff(46,plain,
% 4.45/3.03 (^[W0: $i, W1: $i] : rewrite(((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))),
% 4.45/3.03 inference(bind,[status(th)],[])).
% 4.45/3.03 tff(47,plain,
% 4.45/3.03 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))),
% 4.45/3.03 inference(quant_intro,[status(thm)],[46])).
% 4.45/3.03 tff(48,plain,
% 4.45/3.03 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))),
% 4.45/3.03 inference(rewrite,[status(thm)],[])).
% 4.45/3.03 tff(49,plain,
% 4.45/3.03 (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite(((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1)))))) <=> ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))), (![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1)))))) <=> ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))), (((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1))))))) <=> ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0))))))))), rewrite(((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))), (((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))))),
% 4.45/3.03 inference(bind,[status(th)],[])).
% 4.45/3.03 tff(50,plain,
% 4.45/3.03 (![W0: $i, W1: $i] : ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))),
% 4.45/3.03 inference(quant_intro,[status(thm)],[49])).
% 4.45/3.03 tff(51,axiom,(![W0: $i, W1: $i] : ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mDefCons')).
% 4.45/3.03 tff(52,plain,
% 4.45/3.03 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))),
% 4.45/3.03 inference(modus_ponens,[status(thm)],[51, 50])).
% 4.45/3.03 tff(53,plain,
% 4.45/3.03 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))),
% 4.45/3.03 inference(modus_ponens,[status(thm)],[52, 48])).
% 4.45/3.03 tff(54,plain,(
% 4.45/3.03 ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))),
% 4.45/3.03 inference(skolemize,[status(sab)],[53])).
% 4.45/3.03 tff(55,plain,
% 4.45/3.03 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | ((~aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))),
% 4.45/3.03 inference(modus_ponens,[status(thm)],[54, 47])).
% 4.45/3.03 tff(56,plain,
% 4.45/3.03 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aSet0(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))))))))))),
% 4.45/3.03 inference(modus_ponens,[status(thm)],[55, 45])).
% 4.45/3.03 tff(57,plain,
% 4.45/3.03 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aSet0(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))))))))))),
% 4.45/3.03 inference(modus_ponens,[status(thm)],[56, 43])).
% 4.45/3.03 tff(58,plain,
% 4.45/3.03 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aSet0(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))))))))))))))),
% 4.45/3.03 inference(modus_ponens,[status(thm)],[57, 38])).
% 4.45/3.03 tff(59,plain,
% 4.45/3.03 (((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aSet0(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))))))))))))))) | ((~aElement0(xx)) | (~aSet0(sdtmndt0(xQ, xy))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy)))))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aSet0(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))))))))))))))) | (~aElement0(xx)) | (~aSet0(sdtmndt0(xQ, xy))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy)))))))))))))))),
% 4.45/3.03 inference(rewrite,[status(thm)],[])).
% 4.45/3.03 tff(60,plain,
% 4.45/3.03 (((~aElement0(xx)) | (~aSet0(sdtmndt0(xQ, xy))) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy))))))))))))))) <=> ((~aElement0(xx)) | (~aSet0(sdtmndt0(xQ, xy))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy)))))))))))))))),
% 4.45/3.03 inference(rewrite,[status(thm)],[])).
% 4.45/3.03 tff(61,plain,
% 4.45/3.03 (((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aSet0(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))))))))))))))) | ((~aElement0(xx)) | (~aSet0(sdtmndt0(xQ, xy))) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy)))))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aSet0(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))))))))))))))) | ((~aElement0(xx)) | (~aSet0(sdtmndt0(xQ, xy))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy))))))))))))))))),
% 4.45/3.04 inference(monotonicity,[status(thm)],[60])).
% 4.45/3.04 tff(62,plain,
% 4.45/3.04 (((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aSet0(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))))))))))))))) | ((~aElement0(xx)) | (~aSet0(sdtmndt0(xQ, xy))) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy)))))))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aSet0(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))))))))))))))) | (~aElement0(xx)) | (~aSet0(sdtmndt0(xQ, xy))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy)))))))))))))))),
% 4.45/3.04 inference(transitivity,[status(thm)],[61, 59])).
% 4.45/3.04 tff(63,plain,
% 4.45/3.04 ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aSet0(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))))))))))))))) | ((~aElement0(xx)) | (~aSet0(sdtmndt0(xQ, xy))) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (~aSet0(W2)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy)))))))))))))))),
% 4.45/3.04 inference(quant_inst,[status(thm)],[])).
% 4.45/3.04 tff(64,plain,
% 4.45/3.04 ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aSet0(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))))))))))))))) | (~aElement0(xx)) | (~aSet0(sdtmndt0(xQ, xy))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy))))))))))))))),
% 4.45/3.04 inference(modus_ponens,[status(thm)],[63, 62])).
% 4.45/3.04 tff(65,plain,
% 4.45/3.04 ((~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy))))))))))))))),
% 4.45/3.04 inference(unit_resolution,[status(thm)],[64, 58, 36])).
% 4.45/3.04 tff(66,plain,
% 4.45/3.04 (![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy))))))))))))))),
% 4.45/3.04 inference(unit_resolution,[status(thm)],[65, 29])).
% 4.45/3.04 tff(67,plain,
% 4.45/3.04 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy))))))))))))))) | (~((~aSet0(sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy))))))))))))))) | (~((~aSet0(sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy)))))))))))),
% 4.45/3.04 inference(rewrite,[status(thm)],[])).
% 4.45/3.04 tff(68,plain,
% 4.45/3.04 ((~((~((~aSet0(sdtpldt0(sdtmndt0(xQ, xy), xx))) | (sdtpldt0(sdtmndt0(xQ, xy), xx) = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (aElementOf0(tptp_fun_W3_2(sdtpldt0(sdtmndt0(xQ, xy), xx), xx, sdtmndt0(xQ, xy)), sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> ((~aElement0(tptp_fun_W3_2(sdtpldt0(sdtmndt0(xQ, xy), xx), xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(sdtpldt0(sdtmndt0(xQ, xy), xx), xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(sdtmndt0(xQ, xy), xx), xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(sdtpldt0(sdtmndt0(xQ, xy), xx) = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy)))))))))))))) <=> (~((~aSet0(sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy))))))))))),
% 4.45/3.04 inference(rewrite,[status(thm)],[])).
