TSTP Solution File: NUM542+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM542+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 0.63s 0.69s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM542+2 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 11:56:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.63/0.69 % SZS status Theorem
% 0.63/0.69 % SZS output start Proof
% 0.63/0.69 tff(aElementOf0_type, type, (
% 0.63/0.69 aElementOf0: ( $i * $i ) > $o)).
% 0.63/0.69 tff(szNzAzT0_type, type, (
% 0.63/0.69 szNzAzT0: $i)).
% 0.63/0.69 tff(szszuzczcdt0_type, type, (
% 0.63/0.69 szszuzczcdt0: $i > $i)).
% 0.63/0.69 tff(tptp_fun_W0_9_type, type, (
% 0.63/0.69 tptp_fun_W0_9: $i)).
% 0.63/0.69 tff(sz00_type, type, (
% 0.63/0.69 sz00: $i)).
% 0.63/0.69 tff(sdtlseqdt0_type, type, (
% 0.63/0.69 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.63/0.69 tff(xm_type, type, (
% 0.63/0.69 xm: $i)).
% 0.63/0.69 tff(slbdtrb0_type, type, (
% 0.63/0.69 slbdtrb0: $i > $i)).
% 0.63/0.69 tff(xn_type, type, (
% 0.63/0.69 xn: $i)).
% 0.63/0.69 tff(aSet0_type, type, (
% 0.63/0.69 aSet0: $i > $o)).
% 0.63/0.69 tff(aSubsetOf0_type, type, (
% 0.63/0.69 aSubsetOf0: ( $i * $i ) > $o)).
% 0.63/0.69 tff(tptp_fun_W1_4_type, type, (
% 0.63/0.69 tptp_fun_W1_4: $i > $i)).
% 0.63/0.69 tff(tptp_fun_W2_8_type, type, (
% 0.63/0.69 tptp_fun_W2_8: ( $i * $i ) > $i)).
% 0.63/0.69 tff(1,plain,
% 0.63/0.69 (aElementOf0(xm, szNzAzT0) <=> aElementOf0(xm, szNzAzT0)),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(2,axiom,(aElementOf0(xm, szNzAzT0) & aElementOf0(xn, szNzAzT0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1964')).
% 0.63/0.69 tff(3,plain,
% 0.63/0.69 (aElementOf0(xm, szNzAzT0)),
% 0.63/0.69 inference(and_elim,[status(thm)],[2])).
% 0.63/0.69 tff(4,plain,
% 0.63/0.69 (aElementOf0(xm, szNzAzT0)),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.63/0.69 tff(5,plain,
% 0.63/0.69 (^[W0: $i] : refl(((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00)))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(6,plain,
% 0.63/0.69 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[5])).
% 0.63/0.69 tff(7,plain,
% 0.63/0.69 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00)))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(8,plain,
% 0.63/0.69 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[7])).
% 0.63/0.69 tff(9,plain,
% 0.63/0.69 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(10,plain,
% 0.63/0.69 (^[W0: $i] : rewrite((aElementOf0(W0, szNzAzT0) => (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(11,plain,
% 0.63/0.69 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[10])).
% 0.63/0.69 tff(12,axiom,(![W0: $i] : (aElementOf0(W0, szNzAzT0) => (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSuccNum')).
% 0.63/0.69 tff(13,plain,
% 0.63/0.69 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.63/0.69 tff(14,plain,
% 0.63/0.69 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.63/0.69 tff(15,plain,(
% 0.63/0.69 ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))),
% 0.63/0.69 inference(skolemize,[status(sab)],[14])).
% 0.63/0.69 tff(16,plain,
% 0.63/0.69 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.63/0.69 tff(17,plain,
% 0.63/0.69 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.63/0.69 tff(18,plain,
% 0.63/0.69 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | ((~aElementOf0(xm, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(xm), szNzAzT0)) | (szszuzczcdt0(xm) = sz00))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | (~aElementOf0(xm, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(xm), szNzAzT0)) | (szszuzczcdt0(xm) = sz00))))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(19,plain,
% 0.63/0.69 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | ((~aElementOf0(xm, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(xm), szNzAzT0)) | (szszuzczcdt0(xm) = sz00))))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(20,plain,
% 0.63/0.69 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | (~aElementOf0(xm, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(xm), szNzAzT0)) | (szszuzczcdt0(xm) = sz00)))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.63/0.69 tff(21,plain,
% 0.63/0.69 (~((~aElementOf0(szszuzczcdt0(xm), szNzAzT0)) | (szszuzczcdt0(xm) = sz00))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[20, 17, 4])).
% 0.63/0.69 tff(22,plain,
% 0.63/0.69 (((~aElementOf0(szszuzczcdt0(xm), szNzAzT0)) | (szszuzczcdt0(xm) = sz00)) | (~(szszuzczcdt0(xm) = sz00))),
% 0.63/0.69 inference(tautology,[status(thm)],[])).
% 0.63/0.69 tff(23,plain,
% 0.63/0.69 (~(szszuzczcdt0(xm) = sz00)),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.63/0.69 tff(24,plain,
% 0.63/0.69 (((~aElementOf0(szszuzczcdt0(xm), szNzAzT0)) | (szszuzczcdt0(xm) = sz00)) | aElementOf0(szszuzczcdt0(xm), szNzAzT0)),
% 0.63/0.69 inference(tautology,[status(thm)],[])).
% 0.63/0.69 tff(25,plain,
% 0.63/0.69 (aElementOf0(szszuzczcdt0(xm), szNzAzT0)),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[24, 21])).
% 0.63/0.69 tff(26,plain,
% 0.63/0.69 (^[W0: $i] : refl(((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0))))))) <=> ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0))))))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(27,plain,
% 0.63/0.69 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0))))))) <=> ![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[26])).
% 0.63/0.69 tff(28,plain,
% 0.63/0.69 (^[W0: $i] : trans(monotonicity(rewrite((aElementOf0(tptp_fun_W1_4(W0), szNzAzT0) & (W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))) <=> (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0))))))), (((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (aElementOf0(tptp_fun_W1_4(W0), szNzAzT0) & (W0 = szszuzczcdt0(tptp_fun_W1_4(W0))))) <=> ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0))))))))), rewrite(((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0))))))) <=> ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))), (((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (aElementOf0(tptp_fun_W1_4(W0), szNzAzT0) & (W0 = szszuzczcdt0(tptp_fun_W1_4(W0))))) <=> ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(29,plain,
% 0.63/0.69 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (aElementOf0(tptp_fun_W1_4(W0), szNzAzT0) & (W0 = szszuzczcdt0(tptp_fun_W1_4(W0))))) <=> ![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[28])).
% 0.63/0.69 tff(30,plain,
% 0.63/0.69 (^[W0: $i] : rewrite(((aElementOf0(tptp_fun_W1_4(W0), szNzAzT0) & (W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))) | (W0 = sz00) | (~aElementOf0(W0, szNzAzT0))) <=> ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (aElementOf0(tptp_fun_W1_4(W0), szNzAzT0) & (W0 = szszuzczcdt0(tptp_fun_W1_4(W0))))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(31,plain,
% 0.63/0.69 (![W0: $i] : ((aElementOf0(tptp_fun_W1_4(W0), szNzAzT0) & (W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))) | (W0 = sz00) | (~aElementOf0(W0, szNzAzT0))) <=> ![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (aElementOf0(tptp_fun_W1_4(W0), szNzAzT0) & (W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[30])).
% 0.63/0.69 tff(32,plain,
% 0.63/0.69 (![W0: $i] : (?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))) | (W0 = sz00) | (~aElementOf0(W0, szNzAzT0))) <=> ![W0: $i] : (?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))) | (W0 = sz00) | (~aElementOf0(W0, szNzAzT0)))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(33,plain,
% 0.63/0.69 (^[W0: $i] : trans(monotonicity(rewrite(((W0 = sz00) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1)))) <=> ((W0 = sz00) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))))), ((aElementOf0(W0, szNzAzT0) => ((W0 = sz00) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))))) <=> (aElementOf0(W0, szNzAzT0) => ((W0 = sz00) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))))))), rewrite((aElementOf0(W0, szNzAzT0) => ((W0 = sz00) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))))) <=> (?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))) | (W0 = sz00) | (~aElementOf0(W0, szNzAzT0)))), ((aElementOf0(W0, szNzAzT0) => ((W0 = sz00) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))))) <=> (?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))) | (W0 = sz00) | (~aElementOf0(W0, szNzAzT0)))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(34,plain,
% 0.63/0.69 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => ((W0 = sz00) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))))) <=> ![W0: $i] : (?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))) | (W0 = sz00) | (~aElementOf0(W0, szNzAzT0)))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[33])).
% 0.63/0.69 tff(35,axiom,(![W0: $i] : (aElementOf0(W0, szNzAzT0) => ((W0 = sz00) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mNatExtra')).
% 0.63/0.69 tff(36,plain,
% 0.63/0.69 (![W0: $i] : (?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))) | (W0 = sz00) | (~aElementOf0(W0, szNzAzT0)))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.63/0.69 tff(37,plain,
% 0.63/0.69 (![W0: $i] : (?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))) | (W0 = sz00) | (~aElementOf0(W0, szNzAzT0)))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.63/0.69 tff(38,plain,(
% 0.63/0.69 ![W0: $i] : ((aElementOf0(tptp_fun_W1_4(W0), szNzAzT0) & (W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))) | (W0 = sz00) | (~aElementOf0(W0, szNzAzT0)))),
% 0.63/0.69 inference(skolemize,[status(sab)],[37])).
% 0.63/0.69 tff(39,plain,
% 0.63/0.69 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (aElementOf0(tptp_fun_W1_4(W0), szNzAzT0) & (W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.63/0.69 tff(40,plain,
% 0.63/0.69 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.63/0.69 tff(41,plain,
% 0.63/0.69 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[40, 27])).
% 0.63/0.69 tff(42,plain,
% 0.63/0.69 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((~aElementOf0(szszuzczcdt0(xm), szNzAzT0)) | (szszuzczcdt0(xm) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm))))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | (~aElementOf0(szszuzczcdt0(xm), szNzAzT0)) | (szszuzczcdt0(xm) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm))))))))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(43,plain,
% 0.63/0.69 (((szszuzczcdt0(xm) = sz00) | (~aElementOf0(szszuzczcdt0(xm), szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm)))))))) <=> ((~aElementOf0(szszuzczcdt0(xm), szNzAzT0)) | (szszuzczcdt0(xm) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm))))))))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(44,plain,
% 0.63/0.69 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((szszuzczcdt0(xm) = sz00) | (~aElementOf0(szszuzczcdt0(xm), szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm))))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((~aElementOf0(szszuzczcdt0(xm), szNzAzT0)) | (szszuzczcdt0(xm) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm)))))))))),
% 0.63/0.69 inference(monotonicity,[status(thm)],[43])).
% 0.63/0.69 tff(45,plain,
% 0.63/0.69 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((szszuzczcdt0(xm) = sz00) | (~aElementOf0(szszuzczcdt0(xm), szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm))))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | (~aElementOf0(szszuzczcdt0(xm), szNzAzT0)) | (szszuzczcdt0(xm) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm))))))))),
% 0.63/0.69 inference(transitivity,[status(thm)],[44, 42])).
% 0.63/0.69 tff(46,plain,
% 0.63/0.69 ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((szszuzczcdt0(xm) = sz00) | (~aElementOf0(szszuzczcdt0(xm), szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm))))))))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(47,plain,
% 0.63/0.69 ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | (~aElementOf0(szszuzczcdt0(xm), szNzAzT0)) | (szszuzczcdt0(xm) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm)))))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.63/0.69 tff(48,plain,
% 0.63/0.69 (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm))))))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[47, 41, 25, 23])).
