TSTP Solution File: RNG112+4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG112+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 : Tue Sep 20 03:18:28 EDT 2022
% Result : Theorem 8.86s 5.86s
% Output : Proof 8.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG112+4 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 22:36:43 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 8.86/5.86 % SZS status Theorem
% 8.86/5.86 % SZS output start Proof
% 8.86/5.86 tff(tptp_fun_W1_39_type, type, (
% 8.86/5.86 tptp_fun_W1_39: $i > $i)).
% 8.86/5.86 tff(tptp_fun_W1_36_type, type, (
% 8.86/5.86 tptp_fun_W1_36: $i)).
% 8.86/5.86 tff(sdtpldt0_type, type, (
% 8.86/5.86 sdtpldt0: ( $i * $i ) > $i)).
% 8.86/5.86 tff(aElementOf0_type, type, (
% 8.86/5.86 aElementOf0: ( $i * $i ) > $o)).
% 8.86/5.86 tff(slsdtgt0_type, type, (
% 8.86/5.86 slsdtgt0: $i > $i)).
% 8.86/5.86 tff(xa_type, type, (
% 8.86/5.86 xa: $i)).
% 8.86/5.86 tff(xb_type, type, (
% 8.86/5.86 xb: $i)).
% 8.86/5.86 tff(sdtpldt1_type, type, (
% 8.86/5.86 sdtpldt1: ( $i * $i ) > $i)).
% 8.86/5.86 tff(tptp_fun_W3_40_type, type, (
% 8.86/5.86 tptp_fun_W3_40: $i > $i)).
% 8.86/5.86 tff(tptp_fun_W2_41_type, type, (
% 8.86/5.86 tptp_fun_W2_41: $i > $i)).
% 8.86/5.86 tff(sz00_type, type, (
% 8.86/5.86 sz00: $i)).
% 8.86/5.86 tff(iLess0_type, type, (
% 8.86/5.86 iLess0: ( $i * $i ) > $o)).
% 8.86/5.86 tff(sbrdtbr0_type, type, (
% 8.86/5.86 sbrdtbr0: $i > $i)).
% 8.86/5.86 tff(tptp_fun_W3_37_type, type, (
% 8.86/5.86 tptp_fun_W3_37: $i)).
% 8.86/5.86 tff(tptp_fun_W2_38_type, type, (
% 8.86/5.86 tptp_fun_W2_38: $i)).
% 8.86/5.86 tff(tptp_fun_W0_31_type, type, (
% 8.86/5.86 tptp_fun_W0_31: $i)).
% 8.86/5.86 tff(tptp_fun_W2_34_type, type, (
% 8.86/5.86 tptp_fun_W2_34: $i)).
% 8.86/5.86 tff(tptp_fun_W1_35_type, type, (
% 8.86/5.86 tptp_fun_W1_35: $i)).
% 8.86/5.86 tff(sdtasdt0_type, type, (
% 8.86/5.86 sdtasdt0: ( $i * $i ) > $i)).
% 8.86/5.86 tff(aElement0_type, type, (
% 8.86/5.86 aElement0: $i > $o)).
% 8.86/5.86 tff(tptp_fun_W2_33_type, type, (
% 8.86/5.86 tptp_fun_W2_33: $i > $i)).
% 8.86/5.86 tff(tptp_fun_W2_32_type, type, (
% 8.86/5.86 tptp_fun_W2_32: $i > $i)).
% 8.86/5.86 tff(xI_type, type, (
% 8.86/5.86 xI: $i)).
% 8.86/5.86 tff(1,plain,
% 8.86/5.86 ((![W1: $i] : (((~aElementOf0(W1, slsdtgt0(xa))) | (aElement0(tptp_fun_W2_32(W1)) & (sdtasdt0(xa, tptp_fun_W2_32(W1)) = W1))) & (aElementOf0(W1, slsdtgt0(xa)) | ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xa, W2) = W1))))) & ![W1: $i] : (((~aElementOf0(W1, slsdtgt0(xb))) | (aElement0(tptp_fun_W2_33(W1)) & (sdtasdt0(xb, tptp_fun_W2_33(W1)) = W1))) & (aElementOf0(W1, slsdtgt0(xb)) | ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xb, W2) = W1))))) & (aElementOf0(W1!35, slsdtgt0(xa)) & aElementOf0(W2!34, slsdtgt0(xb)) & (sdtpldt0(W1!35, W2!34) = W0!31)) & aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0!31 = sz00))) <=> (![W1: $i] : (((~aElementOf0(W1, slsdtgt0(xa))) | (aElement0(tptp_fun_W2_32(W1)) & (sdtasdt0(xa, tptp_fun_W2_32(W1)) = W1))) & (aElementOf0(W1, slsdtgt0(xa)) | ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xa, W2) = W1))))) & ![W1: $i] : (((~aElementOf0(W1, slsdtgt0(xb))) | (aElement0(tptp_fun_W2_33(W1)) & (sdtasdt0(xb, tptp_fun_W2_33(W1)) = W1))) & (aElementOf0(W1, slsdtgt0(xb)) | ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xb, W2) = W1))))) & aElementOf0(W1!35, slsdtgt0(xa)) & aElementOf0(W2!34, slsdtgt0(xb)) & (sdtpldt0(W1!35, W2!34) = W0!31) & aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0!31 = sz00)))),
% 8.86/5.86 inference(rewrite,[status(thm)],[])).
% 8.86/5.86 tff(2,plain,
% 8.86/5.86 (?[W0: $i] : (![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)) & aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00))) <=> ?[W0: $i] : (![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)) & aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)))),
% 8.86/5.86 inference(rewrite,[status(thm)],[])).
% 8.86/5.86 tff(3,plain,
% 8.86/5.86 (^[W0: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1)))) <=> (![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))))), quant_intro(proof_bind(^[W1: $i, W2: $i] : rewrite(((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0)) <=> (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))), (?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0)) <=> ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))), (((![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1)))) & ?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0))) <=> ((![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1)))) & ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))))), rewrite(((![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1)))) & ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) <=> (![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))), (((![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1)))) & ?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0))) <=> (![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))))), ((((![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1)))) & ?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0))) & aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) <=> ((![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))), rewrite(((![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) <=> (![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)) & aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))), ((((![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1)))) & ?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0))) & aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) <=> (![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)) & aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))), (((((![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1)))) & ?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0))) & aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & (~(W0 = sz00))) <=> ((![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)) & aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & (~(W0 = sz00))))), rewrite(((![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)) & aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & (~(W0 = sz00))) <=> (![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)) & aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)))), (((((![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1)))) & ?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0))) & aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & (~(W0 = sz00))) <=> (![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)) & aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)))))),
% 8.86/5.87 inference(bind,[status(th)],[])).
