TSTP Solution File: NUM600+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM600+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:10:47 EDT 2022
% Result : Theorem 71.54s 45.80s
% Output : Proof 71.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : NUM600+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32 % Computer : n015.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Sep 2 12:25:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 71.54/45.80 % SZS status Theorem
% 71.54/45.80 % SZS output start Proof
% 71.54/45.80 tff(aElementOf0_type, type, (
% 71.54/45.80 aElementOf0: ( $i * $i ) > $o)).
% 71.54/45.80 tff(szDzozmdt0_type, type, (
% 71.54/45.80 szDzozmdt0: $i > $i)).
% 71.54/45.80 tff(xN_type, type, (
% 71.54/45.80 xN: $i)).
% 71.54/45.80 tff(tptp_fun_W4_13_type, type, (
% 71.54/45.80 tptp_fun_W4_13: ( $i * $i * $i ) > $i)).
% 71.54/45.80 tff(xe_type, type, (
% 71.54/45.80 xe: $i)).
% 71.54/45.80 tff(sdtlbdtrb0_type, type, (
% 71.54/45.80 sdtlbdtrb0: ( $i * $i ) > $i)).
% 71.54/45.80 tff(szDzizrdt0_type, type, (
% 71.54/45.80 szDzizrdt0: $i > $i)).
% 71.54/45.80 tff(xd_type, type, (
% 71.54/45.80 xd: $i)).
% 71.54/45.80 tff(tptp_fun_W0_24_type, type, (
% 71.54/45.80 tptp_fun_W0_24: $i)).
% 71.54/45.80 tff(sdtlpdtrp0_type, type, (
% 71.54/45.80 sdtlpdtrp0: ( $i * $i ) > $i)).
% 71.54/45.80 tff(sdtlcdtrc0_type, type, (
% 71.54/45.80 sdtlcdtrc0: ( $i * $i ) > $i)).
% 71.54/45.80 tff(aSet0_type, type, (
% 71.54/45.80 aSet0: $i > $o)).
% 71.54/45.80 tff(tptp_fun_W3_14_type, type, (
% 71.54/45.80 tptp_fun_W3_14: ( $i * $i * $i ) > $i)).
% 71.54/45.80 tff(tptp_fun_W4_15_type, type, (
% 71.54/45.80 tptp_fun_W4_15: ( $i * $i * $i ) > $i)).
% 71.54/45.80 tff(aSubsetOf0_type, type, (
% 71.54/45.80 aSubsetOf0: ( $i * $i ) > $o)).
% 71.54/45.80 tff(szNzAzT0_type, type, (
% 71.54/45.80 szNzAzT0: $i)).
% 71.54/45.80 tff(aFunction0_type, type, (
% 71.54/45.80 aFunction0: $i > $o)).
% 71.54/45.80 tff(xC_type, type, (
% 71.54/45.80 xC: $i)).
% 71.54/45.80 tff(slbdtsldtrb0_type, type, (
% 71.54/45.80 slbdtsldtrb0: ( $i * $i ) > $i)).
% 71.54/45.80 tff(xk_type, type, (
% 71.54/45.80 xk: $i)).
% 71.54/45.80 tff(szszuzczcdt0_type, type, (
% 71.54/45.80 szszuzczcdt0: $i > $i)).
% 71.54/45.80 tff(szmzizndt0_type, type, (
% 71.54/45.80 szmzizndt0: $i > $i)).
% 71.54/45.80 tff(aElement0_type, type, (
% 71.54/45.80 aElement0: $i > $o)).
% 71.54/45.80 tff(xT_type, type, (
% 71.54/45.80 xT: $i)).
% 71.54/45.80 tff(isFinite0_type, type, (
% 71.54/45.80 isFinite0: $i > $o)).
% 71.54/45.80 tff(isCountable0_type, type, (
% 71.54/45.80 isCountable0: $i > $o)).
% 71.54/45.80 tff(xO_type, type, (
% 71.54/45.80 xO: $i)).
% 71.54/45.80 tff(tptp_fun_W2_1_type, type, (
% 71.54/45.80 tptp_fun_W2_1: ( $i * $i ) > $i)).
% 71.54/45.80 tff(1,plain,
% 71.54/45.80 ((szDzozmdt0(xd) = szNzAzT0) <=> (szDzozmdt0(xd) = szDzozmdt0(xN))),
% 71.54/45.80 inference(rewrite,[status(thm)],[])).
% 71.54/45.80 tff(2,plain,
% 71.54/45.80 ((szDzozmdt0(xd) = szNzAzT0) <=> (szDzozmdt0(xd) = szNzAzT0)),
% 71.54/45.80 inference(rewrite,[status(thm)],[])).
% 71.54/45.80 tff(3,axiom,((aFunction0(xd) & (szDzozmdt0(xd) = szNzAzT0)) & ![W0: $i] : (aElementOf0(W0, szNzAzT0) => ![W1: $i] : ((aSet0(W1) & aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk))) => (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__4730')).
% 71.54/45.80 tff(4,plain,
% 71.54/45.80 (aFunction0(xd) & (szDzozmdt0(xd) = szNzAzT0)),
% 71.54/45.80 inference(and_elim,[status(thm)],[3])).
% 71.54/45.80 tff(5,plain,
% 71.54/45.80 (szDzozmdt0(xd) = szNzAzT0),
% 71.54/45.80 inference(and_elim,[status(thm)],[4])).
% 71.54/45.80 tff(6,plain,
% 71.54/45.80 (szDzozmdt0(xd) = szNzAzT0),
% 71.54/45.80 inference(modus_ponens,[status(thm)],[5, 2])).
% 71.54/45.80 tff(7,plain,
% 71.54/45.80 (szDzozmdt0(xd) = szDzozmdt0(xN)),
% 71.54/45.80 inference(modus_ponens,[status(thm)],[6, 1])).
% 71.54/45.80 tff(8,plain,
% 71.54/45.80 (szDzozmdt0(xN) = szDzozmdt0(xd)),
% 71.54/45.80 inference(symmetry,[status(thm)],[7])).
% 71.54/45.80 tff(9,plain,
% 71.54/45.80 ((szDzozmdt0(xe) = szNzAzT0) <=> (szDzozmdt0(xe) = szDzozmdt0(xN))),
% 71.54/45.80 inference(rewrite,[status(thm)],[])).
% 71.54/45.80 tff(10,plain,
% 71.54/45.80 ((szDzozmdt0(xe) = szNzAzT0) <=> (szDzozmdt0(xe) = szNzAzT0)),
% 71.54/45.80 inference(rewrite,[status(thm)],[])).
% 71.54/45.80 tff(11,axiom,((aFunction0(xe) & (szDzozmdt0(xe) = szNzAzT0)) & ![W0: $i] : (aElementOf0(W0, szNzAzT0) => (sdtlpdtrp0(xe, W0) = szmzizndt0(sdtlpdtrp0(xN, W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__4660')).
% 71.54/45.80 tff(12,plain,
% 71.54/45.80 (aFunction0(xe) & (szDzozmdt0(xe) = szNzAzT0)),
% 71.54/45.80 inference(and_elim,[status(thm)],[11])).
% 71.54/45.80 tff(13,plain,
% 71.54/45.80 (szDzozmdt0(xe) = szNzAzT0),
% 71.54/45.80 inference(and_elim,[status(thm)],[12])).
% 71.54/45.80 tff(14,plain,
% 71.54/45.80 (szDzozmdt0(xe) = szNzAzT0),
% 71.54/45.80 inference(modus_ponens,[status(thm)],[13, 10])).
% 71.54/45.80 tff(15,plain,
% 71.54/45.80 (szDzozmdt0(xe) = szDzozmdt0(xN)),
% 71.54/45.80 inference(modus_ponens,[status(thm)],[14, 9])).
% 71.54/45.80 tff(16,plain,
% 71.54/45.80 (szDzozmdt0(xe) = szDzozmdt0(xd)),
% 71.54/45.80 inference(transitivity,[status(thm)],[15, 8])).
% 71.54/45.80 tff(17,plain,
% 71.54/45.80 (aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xe)) <=> aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xd))),
% 71.54/45.80 inference(monotonicity,[status(thm)],[16])).
