TSTP Solution File: NUM545+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM545+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 13:10:24 EDT 2022
% Result : Theorem 1.20s 1.01s
% Output : Proof 1.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM545+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Sep 2 11:38:48 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.20/1.01 % SZS status Theorem
% 1.20/1.01 % SZS output start Proof
% 1.20/1.01 tff(sdtlseqdt0_type, type, (
% 1.20/1.01 sdtlseqdt0: ( $i * $i ) > $o)).
% 1.20/1.01 tff(szmzazxdt0_type, type, (
% 1.20/1.01 szmzazxdt0: $i > $i)).
% 1.20/1.01 tff(xS_type, type, (
% 1.20/1.01 xS: $i)).
% 1.20/1.01 tff(aElementOf0_type, type, (
% 1.20/1.01 aElementOf0: ( $i * $i ) > $o)).
% 1.20/1.01 tff(szNzAzT0_type, type, (
% 1.20/1.01 szNzAzT0: $i)).
% 1.20/1.01 tff(sz00_type, type, (
% 1.20/1.01 sz00: $i)).
% 1.20/1.01 tff(szszuzczcdt0_type, type, (
% 1.20/1.01 szszuzczcdt0: $i > $i)).
% 1.20/1.01 tff(aSubsetOf0_type, type, (
% 1.20/1.01 aSubsetOf0: ( $i * $i ) > $o)).
% 1.20/1.01 tff(slbdtrb0_type, type, (
% 1.20/1.01 slbdtrb0: $i > $i)).
% 1.20/1.01 tff(slcrc0_type, type, (
% 1.20/1.01 slcrc0: $i)).
% 1.20/1.01 tff(aSet0_type, type, (
% 1.20/1.01 aSet0: $i > $o)).
% 1.20/1.01 tff(tptp_fun_W2_1_type, type, (
% 1.20/1.01 tptp_fun_W2_1: ( $i * $i ) > $i)).
% 1.20/1.01 tff(isCountable0_type, type, (
% 1.20/1.01 isCountable0: $i > $o)).
% 1.20/1.01 tff(isFinite0_type, type, (
% 1.20/1.01 isFinite0: $i > $o)).
% 1.20/1.01 tff(tptp_fun_W2_7_type, type, (
% 1.20/1.01 tptp_fun_W2_7: ( $i * $i ) > $i)).
% 1.20/1.01 tff(1,plain,
% 1.20/1.01 (^[W0: $i] : refl(((~aElementOf0(W0, szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(W0)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(W0)))))),
% 1.20/1.01 inference(bind,[status(th)],[])).
% 1.20/1.01 tff(2,plain,
% 1.20/1.01 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(W0)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(W0))))),
% 1.20/1.01 inference(quant_intro,[status(thm)],[1])).
% 1.20/1.01 tff(3,plain,
% 1.20/1.01 (^[W0: $i] : trans(monotonicity(rewrite((aElementOf0(W0, szNzAzT0) & aSubsetOf0(xS, slbdtrb0(W0))) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(W0)))))), ((~(aElementOf0(W0, szNzAzT0) & aSubsetOf0(xS, slbdtrb0(W0)))) <=> (~(~((~aElementOf0(W0, szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(W0)))))))), rewrite((~(~((~aElementOf0(W0, szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(W0)))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(W0))))), ((~(aElementOf0(W0, szNzAzT0) & aSubsetOf0(xS, slbdtrb0(W0)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(W0))))))),
% 1.20/1.01 inference(bind,[status(th)],[])).
% 1.20/1.01 tff(4,plain,
% 1.20/1.01 (![W0: $i] : (~(aElementOf0(W0, szNzAzT0) & aSubsetOf0(xS, slbdtrb0(W0)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(W0))))),
% 1.20/1.01 inference(quant_intro,[status(thm)],[3])).
% 1.20/1.01 tff(5,plain,
% 1.20/1.01 ((~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & aSubsetOf0(xS, slbdtrb0(W0)))) <=> (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & aSubsetOf0(xS, slbdtrb0(W0))))),
% 1.20/1.01 inference(rewrite,[status(thm)],[])).
% 1.20/1.01 tff(6,axiom,(~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & aSubsetOf0(xS, slbdtrb0(W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 1.20/1.01 tff(7,plain,
% 1.20/1.01 (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & aSubsetOf0(xS, slbdtrb0(W0)))),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.20/1.01 tff(8,plain,
% 1.20/1.01 (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & aSubsetOf0(xS, slbdtrb0(W0)))),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[7, 5])).
% 1.20/1.01 tff(9,plain,
% 1.20/1.01 (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & aSubsetOf0(xS, slbdtrb0(W0)))),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[8, 5])).
% 1.20/1.01 tff(10,plain,
% 1.20/1.01 (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & aSubsetOf0(xS, slbdtrb0(W0)))),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[9, 5])).
% 1.20/1.01 tff(11,plain,
% 1.20/1.01 (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & aSubsetOf0(xS, slbdtrb0(W0)))),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[10, 5])).
% 1.20/1.01 tff(12,plain,
% 1.20/1.01 (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & aSubsetOf0(xS, slbdtrb0(W0)))),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[11, 5])).
% 1.20/1.01 tff(13,plain,
% 1.20/1.01 (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & aSubsetOf0(xS, slbdtrb0(W0)))),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[12, 5])).
% 1.20/1.01 tff(14,plain,
% 1.20/1.01 (~?[W0: $i] : (aElementOf0(W0, szNzAzT0) & aSubsetOf0(xS, slbdtrb0(W0)))),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[13, 5])).
% 1.20/1.01 tff(15,plain,
% 1.20/1.01 (^[W0: $i] : refl($oeq((~(aElementOf0(W0, szNzAzT0) & aSubsetOf0(xS, slbdtrb0(W0)))), (~(aElementOf0(W0, szNzAzT0) & aSubsetOf0(xS, slbdtrb0(W0))))))),
% 1.20/1.01 inference(bind,[status(th)],[])).
% 1.20/1.01 tff(16,plain,(
% 1.20/1.01 ![W0: $i] : (~(aElementOf0(W0, szNzAzT0) & aSubsetOf0(xS, slbdtrb0(W0))))),
% 1.20/1.01 inference(nnf-neg,[status(sab)],[14, 15])).
% 1.20/1.01 tff(17,plain,
% 1.20/1.01 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(W0))))),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[16, 4])).
% 1.20/1.01 tff(18,plain,
% 1.20/1.01 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(W0))))),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[17, 2])).
% 1.20/1.01 tff(19,assumption,(xS = slbdtrb0(sz00)), introduced(assumption)).
% 1.20/1.01 tff(20,plain,
% 1.20/1.01 (aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(sz00))) <=> aSubsetOf0(slbdtrb0(sz00), slbdtrb0(szszuzczcdt0(sz00)))),
% 1.20/1.01 inference(monotonicity,[status(thm)],[19])).
% 1.20/1.01 tff(21,plain,
% 1.20/1.01 (aSubsetOf0(slbdtrb0(sz00), slbdtrb0(szszuzczcdt0(sz00))) <=> aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(sz00)))),
% 1.20/1.01 inference(symmetry,[status(thm)],[20])).
% 1.20/1.01 tff(22,plain,
% 1.20/1.01 (^[W0: $i] : refl(((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00)))))),
% 1.20/1.01 inference(bind,[status(th)],[])).