% 4.45/3.04 tff(69,plain,
% 4.45/3.04 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy))))))))))))))) | (~((~((~aSet0(sdtpldt0(sdtmndt0(xQ, xy), xx))) | (sdtpldt0(sdtmndt0(xQ, xy), xx) = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (aElementOf0(tptp_fun_W3_2(sdtpldt0(sdtmndt0(xQ, xy), xx), xx, sdtmndt0(xQ, xy)), sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> ((~aElement0(tptp_fun_W3_2(sdtpldt0(sdtmndt0(xQ, xy), xx), xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(sdtpldt0(sdtmndt0(xQ, xy), xx), xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(sdtmndt0(xQ, xy), xx), xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(sdtpldt0(sdtmndt0(xQ, xy), xx) = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy))))))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy))))))))))))))) | (~((~aSet0(sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy)))))))))))),
% 4.45/3.04 inference(monotonicity,[status(thm)],[68])).
% 4.45/3.04 tff(70,plain,
% 4.45/3.04 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy))))))))))))))) | (~((~((~aSet0(sdtpldt0(sdtmndt0(xQ, xy), xx))) | (sdtpldt0(sdtmndt0(xQ, xy), xx) = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (aElementOf0(tptp_fun_W3_2(sdtpldt0(sdtmndt0(xQ, xy), xx), xx, sdtmndt0(xQ, xy)), sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> ((~aElement0(tptp_fun_W3_2(sdtpldt0(sdtmndt0(xQ, xy), xx), xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(sdtpldt0(sdtmndt0(xQ, xy), xx), xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(sdtmndt0(xQ, xy), xx), xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(sdtpldt0(sdtmndt0(xQ, xy), xx) = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy))))))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy))))))))))))))) | (~((~aSet0(sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy)))))))))))),
% 4.45/3.05 inference(transitivity,[status(thm)],[69, 67])).
% 4.45/3.05 tff(71,plain,
% 4.45/3.05 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy))))))))))))))) | (~((~((~aSet0(sdtpldt0(sdtmndt0(xQ, xy), xx))) | (sdtpldt0(sdtmndt0(xQ, xy), xx) = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (aElementOf0(tptp_fun_W3_2(sdtpldt0(sdtmndt0(xQ, xy), xx), xx, sdtmndt0(xQ, xy)), sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> ((~aElement0(tptp_fun_W3_2(sdtpldt0(sdtmndt0(xQ, xy), xx), xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(sdtpldt0(sdtmndt0(xQ, xy), xx), xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(sdtmndt0(xQ, xy), xx), xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(sdtpldt0(sdtmndt0(xQ, xy), xx) = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy))))))))))))))),
% 4.45/3.05 inference(quant_inst,[status(thm)],[])).
% 4.45/3.05 tff(72,plain,
% 4.45/3.05 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xQ, xy), xx)) | (aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), W2) <=> ((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xQ, xy)), sdtmndt0(xQ, xy)))))))) | (~((~(W2 = sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (aElementOf0(W3, W2) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy))))))))))))))) | (~((~aSet0(sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy))))))))))),
% 4.45/3.05 inference(modus_ponens,[status(thm)],[71, 70])).
% 4.45/3.05 tff(73,plain,
% 4.45/3.05 (~((~aSet0(sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy)))))))))),
% 4.45/3.05 inference(unit_resolution,[status(thm)],[72, 66])).
% 4.45/3.05 tff(74,plain,
% 4.45/3.05 (((~aSet0(sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy))))))))) | ![W3: $i] : (aElementOf0(W3, sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy)))))))),
% 4.45/3.05 inference(tautology,[status(thm)],[])).
% 4.45/3.05 tff(75,plain,
% 4.45/3.05 (![W3: $i] : (aElementOf0(W3, sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy)))))))),
% 4.45/3.05 inference(unit_resolution,[status(thm)],[74, 73])).
% 4.45/3.05 tff(76,plain,
% 4.45/3.05 ((~![W3: $i] : (aElementOf0(W3, sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy)))))))) | (aElementOf0(W0!14, sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> (~((~aElement0(W0!14)) | (~((W0!14 = xx) | aElementOf0(W0!14, sdtmndt0(xQ, xy)))))))),
% 4.45/3.05 inference(quant_inst,[status(thm)],[])).
% 4.45/3.05 tff(77,plain,
% 4.45/3.05 (aElementOf0(W0!14, sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> (~((~aElement0(W0!14)) | (~((W0!14 = xx) | aElementOf0(W0!14, sdtmndt0(xQ, xy))))))),
% 4.45/3.05 inference(unit_resolution,[status(thm)],[76, 75])).
% 4.45/3.05 tff(78,plain,
% 4.45/3.05 (aSet0(xQ) <=> aSet0(xQ)),
% 4.45/3.05 inference(rewrite,[status(thm)],[])).
% 4.45/3.05 tff(79,axiom,((((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))) & aSubsetOf0(xQ, xS)) & (sbrdtbr0(xQ) = xk)) & aElementOf0(xQ, slbdtsldtrb0(xS, xk))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2270')).
% 4.45/3.05 tff(80,plain,
% 4.45/3.05 (((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))) & aSubsetOf0(xQ, xS)) & (sbrdtbr0(xQ) = xk)),
% 4.45/3.05 inference(and_elim,[status(thm)],[79])).
% 4.45/3.05 tff(81,plain,
% 4.45/3.05 ((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))) & aSubsetOf0(xQ, xS)),
% 4.45/3.05 inference(and_elim,[status(thm)],[80])).
% 4.45/3.05 tff(82,plain,
% 4.45/3.05 (aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))),
% 4.45/3.05 inference(and_elim,[status(thm)],[81])).
% 4.45/3.05 tff(83,plain,
% 4.45/3.05 (aSet0(xQ)),
% 4.45/3.05 inference(and_elim,[status(thm)],[82])).
% 4.45/3.05 tff(84,plain,
% 4.45/3.05 (aSet0(xQ)),
% 4.45/3.05 inference(modus_ponens,[status(thm)],[83, 78])).
% 4.45/3.05 tff(85,plain,
% 4.45/3.05 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0)))))),
% 4.45/3.05 inference(bind,[status(th)],[])).
% 4.45/3.05 tff(86,plain,
% 4.45/3.05 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))),
% 4.45/3.05 inference(quant_intro,[status(thm)],[85])).
% 4.45/3.05 tff(87,plain,
% 4.45/3.05 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0)))))),
% 4.45/3.05 inference(bind,[status(th)],[])).
% 4.45/3.05 tff(88,plain,
% 4.45/3.05 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))),
% 4.45/3.05 inference(quant_intro,[status(thm)],[87])).