% 71.54/45.80 tff(18,plain,
% 71.54/45.80 (aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xd)) <=> aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xe))),
% 71.54/45.80 inference(symmetry,[status(thm)],[17])).
% 71.54/45.80 tff(19,plain,
% 71.54/45.80 (aSet0(xT) <=> aSet0(xT)),
% 71.54/45.80 inference(rewrite,[status(thm)],[])).
% 71.54/45.80 tff(20,axiom,(aSet0(xT) & isFinite0(xT)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__3291')).
% 71.54/45.80 tff(21,plain,
% 71.54/45.80 (aSet0(xT)),
% 71.54/45.80 inference(and_elim,[status(thm)],[20])).
% 71.54/45.80 tff(22,plain,
% 71.54/45.80 (aSet0(xT)),
% 71.54/45.80 inference(modus_ponens,[status(thm)],[21, 19])).
% 71.54/45.80 tff(23,plain,
% 71.54/45.80 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 71.54/45.80 inference(bind,[status(th)],[])).
% 71.54/45.80 tff(24,plain,
% 71.54/45.80 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 71.54/45.80 inference(quant_intro,[status(thm)],[23])).
% 71.54/45.80 tff(25,plain,
% 71.54/45.80 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 71.54/45.80 inference(bind,[status(th)],[])).
% 71.54/45.80 tff(26,plain,
% 71.54/45.80 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 71.54/45.80 inference(quant_intro,[status(thm)],[25])).
% 71.54/45.80 tff(27,plain,
% 71.54/45.80 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 71.54/45.80 inference(transitivity,[status(thm)],[26, 24])).
% 71.54/45.80 tff(28,plain,
% 71.54/45.80 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 71.54/45.80 inference(rewrite,[status(thm)],[])).
% 71.54/45.80 tff(29,plain,
% 71.54/45.80 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, W0) => aElement0(W1)) <=> (aElement0(W1) | (~aElementOf0(W1, W0))))), (![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)) <=> ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))), ((aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> (aSet0(W0) => ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))), rewrite((aSet0(W0) => ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))), ((aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))))),
% 71.54/45.80 inference(bind,[status(th)],[])).
% 71.54/45.80 tff(30,plain,
% 71.54/45.80 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 71.54/45.80 inference(quant_intro,[status(thm)],[29])).
% 71.54/45.80 tff(31,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mEOfElem')).
% 71.54/45.80 tff(32,plain,
% 71.54/45.80 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 71.54/45.80 inference(modus_ponens,[status(thm)],[31, 30])).
% 71.54/45.80 tff(33,plain,
% 71.54/45.80 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 71.54/45.80 inference(modus_ponens,[status(thm)],[32, 28])).
% 71.54/45.80 tff(34,plain,(
% 71.54/45.80 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 71.54/45.80 inference(skolemize,[status(sab)],[33])).
% 71.54/45.80 tff(35,plain,
% 71.54/45.80 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 71.54/45.80 inference(modus_ponens,[status(thm)],[34, 27])).
% 71.54/45.80 tff(36,plain,
% 71.54/45.80 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(xT)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xT))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(xT)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xT))))),
% 71.54/45.80 inference(rewrite,[status(thm)],[])).
% 71.54/45.80 tff(37,plain,
% 71.54/45.80 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(xT)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xT))))),
% 71.54/45.80 inference(quant_inst,[status(thm)],[])).
% 71.54/45.80 tff(38,plain,
% 71.54/45.80 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(xT)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xT)))),
% 71.54/45.80 inference(modus_ponens,[status(thm)],[37, 36])).
% 71.54/45.80 tff(39,plain,
% 71.54/45.80 (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xT)))),
% 71.54/45.80 inference(unit_resolution,[status(thm)],[38, 35, 22])).
% 71.54/45.80 tff(40,plain,
% 71.54/45.80 (aElementOf0(szDzizrdt0(xd), xT) <=> aElementOf0(szDzizrdt0(xd), xT)),
% 71.54/45.80 inference(rewrite,[status(thm)],[])).
% 71.54/45.80 tff(41,axiom,(aElementOf0(szDzizrdt0(xd), xT) & isCountable0(sdtlbdtrb0(xd, szDzizrdt0(xd)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__4854')).
% 71.54/45.80 tff(42,plain,
% 71.54/45.80 (aElementOf0(szDzizrdt0(xd), xT)),
% 71.54/45.80 inference(and_elim,[status(thm)],[41])).
% 71.54/45.80 tff(43,plain,
% 71.54/45.80 (aElementOf0(szDzizrdt0(xd), xT)),
% 71.54/45.80 inference(modus_ponens,[status(thm)],[42, 40])).
% 71.54/45.80 tff(44,plain,
% 71.54/45.80 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xT)))) | (aElement0(szDzizrdt0(xd)) | (~aElementOf0(szDzizrdt0(xd), xT)))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xT)))) | aElement0(szDzizrdt0(xd)) | (~aElementOf0(szDzizrdt0(xd), xT)))),
% 71.54/45.80 inference(rewrite,[status(thm)],[])).
% 71.54/45.80 tff(45,plain,
% 71.54/45.80 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xT)))) | (aElement0(szDzizrdt0(xd)) | (~aElementOf0(szDzizrdt0(xd), xT)))),
% 71.54/45.80 inference(quant_inst,[status(thm)],[])).
% 71.54/45.80 tff(46,plain,
% 71.54/45.80 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xT)))) | aElement0(szDzizrdt0(xd)) | (~aElementOf0(szDzizrdt0(xd), xT))),
% 71.54/45.80 inference(modus_ponens,[status(thm)],[45, 44])).
% 71.54/45.80 tff(47,plain,
% 71.54/45.80 (aElement0(szDzizrdt0(xd))),
% 71.54/45.80 inference(unit_resolution,[status(thm)],[46, 43, 39])).
% 71.54/45.80 tff(48,plain,
% 71.54/45.80 (aFunction0(xd) <=> aFunction0(xd)),
% 71.54/45.80 inference(rewrite,[status(thm)],[])).
% 71.54/45.80 tff(49,plain,
% 71.54/45.80 (aFunction0(xd)),
% 71.54/45.80 inference(and_elim,[status(thm)],[4])).
% 71.54/45.80 tff(50,plain,
% 71.54/45.80 (aFunction0(xd)),
% 71.54/45.80 inference(modus_ponens,[status(thm)],[49, 48])).
% 71.54/45.80 tff(51,plain,
% 71.54/45.80 (^[W0: $i, W1: $i] : refl((aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)) | (~aElement0(W1)) | (~aFunction0(W0))) <=> (aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)) | (~aElement0(W1)) | (~aFunction0(W0))))),
% 71.54/45.80 inference(bind,[status(th)],[])).
% 71.54/45.80 tff(52,plain,
% 71.54/45.80 (![W0: $i, W1: $i] : (aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)) | (~aElement0(W1)) | (~aFunction0(W0))) <=> ![W0: $i, W1: $i] : (aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)) | (~aElement0(W1)) | (~aFunction0(W0)))),
% 71.54/45.80 inference(quant_intro,[status(thm)],[51])).
% 71.54/45.80 tff(53,plain,
% 71.54/45.80 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aFunction0(W0) & aElement0(W1)) <=> (~((~aElement0(W1)) | (~aFunction0(W0))))), ((~(aFunction0(W0) & aElement0(W1))) <=> (~(~((~aElement0(W1)) | (~aFunction0(W0))))))), rewrite((~(~((~aElement0(W1)) | (~aFunction0(W0))))) <=> ((~aElement0(W1)) | (~aFunction0(W0)))), ((~(aFunction0(W0) & aElement0(W1))) <=> ((~aElement0(W1)) | (~aFunction0(W0))))), (((~(aFunction0(W0) & aElement0(W1))) | aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0))) <=> (((~aElement0(W1)) | (~aFunction0(W0))) | aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0))))), rewrite((((~aElement0(W1)) | (~aFunction0(W0))) | aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0))) <=> (aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)) | (~aElement0(W1)) | (~aFunction0(W0)))), (((~(aFunction0(W0) & aElement0(W1))) | aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0))) <=> (aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)) | (~aElement0(W1)) | (~aFunction0(W0)))))),
% 71.54/45.80 inference(bind,[status(th)],[])).