% 1.20/1.01 tff(23,plain,
% 1.20/1.01 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))),
% 1.20/1.01 inference(quant_intro,[status(thm)],[22])).
% 1.20/1.01 tff(24,plain,
% 1.20/1.01 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00)))))),
% 1.20/1.01 inference(bind,[status(th)],[])).
% 1.20/1.01 tff(25,plain,
% 1.20/1.01 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))),
% 1.20/1.01 inference(quant_intro,[status(thm)],[24])).
% 1.20/1.01 tff(26,plain,
% 1.20/1.01 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))),
% 1.20/1.01 inference(rewrite,[status(thm)],[])).
% 1.20/1.01 tff(27,plain,
% 1.20/1.01 (^[W0: $i] : rewrite((aElementOf0(W0, szNzAzT0) => (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))))),
% 1.20/1.01 inference(bind,[status(th)],[])).
% 1.20/1.01 tff(28,plain,
% 1.20/1.01 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))),
% 1.20/1.01 inference(quant_intro,[status(thm)],[27])).
% 1.20/1.01 tff(29,axiom,(![W0: $i] : (aElementOf0(W0, szNzAzT0) => (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSuccNum')).
% 1.20/1.01 tff(30,plain,
% 1.20/1.01 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[29, 28])).
% 1.20/1.01 tff(31,plain,
% 1.20/1.01 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[30, 26])).
% 1.20/1.01 tff(32,plain,(
% 1.20/1.01 ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))),
% 1.20/1.01 inference(skolemize,[status(sab)],[31])).
% 1.20/1.01 tff(33,plain,
% 1.20/1.01 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[32, 25])).
% 1.20/1.01 tff(34,plain,
% 1.20/1.01 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[33, 23])).
% 1.20/1.01 tff(35,plain,
% 1.20/1.01 (aElementOf0(sz00, szNzAzT0) <=> aElementOf0(sz00, szNzAzT0)),
% 1.20/1.01 inference(rewrite,[status(thm)],[])).
% 1.20/1.01 tff(36,axiom,(aElementOf0(sz00, szNzAzT0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mZeroNum')).
% 1.20/1.01 tff(37,plain,
% 1.20/1.01 (aElementOf0(sz00, szNzAzT0)),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.20/1.01 tff(38,plain,
% 1.20/1.01 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | ((~aElementOf0(sz00, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(sz00), szNzAzT0)) | (szszuzczcdt0(sz00) = sz00))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | (~aElementOf0(sz00, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(sz00), szNzAzT0)) | (szszuzczcdt0(sz00) = sz00))))),
% 1.20/1.01 inference(rewrite,[status(thm)],[])).
% 1.20/1.01 tff(39,plain,
% 1.20/1.01 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | ((~aElementOf0(sz00, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(sz00), szNzAzT0)) | (szszuzczcdt0(sz00) = sz00))))),
% 1.20/1.01 inference(quant_inst,[status(thm)],[])).
% 1.20/1.01 tff(40,plain,
% 1.20/1.01 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | (~aElementOf0(sz00, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(sz00), szNzAzT0)) | (szszuzczcdt0(sz00) = sz00)))),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[39, 38])).
% 1.20/1.01 tff(41,plain,
% 1.20/1.01 (~((~aElementOf0(szszuzczcdt0(sz00), szNzAzT0)) | (szszuzczcdt0(sz00) = sz00))),
% 1.20/1.01 inference(unit_resolution,[status(thm)],[40, 37, 34])).
% 1.20/1.01 tff(42,plain,
% 1.20/1.01 (((~aElementOf0(szszuzczcdt0(sz00), szNzAzT0)) | (szszuzczcdt0(sz00) = sz00)) | aElementOf0(szszuzczcdt0(sz00), szNzAzT0)),
% 1.20/1.01 inference(tautology,[status(thm)],[])).
% 1.20/1.01 tff(43,plain,
% 1.20/1.01 (aElementOf0(szszuzczcdt0(sz00), szNzAzT0)),
% 1.20/1.01 inference(unit_resolution,[status(thm)],[42, 41])).
% 1.20/1.01 tff(44,plain,
% 1.20/1.01 (^[W0: $i, W1: $i] : refl(((sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))) <=> ((sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))))),
% 1.20/1.01 inference(bind,[status(th)],[])).
% 1.20/1.01 tff(45,plain,
% 1.20/1.01 (![W0: $i, W1: $i] : ((sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))) <=> ![W0: $i, W1: $i] : ((sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))),
% 1.20/1.01 inference(quant_intro,[status(thm)],[44])).
% 1.20/1.01 tff(46,plain,
% 1.20/1.01 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) <=> (~((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))))), ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) <=> (~(~((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))))))), rewrite((~(~((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))), ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))))), (((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1)))) <=> (((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))) | (sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1)))))), rewrite((((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))) | (sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1)))) <=> ((sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))), (((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1)))) <=> ((sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))))),
% 1.20/1.01 inference(bind,[status(th)],[])).
% 1.20/1.01 tff(47,plain,
% 1.20/1.01 (![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1)))) <=> ![W0: $i, W1: $i] : ((sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))),
% 1.20/1.01 inference(quant_intro,[status(thm)],[46])).
% 1.20/1.01 tff(48,plain,
% 1.20/1.01 (![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1)))) <=> ![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))))),
% 1.20/1.01 inference(rewrite,[status(thm)],[])).
% 1.20/1.01 tff(49,plain,
% 1.20/1.01 (^[W0: $i, W1: $i] : rewrite(((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1)))) <=> ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1)))))),
% 1.20/1.01 inference(bind,[status(th)],[])).
% 1.20/1.01 tff(50,plain,
% 1.20/1.01 (![W0: $i, W1: $i] : ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1)))) <=> ![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))))),
% 1.20/1.01 inference(quant_intro,[status(thm)],[49])).
% 1.20/1.01 tff(51,axiom,(![W0: $i, W1: $i] : ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSegLess')).
% 1.20/1.01 tff(52,plain,
% 1.20/1.01 (![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))))),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.20/1.01 tff(53,plain,
% 1.20/1.01 (![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))))),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[52, 48])).
% 1.20/1.01 tff(54,plain,(
% 1.20/1.01 ![W0: $i, W1: $i] : ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))))),
% 1.20/1.01 inference(skolemize,[status(sab)],[53])).
% 1.20/1.01 tff(55,plain,
% 1.20/1.01 (![W0: $i, W1: $i] : ((sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[54, 47])).
% 1.20/1.01 tff(56,plain,
% 1.20/1.01 (![W0: $i, W1: $i] : ((sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[55, 45])).
% 1.20/1.01 tff(57,plain,
% 1.20/1.01 (((~![W0: $i, W1: $i] : ((sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))) | ((~aElementOf0(sz00, szNzAzT0)) | (~aElementOf0(szszuzczcdt0(sz00), szNzAzT0)) | (sdtlseqdt0(sz00, szszuzczcdt0(sz00)) <=> aSubsetOf0(slbdtrb0(sz00), slbdtrb0(szszuzczcdt0(sz00)))))) <=> ((~![W0: $i, W1: $i] : ((sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(sz00, szNzAzT0)) | (~aElementOf0(szszuzczcdt0(sz00), szNzAzT0)) | (sdtlseqdt0(sz00, szszuzczcdt0(sz00)) <=> aSubsetOf0(slbdtrb0(sz00), slbdtrb0(szszuzczcdt0(sz00)))))),
% 1.20/1.01 inference(rewrite,[status(thm)],[])).