% 4.45/3.05 tff(89,plain,
% 4.45/3.05 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))),
% 4.45/3.05 inference(transitivity,[status(thm)],[88, 86])).
% 4.45/3.05 tff(90,plain,
% 4.45/3.05 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0)))))),
% 4.45/3.05 inference(bind,[status(th)],[])).
% 4.45/3.05 tff(91,plain,
% 4.45/3.05 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))),
% 4.45/3.05 inference(quant_intro,[status(thm)],[90])).
% 4.45/3.05 tff(92,plain,
% 4.45/3.05 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))),
% 4.45/3.05 inference(rewrite,[status(thm)],[])).
% 4.45/3.05 tff(93,plain,
% 4.45/3.05 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite(((isFinite0(W0) & aElementOf0(W1, W0)) => (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))) <=> ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))), (![W1: $i] : ((isFinite0(W0) & aElementOf0(W1, W0)) => (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))) <=> ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))), ((aSet0(W0) => ![W1: $i] : ((isFinite0(W0) & aElementOf0(W1, W0)) => (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)))) <=> (aSet0(W0) => ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)))))), rewrite((aSet0(W0) => ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))), ((aSet0(W0) => ![W1: $i] : ((isFinite0(W0) & aElementOf0(W1, W0)) => (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))))),
% 4.45/3.05 inference(bind,[status(th)],[])).
% 4.45/3.05 tff(94,plain,
% 4.45/3.05 (![W0: $i] : (aSet0(W0) => ![W1: $i] : ((isFinite0(W0) & aElementOf0(W1, W0)) => (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))),
% 4.45/3.05 inference(quant_intro,[status(thm)],[93])).
% 4.45/3.05 tff(95,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : ((isFinite0(W0) & aElementOf0(W1, W0)) => (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mCardDiff')).
% 4.45/3.05 tff(96,plain,
% 4.45/3.05 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))),
% 4.45/3.05 inference(modus_ponens,[status(thm)],[95, 94])).
% 4.45/3.05 tff(97,plain,
% 4.45/3.05 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))),
% 4.45/3.05 inference(modus_ponens,[status(thm)],[96, 92])).
% 4.45/3.05 tff(98,plain,(
% 4.45/3.05 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))),
% 4.45/3.05 inference(skolemize,[status(sab)],[97])).
% 4.45/3.05 tff(99,plain,
% 4.45/3.05 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))),
% 4.45/3.05 inference(modus_ponens,[status(thm)],[98, 91])).
% 4.45/3.05 tff(100,plain,
% 4.45/3.05 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))),
% 4.45/3.05 inference(modus_ponens,[status(thm)],[99, 89])).
% 4.45/3.05 tff(101,plain,
% 4.45/3.05 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))) | ((~aSet0(xQ)) | ![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))) | (~aSet0(xQ)) | ![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ))))),
% 4.45/3.05 inference(rewrite,[status(thm)],[])).
% 4.45/3.05 tff(102,plain,
% 4.45/3.05 (((~aSet0(xQ)) | ![W1: $i] : ((~aElementOf0(W1, xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)) | (~isFinite0(xQ)))) <=> ((~aSet0(xQ)) | ![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ))))),
% 4.45/3.05 inference(rewrite,[status(thm)],[])).
% 4.45/3.05 tff(103,plain,
% 4.45/3.05 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))) | ((~aSet0(xQ)) | ![W1: $i] : ((~aElementOf0(W1, xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)) | (~isFinite0(xQ))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))) | ((~aSet0(xQ)) | ![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))))),
% 4.45/3.05 inference(monotonicity,[status(thm)],[102])).
% 4.45/3.05 tff(104,plain,
% 4.45/3.05 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))) | ((~aSet0(xQ)) | ![W1: $i] : ((~aElementOf0(W1, xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)) | (~isFinite0(xQ))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))) | (~aSet0(xQ)) | ![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ))))),
% 4.45/3.05 inference(transitivity,[status(thm)],[103, 101])).
% 4.45/3.05 tff(105,plain,
% 4.45/3.05 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))) | ((~aSet0(xQ)) | ![W1: $i] : ((~aElementOf0(W1, xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)) | (~isFinite0(xQ))))),
% 4.45/3.05 inference(quant_inst,[status(thm)],[])).
% 4.45/3.05 tff(106,plain,
% 4.45/3.05 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))) | (~aSet0(xQ)) | ![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))),
% 4.45/3.05 inference(modus_ponens,[status(thm)],[105, 104])).
% 4.45/3.05 tff(107,plain,
% 4.45/3.05 (![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))),
% 4.45/3.05 inference(unit_resolution,[status(thm)],[106, 100, 84])).
% 4.45/3.05 tff(108,plain,
% 4.45/3.05 (aElementOf0(xy, xQ) <=> aElementOf0(xy, xQ)),
% 4.45/3.05 inference(rewrite,[status(thm)],[])).
% 4.45/3.05 tff(109,axiom,(aElement0(xy) & aElementOf0(xy, xQ)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2304')).
% 4.45/3.05 tff(110,plain,
% 4.45/3.05 (aElementOf0(xy, xQ)),
% 4.45/3.05 inference(and_elim,[status(thm)],[109])).
% 4.45/3.05 tff(111,plain,
% 4.45/3.05 (aElementOf0(xy, xQ)),
% 4.45/3.05 inference(modus_ponens,[status(thm)],[110, 108])).
% 4.45/3.05 tff(112,plain,
% 4.45/3.05 (isFinite0(xQ) <=> isFinite0(xQ)),
% 4.45/3.05 inference(rewrite,[status(thm)],[])).
% 4.45/3.05 tff(113,axiom,((aSet0(xQ) & isFinite0(xQ)) & (sbrdtbr0(xQ) = xk)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2291')).
% 4.45/3.05 tff(114,plain,
% 4.45/3.05 (aSet0(xQ) & isFinite0(xQ)),
% 4.45/3.05 inference(and_elim,[status(thm)],[113])).
% 4.45/3.05 tff(115,plain,
% 4.45/3.05 (isFinite0(xQ)),
% 4.45/3.05 inference(and_elim,[status(thm)],[114])).
% 4.45/3.05 tff(116,plain,
% 4.45/3.05 (isFinite0(xQ)),
% 4.45/3.05 inference(modus_ponens,[status(thm)],[115, 112])).
% 4.45/3.05 tff(117,plain,
% 4.45/3.05 (((~![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))) | ((~isFinite0(xQ)) | (~aElementOf0(xy, xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ)))) <=> ((~![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))) | (~isFinite0(xQ)) | (~aElementOf0(xy, xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ)))),
% 4.45/3.06 inference(rewrite,[status(thm)],[])).