% 71.54/45.80 tff(54,plain,
% 71.54/45.80 (![W0: $i, W1: $i] : ((~(aFunction0(W0) & aElement0(W1))) | aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0))) <=> ![W0: $i, W1: $i] : (aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)) | (~aElement0(W1)) | (~aFunction0(W0)))),
% 71.54/45.80 inference(quant_intro,[status(thm)],[53])).
% 71.54/45.80 tff(55,plain,
% 71.54/45.80 (![W0: $i, W1: $i] : ((~(aFunction0(W0) & aElement0(W1))) | aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0))) <=> ![W0: $i, W1: $i] : ((~(aFunction0(W0) & aElement0(W1))) | aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)))),
% 71.54/45.80 inference(rewrite,[status(thm)],[])).
% 71.54/45.80 tff(56,plain,
% 71.54/45.80 (^[W0: $i, W1: $i] : rewrite(((aFunction0(W0) & aElement0(W1)) => aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0))) <=> ((~(aFunction0(W0) & aElement0(W1))) | aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0))))),
% 71.54/45.80 inference(bind,[status(th)],[])).
% 71.54/45.80 tff(57,plain,
% 71.54/45.80 (![W0: $i, W1: $i] : ((aFunction0(W0) & aElement0(W1)) => aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0))) <=> ![W0: $i, W1: $i] : ((~(aFunction0(W0) & aElement0(W1))) | aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)))),
% 71.54/45.80 inference(quant_intro,[status(thm)],[56])).
% 71.54/45.80 tff(58,axiom,(![W0: $i, W1: $i] : ((aFunction0(W0) & aElement0(W1)) => aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mPttSet')).
% 71.54/45.80 tff(59,plain,
% 71.54/45.80 (![W0: $i, W1: $i] : ((~(aFunction0(W0) & aElement0(W1))) | aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)))),
% 71.54/45.80 inference(modus_ponens,[status(thm)],[58, 57])).
% 71.54/45.80 tff(60,plain,
% 71.54/45.80 (![W0: $i, W1: $i] : ((~(aFunction0(W0) & aElement0(W1))) | aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)))),
% 71.54/45.80 inference(modus_ponens,[status(thm)],[59, 55])).
% 71.54/45.80 tff(61,plain,(
% 71.54/45.80 ![W0: $i, W1: $i] : ((~(aFunction0(W0) & aElement0(W1))) | aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)))),
% 71.54/45.80 inference(skolemize,[status(sab)],[60])).
% 71.54/45.80 tff(62,plain,
% 71.54/45.80 (![W0: $i, W1: $i] : (aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)) | (~aElement0(W1)) | (~aFunction0(W0)))),
% 71.54/45.80 inference(modus_ponens,[status(thm)],[61, 54])).
% 71.54/45.80 tff(63,plain,
% 71.54/45.80 (![W0: $i, W1: $i] : (aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)) | (~aElement0(W1)) | (~aFunction0(W0)))),
% 71.54/45.80 inference(modus_ponens,[status(thm)],[62, 52])).
% 71.54/45.80 tff(64,plain,
% 71.54/45.80 (((~![W0: $i, W1: $i] : (aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)) | (~aElement0(W1)) | (~aFunction0(W0)))) | ((~aFunction0(xd)) | (~aElement0(szDzizrdt0(xd))) | aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xd)))) <=> ((~![W0: $i, W1: $i] : (aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)) | (~aElement0(W1)) | (~aFunction0(W0)))) | (~aFunction0(xd)) | (~aElement0(szDzizrdt0(xd))) | aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xd)))),
% 71.54/45.80 inference(rewrite,[status(thm)],[])).
% 71.54/45.80 tff(65,plain,
% 71.54/45.80 ((aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xd)) | (~aElement0(szDzizrdt0(xd))) | (~aFunction0(xd))) <=> ((~aFunction0(xd)) | (~aElement0(szDzizrdt0(xd))) | aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xd)))),
% 71.54/45.80 inference(rewrite,[status(thm)],[])).
% 71.54/45.80 tff(66,plain,
% 71.54/45.80 (((~![W0: $i, W1: $i] : (aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)) | (~aElement0(W1)) | (~aFunction0(W0)))) | (aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xd)) | (~aElement0(szDzizrdt0(xd))) | (~aFunction0(xd)))) <=> ((~![W0: $i, W1: $i] : (aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)) | (~aElement0(W1)) | (~aFunction0(W0)))) | ((~aFunction0(xd)) | (~aElement0(szDzizrdt0(xd))) | aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xd))))),
% 71.54/45.80 inference(monotonicity,[status(thm)],[65])).
% 71.54/45.80 tff(67,plain,
% 71.54/45.80 (((~![W0: $i, W1: $i] : (aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)) | (~aElement0(W1)) | (~aFunction0(W0)))) | (aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xd)) | (~aElement0(szDzizrdt0(xd))) | (~aFunction0(xd)))) <=> ((~![W0: $i, W1: $i] : (aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)) | (~aElement0(W1)) | (~aFunction0(W0)))) | (~aFunction0(xd)) | (~aElement0(szDzizrdt0(xd))) | aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xd)))),
% 71.54/45.80 inference(transitivity,[status(thm)],[66, 64])).
% 71.54/45.80 tff(68,plain,
% 71.54/45.80 ((~![W0: $i, W1: $i] : (aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)) | (~aElement0(W1)) | (~aFunction0(W0)))) | (aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xd)) | (~aElement0(szDzizrdt0(xd))) | (~aFunction0(xd)))),
% 71.54/45.80 inference(quant_inst,[status(thm)],[])).
% 71.54/45.80 tff(69,plain,
% 71.54/45.80 ((~![W0: $i, W1: $i] : (aSubsetOf0(sdtlbdtrb0(W0, W1), szDzozmdt0(W0)) | (~aElement0(W1)) | (~aFunction0(W0)))) | (~aFunction0(xd)) | (~aElement0(szDzizrdt0(xd))) | aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xd))),
% 71.54/45.80 inference(modus_ponens,[status(thm)],[68, 67])).
% 71.54/45.80 tff(70,plain,
% 71.54/45.80 ((~aElement0(szDzizrdt0(xd))) | aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xd))),
% 71.54/45.80 inference(unit_resolution,[status(thm)],[69, 63, 50])).
% 71.54/45.80 tff(71,plain,
% 71.54/45.80 (aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xd))),
% 71.54/45.80 inference(unit_resolution,[status(thm)],[70, 47])).
% 71.54/45.80 tff(72,plain,
% 71.54/45.80 (aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xe))),
% 71.54/45.80 inference(modus_ponens,[status(thm)],[71, 18])).
% 71.54/45.80 tff(73,plain,
% 71.54/45.80 (aFunction0(xe) <=> aFunction0(xe)),
% 71.54/45.80 inference(rewrite,[status(thm)],[])).
% 71.54/45.80 tff(74,plain,
% 71.54/45.80 (aFunction0(xe)),
% 71.54/45.80 inference(and_elim,[status(thm)],[12])).
% 71.54/45.80 tff(75,plain,
% 71.54/45.80 (aFunction0(xe)),
% 71.54/45.80 inference(modus_ponens,[status(thm)],[74, 73])).
% 71.54/45.80 tff(76,plain,
% 71.54/45.80 (^[W0: $i] : rewrite(((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3)))))))))))) | (~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))))))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))) | (~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3)))))))))))))))))),
% 71.54/45.80 inference(bind,[status(th)],[])).
% 71.54/45.80 tff(77,plain,
% 71.54/45.80 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3)))))))))))) | (~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))))))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))) | (~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3))))))))))))))))),
% 71.54/45.81 inference(quant_intro,[status(thm)],[76])).
% 71.54/45.81 tff(78,plain,
% 71.54/45.81 (^[W0: $i] : refl(((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3)))))))))))) | (~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))))))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3)))))))))))) | (~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))))))))),
% 71.54/45.81 inference(bind,[status(th)],[])).
% 71.54/45.81 tff(79,plain,
% 71.54/45.81 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3)))))))))))) | (~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))))))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3)))))))))))) | (~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0))))))))))))))),
% 71.54/45.81 inference(quant_intro,[status(thm)],[78])).