% 1.20/1.01 tff(58,plain,
% 1.20/1.01 (((sdtlseqdt0(sz00, szszuzczcdt0(sz00)) <=> aSubsetOf0(slbdtrb0(sz00), slbdtrb0(szszuzczcdt0(sz00)))) | (~aElementOf0(szszuzczcdt0(sz00), szNzAzT0)) | (~aElementOf0(sz00, szNzAzT0))) <=> ((~aElementOf0(sz00, szNzAzT0)) | (~aElementOf0(szszuzczcdt0(sz00), szNzAzT0)) | (sdtlseqdt0(sz00, szszuzczcdt0(sz00)) <=> aSubsetOf0(slbdtrb0(sz00), slbdtrb0(szszuzczcdt0(sz00)))))),
% 1.20/1.01 inference(rewrite,[status(thm)],[])).
% 1.20/1.01 tff(59,plain,
% 1.20/1.01 (((~![W0: $i, W1: $i] : ((sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))) | ((sdtlseqdt0(sz00, szszuzczcdt0(sz00)) <=> aSubsetOf0(slbdtrb0(sz00), slbdtrb0(szszuzczcdt0(sz00)))) | (~aElementOf0(szszuzczcdt0(sz00), szNzAzT0)) | (~aElementOf0(sz00, szNzAzT0)))) <=> ((~![W0: $i, W1: $i] : ((sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))) | ((~aElementOf0(sz00, szNzAzT0)) | (~aElementOf0(szszuzczcdt0(sz00), szNzAzT0)) | (sdtlseqdt0(sz00, szszuzczcdt0(sz00)) <=> aSubsetOf0(slbdtrb0(sz00), slbdtrb0(szszuzczcdt0(sz00))))))),
% 1.20/1.01 inference(monotonicity,[status(thm)],[58])).
% 1.20/1.01 tff(60,plain,
% 1.20/1.01 (((~![W0: $i, W1: $i] : ((sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))) | ((sdtlseqdt0(sz00, szszuzczcdt0(sz00)) <=> aSubsetOf0(slbdtrb0(sz00), slbdtrb0(szszuzczcdt0(sz00)))) | (~aElementOf0(szszuzczcdt0(sz00), szNzAzT0)) | (~aElementOf0(sz00, szNzAzT0)))) <=> ((~![W0: $i, W1: $i] : ((sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(sz00, szNzAzT0)) | (~aElementOf0(szszuzczcdt0(sz00), szNzAzT0)) | (sdtlseqdt0(sz00, szszuzczcdt0(sz00)) <=> aSubsetOf0(slbdtrb0(sz00), slbdtrb0(szszuzczcdt0(sz00)))))),
% 1.20/1.01 inference(transitivity,[status(thm)],[59, 57])).
% 1.20/1.01 tff(61,plain,
% 1.20/1.01 ((~![W0: $i, W1: $i] : ((sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))) | ((sdtlseqdt0(sz00, szszuzczcdt0(sz00)) <=> aSubsetOf0(slbdtrb0(sz00), slbdtrb0(szszuzczcdt0(sz00)))) | (~aElementOf0(szszuzczcdt0(sz00), szNzAzT0)) | (~aElementOf0(sz00, szNzAzT0)))),
% 1.20/1.01 inference(quant_inst,[status(thm)],[])).
% 1.20/1.01 tff(62,plain,
% 1.20/1.01 ((~![W0: $i, W1: $i] : ((sdtlseqdt0(W0, W1) <=> aSubsetOf0(slbdtrb0(W0), slbdtrb0(W1))) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(sz00, szNzAzT0)) | (~aElementOf0(szszuzczcdt0(sz00), szNzAzT0)) | (sdtlseqdt0(sz00, szszuzczcdt0(sz00)) <=> aSubsetOf0(slbdtrb0(sz00), slbdtrb0(szszuzczcdt0(sz00))))),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[61, 60])).
% 1.20/1.01 tff(63,plain,
% 1.20/1.01 ((~aElementOf0(szszuzczcdt0(sz00), szNzAzT0)) | (sdtlseqdt0(sz00, szszuzczcdt0(sz00)) <=> aSubsetOf0(slbdtrb0(sz00), slbdtrb0(szszuzczcdt0(sz00))))),
% 1.20/1.01 inference(unit_resolution,[status(thm)],[62, 37, 56])).
% 1.20/1.01 tff(64,plain,
% 1.20/1.01 (sdtlseqdt0(sz00, szszuzczcdt0(sz00)) <=> aSubsetOf0(slbdtrb0(sz00), slbdtrb0(szszuzczcdt0(sz00)))),
% 1.20/1.01 inference(unit_resolution,[status(thm)],[63, 43])).
% 1.20/1.01 tff(65,plain,
% 1.20/1.01 (^[W0: $i] : refl(((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0))) <=> ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0))))),
% 1.20/1.01 inference(bind,[status(th)],[])).
% 1.20/1.01 tff(66,plain,
% 1.20/1.01 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0)))),
% 1.20/1.01 inference(quant_intro,[status(thm)],[65])).
% 1.20/1.01 tff(67,plain,
% 1.20/1.01 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0)))),
% 1.20/1.01 inference(rewrite,[status(thm)],[])).
% 1.20/1.01 tff(68,plain,
% 1.20/1.01 (^[W0: $i] : rewrite((aElementOf0(W0, szNzAzT0) => sdtlseqdt0(W0, szszuzczcdt0(W0))) <=> ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0))))),
% 1.20/1.01 inference(bind,[status(th)],[])).
% 1.20/1.01 tff(69,plain,
% 1.20/1.01 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => sdtlseqdt0(W0, szszuzczcdt0(W0))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0)))),
% 1.20/1.01 inference(quant_intro,[status(thm)],[68])).
% 1.20/1.01 tff(70,axiom,(![W0: $i] : (aElementOf0(W0, szNzAzT0) => sdtlseqdt0(W0, szszuzczcdt0(W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mLessSucc')).
% 1.20/1.01 tff(71,plain,
% 1.20/1.01 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0)))),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[70, 69])).
% 1.20/1.01 tff(72,plain,
% 1.20/1.01 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0)))),
% 1.20/1.01 inference(modus_ponens,[status(thm)],[71, 67])).
% 1.20/1.01 tff(73,plain,(
% 1.20/1.01 ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0)))),
% 1.20/1.02 inference(skolemize,[status(sab)],[72])).
% 1.20/1.02 tff(74,plain,
% 1.20/1.02 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0)))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[73, 66])).
% 1.20/1.02 tff(75,plain,
% 1.20/1.02 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0)))) | ((~aElementOf0(sz00, szNzAzT0)) | sdtlseqdt0(sz00, szszuzczcdt0(sz00)))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0)))) | (~aElementOf0(sz00, szNzAzT0)) | sdtlseqdt0(sz00, szszuzczcdt0(sz00)))),
% 1.20/1.02 inference(rewrite,[status(thm)],[])).