% 8.86/5.87 tff(4,plain,
% 8.86/5.87 (?[W0: $i] : ((((![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1)))) & ?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0))) & aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & (~(W0 = sz00))) <=> ?[W0: $i] : (![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)) & aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)))),
% 8.86/5.87 inference(quant_intro,[status(thm)],[3])).
% 8.86/5.87 tff(5,axiom,(?[W0: $i] : ((((![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1)))) & ?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0))) & aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & (~(W0 = sz00)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2228')).
% 8.86/5.87 tff(6,plain,
% 8.86/5.87 (?[W0: $i] : (![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)) & aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)))),
% 8.86/5.87 inference(modus_ponens,[status(thm)],[5, 4])).
% 8.86/5.87 tff(7,plain,
% 8.86/5.87 (?[W0: $i] : (![W1: $i] : (aElementOf0(W1, slsdtgt0(xa)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xa, W2) = W1))) & ![W1: $i] : (aElementOf0(W1, slsdtgt0(xb)) <=> ?[W2: $i] : (aElement0(W2) & (sdtasdt0(xb, W2) = W1))) & ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)) & aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0 = sz00)))),
% 8.86/5.87 inference(modus_ponens,[status(thm)],[6, 2])).
% 8.86/5.87 tff(8,plain,
% 8.86/5.87 (![W1: $i] : (((~aElementOf0(W1, slsdtgt0(xa))) | (aElement0(tptp_fun_W2_32(W1)) & (sdtasdt0(xa, tptp_fun_W2_32(W1)) = W1))) & (aElementOf0(W1, slsdtgt0(xa)) | ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xa, W2) = W1))))) & ![W1: $i] : (((~aElementOf0(W1, slsdtgt0(xb))) | (aElement0(tptp_fun_W2_33(W1)) & (sdtasdt0(xb, tptp_fun_W2_33(W1)) = W1))) & (aElementOf0(W1, slsdtgt0(xb)) | ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xb, W2) = W1))))) & aElementOf0(W1!35, slsdtgt0(xa)) & aElementOf0(W2!34, slsdtgt0(xb)) & (sdtpldt0(W1!35, W2!34) = W0!31) & aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W0!31 = sz00))),
% 8.86/5.87 inference(modus_ponens,[status(thm)],[7, 1])).
% 8.86/5.87 tff(9,plain,
% 8.86/5.87 (aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))),
% 8.86/5.87 inference(and_elim,[status(thm)],[8])).
% 8.86/5.87 tff(10,plain,
% 8.86/5.87 ((aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W0!31))))) | (~aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))),
% 8.86/5.87 inference(tautology,[status(thm)],[])).
% 8.86/5.87 tff(11,plain,
% 8.86/5.87 (aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W0!31))))),
% 8.86/5.87 inference(unit_resolution,[status(thm)],[10, 9])).
% 8.86/5.87 tff(12,plain,
% 8.86/5.87 (^[W0: $i] : refl(((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))))))))) <=> ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))))))))))),
% 8.86/5.87 inference(bind,[status(th)],[])).
% 8.86/5.87 tff(13,plain,
% 8.86/5.87 (![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))))))))) <=> ![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))))),
% 8.86/5.87 inference(quant_intro,[status(thm)],[12])).
% 8.86/5.87 tff(14,plain,
% 8.86/5.87 (^[W0: $i] : rewrite(((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))))))))) <=> ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))))))))))),
% 8.86/5.87 inference(bind,[status(th)],[])).
% 8.86/5.87 tff(15,plain,
% 8.86/5.87 (![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))))))))) <=> ![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))))),
% 8.86/5.87 inference(quant_intro,[status(thm)],[14])).
% 8.86/5.87 tff(16,plain,
% 8.86/5.87 (![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))))))))) <=> ![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))))),
% 8.86/5.87 inference(transitivity,[status(thm)],[15, 13])).
% 8.86/5.87 tff(17,plain,
% 8.86/5.87 (^[W0: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W1: $i, W2: $i] : trans(monotonicity(rewrite((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)) <=> (~((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa)))))), ((~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) <=> (~(~((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa)))))))), rewrite((~(~((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa)))))) <=> ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))), ((~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) <=> ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))), (![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) <=> ![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa)))))), (((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) <=> ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))), rewrite(((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))) <=> (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa)))))))), (((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) <=> (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))))), trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W3: $i, W4: $i] : trans(monotonicity(rewrite((aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)) <=> (~((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))), ((~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) <=> (~(~((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))))), rewrite((~(~((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))) <=> ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))), ((~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) <=> ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))), (![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) <=> ![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))), (((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))) <=> ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))), rewrite(((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))) <=> (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))))), (((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))) <=> (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))), (((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))))) <=> ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))))))), rewrite(((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))))) <=> ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))), (((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))))) <=> ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))), (![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))))) <=> ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))))))), ((aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))))) <=> (aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))), rewrite((aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))) <=> (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))))))))), ((aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))))) <=> (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))))), (((W0 = sz00) | ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))))))) <=> ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))))))))))), rewrite(((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))))))))) <=> ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))))), (((W0 = sz00) | ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))))))) <=> ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))))))),
% 8.86/5.88 inference(bind,[status(th)],[])).
% 8.86/5.88 tff(18,plain,
% 8.86/5.88 (![W0: $i] : ((W0 = sz00) | ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))))))) <=> ![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))))),
% 8.86/5.88 inference(quant_intro,[status(thm)],[17])).
% 8.86/5.88 tff(19,plain,
% 8.86/5.88 (^[W0: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) <=> ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))))), rewrite((~(~(W0 = sz00))) <=> (W0 = sz00)), ((((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (~(~(W0 = sz00)))) <=> (((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (W0 = sz00)))), rewrite((((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (W0 = sz00)) <=> ((W0 = sz00) | ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))))), ((((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (~(~(W0 = sz00)))) <=> ((W0 = sz00) | ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))))))), trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))) <=> ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))))), rewrite((~(~(W2 = sz00))) <=> (W2 = sz00)), ((((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))) | (~(~(W2 = sz00)))) <=> (((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))) | (W2 = sz00)))), rewrite((((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))) | (W2 = sz00)) <=> ((W2 = sz00) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))))), ((((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))) | (~(~(W2 = sz00)))) <=> ((W2 = sz00) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))))))), (((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))) | (~(~(W2 = sz00))))) <=> ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((W2 = sz00) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))))))), rewrite(((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((W2 = sz00) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))))) <=> ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))))), (((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))) | (~(~(W2 = sz00))))) <=> ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))))))), (![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))) | (~(~(W2 = sz00))))) <=> ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))))))), (((aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36)) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))) | (~(~(W2 = sz00)))))) <=> ((aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36)) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))))))), rewrite(((aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36)) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))))) <=> (aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))))))), (((aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36)) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))) | (~(~(W2 = sz00)))))) <=> (aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))))))), (((((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (~(~(W0 = sz00)))) | ((aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36)) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))) | (~(~(W2 = sz00))))))) <=> (((W0 = sz00) | ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))))) | (aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))))))))), rewrite((((W0 = sz00) | ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))))) | (aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))))))) <=> ((W0 = sz00) | ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))))))), (((((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (~(~(W0 = sz00)))) | ((aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36)) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))) | (~(~(W2 = sz00))))))) <=> ((W0 = sz00) | ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))))))))),
% 8.86/5.88 inference(bind,[status(th)],[])).