% 4.45/3.06 tff(118,plain,
% 4.45/3.06 (((~aElementOf0(xy, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ))) <=> ((~isFinite0(xQ)) | (~aElementOf0(xy, xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ)))),
% 4.45/3.06 inference(rewrite,[status(thm)],[])).
% 4.45/3.06 tff(119,plain,
% 4.45/3.06 (((~![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))) | ((~aElementOf0(xy, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ)))) <=> ((~![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))) | ((~isFinite0(xQ)) | (~aElementOf0(xy, xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ))))),
% 4.45/3.06 inference(monotonicity,[status(thm)],[118])).
% 4.45/3.06 tff(120,plain,
% 4.45/3.06 (((~![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))) | ((~aElementOf0(xy, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ)))) <=> ((~![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))) | (~isFinite0(xQ)) | (~aElementOf0(xy, xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ)))),
% 4.45/3.06 inference(transitivity,[status(thm)],[119, 117])).
% 4.45/3.06 tff(121,plain,
% 4.45/3.06 ((~![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))) | ((~aElementOf0(xy, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ)))),
% 4.45/3.06 inference(quant_inst,[status(thm)],[])).
% 4.45/3.06 tff(122,plain,
% 4.45/3.06 ((~![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))) | (~isFinite0(xQ)) | (~aElementOf0(xy, xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ))),
% 4.45/3.06 inference(modus_ponens,[status(thm)],[121, 120])).
% 4.45/3.06 tff(123,plain,
% 4.45/3.06 (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ)),
% 4.45/3.06 inference(unit_resolution,[status(thm)],[122, 116, 111, 107])).
% 4.45/3.06 tff(124,plain,
% 4.45/3.06 (aElement0(xy) <=> aElement0(xy)),
% 4.45/3.06 inference(rewrite,[status(thm)],[])).
% 4.45/3.06 tff(125,plain,
% 4.45/3.06 (aElement0(xy)),
% 4.45/3.06 inference(and_elim,[status(thm)],[109])).
% 4.45/3.06 tff(126,plain,
% 4.45/3.06 (aElement0(xy)),
% 4.45/3.06 inference(modus_ponens,[status(thm)],[125, 124])).
% 4.45/3.06 tff(127,plain,
% 4.45/3.06 (^[W0: $i] : refl(((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1)))) <=> ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1)))))),
% 4.45/3.06 inference(bind,[status(th)],[])).
% 4.45/3.06 tff(128,plain,
% 4.45/3.06 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1)))) <=> ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))),
% 4.45/3.06 inference(quant_intro,[status(thm)],[127])).
% 4.45/3.06 tff(129,plain,
% 4.45/3.06 (^[W0: $i] : rewrite(((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1)))) <=> ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1)))))),
% 4.45/3.06 inference(bind,[status(th)],[])).
% 4.45/3.06 tff(130,plain,
% 4.45/3.06 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1)))) <=> ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))),
% 4.45/3.06 inference(quant_intro,[status(thm)],[129])).
% 4.45/3.06 tff(131,plain,
% 4.45/3.06 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1)))) <=> ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))),
% 4.45/3.06 inference(transitivity,[status(thm)],[130, 128])).
% 4.45/3.06 tff(132,plain,
% 4.45/3.06 (^[W0: $i] : rewrite(((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1))))) <=> ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1)))))),
% 4.52/3.06 inference(bind,[status(th)],[])).
% 4.52/3.06 tff(133,plain,
% 4.52/3.06 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1))))) <=> ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))),
% 4.52/3.06 inference(quant_intro,[status(thm)],[132])).
% 4.52/3.06 tff(134,plain,
% 4.52/3.06 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1))))) <=> ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))),
% 4.52/3.06 inference(rewrite,[status(thm)],[])).
% 4.52/3.06 tff(135,plain,
% 4.52/3.06 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite(((aSet0(W1) & isFinite0(W1)) => isFinite0(sdtmndt0(W1, W0))) <=> (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))), (![W1: $i] : ((aSet0(W1) & isFinite0(W1)) => isFinite0(sdtmndt0(W1, W0))) <=> ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))), ((aElement0(W0) => ![W1: $i] : ((aSet0(W1) & isFinite0(W1)) => isFinite0(sdtmndt0(W1, W0)))) <=> (aElement0(W0) => ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1))))))), rewrite((aElement0(W0) => ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1))))) <=> ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))), ((aElement0(W0) => ![W1: $i] : ((aSet0(W1) & isFinite0(W1)) => isFinite0(sdtmndt0(W1, W0)))) <=> ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))))),
% 4.52/3.06 inference(bind,[status(th)],[])).
% 4.52/3.06 tff(136,plain,
% 4.52/3.06 (![W0: $i] : (aElement0(W0) => ![W1: $i] : ((aSet0(W1) & isFinite0(W1)) => isFinite0(sdtmndt0(W1, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))),
% 4.52/3.06 inference(quant_intro,[status(thm)],[135])).
% 4.52/3.06 tff(137,axiom,(![W0: $i] : (aElement0(W0) => ![W1: $i] : ((aSet0(W1) & isFinite0(W1)) => isFinite0(sdtmndt0(W1, W0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mFDiffSet')).
% 4.52/3.06 tff(138,plain,
% 4.52/3.06 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))),
% 4.52/3.06 inference(modus_ponens,[status(thm)],[137, 136])).
% 4.52/3.06 tff(139,plain,
% 4.52/3.06 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))),
% 4.52/3.06 inference(modus_ponens,[status(thm)],[138, 134])).
% 4.52/3.06 tff(140,plain,(
% 4.52/3.06 ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))),
% 4.52/3.06 inference(skolemize,[status(sab)],[139])).
% 4.52/3.06 tff(141,plain,
% 4.52/3.06 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))),
% 4.52/3.06 inference(modus_ponens,[status(thm)],[140, 133])).
% 4.52/3.06 tff(142,plain,
% 4.52/3.06 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))),
% 4.52/3.06 inference(modus_ponens,[status(thm)],[141, 131])).
% 4.52/3.06 tff(143,plain,
% 4.52/3.06 (((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))) | ((~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy))))) <=> ((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))) | (~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy))))),
% 4.52/3.06 inference(rewrite,[status(thm)],[])).
% 4.52/3.06 tff(144,plain,
% 4.52/3.06 (((~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, xy)) | (~aSet0(W1)))) <=> ((~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy))))),
% 4.52/3.06 inference(rewrite,[status(thm)],[])).