% 1.20/1.02 tff(76,plain,
% 1.20/1.02 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0)))) | ((~aElementOf0(sz00, szNzAzT0)) | sdtlseqdt0(sz00, szszuzczcdt0(sz00)))),
% 1.20/1.02 inference(quant_inst,[status(thm)],[])).
% 1.20/1.02 tff(77,plain,
% 1.20/1.02 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0)))) | (~aElementOf0(sz00, szNzAzT0)) | sdtlseqdt0(sz00, szszuzczcdt0(sz00))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[76, 75])).
% 1.20/1.02 tff(78,plain,
% 1.20/1.02 (sdtlseqdt0(sz00, szszuzczcdt0(sz00))),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[77, 37, 74])).
% 1.20/1.02 tff(79,plain,
% 1.20/1.02 ((~(sdtlseqdt0(sz00, szszuzczcdt0(sz00)) <=> aSubsetOf0(slbdtrb0(sz00), slbdtrb0(szszuzczcdt0(sz00))))) | (~sdtlseqdt0(sz00, szszuzczcdt0(sz00))) | aSubsetOf0(slbdtrb0(sz00), slbdtrb0(szszuzczcdt0(sz00)))),
% 1.20/1.02 inference(tautology,[status(thm)],[])).
% 1.20/1.02 tff(80,plain,
% 1.20/1.02 ((~(sdtlseqdt0(sz00, szszuzczcdt0(sz00)) <=> aSubsetOf0(slbdtrb0(sz00), slbdtrb0(szszuzczcdt0(sz00))))) | aSubsetOf0(slbdtrb0(sz00), slbdtrb0(szszuzczcdt0(sz00)))),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[79, 78])).
% 1.20/1.02 tff(81,plain,
% 1.20/1.02 (aSubsetOf0(slbdtrb0(sz00), slbdtrb0(szszuzczcdt0(sz00)))),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[80, 64])).
% 1.20/1.02 tff(82,plain,
% 1.20/1.02 (aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(sz00)))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[81, 21])).
% 1.20/1.02 tff(83,plain,
% 1.20/1.02 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(W0))))) | ((~aElementOf0(szszuzczcdt0(sz00), szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(sz00)))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(W0))))) | (~aElementOf0(szszuzczcdt0(sz00), szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(sz00)))))),
% 1.20/1.02 inference(rewrite,[status(thm)],[])).
% 1.20/1.02 tff(84,plain,
% 1.20/1.02 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(W0))))) | ((~aElementOf0(szszuzczcdt0(sz00), szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(sz00)))))),
% 1.20/1.02 inference(quant_inst,[status(thm)],[])).
% 1.20/1.02 tff(85,plain,
% 1.20/1.02 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(W0))))) | (~aElementOf0(szszuzczcdt0(sz00), szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(sz00))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[84, 83])).
% 1.20/1.02 tff(86,plain,
% 1.20/1.02 (~aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(sz00)))),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[85, 18, 43])).
% 1.20/1.02 tff(87,plain,
% 1.20/1.02 ($false),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[86, 82])).
% 1.20/1.02 tff(88,plain,(~(xS = slbdtrb0(sz00))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.02 tff(89,plain,
% 1.20/1.02 (((xS = slcrc0) | aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))) <=> ((xS = slbdtrb0(sz00)) | aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))),
% 1.20/1.02 inference(rewrite,[status(thm)],[])).
% 1.20/1.02 tff(90,plain,
% 1.20/1.02 (((xS = slcrc0) | aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))) <=> ((xS = slcrc0) | aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))),
% 1.20/1.02 inference(rewrite,[status(thm)],[])).
% 1.20/1.02 tff(91,plain,
% 1.20/1.02 (((~(xS = slcrc0)) => aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))) <=> ((xS = slcrc0) | aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))),
% 1.20/1.02 inference(rewrite,[status(thm)],[])).
% 1.20/1.02 tff(92,axiom,((~(xS = slcrc0)) => aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2035')).
% 1.20/1.02 tff(93,plain,
% 1.20/1.02 ((xS = slcrc0) | aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[92, 91])).
% 1.20/1.02 tff(94,plain,
% 1.20/1.02 ((xS = slcrc0) | aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[93, 90])).
% 1.20/1.02 tff(95,plain,
% 1.20/1.02 ((xS = slbdtrb0(sz00)) | aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[94, 89])).
% 1.20/1.02 tff(96,plain,
% 1.20/1.02 (aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[95, 88])).
% 1.20/1.02 tff(97,plain,
% 1.20/1.02 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(W0))))) | ((~aElementOf0(szszuzczcdt0(szmzazxdt0(xS)), szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(W0))))) | (~aElementOf0(szszuzczcdt0(szmzazxdt0(xS)), szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))))),
% 1.20/1.02 inference(rewrite,[status(thm)],[])).
% 1.20/1.02 tff(98,plain,
% 1.20/1.02 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(W0))))) | ((~aElementOf0(szszuzczcdt0(szmzazxdt0(xS)), szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))))),
% 1.20/1.02 inference(quant_inst,[status(thm)],[])).
% 1.20/1.02 tff(99,plain,
% 1.20/1.02 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(W0))))) | (~aElementOf0(szszuzczcdt0(szmzazxdt0(xS)), szNzAzT0)) | (~aSubsetOf0(xS, slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[98, 97])).
% 1.20/1.02 tff(100,plain,
% 1.20/1.02 (~aElementOf0(szszuzczcdt0(szmzazxdt0(xS)), szNzAzT0)),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[99, 96, 18])).
% 1.20/1.02 tff(101,plain,
% 1.20/1.02 (((~aElementOf0(szszuzczcdt0(szmzazxdt0(xS)), szNzAzT0)) | (szszuzczcdt0(szmzazxdt0(xS)) = sz00)) | aElementOf0(szszuzczcdt0(szmzazxdt0(xS)), szNzAzT0)),
% 1.20/1.02 inference(tautology,[status(thm)],[])).
% 1.20/1.02 tff(102,plain,
% 1.20/1.02 ((~aElementOf0(szszuzczcdt0(szmzazxdt0(xS)), szNzAzT0)) | (szszuzczcdt0(szmzazxdt0(xS)) = sz00)),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[101, 100])).
% 1.20/1.02 tff(103,plain,
% 1.20/1.02 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | ((~aElementOf0(szmzazxdt0(xS), szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(szmzazxdt0(xS)), szNzAzT0)) | (szszuzczcdt0(szmzazxdt0(xS)) = sz00))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | (~aElementOf0(szmzazxdt0(xS), szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(szmzazxdt0(xS)), szNzAzT0)) | (szszuzczcdt0(szmzazxdt0(xS)) = sz00))))),
% 1.20/1.02 inference(rewrite,[status(thm)],[])).
% 1.20/1.02 tff(104,plain,
% 1.20/1.02 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | ((~aElementOf0(szmzazxdt0(xS), szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(szmzazxdt0(xS)), szNzAzT0)) | (szszuzczcdt0(szmzazxdt0(xS)) = sz00))))),
% 1.20/1.02 inference(quant_inst,[status(thm)],[])).
% 1.20/1.02 tff(105,plain,
% 1.20/1.02 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | (~aElementOf0(szmzazxdt0(xS), szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(szmzazxdt0(xS)), szNzAzT0)) | (szszuzczcdt0(szmzazxdt0(xS)) = sz00)))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[104, 103])).
