TSTP Solution File: NUM554+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM554+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:10:28 EDT 2022
% Result : Theorem 4.31s 2.94s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : NUM554+3 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.30 % Computer : n012.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri Sep 2 11:42:19 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31 Usage: tptp [options] [-file:]file
% 0.10/0.31 -h, -? prints this message.
% 0.10/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.31 -m, -model generate model.
% 0.10/0.31 -p, -proof generate proof.
% 0.10/0.31 -c, -core generate unsat core of named formulas.
% 0.10/0.31 -st, -statistics display statistics.
% 0.10/0.31 -t:timeout set timeout (in second).
% 0.10/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31 -<param>:<value> configuration parameter and value.
% 0.10/0.31 -o:<output-file> file to place output in.
% 4.31/2.94 % SZS status Theorem
% 4.31/2.94 % SZS output start Proof
% 4.31/2.94 tff(aElementOf0_type, type, (
% 4.31/2.94 aElementOf0: ( $i * $i ) > $o)).
% 4.31/2.94 tff(xS_type, type, (
% 4.31/2.94 xS: $i)).
% 4.31/2.94 tff(tptp_fun_W0_14_type, type, (
% 4.31/2.94 tptp_fun_W0_14: $i)).
% 4.31/2.94 tff(xx_type, type, (
% 4.31/2.94 xx: $i)).
% 4.31/2.94 tff(sdtmndt0_type, type, (
% 4.31/2.94 sdtmndt0: ( $i * $i ) > $i)).
% 4.31/2.94 tff(xy_type, type, (
% 4.31/2.94 xy: $i)).
% 4.31/2.94 tff(xQ_type, type, (
% 4.31/2.94 xQ: $i)).
% 4.31/2.94 tff(aElement0_type, type, (
% 4.31/2.94 aElement0: $i > $o)).
% 4.31/2.94 tff(sdtpldt0_type, type, (
% 4.31/2.94 sdtpldt0: ( $i * $i ) > $i)).
% 4.31/2.94 tff(aSet0_type, type, (
% 4.31/2.94 aSet0: $i > $o)).
% 4.31/2.94 tff(tptp_fun_W3_2_type, type, (
% 4.31/2.94 tptp_fun_W3_2: ( $i * $i * $i ) > $i)).
% 4.31/2.94 tff(xT_type, type, (
% 4.31/2.94 xT: $i)).
% 4.31/2.94 tff(sz00_type, type, (
% 4.31/2.94 sz00: $i)).
% 4.31/2.94 tff(xk_type, type, (
% 4.31/2.94 xk: $i)).
% 4.31/2.94 tff(xP_type, type, (
% 4.31/2.94 xP: $i)).
% 4.31/2.94 tff(aSubsetOf0_type, type, (
% 4.31/2.94 aSubsetOf0: ( $i * $i ) > $o)).
% 4.31/2.94 tff(sbrdtbr0_type, type, (
% 4.31/2.94 sbrdtbr0: $i > $i)).
% 4.31/2.94 tff(szszuzczcdt0_type, type, (
% 4.31/2.94 szszuzczcdt0: $i > $i)).
% 4.31/2.94 tff(isFinite0_type, type, (
% 4.31/2.94 isFinite0: $i > $o)).
% 4.31/2.94 tff(slbdtsldtrb0_type, type, (
% 4.31/2.94 slbdtsldtrb0: ( $i * $i ) > $i)).
% 4.31/2.94 tff(tptp_fun_W3_3_type, type, (
% 4.31/2.94 tptp_fun_W3_3: ( $i * $i * $i ) > $i)).
% 4.31/2.94 tff(tptp_fun_W2_1_type, type, (
% 4.31/2.94 tptp_fun_W2_1: ( $i * $i ) > $i)).
% 4.31/2.94 tff(1,plain,
% 4.31/2.94 (aSet0(xS) <=> aSet0(xS)),
% 4.31/2.94 inference(rewrite,[status(thm)],[])).
% 4.31/2.94 tff(2,axiom,((aSet0(xS) & aSet0(xT)) & (~(xk = sz00))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2202_02')).
% 4.31/2.94 tff(3,plain,
% 4.31/2.94 (aSet0(xS) & aSet0(xT)),
% 4.31/2.94 inference(and_elim,[status(thm)],[2])).
% 4.31/2.94 tff(4,plain,
% 4.31/2.94 (aSet0(xS)),
% 4.31/2.94 inference(and_elim,[status(thm)],[3])).
% 4.31/2.94 tff(5,plain,
% 4.31/2.94 (aSet0(xS)),
% 4.31/2.94 inference(modus_ponens,[status(thm)],[4, 1])).
% 4.31/2.94 tff(6,plain,
% 4.31/2.94 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 4.31/2.94 inference(bind,[status(th)],[])).
% 4.31/2.94 tff(7,plain,
% 4.31/2.94 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.31/2.94 inference(quant_intro,[status(thm)],[6])).
% 4.31/2.94 tff(8,plain,
% 4.31/2.94 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 4.31/2.94 inference(bind,[status(th)],[])).
% 4.31/2.94 tff(9,plain,
% 4.31/2.94 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.31/2.94 inference(quant_intro,[status(thm)],[8])).
% 4.31/2.94 tff(10,plain,
% 4.31/2.94 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.31/2.94 inference(transitivity,[status(thm)],[9, 7])).
% 4.31/2.94 tff(11,plain,
% 4.31/2.94 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.31/2.94 inference(rewrite,[status(thm)],[])).
% 4.31/2.94 tff(12,plain,
% 4.31/2.94 (^[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))))))),
% 4.31/2.94 inference(bind,[status(th)],[])).
% 4.31/2.94 tff(13,plain,
% 4.31/2.94 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.31/2.94 inference(quant_intro,[status(thm)],[12])).
% 4.31/2.94 tff(14,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mEOfElem')).
% 4.31/2.95 tff(15,plain,
% 4.31/2.95 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.31/2.95 inference(modus_ponens,[status(thm)],[14, 13])).
% 4.31/2.95 tff(16,plain,
% 4.31/2.95 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.31/2.95 inference(modus_ponens,[status(thm)],[15, 11])).
% 4.31/2.95 tff(17,plain,(
% 4.31/2.95 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.31/2.95 inference(skolemize,[status(sab)],[16])).
% 4.31/2.95 tff(18,plain,
% 4.31/2.95 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 4.31/2.95 inference(modus_ponens,[status(thm)],[17, 10])).