% 8.86/5.88 tff(20,plain,
% 8.86/5.88 (![W0: $i] : ((((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (~(~(W0 = sz00)))) | ((aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36)) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))) | (~(~(W2 = sz00))))))) <=> ![W0: $i] : ((W0 = sz00) | ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))))))),
% 8.86/5.88 inference(quant_intro,[status(thm)],[19])).
% 8.86/5.88 tff(21,plain,
% 8.86/5.88 (^[W0: $i] : rewrite(((~((aElementOf0(W0, xI) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)))) | ?[W1: $i] : (?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~((aElementOf0(W2, xI) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00))))))) <=> ((~((aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)))) | ?[W1: $i] : (?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~((aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00))))))))),
% 8.86/5.88 inference(bind,[status(th)],[])).
% 8.86/5.88 tff(22,plain,
% 8.86/5.88 (![W0: $i] : ((~((aElementOf0(W0, xI) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)))) | ?[W1: $i] : (?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~((aElementOf0(W2, xI) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00))))))) <=> ![W0: $i] : ((~((aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)))) | ?[W1: $i] : (?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~((aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00)))))))),
% 8.86/5.88 inference(quant_intro,[status(thm)],[21])).
% 8.86/5.88 tff(23,plain,
% 8.86/5.88 (![W0: $i] : ((~((aElementOf0(W0, xI) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)))) | ?[W1: $i] : (?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~((aElementOf0(W2, xI) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00))))))) <=> ![W0: $i] : ((~((aElementOf0(W0, xI) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)))) | ?[W1: $i] : (?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~((aElementOf0(W2, xI) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00)))))))),
% 8.86/5.88 inference(rewrite,[status(thm)],[])).
% 8.86/5.88 tff(24,plain,
% 8.86/5.88 (^[W0: $i] : trans(monotonicity(rewrite(((?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0)) | aElementOf0(W0, xI)) & (~(W0 = sz00))) <=> ((aElementOf0(W0, xI) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)))), quant_intro(proof_bind(^[W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((?[W2: $i, W3: $i] : ((aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb))) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI)) <=> (?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI))), (((?[W2: $i, W3: $i] : ((aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb))) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI)) & (~(W1 = sz00))) <=> ((?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI)) & (~(W1 = sz00))))), rewrite(((?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI)) & (~(W1 = sz00))) <=> (?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00)))), (((?[W2: $i, W3: $i] : ((aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb))) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI)) & (~(W1 = sz00))) <=> (?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00))))), quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(rewrite(((?[W3: $i, W4: $i] : ((aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb))) & (sdtpldt0(W3, W4) = W2)) | aElementOf0(W2, xI)) & (~(W2 = sz00))) <=> ((aElementOf0(W2, xI) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00)))), ((((?[W3: $i, W4: $i] : ((aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb))) & (sdtpldt0(W3, W4) = W2)) | aElementOf0(W2, xI)) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1)))) <=> (((aElementOf0(W2, xI) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1)))))), rewrite((((aElementOf0(W2, xI) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1)))) <=> ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~((aElementOf0(W2, xI) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00)))))), ((((?[W3: $i, W4: $i] : ((aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb))) & (sdtpldt0(W3, W4) = W2)) | aElementOf0(W2, xI)) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1)))) <=> ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~((aElementOf0(W2, xI) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00)))))))), (![W2: $i] : (((?[W3: $i, W4: $i] : ((aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb))) & (sdtpldt0(W3, W4) = W2)) | aElementOf0(W2, xI)) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1)))) <=> ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~((aElementOf0(W2, xI) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00))))))), ((((?[W2: $i, W3: $i] : ((aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb))) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI)) & (~(W1 = sz00))) & ![W2: $i] : (((?[W3: $i, W4: $i] : ((aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb))) & (sdtpldt0(W3, W4) = W2)) | aElementOf0(W2, xI)) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))))) <=> ((?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00))) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~((aElementOf0(W2, xI) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00)))))))), rewrite(((?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00))) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~((aElementOf0(W2, xI) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00)))))) <=> (?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~((aElementOf0(W2, xI) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00))))))), ((((?[W2: $i, W3: $i] : ((aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb))) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI)) & (~(W1 = sz00))) & ![W2: $i] : (((?[W3: $i, W4: $i] : ((aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb))) & (sdtpldt0(W3, W4) = W2)) | aElementOf0(W2, xI)) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))))) <=> (?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~((aElementOf0(W2, xI) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00))))))))), (?[W1: $i] : (((?[W2: $i, W3: $i] : ((aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb))) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI)) & (~(W1 = sz00))) & ![W2: $i] : (((?[W3: $i, W4: $i] : ((aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb))) & (sdtpldt0(W3, W4) = W2)) | aElementOf0(W2, xI)) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))))) <=> ?[W1: $i] : (?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~((aElementOf0(W2, xI) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00)))))))), ((((?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0)) | aElementOf0(W0, xI)) & (~(W0 = sz00))) => ?[W1: $i] : (((?[W2: $i, W3: $i] : ((aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb))) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI)) & (~(W1 = sz00))) & ![W2: $i] : (((?[W3: $i, W4: $i] : ((aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb))) & (sdtpldt0(W3, W4) = W2)) | aElementOf0(W2, xI)) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1)))))) <=> (((aElementOf0(W0, xI) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00))) => ?[W1: $i] : (?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~((aElementOf0(W2, xI) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00))))))))), rewrite((((aElementOf0(W0, xI) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00))) => ?[W1: $i] : (?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~((aElementOf0(W2, xI) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00))))))) <=> ((~((aElementOf0(W0, xI) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)))) | ?[W1: $i] : (?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~((aElementOf0(W2, xI) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00)))))))), ((((?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0)) | aElementOf0(W0, xI)) & (~(W0 = sz00))) => ?[W1: $i] : (((?[W2: $i, W3: $i] : ((aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb))) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI)) & (~(W1 = sz00))) & ![W2: $i] : (((?[W3: $i, W4: $i] : ((aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb))) & (sdtpldt0(W3, W4) = W2)) | aElementOf0(W2, xI)) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1)))))) <=> ((~((aElementOf0(W0, xI) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)))) | ?[W1: $i] : (?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~((aElementOf0(W2, xI) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00)))))))))),
% 8.86/5.89 inference(bind,[status(th)],[])).