% 0.63/0.69 tff(49,plain,
% 0.63/0.69 (((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm)))))) | aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)),
% 0.63/0.69 inference(tautology,[status(thm)],[])).
% 0.63/0.69 tff(50,plain,
% 0.63/0.69 (aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.63/0.69 tff(51,plain,
% 0.63/0.69 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))) | (~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0))))))))) <=> ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))) | (~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0))))))))))))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(52,plain,
% 0.63/0.69 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))) | (~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))) | (~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[51])).
% 0.63/0.69 tff(53,plain,
% 0.63/0.69 (^[W0: $i] : refl(((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))) | (~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0))))))))) <=> ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))) | (~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0))))))))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(54,plain,
% 0.63/0.69 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))) | (~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))) | (~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[53])).
% 0.63/0.69 tff(55,plain,
% 0.63/0.69 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))) | (~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0))))))))) <=> ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))) | (~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0))))))))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(56,plain,
% 0.63/0.69 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))) | (~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))) | (~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[55])).
% 0.63/0.69 tff(57,plain,
% 0.63/0.69 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))) | (~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))) | (~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))))))),
% 0.63/0.69 inference(transitivity,[status(thm)],[56, 54])).
% 0.63/0.69 tff(58,plain,
% 0.63/0.69 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (((~(W1 = slbdtrb0(W0))) | (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) <=> (aElementOf0(W2, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W2), W0))))) & ((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | ((~aElementOf0(tptp_fun_W2_8(W1, W0), W1)) <=> (aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0) & sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))) <=> ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))) | (~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0))))))))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(59,plain,
% 0.63/0.69 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (((~(W1 = slbdtrb0(W0))) | (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) <=> (aElementOf0(W2, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W2), W0))))) & ((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | ((~aElementOf0(tptp_fun_W2_8(W1, W0), W1)) <=> (aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0) & sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))) | (~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))))))),
% 0.63/0.70 inference(quant_intro,[status(thm)],[58])).
% 0.63/0.70 tff(60,plain,
% 0.63/0.70 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (((~(W1 = slbdtrb0(W0))) | (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) <=> (aElementOf0(W2, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W2), W0))))) & ((W1 = slbdtrb0(W0)) | ((~aSet0(W1)) | (~(aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> (aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0) & sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))))) <=> ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (((~(W1 = slbdtrb0(W0))) | (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) <=> (aElementOf0(W2, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W2), W0))))) & ((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | ((~aElementOf0(tptp_fun_W2_8(W1, W0), W1)) <=> (aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0) & sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))))),
% 0.63/0.70 inference(bind,[status(th)],[])).
% 0.63/0.70 tff(61,plain,
% 0.63/0.70 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (((~(W1 = slbdtrb0(W0))) | (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) <=> (aElementOf0(W2, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W2), W0))))) & ((W1 = slbdtrb0(W0)) | ((~aSet0(W1)) | (~(aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> (aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0) & sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (((~(W1 = slbdtrb0(W0))) | (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) <=> (aElementOf0(W2, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W2), W0))))) & ((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | ((~aElementOf0(tptp_fun_W2_8(W1, W0), W1)) <=> (aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0) & sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0))))))),
% 0.63/0.70 inference(quant_intro,[status(thm)],[60])).
% 0.63/0.70 tff(62,plain,
% 0.63/0.70 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((W1 = slbdtrb0(W0)) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) <=> (aElementOf0(W2, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W2), W0)))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((W1 = slbdtrb0(W0)) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) <=> (aElementOf0(W2, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W2), W0))))))),
% 0.63/0.70 inference(rewrite,[status(thm)],[])).
% 0.63/0.70 tff(63,plain,
% 0.63/0.70 (^[W0: $i] : rewrite((aElementOf0(W0, szNzAzT0) => ![W1: $i] : ((W1 = slbdtrb0(W0)) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) <=> (aElementOf0(W2, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W2), W0)))))) <=> ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((W1 = slbdtrb0(W0)) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) <=> (aElementOf0(W2, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W2), W0)))))))),
% 0.63/0.70 inference(bind,[status(th)],[])).
% 0.63/0.70 tff(64,plain,
% 0.63/0.70 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => ![W1: $i] : ((W1 = slbdtrb0(W0)) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) <=> (aElementOf0(W2, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W2), W0)))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((W1 = slbdtrb0(W0)) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) <=> (aElementOf0(W2, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W2), W0))))))),
% 0.63/0.70 inference(quant_intro,[status(thm)],[63])).
% 0.63/0.70 tff(65,axiom,(![W0: $i] : (aElementOf0(W0, szNzAzT0) => ![W1: $i] : ((W1 = slbdtrb0(W0)) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) <=> (aElementOf0(W2, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W2), W0))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefSeg')).
% 0.63/0.70 tff(66,plain,
% 0.63/0.70 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((W1 = slbdtrb0(W0)) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) <=> (aElementOf0(W2, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W2), W0))))))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.63/0.70 tff(67,plain,
% 0.63/0.70 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((W1 = slbdtrb0(W0)) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) <=> (aElementOf0(W2, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W2), W0))))))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.63/0.70 tff(68,plain,(
% 0.63/0.70 ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (((~(W1 = slbdtrb0(W0))) | (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) <=> (aElementOf0(W2, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W2), W0))))) & ((W1 = slbdtrb0(W0)) | ((~aSet0(W1)) | (~(aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> (aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0) & sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0))))))))),
% 0.63/0.70 inference(skolemize,[status(sab)],[67])).
% 0.63/0.70 tff(69,plain,
% 0.63/0.70 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (((~(W1 = slbdtrb0(W0))) | (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) <=> (aElementOf0(W2, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W2), W0))))) & ((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | ((~aElementOf0(tptp_fun_W2_8(W1, W0), W1)) <=> (aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0) & sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0))))))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.63/0.70 tff(70,plain,
% 0.63/0.70 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))) | (~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))))))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.63/0.70 tff(71,plain,
% 0.63/0.70 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))) | (~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))))))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[70, 57])).
% 0.63/0.70 tff(72,plain,
% 0.63/0.70 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))) | (~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))))))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[71, 52])).
% 0.63/0.70 tff(73,plain,
% 0.63/0.70 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))) | (~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))))))) | ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | ![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm)))))))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))) | (~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))))))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | ![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm)))))))))))))))),
% 0.63/0.70 inference(rewrite,[status(thm)],[])).
% 0.63/0.70 tff(74,plain,
% 0.63/0.70 (((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm))))))))))))))) <=> ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | ![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm)))))))))))))))),
% 0.63/0.70 inference(rewrite,[status(thm)],[])).
% 0.63/0.70 tff(75,plain,
% 0.63/0.70 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))) | (~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))))))) | ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm)))))))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))) | (~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))))))) | ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | ![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm))))))))))))))))),
% 0.63/0.70 inference(monotonicity,[status(thm)],[74])).
% 0.63/0.70 tff(76,plain,
% 0.63/0.70 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))) | (~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))))))) | ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm)))))))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))) | (~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))))))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | ![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm)))))))))))))))),
% 0.63/0.70 inference(transitivity,[status(thm)],[75, 73])).
% 0.63/0.70 tff(77,plain,
% 0.63/0.70 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))) | (~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))))))) | ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm)))))))))))))))),
% 0.63/0.70 inference(quant_inst,[status(thm)],[])).
% 0.63/0.70 tff(78,plain,
% 0.63/0.70 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))) | (~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))))))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | ![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm))))))))))))))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.63/0.70 tff(79,plain,
% 0.63/0.70 (![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm))))))))))))))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[78, 72, 50])).
% 0.63/0.70 tff(80,plain,
% 0.63/0.70 (((~![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm))))))))))))))) | (~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm))))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm))))))))))))))) | (~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm)))))))))))),
% 0.63/0.70 inference(rewrite,[status(thm)],[])).
% 0.63/0.70 tff(81,plain,
% 0.63/0.70 ((~((~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))) = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (aElementOf0(tptp_fun_W2_8(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))), tptp_fun_W1_4(szszuzczcdt0(xm))), slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> ((~aElementOf0(tptp_fun_W2_8(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))), tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))), tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))) = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm)))))))))))))) <=> (~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm))))))))))),
% 0.63/0.70 inference(rewrite,[status(thm)],[])).
% 0.63/0.70 tff(82,plain,
% 0.63/0.70 (((~![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm))))))))))))))) | (~((~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))) = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (aElementOf0(tptp_fun_W2_8(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))), tptp_fun_W1_4(szszuzczcdt0(xm))), slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> ((~aElementOf0(tptp_fun_W2_8(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))), tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))), tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))) = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm))))))))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm))))))))))))))) | (~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm)))))))))))),
% 0.63/0.70 inference(monotonicity,[status(thm)],[81])).
% 0.63/0.70 tff(83,plain,
% 0.63/0.70 (((~![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm))))))))))))))) | (~((~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))) = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (aElementOf0(tptp_fun_W2_8(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))), tptp_fun_W1_4(szszuzczcdt0(xm))), slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> ((~aElementOf0(tptp_fun_W2_8(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))), tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))), tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))) = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm))))))))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm))))))))))))))) | (~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm)))))))))))),
% 0.74/0.70 inference(transitivity,[status(thm)],[82, 80])).
% 0.74/0.70 tff(84,plain,
% 0.74/0.70 ((~![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm))))))))))))))) | (~((~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))) = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (aElementOf0(tptp_fun_W2_8(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))), tptp_fun_W1_4(szszuzczcdt0(xm))), slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> ((~aElementOf0(tptp_fun_W2_8(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))), tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))), tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))) = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm))))))))))))))),
% 0.74/0.70 inference(quant_inst,[status(thm)],[])).
% 0.74/0.70 tff(85,plain,
% 0.74/0.70 ((~![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | (aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm))), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, tptp_fun_W1_4(szszuzczcdt0(xm)))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (~((~(W1 = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm))))))))))))))) | (~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm))))))))))),
% 0.74/0.70 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.74/0.70 tff(86,plain,
% 0.74/0.70 (~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm)))))))))),
% 0.74/0.70 inference(unit_resolution,[status(thm)],[85, 79])).
% 0.74/0.70 tff(87,plain,
% 0.74/0.70 (((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm))))))))) | ![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm)))))))),
% 0.74/0.70 inference(tautology,[status(thm)],[])).
% 0.74/0.70 tff(88,plain,
% 0.74/0.70 (![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm)))))))),
% 0.74/0.70 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.74/0.70 tff(89,plain,
% 0.74/0.70 ((~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | (aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))),
% 0.74/0.70 inference(quant_inst,[status(thm)],[])).
% 0.74/0.70 tff(90,plain,
% 0.74/0.70 (aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), tptp_fun_W1_4(szszuzczcdt0(xm))))))),
% 0.74/0.70 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.74/0.70 tff(91,plain,
% 0.74/0.70 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))) | (~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))))))) | ((~aElementOf0(xm, szNzAzT0)) | ![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(xm)) | (aElementOf0(tptp_fun_W2_8(W1, xm), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, xm), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, xm)), xm)))))) | (~((~(W1 = slbdtrb0(xm))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm)))))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))) | (~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))))))) | (~aElementOf0(xm, szNzAzT0)) | ![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(xm)) | (aElementOf0(tptp_fun_W2_8(W1, xm), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, xm), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, xm)), xm)))))) | (~((~(W1 = slbdtrb0(xm))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm)))))))))))))),
% 0.74/0.70 inference(rewrite,[status(thm)],[])).
% 0.74/0.70 tff(92,plain,
% 0.74/0.70 (((~aElementOf0(xm, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(xm)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, xm), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, xm), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, xm)), xm)))))) | (~((~(W1 = slbdtrb0(xm))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm))))))))))))) <=> ((~aElementOf0(xm, szNzAzT0)) | ![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(xm)) | (aElementOf0(tptp_fun_W2_8(W1, xm), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, xm), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, xm)), xm)))))) | (~((~(W1 = slbdtrb0(xm))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm)))))))))))))),
% 0.74/0.70 inference(rewrite,[status(thm)],[])).