% 4.31/2.95 tff(19,plain,
% 4.31/2.95 (((~![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))))),
% 4.31/2.95 inference(rewrite,[status(thm)],[])).
% 4.31/2.95 tff(20,plain,
% 4.31/2.95 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))),
% 4.31/2.95 inference(quant_inst,[status(thm)],[])).
% 4.31/2.95 tff(21,plain,
% 4.31/2.95 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 4.31/2.95 inference(modus_ponens,[status(thm)],[20, 19])).
% 4.31/2.95 tff(22,plain,
% 4.31/2.95 (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 4.31/2.95 inference(unit_resolution,[status(thm)],[21, 18, 5])).
% 4.31/2.95 tff(23,plain,
% 4.31/2.95 (aElementOf0(xx, xS) <=> aElementOf0(xx, xS)),
% 4.31/2.95 inference(rewrite,[status(thm)],[])).
% 4.31/2.95 tff(24,axiom,(aElementOf0(xx, xS)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2256')).
% 4.31/2.95 tff(25,plain,
% 4.31/2.95 (aElementOf0(xx, xS)),
% 4.31/2.95 inference(modus_ponens,[status(thm)],[24, 23])).
% 4.31/2.95 tff(26,plain,
% 4.31/2.95 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(xx) | (~aElementOf0(xx, xS)))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(xx) | (~aElementOf0(xx, xS)))),
% 4.31/2.95 inference(rewrite,[status(thm)],[])).
% 4.31/2.95 tff(27,plain,
% 4.31/2.95 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(xx) | (~aElementOf0(xx, xS)))),
% 4.31/2.95 inference(quant_inst,[status(thm)],[])).
% 4.31/2.95 tff(28,plain,
% 4.31/2.95 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(xx) | (~aElementOf0(xx, xS))),
% 4.31/2.95 inference(modus_ponens,[status(thm)],[27, 26])).
% 4.31/2.95 tff(29,plain,
% 4.31/2.95 (aElement0(xx)),
% 4.31/2.95 inference(unit_resolution,[status(thm)],[28, 25, 22])).
% 4.31/2.95 tff(30,plain,
% 4.31/2.95 (aSet0(sdtmndt0(xQ, xy)) <=> aSet0(sdtmndt0(xQ, xy))),
% 4.31/2.95 inference(rewrite,[status(thm)],[])).
% 4.31/2.95 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')).
% 4.31/2.95 tff(32,plain,
% 4.31/2.95 (((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))))),
% 4.31/2.95 inference(and_elim,[status(thm)],[31])).
% 4.31/2.95 tff(33,plain,
% 4.31/2.95 ((aSet0(sdtmndt0(xQ, xy)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = xy))))) & aSet0(xP)),
% 4.31/2.95 inference(and_elim,[status(thm)],[32])).
% 4.31/2.95 tff(34,plain,
% 4.31/2.95 (aSet0(sdtmndt0(xQ, xy)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = xy))))),
% 4.31/2.95 inference(and_elim,[status(thm)],[33])).
% 4.31/2.95 tff(35,plain,
% 4.31/2.95 (aSet0(sdtmndt0(xQ, xy))),
% 4.31/2.95 inference(and_elim,[status(thm)],[34])).
% 4.31/2.95 tff(36,plain,
% 4.31/2.95 (aSet0(sdtmndt0(xQ, xy))),
% 4.31/2.95 inference(modus_ponens,[status(thm)],[35, 30])).
% 4.31/2.95 tff(37,plain,
% 4.31/2.95 (^[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)))))))))))))))),
% 4.31/2.95 inference(bind,[status(th)],[])).
% 4.31/2.95 tff(38,plain,
% 4.31/2.95 (![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))))))))))))))),
% 4.31/2.95 inference(quant_intro,[status(thm)],[37])).
% 4.31/2.95 tff(39,plain,
% 4.31/2.95 (^[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)))))))))))),
% 4.31/2.95 inference(bind,[status(th)],[])).
% 4.31/2.95 tff(40,plain,
% 4.31/2.95 (![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))))))))))),
% 4.31/2.95 inference(quant_intro,[status(thm)],[39])).
% 4.31/2.95 tff(41,plain,
% 4.31/2.95 (^[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)))))))))))),
% 4.31/2.95 inference(bind,[status(th)],[])).
% 4.31/2.95 tff(42,plain,
% 4.31/2.95 (![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))))))))))),
% 4.31/2.95 inference(quant_intro,[status(thm)],[41])).
% 4.31/2.95 tff(43,plain,
% 4.31/2.95 (![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))))))))))),
% 4.31/2.95 inference(transitivity,[status(thm)],[42, 40])).
% 4.31/2.95 tff(44,plain,
% 4.31/2.95 (^[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))))))))))))),
% 4.31/2.95 inference(bind,[status(th)],[])).
% 4.31/2.95 tff(45,plain,
% 4.31/2.95 (![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))))))))))),
% 4.31/2.95 inference(quant_intro,[status(thm)],[44])).
% 4.31/2.95 tff(46,plain,
% 4.31/2.95 (^[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))))))))),
% 4.31/2.95 inference(bind,[status(th)],[])).
% 4.31/2.95 tff(47,plain,
% 4.31/2.95 (![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)))))))),
% 4.31/2.95 inference(quant_intro,[status(thm)],[46])).
% 4.31/2.95 tff(48,plain,
% 4.31/2.95 (![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)))))))),
% 4.31/2.95 inference(rewrite,[status(thm)],[])).
% 4.31/2.95 tff(49,plain,
% 4.31/2.95 (^[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)))))))))),
% 4.31/2.95 inference(bind,[status(th)],[])).
% 4.31/2.95 tff(50,plain,
% 4.31/2.95 (![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)))))))),
% 4.31/2.95 inference(quant_intro,[status(thm)],[49])).
% 4.31/2.95 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')).
% 4.31/2.95 tff(52,plain,
% 4.31/2.95 (![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)))))))),
% 4.31/2.95 inference(modus_ponens,[status(thm)],[51, 50])).
% 4.31/2.95 tff(53,plain,
% 4.31/2.95 (![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)))))))),
% 4.31/2.95 inference(modus_ponens,[status(thm)],[52, 48])).
% 4.31/2.95 tff(54,plain,(
% 4.31/2.95 ![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)))))))))),
% 4.31/2.95 inference(skolemize,[status(sab)],[53])).
% 4.31/2.95 tff(55,plain,
% 4.31/2.95 (![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)))))))),
% 4.31/2.95 inference(modus_ponens,[status(thm)],[54, 47])).