% 71.54/45.81 tff(80,plain,
% 71.54/45.81 (^[W0: $i] : rewrite(((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3)))))))))))) | (~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))))))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3)))))))))))) | (~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))))))))),
% 71.54/45.81 inference(bind,[status(th)],[])).
% 71.54/45.81 tff(81,plain,
% 71.54/45.81 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3)))))))))))) | (~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))))))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3)))))))))))) | (~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0))))))))))))))),
% 71.54/45.81 inference(quant_intro,[status(thm)],[80])).
% 71.54/45.81 tff(82,plain,
% 71.54/45.81 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3)))))))))))) | (~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))))))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3)))))))))))) | (~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0))))))))))))))),
% 71.54/45.81 inference(transitivity,[status(thm)],[81, 79])).
% 71.54/45.81 tff(83,plain,
% 71.54/45.81 (^[W0: $i] : rewrite(((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (((~(W2 = sdtlcdtrc0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (((~aElementOf0(W3, W2)) | (aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1) & (sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3))) & (aElementOf0(W3, W2) | ![W4: $i] : (~(aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3))))))) & ((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | ((aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1) & (sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0)))) & ((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : (~(aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3)))))))))))) | (~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))))))))),
% 71.54/45.81 inference(bind,[status(th)],[])).
% 71.54/45.81 tff(84,plain,
% 71.54/45.81 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (((~(W2 = sdtlcdtrc0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (((~aElementOf0(W3, W2)) | (aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1) & (sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3))) & (aElementOf0(W3, W2) | ![W4: $i] : (~(aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3))))))) & ((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | ((aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1) & (sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0)))) & ((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : (~(aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3)))))))))))) | (~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0))))))))))))))),
% 71.54/45.81 inference(quant_intro,[status(thm)],[83])).
% 71.54/45.81 tff(85,plain,
% 71.54/45.81 (^[W0: $i] : rewrite(((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (((~(W2 = sdtlcdtrc0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (((~aElementOf0(W3, W2)) | (aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1) & (sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3))) & (aElementOf0(W3, W2) | ![W4: $i] : (~(aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3))))))) & ((W2 = sdtlcdtrc0(W0, W1)) | ((~aSet0(W2)) | ((aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1) & (sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0)))) & ((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : (~(aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0))))))))))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (((~(W2 = sdtlcdtrc0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (((~aElementOf0(W3, W2)) | (aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1) & (sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3))) & (aElementOf0(W3, W2) | ![W4: $i] : (~(aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3))))))) & ((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | ((aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1) & (sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0)))) & ((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : (~(aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))))),
% 71.54/45.81 inference(bind,[status(th)],[])).
% 71.54/45.81 tff(86,plain,
% 71.54/45.81 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (((~(W2 = sdtlcdtrc0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (((~aElementOf0(W3, W2)) | (aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1) & (sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3))) & (aElementOf0(W3, W2) | ![W4: $i] : (~(aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3))))))) & ((W2 = sdtlcdtrc0(W0, W1)) | ((~aSet0(W2)) | ((aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1) & (sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0)))) & ((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : (~(aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0))))))))))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (((~(W2 = sdtlcdtrc0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (((~aElementOf0(W3, W2)) | (aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1) & (sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3))) & (aElementOf0(W3, W2) | ![W4: $i] : (~(aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3))))))) & ((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | ((aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1) & (sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0)))) & ((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : (~(aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0))))))))))),
% 71.54/45.81 inference(quant_intro,[status(thm)],[85])).
% 71.54/45.81 tff(87,plain,
% 71.54/45.81 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : ((W2 = sdtlcdtrc0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ?[W4: $i] : (aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3))))))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : ((W2 = sdtlcdtrc0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ?[W4: $i] : (aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3)))))))),
% 71.54/45.81 inference(rewrite,[status(thm)],[])).
% 71.54/45.81 tff(88,plain,
% 71.54/45.81 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aSubsetOf0(W1, szDzozmdt0(W0)) => ![W2: $i] : ((W2 = sdtlcdtrc0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ?[W4: $i] : (aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3)))))) <=> ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : ((W2 = sdtlcdtrc0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ?[W4: $i] : (aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3)))))))), (![W1: $i] : (aSubsetOf0(W1, szDzozmdt0(W0)) => ![W2: $i] : ((W2 = sdtlcdtrc0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ?[W4: $i] : (aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3)))))) <=> ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : ((W2 = sdtlcdtrc0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ?[W4: $i] : (aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3)))))))), ((aFunction0(W0) => ![W1: $i] : (aSubsetOf0(W1, szDzozmdt0(W0)) => ![W2: $i] : ((W2 = sdtlcdtrc0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ?[W4: $i] : (aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3))))))) <=> (aFunction0(W0) => ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : ((W2 = sdtlcdtrc0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ?[W4: $i] : (aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3))))))))), rewrite((aFunction0(W0) => ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : ((W2 = sdtlcdtrc0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ?[W4: $i] : (aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3))))))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : ((W2 = sdtlcdtrc0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ?[W4: $i] : (aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3)))))))), ((aFunction0(W0) => ![W1: $i] : (aSubsetOf0(W1, szDzozmdt0(W0)) => ![W2: $i] : ((W2 = sdtlcdtrc0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ?[W4: $i] : (aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3))))))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : ((W2 = sdtlcdtrc0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ?[W4: $i] : (aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3)))))))))),
% 71.54/45.81 inference(bind,[status(th)],[])).
% 71.54/45.81 tff(89,plain,
% 71.54/45.81 (![W0: $i] : (aFunction0(W0) => ![W1: $i] : (aSubsetOf0(W1, szDzozmdt0(W0)) => ![W2: $i] : ((W2 = sdtlcdtrc0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ?[W4: $i] : (aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3))))))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : ((W2 = sdtlcdtrc0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ?[W4: $i] : (aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3)))))))),
% 71.54/45.81 inference(quant_intro,[status(thm)],[88])).
% 71.54/45.81 tff(90,axiom,(![W0: $i] : (aFunction0(W0) => ![W1: $i] : (aSubsetOf0(W1, szDzozmdt0(W0)) => ![W2: $i] : ((W2 = sdtlcdtrc0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ?[W4: $i] : (aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefSImg')).
% 71.54/45.81 tff(91,plain,
% 71.54/45.81 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : ((W2 = sdtlcdtrc0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ?[W4: $i] : (aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3)))))))),
% 71.54/45.81 inference(modus_ponens,[status(thm)],[90, 89])).
% 71.54/45.81 tff(92,plain,
% 71.54/45.81 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : ((W2 = sdtlcdtrc0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ?[W4: $i] : (aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3)))))))),
% 71.54/45.81 inference(modus_ponens,[status(thm)],[91, 87])).
% 71.54/45.81 tff(93,plain,(
% 71.54/45.81 ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (((~(W2 = sdtlcdtrc0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (((~aElementOf0(W3, W2)) | (aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1) & (sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3))) & (aElementOf0(W3, W2) | ![W4: $i] : (~(aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3))))))) & ((W2 = sdtlcdtrc0(W0, W1)) | ((~aSet0(W2)) | ((aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1) & (sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0)))) & ((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : (~(aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))))),
% 71.54/45.81 inference(skolemize,[status(sab)],[92])).
% 71.54/45.81 tff(94,plain,
% 71.54/45.81 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (((~(W2 = sdtlcdtrc0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (((~aElementOf0(W3, W2)) | (aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1) & (sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3))) & (aElementOf0(W3, W2) | ![W4: $i] : (~(aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = W3))))))) & ((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | ((aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1) & (sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0)))) & ((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : (~(aElementOf0(W4, W1) & (sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0))))))))))),
% 71.54/45.81 inference(modus_ponens,[status(thm)],[93, 86])).
% 71.54/45.81 tff(95,plain,
% 71.54/45.81 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3)))))))))))) | (~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0))))))))))))))),
% 71.54/45.81 inference(modus_ponens,[status(thm)],[94, 84])).
% 71.54/45.81 tff(96,plain,
% 71.54/45.81 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3)))))))))))) | (~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0))))))))))))))),
% 71.54/45.81 inference(modus_ponens,[status(thm)],[95, 82])).
% 71.54/45.81 tff(97,plain,
% 71.54/45.81 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))) | (~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3))))))))))))))))),
% 71.54/45.81 inference(modus_ponens,[status(thm)],[96, 77])).