% 0.74/0.70 tff(93,plain,
% 0.74/0.70 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))) | (~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))))))) | ((~aElementOf0(xm, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(xm)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, xm), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, xm), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, xm)), xm)))))) | (~((~(W1 = slbdtrb0(xm))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm)))))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))) | (~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))))))) | ((~aElementOf0(xm, szNzAzT0)) | ![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(xm)) | (aElementOf0(tptp_fun_W2_8(W1, xm), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, xm), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, xm)), xm)))))) | (~((~(W1 = slbdtrb0(xm))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm))))))))))))))),
% 0.74/0.71 inference(monotonicity,[status(thm)],[92])).
% 0.74/0.71 tff(94,plain,
% 0.74/0.71 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))) | (~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))))))) | ((~aElementOf0(xm, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(xm)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, xm), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, xm), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, xm)), xm)))))) | (~((~(W1 = slbdtrb0(xm))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm)))))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))) | (~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))))))) | (~aElementOf0(xm, szNzAzT0)) | ![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(xm)) | (aElementOf0(tptp_fun_W2_8(W1, xm), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, xm), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, xm)), xm)))))) | (~((~(W1 = slbdtrb0(xm))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm)))))))))))))),
% 0.74/0.71 inference(transitivity,[status(thm)],[93, 91])).
% 0.74/0.71 tff(95,plain,
% 0.74/0.71 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))) | (~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))))))) | ((~aElementOf0(xm, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(xm)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, xm), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, xm), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, xm)), xm)))))) | (~((~(W1 = slbdtrb0(xm))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm)))))))))))))),
% 0.74/0.71 inference(quant_inst,[status(thm)],[])).
% 0.74/0.71 tff(96,plain,
% 0.74/0.71 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((W1 = slbdtrb0(W0)) | (~aSet0(W1)) | (aElementOf0(tptp_fun_W2_8(W1, W0), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, W0), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, W0)), W0)))))) | (~((~(W1 = slbdtrb0(W0))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), W0)))))))))))))) | (~aElementOf0(xm, szNzAzT0)) | ![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(xm)) | (aElementOf0(tptp_fun_W2_8(W1, xm), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, xm), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, xm)), xm)))))) | (~((~(W1 = slbdtrb0(xm))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm))))))))))))),
% 0.74/0.71 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.74/0.71 tff(97,plain,
% 0.74/0.71 (![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(xm)) | (aElementOf0(tptp_fun_W2_8(W1, xm), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, xm), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, xm)), xm)))))) | (~((~(W1 = slbdtrb0(xm))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm))))))))))))),
% 0.74/0.71 inference(unit_resolution,[status(thm)],[96, 72, 4])).
% 0.74/0.71 tff(98,plain,
% 0.74/0.71 ((~![W1: $i] : (~((~((~aSet0(W1)) | (W1 = slbdtrb0(xm)) | (aElementOf0(tptp_fun_W2_8(W1, xm), W1) <=> ((~aElementOf0(tptp_fun_W2_8(W1, xm), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(W1, xm)), xm)))))) | (~((~(W1 = slbdtrb0(xm))) | (~((~aSet0(W1)) | (~![W2: $i] : (aElementOf0(W2, W1) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm))))))))))))) | (~((~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))) = slbdtrb0(xm)) | (aElementOf0(tptp_fun_W2_8(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))), xm), slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> ((~aElementOf0(tptp_fun_W2_8(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))), xm), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))), xm)), xm)))))) | (~((~(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))) = slbdtrb0(xm))) | (~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm))))))))))))),
% 0.74/0.71 inference(quant_inst,[status(thm)],[])).
% 0.74/0.71 tff(99,plain,
% 0.74/0.71 (~((~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))) = slbdtrb0(xm)) | (aElementOf0(tptp_fun_W2_8(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))), xm), slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> ((~aElementOf0(tptp_fun_W2_8(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))), xm), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))), xm)), xm)))))) | (~((~(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))) = slbdtrb0(xm))) | (~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm)))))))))))),
% 0.74/0.71 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.74/0.71 tff(100,plain,
% 0.74/0.71 (((~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))) = slbdtrb0(xm)) | (aElementOf0(tptp_fun_W2_8(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))), xm), slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> ((~aElementOf0(tptp_fun_W2_8(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))), xm), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W2_8(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))), xm)), xm)))))) | (~((~(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))) = slbdtrb0(xm))) | (~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm))))))))))) | ((~(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))) = slbdtrb0(xm))) | (~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm)))))))))),
% 0.74/0.71 inference(tautology,[status(thm)],[])).
% 0.74/0.71 tff(101,plain,
% 0.74/0.71 ((~(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))) = slbdtrb0(xm))) | (~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm))))))))),
% 0.74/0.71 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.74/0.71 tff(102,plain,
% 0.74/0.71 (((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm)))))) | (szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm))))),
% 0.74/0.71 inference(tautology,[status(thm)],[])).
% 0.74/0.71 tff(103,plain,
% 0.74/0.71 (szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm)))),
% 0.74/0.71 inference(unit_resolution,[status(thm)],[102, 48])).
% 0.74/0.71 tff(104,plain,
% 0.74/0.71 (^[W0: $i, W1: $i] : refl(((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0))) <=> ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0))))),
% 0.74/0.71 inference(bind,[status(th)],[])).
% 0.74/0.71 tff(105,plain,
% 0.74/0.71 (![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))),
% 0.74/0.71 inference(quant_intro,[status(thm)],[104])).
% 0.74/0.71 tff(106,plain,
% 0.74/0.71 (^[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))))), (((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)))) <=> ((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | ((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))))), rewrite(((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | ((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))) <=> ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))), (((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)))) <=> ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))))),
% 0.74/0.71 inference(bind,[status(th)],[])).
% 0.74/0.71 tff(107,plain,
% 0.74/0.71 (![W0: $i, W1: $i] : ((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))),
% 0.74/0.71 inference(quant_intro,[status(thm)],[106])).
% 0.74/0.71 tff(108,plain,
% 0.74/0.71 (![W0: $i, W1: $i] : ((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))))),
% 0.74/0.71 inference(rewrite,[status(thm)],[])).
% 0.74/0.71 tff(109,plain,
% 0.74/0.71 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite(((szszuzczcdt0(W0) = szszuzczcdt0(W1)) => (W0 = W1)) <=> ((~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (W0 = W1))), (((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((szszuzczcdt0(W0) = szszuzczcdt0(W1)) => (W0 = W1))) <=> ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (W0 = W1))))), rewrite(((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (W0 = W1))) <=> ((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))))), (((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((szszuzczcdt0(W0) = szszuzczcdt0(W1)) => (W0 = W1))) <=> ((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))))))),
% 0.74/0.71 inference(bind,[status(th)],[])).
% 0.74/0.71 tff(110,plain,
% 0.74/0.71 (![W0: $i, W1: $i] : ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((szszuzczcdt0(W0) = szszuzczcdt0(W1)) => (W0 = W1))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))))),
% 0.74/0.71 inference(quant_intro,[status(thm)],[109])).
% 0.74/0.71 tff(111,axiom,(![W0: $i, W1: $i] : ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((szszuzczcdt0(W0) = szszuzczcdt0(W1)) => (W0 = W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSuccEquSucc')).
% 0.74/0.71 tff(112,plain,
% 0.74/0.71 (![W0: $i, W1: $i] : ((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))))),
% 0.74/0.71 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.74/0.71 tff(113,plain,
% 0.74/0.71 (![W0: $i, W1: $i] : ((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))))),
% 0.74/0.71 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.74/0.71 tff(114,plain,(
% 0.74/0.71 ![W0: $i, W1: $i] : ((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))))),
% 0.74/0.71 inference(skolemize,[status(sab)],[113])).
% 0.74/0.71 tff(115,plain,
% 0.74/0.71 (![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))),
% 0.74/0.71 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.74/0.71 tff(116,plain,
% 0.74/0.71 (![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))),
% 0.74/0.71 inference(modus_ponens,[status(thm)],[115, 105])).
% 0.74/0.71 tff(117,plain,
% 0.74/0.71 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((~aElementOf0(xm, szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (xm = tptp_fun_W1_4(szszuzczcdt0(xm))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(xm, szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (xm = tptp_fun_W1_4(szszuzczcdt0(xm))))),
% 0.74/0.71 inference(rewrite,[status(thm)],[])).
% 0.74/0.71 tff(118,plain,
% 0.74/0.71 (((xm = tptp_fun_W1_4(szszuzczcdt0(xm))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~aElementOf0(xm, szNzAzT0))) <=> ((~aElementOf0(xm, szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (xm = tptp_fun_W1_4(szszuzczcdt0(xm))))),
% 0.74/0.71 inference(rewrite,[status(thm)],[])).
% 0.74/0.71 tff(119,plain,
% 0.74/0.71 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((xm = tptp_fun_W1_4(szszuzczcdt0(xm))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~aElementOf0(xm, szNzAzT0)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((~aElementOf0(xm, szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (xm = tptp_fun_W1_4(szszuzczcdt0(xm)))))),
% 0.74/0.71 inference(monotonicity,[status(thm)],[118])).
% 0.74/0.71 tff(120,plain,
% 0.74/0.71 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((xm = tptp_fun_W1_4(szszuzczcdt0(xm))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~aElementOf0(xm, szNzAzT0)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(xm, szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (xm = tptp_fun_W1_4(szszuzczcdt0(xm))))),
% 0.74/0.71 inference(transitivity,[status(thm)],[119, 117])).
% 0.74/0.71 tff(121,plain,
% 0.74/0.71 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((xm = tptp_fun_W1_4(szszuzczcdt0(xm))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~aElementOf0(xm, szNzAzT0)))),
% 0.74/0.71 inference(quant_inst,[status(thm)],[])).
% 0.74/0.71 tff(122,plain,
% 0.74/0.71 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(xm, szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~(szszuzczcdt0(xm) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (xm = tptp_fun_W1_4(szszuzczcdt0(xm)))),
% 0.74/0.71 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.74/0.71 tff(123,plain,
% 0.74/0.71 (xm = tptp_fun_W1_4(szszuzczcdt0(xm))),
% 0.74/0.71 inference(unit_resolution,[status(thm)],[122, 116, 4, 50, 103])).
% 0.74/0.71 tff(124,plain,
% 0.74/0.71 (slbdtrb0(xm) = slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))),
% 0.74/0.71 inference(monotonicity,[status(thm)],[123])).
% 0.74/0.71 tff(125,plain,
% 0.74/0.71 (slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))) = slbdtrb0(xm)),
% 0.74/0.71 inference(symmetry,[status(thm)],[124])).
% 0.74/0.71 tff(126,plain,
% 0.74/0.71 ((~((~(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))) = slbdtrb0(xm))) | (~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm)))))))))) | (~(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))) = slbdtrb0(xm))) | (~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm))))))))),
% 0.74/0.71 inference(tautology,[status(thm)],[])).
% 0.74/0.71 tff(127,plain,
% 0.74/0.71 ((~((~(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))) = slbdtrb0(xm))) | (~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm)))))))))) | (~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm))))))))),
% 0.74/0.71 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.74/0.71 tff(128,plain,
% 0.74/0.71 (~((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm)))))))),
% 0.74/0.71 inference(unit_resolution,[status(thm)],[127, 101])).
% 0.74/0.71 tff(129,plain,
% 0.74/0.71 (((~aSet0(slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm))))))) | ![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm)))))),
% 0.74/0.71 inference(tautology,[status(thm)],[])).