% 4.31/2.95 tff(56,plain,
% 4.31/2.95 (![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))))))))))),
% 4.31/2.95 inference(modus_ponens,[status(thm)],[55, 45])).
% 4.31/2.95 tff(57,plain,
% 4.31/2.95 (![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))))))))))),
% 4.31/2.95 inference(modus_ponens,[status(thm)],[56, 43])).
% 4.31/2.95 tff(58,plain,
% 4.31/2.95 (![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))))))))))))))),
% 4.31/2.96 inference(modus_ponens,[status(thm)],[57, 38])).
% 4.31/2.96 tff(59,plain,
% 4.31/2.96 (((~![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)))))))))))))))),
% 4.31/2.96 inference(rewrite,[status(thm)],[])).
% 4.31/2.96 tff(60,plain,
% 4.31/2.96 (((~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)))))))))))))))),
% 4.31/2.96 inference(rewrite,[status(thm)],[])).
% 4.31/2.96 tff(61,plain,
% 4.31/2.96 (((~![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))))))))))))))))),
% 4.31/2.96 inference(monotonicity,[status(thm)],[60])).
% 4.31/2.96 tff(62,plain,
% 4.31/2.96 (((~![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)))))))))))))))),
% 4.31/2.96 inference(transitivity,[status(thm)],[61, 59])).
% 4.31/2.96 tff(63,plain,
% 4.31/2.96 ((~![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)))))))))))))))),
% 4.31/2.96 inference(quant_inst,[status(thm)],[])).
% 4.31/2.96 tff(64,plain,
% 4.31/2.96 ((~![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))))))))))))))),
% 4.31/2.96 inference(modus_ponens,[status(thm)],[63, 62])).
% 4.31/2.96 tff(65,plain,
% 4.31/2.96 ((~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))))))))))))))),
% 4.31/2.96 inference(unit_resolution,[status(thm)],[64, 58, 36])).
% 4.31/2.96 tff(66,plain,
% 4.31/2.96 (![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))))))))))))))),
% 4.31/2.96 inference(unit_resolution,[status(thm)],[65, 29])).
% 4.31/2.96 tff(67,plain,
% 4.31/2.96 (((~![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)))))))))))),
% 4.31/2.97 inference(rewrite,[status(thm)],[])).
% 4.31/2.97 tff(68,plain,
% 4.31/2.97 ((~((~((~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))))))))))),
% 4.31/2.97 inference(rewrite,[status(thm)],[])).
% 4.31/2.97 tff(69,plain,
% 4.31/2.97 (((~![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)))))))))))),
% 4.31/2.97 inference(monotonicity,[status(thm)],[68])).
% 4.31/2.97 tff(70,plain,
% 4.31/2.97 (((~![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)))))))))))),
% 4.31/2.97 inference(transitivity,[status(thm)],[69, 67])).
% 4.31/2.97 tff(71,plain,
% 4.31/2.97 ((~![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))))))))))))))),
% 4.31/2.97 inference(quant_inst,[status(thm)],[])).
% 4.31/2.97 tff(72,plain,
% 4.31/2.97 ((~![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))))))))))),
% 4.31/2.97 inference(modus_ponens,[status(thm)],[71, 70])).
% 4.31/2.97 tff(73,plain,
% 4.31/2.97 (~((~aSet0(sdtpldt0(sdtmndt0(xQ, xy), xx))) | (~![W3: $i] : (aElementOf0(W3, sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy)))))))))),
% 4.31/2.97 inference(unit_resolution,[status(thm)],[72, 66])).
% 4.31/2.97 tff(74,plain,
% 4.31/2.97 (((~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)))))))),
% 4.31/2.98 inference(tautology,[status(thm)],[])).
% 4.31/2.98 tff(75,plain,
% 4.31/2.98 (![W3: $i] : (aElementOf0(W3, sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> (~((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xQ, xy)))))))),
% 4.31/2.98 inference(unit_resolution,[status(thm)],[74, 73])).
% 4.31/2.98 tff(76,plain,
% 4.31/2.98 ((~![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)))))))),
% 4.31/2.98 inference(quant_inst,[status(thm)],[])).
% 4.31/2.98 tff(77,plain,
% 4.31/2.98 (aElementOf0(W0!14, sdtpldt0(sdtmndt0(xQ, xy), xx)) <=> (~((~aElement0(W0!14)) | (~((W0!14 = xx) | aElementOf0(W0!14, sdtmndt0(xQ, xy))))))),
% 4.31/2.98 inference(unit_resolution,[status(thm)],[76, 75])).
% 4.31/2.98 tff(78,plain,
% 4.31/2.98 (aSet0(xQ) <=> aSet0(xQ)),
% 4.31/2.98 inference(rewrite,[status(thm)],[])).
% 4.31/2.98 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')).
% 4.31/2.98 tff(80,plain,
% 4.31/2.98 (((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))) & aSubsetOf0(xQ, xS)) & (sbrdtbr0(xQ) = xk)),
% 4.31/2.98 inference(and_elim,[status(thm)],[79])).
% 4.31/2.98 tff(81,plain,
% 4.31/2.98 ((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))) & aSubsetOf0(xQ, xS)),
% 4.31/2.98 inference(and_elim,[status(thm)],[80])).
% 4.31/2.98 tff(82,plain,
% 4.31/2.98 (aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xS))),
% 4.31/2.98 inference(and_elim,[status(thm)],[81])).
% 4.31/2.98 tff(83,plain,
% 4.31/2.98 (aSet0(xQ)),
% 4.31/2.98 inference(and_elim,[status(thm)],[82])).
% 4.31/2.98 tff(84,plain,
% 4.31/2.98 (aSet0(xQ)),
% 4.31/2.98 inference(modus_ponens,[status(thm)],[83, 78])).
% 4.31/2.98 tff(85,plain,
% 4.31/2.98 (^[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)))))),
% 4.31/2.98 inference(bind,[status(th)],[])).
% 4.31/2.98 tff(86,plain,
% 4.31/2.98 (![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))))),
% 4.31/2.98 inference(quant_intro,[status(thm)],[85])).
% 4.31/2.98 tff(87,plain,
% 4.31/2.98 (^[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)))))),
% 4.31/2.98 inference(bind,[status(th)],[])).
% 4.31/2.98 tff(88,plain,
% 4.31/2.98 (![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))))),
% 4.31/2.98 inference(quant_intro,[status(thm)],[87])).