% 4.52/3.06 tff(145,plain,
% 4.52/3.06 (((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))) | ((~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, xy)) | (~aSet0(W1))))) <=> ((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))) | ((~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))))),
% 4.52/3.06 inference(monotonicity,[status(thm)],[144])).
% 4.52/3.06 tff(146,plain,
% 4.52/3.06 (((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))) | ((~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, xy)) | (~aSet0(W1))))) <=> ((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))) | (~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy))))),
% 4.52/3.06 inference(transitivity,[status(thm)],[145, 143])).
% 4.52/3.06 tff(147,plain,
% 4.52/3.06 ((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))) | ((~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, xy)) | (~aSet0(W1))))),
% 4.52/3.06 inference(quant_inst,[status(thm)],[])).
% 4.52/3.06 tff(148,plain,
% 4.52/3.06 ((~![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))) | (~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))),
% 4.52/3.06 inference(modus_ponens,[status(thm)],[147, 146])).
% 4.52/3.06 tff(149,plain,
% 4.52/3.06 (![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))),
% 4.52/3.06 inference(unit_resolution,[status(thm)],[148, 142, 126])).
% 4.52/3.06 tff(150,plain,
% 4.52/3.06 (((~![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))) | ((~aSet0(xQ)) | (~isFinite0(xQ)) | isFinite0(sdtmndt0(xQ, xy)))) <=> ((~![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))) | (~aSet0(xQ)) | (~isFinite0(xQ)) | isFinite0(sdtmndt0(xQ, xy)))),
% 4.52/3.06 inference(rewrite,[status(thm)],[])).
% 4.52/3.06 tff(151,plain,
% 4.52/3.06 (((~isFinite0(xQ)) | (~aSet0(xQ)) | isFinite0(sdtmndt0(xQ, xy))) <=> ((~aSet0(xQ)) | (~isFinite0(xQ)) | isFinite0(sdtmndt0(xQ, xy)))),
% 4.52/3.06 inference(rewrite,[status(thm)],[])).
% 4.52/3.06 tff(152,plain,
% 4.52/3.06 (((~![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))) | ((~isFinite0(xQ)) | (~aSet0(xQ)) | isFinite0(sdtmndt0(xQ, xy)))) <=> ((~![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))) | ((~aSet0(xQ)) | (~isFinite0(xQ)) | isFinite0(sdtmndt0(xQ, xy))))),
% 4.52/3.06 inference(monotonicity,[status(thm)],[151])).
% 4.52/3.06 tff(153,plain,
% 4.52/3.06 (((~![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))) | ((~isFinite0(xQ)) | (~aSet0(xQ)) | isFinite0(sdtmndt0(xQ, xy)))) <=> ((~![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))) | (~aSet0(xQ)) | (~isFinite0(xQ)) | isFinite0(sdtmndt0(xQ, xy)))),
% 4.52/3.06 inference(transitivity,[status(thm)],[152, 150])).
% 4.52/3.06 tff(154,plain,
% 4.52/3.06 ((~![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))) | ((~isFinite0(xQ)) | (~aSet0(xQ)) | isFinite0(sdtmndt0(xQ, xy)))),
% 4.52/3.06 inference(quant_inst,[status(thm)],[])).
% 4.52/3.06 tff(155,plain,
% 4.52/3.06 ((~![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))) | (~aSet0(xQ)) | (~isFinite0(xQ)) | isFinite0(sdtmndt0(xQ, xy))),
% 4.52/3.06 inference(modus_ponens,[status(thm)],[154, 153])).
% 4.52/3.06 tff(156,plain,
% 4.52/3.06 (isFinite0(sdtmndt0(xQ, xy))),
% 4.52/3.06 inference(unit_resolution,[status(thm)],[155, 84, 116, 149])).
% 4.52/3.06 tff(157,plain,
% 4.52/3.06 (^[W0: $i] : refl(((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))) <=> ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))))),
% 4.52/3.06 inference(bind,[status(th)],[])).
% 4.52/3.06 tff(158,plain,
% 4.52/3.06 (![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))) <=> ![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 4.52/3.06 inference(quant_intro,[status(thm)],[157])).
% 4.52/3.06 tff(159,plain,
% 4.52/3.06 (^[W0: $i] : rewrite(((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))) <=> ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))))),
% 4.52/3.06 inference(bind,[status(th)],[])).
% 4.52/3.06 tff(160,plain,
% 4.52/3.06 (![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))) <=> ![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 4.52/3.06 inference(quant_intro,[status(thm)],[159])).
% 4.52/3.06 tff(161,plain,
% 4.52/3.06 (![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))) <=> ![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 4.52/3.06 inference(transitivity,[status(thm)],[160, 158])).
% 4.52/3.06 tff(162,plain,
% 4.52/3.06 (^[W0: $i] : trans(monotonicity(trans(monotonicity(rewrite((aSet0(W0) & isFinite0(W0)) <=> (~((~aSet0(W0)) | (~isFinite0(W0))))), ((~(aSet0(W0) & isFinite0(W0))) <=> (~(~((~aSet0(W0)) | (~isFinite0(W0))))))), rewrite((~(~((~aSet0(W0)) | (~isFinite0(W0))))) <=> ((~aSet0(W0)) | (~isFinite0(W0)))), ((~(aSet0(W0) & isFinite0(W0))) <=> ((~aSet0(W0)) | (~isFinite0(W0))))), (((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))) <=> (((~aSet0(W0)) | (~isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))))), rewrite((((~aSet0(W0)) | (~isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))) <=> ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))), (((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))) <=> ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))))),
% 4.52/3.06 inference(bind,[status(th)],[])).
% 4.52/3.06 tff(163,plain,
% 4.52/3.06 (![W0: $i] : ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))) <=> ![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 4.52/3.06 inference(quant_intro,[status(thm)],[162])).
% 4.52/3.06 tff(164,plain,
% 4.52/3.06 (![W0: $i] : ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))) <=> ![W0: $i] : ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 4.52/3.06 inference(rewrite,[status(thm)],[])).