% 0.74/0.71 tff(130,plain,
% 0.74/0.71 (![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm)))))),
% 0.74/0.71 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.74/0.71 tff(131,plain,
% 0.74/0.71 ((~![W2: $i] : (aElementOf0(W2, slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W2), xm)))))) | (aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), xm)))))),
% 0.74/0.71 inference(quant_inst,[status(thm)],[])).
% 0.74/0.71 tff(132,plain,
% 0.74/0.71 (aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), xm))))),
% 0.74/0.71 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.74/0.71 tff(133,assumption,(~(sdtlseqdt0(xm, xn) | (~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) | (~aSet0(slbdtrb0(xn))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))) | (~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn)))))), introduced(assumption)).
% 0.74/0.71 tff(134,plain,
% 0.74/0.71 ((sdtlseqdt0(xm, xn) | (~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) | (~aSet0(slbdtrb0(xn))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))) | (~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))))) | ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))),
% 0.74/0.71 inference(tautology,[status(thm)],[])).
% 0.74/0.71 tff(135,plain,
% 0.74/0.71 (![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))),
% 0.74/0.71 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.74/0.71 tff(136,plain,
% 0.74/0.71 ((~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))) | (aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(xm)) <=> (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), xm)))))),
% 0.74/0.71 inference(quant_inst,[status(thm)],[])).
% 0.74/0.71 tff(137,plain,
% 0.74/0.71 (aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(xm)) <=> (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), xm))))),
% 0.74/0.71 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.74/0.71 tff(138,plain,
% 0.74/0.71 ((sdtlseqdt0(xm, xn) | (~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) | (~aSet0(slbdtrb0(xn))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))) | (~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))))) | ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))),
% 0.74/0.71 inference(tautology,[status(thm)],[])).
% 0.74/0.71 tff(139,plain,
% 0.74/0.71 (![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))),
% 0.74/0.71 inference(unit_resolution,[status(thm)],[138, 133])).
% 0.74/0.71 tff(140,plain,
% 0.74/0.71 ((~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(xn)) <=> (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), xn)))))),
% 0.74/0.71 inference(quant_inst,[status(thm)],[])).
% 0.74/0.71 tff(141,plain,
% 0.74/0.71 (aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(xn)) <=> (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), xn))))),
% 0.74/0.71 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.74/0.71 tff(142,plain,
% 0.74/0.71 (aElementOf0(xn, szNzAzT0) <=> aElementOf0(xn, szNzAzT0)),
% 0.74/0.71 inference(rewrite,[status(thm)],[])).
% 0.74/0.71 tff(143,plain,
% 0.74/0.71 (aElementOf0(xn, szNzAzT0)),
% 0.74/0.71 inference(and_elim,[status(thm)],[2])).
% 0.74/0.71 tff(144,plain,
% 0.74/0.71 (aElementOf0(xn, szNzAzT0)),
% 0.74/0.71 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.74/0.71 tff(145,plain,
% 0.74/0.71 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | ((~aElementOf0(xn, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (szszuzczcdt0(xn) = sz00))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | (~aElementOf0(xn, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (szszuzczcdt0(xn) = sz00))))),
% 0.74/0.71 inference(rewrite,[status(thm)],[])).
% 0.74/0.71 tff(146,plain,
% 0.74/0.71 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | ((~aElementOf0(xn, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (szszuzczcdt0(xn) = sz00))))),
% 0.74/0.71 inference(quant_inst,[status(thm)],[])).
% 0.74/0.71 tff(147,plain,
% 0.74/0.71 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | (~aElementOf0(xn, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (szszuzczcdt0(xn) = sz00)))),
% 0.74/0.71 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.74/0.71 tff(148,plain,
% 0.74/0.71 (~((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (szszuzczcdt0(xn) = sz00))),
% 0.74/0.71 inference(unit_resolution,[status(thm)],[147, 17, 144])).
% 0.74/0.71 tff(149,plain,
% 0.74/0.71 (((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (szszuzczcdt0(xn) = sz00)) | (~(szszuzczcdt0(xn) = sz00))),
% 0.74/0.71 inference(tautology,[status(thm)],[])).
% 0.74/0.71 tff(150,plain,
% 0.74/0.71 (~(szszuzczcdt0(xn) = sz00)),
% 0.74/0.71 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.74/0.71 tff(151,plain,
% 0.74/0.71 (((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (szszuzczcdt0(xn) = sz00)) | aElementOf0(szszuzczcdt0(xn), szNzAzT0)),
% 0.74/0.71 inference(tautology,[status(thm)],[])).
% 0.74/0.71 tff(152,plain,
% 0.74/0.71 (aElementOf0(szszuzczcdt0(xn), szNzAzT0)),
% 0.74/0.71 inference(unit_resolution,[status(thm)],[151, 148])).
% 0.74/0.71 tff(153,plain,
% 0.74/0.71 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (szszuzczcdt0(xn) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (szszuzczcdt0(xn) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))))))))),
% 0.74/0.71 inference(rewrite,[status(thm)],[])).
% 0.74/0.71 tff(154,plain,
% 0.74/0.71 (((szszuzczcdt0(xn) = sz00) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn)))))))) <=> ((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (szszuzczcdt0(xn) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))))))))),
% 0.74/0.71 inference(rewrite,[status(thm)],[])).
% 0.74/0.71 tff(155,plain,
% 0.74/0.71 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((szszuzczcdt0(xn) = sz00) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (szszuzczcdt0(xn) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn)))))))))),
% 0.74/0.72 inference(monotonicity,[status(thm)],[154])).
% 0.74/0.72 tff(156,plain,
% 0.74/0.72 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((szszuzczcdt0(xn) = sz00) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (szszuzczcdt0(xn) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))))))))),
% 0.74/0.72 inference(transitivity,[status(thm)],[155, 153])).
% 0.74/0.72 tff(157,plain,
% 0.74/0.72 ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((szszuzczcdt0(xn) = sz00) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))))))))),
% 0.74/0.72 inference(quant_inst,[status(thm)],[])).
% 0.74/0.72 tff(158,plain,
% 0.74/0.72 ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (szszuzczcdt0(xn) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn)))))))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.74/0.72 tff(159,plain,
% 0.74/0.72 (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))))))),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[158, 41, 152, 150])).
% 0.74/0.72 tff(160,plain,
% 0.74/0.72 (((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn)))))) | (szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))))),
% 0.74/0.72 inference(tautology,[status(thm)],[])).
% 0.74/0.72 tff(161,plain,
% 0.74/0.72 (szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn)))),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.74/0.72 tff(162,plain,
% 0.74/0.72 (szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))) = szszuzczcdt0(xn)),
% 0.74/0.72 inference(symmetry,[status(thm)],[161])).
% 0.74/0.72 tff(163,plain,
% 0.74/0.72 (sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), xn) <=> sdtlseqdt0(szszuzczcdt0(xn), xn)),
% 0.74/0.72 inference(monotonicity,[status(thm)],[162])).
% 0.74/0.72 tff(164,plain,
% 0.74/0.72 (sdtlseqdt0(szszuzczcdt0(xn), xn) <=> sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), xn)),
% 0.74/0.72 inference(symmetry,[status(thm)],[163])).
% 0.74/0.72 tff(165,plain,
% 0.74/0.72 ((~sdtlseqdt0(szszuzczcdt0(xn), xn)) <=> (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), xn))),
% 0.74/0.72 inference(monotonicity,[status(thm)],[164])).
% 0.74/0.72 tff(166,plain,
% 0.74/0.72 (^[W0: $i] : refl(((~aElementOf0(W0, szNzAzT0)) | (~(W0 = szszuzczcdt0(W0)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~(W0 = szszuzczcdt0(W0)))))),
% 0.74/0.72 inference(bind,[status(th)],[])).
% 0.74/0.72 tff(167,plain,
% 0.74/0.72 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(W0 = szszuzczcdt0(W0)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(W0 = szszuzczcdt0(W0))))),
% 0.74/0.72 inference(quant_intro,[status(thm)],[166])).
% 0.74/0.72 tff(168,plain,
% 0.74/0.72 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(W0 = szszuzczcdt0(W0)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(W0 = szszuzczcdt0(W0))))),
% 0.74/0.72 inference(rewrite,[status(thm)],[])).
% 0.74/0.72 tff(169,plain,
% 0.74/0.72 (^[W0: $i] : rewrite((aElementOf0(W0, szNzAzT0) => (~(W0 = szszuzczcdt0(W0)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~(W0 = szszuzczcdt0(W0)))))),
% 0.74/0.72 inference(bind,[status(th)],[])).
% 0.74/0.72 tff(170,plain,
% 0.74/0.72 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => (~(W0 = szszuzczcdt0(W0)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(W0 = szszuzczcdt0(W0))))),
% 0.74/0.72 inference(quant_intro,[status(thm)],[169])).
% 0.74/0.72 tff(171,axiom,(![W0: $i] : (aElementOf0(W0, szNzAzT0) => (~(W0 = szszuzczcdt0(W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mNatNSucc')).
% 0.74/0.72 tff(172,plain,
% 0.74/0.72 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(W0 = szszuzczcdt0(W0))))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.74/0.72 tff(173,plain,
% 0.74/0.72 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(W0 = szszuzczcdt0(W0))))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[172, 168])).
% 0.74/0.72 tff(174,plain,(
% 0.74/0.72 ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(W0 = szszuzczcdt0(W0))))),
% 0.74/0.72 inference(skolemize,[status(sab)],[173])).
% 0.74/0.72 tff(175,plain,
% 0.74/0.72 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(W0 = szszuzczcdt0(W0))))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[174, 167])).
% 0.74/0.72 tff(176,plain,
% 0.74/0.72 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(W0 = szszuzczcdt0(W0))))) | ((~aElementOf0(xn, szNzAzT0)) | (~(xn = szszuzczcdt0(xn))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(W0 = szszuzczcdt0(W0))))) | (~aElementOf0(xn, szNzAzT0)) | (~(xn = szszuzczcdt0(xn))))),
% 0.74/0.72 inference(rewrite,[status(thm)],[])).
% 0.74/0.72 tff(177,plain,
% 0.74/0.72 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(W0 = szszuzczcdt0(W0))))) | ((~aElementOf0(xn, szNzAzT0)) | (~(xn = szszuzczcdt0(xn))))),
% 0.74/0.72 inference(quant_inst,[status(thm)],[])).
% 0.74/0.72 tff(178,plain,
% 0.74/0.72 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~(W0 = szszuzczcdt0(W0))))) | (~aElementOf0(xn, szNzAzT0)) | (~(xn = szszuzczcdt0(xn)))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.74/0.72 tff(179,plain,
% 0.74/0.72 (~(xn = szszuzczcdt0(xn))),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[178, 175, 144])).
% 0.74/0.72 tff(180,plain,
% 0.74/0.72 (^[W0: $i] : refl(((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0))) <=> ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0))))),
% 0.74/0.72 inference(bind,[status(th)],[])).
% 0.74/0.72 tff(181,plain,
% 0.74/0.72 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0)))),
% 0.74/0.72 inference(quant_intro,[status(thm)],[180])).
% 0.74/0.72 tff(182,plain,
% 0.74/0.72 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0)))),
% 0.74/0.72 inference(rewrite,[status(thm)],[])).
% 0.74/0.72 tff(183,plain,
% 0.74/0.72 (^[W0: $i] : rewrite((aElementOf0(W0, szNzAzT0) => sdtlseqdt0(W0, szszuzczcdt0(W0))) <=> ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0))))),
% 0.74/0.72 inference(bind,[status(th)],[])).
% 0.74/0.72 tff(184,plain,
% 0.74/0.72 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => sdtlseqdt0(W0, szszuzczcdt0(W0))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0)))),
% 0.74/0.72 inference(quant_intro,[status(thm)],[183])).
% 0.74/0.72 tff(185,axiom,(![W0: $i] : (aElementOf0(W0, szNzAzT0) => sdtlseqdt0(W0, szszuzczcdt0(W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mLessSucc')).