% 71.54/45.81 tff(98,plain,
% 71.54/45.81 (((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))) | (~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3))))))))))))))))) | ((~aFunction0(xe)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(xe))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, W1)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, W1, xe)) = tptp_fun_W3_14(W2, W1, xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, W1, xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, W1, xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))))))))) <=> ((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))) | (~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3))))))))))))))))) | (~aFunction0(xe)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(xe))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, W1)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, W1, xe)) = tptp_fun_W3_14(W2, W1, xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, W1, xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, W1, xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))))))))),
% 71.54/45.81 inference(rewrite,[status(thm)],[])).
% 71.54/45.81 tff(99,plain,
% 71.54/45.81 (((~aFunction0(xe)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(xe))) | ![W2: $i] : (~((~((W2 = sdtlcdtrc0(xe, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, W1, xe)) = tptp_fun_W3_14(W2, W1, xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, W1, xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, W1, xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = W3)))))))))))))))) <=> ((~aFunction0(xe)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(xe))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, W1)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, W1, xe)) = tptp_fun_W3_14(W2, W1, xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, W1, xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, W1, xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))))))))),
% 71.54/45.81 inference(rewrite,[status(thm)],[])).
% 71.54/45.81 tff(100,plain,
% 71.54/45.81 (((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))) | (~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3))))))))))))))))) | ((~aFunction0(xe)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(xe))) | ![W2: $i] : (~((~((W2 = sdtlcdtrc0(xe, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, W1, xe)) = tptp_fun_W3_14(W2, W1, xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, W1, xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, W1, xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))))))))) <=> ((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))) | (~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3))))))))))))))))) | ((~aFunction0(xe)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(xe))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, W1)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, W1, xe)) = tptp_fun_W3_14(W2, W1, xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, W1, xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, W1, xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = W3)))))))))))))))))),
% 71.54/45.81 inference(monotonicity,[status(thm)],[99])).
% 71.54/45.81 tff(101,plain,
% 71.54/45.81 (((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))) | (~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3))))))))))))))))) | ((~aFunction0(xe)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(xe))) | ![W2: $i] : (~((~((W2 = sdtlcdtrc0(xe, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, W1, xe)) = tptp_fun_W3_14(W2, W1, xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, W1, xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, W1, xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))))))))) <=> ((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))) | (~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3))))))))))))))))) | (~aFunction0(xe)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(xe))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, W1)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, W1, xe)) = tptp_fun_W3_14(W2, W1, xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, W1, xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, W1, xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))))))))),
% 71.54/45.81 inference(transitivity,[status(thm)],[100, 98])).
% 71.54/45.81 tff(102,plain,
% 71.54/45.81 ((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))) | (~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3))))))))))))))))) | ((~aFunction0(xe)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(xe))) | ![W2: $i] : (~((~((W2 = sdtlcdtrc0(xe, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, W1, xe)) = tptp_fun_W3_14(W2, W1, xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, W1, xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, W1, xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))))))))),
% 71.54/45.81 inference(quant_inst,[status(thm)],[])).
% 71.54/45.81 tff(103,plain,
% 71.54/45.81 ((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(W0))) | ![W2: $i] : (~((~((W2 = sdtlcdtrc0(W0, W1)) | (~aSet0(W2)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_15(W2, W1, W0)) = tptp_fun_W3_14(W2, W1, W0))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, W0), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = tptp_fun_W3_14(W2, W1, W0)))))))))) | (~((~(W2 = sdtlcdtrc0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, W0), W1)) | (~(sdtlpdtrp0(W0, tptp_fun_W4_13(W3, W1, W0)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(W0, W4) = W3))))))))))))))))) | (~aFunction0(xe)) | ![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(xe))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, W1)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, W1, xe)) = tptp_fun_W3_14(W2, W1, xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, W1, xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, W1, xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = W3)))))))))))))))),
% 71.54/45.81 inference(modus_ponens,[status(thm)],[102, 101])).
% 71.54/45.81 tff(104,plain,
% 71.54/45.81 (![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(xe))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, W1)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, W1, xe)) = tptp_fun_W3_14(W2, W1, xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, W1, xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, W1, xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = W3)))))))))))))))),
% 71.54/45.81 inference(unit_resolution,[status(thm)],[103, 97, 75])).
% 71.54/45.81 tff(105,plain,
% 71.54/45.81 (((~![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(xe))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, W1)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, W1, xe)) = tptp_fun_W3_14(W2, W1, xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, W1, xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, W1, xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = W3)))))))))))))))) | ((~aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xe))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3)))))))))))))))) <=> ((~![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(xe))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, W1)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, W1, xe)) = tptp_fun_W3_14(W2, W1, xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, W1, xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, W1, xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = W3)))))))))))))))) | (~aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xe))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3)))))))))))))))),
% 71.54/45.82 inference(rewrite,[status(thm)],[])).
% 71.54/45.82 tff(106,plain,
% 71.54/45.82 ((~![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(xe))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, W1)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, W1, xe)) = tptp_fun_W3_14(W2, W1, xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, W1, xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, W1, xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = W3)))))))))))))))) | ((~aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xe))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3)))))))))))))))),
% 71.54/45.82 inference(quant_inst,[status(thm)],[])).
% 71.54/45.82 tff(107,plain,
% 71.54/45.82 ((~![W1: $i] : ((~aSubsetOf0(W1, szDzozmdt0(xe))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, W1)) | (~((~(aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, W1, xe)) = tptp_fun_W3_14(W2, W1, xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, W1, xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, W1, xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, W1, xe), W1)) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, W1, xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, W1)) | (~(sdtlpdtrp0(xe, W4) = W3)))))))))))))))) | (~aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xe))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))))))),
% 71.54/45.82 inference(modus_ponens,[status(thm)],[106, 105])).
% 71.54/45.82 tff(108,plain,
% 71.54/45.82 ((~aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xe))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))))))),
% 71.54/45.82 inference(unit_resolution,[status(thm)],[107, 104])).
% 71.54/45.82 tff(109,plain,
% 71.54/45.82 (![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))))))),
% 71.54/45.82 inference(unit_resolution,[status(thm)],[108, 72])).
% 71.54/45.82 tff(110,plain,
% 71.54/45.82 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))))))) | (~((~aSet0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~![W3: $i] : (~((~((~aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))))))) | (~((~aSet0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~![W3: $i] : (~((~((~aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3)))))))))))),
% 71.54/45.82 inference(rewrite,[status(thm)],[])).
% 71.54/45.82 tff(111,plain,
% 71.54/45.82 ((~((~((~aSet0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))) = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~aElementOf0(tptp_fun_W4_15(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = tptp_fun_W3_14(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)))))))))) | (~((~(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))) = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aSet0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~![W3: $i] : (~((~((~aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3)))))))))))))) <=> (~((~aSet0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~![W3: $i] : (~((~((~aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))),
% 71.54/45.82 inference(rewrite,[status(thm)],[])).
% 71.54/45.82 tff(112,plain,
% 71.54/45.82 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))))))) | (~((~((~aSet0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))) = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~aElementOf0(tptp_fun_W4_15(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = tptp_fun_W3_14(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)))))))))) | (~((~(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))) = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aSet0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~![W3: $i] : (~((~((~aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))))))) | (~((~aSet0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~![W3: $i] : (~((~((~aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3)))))))))))),
% 71.54/45.82 inference(monotonicity,[status(thm)],[111])).
% 71.54/45.82 tff(113,plain,
% 71.54/45.82 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))))))) | (~((~((~aSet0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))) = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~aElementOf0(tptp_fun_W4_15(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = tptp_fun_W3_14(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)))))))))) | (~((~(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))) = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aSet0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~![W3: $i] : (~((~((~aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))))))) | (~((~aSet0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~![W3: $i] : (~((~((~aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3)))))))))))),
% 71.54/45.82 inference(transitivity,[status(thm)],[112, 110])).
% 71.54/45.82 tff(114,plain,
% 71.54/45.82 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))))))) | (~((~((~aSet0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))) = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~aElementOf0(tptp_fun_W4_15(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = tptp_fun_W3_14(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))), sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)))))))))) | (~((~(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))) = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aSet0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~![W3: $i] : (~((~((~aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))))))),
% 71.54/45.83 inference(quant_inst,[status(thm)],[])).