% 8.86/5.89 tff(25,plain,
% 8.86/5.89 (![W0: $i] : (((?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0)) | aElementOf0(W0, xI)) & (~(W0 = sz00))) => ?[W1: $i] : (((?[W2: $i, W3: $i] : ((aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb))) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI)) & (~(W1 = sz00))) & ![W2: $i] : (((?[W3: $i, W4: $i] : ((aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb))) & (sdtpldt0(W3, W4) = W2)) | aElementOf0(W2, xI)) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1)))))) <=> ![W0: $i] : ((~((aElementOf0(W0, xI) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)))) | ?[W1: $i] : (?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~((aElementOf0(W2, xI) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00)))))))),
% 8.86/5.89 inference(quant_intro,[status(thm)],[24])).
% 8.86/5.89 tff(26,axiom,(![W0: $i] : (((?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0)) | aElementOf0(W0, xI)) & (~(W0 = sz00))) => ?[W1: $i] : (((?[W2: $i, W3: $i] : ((aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb))) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI)) & (~(W1 = sz00))) & ![W2: $i] : (((?[W3: $i, W4: $i] : ((aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb))) & (sdtpldt0(W3, W4) = W2)) | aElementOf0(W2, xI)) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2351')).
% 8.86/5.89 tff(27,plain,
% 8.86/5.89 (![W0: $i] : ((~((aElementOf0(W0, xI) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)))) | ?[W1: $i] : (?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~((aElementOf0(W2, xI) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00)))))))),
% 8.86/5.89 inference(modus_ponens,[status(thm)],[26, 25])).
% 8.86/5.89 tff(28,plain,
% 8.86/5.89 (![W0: $i] : ((~((aElementOf0(W0, xI) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)))) | ?[W1: $i] : (?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~((aElementOf0(W2, xI) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00)))))))),
% 8.86/5.89 inference(modus_ponens,[status(thm)],[27, 23])).
% 8.86/5.89 tff(29,plain,
% 8.86/5.89 (![W0: $i] : ((~((aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)))) | ?[W1: $i] : (?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~((aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | ?[W3: $i, W4: $i] : (aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2))) & (~(W2 = sz00)))))))),
% 8.86/5.89 inference(modus_ponens,[status(thm)],[28, 22])).
% 8.86/5.89 tff(30,plain,(
% 8.86/5.89 ![W0: $i] : ((((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (~(~(W0 = sz00)))) | ((aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36)) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))) | (~(~(W2 = sz00)))))))),
% 8.86/5.89 inference(skolemize,[status(sab)],[29])).
% 8.86/5.89 tff(31,plain,
% 8.86/5.89 (![W0: $i] : ((W0 = sz00) | ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (aElementOf0(W2!38, slsdtgt0(xa)) & aElementOf0(W3!37, slsdtgt0(xb)) & (sdtpldt0(W2!38, W3!37) = W1!36) & aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1!36 = sz00)) & ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | ((~aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W3: $i, W4: $i] : (~(aElementOf0(W3, slsdtgt0(xa)) & aElementOf0(W4, slsdtgt0(xb)) & (sdtpldt0(W3, W4) = W2)))))))),
% 8.86/5.89 inference(modus_ponens,[status(thm)],[30, 20])).
% 8.86/5.89 tff(32,plain,
% 8.86/5.89 (![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))))),
% 8.86/5.89 inference(modus_ponens,[status(thm)],[31, 18])).
% 8.86/5.89 tff(33,plain,
% 8.86/5.89 (![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))))),
% 8.86/5.89 inference(modus_ponens,[status(thm)],[32, 16])).
% 8.86/5.89 tff(34,plain,
% 8.86/5.89 (~(W0!31 = sz00)),
% 8.86/5.89 inference(and_elim,[status(thm)],[8])).
% 8.86/5.89 tff(35,plain,
% 8.86/5.89 (((~![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))))) | ((W0!31 = sz00) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))) | (~(aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W0!31)))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))))) | (W0!31 = sz00) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))) | (~(aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W0!31)))))))),
% 8.86/5.89 inference(rewrite,[status(thm)],[])).
% 8.86/5.89 tff(36,plain,
% 8.86/5.89 (((W0!31 = sz00) | (~(aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W0!31)))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))))))))) <=> ((W0!31 = sz00) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))) | (~(aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W0!31)))))))),
% 8.86/5.89 inference(rewrite,[status(thm)],[])).
% 8.86/5.89 tff(37,plain,
% 8.86/5.89 ((~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))) <=> (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))))))))),
% 8.86/5.89 inference(rewrite,[status(thm)],[])).
% 8.86/5.89 tff(38,plain,
% 8.86/5.89 ((~(aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0!31)) | (~aElementOf0(W1, slsdtgt0(xa))))))) <=> (~(aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W0!31))))))),
% 8.86/5.89 inference(rewrite,[status(thm)],[])).
% 8.86/5.89 tff(39,plain,
% 8.86/5.89 (((W0!31 = sz00) | (~(aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0!31)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))))))))) <=> ((W0!31 = sz00) | (~(aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W0!31)))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))))),
% 8.86/5.89 inference(monotonicity,[status(thm)],[38, 37])).
% 8.86/5.89 tff(40,plain,
% 8.86/5.89 (((W0!31 = sz00) | (~(aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0!31)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))))))))) <=> ((W0!31 = sz00) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))) | (~(aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W0!31)))))))),
% 8.86/5.90 inference(transitivity,[status(thm)],[39, 36])).
% 8.86/5.90 tff(41,plain,
% 8.86/5.90 (((~![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))))) | ((W0!31 = sz00) | (~(aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0!31)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))))) | ((W0!31 = sz00) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))) | (~(aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W0!31))))))))),
% 8.86/5.90 inference(monotonicity,[status(thm)],[40])).
% 8.86/5.90 tff(42,plain,
% 8.86/5.90 (((~![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))))) | ((W0!31 = sz00) | (~(aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0!31)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))))) | (W0!31 = sz00) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))) | (~(aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W0!31)))))))),
% 8.86/5.90 inference(transitivity,[status(thm)],[41, 35])).
% 8.86/5.90 tff(43,plain,
% 8.86/5.90 ((~![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))))) | ((W0!31 = sz00) | (~(aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0!31)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))))),
% 8.86/5.90 inference(quant_inst,[status(thm)],[])).