% 1.20/1.02 tff(106,plain,
% 1.20/1.02 (~aElementOf0(szmzazxdt0(xS), szNzAzT0)),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[105, 34, 102])).
% 1.20/1.02 tff(107,plain,
% 1.20/1.02 (aSet0(szNzAzT0) <=> aSet0(szNzAzT0)),
% 1.20/1.02 inference(rewrite,[status(thm)],[])).
% 1.20/1.02 tff(108,axiom,(aSet0(szNzAzT0) & isCountable0(szNzAzT0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mNATSet')).
% 1.20/1.02 tff(109,plain,
% 1.20/1.02 (aSet0(szNzAzT0)),
% 1.20/1.02 inference(and_elim,[status(thm)],[108])).
% 1.20/1.02 tff(110,plain,
% 1.20/1.02 (aSet0(szNzAzT0)),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[109, 107])).
% 1.20/1.02 tff(111,plain,
% 1.20/1.02 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))))))))),
% 1.20/1.02 inference(bind,[status(th)],[])).
% 1.20/1.02 tff(112,plain,
% 1.20/1.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 1.20/1.02 inference(quant_intro,[status(thm)],[111])).
% 1.20/1.02 tff(113,plain,
% 1.20/1.02 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 1.20/1.02 inference(bind,[status(th)],[])).
% 1.20/1.02 tff(114,plain,
% 1.20/1.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 1.20/1.02 inference(quant_intro,[status(thm)],[113])).
% 1.20/1.02 tff(115,plain,
% 1.20/1.02 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 1.20/1.02 inference(bind,[status(th)],[])).
% 1.20/1.02 tff(116,plain,
% 1.20/1.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 1.20/1.02 inference(quant_intro,[status(thm)],[115])).
% 1.20/1.02 tff(117,plain,
% 1.20/1.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 1.20/1.02 inference(transitivity,[status(thm)],[116, 114])).
% 1.20/1.02 tff(118,plain,
% 1.20/1.02 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 1.20/1.02 inference(bind,[status(th)],[])).
% 1.20/1.02 tff(119,plain,
% 1.20/1.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 1.20/1.02 inference(quant_intro,[status(thm)],[118])).
% 1.20/1.02 tff(120,plain,
% 1.20/1.02 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))),
% 1.20/1.02 inference(bind,[status(th)],[])).
% 1.20/1.02 tff(121,plain,
% 1.20/1.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))),
% 1.20/1.02 inference(quant_intro,[status(thm)],[120])).
% 1.20/1.02 tff(122,plain,
% 1.20/1.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 1.20/1.02 inference(rewrite,[status(thm)],[])).
% 1.20/1.02 tff(123,plain,
% 1.20/1.02 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))) <=> (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), (![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))) <=> ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), ((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))), rewrite((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))) <=> ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), ((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))))),
% 1.20/1.02 inference(bind,[status(th)],[])).
% 1.20/1.02 tff(124,plain,
% 1.20/1.02 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 1.20/1.02 inference(quant_intro,[status(thm)],[123])).
% 1.20/1.02 tff(125,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefSub')).
% 1.20/1.02 tff(126,plain,
% 1.20/1.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[125, 124])).
% 1.20/1.02 tff(127,plain,
% 1.20/1.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[126, 122])).
% 1.20/1.02 tff(128,plain,(
% 1.20/1.02 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))),
% 1.20/1.02 inference(skolemize,[status(sab)],[127])).
% 1.20/1.02 tff(129,plain,
% 1.20/1.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[128, 121])).
% 1.20/1.02 tff(130,plain,
% 1.20/1.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[129, 119])).
% 1.20/1.02 tff(131,plain,
% 1.20/1.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[130, 117])).
% 1.20/1.02 tff(132,plain,
% 1.20/1.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[131, 112])).
% 1.20/1.02 tff(133,plain,
% 1.20/1.02 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(szNzAzT0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, szNzAzT0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), W1)) | aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), szNzAzT0))))) | (~((~aSubsetOf0(W1, szNzAzT0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szNzAzT0))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(szNzAzT0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, szNzAzT0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), W1)) | aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), szNzAzT0))))) | (~((~aSubsetOf0(W1, szNzAzT0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szNzAzT0))))))))))),
% 1.20/1.02 inference(rewrite,[status(thm)],[])).
% 1.20/1.02 tff(134,plain,
% 1.20/1.02 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(szNzAzT0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, szNzAzT0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), W1)) | aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), szNzAzT0))))) | (~((~aSubsetOf0(W1, szNzAzT0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szNzAzT0))))))))))),
% 1.20/1.02 inference(quant_inst,[status(thm)],[])).
% 1.20/1.02 tff(135,plain,
% 1.20/1.02 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(szNzAzT0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, szNzAzT0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), W1)) | aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), szNzAzT0))))) | (~((~aSubsetOf0(W1, szNzAzT0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szNzAzT0)))))))))),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[134, 133])).
% 1.20/1.02 tff(136,plain,
% 1.20/1.02 (![W1: $i] : (~((~(aSubsetOf0(W1, szNzAzT0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), W1)) | aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), szNzAzT0))))) | (~((~aSubsetOf0(W1, szNzAzT0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szNzAzT0)))))))))),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[135, 132, 110])).
% 1.20/1.02 tff(137,plain,
% 1.20/1.02 ((~![W1: $i] : (~((~(aSubsetOf0(W1, szNzAzT0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), W1)) | aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), szNzAzT0))))) | (~((~aSubsetOf0(W1, szNzAzT0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szNzAzT0)))))))))) | (~((~(aSubsetOf0(xS, szNzAzT0) | (~aSet0(xS)) | (~((~aElementOf0(tptp_fun_W2_1(xS, szNzAzT0), xS)) | aElementOf0(tptp_fun_W2_1(xS, szNzAzT0), szNzAzT0))))) | (~((~aSubsetOf0(xS, szNzAzT0)) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0)))))))))),
% 1.20/1.02 inference(quant_inst,[status(thm)],[])).
% 1.20/1.02 tff(138,plain,
% 1.20/1.02 (~((~(aSubsetOf0(xS, szNzAzT0) | (~aSet0(xS)) | (~((~aElementOf0(tptp_fun_W2_1(xS, szNzAzT0), xS)) | aElementOf0(tptp_fun_W2_1(xS, szNzAzT0), szNzAzT0))))) | (~((~aSubsetOf0(xS, szNzAzT0)) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))))))))),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[137, 136])).
% 1.20/1.02 tff(139,plain,
% 1.20/1.02 (((~(aSubsetOf0(xS, szNzAzT0) | (~aSet0(xS)) | (~((~aElementOf0(tptp_fun_W2_1(xS, szNzAzT0), xS)) | aElementOf0(tptp_fun_W2_1(xS, szNzAzT0), szNzAzT0))))) | (~((~aSubsetOf0(xS, szNzAzT0)) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0)))))))) | ((~aSubsetOf0(xS, szNzAzT0)) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))))))),
% 1.20/1.02 inference(tautology,[status(thm)],[])).
% 1.20/1.02 tff(140,plain,
% 1.20/1.02 ((~aSubsetOf0(xS, szNzAzT0)) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0)))))),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[139, 138])).
% 1.20/1.02 tff(141,plain,
% 1.20/1.02 (aSubsetOf0(xS, szNzAzT0) <=> aSubsetOf0(xS, szNzAzT0)),
% 1.20/1.02 inference(rewrite,[status(thm)],[])).