% 4.31/2.98 tff(89,plain,
% 4.31/2.98 (![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))))),
% 4.31/2.98 inference(transitivity,[status(thm)],[88, 86])).
% 4.31/2.98 tff(90,plain,
% 4.31/2.98 (^[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)))))),
% 4.31/2.98 inference(bind,[status(th)],[])).
% 4.31/2.98 tff(91,plain,
% 4.31/2.98 (![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))))),
% 4.40/2.98 inference(quant_intro,[status(thm)],[90])).
% 4.40/2.98 tff(92,plain,
% 4.40/2.98 (![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))))),
% 4.40/2.98 inference(rewrite,[status(thm)],[])).
% 4.40/2.98 tff(93,plain,
% 4.40/2.98 (^[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))))))),
% 4.40/2.98 inference(bind,[status(th)],[])).
% 4.40/2.98 tff(94,plain,
% 4.40/2.98 (![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))))),
% 4.40/2.98 inference(quant_intro,[status(thm)],[93])).
% 4.40/2.98 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')).
% 4.40/2.98 tff(96,plain,
% 4.40/2.98 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))),
% 4.40/2.98 inference(modus_ponens,[status(thm)],[95, 94])).
% 4.40/2.98 tff(97,plain,
% 4.40/2.98 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))),
% 4.40/2.98 inference(modus_ponens,[status(thm)],[96, 92])).
% 4.40/2.98 tff(98,plain,(
% 4.40/2.98 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~(isFinite0(W0) & aElementOf0(W1, W0))) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0))))),
% 4.40/2.98 inference(skolemize,[status(sab)],[97])).
% 4.40/2.98 tff(99,plain,
% 4.40/2.98 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))),
% 4.40/2.98 inference(modus_ponens,[status(thm)],[98, 91])).
% 4.40/2.98 tff(100,plain,
% 4.40/2.98 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : ((~aElementOf0(W1, W0)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(W0, W1))) = sbrdtbr0(W0)) | (~isFinite0(W0))))),
% 4.40/2.98 inference(modus_ponens,[status(thm)],[99, 89])).
% 4.40/2.98 tff(101,plain,
% 4.40/2.98 (((~![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))))),
% 4.40/2.98 inference(rewrite,[status(thm)],[])).
% 4.40/2.98 tff(102,plain,
% 4.40/2.98 (((~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))))),
% 4.40/2.98 inference(rewrite,[status(thm)],[])).
% 4.40/2.98 tff(103,plain,
% 4.40/2.98 (((~![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)))))),
% 4.40/2.98 inference(monotonicity,[status(thm)],[102])).
% 4.40/2.98 tff(104,plain,
% 4.40/2.98 (((~![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))))),
% 4.40/2.98 inference(transitivity,[status(thm)],[103, 101])).
% 4.40/2.98 tff(105,plain,
% 4.40/2.98 ((~![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))))),
% 4.40/2.98 inference(quant_inst,[status(thm)],[])).
% 4.40/2.98 tff(106,plain,
% 4.40/2.98 ((~![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)))),
% 4.40/2.98 inference(modus_ponens,[status(thm)],[105, 104])).
% 4.40/2.98 tff(107,plain,
% 4.40/2.98 (![W1: $i] : ((~aElementOf0(W1, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, W1))) = sbrdtbr0(xQ)))),
% 4.40/2.98 inference(unit_resolution,[status(thm)],[106, 100, 84])).
% 4.40/2.98 tff(108,plain,
% 4.40/2.98 (aElementOf0(xy, xQ) <=> aElementOf0(xy, xQ)),
% 4.40/2.98 inference(rewrite,[status(thm)],[])).
% 4.40/2.98 tff(109,axiom,(aElement0(xy) & aElementOf0(xy, xQ)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2304')).
% 4.40/2.98 tff(110,plain,
% 4.40/2.98 (aElementOf0(xy, xQ)),
% 4.40/2.98 inference(and_elim,[status(thm)],[109])).
% 4.40/2.98 tff(111,plain,
% 4.40/2.98 (aElementOf0(xy, xQ)),
% 4.40/2.98 inference(modus_ponens,[status(thm)],[110, 108])).
% 4.40/2.98 tff(112,plain,
% 4.40/2.98 (isFinite0(xQ) <=> isFinite0(xQ)),
% 4.40/2.98 inference(rewrite,[status(thm)],[])).
% 4.40/2.98 tff(113,axiom,((aSet0(xQ) & isFinite0(xQ)) & (sbrdtbr0(xQ) = xk)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2291')).
% 4.40/2.98 tff(114,plain,
% 4.40/2.98 (aSet0(xQ) & isFinite0(xQ)),
% 4.40/2.98 inference(and_elim,[status(thm)],[113])).
% 4.40/2.98 tff(115,plain,
% 4.40/2.98 (isFinite0(xQ)),
% 4.40/2.98 inference(and_elim,[status(thm)],[114])).
% 4.40/2.98 tff(116,plain,
% 4.40/2.98 (isFinite0(xQ)),
% 4.40/2.98 inference(modus_ponens,[status(thm)],[115, 112])).
% 4.40/2.98 tff(117,plain,
% 4.40/2.98 (((~![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)))),
% 4.40/2.98 inference(rewrite,[status(thm)],[])).
% 4.40/2.98 tff(118,plain,
% 4.40/2.98 (((~aElementOf0(xy, xQ)) | (~isFinite0(xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ))) <=> ((~isFinite0(xQ)) | (~aElementOf0(xy, xQ)) | (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ)))),
% 4.40/2.98 inference(rewrite,[status(thm)],[])).
% 4.40/2.98 tff(119,plain,
% 4.40/2.98 (((~![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))))),
% 4.40/2.98 inference(monotonicity,[status(thm)],[118])).
% 4.40/2.98 tff(120,plain,
% 4.40/2.98 (((~![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)))),
% 4.40/2.98 inference(transitivity,[status(thm)],[119, 117])).
% 4.40/2.98 tff(121,plain,
% 4.40/2.98 ((~![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)))),
% 4.40/2.98 inference(quant_inst,[status(thm)],[])).
% 4.40/2.98 tff(122,plain,
% 4.40/2.98 ((~![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))),
% 4.40/2.98 inference(modus_ponens,[status(thm)],[121, 120])).
% 4.40/2.98 tff(123,plain,
% 4.40/2.98 (szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))) = sbrdtbr0(xQ)),
% 4.40/2.98 inference(unit_resolution,[status(thm)],[122, 116, 111, 107])).