% 71.54/45.83 tff(115,plain,
% 71.54/45.83 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2) | (~((~aElementOf0(tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_15(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe))))))) | (~((~aElementOf0(tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), W2)) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = tptp_fun_W3_14(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)))))))))) | (~((~(W2 = sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aSet0(W2)) | (~![W3: $i] : (~((~((~aElementOf0(W3, W2)) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, W2) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))))))) | (~((~aSet0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~![W3: $i] : (~((~((~aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3))))))))))),
% 71.54/45.83 inference(modus_ponens,[status(thm)],[114, 113])).
% 71.54/45.83 tff(116,plain,
% 71.54/45.83 (~((~aSet0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~![W3: $i] : (~((~((~aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3)))))))))),
% 71.54/45.83 inference(unit_resolution,[status(thm)],[115, 109])).
% 71.54/45.83 tff(117,plain,
% 71.54/45.83 (((~aSet0(sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~![W3: $i] : (~((~((~aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3))))))))) | ![W3: $i] : (~((~((~aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3)))))))),
% 71.54/45.83 inference(tautology,[status(thm)],[])).
% 71.54/45.83 tff(118,plain,
% 71.54/45.83 (![W3: $i] : (~((~((~aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3)))))))),
% 71.54/45.83 inference(unit_resolution,[status(thm)],[117, 116])).
% 71.54/45.83 tff(119,plain,
% 71.54/45.83 ((~![W3: $i] : (~((~((~aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W3, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W3)))))) | (~(aElementOf0(W3, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W3)))))))) | (~((~((~aElementOf0(W0!24, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W0!24)))))) | (~(aElementOf0(W0!24, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W0!24)))))))),
% 71.54/45.83 inference(quant_inst,[status(thm)],[])).
% 71.54/45.83 tff(120,plain,
% 71.54/45.83 (~((~((~aElementOf0(W0!24, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W0!24)))))) | (~(aElementOf0(W0!24, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W0!24))))))),
% 71.54/45.83 inference(unit_resolution,[status(thm)],[119, 118])).
% 71.54/45.83 tff(121,plain,
% 71.54/45.83 (((~((~aElementOf0(W0!24, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W0!24)))))) | (~(aElementOf0(W0!24, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | ![W4: $i] : ((~aElementOf0(W4, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W4) = W0!24)))))) | ((~aElementOf0(W0!24, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W0!24)))))),
% 71.54/45.83 inference(tautology,[status(thm)],[])).
% 71.54/45.83 tff(122,plain,
% 71.54/45.83 ((~aElementOf0(W0!24, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W0!24))))),
% 71.54/45.83 inference(unit_resolution,[status(thm)],[121, 120])).
% 71.54/45.83 tff(123,plain,
% 71.54/45.83 (((~(~aElementOf0(W0!24, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) & ![W1: $i] : (~(aElementOf0(W1, szDzozmdt0(xN)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0!24)))) <=> (aElementOf0(W0!24, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & ![W1: $i] : (~(aElementOf0(W1, szDzozmdt0(xN)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0!24))))),
% 71.54/45.83 inference(rewrite,[status(thm)],[])).
% 71.54/45.83 tff(124,plain,
% 71.54/45.83 ((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xN)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))) <=> (~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xN)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))))),
% 71.54/45.83 inference(rewrite,[status(thm)],[])).
% 71.54/45.83 tff(125,plain,
% 71.54/45.83 ((~![W0: $i] : ((~aElementOf0(W0, xO)) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))) <=> (~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xN)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))))),
% 71.54/45.83 inference(rewrite,[status(thm)],[])).
% 71.54/45.83 tff(126,plain,
% 71.54/45.83 ((~![W0: $i] : ((~aElementOf0(W0, xO)) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))) <=> (~![W0: $i] : ((~aElementOf0(W0, xO)) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))))),
% 71.54/45.83 inference(rewrite,[status(thm)],[])).
% 71.54/45.83 tff(127,plain,
% 71.54/45.83 ((~![W0: $i] : (aElementOf0(W0, xO) => ?[W1: $i] : ((aElementOf0(W1, szNzAzT0) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0)))) <=> (~![W0: $i] : ((~aElementOf0(W0, xO)) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0))))),
% 71.54/45.83 inference(rewrite,[status(thm)],[])).
% 71.54/45.83 tff(128,axiom,(~![W0: $i] : (aElementOf0(W0, xO) => ?[W1: $i] : ((aElementOf0(W1, szNzAzT0) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 71.54/45.83 tff(129,plain,
% 71.54/45.83 (~![W0: $i] : ((~aElementOf0(W0, xO)) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))),
% 71.54/45.83 inference(modus_ponens,[status(thm)],[128, 127])).
% 71.54/45.83 tff(130,plain,
% 71.54/45.83 (~![W0: $i] : ((~aElementOf0(W0, xO)) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))),
% 71.54/45.83 inference(modus_ponens,[status(thm)],[129, 126])).
% 71.54/45.83 tff(131,plain,
% 71.54/45.83 (~![W0: $i] : ((~aElementOf0(W0, xO)) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))),
% 71.54/45.83 inference(modus_ponens,[status(thm)],[130, 126])).
% 71.54/45.83 tff(132,plain,
% 71.54/45.83 (~![W0: $i] : ((~aElementOf0(W0, xO)) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))),
% 71.54/45.83 inference(modus_ponens,[status(thm)],[131, 126])).
% 71.54/45.83 tff(133,plain,
% 71.54/45.83 (~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xN)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))),
% 71.54/45.83 inference(modus_ponens,[status(thm)],[132, 125])).
% 71.54/45.83 tff(134,plain,
% 71.54/45.83 (~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xN)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))),
% 71.54/45.83 inference(modus_ponens,[status(thm)],[133, 124])).
% 71.54/45.83 tff(135,plain,
% 71.54/45.83 (~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xN)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))),
% 71.54/45.83 inference(modus_ponens,[status(thm)],[134, 124])).
% 71.54/45.83 tff(136,plain,
% 71.54/45.83 (~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xN)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)))),
% 71.54/45.83 inference(modus_ponens,[status(thm)],[135, 124])).
% 71.54/45.83 tff(137,plain,
% 71.54/45.83 (aElementOf0(W0!24, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & ![W1: $i] : (~(aElementOf0(W1, szDzozmdt0(xN)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0!24)))),
% 71.54/45.83 inference(modus_ponens,[status(thm)],[136, 123])).
% 71.54/45.83 tff(138,plain,
% 71.54/45.83 (aElementOf0(W0!24, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))),
% 71.54/45.83 inference(and_elim,[status(thm)],[137])).
% 71.54/45.83 tff(139,plain,
% 71.54/45.83 ((~((~aElementOf0(W0!24, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W0!24)))))) | (~aElementOf0(W0!24, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W0!24))))),
% 71.54/45.83 inference(tautology,[status(thm)],[])).
% 71.54/45.83 tff(140,plain,
% 71.54/45.83 ((~((~aElementOf0(W0!24, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~((~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W0!24)))))) | (~((~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W0!24))))),
% 71.54/45.83 inference(unit_resolution,[status(thm)],[139, 138])).
% 71.54/45.83 tff(141,plain,
% 71.54/45.83 (~((~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W0!24)))),
% 71.54/45.83 inference(unit_resolution,[status(thm)],[140, 122])).
% 71.54/45.83 tff(142,plain,
% 71.54/45.83 (((~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W0!24))) | aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))),
% 71.54/45.83 inference(tautology,[status(thm)],[])).
% 71.54/45.83 tff(143,plain,
% 71.54/45.83 (aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))),
% 71.54/45.83 inference(unit_resolution,[status(thm)],[142, 141])).
% 71.54/45.83 tff(144,plain,
% 71.54/45.83 (aSet0(szNzAzT0) <=> aSet0(szDzozmdt0(xN))),
% 71.54/45.83 inference(rewrite,[status(thm)],[])).
% 71.54/45.83 tff(145,plain,
% 71.54/45.83 (aSet0(szNzAzT0) <=> aSet0(szNzAzT0)),
% 71.54/45.83 inference(rewrite,[status(thm)],[])).
% 71.54/45.83 tff(146,axiom,(aSet0(szNzAzT0) & isCountable0(szNzAzT0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mNATSet')).