% 8.86/5.90 tff(44,plain,
% 8.86/5.90 ((~![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))))) | (W0!31 = sz00) | (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))) | (~(aElementOf0(W0!31, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W0!31))))))),
% 8.86/5.90 inference(modus_ponens,[status(thm)],[43, 42])).
% 8.86/5.90 tff(45,plain,
% 8.86/5.90 (~((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))))),
% 8.86/5.90 inference(unit_resolution,[status(thm)],[44, 34, 33, 11])).
% 8.86/5.90 tff(46,plain,
% 8.86/5.90 (((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))))))) | aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))),
% 8.86/5.90 inference(tautology,[status(thm)],[])).
% 8.86/5.90 tff(47,plain,
% 8.86/5.90 (aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))),
% 8.86/5.90 inference(unit_resolution,[status(thm)],[46, 45])).
% 8.86/5.90 tff(48,plain,
% 8.86/5.90 ((aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W1!36))))) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))),
% 8.86/5.90 inference(tautology,[status(thm)],[])).
% 8.86/5.90 tff(49,plain,
% 8.86/5.90 (aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W1!36))))),
% 8.86/5.90 inference(unit_resolution,[status(thm)],[48, 47])).
% 8.86/5.90 tff(50,plain,
% 8.86/5.90 (((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))))))) | (~(W1!36 = sz00))),
% 8.86/5.90 inference(tautology,[status(thm)],[])).
% 8.86/5.90 tff(51,plain,
% 8.86/5.90 (~(W1!36 = sz00)),
% 8.86/5.90 inference(unit_resolution,[status(thm)],[50, 45])).
% 8.86/5.90 tff(52,plain,
% 8.86/5.90 (^[W0: $i] : trans(monotonicity(rewrite((~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) <=> (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa)))))))), rewrite((~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) <=> (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))), (((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) <=> ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))))), rewrite(((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) <=> ((W0 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))))), (((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) <=> ((W0 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))))))),
% 8.86/5.90 inference(bind,[status(th)],[])).
% 8.86/5.90 tff(53,plain,
% 8.86/5.90 (![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) <=> ![W0: $i] : ((W0 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))))),
% 8.86/5.90 inference(quant_intro,[status(thm)],[52])).
% 8.86/5.90 tff(54,plain,
% 8.86/5.90 (^[W0: $i] : refl(((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) <=> ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))))),
% 8.86/5.90 inference(bind,[status(th)],[])).
% 8.86/5.90 tff(55,plain,
% 8.86/5.90 (![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) <=> ![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))),
% 8.86/5.90 inference(quant_intro,[status(thm)],[54])).
% 8.86/5.90 tff(56,plain,
% 8.86/5.90 (^[W0: $i] : rewrite(((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) <=> ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))))),
% 8.86/5.90 inference(bind,[status(th)],[])).
% 8.86/5.90 tff(57,plain,
% 8.86/5.90 (![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) <=> ![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))),
% 8.86/5.90 inference(quant_intro,[status(thm)],[56])).
% 8.86/5.90 tff(58,plain,
% 8.86/5.90 (![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) <=> ![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))),
% 8.86/5.90 inference(transitivity,[status(thm)],[57, 55])).
% 8.86/5.90 tff(59,plain,
% 8.86/5.90 (^[W0: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W1: $i, W2: $i] : trans(monotonicity(rewrite((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)) <=> (~((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa)))))), ((~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) <=> (~(~((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa)))))))), rewrite((~(~((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa)))))) <=> ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))), ((~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) <=> ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))), (![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) <=> ![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa)))))), (((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) <=> ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))), rewrite(((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))) <=> (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa)))))))), (((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) <=> (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))))), rewrite((iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)) & aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0)) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00))) <=> (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))), (((W0 = sz00) | ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)) & aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0)) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00)))) <=> ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))))), rewrite(((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))) <=> ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))), (((W0 = sz00) | ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)) & aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0)) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00)))) <=> ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))))),
% 8.86/5.90 inference(bind,[status(th)],[])).
% 8.86/5.90 tff(60,plain,
% 8.86/5.90 (![W0: $i] : ((W0 = sz00) | ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)) & aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0)) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00)))) <=> ![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))),
% 8.86/5.90 inference(quant_intro,[status(thm)],[59])).
% 8.86/5.90 tff(61,plain,
% 8.86/5.90 (^[W0: $i] : trans(monotonicity(rewrite(((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) <=> ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))))), rewrite((~(~(W0 = sz00))) <=> (W0 = sz00)), trans(monotonicity(rewrite((~(~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)))) <=> iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))), rewrite(((aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00))) <=> (aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0)) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00)))), (((~(~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)))) & ((aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00)))) <=> (iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)) & (aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0)) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00)))))), rewrite((iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)) & (aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0)) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00)))) <=> (iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)) & aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0)) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00)))), (((~(~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)))) & ((aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00)))) <=> (iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)) & aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0)) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00))))), ((((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (~(~(W0 = sz00))) | ((~(~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)))) & ((aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00))))) <=> (((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (W0 = sz00) | (iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)) & aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0)) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00)))))), rewrite((((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (W0 = sz00) | (iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)) & aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0)) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00)))) <=> ((W0 = sz00) | ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)) & aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0)) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00))))), ((((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (~(~(W0 = sz00))) | ((~(~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)))) & ((aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00))))) <=> ((W0 = sz00) | ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)) & aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0)) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00))))))),
% 8.86/5.91 inference(bind,[status(th)],[])).
% 8.86/5.91 tff(62,plain,
% 8.86/5.91 (![W0: $i] : (((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (~(~(W0 = sz00))) | ((~(~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)))) & ((aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00))))) <=> ![W0: $i] : ((W0 = sz00) | ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)) & aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0)) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00))))),
% 8.86/5.91 inference(quant_intro,[status(thm)],[61])).
% 8.86/5.91 tff(63,plain,
% 8.86/5.91 ((~?[W0: $i] : ((aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00))))))) <=> (~?[W0: $i] : ((aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00)))))))),
% 8.86/5.91 inference(rewrite,[status(thm)],[])).
% 8.86/5.91 tff(64,plain,
% 8.86/5.91 ((~?[W0: $i] : ((aElementOf0(W0, xI) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00))))))) <=> (~?[W0: $i] : ((aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00)))))))),
% 8.86/5.91 inference(rewrite,[status(thm)],[])).
% 8.86/5.91 tff(65,plain,
% 8.86/5.91 ((~?[W0: $i] : ((aElementOf0(W0, xI) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00))))))) <=> (~?[W0: $i] : ((aElementOf0(W0, xI) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00)))))))),
% 8.86/5.91 inference(rewrite,[status(thm)],[])).