% 4.40/2.98 tff(124,plain,
% 4.40/2.98 (^[W0: $i] : refl((aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy)))) <=> (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy)))))),
% 4.40/2.98 inference(bind,[status(th)],[])).
% 4.40/2.98 tff(125,plain,
% 4.40/2.98 (![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy)))) <=> ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy))))),
% 4.40/2.98 inference(quant_intro,[status(thm)],[124])).
% 4.40/2.98 tff(126,plain,
% 4.40/2.98 (^[W0: $i] : rewrite((aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = xy)))) <=> (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy)))))),
% 4.40/2.98 inference(bind,[status(th)],[])).
% 4.40/2.98 tff(127,plain,
% 4.40/2.98 (![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = xy)))) <=> ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy))))),
% 4.40/2.98 inference(quant_intro,[status(thm)],[126])).
% 4.40/2.98 tff(128,plain,
% 4.40/2.98 (![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = xy)))) <=> ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = xy))))),
% 4.40/2.98 inference(rewrite,[status(thm)],[])).
% 4.40/2.98 tff(129,plain,
% 4.40/2.98 (^[W0: $i] : rewrite((aElementOf0(W0, sdtmndt0(xQ, xy)) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = xy)))) <=> (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = xy)))))),
% 4.40/2.98 inference(bind,[status(th)],[])).
% 4.40/2.98 tff(130,plain,
% 4.40/2.98 (![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = xy)))) <=> ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = xy))))),
% 4.40/2.99 inference(quant_intro,[status(thm)],[129])).
% 4.40/2.99 tff(131,plain,
% 4.40/2.99 (![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> ((aElement0(W0) & aElementOf0(W0, xQ)) & (~(W0 = xy))))),
% 4.40/2.99 inference(and_elim,[status(thm)],[34])).
% 4.40/2.99 tff(132,plain,
% 4.40/2.99 (![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = xy))))),
% 4.40/2.99 inference(modus_ponens,[status(thm)],[131, 130])).
% 4.40/2.99 tff(133,plain,
% 4.40/2.99 (![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = xy))))),
% 4.40/2.99 inference(modus_ponens,[status(thm)],[132, 128])).
% 4.40/2.99 tff(134,plain,(
% 4.40/2.99 ![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (aElement0(W0) & aElementOf0(W0, xQ) & (~(W0 = xy))))),
% 4.40/2.99 inference(skolemize,[status(sab)],[133])).
% 4.40/2.99 tff(135,plain,
% 4.40/2.99 (![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy))))),
% 4.40/2.99 inference(modus_ponens,[status(thm)],[134, 127])).
% 4.40/2.99 tff(136,plain,
% 4.40/2.99 (![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy))))),
% 4.40/2.99 inference(modus_ponens,[status(thm)],[135, 125])).
% 4.40/2.99 tff(137,plain,
% 4.40/2.99 ((~![W0: $i] : (aElementOf0(W0, sdtmndt0(xQ, xy)) <=> (~((~aElement0(W0)) | (~aElementOf0(W0, xQ)) | (W0 = xy))))) | (aElementOf0(xx, sdtmndt0(xQ, xy)) <=> (~((~aElement0(xx)) | (~aElementOf0(xx, xQ)) | (xx = xy))))),
% 4.40/2.99 inference(quant_inst,[status(thm)],[])).
% 4.40/2.99 tff(138,plain,
% 4.40/2.99 (aElementOf0(xx, sdtmndt0(xQ, xy)) <=> (~((~aElement0(xx)) | (~aElementOf0(xx, xQ)) | (xx = xy)))),
% 4.40/2.99 inference(unit_resolution,[status(thm)],[137, 136])).
% 4.40/2.99 tff(139,plain,
% 4.40/2.99 ((~aElementOf0(xx, xQ)) <=> (~aElementOf0(xx, xQ))),
% 4.40/2.99 inference(rewrite,[status(thm)],[])).
% 4.40/2.99 tff(140,axiom,(~aElementOf0(xx, xQ)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2323')).
% 4.40/2.99 tff(141,plain,
% 4.40/2.99 (~aElementOf0(xx, xQ)),
% 4.40/2.99 inference(modus_ponens,[status(thm)],[140, 139])).
% 4.40/2.99 tff(142,plain,
% 4.40/2.99 (((~aElement0(xx)) | (~aElementOf0(xx, xQ)) | (xx = xy)) | aElementOf0(xx, xQ)),
% 4.40/2.99 inference(tautology,[status(thm)],[])).
% 4.40/2.99 tff(143,plain,
% 4.40/2.99 ((~aElement0(xx)) | (~aElementOf0(xx, xQ)) | (xx = xy)),
% 4.40/2.99 inference(unit_resolution,[status(thm)],[142, 141])).
% 4.40/2.99 tff(144,plain,
% 4.40/2.99 ((~(aElementOf0(xx, sdtmndt0(xQ, xy)) <=> (~((~aElement0(xx)) | (~aElementOf0(xx, xQ)) | (xx = xy))))) | (~aElementOf0(xx, sdtmndt0(xQ, xy))) | (~((~aElement0(xx)) | (~aElementOf0(xx, xQ)) | (xx = xy)))),
% 4.40/2.99 inference(tautology,[status(thm)],[])).
% 4.40/2.99 tff(145,plain,
% 4.40/2.99 ((~(aElementOf0(xx, sdtmndt0(xQ, xy)) <=> (~((~aElement0(xx)) | (~aElementOf0(xx, xQ)) | (xx = xy))))) | (~aElementOf0(xx, sdtmndt0(xQ, xy)))),
% 4.40/2.99 inference(unit_resolution,[status(thm)],[144, 143])).
% 4.40/2.99 tff(146,plain,
% 4.40/2.99 (~aElementOf0(xx, sdtmndt0(xQ, xy))),
% 4.40/2.99 inference(unit_resolution,[status(thm)],[145, 138])).
% 4.40/2.99 tff(147,plain,
% 4.40/2.99 (aElement0(xy) <=> aElement0(xy)),
% 4.40/2.99 inference(rewrite,[status(thm)],[])).
% 4.40/2.99 tff(148,plain,
% 4.40/2.99 (aElement0(xy)),
% 4.40/2.99 inference(and_elim,[status(thm)],[109])).
% 4.40/2.99 tff(149,plain,
% 4.40/2.99 (aElement0(xy)),
% 4.40/2.99 inference(modus_ponens,[status(thm)],[148, 147])).
% 4.40/2.99 tff(150,plain,
% 4.40/2.99 (^[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)))))),
% 4.40/2.99 inference(bind,[status(th)],[])).