% 0.74/0.72 tff(186,plain,
% 0.74/0.72 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0)))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.74/0.72 tff(187,plain,
% 0.74/0.72 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0)))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[186, 182])).
% 0.74/0.72 tff(188,plain,(
% 0.74/0.72 ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0)))),
% 0.74/0.72 inference(skolemize,[status(sab)],[187])).
% 0.74/0.72 tff(189,plain,
% 0.74/0.72 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0)))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[188, 181])).
% 0.74/0.72 tff(190,plain,
% 0.74/0.72 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0)))) | ((~aElementOf0(xn, szNzAzT0)) | sdtlseqdt0(xn, szszuzczcdt0(xn)))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0)))) | (~aElementOf0(xn, szNzAzT0)) | sdtlseqdt0(xn, szszuzczcdt0(xn)))),
% 0.74/0.72 inference(rewrite,[status(thm)],[])).
% 0.74/0.72 tff(191,plain,
% 0.74/0.72 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0)))) | ((~aElementOf0(xn, szNzAzT0)) | sdtlseqdt0(xn, szszuzczcdt0(xn)))),
% 0.74/0.72 inference(quant_inst,[status(thm)],[])).
% 0.74/0.72 tff(192,plain,
% 0.74/0.72 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | sdtlseqdt0(W0, szszuzczcdt0(W0)))) | (~aElementOf0(xn, szNzAzT0)) | sdtlseqdt0(xn, szszuzczcdt0(xn))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.74/0.72 tff(193,plain,
% 0.74/0.72 (sdtlseqdt0(xn, szszuzczcdt0(xn))),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[192, 189, 144])).
% 0.74/0.72 tff(194,plain,
% 0.74/0.72 (^[W0: $i, W1: $i] : refl(((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))) <=> ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))),
% 0.74/0.72 inference(bind,[status(th)],[])).
% 0.74/0.72 tff(195,plain,
% 0.74/0.72 (![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))),
% 0.74/0.72 inference(quant_intro,[status(thm)],[194])).
% 0.74/0.72 tff(196,plain,
% 0.74/0.72 (^[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))))), trans(monotonicity(rewrite((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) <=> (~((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))), ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) <=> (~(~((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))))), rewrite((~(~((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))) <=> ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))), ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) <=> ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))), (((W0 = W1) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)))) <=> ((W0 = W1) | ((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))) | ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))))), rewrite(((W0 = W1) | ((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))) | ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))) <=> ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))), (((W0 = W1) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)))) <=> ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))))),
% 0.74/0.72 inference(bind,[status(th)],[])).
% 0.74/0.72 tff(197,plain,
% 0.74/0.72 (![W0: $i, W1: $i] : ((W0 = W1) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))),
% 0.74/0.72 inference(quant_intro,[status(thm)],[196])).
% 0.74/0.72 tff(198,plain,
% 0.74/0.72 (![W0: $i, W1: $i] : ((W0 = W1) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))),
% 0.74/0.72 inference(rewrite,[status(thm)],[])).
% 0.74/0.72 tff(199,plain,
% 0.74/0.72 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite(((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1)) <=> ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (W0 = W1))), (((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1))) <=> ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (W0 = W1))))), rewrite(((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (W0 = W1))) <=> ((W0 = W1) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))), (((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1))) <=> ((W0 = W1) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))))),
% 0.74/0.72 inference(bind,[status(th)],[])).
% 0.74/0.72 tff(200,plain,
% 0.74/0.72 (![W0: $i, W1: $i] : ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))),
% 0.74/0.72 inference(quant_intro,[status(thm)],[199])).
% 0.74/0.72 tff(201,axiom,(![W0: $i, W1: $i] : ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mLessASymm')).
% 0.74/0.72 tff(202,plain,
% 0.74/0.72 (![W0: $i, W1: $i] : ((W0 = W1) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.74/0.72 tff(203,plain,
% 0.74/0.72 (![W0: $i, W1: $i] : ((W0 = W1) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[202, 198])).
% 0.74/0.72 tff(204,plain,(
% 0.74/0.72 ![W0: $i, W1: $i] : ((W0 = W1) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))),
% 0.74/0.72 inference(skolemize,[status(sab)],[203])).
% 0.74/0.72 tff(205,plain,
% 0.74/0.72 (![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[204, 197])).
% 0.74/0.72 tff(206,plain,
% 0.74/0.72 (![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[205, 195])).
% 0.74/0.72 tff(207,plain,
% 0.74/0.72 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))) | ((~aElementOf0(xn, szNzAzT0)) | (xn = szszuzczcdt0(xn)) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(xn), xn)) | (~sdtlseqdt0(xn, szszuzczcdt0(xn))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))) | (~aElementOf0(xn, szNzAzT0)) | (xn = szszuzczcdt0(xn)) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(xn), xn)) | (~sdtlseqdt0(xn, szszuzczcdt0(xn))))),
% 0.74/0.72 inference(rewrite,[status(thm)],[])).
% 0.74/0.72 tff(208,plain,
% 0.74/0.72 (((xn = szszuzczcdt0(xn)) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~aElementOf0(xn, szNzAzT0)) | (~sdtlseqdt0(xn, szszuzczcdt0(xn))) | (~sdtlseqdt0(szszuzczcdt0(xn), xn))) <=> ((~aElementOf0(xn, szNzAzT0)) | (xn = szszuzczcdt0(xn)) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(xn), xn)) | (~sdtlseqdt0(xn, szszuzczcdt0(xn))))),
% 0.74/0.72 inference(rewrite,[status(thm)],[])).
% 0.74/0.72 tff(209,plain,
% 0.74/0.72 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))) | ((xn = szszuzczcdt0(xn)) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~aElementOf0(xn, szNzAzT0)) | (~sdtlseqdt0(xn, szszuzczcdt0(xn))) | (~sdtlseqdt0(szszuzczcdt0(xn), xn)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))) | ((~aElementOf0(xn, szNzAzT0)) | (xn = szszuzczcdt0(xn)) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(xn), xn)) | (~sdtlseqdt0(xn, szszuzczcdt0(xn)))))),
% 0.74/0.72 inference(monotonicity,[status(thm)],[208])).
% 0.74/0.72 tff(210,plain,
% 0.74/0.72 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))) | ((xn = szszuzczcdt0(xn)) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~aElementOf0(xn, szNzAzT0)) | (~sdtlseqdt0(xn, szszuzczcdt0(xn))) | (~sdtlseqdt0(szszuzczcdt0(xn), xn)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))) | (~aElementOf0(xn, szNzAzT0)) | (xn = szszuzczcdt0(xn)) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(xn), xn)) | (~sdtlseqdt0(xn, szszuzczcdt0(xn))))),
% 0.74/0.72 inference(transitivity,[status(thm)],[209, 207])).
% 0.74/0.72 tff(211,plain,
% 0.74/0.72 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))) | ((xn = szszuzczcdt0(xn)) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~aElementOf0(xn, szNzAzT0)) | (~sdtlseqdt0(xn, szszuzczcdt0(xn))) | (~sdtlseqdt0(szszuzczcdt0(xn), xn)))),
% 0.74/0.72 inference(quant_inst,[status(thm)],[])).
% 0.74/0.72 tff(212,plain,
% 0.74/0.72 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))) | (~aElementOf0(xn, szNzAzT0)) | (xn = szszuzczcdt0(xn)) | (~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(xn), xn)) | (~sdtlseqdt0(xn, szszuzczcdt0(xn)))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.74/0.72 tff(213,plain,
% 0.74/0.72 ((~aElementOf0(szszuzczcdt0(xn), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(xn), xn))),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[212, 206, 144, 193, 179])).
% 0.74/0.72 tff(214,plain,
% 0.74/0.72 (~sdtlseqdt0(szszuzczcdt0(xn), xn)),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[213, 152])).
% 0.74/0.72 tff(215,plain,
% 0.74/0.72 (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), xn)),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[214, 165])).
% 0.74/0.72 tff(216,plain,
% 0.74/0.72 (((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), xn))) | sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), xn)),
% 0.74/0.72 inference(tautology,[status(thm)],[])).
% 0.74/0.72 tff(217,plain,
% 0.74/0.72 ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), xn))),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[216, 215])).
% 0.74/0.72 tff(218,plain,
% 0.74/0.72 ((~(aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(xn)) <=> (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), xn)))))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(xn))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), xn))))),
% 0.74/0.72 inference(tautology,[status(thm)],[])).
% 0.74/0.72 tff(219,plain,
% 0.74/0.72 ((~(aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(xn)) <=> (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), xn)))))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(xn)))),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[218, 217])).
% 0.74/0.72 tff(220,plain,
% 0.74/0.72 (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(xn))),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[219, 141])).
% 0.74/0.72 tff(221,plain,
% 0.74/0.72 ((sdtlseqdt0(xm, xn) | (~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) | (~aSet0(slbdtrb0(xn))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))) | (~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))))) | ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn)))),
% 0.74/0.72 inference(tautology,[status(thm)],[])).
% 0.74/0.72 tff(222,plain,
% 0.74/0.72 (![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn)))),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[221, 133])).
% 0.74/0.72 tff(223,plain,
% 0.74/0.72 (((~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn)))) | ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(xm))) | aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(xn)))) <=> ((~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(xm))) | aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(xn)))),
% 0.74/0.72 inference(rewrite,[status(thm)],[])).
% 0.74/0.72 tff(224,plain,
% 0.74/0.72 ((~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn)))) | ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(xm))) | aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(xn)))),
% 0.74/0.72 inference(quant_inst,[status(thm)],[])).
% 0.74/0.72 tff(225,plain,
% 0.74/0.72 ((~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(xm))) | aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(xn))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.74/0.72 tff(226,plain,
% 0.74/0.72 (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(xm))),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[225, 222, 220])).
% 0.74/0.72 tff(227,plain,
% 0.74/0.72 ((~(aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(xm)) <=> (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), xm)))))) | aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(xm)) | ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), xm)))),
% 0.74/0.72 inference(tautology,[status(thm)],[])).
% 0.74/0.72 tff(228,plain,
% 0.74/0.72 ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), xm))),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[227, 226, 137])).
% 0.74/0.72 tff(229,plain,
% 0.74/0.72 ((~(aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), xm)))))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), xm))))),
% 0.74/0.72 inference(tautology,[status(thm)],[])).
% 0.74/0.72 tff(230,plain,
% 0.74/0.72 (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm))))),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[229, 228, 132])).
% 0.74/0.72 tff(231,plain,
% 0.74/0.72 ((~(aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) <=> (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), tptp_fun_W1_4(szszuzczcdt0(xm)))))))) | aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), slbdtrb0(tptp_fun_W1_4(szszuzczcdt0(xm)))) | ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), tptp_fun_W1_4(szszuzczcdt0(xm)))))),
% 0.74/0.72 inference(tautology,[status(thm)],[])).
% 0.74/0.72 tff(232,plain,
% 0.74/0.72 ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), tptp_fun_W1_4(szszuzczcdt0(xm))))),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[231, 230, 90])).
% 0.74/0.72 tff(233,plain,
% 0.74/0.72 (((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn)))))) | aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)),
% 0.74/0.72 inference(tautology,[status(thm)],[])).
% 0.74/0.72 tff(234,plain,
% 0.74/0.72 (aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[233, 159])).
% 0.74/0.72 tff(235,plain,
% 0.74/0.72 ((~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), tptp_fun_W1_4(szszuzczcdt0(xm)))))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), tptp_fun_W1_4(szszuzczcdt0(xm))))),
% 0.74/0.72 inference(tautology,[status(thm)],[])).
% 0.74/0.72 tff(236,plain,
% 0.74/0.72 ((~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), tptp_fun_W1_4(szszuzczcdt0(xm)))))) | (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), tptp_fun_W1_4(szszuzczcdt0(xm))))),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[235, 234])).