% 1.20/1.02 tff(142,axiom,(aSubsetOf0(xS, szNzAzT0) & isFinite0(xS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1986')).
% 1.20/1.02 tff(143,plain,
% 1.20/1.02 (aSubsetOf0(xS, szNzAzT0)),
% 1.20/1.02 inference(and_elim,[status(thm)],[142])).
% 1.20/1.02 tff(144,plain,
% 1.20/1.02 (aSubsetOf0(xS, szNzAzT0)),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[143, 141])).
% 1.20/1.02 tff(145,plain,
% 1.20/1.02 ((~((~aSubsetOf0(xS, szNzAzT0)) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))))))) | (~aSubsetOf0(xS, szNzAzT0)) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0)))))),
% 1.20/1.02 inference(tautology,[status(thm)],[])).
% 1.20/1.02 tff(146,plain,
% 1.20/1.02 ((~((~aSubsetOf0(xS, szNzAzT0)) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))))))) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0)))))),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[145, 144])).
% 1.20/1.02 tff(147,plain,
% 1.20/1.02 (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))))),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[146, 140])).
% 1.20/1.02 tff(148,plain,
% 1.20/1.02 (((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0)))) | ![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))),
% 1.20/1.02 inference(tautology,[status(thm)],[])).
% 1.20/1.02 tff(149,plain,
% 1.20/1.02 (![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[148, 147])).
% 1.20/1.02 tff(150,plain,
% 1.20/1.02 (((~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))) | ((~aElementOf0(szmzazxdt0(xS), xS)) | aElementOf0(szmzazxdt0(xS), szNzAzT0))) <=> ((~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))) | (~aElementOf0(szmzazxdt0(xS), xS)) | aElementOf0(szmzazxdt0(xS), szNzAzT0))),
% 1.20/1.02 inference(rewrite,[status(thm)],[])).
% 1.20/1.02 tff(151,plain,
% 1.20/1.02 ((~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))) | ((~aElementOf0(szmzazxdt0(xS), xS)) | aElementOf0(szmzazxdt0(xS), szNzAzT0))),
% 1.20/1.02 inference(quant_inst,[status(thm)],[])).
% 1.20/1.02 tff(152,plain,
% 1.20/1.02 ((~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))) | (~aElementOf0(szmzazxdt0(xS), xS)) | aElementOf0(szmzazxdt0(xS), szNzAzT0)),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[151, 150])).
% 1.20/1.02 tff(153,plain,
% 1.20/1.02 (~aElementOf0(szmzazxdt0(xS), xS)),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[152, 149, 106])).
% 1.20/1.02 tff(154,plain,
% 1.20/1.02 (((~aElementOf0(szmzazxdt0(xS), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, szmzazxdt0(xS))))) | aElementOf0(szmzazxdt0(xS), xS)),
% 1.20/1.02 inference(tautology,[status(thm)],[])).
% 1.20/1.02 tff(155,plain,
% 1.20/1.02 ((~aElementOf0(szmzazxdt0(xS), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, szmzazxdt0(xS))))),
% 1.20/1.02 inference(unit_resolution,[status(thm)],[154, 153])).
% 1.20/1.02 tff(156,plain,
% 1.20/1.02 (isFinite0(xS) <=> isFinite0(xS)),
% 1.20/1.02 inference(rewrite,[status(thm)],[])).
% 1.20/1.02 tff(157,plain,
% 1.20/1.02 (isFinite0(xS)),
% 1.20/1.02 inference(and_elim,[status(thm)],[142])).
% 1.20/1.02 tff(158,plain,
% 1.20/1.02 (isFinite0(xS)),
% 1.20/1.02 inference(modus_ponens,[status(thm)],[157, 156])).
% 1.20/1.02 tff(159,plain,
% 1.20/1.02 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))))) <=> (~((~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))) | (~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))))))), (![W1: $i] : (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))))) <=> ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))) | (~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))))))), (((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1)))))))) <=> ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))) | (~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))))))))))), rewrite(((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))) | (~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))))))))) <=> ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))) | (~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))))))), (((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1)))))))) <=> ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))) | (~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))))))))),
% 1.27/1.02 inference(bind,[status(th)],[])).
% 1.27/1.02 tff(160,plain,
% 1.27/1.02 (![W0: $i] : ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1)))))))) <=> ![W0: $i] : ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))) | (~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))))))),
% 1.27/1.02 inference(quant_intro,[status(thm)],[159])).
% 1.27/1.02 tff(161,plain,
% 1.27/1.02 (^[W0: $i] : refl(((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1)))))))) <=> ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1)))))))))),
% 1.27/1.02 inference(bind,[status(th)],[])).
% 1.27/1.02 tff(162,plain,
% 1.27/1.02 (![W0: $i] : ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1)))))))) <=> ![W0: $i] : ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))))))),
% 1.27/1.02 inference(quant_intro,[status(thm)],[161])).
% 1.27/1.02 tff(163,plain,
% 1.27/1.02 (^[W0: $i] : rewrite(((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1)))))))) <=> ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1)))))))))),
% 1.27/1.02 inference(bind,[status(th)],[])).
% 1.27/1.02 tff(164,plain,
% 1.27/1.02 (![W0: $i] : ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1)))))))) <=> ![W0: $i] : ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))))))),
% 1.27/1.02 inference(quant_intro,[status(thm)],[163])).
% 1.27/1.02 tff(165,plain,
% 1.27/1.02 (![W0: $i] : ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1)))))))) <=> ![W0: $i] : ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))))))),
% 1.27/1.02 inference(transitivity,[status(thm)],[164, 162])).
% 1.27/1.02 tff(166,plain,
% 1.27/1.02 (^[W0: $i] : trans(monotonicity(trans(monotonicity(rewrite((aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slbdtrb0(sz00)))) <=> (~((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0))))), ((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slbdtrb0(sz00))))) <=> (~(~((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0))))))), rewrite((~(~((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0))))) <=> ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)))), ((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slbdtrb0(sz00))))) <=> ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0))))), quant_intro(proof_bind(^[W1: $i] : trans(monotonicity(rewrite(((~(W1 = szmzazxdt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))) <=> ((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))), rewrite(((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1)))) <=> ((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))), ((((~(W1 = szmzazxdt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))) <=> (((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))))) & ((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))))), rewrite((((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))))) & ((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))) <=> (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1)))))))), ((((~(W1 = szmzazxdt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))) <=> (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1)))))))))), (![W1: $i] : (((~(W1 = szmzazxdt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))) <=> ![W1: $i] : (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))))))), (((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : (((~(W1 = szmzazxdt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1)))))) <=> (((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0))) | ![W1: $i] : (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1)))))))))), rewrite((((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0))) | ![W1: $i] : (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1)))))))) <=> ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))))))), (((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : (((~(W1 = szmzazxdt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1)))))) <=> ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))))))))),
% 1.27/1.03 inference(bind,[status(th)],[])).
% 1.27/1.03 tff(167,plain,
% 1.27/1.03 (![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : (((~(W1 = szmzazxdt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1)))))) <=> ![W0: $i] : ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))))))),
% 1.27/1.03 inference(quant_intro,[status(thm)],[166])).