% 8.86/5.91 tff(66,plain,
% 8.86/5.91 ((~?[W0: $i] : (((?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0)) | aElementOf0(W0, xI)) & (~(W0 = sz00))) & ![W1: $i] : (((?[W2: $i, W3: $i] : ((aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb))) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI)) & (~(W1 = sz00))) => (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0)))))) <=> (~?[W0: $i] : ((aElementOf0(W0, xI) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00)))))))),
% 8.86/5.91 inference(rewrite,[status(thm)],[])).
% 8.86/5.91 tff(67,axiom,(~?[W0: $i] : (((?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0)) | aElementOf0(W0, xI)) & (~(W0 = sz00))) & ![W1: $i] : (((?[W2: $i, W3: $i] : ((aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb))) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI)) & (~(W1 = sz00))) => (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 8.86/5.91 tff(68,plain,
% 8.86/5.91 (~?[W0: $i] : ((aElementOf0(W0, xI) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00))))))),
% 8.86/5.91 inference(modus_ponens,[status(thm)],[67, 66])).
% 8.86/5.91 tff(69,plain,
% 8.86/5.91 (~?[W0: $i] : ((aElementOf0(W0, xI) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00))))))),
% 8.86/5.91 inference(modus_ponens,[status(thm)],[68, 65])).
% 8.86/5.91 tff(70,plain,
% 8.86/5.91 (~?[W0: $i] : ((aElementOf0(W0, xI) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00))))))),
% 8.86/5.91 inference(modus_ponens,[status(thm)],[69, 65])).
% 8.86/5.91 tff(71,plain,
% 8.86/5.91 (~?[W0: $i] : ((aElementOf0(W0, xI) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, xI) & (~(W1 = sz00))))))),
% 8.86/5.91 inference(modus_ponens,[status(thm)],[70, 65])).
% 8.86/5.91 tff(72,plain,
% 8.86/5.91 (~?[W0: $i] : ((aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00))))))),
% 8.86/5.91 inference(modus_ponens,[status(thm)],[71, 64])).
% 8.86/5.91 tff(73,plain,
% 8.86/5.91 (~?[W0: $i] : ((aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00))))))),
% 8.86/5.91 inference(modus_ponens,[status(thm)],[72, 63])).
% 8.86/5.91 tff(74,plain,
% 8.86/5.91 (~?[W0: $i] : ((aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00))))))),
% 8.86/5.91 inference(modus_ponens,[status(thm)],[73, 63])).
% 8.86/5.91 tff(75,plain,
% 8.86/5.91 (~?[W0: $i] : ((aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00))))))),
% 8.86/5.91 inference(modus_ponens,[status(thm)],[74, 63])).
% 8.86/5.91 tff(76,plain,
% 8.86/5.91 (^[W0: $i] : nnf_neg(nnf_neg(refl($oeq((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))), (~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))), nnf_neg(proof_bind(^[W1: $i, W2: $i] : refl($oeq((~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))), (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))))), $oeq((~?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))), ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))))), $oeq((~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))), ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))))), refl($oeq((~(~(W0 = sz00))), (~(~(W0 = sz00))))), trans(sk($oeq((~![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00)))))), (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (~(?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = tptp_fun_W1_39(W0))) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00)))))))), nnf_neg(refl($oeq((~(~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)))), (~(~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)))))), nnf_neg(monotonicity(sk($oeq(?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = tptp_fun_W1_39(W0))), (aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))))), refl($oeq(aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))), aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))), refl($oeq((~(tptp_fun_W1_39(W0) = sz00)), (~(tptp_fun_W1_39(W0) = sz00)))), $oeq((?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = tptp_fun_W1_39(W0))) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00))), ((aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00))))), $oeq((~(~(?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = tptp_fun_W1_39(W0))) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00))))), ((aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00))))), $oeq((~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (~(?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = tptp_fun_W1_39(W0))) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00)))))), ((~(~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)))) & ((aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00)))))), $oeq((~![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00)))))), ((~(~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)))) & ((aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00)))))), $oeq((~((aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | ?[W1: $i, W2: $i] : (aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0))) & (~(W0 = sz00)) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(?[W2: $i, W3: $i] : (aElementOf0(W2, slsdtgt0(xa)) & aElementOf0(W3, slsdtgt0(xb)) & (sdtpldt0(W2, W3) = W1)) & aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(W1 = sz00))))))), (((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (~(~(W0 = sz00))) | ((~(~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)))) & ((aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00)))))))),
% 8.86/5.91 inference(bind,[status(th)],[])).
% 8.86/5.91 tff(77,plain,(
% 8.86/5.91 ![W0: $i] : (((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (~(~(W0 = sz00))) | ((~(~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)))) & ((aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00)))))),
% 8.86/5.91 inference(nnf-neg,[status(sab)],[75, 76])).
% 8.86/5.91 tff(78,plain,
% 8.86/5.91 (![W0: $i] : ((W0 = sz00) | ((~aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) & ![W1: $i, W2: $i] : (~(aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb)) & (sdtpldt0(W1, W2) = W0)))) | (iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0)) & aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa)) & aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb)) & (sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0)) & aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) & (~(tptp_fun_W1_39(W0) = sz00))))),
% 8.86/5.91 inference(modus_ponens,[status(thm)],[77, 62])).
% 8.86/5.91 tff(79,plain,
% 8.86/5.91 (![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))),
% 8.86/5.91 inference(modus_ponens,[status(thm)],[78, 60])).
% 8.86/5.91 tff(80,plain,
% 8.86/5.91 (![W0: $i] : ((W0 = sz00) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))))),
% 8.86/5.91 inference(modus_ponens,[status(thm)],[79, 58])).
% 8.86/5.91 tff(81,plain,
% 8.86/5.91 (![W0: $i] : ((W0 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))))),
% 8.86/5.91 inference(modus_ponens,[status(thm)],[80, 53])).
% 8.86/5.91 tff(82,plain,
% 8.86/5.91 (((~![W0: $i] : ((W0 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))))) | ((W1!36 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~aElementOf0(tptp_fun_W2_41(W1!36), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W1!36), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W1!36), tptp_fun_W3_40(W1!36)) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W1!36)))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))))) | (W1!36 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~aElementOf0(tptp_fun_W2_41(W1!36), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W1!36), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W1!36), tptp_fun_W3_40(W1!36)) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W1!36)))))))),
% 8.86/5.91 inference(rewrite,[status(thm)],[])).