% 71.54/45.83 tff(147,plain,
% 71.54/45.83 (aSet0(szNzAzT0)),
% 71.54/45.83 inference(and_elim,[status(thm)],[146])).
% 71.54/45.83 tff(148,plain,
% 71.54/45.83 (aSet0(szNzAzT0)),
% 71.54/45.83 inference(modus_ponens,[status(thm)],[147, 145])).
% 71.54/45.83 tff(149,plain,
% 71.54/45.83 (aSet0(szDzozmdt0(xN))),
% 71.54/45.83 inference(modus_ponens,[status(thm)],[148, 144])).
% 71.54/45.83 tff(150,plain,
% 71.54/45.83 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))))))))),
% 71.54/45.83 inference(bind,[status(th)],[])).
% 71.54/45.83 tff(151,plain,
% 71.54/45.83 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 71.54/45.83 inference(quant_intro,[status(thm)],[150])).
% 71.54/45.83 tff(152,plain,
% 71.54/45.83 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 71.54/45.83 inference(bind,[status(th)],[])).
% 71.54/45.83 tff(153,plain,
% 71.54/45.83 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 71.54/45.83 inference(quant_intro,[status(thm)],[152])).
% 71.54/45.83 tff(154,plain,
% 71.54/45.83 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 71.54/45.83 inference(bind,[status(th)],[])).
% 71.54/45.83 tff(155,plain,
% 71.54/45.83 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 71.54/45.83 inference(quant_intro,[status(thm)],[154])).
% 71.54/45.83 tff(156,plain,
% 71.54/45.83 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 71.54/45.83 inference(transitivity,[status(thm)],[155, 153])).
% 71.54/45.83 tff(157,plain,
% 71.54/45.83 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 71.54/45.83 inference(bind,[status(th)],[])).
% 71.54/45.83 tff(158,plain,
% 71.54/45.83 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 71.54/45.83 inference(quant_intro,[status(thm)],[157])).
% 71.54/45.83 tff(159,plain,
% 71.54/45.83 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))),
% 71.54/45.83 inference(bind,[status(th)],[])).
% 71.54/45.83 tff(160,plain,
% 71.54/45.83 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))),
% 71.54/45.83 inference(quant_intro,[status(thm)],[159])).
% 71.54/45.83 tff(161,plain,
% 71.54/45.83 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 71.54/45.83 inference(rewrite,[status(thm)],[])).
% 71.54/45.83 tff(162,plain,
% 71.54/45.83 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))) <=> (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), (![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))) <=> ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), ((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))), rewrite((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))) <=> ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), ((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))))),
% 71.54/45.83 inference(bind,[status(th)],[])).
% 71.54/45.83 tff(163,plain,
% 71.54/45.83 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 71.54/45.83 inference(quant_intro,[status(thm)],[162])).
% 71.54/45.83 tff(164,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefSub')).
% 71.54/45.83 tff(165,plain,
% 71.54/45.83 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 71.54/45.83 inference(modus_ponens,[status(thm)],[164, 163])).
% 71.54/45.83 tff(166,plain,
% 71.54/45.83 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 71.54/45.83 inference(modus_ponens,[status(thm)],[165, 161])).
% 71.54/45.83 tff(167,plain,(
% 71.54/45.83 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))),
% 71.54/45.83 inference(skolemize,[status(sab)],[166])).
% 71.54/45.83 tff(168,plain,
% 71.54/45.83 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))),
% 71.54/45.83 inference(modus_ponens,[status(thm)],[167, 160])).
% 71.54/45.83 tff(169,plain,
% 71.54/45.83 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 71.54/45.83 inference(modus_ponens,[status(thm)],[168, 158])).
% 71.54/45.83 tff(170,plain,
% 71.54/45.83 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 71.54/45.83 inference(modus_ponens,[status(thm)],[169, 156])).
% 71.54/45.83 tff(171,plain,
% 71.54/45.83 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 71.54/45.83 inference(modus_ponens,[status(thm)],[170, 151])).
% 71.54/45.83 tff(172,plain,
% 71.54/45.83 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, szDzozmdt0(xN)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), W1)) | aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), szDzozmdt0(xN)))))) | (~((~aSubsetOf0(W1, szDzozmdt0(xN))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szDzozmdt0(xN)))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, szDzozmdt0(xN)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), W1)) | aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), szDzozmdt0(xN)))))) | (~((~aSubsetOf0(W1, szDzozmdt0(xN))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szDzozmdt0(xN)))))))))))),
% 71.54/45.83 inference(rewrite,[status(thm)],[])).
% 71.54/45.83 tff(173,plain,
% 71.54/45.83 (((~aSet0(szDzozmdt0(xN))) | ![W1: $i] : (~((~(aSubsetOf0(W1, szDzozmdt0(xN)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), W1)) | aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), szDzozmdt0(xN)))))) | (~((~aSubsetOf0(W1, szDzozmdt0(xN))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szDzozmdt0(xN))))))))))) <=> ((~aSet0(szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, szDzozmdt0(xN)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), W1)) | aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), szDzozmdt0(xN)))))) | (~((~aSubsetOf0(W1, szDzozmdt0(xN))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szDzozmdt0(xN)))))))))))),
% 71.54/45.83 inference(rewrite,[status(thm)],[])).
% 71.54/45.83 tff(174,plain,
% 71.54/45.83 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(szDzozmdt0(xN))) | ![W1: $i] : (~((~(aSubsetOf0(W1, szDzozmdt0(xN)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), W1)) | aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), szDzozmdt0(xN)))))) | (~((~aSubsetOf0(W1, szDzozmdt0(xN))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szDzozmdt0(xN)))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, szDzozmdt0(xN)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), W1)) | aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), szDzozmdt0(xN)))))) | (~((~aSubsetOf0(W1, szDzozmdt0(xN))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szDzozmdt0(xN))))))))))))),
% 71.54/45.83 inference(monotonicity,[status(thm)],[173])).
% 71.54/45.83 tff(175,plain,
% 71.54/45.83 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(szDzozmdt0(xN))) | ![W1: $i] : (~((~(aSubsetOf0(W1, szDzozmdt0(xN)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), W1)) | aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), szDzozmdt0(xN)))))) | (~((~aSubsetOf0(W1, szDzozmdt0(xN))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szDzozmdt0(xN)))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, szDzozmdt0(xN)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), W1)) | aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), szDzozmdt0(xN)))))) | (~((~aSubsetOf0(W1, szDzozmdt0(xN))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szDzozmdt0(xN)))))))))))),
% 71.54/45.83 inference(transitivity,[status(thm)],[174, 172])).
% 71.54/45.83 tff(176,plain,
% 71.54/45.83 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(szDzozmdt0(xN))) | ![W1: $i] : (~((~(aSubsetOf0(W1, szDzozmdt0(xN)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), W1)) | aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), szDzozmdt0(xN)))))) | (~((~aSubsetOf0(W1, szDzozmdt0(xN))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szDzozmdt0(xN)))))))))))),
% 71.54/45.83 inference(quant_inst,[status(thm)],[])).
% 71.54/45.83 tff(177,plain,
% 71.54/45.83 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(szDzozmdt0(xN))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, szDzozmdt0(xN)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), W1)) | aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), szDzozmdt0(xN)))))) | (~((~aSubsetOf0(W1, szDzozmdt0(xN))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szDzozmdt0(xN))))))))))),
% 71.54/45.84 inference(modus_ponens,[status(thm)],[176, 175])).
% 71.54/45.84 tff(178,plain,
% 71.54/45.84 (![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, szDzozmdt0(xN)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), W1)) | aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), szDzozmdt0(xN)))))) | (~((~aSubsetOf0(W1, szDzozmdt0(xN))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szDzozmdt0(xN))))))))))),
% 71.54/45.84 inference(unit_resolution,[status(thm)],[177, 171, 149])).
% 71.54/45.84 tff(179,plain,
% 71.54/45.84 ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, szDzozmdt0(xN)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), W1)) | aElementOf0(tptp_fun_W2_1(W1, szDzozmdt0(xN)), szDzozmdt0(xN)))))) | (~((~aSubsetOf0(W1, szDzozmdt0(xN))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szDzozmdt0(xN))))))))))) | (~((~((~aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xN)) | (~((~aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xN)), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xN)), szDzozmdt0(xN)))))) | (~((~aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xN))) | (~((~aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(W2, szDzozmdt0(xN))))))))))),
% 71.54/45.84 inference(quant_inst,[status(thm)],[])).