% 0.74/0.72 tff(237,plain,
% 0.74/0.72 (~sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), tptp_fun_W1_4(szszuzczcdt0(xm)))),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[236, 232])).
% 0.74/0.72 tff(238,plain,
% 0.74/0.72 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((~aElementOf0(xn, szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))))) | (xn = tptp_fun_W1_4(szszuzczcdt0(xn))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(xn, szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))))) | (xn = tptp_fun_W1_4(szszuzczcdt0(xn))))),
% 0.74/0.72 inference(rewrite,[status(thm)],[])).
% 0.74/0.72 tff(239,plain,
% 0.74/0.72 (((xn = tptp_fun_W1_4(szszuzczcdt0(xn))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))))) | (~aElementOf0(xn, szNzAzT0))) <=> ((~aElementOf0(xn, szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))))) | (xn = tptp_fun_W1_4(szszuzczcdt0(xn))))),
% 0.74/0.72 inference(rewrite,[status(thm)],[])).
% 0.74/0.72 tff(240,plain,
% 0.74/0.72 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((xn = tptp_fun_W1_4(szszuzczcdt0(xn))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))))) | (~aElementOf0(xn, szNzAzT0)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((~aElementOf0(xn, szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))))) | (xn = tptp_fun_W1_4(szszuzczcdt0(xn)))))),
% 0.74/0.72 inference(monotonicity,[status(thm)],[239])).
% 0.74/0.72 tff(241,plain,
% 0.74/0.72 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((xn = tptp_fun_W1_4(szszuzczcdt0(xn))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))))) | (~aElementOf0(xn, szNzAzT0)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(xn, szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))))) | (xn = tptp_fun_W1_4(szszuzczcdt0(xn))))),
% 0.74/0.72 inference(transitivity,[status(thm)],[240, 238])).
% 0.74/0.72 tff(242,plain,
% 0.74/0.72 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((xn = tptp_fun_W1_4(szszuzczcdt0(xn))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))))) | (~aElementOf0(xn, szNzAzT0)))),
% 0.74/0.72 inference(quant_inst,[status(thm)],[])).
% 0.74/0.72 tff(243,plain,
% 0.74/0.72 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(xn, szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~(szszuzczcdt0(xn) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))))) | (xn = tptp_fun_W1_4(szszuzczcdt0(xn)))),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.74/0.73 tff(244,plain,
% 0.74/0.73 (xn = tptp_fun_W1_4(szszuzczcdt0(xn))),
% 0.74/0.73 inference(unit_resolution,[status(thm)],[243, 116, 144, 234, 161])).
% 0.74/0.73 tff(245,plain,
% 0.74/0.73 (tptp_fun_W1_4(szszuzczcdt0(xn)) = xn),
% 0.74/0.73 inference(symmetry,[status(thm)],[244])).
% 0.74/0.73 tff(246,plain,
% 0.74/0.73 (tptp_fun_W1_4(szszuzczcdt0(xm)) = xm),
% 0.74/0.73 inference(symmetry,[status(thm)],[123])).
% 0.74/0.73 tff(247,plain,
% 0.74/0.73 (sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(xm)), tptp_fun_W1_4(szszuzczcdt0(xn))) <=> sdtlseqdt0(xm, xn)),
% 0.74/0.73 inference(monotonicity,[status(thm)],[246, 245])).
% 0.74/0.73 tff(248,plain,
% 0.74/0.73 (sdtlseqdt0(xm, xn) <=> sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(xm)), tptp_fun_W1_4(szszuzczcdt0(xn)))),
% 0.74/0.73 inference(symmetry,[status(thm)],[247])).
% 0.74/0.73 tff(249,plain,
% 0.74/0.73 ((~sdtlseqdt0(xm, xn)) <=> (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(xm)), tptp_fun_W1_4(szszuzczcdt0(xn))))),
% 0.74/0.73 inference(monotonicity,[status(thm)],[248])).
% 0.74/0.73 tff(250,plain,
% 0.74/0.73 ((sdtlseqdt0(xm, xn) | (~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) | (~aSet0(slbdtrb0(xn))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))) | (~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))))) | (~sdtlseqdt0(xm, xn))),
% 0.74/0.73 inference(tautology,[status(thm)],[])).
% 0.74/0.73 tff(251,plain,
% 0.74/0.73 (~sdtlseqdt0(xm, xn)),
% 0.74/0.73 inference(unit_resolution,[status(thm)],[250, 133])).
% 0.74/0.73 tff(252,plain,
% 0.74/0.73 (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(xm)), tptp_fun_W1_4(szszuzczcdt0(xn)))),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[251, 249])).
% 0.74/0.73 tff(253,plain,
% 0.74/0.73 (^[W0: $i, W1: $i] : refl((sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))) <=> (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))))),
% 0.74/0.73 inference(bind,[status(th)],[])).
% 0.74/0.73 tff(254,plain,
% 0.74/0.73 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))) <=> ![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))),
% 0.74/0.73 inference(quant_intro,[status(thm)],[253])).
% 0.74/0.73 tff(255,plain,
% 0.74/0.73 (^[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))))), ((sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)))) <=> (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | ((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))))), rewrite((sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | ((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))) <=> (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))), ((sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)))) <=> (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))))),
% 0.74/0.73 inference(bind,[status(th)],[])).
% 0.74/0.73 tff(256,plain,
% 0.74/0.73 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)))) <=> ![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))),
% 0.74/0.73 inference(quant_intro,[status(thm)],[255])).
% 0.74/0.73 tff(257,plain,
% 0.74/0.73 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)))) <=> ![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))))),
% 0.74/0.73 inference(rewrite,[status(thm)],[])).
% 0.74/0.73 tff(258,plain,
% 0.74/0.73 (^[W0: $i, W1: $i] : rewrite(((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0))) <=> (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)))))),
% 0.74/0.73 inference(bind,[status(th)],[])).
% 0.74/0.73 tff(259,plain,
% 0.74/0.73 (![W0: $i, W1: $i] : ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0))) <=> ![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))))),
% 0.74/0.73 inference(quant_intro,[status(thm)],[258])).
% 0.74/0.73 tff(260,axiom,(![W0: $i, W1: $i] : ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mLessTotal')).
% 0.74/0.73 tff(261,plain,
% 0.74/0.73 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))))),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.74/0.73 tff(262,plain,
% 0.74/0.73 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))))),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[261, 257])).
% 0.74/0.73 tff(263,plain,(
% 0.74/0.73 ![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))))),
% 0.74/0.73 inference(skolemize,[status(sab)],[262])).
% 0.74/0.73 tff(264,plain,
% 0.74/0.73 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[263, 256])).
% 0.74/0.73 tff(265,plain,
% 0.74/0.73 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[264, 254])).
% 0.74/0.73 tff(266,plain,
% 0.74/0.73 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))) | ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(xm)), tptp_fun_W1_4(szszuzczcdt0(xn))) | sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), tptp_fun_W1_4(szszuzczcdt0(xm))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(xm)), tptp_fun_W1_4(szszuzczcdt0(xn))) | sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), tptp_fun_W1_4(szszuzczcdt0(xm))))),
% 0.74/0.73 inference(rewrite,[status(thm)],[])).
% 0.74/0.73 tff(267,plain,
% 0.74/0.73 ((sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(xm)), tptp_fun_W1_4(szszuzczcdt0(xn))) | sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), tptp_fun_W1_4(szszuzczcdt0(xm))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0))) <=> ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(xm)), tptp_fun_W1_4(szszuzczcdt0(xn))) | sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), tptp_fun_W1_4(szszuzczcdt0(xm))))),
% 0.74/0.73 inference(rewrite,[status(thm)],[])).
% 0.74/0.73 tff(268,plain,
% 0.74/0.73 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))) | (sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(xm)), tptp_fun_W1_4(szszuzczcdt0(xn))) | sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), tptp_fun_W1_4(szszuzczcdt0(xm))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))) | ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(xm)), tptp_fun_W1_4(szszuzczcdt0(xn))) | sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), tptp_fun_W1_4(szszuzczcdt0(xm)))))),
% 0.74/0.73 inference(monotonicity,[status(thm)],[267])).
% 0.74/0.73 tff(269,plain,
% 0.74/0.73 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))) | (sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(xm)), tptp_fun_W1_4(szszuzczcdt0(xn))) | sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), tptp_fun_W1_4(szszuzczcdt0(xm))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(xm)), tptp_fun_W1_4(szszuzczcdt0(xn))) | sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), tptp_fun_W1_4(szszuzczcdt0(xm))))),
% 0.74/0.73 inference(transitivity,[status(thm)],[268, 266])).
% 0.74/0.73 tff(270,plain,
% 0.74/0.73 ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))) | (sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(xm)), tptp_fun_W1_4(szszuzczcdt0(xn))) | sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), tptp_fun_W1_4(szszuzczcdt0(xm))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)))),
% 0.74/0.73 inference(quant_inst,[status(thm)],[])).
% 0.74/0.73 tff(271,plain,
% 0.74/0.73 ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | sdtlseqdt0(szszuzczcdt0(W1), W0) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xm)), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(xn)), szNzAzT0)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(xm)), tptp_fun_W1_4(szszuzczcdt0(xn))) | sdtlseqdt0(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(xn))), tptp_fun_W1_4(szszuzczcdt0(xm)))),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.74/0.73 tff(272,plain,
% 0.74/0.73 ($false),
% 0.74/0.73 inference(unit_resolution,[status(thm)],[271, 265, 50, 234, 252, 237])).
% 0.74/0.73 tff(273,plain,(sdtlseqdt0(xm, xn) | (~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) | (~aSet0(slbdtrb0(xn))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))) | (~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.73 tff(274,plain,
% 0.74/0.73 (((~(aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | (~sdtlseqdt0(xm, xn)) | (~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)) | (~aSet0(slbdtrb0(xn))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))))) | (~(sdtlseqdt0(xm, xn) | (~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) | (~aSet0(slbdtrb0(xn))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))) | (~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))))))) <=> ((~(aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | (~sdtlseqdt0(xm, xn)) | (~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)) | (~aSet0(slbdtrb0(xn))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))))) | (~(sdtlseqdt0(xm, xn) | (~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) | (~aSet0(slbdtrb0(xn))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))) | (~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn)))))))),
% 0.74/0.73 inference(rewrite,[status(thm)],[])).
% 0.74/0.73 tff(275,plain,
% 0.74/0.73 ((~(sdtlseqdt0(xm, xn) | (~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) | (~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn)))) | (~aSet0(slbdtrb0(xn))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))))) <=> (~(sdtlseqdt0(xm, xn) | (~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) | (~aSet0(slbdtrb0(xn))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))) | (~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))))))),
% 0.74/0.73 inference(rewrite,[status(thm)],[])).
% 0.74/0.73 tff(276,plain,
% 0.74/0.73 ((~(aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | (~sdtlseqdt0(xm, xn)) | (~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)) | (~aSet0(slbdtrb0(xn))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))))) <=> (~(aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | (~sdtlseqdt0(xm, xn)) | (~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)) | (~aSet0(slbdtrb0(xn))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm))))))))),
% 0.74/0.73 inference(rewrite,[status(thm)],[])).
% 0.74/0.73 tff(277,plain,
% 0.74/0.73 (((~(aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | (~sdtlseqdt0(xm, xn)) | (~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)) | (~aSet0(slbdtrb0(xn))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))))) | (~(sdtlseqdt0(xm, xn) | (~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) | (~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn)))) | (~aSet0(slbdtrb0(xn))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm))))))))) <=> ((~(aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | (~sdtlseqdt0(xm, xn)) | (~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)) | (~aSet0(slbdtrb0(xn))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))))) | (~(sdtlseqdt0(xm, xn) | (~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) | (~aSet0(slbdtrb0(xn))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))) | (~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn)))))))),
% 0.74/0.73 inference(monotonicity,[status(thm)],[276, 275])).