% 4.40/2.99 tff(151,plain,
% 4.40/2.99 (![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))))),
% 4.40/2.99 inference(quant_intro,[status(thm)],[150])).
% 4.40/2.99 tff(152,plain,
% 4.40/2.99 (^[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)))))),
% 4.40/2.99 inference(bind,[status(th)],[])).
% 4.40/2.99 tff(153,plain,
% 4.40/2.99 (![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))))),
% 4.40/2.99 inference(quant_intro,[status(thm)],[152])).
% 4.40/2.99 tff(154,plain,
% 4.40/2.99 (![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))))),
% 4.40/2.99 inference(transitivity,[status(thm)],[153, 151])).
% 4.40/2.99 tff(155,plain,
% 4.40/2.99 (^[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)))))),
% 4.40/2.99 inference(bind,[status(th)],[])).
% 4.40/2.99 tff(156,plain,
% 4.40/2.99 (![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))))),
% 4.40/2.99 inference(quant_intro,[status(thm)],[155])).
% 4.40/2.99 tff(157,plain,
% 4.40/2.99 (![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)))))),
% 4.40/2.99 inference(rewrite,[status(thm)],[])).
% 4.40/2.99 tff(158,plain,
% 4.40/2.99 (^[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)))))))),
% 4.40/2.99 inference(bind,[status(th)],[])).
% 4.40/2.99 tff(159,plain,
% 4.40/2.99 (![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)))))),
% 4.40/2.99 inference(quant_intro,[status(thm)],[158])).
% 4.40/2.99 tff(160,axiom,(![W0: $i] : (aElement0(W0) => ![W1: $i] : ((aSet0(W1) & isFinite0(W1)) => isFinite0(sdtmndt0(W1, W0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mFDiffSet')).
% 4.40/2.99 tff(161,plain,
% 4.40/2.99 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))),
% 4.40/2.99 inference(modus_ponens,[status(thm)],[160, 159])).
% 4.40/2.99 tff(162,plain,
% 4.40/2.99 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))),
% 4.40/2.99 inference(modus_ponens,[status(thm)],[161, 157])).
% 4.40/2.99 tff(163,plain,(
% 4.40/2.99 ![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : (isFinite0(sdtmndt0(W1, W0)) | (~(aSet0(W1) & isFinite0(W1)))))),
% 4.40/2.99 inference(skolemize,[status(sab)],[162])).
% 4.40/2.99 tff(164,plain,
% 4.40/2.99 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))),
% 4.40/2.99 inference(modus_ponens,[status(thm)],[163, 156])).
% 4.40/2.99 tff(165,plain,
% 4.40/2.99 (![W0: $i] : ((~aElement0(W0)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, W0)) | (~aSet0(W1))))),
% 4.40/2.99 inference(modus_ponens,[status(thm)],[164, 154])).
% 4.40/2.99 tff(166,plain,
% 4.40/2.99 (((~![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))))),
% 4.40/2.99 inference(rewrite,[status(thm)],[])).
% 4.40/2.99 tff(167,plain,
% 4.40/2.99 (((~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | isFinite0(sdtmndt0(W1, xy)) | (~aSet0(W1)))) <=> ((~aElement0(xy)) | ![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy))))),
% 4.40/2.99 inference(rewrite,[status(thm)],[])).
% 4.40/2.99 tff(168,plain,
% 4.40/2.99 (((~![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)))))),
% 4.40/2.99 inference(monotonicity,[status(thm)],[167])).
% 4.40/2.99 tff(169,plain,
% 4.40/2.99 (((~![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))))),
% 4.40/2.99 inference(transitivity,[status(thm)],[168, 166])).
% 4.40/2.99 tff(170,plain,
% 4.40/2.99 ((~![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))))),
% 4.40/2.99 inference(quant_inst,[status(thm)],[])).
% 4.40/2.99 tff(171,plain,
% 4.40/2.99 ((~![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)))),
% 4.40/2.99 inference(modus_ponens,[status(thm)],[170, 169])).
% 4.40/2.99 tff(172,plain,
% 4.40/2.99 (![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))),
% 4.40/2.99 inference(unit_resolution,[status(thm)],[171, 165, 149])).
% 4.40/2.99 tff(173,plain,
% 4.40/2.99 (((~![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)))),
% 4.40/2.99 inference(rewrite,[status(thm)],[])).
% 4.40/2.99 tff(174,plain,
% 4.40/2.99 (((~isFinite0(xQ)) | (~aSet0(xQ)) | isFinite0(sdtmndt0(xQ, xy))) <=> ((~aSet0(xQ)) | (~isFinite0(xQ)) | isFinite0(sdtmndt0(xQ, xy)))),
% 4.40/2.99 inference(rewrite,[status(thm)],[])).
% 4.40/2.99 tff(175,plain,
% 4.40/2.99 (((~![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))))),
% 4.40/2.99 inference(monotonicity,[status(thm)],[174])).
% 4.40/2.99 tff(176,plain,
% 4.40/2.99 (((~![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)))),
% 4.40/2.99 inference(transitivity,[status(thm)],[175, 173])).
% 4.40/2.99 tff(177,plain,
% 4.40/2.99 ((~![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))) | ((~isFinite0(xQ)) | (~aSet0(xQ)) | isFinite0(sdtmndt0(xQ, xy)))),
% 4.40/2.99 inference(quant_inst,[status(thm)],[])).
% 4.40/2.99 tff(178,plain,
% 4.40/2.99 ((~![W1: $i] : ((~isFinite0(W1)) | (~aSet0(W1)) | isFinite0(sdtmndt0(W1, xy)))) | (~aSet0(xQ)) | (~isFinite0(xQ)) | isFinite0(sdtmndt0(xQ, xy))),
% 4.40/2.99 inference(modus_ponens,[status(thm)],[177, 176])).
% 4.40/2.99 tff(179,plain,
% 4.40/2.99 (isFinite0(sdtmndt0(xQ, xy))),
% 4.40/2.99 inference(unit_resolution,[status(thm)],[178, 84, 116, 172])).
% 4.40/2.99 tff(180,plain,
% 4.40/2.99 (^[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)))))),
% 4.40/2.99 inference(bind,[status(th)],[])).
% 4.40/2.99 tff(181,plain,
% 4.40/2.99 (![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))))),
% 4.40/2.99 inference(quant_intro,[status(thm)],[180])).