% 4.52/3.06 tff(165,plain,
% 4.52/3.06 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : trans(monotonicity(rewrite(((~aElementOf0(W1, W0)) => (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0)))) <=> (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))))), ((aElement0(W1) => ((~aElementOf0(W1, W0)) => (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))))) <=> (aElement0(W1) => (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))))))), rewrite((aElement0(W1) => (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))))) <=> (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))), ((aElement0(W1) => ((~aElementOf0(W1, W0)) => (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))))) <=> (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))))), (![W1: $i] : (aElement0(W1) => ((~aElementOf0(W1, W0)) => (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))))) <=> ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))), (((aSet0(W0) & isFinite0(W0)) => ![W1: $i] : (aElement0(W1) => ((~aElementOf0(W1, W0)) => (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0)))))) <=> ((aSet0(W0) & isFinite0(W0)) => ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))))), rewrite(((aSet0(W0) & isFinite0(W0)) => ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1)))) <=> ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))), (((aSet0(W0) & isFinite0(W0)) => ![W1: $i] : (aElement0(W1) => ((~aElementOf0(W1, W0)) => (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0)))))) <=> ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))))),
% 4.52/3.06 inference(bind,[status(th)],[])).
% 4.52/3.06 tff(166,plain,
% 4.52/3.06 (![W0: $i] : ((aSet0(W0) & isFinite0(W0)) => ![W1: $i] : (aElement0(W1) => ((~aElementOf0(W1, W0)) => (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0)))))) <=> ![W0: $i] : ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 4.52/3.06 inference(quant_intro,[status(thm)],[165])).
% 4.52/3.06 tff(167,axiom,(![W0: $i] : ((aSet0(W0) & isFinite0(W0)) => ![W1: $i] : (aElement0(W1) => ((~aElementOf0(W1, W0)) => (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mCardCons')).
% 4.52/3.06 tff(168,plain,
% 4.52/3.06 (![W0: $i] : ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 4.52/3.06 inference(modus_ponens,[status(thm)],[167, 166])).
% 4.52/3.06 tff(169,plain,
% 4.52/3.06 (![W0: $i] : ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 4.52/3.06 inference(modus_ponens,[status(thm)],[168, 164])).
% 4.52/3.06 tff(170,plain,(
% 4.52/3.06 ![W0: $i] : ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 4.52/3.06 inference(skolemize,[status(sab)],[169])).
% 4.52/3.06 tff(171,plain,
% 4.52/3.06 (![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 4.52/3.06 inference(modus_ponens,[status(thm)],[170, 163])).
% 4.52/3.06 tff(172,plain,
% 4.52/3.06 (![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 4.52/3.07 inference(modus_ponens,[status(thm)],[171, 161])).
% 4.52/3.07 tff(173,plain,
% 4.52/3.07 (((~![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))) | ((~aSet0(sdtmndt0(xQ, xy))) | (~isFinite0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))))))) <=> ((~![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))) | (~aSet0(sdtmndt0(xQ, xy))) | (~isFinite0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))))))),
% 4.52/3.07 inference(rewrite,[status(thm)],[])).
% 4.52/3.07 tff(174,plain,
% 4.52/3.07 (((~isFinite0(sdtmndt0(xQ, xy))) | (~aSet0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))) <=> ((~aSet0(sdtmndt0(xQ, xy))) | (~isFinite0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))))))),
% 4.52/3.07 inference(rewrite,[status(thm)],[])).
% 4.52/3.07 tff(175,plain,
% 4.52/3.07 (^[W1: $i] : rewrite((aElementOf0(W1, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))) | (~aElement0(W1))) <=> (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))))))),
% 4.52/3.07 inference(bind,[status(th)],[])).
% 4.52/3.07 tff(176,plain,
% 4.52/3.07 (![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))) | (~aElement0(W1))) <=> ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))),
% 4.52/3.07 inference(quant_intro,[status(thm)],[175])).
% 4.52/3.07 tff(177,plain,
% 4.52/3.07 (((~isFinite0(sdtmndt0(xQ, xy))) | (~aSet0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))) | (~aElement0(W1)))) <=> ((~isFinite0(sdtmndt0(xQ, xy))) | (~aSet0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))))))),
% 4.52/3.07 inference(monotonicity,[status(thm)],[176])).
% 4.52/3.07 tff(178,plain,
% 4.52/3.07 (((~isFinite0(sdtmndt0(xQ, xy))) | (~aSet0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))) | (~aElement0(W1)))) <=> ((~aSet0(sdtmndt0(xQ, xy))) | (~isFinite0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))))))),
% 4.52/3.07 inference(transitivity,[status(thm)],[177, 174])).
% 4.52/3.07 tff(179,plain,
% 4.52/3.07 (((~![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))) | ((~isFinite0(sdtmndt0(xQ, xy))) | (~aSet0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))) | (~aElement0(W1))))) <=> ((~![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))) | ((~aSet0(sdtmndt0(xQ, xy))) | (~isFinite0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))))),
% 4.52/3.07 inference(monotonicity,[status(thm)],[178])).
% 4.52/3.07 tff(180,plain,
% 4.52/3.07 (((~![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))) | ((~isFinite0(sdtmndt0(xQ, xy))) | (~aSet0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))) | (~aElement0(W1))))) <=> ((~![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))) | (~aSet0(sdtmndt0(xQ, xy))) | (~isFinite0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))))))),
% 4.52/3.07 inference(transitivity,[status(thm)],[179, 173])).
% 4.52/3.07 tff(181,plain,
% 4.52/3.07 ((~![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))) | ((~isFinite0(sdtmndt0(xQ, xy))) | (~aSet0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))) | (~aElement0(W1))))),
% 4.52/3.07 inference(quant_inst,[status(thm)],[])).
% 4.52/3.07 tff(182,plain,
% 4.52/3.07 ((~![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))) | (~aSet0(sdtmndt0(xQ, xy))) | (~isFinite0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))),
% 4.52/3.07 inference(modus_ponens,[status(thm)],[181, 180])).
% 4.52/3.07 tff(183,plain,
% 4.52/3.07 ((~isFinite0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))),
% 4.52/3.07 inference(unit_resolution,[status(thm)],[182, 172, 36])).
% 4.52/3.07 tff(184,plain,
% 4.52/3.07 (![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))),
% 4.52/3.07 inference(unit_resolution,[status(thm)],[183, 156])).
% 4.52/3.07 tff(185,plain,
% 4.52/3.07 ((~aElementOf0(xx, sdtmndt0(xQ, xy))) <=> (~aElementOf0(xx, sdtmndt0(xQ, xy)))),
% 4.52/3.07 inference(rewrite,[status(thm)],[])).
% 4.52/3.07 tff(186,axiom,(((~aElementOf0(xx, sdtmndt0(xQ, xy))) & aSet0(sdtmndt0(xQ, xy))) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = xy))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2411')).