% 0.74/0.73 tff(278,plain,
% 0.74/0.73 (((~(aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | (~sdtlseqdt0(xm, xn)) | (~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)) | (~aSet0(slbdtrb0(xn))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))))) | (~(sdtlseqdt0(xm, xn) | (~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) | (~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn)))) | (~aSet0(slbdtrb0(xn))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm))))))))) <=> ((~(aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | (~sdtlseqdt0(xm, xn)) | (~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)) | (~aSet0(slbdtrb0(xn))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))))) | (~(sdtlseqdt0(xm, xn) | (~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) | (~aSet0(slbdtrb0(xn))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))) | (~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn)))))))),
% 0.74/0.73 inference(transitivity,[status(thm)],[277, 274])).
% 0.74/0.73 tff(279,plain,
% 0.74/0.73 (((~(aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | (~sdtlseqdt0(xm, xn)) | (~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)) | (~aSet0(slbdtrb0(xn))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))))) | (~(sdtlseqdt0(xm, xn) | (~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) | (~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn)))) | (~aSet0(slbdtrb0(xn))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm))))))))) <=> ((~(aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | (~sdtlseqdt0(xm, xn)) | (~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)) | (~aSet0(slbdtrb0(xn))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))))) | (~(sdtlseqdt0(xm, xn) | (~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) | (~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn)))) | (~aSet0(slbdtrb0(xn))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))))))),
% 0.74/0.74 inference(rewrite,[status(thm)],[])).
% 0.74/0.74 tff(280,plain,
% 0.74/0.74 (((~(aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | (~sdtlseqdt0(xm, xn)) | (~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)) | (~aSet0(slbdtrb0(xn))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))))) | (~(sdtlseqdt0(xm, xn) | (~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) | (~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn)))) | (~aSet0(slbdtrb0(xn))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm))))))))) <=> ((~(aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | (~sdtlseqdt0(xm, xn)) | (~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)) | (~aSet0(slbdtrb0(xn))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))))) | (~(sdtlseqdt0(xm, xn) | (~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) | (~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn)))) | (~aSet0(slbdtrb0(xn))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))))))),
% 0.74/0.74 inference(rewrite,[status(thm)],[])).
% 0.74/0.74 tff(281,plain,
% 0.74/0.74 ((aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm))))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn))))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) & (~sdtlseqdt0(xm, xn))) <=> (~(sdtlseqdt0(xm, xn) | (~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) | (~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn)))) | (~aSet0(slbdtrb0(xn))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm))))))))),
% 0.74/0.74 inference(rewrite,[status(thm)],[])).
% 0.74/0.74 tff(282,plain,
% 0.74/0.74 (^[W0: $i] : rewrite((aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) <=> (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn))))))),
% 0.74/0.74 inference(bind,[status(th)],[])).
% 0.74/0.74 tff(283,plain,
% 0.74/0.74 (![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) <=> ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))),
% 0.74/0.74 inference(quant_intro,[status(thm)],[282])).
% 0.74/0.74 tff(284,plain,
% 0.74/0.74 (^[W0: $i] : rewrite((aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) <=> (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm))))))),
% 0.74/0.74 inference(bind,[status(th)],[])).
% 0.74/0.74 tff(285,plain,
% 0.74/0.74 (![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) <=> ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))),
% 0.74/0.74 inference(quant_intro,[status(thm)],[284])).
% 0.74/0.74 tff(286,plain,
% 0.74/0.74 ((aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) & (~sdtlseqdt0(xm, xn))) <=> (aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm))))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn))))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) & (~sdtlseqdt0(xm, xn)))),
% 0.74/0.74 inference(monotonicity,[status(thm)],[285, 283])).
% 0.74/0.74 tff(287,plain,
% 0.74/0.74 ((aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) & (~sdtlseqdt0(xm, xn))) <=> (~(sdtlseqdt0(xm, xn) | (~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) | (~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn)))) | (~aSet0(slbdtrb0(xn))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm))))))))),
% 0.74/0.74 inference(transitivity,[status(thm)],[286, 281])).
% 0.74/0.74 tff(288,plain,
% 0.74/0.74 (((~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~((~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn))))) & aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm))))) & sdtlseqdt0(xm, xn)) <=> (~(aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | (~sdtlseqdt0(xm, xn)) | (~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)) | (~aSet0(slbdtrb0(xn))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm))))))))),
% 0.74/0.74 inference(rewrite,[status(thm)],[])).
% 0.74/0.74 tff(289,plain,
% 0.74/0.74 (((~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~((~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & sdtlseqdt0(xm, xn)) <=> ((~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~((~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn))))) & aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm))))) & sdtlseqdt0(xm, xn))),
% 0.74/0.74 inference(monotonicity,[status(thm)],[283, 285])).
% 0.74/0.74 tff(290,plain,
% 0.74/0.74 (((~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~((~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & sdtlseqdt0(xm, xn)) <=> (~(aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | (~sdtlseqdt0(xm, xn)) | (~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)) | (~aSet0(slbdtrb0(xn))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm))))))))),
% 0.74/0.74 inference(transitivity,[status(thm)],[289, 288])).
% 0.74/0.74 tff(291,plain,
% 0.74/0.74 ((((~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~((~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & sdtlseqdt0(xm, xn)) | (aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) & (~sdtlseqdt0(xm, xn)))) <=> ((~(aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | (~sdtlseqdt0(xm, xn)) | (~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)) | (~aSet0(slbdtrb0(xn))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))))) | (~(sdtlseqdt0(xm, xn) | (~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) | (~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn)))) | (~aSet0(slbdtrb0(xn))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))))))),
% 0.74/0.74 inference(monotonicity,[status(thm)],[290, 287])).
% 0.74/0.74 tff(292,plain,
% 0.74/0.74 ((((~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~((~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & sdtlseqdt0(xm, xn)) | (aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) & (~sdtlseqdt0(xm, xn)))) <=> ((~(aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | (~sdtlseqdt0(xm, xn)) | (~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)) | (~aSet0(slbdtrb0(xn))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))))) | (~(sdtlseqdt0(xm, xn) | (~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) | (~![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn)))) | (~aSet0(slbdtrb0(xn))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xn)))))) | (~aSet0(slbdtrb0(xm))) | (~![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (~((~aElementOf0(W0, szNzAzT0)) | (~sdtlseqdt0(szszuzczcdt0(W0), xm)))))))))),
% 0.74/0.74 inference(transitivity,[status(thm)],[291, 280])).
% 0.74/0.74 tff(293,plain,
% 0.74/0.74 ((((~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~((~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & sdtlseqdt0(xm, xn)) | (aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) & (~sdtlseqdt0(xm, xn)))) <=> (((~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~((~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & sdtlseqdt0(xm, xn)) | (aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) & (~sdtlseqdt0(xm, xn))))),
% 0.74/0.74 inference(rewrite,[status(thm)],[])).
% 0.74/0.74 tff(294,plain,
% 0.74/0.74 (((aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~sdtlseqdt0(xm, xn))) <=> (aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) & (~sdtlseqdt0(xm, xn)))),
% 0.74/0.74 inference(rewrite,[status(thm)],[])).
% 0.74/0.74 tff(295,plain,
% 0.74/0.74 ((aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) <=> (aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)))),
% 0.74/0.74 inference(rewrite,[status(thm)],[])).
% 0.74/0.74 tff(296,plain,
% 0.74/0.74 (((aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~sdtlseqdt0(xm, xn))) <=> ((aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~sdtlseqdt0(xm, xn)))),
% 0.74/0.74 inference(monotonicity,[status(thm)],[295])).
% 0.74/0.74 tff(297,plain,
% 0.74/0.74 (((aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~sdtlseqdt0(xm, xn))) <=> (aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) & (~sdtlseqdt0(xm, xn)))),
% 0.74/0.74 inference(transitivity,[status(thm)],[296, 294])).
% 0.74/0.74 tff(298,plain,
% 0.74/0.74 (((~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~((~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)))) & (aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn)))) & (aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm)))) & sdtlseqdt0(xm, xn)) <=> ((~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~((~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & sdtlseqdt0(xm, xn))),
% 0.74/0.74 inference(rewrite,[status(thm)],[])).
% 0.74/0.74 tff(299,plain,
% 0.74/0.74 ((~(~sdtlseqdt0(xm, xn))) <=> sdtlseqdt0(xm, xn)),
% 0.74/0.74 inference(rewrite,[status(thm)],[])).
% 0.74/0.74 tff(300,plain,
% 0.74/0.74 ((aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm)))) <=> (aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))))),
% 0.74/0.74 inference(rewrite,[status(thm)],[])).
% 0.74/0.74 tff(301,plain,
% 0.74/0.74 ((aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn)))) <=> (aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))))),
% 0.74/0.74 inference(rewrite,[status(thm)],[])).
% 0.74/0.74 tff(302,plain,
% 0.74/0.74 (((~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~((~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)))) & (aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn)))) & (aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm)))) & (~(~sdtlseqdt0(xm, xn)))) <=> ((~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~((~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)))) & (aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn)))) & (aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm)))) & sdtlseqdt0(xm, xn))),
% 0.74/0.75 inference(monotonicity,[status(thm)],[301, 300, 299])).
% 0.74/0.75 tff(303,plain,
% 0.74/0.75 (((~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~((~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)))) & (aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn)))) & (aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm)))) & (~(~sdtlseqdt0(xm, xn)))) <=> ((~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~((~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & sdtlseqdt0(xm, xn))),
% 0.74/0.75 inference(transitivity,[status(thm)],[302, 298])).
% 0.74/0.75 tff(304,plain,
% 0.74/0.75 ((((~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~((~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)))) & (aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn)))) & (aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm)))) & (~(~sdtlseqdt0(xm, xn)))) | ((aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~sdtlseqdt0(xm, xn)))) <=> (((~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~((~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & sdtlseqdt0(xm, xn)) | (aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) & (~sdtlseqdt0(xm, xn))))),
% 0.74/0.75 inference(monotonicity,[status(thm)],[303, 297])).
% 0.74/0.75 tff(305,plain,
% 0.74/0.75 ((((~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~((~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)))) & (aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn)))) & (aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm)))) & (~(~sdtlseqdt0(xm, xn)))) | ((aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~sdtlseqdt0(xm, xn)))) <=> (((~aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) & (~((~aElementOf0(W0!9, slbdtrb0(xm))) | aElementOf0(W0!9, slbdtrb0(xn)))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & sdtlseqdt0(xm, xn)) | (aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) & (~sdtlseqdt0(xm, xn))))),
% 0.74/0.75 inference(transitivity,[status(thm)],[304, 293])).
% 0.74/0.75 tff(306,plain,
% 0.74/0.75 (((aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) | (~(aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))))) | (~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))))) | (~sdtlseqdt0(xm, xn))) & ((~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)))) | sdtlseqdt0(xm, xn))) <=> ((aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) | (~(aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))))) | (~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))))) | (~sdtlseqdt0(xm, xn))) & ((~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)))) | sdtlseqdt0(xm, xn)))),
% 0.74/0.75 inference(rewrite,[status(thm)],[])).
% 0.74/0.75 tff(307,plain,
% 0.74/0.75 ((~((aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) | (~(aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))))) | (~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))))) | (~sdtlseqdt0(xm, xn))) & ((~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)))) | sdtlseqdt0(xm, xn)))) <=> (~((aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) | (~(aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))))) | (~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))))) | (~sdtlseqdt0(xm, xn))) & ((~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)))) | sdtlseqdt0(xm, xn))))),
% 0.74/0.75 inference(monotonicity,[status(thm)],[306])).