% 4.40/2.99 tff(182,plain,
% 4.40/2.99 (^[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)))))),
% 4.40/2.99 inference(bind,[status(th)],[])).
% 4.40/2.99 tff(183,plain,
% 4.40/2.99 (![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))))),
% 4.40/2.99 inference(quant_intro,[status(thm)],[182])).
% 4.40/2.99 tff(184,plain,
% 4.40/2.99 (![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))))),
% 4.40/2.99 inference(transitivity,[status(thm)],[183, 181])).
% 4.40/2.99 tff(185,plain,
% 4.40/2.99 (^[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))))))),
% 4.40/2.99 inference(bind,[status(th)],[])).
% 4.40/2.99 tff(186,plain,
% 4.40/2.99 (![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))))),
% 4.40/2.99 inference(quant_intro,[status(thm)],[185])).
% 4.40/2.99 tff(187,plain,
% 4.40/2.99 (![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))))),
% 4.40/2.99 inference(rewrite,[status(thm)],[])).
% 4.40/2.99 tff(188,plain,
% 4.40/2.99 (^[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))))))),
% 4.40/2.99 inference(bind,[status(th)],[])).
% 4.40/2.99 tff(189,plain,
% 4.40/2.99 (![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))))),
% 4.40/2.99 inference(quant_intro,[status(thm)],[188])).
% 4.40/2.99 tff(190,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')).
% 4.40/2.99 tff(191,plain,
% 4.40/2.99 (![W0: $i] : ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 4.40/2.99 inference(modus_ponens,[status(thm)],[190, 189])).
% 4.40/2.99 tff(192,plain,
% 4.40/2.99 (![W0: $i] : ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 4.40/2.99 inference(modus_ponens,[status(thm)],[191, 187])).
% 4.40/2.99 tff(193,plain,(
% 4.40/2.99 ![W0: $i] : ((~(aSet0(W0) & isFinite0(W0))) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 4.40/2.99 inference(skolemize,[status(sab)],[192])).
% 4.40/2.99 tff(194,plain,
% 4.40/2.99 (![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 4.40/2.99 inference(modus_ponens,[status(thm)],[193, 186])).
% 4.40/2.99 tff(195,plain,
% 4.40/2.99 (![W0: $i] : ((~isFinite0(W0)) | (~aSet0(W0)) | ![W1: $i] : (aElementOf0(W1, W0) | (sbrdtbr0(sdtpldt0(W0, W1)) = szszuzczcdt0(sbrdtbr0(W0))) | (~aElement0(W1))))),
% 4.40/2.99 inference(modus_ponens,[status(thm)],[194, 184])).
% 4.40/2.99 tff(196,plain,
% 4.40/2.99 (((~![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))))))),
% 4.40/3.00 inference(rewrite,[status(thm)],[])).
% 4.40/3.00 tff(197,plain,
% 4.40/3.00 (((~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))))))),
% 4.40/3.00 inference(rewrite,[status(thm)],[])).
% 4.40/3.00 tff(198,plain,
% 4.40/3.00 (^[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))))))),
% 4.40/3.00 inference(bind,[status(th)],[])).
% 4.40/3.00 tff(199,plain,
% 4.40/3.00 (![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)))))),
% 4.40/3.00 inference(quant_intro,[status(thm)],[198])).
% 4.40/3.00 tff(200,plain,
% 4.40/3.00 (((~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))))))),
% 4.40/3.00 inference(monotonicity,[status(thm)],[199])).
% 4.40/3.00 tff(201,plain,
% 4.40/3.00 (((~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))))))),
% 4.40/3.00 inference(transitivity,[status(thm)],[200, 197])).
% 4.40/3.00 tff(202,plain,
% 4.40/3.00 (((~![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)))))))),
% 4.40/3.00 inference(monotonicity,[status(thm)],[201])).
% 4.40/3.00 tff(203,plain,
% 4.40/3.00 (((~![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))))))),
% 4.40/3.00 inference(transitivity,[status(thm)],[202, 196])).
% 4.40/3.00 tff(204,plain,
% 4.40/3.00 ((~![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))))),
% 4.40/3.00 inference(quant_inst,[status(thm)],[])).
% 4.40/3.00 tff(205,plain,
% 4.40/3.00 ((~![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)))))),
% 4.40/3.00 inference(modus_ponens,[status(thm)],[204, 203])).
% 4.40/3.00 tff(206,plain,
% 4.40/3.00 ((~isFinite0(sdtmndt0(xQ, xy))) | ![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))),
% 4.40/3.00 inference(unit_resolution,[status(thm)],[205, 195, 36])).
% 4.40/3.00 tff(207,plain,
% 4.40/3.00 (![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))),
% 4.40/3.00 inference(unit_resolution,[status(thm)],[206, 179])).
% 4.40/3.00 tff(208,plain,
% 4.40/3.00 (((~![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))) | ((~aElement0(xx)) | aElementOf0(xx, sdtmndt0(xQ, xy)) | (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)))))) | (~aElement0(xx)) | aElementOf0(xx, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))),
% 4.40/3.00 inference(rewrite,[status(thm)],[])).
% 4.40/3.00 tff(209,plain,
% 4.40/3.00 ((aElementOf0(xx, sdtmndt0(xQ, xy)) | (~aElement0(xx)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))))) <=> ((~aElement0(xx)) | aElementOf0(xx, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))),
% 4.40/3.00 inference(rewrite,[status(thm)],[])).
% 4.40/3.00 tff(210,plain,
% 4.40/3.00 (((~![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)))))) | ((~aElement0(xx)) | aElementOf0(xx, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))))))),
% 4.40/3.00 inference(monotonicity,[status(thm)],[209])).
% 4.40/3.00 tff(211,plain,
% 4.40/3.00 (((~![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)))))) | (~aElement0(xx)) | aElementOf0(xx, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))),
% 4.40/3.00 inference(transitivity,[status(thm)],[210, 208])).
% 4.40/3.00 tff(212,plain,
% 4.40/3.00 ((~![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)))))),
% 4.40/3.00 inference(quant_inst,[status(thm)],[])).
% 4.40/3.00 tff(213,plain,
% 4.40/3.00 ((~![W1: $i] : (aElementOf0(W1, sdtmndt0(xQ, xy)) | (~aElement0(W1)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))))) | (~aElement0(xx)) | aElementOf0(xx, sdtmndt0(xQ, xy)) | (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy))))),
% 4.40/3.00 inference(modus_ponens,[status(thm)],[212, 211])).