% 1.27/1.03 tff(168,plain,
% 1.27/1.03 (^[W0: $i] : rewrite(((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : (((~(W1 = szmzazxdt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))) & ((W1 = szmzazxdt0(W0)) | ((~aElementOf0(W1, W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))))) <=> ((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : (((~(W1 = szmzazxdt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1)))))))),
% 1.27/1.03 inference(bind,[status(th)],[])).
% 1.27/1.03 tff(169,plain,
% 1.27/1.03 (![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : (((~(W1 = szmzazxdt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))) & ((W1 = szmzazxdt0(W0)) | ((~aElementOf0(W1, W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))))) <=> ![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : (((~(W1 = szmzazxdt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))))),
% 1.27/1.03 inference(quant_intro,[status(thm)],[168])).
% 1.27/1.03 tff(170,plain,
% 1.27/1.03 (^[W0: $i] : rewrite(((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzazxdt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))) <=> ((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : ((W1 = szmzazxdt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))),
% 1.27/1.03 inference(bind,[status(th)],[])).
% 1.27/1.03 tff(171,plain,
% 1.27/1.03 (![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzazxdt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))) <=> ![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : ((W1 = szmzazxdt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))))),
% 1.27/1.03 inference(quant_intro,[status(thm)],[170])).
% 1.27/1.03 tff(172,plain,
% 1.27/1.03 (![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzazxdt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))) <=> ![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzazxdt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))))),
% 1.27/1.03 inference(rewrite,[status(thm)],[])).
% 1.27/1.03 tff(173,plain,
% 1.27/1.03 (^[W0: $i] : trans(monotonicity(rewrite(((aSubsetOf0(W0, szNzAzT0) & isFinite0(W0)) & (~(W0 = slcrc0))) <=> (aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slcrc0)))), quant_intro(proof_bind(^[W1: $i] : rewrite(((W1 = szmzazxdt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W2, W1)))) <=> ((W1 = szmzazxdt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))))), (![W1: $i] : ((W1 = szmzazxdt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W2, W1)))) <=> ![W1: $i] : ((W1 = szmzazxdt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))))), ((((aSubsetOf0(W0, szNzAzT0) & isFinite0(W0)) & (~(W0 = slcrc0))) => ![W1: $i] : ((W1 = szmzazxdt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W2, W1))))) <=> ((aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slcrc0))) => ![W1: $i] : ((W1 = szmzazxdt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))), rewrite(((aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slcrc0))) => ![W1: $i] : ((W1 = szmzazxdt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))) <=> ((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzazxdt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))))), ((((aSubsetOf0(W0, szNzAzT0) & isFinite0(W0)) & (~(W0 = slcrc0))) => ![W1: $i] : ((W1 = szmzazxdt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W2, W1))))) <=> ((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzazxdt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))))))),
% 1.27/1.03 inference(bind,[status(th)],[])).
% 1.27/1.03 tff(174,plain,
% 1.27/1.03 (![W0: $i] : (((aSubsetOf0(W0, szNzAzT0) & isFinite0(W0)) & (~(W0 = slcrc0))) => ![W1: $i] : ((W1 = szmzazxdt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W2, W1))))) <=> ![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzazxdt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))))),
% 1.27/1.03 inference(quant_intro,[status(thm)],[173])).
% 1.27/1.03 tff(175,axiom,(![W0: $i] : (((aSubsetOf0(W0, szNzAzT0) & isFinite0(W0)) & (~(W0 = slcrc0))) => ![W1: $i] : ((W1 = szmzazxdt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W2, W1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefMax')).
% 1.27/1.03 tff(176,plain,
% 1.27/1.03 (![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzazxdt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))))),
% 1.27/1.03 inference(modus_ponens,[status(thm)],[175, 174])).
% 1.27/1.03 tff(177,plain,
% 1.27/1.03 (![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzazxdt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))))),
% 1.27/1.03 inference(modus_ponens,[status(thm)],[176, 172])).
% 1.27/1.03 tff(178,plain,
% 1.27/1.03 (![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : ((W1 = szmzazxdt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))))),
% 1.27/1.03 inference(modus_ponens,[status(thm)],[177, 171])).
% 1.27/1.03 tff(179,plain,(
% 1.27/1.03 ![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : (((~(W1 = szmzazxdt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))) & ((W1 = szmzazxdt0(W0)) | ((~aElementOf0(W1, W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1)))))))),
% 1.27/1.03 inference(skolemize,[status(sab)],[178])).
% 1.27/1.03 tff(180,plain,
% 1.27/1.03 (![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & isFinite0(W0) & (~(W0 = slbdtrb0(sz00))))) | ![W1: $i] : (((~(W1 = szmzazxdt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))))),
% 1.27/1.03 inference(modus_ponens,[status(thm)],[179, 169])).
% 1.27/1.03 tff(181,plain,
% 1.27/1.03 (![W0: $i] : ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))))))),
% 1.27/1.03 inference(modus_ponens,[status(thm)],[180, 167])).
% 1.27/1.03 tff(182,plain,
% 1.27/1.03 (![W0: $i] : ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))))))),
% 1.27/1.03 inference(modus_ponens,[status(thm)],[181, 165])).
% 1.27/1.03 tff(183,plain,
% 1.27/1.03 (![W0: $i] : ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))) | (~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))))))),
% 1.27/1.03 inference(modus_ponens,[status(thm)],[182, 160])).
% 1.27/1.03 tff(184,plain,
% 1.27/1.03 (((~![W0: $i] : ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))) | (~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))))))) | ((xS = slbdtrb0(sz00)) | (~isFinite0(xS)) | (~aSubsetOf0(xS, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(W1, xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(W1, xS), W1))))) | (~((~(W1 = szmzazxdt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, W1))))))))))) <=> ((~![W0: $i] : ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))) | (~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))))))) | (xS = slbdtrb0(sz00)) | (~isFinite0(xS)) | (~aSubsetOf0(xS, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(W1, xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(W1, xS), W1))))) | (~((~(W1 = szmzazxdt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, W1))))))))))),
% 1.27/1.03 inference(rewrite,[status(thm)],[])).
% 1.27/1.03 tff(185,plain,
% 1.27/1.03 (((~isFinite0(xS)) | (xS = slbdtrb0(sz00)) | (~aSubsetOf0(xS, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(W1, xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(W1, xS), W1))))) | (~((~(W1 = szmzazxdt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, W1)))))))))) <=> ((xS = slbdtrb0(sz00)) | (~isFinite0(xS)) | (~aSubsetOf0(xS, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(W1, xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(W1, xS), W1))))) | (~((~(W1 = szmzazxdt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, W1))))))))))),
% 1.27/1.03 inference(rewrite,[status(thm)],[])).
% 1.27/1.03 tff(186,plain,
% 1.27/1.03 (((~![W0: $i] : ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))) | (~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))))))) | ((~isFinite0(xS)) | (xS = slbdtrb0(sz00)) | (~aSubsetOf0(xS, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(W1, xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(W1, xS), W1))))) | (~((~(W1 = szmzazxdt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, W1))))))))))) <=> ((~![W0: $i] : ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))) | (~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))))))) | ((xS = slbdtrb0(sz00)) | (~isFinite0(xS)) | (~aSubsetOf0(xS, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(W1, xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(W1, xS), W1))))) | (~((~(W1 = szmzazxdt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, W1)))))))))))),
% 1.27/1.03 inference(monotonicity,[status(thm)],[185])).