% 8.86/5.91 tff(83,plain,
% 8.86/5.91 (((W1!36 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~aElementOf0(tptp_fun_W2_41(W1!36), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W1!36), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W1!36), tptp_fun_W3_40(W1!36)) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W1!36))))))) <=> ((W1!36 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~aElementOf0(tptp_fun_W2_41(W1!36), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W1!36), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W1!36), tptp_fun_W3_40(W1!36)) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W1!36)))))))),
% 8.86/5.91 inference(rewrite,[status(thm)],[])).
% 8.86/5.91 tff(84,plain,
% 8.86/5.91 ((~(aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W1!36)) | (~aElementOf0(W1, slsdtgt0(xa))))))) <=> (~(aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W1!36))))))),
% 8.86/5.91 inference(rewrite,[status(thm)],[])).
% 8.86/5.91 tff(85,plain,
% 8.86/5.91 ((~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~aElementOf0(tptp_fun_W2_41(W1!36), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W1!36), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W1!36), tptp_fun_W3_40(W1!36)) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) <=> (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~aElementOf0(tptp_fun_W2_41(W1!36), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W1!36), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W1!36), tptp_fun_W3_40(W1!36)) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))))),
% 8.86/5.91 inference(rewrite,[status(thm)],[])).
% 8.86/5.91 tff(86,plain,
% 8.86/5.91 (((W1!36 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~aElementOf0(tptp_fun_W2_41(W1!36), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W1!36), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W1!36), tptp_fun_W3_40(W1!36)) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W1!36)) | (~aElementOf0(W1, slsdtgt0(xa)))))))) <=> ((W1!36 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~aElementOf0(tptp_fun_W2_41(W1!36), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W1!36), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W1!36), tptp_fun_W3_40(W1!36)) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W1!36)))))))),
% 8.86/5.91 inference(monotonicity,[status(thm)],[85, 84])).
% 8.86/5.91 tff(87,plain,
% 8.86/5.91 (((W1!36 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~aElementOf0(tptp_fun_W2_41(W1!36), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W1!36), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W1!36), tptp_fun_W3_40(W1!36)) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W1!36)) | (~aElementOf0(W1, slsdtgt0(xa)))))))) <=> ((W1!36 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~aElementOf0(tptp_fun_W2_41(W1!36), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W1!36), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W1!36), tptp_fun_W3_40(W1!36)) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W1!36)))))))),
% 8.86/5.91 inference(transitivity,[status(thm)],[86, 83])).
% 8.86/5.91 tff(88,plain,
% 8.86/5.91 (((~![W0: $i] : ((W0 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))))) | ((W1!36 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~aElementOf0(tptp_fun_W2_41(W1!36), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W1!36), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W1!36), tptp_fun_W3_40(W1!36)) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W1!36)) | (~aElementOf0(W1, slsdtgt0(xa))))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))))) | ((W1!36 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~aElementOf0(tptp_fun_W2_41(W1!36), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W1!36), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W1!36), tptp_fun_W3_40(W1!36)) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W1!36))))))))),
% 8.86/5.91 inference(monotonicity,[status(thm)],[87])).
% 8.86/5.91 tff(89,plain,
% 8.86/5.91 (((~![W0: $i] : ((W0 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))))) | ((W1!36 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~aElementOf0(tptp_fun_W2_41(W1!36), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W1!36), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W1!36), tptp_fun_W3_40(W1!36)) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W1!36)) | (~aElementOf0(W1, slsdtgt0(xa))))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))))) | (W1!36 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~aElementOf0(tptp_fun_W2_41(W1!36), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W1!36), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W1!36), tptp_fun_W3_40(W1!36)) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W1!36)))))))),
% 8.86/5.92 inference(transitivity,[status(thm)],[88, 82])).
% 8.86/5.92 tff(90,plain,
% 8.86/5.92 ((~![W0: $i] : ((W0 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))))) | ((W1!36 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~aElementOf0(tptp_fun_W2_41(W1!36), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W1!36), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W1!36), tptp_fun_W3_40(W1!36)) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W1!36)) | (~aElementOf0(W1, slsdtgt0(xa))))))))),
% 8.86/5.92 inference(quant_inst,[status(thm)],[])).
% 8.86/5.92 tff(91,plain,
% 8.86/5.92 ((~![W0: $i] : ((W0 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W0)), sbrdtbr0(W0))) | (tptp_fun_W1_39(W0) = sz00) | (~aElementOf0(tptp_fun_W2_41(W0), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W0), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W0), tptp_fun_W3_40(W0)) = tptp_fun_W1_39(W0))) | (~aElementOf0(tptp_fun_W1_39(W0), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W0, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~(sdtpldt0(W1, W2) = W0)) | (~aElementOf0(W1, slsdtgt0(xa))))))))) | (W1!36 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~aElementOf0(tptp_fun_W2_41(W1!36), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W1!36), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W1!36), tptp_fun_W3_40(W1!36)) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))) | (~(aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W1: $i, W2: $i] : ((~aElementOf0(W2, slsdtgt0(xb))) | (~aElementOf0(W1, slsdtgt0(xa))) | (~(sdtpldt0(W1, W2) = W1!36))))))),
% 8.86/5.92 inference(modus_ponens,[status(thm)],[90, 89])).
% 8.86/5.92 tff(92,plain,
% 8.86/5.92 (~((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~aElementOf0(tptp_fun_W2_41(W1!36), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W1!36), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W1!36), tptp_fun_W3_40(W1!36)) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))))),
% 8.86/5.92 inference(unit_resolution,[status(thm)],[91, 81, 51, 49])).
% 8.86/5.92 tff(93,plain,
% 8.86/5.92 (((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~aElementOf0(tptp_fun_W2_41(W1!36), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W1!36), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W1!36), tptp_fun_W3_40(W1!36)) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))) | aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))),
% 8.86/5.92 inference(tautology,[status(thm)],[])).
% 8.86/5.92 tff(94,plain,
% 8.86/5.92 (aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))),
% 8.86/5.92 inference(unit_resolution,[status(thm)],[93, 92])).
% 8.86/5.92 tff(95,plain,
% 8.86/5.92 ((aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~aElementOf0(W3, slsdtgt0(xa))) | (~(sdtpldt0(W3, W4) = tptp_fun_W1_39(W1!36)))))) | (~aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))),
% 8.86/5.92 inference(tautology,[status(thm)],[])).
% 8.86/5.92 tff(96,plain,
% 8.86/5.92 (aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~aElementOf0(W3, slsdtgt0(xa))) | (~(sdtpldt0(W3, W4) = tptp_fun_W1_39(W1!36)))))),
% 8.86/5.92 inference(unit_resolution,[status(thm)],[95, 94])).
% 8.86/5.92 tff(97,plain,
% 8.86/5.92 (((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~aElementOf0(tptp_fun_W2_41(W1!36), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W1!36), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W1!36), tptp_fun_W3_40(W1!36)) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))) | (~(tptp_fun_W1_39(W1!36) = sz00))),
% 8.86/5.92 inference(tautology,[status(thm)],[])).