% 71.54/45.84 tff(180,plain,
% 71.54/45.84 (~((~((~aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xN)) | (~((~aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xN)), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xN)), szDzozmdt0(xN)))))) | (~((~aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xN))) | (~((~aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(W2, szDzozmdt0(xN)))))))))),
% 71.54/45.84 inference(unit_resolution,[status(thm)],[179, 178])).
% 71.54/45.84 tff(181,plain,
% 71.54/45.84 (((~((~aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xN)) | (~((~aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xN)), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(tptp_fun_W2_1(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xN)), szDzozmdt0(xN)))))) | (~((~aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xN))) | (~((~aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(W2, szDzozmdt0(xN))))))))) | ((~aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xN))) | (~((~aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(W2, szDzozmdt0(xN)))))))),
% 71.54/45.84 inference(tautology,[status(thm)],[])).
% 71.54/45.84 tff(182,plain,
% 71.54/45.84 ((~aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xN))) | (~((~aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(W2, szDzozmdt0(xN))))))),
% 71.54/45.84 inference(unit_resolution,[status(thm)],[181, 180])).
% 71.54/45.84 tff(183,plain,
% 71.54/45.84 (aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xN)) <=> aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xd))),
% 71.54/45.84 inference(monotonicity,[status(thm)],[8])).
% 71.54/45.84 tff(184,plain,
% 71.54/45.84 (aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xd)) <=> aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xN))),
% 71.54/45.84 inference(symmetry,[status(thm)],[183])).
% 71.54/45.84 tff(185,plain,
% 71.54/45.84 (aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xN))),
% 71.54/45.84 inference(modus_ponens,[status(thm)],[71, 184])).
% 71.54/45.84 tff(186,plain,
% 71.54/45.84 ((~((~aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xN))) | (~((~aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(W2, szDzozmdt0(xN)))))))) | (~aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xN))) | (~((~aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(W2, szDzozmdt0(xN))))))),
% 71.54/45.84 inference(tautology,[status(thm)],[])).
% 71.54/45.84 tff(187,plain,
% 71.54/45.84 ((~((~aSubsetOf0(sdtlbdtrb0(xd, szDzizrdt0(xd)), szDzozmdt0(xN))) | (~((~aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(W2, szDzozmdt0(xN)))))))) | (~((~aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(W2, szDzozmdt0(xN))))))),
% 71.54/45.84 inference(unit_resolution,[status(thm)],[186, 185])).
% 71.54/45.84 tff(188,plain,
% 71.54/45.84 (~((~aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(W2, szDzozmdt0(xN)))))),
% 71.54/45.84 inference(unit_resolution,[status(thm)],[187, 182])).
% 71.54/45.84 tff(189,plain,
% 71.54/45.84 (((~aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(W2, szDzozmdt0(xN))))) | ![W2: $i] : ((~aElementOf0(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(W2, szDzozmdt0(xN)))),
% 71.54/45.84 inference(tautology,[status(thm)],[])).
% 71.54/45.84 tff(190,plain,
% 71.54/45.84 (![W2: $i] : ((~aElementOf0(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(W2, szDzozmdt0(xN)))),
% 71.54/45.84 inference(unit_resolution,[status(thm)],[189, 188])).
% 71.54/45.84 tff(191,plain,
% 71.54/45.84 (((~![W2: $i] : ((~aElementOf0(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(W2, szDzozmdt0(xN)))) | ((~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), szDzozmdt0(xN)))) <=> ((~![W2: $i] : ((~aElementOf0(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(W2, szDzozmdt0(xN)))) | (~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), szDzozmdt0(xN)))),
% 71.54/45.84 inference(rewrite,[status(thm)],[])).
% 71.54/45.84 tff(192,plain,
% 71.54/45.84 ((~![W2: $i] : ((~aElementOf0(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(W2, szDzozmdt0(xN)))) | ((~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), szDzozmdt0(xN)))),
% 71.54/45.84 inference(quant_inst,[status(thm)],[])).
% 71.54/45.84 tff(193,plain,
% 71.54/45.84 ((~![W2: $i] : ((~aElementOf0(W2, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(W2, szDzozmdt0(xN)))) | (~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), szDzozmdt0(xN))),
% 71.54/45.84 inference(modus_ponens,[status(thm)],[192, 191])).
% 71.54/45.84 tff(194,plain,
% 71.54/45.84 (aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), szDzozmdt0(xN))),
% 71.54/45.84 inference(unit_resolution,[status(thm)],[193, 190, 143])).
% 71.54/45.84 tff(195,plain,
% 71.54/45.84 (((~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W0!24))) | (sdtlpdtrp0(xe, tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W0!24)),
% 71.54/45.84 inference(tautology,[status(thm)],[])).
% 71.54/45.84 tff(196,plain,
% 71.54/45.84 (sdtlpdtrp0(xe, tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W0!24),
% 71.54/45.84 inference(unit_resolution,[status(thm)],[195, 141])).
% 71.54/45.84 tff(197,plain,
% 71.54/45.84 (^[W1: $i] : refl(((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!24))) <=> ((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!24))))),
% 71.54/45.84 inference(bind,[status(th)],[])).
% 71.54/45.84 tff(198,plain,
% 71.54/45.84 (![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!24))) <=> ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!24)))),
% 71.54/45.84 inference(quant_intro,[status(thm)],[197])).
% 71.54/45.84 tff(199,plain,
% 71.54/45.84 (^[W1: $i] : trans(monotonicity(rewrite((aElementOf0(W1, szDzozmdt0(xN)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0!24)) <=> (~((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!24))))), ((~(aElementOf0(W1, szDzozmdt0(xN)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0!24))) <=> (~(~((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!24))))))), rewrite((~(~((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!24))))) <=> ((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!24)))), ((~(aElementOf0(W1, szDzozmdt0(xN)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0!24))) <=> ((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!24)))))),
% 71.54/45.84 inference(bind,[status(th)],[])).
% 71.54/45.84 tff(200,plain,
% 71.54/45.84 (![W1: $i] : (~(aElementOf0(W1, szDzozmdt0(xN)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0!24))) <=> ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!24)))),
% 71.54/45.84 inference(quant_intro,[status(thm)],[199])).
% 71.54/45.84 tff(201,plain,
% 71.54/45.84 (![W1: $i] : (~(aElementOf0(W1, szDzozmdt0(xN)) & aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0!24)))),
% 71.54/45.84 inference(and_elim,[status(thm)],[137])).
% 71.54/45.84 tff(202,plain,
% 71.54/45.84 (![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!24)))),
% 71.54/45.84 inference(modus_ponens,[status(thm)],[201, 200])).
% 71.54/45.84 tff(203,plain,
% 71.54/45.84 (![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!24)))),
% 71.54/45.84 inference(modus_ponens,[status(thm)],[202, 198])).
% 71.54/45.84 tff(204,plain,
% 71.54/45.84 (((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!24)))) | ((~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), szDzozmdt0(xN))) | (~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W0!24)))) <=> ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!24)))) | (~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), szDzozmdt0(xN))) | (~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W0!24)))),
% 71.54/45.84 inference(rewrite,[status(thm)],[])).
% 71.54/45.84 tff(205,plain,
% 71.54/45.84 ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!24)))) | ((~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), szDzozmdt0(xN))) | (~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W0!24)))),
% 71.54/45.84 inference(quant_inst,[status(thm)],[])).
% 71.54/45.84 tff(206,plain,
% 71.54/45.84 ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, W1) = W0!24)))) | (~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), szDzozmdt0(xN))) | (~aElementOf0(tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe), sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(sdtlpdtrp0(xe, tptp_fun_W4_13(W0!24, sdtlbdtrb0(xd, szDzizrdt0(xd)), xe)) = W0!24))),
% 71.54/45.84 inference(modus_ponens,[status(thm)],[205, 204])).
% 71.54/45.84 tff(207,plain,
% 71.68/45.96 ($false),
% 71.68/45.96 inference(unit_resolution,[status(thm)],[206, 203, 143, 196, 194])).
% 71.68/45.96 % SZS output end Proof
%------------------------------------------------------------------------------