% 0.74/0.75 tff(308,plain,
% 0.74/0.75 ((~((aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) | (~(aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))))) | (~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))))) | (~sdtlseqdt0(xm, xn))) & ((~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)))) | sdtlseqdt0(xm, xn)))) <=> (~((aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) | (~(aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))))) | (~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))))) | (~sdtlseqdt0(xm, xn))) & ((~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)))) | sdtlseqdt0(xm, xn))))),
% 0.74/0.75 inference(rewrite,[status(thm)],[])).
% 0.74/0.75 tff(309,plain,
% 0.74/0.75 ((~((sdtlseqdt0(xm, xn) => ((aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm)))) => ((aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn)))) => (![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) => aElementOf0(W0, slbdtrb0(xn))) | aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)))))) & ((((((aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm)))) & aSet0(slbdtrb0(xn))) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn)))) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) => aElementOf0(W0, slbdtrb0(xn)))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) => sdtlseqdt0(xm, xn)))) <=> (~((aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) | (~(aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))))) | (~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))))) | (~sdtlseqdt0(xm, xn))) & ((~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)))) | sdtlseqdt0(xm, xn))))),
% 0.74/0.75 inference(rewrite,[status(thm)],[])).
% 0.74/0.75 tff(310,axiom,(~((sdtlseqdt0(xm, xn) => ((aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm)))) => ((aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn)))) => (![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) => aElementOf0(W0, slbdtrb0(xn))) | aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)))))) & ((((((aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm)))) & aSet0(slbdtrb0(xn))) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn)))) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) => aElementOf0(W0, slbdtrb0(xn)))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn))) => sdtlseqdt0(xm, xn)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.74/0.75 tff(311,plain,
% 0.74/0.75 (~((aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) | (~(aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))))) | (~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))))) | (~sdtlseqdt0(xm, xn))) & ((~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)))) | sdtlseqdt0(xm, xn)))),
% 0.74/0.75 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.74/0.75 tff(312,plain,
% 0.74/0.75 (~((aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) | (~(aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))))) | (~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))))) | (~sdtlseqdt0(xm, xn))) & ((~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)))) | sdtlseqdt0(xm, xn)))),
% 0.74/0.75 inference(modus_ponens,[status(thm)],[311, 307])).
% 0.74/0.75 tff(313,plain,
% 0.74/0.75 (~((aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) | (~(aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))))) | (~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))))) | (~sdtlseqdt0(xm, xn))) & ((~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)))) | sdtlseqdt0(xm, xn)))),
% 0.74/0.75 inference(modus_ponens,[status(thm)],[312, 308])).
% 0.74/0.75 tff(314,plain,
% 0.74/0.75 (~((aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) | (~(aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))))) | (~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))))) | (~sdtlseqdt0(xm, xn))) & ((~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)))) | sdtlseqdt0(xm, xn)))),
% 0.74/0.76 inference(modus_ponens,[status(thm)],[313, 307])).
% 0.74/0.76 tff(315,plain,
% 0.74/0.76 (~((aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) | (~(aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))))) | (~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))))) | (~sdtlseqdt0(xm, xn))) & ((~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)))) | sdtlseqdt0(xm, xn)))),
% 0.74/0.76 inference(modus_ponens,[status(thm)],[314, 307])).
% 0.74/0.76 tff(316,plain,
% 0.74/0.76 (~((aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) | (~(aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))))) | (~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))))) | (~sdtlseqdt0(xm, xn))) & ((~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)))) | sdtlseqdt0(xm, xn)))),
% 0.74/0.76 inference(modus_ponens,[status(thm)],[315, 307])).
% 0.74/0.76 tff(317,plain,
% 0.74/0.76 (~((aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) | (~(aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))))) | (~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))))) | (~sdtlseqdt0(xm, xn))) & ((~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)))) | sdtlseqdt0(xm, xn)))),
% 0.74/0.76 inference(modus_ponens,[status(thm)],[316, 307])).
% 0.74/0.76 tff(318,plain,
% 0.74/0.76 (~((aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)) | ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) | (~(aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))))) | (~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))))) | (~sdtlseqdt0(xm, xn))) & ((~(aSet0(slbdtrb0(xm)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xm)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xm))) & aSet0(slbdtrb0(xn)) & ![W0: $i] : (aElementOf0(W0, slbdtrb0(xn)) <=> (aElementOf0(W0, szNzAzT0) & sdtlseqdt0(szszuzczcdt0(W0), xn))) & ![W0: $i] : ((~aElementOf0(W0, slbdtrb0(xm))) | aElementOf0(W0, slbdtrb0(xn))) & aSubsetOf0(slbdtrb0(xm), slbdtrb0(xn)))) | sdtlseqdt0(xm, xn)))),
% 0.74/0.76 inference(modus_ponens,[status(thm)],[317, 307])).
% 0.74/0.76 unexpected number of arguments: (let ((a!1 (~ (not (aSubsetOf0 (slbdtrb0 xm) (slbdtrb0 xn)))
% 0.74/0.76 (not (aSubsetOf0 (slbdtrb0 xm) (slbdtrb0 xn)))))
% 0.74/0.76 (a!2 (forall ((W0 $i))
% 0.74/0.76 (or (not (aElementOf0 W0 (slbdtrb0 xm)))
% 0.74/0.76 (aElementOf0 W0 (slbdtrb0 xn)))))
% 0.74/0.76 (a!3 (or (not (aElementOf0 W0!9 (slbdtrb0 xm)))
% 0.74/0.76 (aElementOf0 W0!9 (slbdtrb0 xn))))
% 0.74/0.76 (a!4 (refl (~ (aSet0 (slbdtrb0 xn)) (aSet0 (slbdtrb0 xn)))))
% 0.74/0.76 (a!5 (proof-bind (lambda ((W0 $i))
% 0.74/0.76 (let ((a!1 (= (aElementOf0 W0 (slbdtrb0 xn))
% 0.74/0.76 (and (aElementOf0 W0 szNzAzT0)
% 0.74/0.76 (sdtlseqdt0 (szszuzczcdt0 W0) xn)))))
% 0.74/0.76 (refl (~ a!1 a!1))))))
% 0.74/0.76 (a!6 (forall ((W0 $i))
% 0.74/0.76 (= (aElementOf0 W0 (slbdtrb0 xn))
% 0.74/0.76 (and (aElementOf0 W0 szNzAzT0)
% 0.74/0.76 (sdtlseqdt0 (szszuzczcdt0 W0) xn)))))
% 0.74/0.76 (a!11 (refl (~ (aSet0 (slbdtrb0 xm)) (aSet0 (slbdtrb0 xm)))))
% 0.74/0.76 (a!12 (proof-bind (lambda ((W0 $i))
% 0.74/0.76 (let ((a!1 (= (aElementOf0 W0 (slbdtrb0 xm))
% 0.74/0.76 (and (aElementOf0 W0 szNzAzT0)
% 0.74/0.76 (sdtlseqdt0 (szszuzczcdt0 W0) xm)))))
% 0.74/0.76 (refl (~ a!1 a!1))))))
% 0.74/0.76 (a!13 (forall ((W0 $i))
% 0.74/0.76 (= (aElementOf0 W0 (slbdtrb0 xm))
% 0.74/0.76 (and (aElementOf0 W0 szNzAzT0)
% 0.74/0.76 (sdtlseqdt0 (szszuzczcdt0 W0) xm)))))
% 0.74/0.76 (a!18 (~ (not (not (sdtlseqdt0 xm xn))) (not (not (sdtlseqdt0 xm xn)))))
% 0.74/0.76 (a!22 (proof-bind (lambda ((W0 $i))
% 0.74/0.76 (let ((a!1 (or (not (aElementOf0 W0 (slbdtrb0 xm)))
% 0.74/0.76 (aElementOf0 W0 (slbdtrb0 xn)))))
% 0.74/0.76 (refl (~ a!1 a!1))))))
% 0.74/0.76 (a!23 (refl (~ (aSubsetOf0 (slbdtrb0 xm) (slbdtrb0 xn))
% 0.74/0.76 (aSubsetOf0 (slbdtrb0 xm) (slbdtrb0 xn)))))
% 0.74/0.76 (a!26 (refl (~ (not (sdtlseqdt0 xm xn)) (not (sdtlseqdt0 xm xn))))))
% 0.74/0.76 (let ((a!7 (~ (and (aSet0 (slbdtrb0 xn)) a!6) (and (aSet0 (slbdtrb0 xn)) a!6)))
% 0.74/0.76 (a!8 (not (and (aSet0 (slbdtrb0 xn)) a!6)))
% 0.74/0.76 (a!14 (~ (and (aSet0 (slbdtrb0 xm)) a!13)
% 0.74/0.76 (and (aSet0 (slbdtrb0 xm)) a!13)))
% 0.74/0.76 (a!15 (not (and (aSet0 (slbdtrb0 xm)) a!13)))
% 0.74/0.76 (a!20 (and (not (aSubsetOf0 (slbdtrb0 xm) (slbdtrb0 xn)))
% 0.74/0.76 (not a!3)
% 0.74/0.76 (and (aSet0 (slbdtrb0 xn)) a!6)
% 0.74/0.76 (and (aSet0 (slbdtrb0 xm)) a!13)
% 0.74/0.76 (not (not (sdtlseqdt0 xm xn)))))
% 0.74/0.76 (a!24 (and (aSet0 (slbdtrb0 xm))
% 0.74/0.76 a!13
% 0.74/0.76 (aSet0 (slbdtrb0 xn))
% 0.74/0.76 a!6
% 0.74/0.76 a!2
% 0.74/0.76 (aSubsetOf0 (slbdtrb0 xm) (slbdtrb0 xn)))))
% 0.74/0.76 (let ((a!9 (~ (not a!8) (and (aSet0 (slbdtrb0 xn)) a!6)))
% 0.74/0.76 (a!16 (~ (not a!15) (and (aSet0 (slbdtrb0 xm)) a!13)))
% 0.74/0.76 (a!19 (or (aSubsetOf0 (slbdtrb0 xm) (slbdtrb0 xn))
% 0.74/0.76 a!2
% 0.74/0.76 a!8
% 0.74/0.76 a!15
% 0.74/0.76 (not (sdtlseqdt0 xm xn))))
% 0.74/0.76 (a!25 (nnf-neg (monotonicity a!11
% 0.74/0.76 (nnf-pos a!12 (~ a!13 a!13))
% 0.74/0.76 a!4
% 0.74/0.76 (nnf-pos a!5 (~ a!6 a!6))
% 0.74/0.76 (nnf-pos a!22 (~ a!2 a!2))
% 0.74/0.76 a!23
% 0.74/0.76 (~ a!24 a!24))
% 0.74/0.76 (~ (not (not a!24)) a!24)))
% 0.74/0.76 (a!27 (~ (not (or (not a!24) (sdtlseqdt0 xm xn)))
% 0.74/0.76 (and a!24 (not (sdtlseqdt0 xm xn)))))
% 0.74/0.76 (a!29 (or a!20 (and a!24 (not (sdtlseqdt0 xm xn))))))
% 0.74/0.76 (let ((a!10 (nnf-neg (monotonicity a!4 (nnf-pos a!5 (~ a!6 a!6)) a!7) a!9))
% 0.74/0.76 (a!17 (nnf-neg (monotonicity a!11 (nnf-pos a!12 (~ a!13 a!13)) a!14) a!16))
% 0.74/0.76 (a!28 (not (and a!19 (or (not a!24) (sdtlseqdt0 xm xn))))))
% 0.74/0.76 (let ((a!21 (nnf-neg (refl a!1)
% 0.74/0.76 (sk (~ (not a!2) (not a!3)))
% 0.74/0.76 a!10
% 0.74/0.76 a!17
% 0.74/0.76 (refl a!18)
% 0.74/0.76 (~ (not a!19) a!20))))
% 0.74/0.76 (nnf-neg a!21 (nnf-neg a!25 a!26 a!27) (~ a!28 a!29)))))))
% 0.74/0.76 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------