% 1.27/1.03 tff(187,plain,
% 1.27/1.03 (((~![W0: $i] : ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))) | (~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))))))) | ((~isFinite0(xS)) | (xS = slbdtrb0(sz00)) | (~aSubsetOf0(xS, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(W1, xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(W1, xS), W1))))) | (~((~(W1 = szmzazxdt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, W1))))))))))) <=> ((~![W0: $i] : ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))) | (~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))))))) | (xS = slbdtrb0(sz00)) | (~isFinite0(xS)) | (~aSubsetOf0(xS, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(W1, xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(W1, xS), W1))))) | (~((~(W1 = szmzazxdt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, W1))))))))))),
% 1.27/1.03 inference(transitivity,[status(thm)],[186, 184])).
% 1.27/1.03 tff(188,plain,
% 1.27/1.03 ((~![W0: $i] : ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))) | (~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))))))) | ((~isFinite0(xS)) | (xS = slbdtrb0(sz00)) | (~aSubsetOf0(xS, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(W1, xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(W1, xS), W1))))) | (~((~(W1 = szmzazxdt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, W1))))))))))),
% 1.27/1.03 inference(quant_inst,[status(thm)],[])).
% 1.27/1.03 tff(189,plain,
% 1.27/1.03 ((~![W0: $i] : ((~isFinite0(W0)) | (W0 = slbdtrb0(sz00)) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzazxdt0(W0)) | (~((~aElementOf0(tptp_fun_W2_7(W1, W0), W0)) | sdtlseqdt0(tptp_fun_W2_7(W1, W0), W1))))) | (~((~(W1 = szmzazxdt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W2, W1))))))))))) | (xS = slbdtrb0(sz00)) | (~isFinite0(xS)) | (~aSubsetOf0(xS, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(W1, xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(W1, xS), W1))))) | (~((~(W1 = szmzazxdt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, W1)))))))))),
% 1.27/1.03 inference(modus_ponens,[status(thm)],[188, 187])).
% 1.27/1.03 tff(190,plain,
% 1.27/1.03 ((xS = slbdtrb0(sz00)) | ![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(W1, xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(W1, xS), W1))))) | (~((~(W1 = szmzazxdt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, W1)))))))))),
% 1.27/1.03 inference(unit_resolution,[status(thm)],[189, 183, 144, 158])).
% 1.27/1.03 tff(191,plain,
% 1.27/1.03 (![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(W1, xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(W1, xS), W1))))) | (~((~(W1 = szmzazxdt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, W1)))))))))),
% 1.27/1.03 inference(unit_resolution,[status(thm)],[190, 88])).
% 1.27/1.03 tff(192,plain,
% 1.27/1.03 (((~![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(W1, xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(W1, xS), W1))))) | (~((~(W1 = szmzazxdt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, W1)))))))))) | (~((~aElementOf0(szmzazxdt0(xS), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, szmzazxdt0(xS))))))) <=> ((~![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(W1, xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(W1, xS), W1))))) | (~((~(W1 = szmzazxdt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, W1)))))))))) | (~((~aElementOf0(szmzazxdt0(xS), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, szmzazxdt0(xS)))))))),
% 1.27/1.03 inference(rewrite,[status(thm)],[])).
% 1.27/1.03 tff(193,plain,
% 1.27/1.03 ((~((~((~aElementOf0(szmzazxdt0(xS), xS)) | (szmzazxdt0(xS) = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(szmzazxdt0(xS), xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(szmzazxdt0(xS), xS), szmzazxdt0(xS)))))) | (~((~(szmzazxdt0(xS) = szmzazxdt0(xS))) | (~((~aElementOf0(szmzazxdt0(xS), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, szmzazxdt0(xS)))))))))) <=> (~((~aElementOf0(szmzazxdt0(xS), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, szmzazxdt0(xS))))))),
% 1.27/1.03 inference(rewrite,[status(thm)],[])).
% 1.27/1.03 tff(194,plain,
% 1.27/1.03 (((~![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(W1, xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(W1, xS), W1))))) | (~((~(W1 = szmzazxdt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, W1)))))))))) | (~((~((~aElementOf0(szmzazxdt0(xS), xS)) | (szmzazxdt0(xS) = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(szmzazxdt0(xS), xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(szmzazxdt0(xS), xS), szmzazxdt0(xS)))))) | (~((~(szmzazxdt0(xS) = szmzazxdt0(xS))) | (~((~aElementOf0(szmzazxdt0(xS), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, szmzazxdt0(xS))))))))))) <=> ((~![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(W1, xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(W1, xS), W1))))) | (~((~(W1 = szmzazxdt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, W1)))))))))) | (~((~aElementOf0(szmzazxdt0(xS), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, szmzazxdt0(xS)))))))),
% 1.27/1.03 inference(monotonicity,[status(thm)],[193])).
% 1.27/1.03 tff(195,plain,
% 1.27/1.03 (((~![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(W1, xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(W1, xS), W1))))) | (~((~(W1 = szmzazxdt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, W1)))))))))) | (~((~((~aElementOf0(szmzazxdt0(xS), xS)) | (szmzazxdt0(xS) = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(szmzazxdt0(xS), xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(szmzazxdt0(xS), xS), szmzazxdt0(xS)))))) | (~((~(szmzazxdt0(xS) = szmzazxdt0(xS))) | (~((~aElementOf0(szmzazxdt0(xS), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, szmzazxdt0(xS))))))))))) <=> ((~![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(W1, xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(W1, xS), W1))))) | (~((~(W1 = szmzazxdt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, W1)))))))))) | (~((~aElementOf0(szmzazxdt0(xS), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, szmzazxdt0(xS)))))))),
% 1.27/1.04 inference(transitivity,[status(thm)],[194, 192])).
% 1.27/1.04 tff(196,plain,
% 1.27/1.04 ((~![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(W1, xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(W1, xS), W1))))) | (~((~(W1 = szmzazxdt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, W1)))))))))) | (~((~((~aElementOf0(szmzazxdt0(xS), xS)) | (szmzazxdt0(xS) = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(szmzazxdt0(xS), xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(szmzazxdt0(xS), xS), szmzazxdt0(xS)))))) | (~((~(szmzazxdt0(xS) = szmzazxdt0(xS))) | (~((~aElementOf0(szmzazxdt0(xS), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, szmzazxdt0(xS))))))))))),
% 1.27/1.04 inference(quant_inst,[status(thm)],[])).
% 1.27/1.04 tff(197,plain,
% 1.27/1.04 ((~![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzazxdt0(xS)) | (~((~aElementOf0(tptp_fun_W2_7(W1, xS), xS)) | sdtlseqdt0(tptp_fun_W2_7(W1, xS), W1))))) | (~((~(W1 = szmzazxdt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, W1)))))))))) | (~((~aElementOf0(szmzazxdt0(xS), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W2, szmzazxdt0(xS))))))),
% 1.27/1.04 inference(modus_ponens,[status(thm)],[196, 195])).
% 1.27/1.04 tff(198,plain,
% 1.27/1.04 ($false),
% 1.27/1.04 inference(unit_resolution,[status(thm)],[197, 191, 155])).
% 1.27/1.04 % SZS output end Proof
%------------------------------------------------------------------------------