% 4.52/3.07 tff(187,plain,
% 4.52/3.07 ((~aElementOf0(xx, sdtmndt0(xQ, xy))) & aSet0(sdtmndt0(xQ, xy))),
% 4.52/3.07 inference(and_elim,[status(thm)],[186])).
% 4.52/3.07 tff(188,plain,
% 4.52/3.07 (~aElementOf0(xx, sdtmndt0(xQ, xy))),
% 4.52/3.07 inference(and_elim,[status(thm)],[187])).
% 4.52/3.07 tff(189,plain,
% 4.52/3.07 (~aElementOf0(xx, sdtmndt0(xQ, xy))),
% 4.52/3.07 inference(modus_ponens,[status(thm)],[188, 185])).
% 4.52/3.07 tff(190,plain,
% 4.52/3.07 (((~![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))) | (aElementOf0(xx, sdtmndt0(xQ, xy)) | (~aElement0(xx)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))) <=> ((~![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))) | aElementOf0(xx, sdtmndt0(xQ, xy)) | (~aElement0(xx)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))),
% 4.52/3.07 inference(rewrite,[status(thm)],[])).
% 4.52/3.07 tff(191,plain,
% 4.52/3.07 ((~![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))) | (aElementOf0(xx, sdtmndt0(xQ, xy)) | (~aElement0(xx)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))),
% 4.52/3.07 inference(quant_inst,[status(thm)],[])).
% 4.52/3.07 tff(192,plain,
% 4.52/3.07 ((~![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))) | aElementOf0(xx, sdtmndt0(xQ, xy)) | (~aElement0(xx)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))))),
% 4.52/3.07 inference(modus_ponens,[status(thm)],[191, 190])).
% 4.52/3.07 tff(193,plain,
% 4.52/3.07 (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))),
% 4.52/3.07 inference(unit_resolution,[status(thm)],[192, 189, 184, 29])).
% 4.52/3.07 tff(194,plain,
% 4.52/3.07 (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = sbrdtbr0(xQ)),
% 4.52/3.07 inference(transitivity,[status(thm)],[193, 123])).
% 4.52/3.07 tff(195,plain,
% 4.52/3.07 (((~(aSubsetOf0(sdtpldt0(sdtmndt0(xQ, xy), xx), xS) | (~aElementOf0(W0!14, sdtpldt0(sdtmndt0(xQ, xy), xx))) | aElementOf0(W0!14, xS))) | (~(sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = sbrdtbr0(xQ)))) <=> ((~(sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = sbrdtbr0(xQ))) | (~(aSubsetOf0(sdtpldt0(sdtmndt0(xQ, xy), xx), xS) | (~aElementOf0(W0!14, sdtpldt0(sdtmndt0(xQ, xy), xx))) | aElementOf0(W0!14, xS))))),
% 4.52/3.08 inference(rewrite,[status(thm)],[])).
% 4.52/3.08 tff(196,plain,
% 4.52/3.08 (((~aSubsetOf0(sdtpldt0(sdtmndt0(xQ, xy), xx), xS)) & (~((~aElementOf0(W0!14, sdtpldt0(sdtmndt0(xQ, xy), xx))) | aElementOf0(W0!14, xS)))) <=> (~(aSubsetOf0(sdtpldt0(sdtmndt0(xQ, xy), xx), xS) | (~aElementOf0(W0!14, sdtpldt0(sdtmndt0(xQ, xy), xx))) | aElementOf0(W0!14, xS)))),
% 4.52/3.08 inference(rewrite,[status(thm)],[])).
% 4.52/3.08 tff(197,plain,
% 4.52/3.08 ((((~aSubsetOf0(sdtpldt0(sdtmndt0(xQ, xy), xx), xS)) & (~((~aElementOf0(W0!14, sdtpldt0(sdtmndt0(xQ, xy), xx))) | aElementOf0(W0!14, xS)))) | (~(sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = sbrdtbr0(xQ)))) <=> ((~(aSubsetOf0(sdtpldt0(sdtmndt0(xQ, xy), xx), xS) | (~aElementOf0(W0!14, sdtpldt0(sdtmndt0(xQ, xy), xx))) | aElementOf0(W0!14, xS))) | (~(sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = sbrdtbr0(xQ))))),
% 4.52/3.08 inference(monotonicity,[status(thm)],[196])).
% 4.52/3.08 tff(198,plain,
% 4.52/3.08 ((((~aSubsetOf0(sdtpldt0(sdtmndt0(xQ, xy), xx), xS)) & (~((~aElementOf0(W0!14, sdtpldt0(sdtmndt0(xQ, xy), xx))) | aElementOf0(W0!14, xS)))) | (~(sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = sbrdtbr0(xQ)))) <=> ((~(sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = sbrdtbr0(xQ))) | (~(aSubsetOf0(sdtpldt0(sdtmndt0(xQ, xy), xx), xS) | (~aElementOf0(W0!14, sdtpldt0(sdtmndt0(xQ, xy), xx))) | aElementOf0(W0!14, xS))))),
% 4.52/3.08 inference(transitivity,[status(thm)],[197, 195])).
% 4.52/3.08 tff(199,plain,
% 4.52/3.08 ((((~aSubsetOf0(sdtpldt0(sdtmndt0(xQ, xy), xx), xS)) & (~((~aElementOf0(W0!14, sdtpldt0(sdtmndt0(xQ, xy), xx))) | aElementOf0(W0!14, xS)))) | (~(sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = sbrdtbr0(xQ)))) <=> (((~aSubsetOf0(sdtpldt0(sdtmndt0(xQ, xy), xx), xS)) & (~((~aElementOf0(W0!14, sdtpldt0(sdtmndt0(xQ, xy), xx))) | aElementOf0(W0!14, xS)))) | (~(sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = sbrdtbr0(xQ))))),
% 4.52/3.08 inference(rewrite,[status(thm)],[])).
% 4.52/3.08 tff(200,plain,
% 4.52/3.08 ((aSubsetOf0(sdtpldt0(sdtmndt0(xQ, xy), xx), xS) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(sdtmndt0(xQ, xy), xx))) | aElementOf0(W0, xS))) <=> (aSubsetOf0(sdtpldt0(sdtmndt0(xQ, xy), xx), xS) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(sdtmndt0(xQ, xy), xx))) | aElementOf0(W0, xS)))),
% 4.52/3.08 inference(rewrite,[status(thm)],[])).