% 4.40/3.00 tff(214,plain,
% 4.40/3.00 (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ, xy)))),
% 4.40/3.00 inference(unit_resolution,[status(thm)],[213, 207, 29, 146])).
% 4.40/3.00 tff(215,plain,
% 4.40/3.00 (sbrdtbr0(sdtpldt0(sdtmndt0(xQ, xy), xx)) = sbrdtbr0(xQ)),
% 4.40/3.00 inference(transitivity,[status(thm)],[214, 123])).
% 4.40/3.00 tff(216,plain,
% 4.40/3.00 (((~(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))))),
% 4.40/3.00 inference(rewrite,[status(thm)],[])).
% 4.40/3.00 tff(217,plain,
% 4.40/3.00 (((~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)))),
% 4.40/3.00 inference(rewrite,[status(thm)],[])).
% 4.40/3.00 tff(218,plain,
% 4.40/3.00 ((((~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))))),
% 4.40/3.00 inference(monotonicity,[status(thm)],[217])).
% 4.40/3.00 tff(219,plain,
% 4.40/3.00 ((((~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))))),
% 4.40/3.00 inference(transitivity,[status(thm)],[218, 216])).
% 4.40/3.00 tff(220,plain,
% 4.40/3.00 ((((~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))))),
% 4.40/3.00 inference(rewrite,[status(thm)],[])).
% 4.40/3.00 tff(221,plain,
% 4.40/3.00 ((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)))),
% 4.40/3.00 inference(rewrite,[status(thm)],[])).
% 4.40/3.00 tff(222,plain,
% 4.40/3.00 (((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)))),
% 4.40/3.01 inference(monotonicity,[status(thm)],[221])).
% 4.40/3.01 tff(223,plain,
% 4.40/3.01 ((~((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))))),
% 4.40/3.01 inference(monotonicity,[status(thm)],[222])).
% 4.40/3.01 tff(224,plain,
% 4.40/3.01 ((~((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))))),
% 4.40/3.01 inference(rewrite,[status(thm)],[])).
% 4.40/3.01 tff(225,plain,
% 4.40/3.01 ((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) <=> (aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS)))),
% 4.40/3.01 inference(rewrite,[status(thm)],[])).
% 4.40/3.01 tff(226,plain,
% 4.40/3.01 (((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))),
% 4.40/3.01 inference(monotonicity,[status(thm)],[225])).
% 4.40/3.01 tff(227,plain,
% 4.40/3.01 ((~((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)))),
% 4.40/3.01 inference(monotonicity,[status(thm)],[226])).
% 4.40/3.01 tff(228,plain,
% 4.40/3.01 ((~((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)))),
% 4.40/3.01 inference(rewrite,[status(thm)],[])).
% 4.40/3.01 tff(229,plain,
% 4.40/3.01 ((~((![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)))),
% 4.40/3.01 inference(rewrite,[status(thm)],[])).
% 4.40/3.01 tff(230,axiom,(~(((![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xS)) | aSubsetOf0(xP, xS)) & (sbrdtbr0(xP) = xk)) | aElementOf0(xP, slbdtsldtrb0(xS, xk)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 4.40/3.01 tff(231,plain,
% 4.40/3.01 (~((![W0: $i] : (aElementOf0(W0, xP) => aElementOf0(W0, xS)) | aSubsetOf0(xP, xS)) & (sbrdtbr0(xP) = xk))),
% 4.40/3.01 inference(or_elim,[status(thm)],[230])).
% 4.40/3.01 tff(232,plain,
% 4.40/3.01 (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 4.40/3.01 inference(modus_ponens,[status(thm)],[231, 229])).
% 4.40/3.01 tff(233,plain,
% 4.40/3.01 (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 4.40/3.01 inference(modus_ponens,[status(thm)],[232, 227])).
% 4.40/3.01 tff(234,plain,
% 4.40/3.01 (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 4.40/3.01 inference(modus_ponens,[status(thm)],[233, 228])).
% 4.40/3.01 tff(235,plain,
% 4.40/3.01 (~((aSubsetOf0(xP, xS) | ![W0: $i] : ((~aElementOf0(W0, xP)) | aElementOf0(W0, xS))) & (sbrdtbr0(xP) = xk))),
% 4.40/3.01 inference(modus_ponens,[status(thm)],[234, 227])).
% 4.40/3.01 tff(236,plain,
% 4.40/3.01 (~((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)))),
% 4.40/3.01 inference(modus_ponens,[status(thm)],[235, 224])).
% 4.40/3.01 tff(237,plain,
% 4.40/3.01 (~((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)))),
% 4.40/3.01 inference(modus_ponens,[status(thm)],[236, 223])).
% 4.40/3.01 tff(238,plain,
% 4.40/3.01 (~((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)))),
% 4.40/3.01 inference(modus_ponens,[status(thm)],[237, 223])).
% 4.40/3.01 tff(239,plain,
% 4.40/3.01 (~((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)))),
% 4.40/3.01 inference(modus_ponens,[status(thm)],[238, 223])).
% 4.40/3.01 unexpected number of arguments: (let ((a!1 (not (aSubsetOf0 (sdtpldt0 (sdtmndt0 xQ xy) xx) xS)))
% 4.40/3.01 (a!2 (forall ((W0 $i))
% 4.40/3.01 (let ((a!1 (not (aElementOf0 W0 (sdtpldt0 (sdtmndt0 xQ xy) xx)))))
% 4.40/3.01 (or a!1 (aElementOf0 W0 xS)))))
% 4.40/3.01 (a!3 (not (aElementOf0 W0!14 (sdtpldt0 (sdtmndt0 xQ xy) xx))))
% 4.40/3.01 (a!7 (= (sbrdtbr0 (sdtpldt0 (sdtmndt0 xQ xy) xx)) (sbrdtbr0 xQ))))
% 4.40/3.01 (let ((a!4 (~ (not a!2) (not (or a!3 (aElementOf0 W0!14 xS)))))
% 4.40/3.01 (a!5 (or (aSubsetOf0 (sdtpldt0 (sdtmndt0 xQ xy) xx) xS) a!2))
% 4.40/3.01 (a!6 (and a!1 (not (or a!3 (aElementOf0 W0!14 xS))))))
% 4.40/3.01 (nnf-neg (nnf-neg (refl (~ a!1 a!1)) (sk a!4) (~ (not a!5) a!6))
% 4.40/3.01 (refl (~ (not a!7) (not a!7)))
% 4.40/3.01 (~ (not (and a!5 a!7)) (or a!6 (not a!7))))))
% 4.40/3.01 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------