% 8.86/5.92 tff(98,plain,
% 8.86/5.92 (~(tptp_fun_W1_39(W1!36) = sz00)),
% 8.86/5.92 inference(unit_resolution,[status(thm)],[97, 92])).
% 8.86/5.92 tff(99,plain,
% 8.86/5.92 (((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~aElementOf0(tptp_fun_W2_41(W1!36), slsdtgt0(xa))) | (~aElementOf0(tptp_fun_W3_40(W1!36), slsdtgt0(xb))) | (~(sdtpldt0(tptp_fun_W2_41(W1!36), tptp_fun_W3_40(W1!36)) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))))) | iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))),
% 8.86/5.92 inference(tautology,[status(thm)],[])).
% 8.86/5.92 tff(100,plain,
% 8.86/5.92 (iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))),
% 8.86/5.92 inference(unit_resolution,[status(thm)],[99, 92])).
% 8.86/5.92 tff(101,plain,
% 8.86/5.92 (((W1!36 = sz00) | (~aElementOf0(W2!38, slsdtgt0(xa))) | (~aElementOf0(W3!37, slsdtgt0(xb))) | (~(sdtpldt0(W2!38, W3!37) = W1!36)) | (~aElementOf0(W1!36, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))) | (~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa)))))))))) | ![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))),
% 8.86/5.92 inference(tautology,[status(thm)],[])).
% 8.86/5.92 tff(102,plain,
% 8.86/5.92 (![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))),
% 8.86/5.92 inference(unit_resolution,[status(thm)],[101, 45])).
% 8.86/5.92 tff(103,plain,
% 8.86/5.92 (((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))) | ((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~(aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~aElementOf0(W3, slsdtgt0(xa))) | (~(sdtpldt0(W3, W4) = tptp_fun_W1_39(W1!36))))))))) <=> ((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))) | (~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~(aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~aElementOf0(W3, slsdtgt0(xa))) | (~(sdtpldt0(W3, W4) = tptp_fun_W1_39(W1!36))))))))),
% 8.97/5.92 inference(rewrite,[status(thm)],[])).
% 8.97/5.92 tff(104,plain,
% 8.97/5.92 (((tptp_fun_W1_39(W1!36) = sz00) | (~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (~(aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~aElementOf0(W3, slsdtgt0(xa))) | (~(sdtpldt0(W3, W4) = tptp_fun_W1_39(W1!36)))))))) <=> ((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~(aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~aElementOf0(W3, slsdtgt0(xa))) | (~(sdtpldt0(W3, W4) = tptp_fun_W1_39(W1!36))))))))),
% 8.97/5.92 inference(rewrite,[status(thm)],[])).
% 8.97/5.92 tff(105,plain,
% 8.97/5.92 ((~(aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(W3, slsdtgt0(xa))))))) <=> (~(aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~aElementOf0(W3, slsdtgt0(xa))) | (~(sdtpldt0(W3, W4) = tptp_fun_W1_39(W1!36)))))))),
% 8.97/5.92 inference(rewrite,[status(thm)],[])).
% 8.97/5.92 tff(106,plain,
% 8.97/5.92 (((tptp_fun_W1_39(W1!36) = sz00) | (~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (~(aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(W3, slsdtgt0(xa)))))))) <=> ((tptp_fun_W1_39(W1!36) = sz00) | (~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (~(aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~aElementOf0(W3, slsdtgt0(xa))) | (~(sdtpldt0(W3, W4) = tptp_fun_W1_39(W1!36))))))))),
% 8.97/5.92 inference(monotonicity,[status(thm)],[105])).
% 8.97/5.92 tff(107,plain,
% 8.97/5.92 (((tptp_fun_W1_39(W1!36) = sz00) | (~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (~(aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(W3, slsdtgt0(xa)))))))) <=> ((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~(aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~aElementOf0(W3, slsdtgt0(xa))) | (~(sdtpldt0(W3, W4) = tptp_fun_W1_39(W1!36))))))))),
% 8.97/5.92 inference(transitivity,[status(thm)],[106, 104])).
% 8.97/5.92 tff(108,plain,
% 8.97/5.92 (((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))) | ((tptp_fun_W1_39(W1!36) = sz00) | (~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (~(aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(W3, slsdtgt0(xa))))))))) <=> ((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))) | ((~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~(aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~aElementOf0(W3, slsdtgt0(xa))) | (~(sdtpldt0(W3, W4) = tptp_fun_W1_39(W1!36)))))))))),
% 8.97/5.93 inference(monotonicity,[status(thm)],[107])).
% 8.97/5.93 tff(109,plain,
% 8.97/5.93 (((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))) | ((tptp_fun_W1_39(W1!36) = sz00) | (~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (~(aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(W3, slsdtgt0(xa))))))))) <=> ((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))) | (~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~(aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~aElementOf0(W3, slsdtgt0(xa))) | (~(sdtpldt0(W3, W4) = tptp_fun_W1_39(W1!36))))))))),
% 8.97/5.93 inference(transitivity,[status(thm)],[108, 103])).
% 8.97/5.93 tff(110,plain,
% 8.97/5.93 ((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))) | ((tptp_fun_W1_39(W1!36) = sz00) | (~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (~(aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = tptp_fun_W1_39(W1!36))) | (~aElementOf0(W3, slsdtgt0(xa))))))))),
% 8.97/5.93 inference(quant_inst,[status(thm)],[])).
% 8.97/5.93 tff(111,plain,
% 8.97/5.93 ((~![W2: $i] : ((W2 = sz00) | (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1!36))) | (~(aElementOf0(W2, sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~(sdtpldt0(W3, W4) = W2)) | (~aElementOf0(W3, slsdtgt0(xa))))))))) | (~iLess0(sbrdtbr0(tptp_fun_W1_39(W1!36)), sbrdtbr0(W1!36))) | (tptp_fun_W1_39(W1!36) = sz00) | (~(aElementOf0(tptp_fun_W1_39(W1!36), sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))) | (~![W3: $i, W4: $i] : ((~aElementOf0(W4, slsdtgt0(xb))) | (~aElementOf0(W3, slsdtgt0(xa))) | (~(sdtpldt0(W3, W4) = tptp_fun_W1_39(W1!36)))))))),
% 8.97/5.93 inference(modus_ponens,[status(thm)],[110, 109])).
% 8.97/5.93 tff(112,plain,
% 8.97/5.93 ($false),
% 8.97/5.93 inference(unit_resolution,[status(thm)],[111, 102, 100, 98, 96])).
% 8.97/5.93 % SZS output end Proof
%------------------------------------------------------------------------------