% 4.52/3.08 tff(201,plain,
% 4.52/3.08 (((aSubsetOf0(sdtpldt0(sdtmndt0(xQ, xy), xx), xS) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(sdtmndt0(xQ, xy), xx))) | aElementOf0(W0, xS))) & (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = sbrdtbr0(xQ))) <=> ((aSubsetOf0(sdtpldt0(sdtmndt0(xQ, xy), xx), xS) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(sdtmndt0(xQ, xy), xx))) | aElementOf0(W0, xS))) & (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = sbrdtbr0(xQ)))),
% 4.52/3.08 inference(monotonicity,[status(thm)],[200])).
% 4.52/3.08 tff(202,plain,
% 4.52/3.08 ((~((aSubsetOf0(sdtpldt0(sdtmndt0(xQ, xy), xx), xS) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(sdtmndt0(xQ, xy), xx))) | aElementOf0(W0, xS))) & (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = sbrdtbr0(xQ)))) <=> (~((aSubsetOf0(sdtpldt0(sdtmndt0(xQ, xy), xx), xS) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(sdtmndt0(xQ, xy), xx))) | aElementOf0(W0, xS))) & (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = sbrdtbr0(xQ))))),
% 4.52/3.08 inference(monotonicity,[status(thm)],[201])).
% 4.52/3.08 tff(203,plain,
% 4.52/3.08 ((~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))) <=> (~((aSubsetOf0(sdtpldt0(sdtmndt0(xQ, xy), xx), xS) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(sdtmndt0(xQ, xy), xx))) | aElementOf0(W0, xS))) & (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = sbrdtbr0(xQ))))),
% 4.52/3.08 inference(rewrite,[status(thm)],[])).
% 4.52/3.08 tff(204,plain,
% 4.52/3.08 ((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) <=> (aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS)))),
% 4.52/3.08 inference(rewrite,[status(thm)],[])).
% 4.52/3.08 tff(205,plain,
% 4.52/3.08 (((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk)) <=> ((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 4.52/3.08 inference(monotonicity,[status(thm)],[204])).
% 4.52/3.08 tff(206,plain,
% 4.52/3.08 ((~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))) <=> (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk)))),
% 4.52/3.08 inference(monotonicity,[status(thm)],[205])).
% 4.52/3.08 tff(207,plain,
% 4.52/3.08 ((~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))) <=> (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk)))),
% 4.52/3.08 inference(rewrite,[status(thm)],[])).
% 4.52/3.08 tff(208,plain,
% 4.52/3.08 ((~((![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xS)) | aSubsetOf0(xP, xS)) & (sbrdtbr0(xP) = xk))) <=> (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk)))),
% 4.52/3.08 inference(rewrite,[status(thm)],[])).
% 4.52/3.08 tff(209,axiom,(~((![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xS)) | aSubsetOf0(xP, xS)) & (sbrdtbr0(xP) = xk))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 4.52/3.08 tff(210,plain,
% 4.52/3.08 (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 4.52/3.08 inference(modus_ponens,[status(thm)],[209, 208])).
% 4.52/3.08 tff(211,plain,
% 4.52/3.08 (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 4.52/3.08 inference(modus_ponens,[status(thm)],[210, 206])).
% 4.52/3.08 tff(212,plain,
% 4.52/3.08 (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 4.52/3.08 inference(modus_ponens,[status(thm)],[211, 207])).
% 4.52/3.08 tff(213,plain,
% 4.52/3.08 (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 4.52/3.08 inference(modus_ponens,[status(thm)],[212, 206])).
% 4.52/3.08 tff(214,plain,
% 4.52/3.08 (~((aSubsetOf0(sdtpldt0(sdtmndt0(xQ, xy), xx), xS) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(sdtmndt0(xQ, xy), xx))) | aElementOf0(W0, xS))) & (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = sbrdtbr0(xQ)))),
% 4.52/3.08 inference(modus_ponens,[status(thm)],[213, 203])).
% 4.52/3.08 tff(215,plain,
% 4.52/3.08 (~((aSubsetOf0(sdtpldt0(sdtmndt0(xQ, xy), xx), xS) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(sdtmndt0(xQ, xy), xx))) | aElementOf0(W0, xS))) & (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = sbrdtbr0(xQ)))),
% 4.52/3.08 inference(modus_ponens,[status(thm)],[214, 202])).
% 4.52/3.08 tff(216,plain,
% 4.52/3.08 (~((aSubsetOf0(sdtpldt0(sdtmndt0(xQ, xy), xx), xS) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(sdtmndt0(xQ, xy), xx))) | aElementOf0(W0, xS))) & (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = sbrdtbr0(xQ)))),
% 4.52/3.08 inference(modus_ponens,[status(thm)],[215, 202])).
% 4.52/3.08 tff(217,plain,
% 4.52/3.08 (~((aSubsetOf0(sdtpldt0(sdtmndt0(xQ, xy), xx), xS) | ![W0: $i] : ((~aElementOf0(W0, sdtpldt0(sdtmndt0(xQ, xy), xx))) | aElementOf0(W0, xS))) & (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = sbrdtbr0(xQ)))),
% 4.52/3.08 inference(modus_ponens,[status(thm)],[216, 202])).
% 4.52/3.08 unexpected number of arguments: (let ((a!1 (not (aSubsetOf0 (sdtpldt0 (sdtmndt0 xQ xy) xx) xS)))
% 4.52/3.08 (a!2 (forall ((W0 $i))
% 4.52/3.08 (let ((a!1 (not (aElementOf0 W0 (sdtpldt0 (sdtmndt0 xQ xy) xx)))))
% 4.52/3.08 (or a!1 (aElementOf0 W0 xS)))))
% 4.52/3.08 (a!3 (not (aElementOf0 W0!14 (sdtpldt0 (sdtmndt0 xQ xy) xx))))
% 4.52/3.08 (a!7 (= (sbrdtbr0 (sdtpldt0 (sdtmndt0 xQ xy) xx)) (sbrdtbr0 xQ))))
% 4.52/3.08 (let ((a!4 (~ (not a!2) (not (or a!3 (aElementOf0 W0!14 xS)))))
% 4.52/3.08 (a!5 (or (aSubsetOf0 (sdtpldt0 (sdtmndt0 xQ xy) xx) xS) a!2))
% 4.52/3.08 (a!6 (and a!1 (not (or a!3 (aElementOf0 W0!14 xS))))))
% 4.52/3.08 (nnf-neg (nnf-neg (refl (~ a!1 a!1)) (sk a!4) (~ (not a!5) a!6))
% 4.52/3.08 (refl (~ (not a!7) (not a!7)))
% 4.52/3.08 (~ (not (and a!5 a!7)) (or a!6 (not a!7))))))
% 4.52/3.08 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------