TSTP Solution File: RNG114+4 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG114+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 03:18:29 EDT 2022
% Result : Theorem 3.19s 2.25s
% Output : Proof 3.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : RNG114+4 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Sep 2 22:44:14 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 3.19/2.25 % SZS status Theorem
% 3.19/2.25 % SZS output start Proof
% 3.19/2.25 tff(sdtpldt0_type, type, (
% 3.19/2.25 sdtpldt0: ( $i * $i ) > $i)).
% 3.19/2.25 tff(sdtasdt0_type, type, (
% 3.19/2.25 sdtasdt0: ( $i * $i ) > $i)).
% 3.19/2.25 tff(tptp_fun_W2_33_type, type, (
% 3.19/2.25 tptp_fun_W2_33: $i > $i)).
% 3.19/2.25 tff(tptp_fun_W1_36_type, type, (
% 3.19/2.25 tptp_fun_W1_36: $i)).
% 3.19/2.25 tff(xb_type, type, (
% 3.19/2.25 xb: $i)).
% 3.19/2.25 tff(tptp_fun_W2_32_type, type, (
% 3.19/2.25 tptp_fun_W2_32: $i > $i)).
% 3.19/2.25 tff(tptp_fun_W0_37_type, type, (
% 3.19/2.25 tptp_fun_W0_37: $i)).
% 3.19/2.25 tff(xa_type, type, (
% 3.19/2.25 xa: $i)).
% 3.19/2.25 tff(xu_type, type, (
% 3.19/2.25 xu: $i)).
% 3.19/2.25 tff(aElement0_type, type, (
% 3.19/2.25 aElement0: $i > $o)).
% 3.19/2.25 tff(aElementOf0_type, type, (
% 3.19/2.25 aElementOf0: ( $i * $i ) > $o)).
% 3.19/2.25 tff(slsdtgt0_type, type, (
% 3.19/2.25 slsdtgt0: $i > $i)).
% 3.19/2.25 tff(sz00_type, type, (
% 3.19/2.25 sz00: $i)).
% 3.19/2.25 tff(tptp_fun_W0_31_type, type, (
% 3.19/2.25 tptp_fun_W0_31: $i)).
% 3.19/2.25 tff(sdtpldt1_type, type, (
% 3.19/2.25 sdtpldt1: ( $i * $i ) > $i)).
% 3.19/2.25 tff(tptp_fun_W2_34_type, type, (
% 3.19/2.25 tptp_fun_W2_34: $i)).
% 3.19/2.25 tff(tptp_fun_W1_35_type, type, (
% 3.19/2.25 tptp_fun_W1_35: $i)).
% 3.19/2.25 tff(xI_type, type, (
% 3.19/2.25 xI: $i)).
% 3.19/2.25 tff(iLess0_type, type, (
% 3.19/2.25 iLess0: ( $i * $i ) > $o)).
% 3.19/2.25 tff(sbrdtbr0_type, type, (
% 3.19/2.25 sbrdtbr0: $i > $i)).
% 3.19/2.25 tff(1,plain,
% 3.19/2.25 (^[W1: $i] : refl((~((~((~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, 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))))))))),
% 3.19/2.25 inference(bind,[status(th)],[])).
% 3.19/2.25 tff(2,plain,
% 3.19/2.25 (![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))))))) <=> ![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)))))))),
% 3.19/2.25 inference(quant_intro,[status(thm)],[1])).
% 3.19/2.25 tff(3,plain,
% 3.19/2.25 (^[W1: $i] : rewrite((~((~((~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, 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))))))))),
% 3.19/2.25 inference(bind,[status(th)],[])).
% 3.19/2.25 tff(4,plain,
% 3.19/2.25 (![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))))))) <=> ![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)))))))),
% 3.19/2.25 inference(quant_intro,[status(thm)],[3])).
% 3.19/2.25 tff(5,plain,
% 3.19/2.25 (![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))))))) <=> ![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)))))))),
% 3.19/2.25 inference(transitivity,[status(thm)],[4, 2])).
% 3.19/2.25 tff(6,plain,
% 3.19/2.25 (^[W1: $i] : trans(monotonicity(rewrite(((~aElementOf0(W1, slsdtgt0(xb))) | (aElement0(tptp_fun_W2_33(W1)) & (sdtasdt0(xb, tptp_fun_W2_33(W1)) = W1))) <=> ((~aElementOf0(W1, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W2_33(W1))) | (~(sdtasdt0(xb, tptp_fun_W2_33(W1)) = W1)))))), rewrite((aElementOf0(W1, slsdtgt0(xb)) | ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xb, W2) = W1)))) <=> (aElementOf0(W1, slsdtgt0(xb)) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1))))), ((((~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, 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))))))), rewrite((((~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, 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, 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, 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)))))))))),
% 3.19/2.25 inference(bind,[status(th)],[])).
% 3.19/2.25 tff(7,plain,
% 3.19/2.25 (![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))))) <=> ![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)))))))),
% 3.19/2.25 inference(quant_intro,[status(thm)],[6])).
% 3.19/2.25 tff(8,plain,
% 3.19/2.25 ((![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)))),
% 3.19/2.25 inference(rewrite,[status(thm)],[])).
% 3.19/2.25 tff(9,plain,
% 3.19/2.25 (?[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)))),
% 3.19/2.26 inference(rewrite,[status(thm)],[])).
% 3.19/2.26 tff(10,plain,
% 3.19/2.26 (^[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)))))),
% 3.19/2.26 inference(bind,[status(th)],[])).
% 3.19/2.26 tff(11,plain,
% 3.19/2.26 (?[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)))),
% 3.19/2.26 inference(quant_intro,[status(thm)],[10])).
% 3.19/2.26 tff(12,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')).
% 3.19/2.26 tff(13,plain,
% 3.19/2.26 (?[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)))),
% 3.19/2.26 inference(modus_ponens,[status(thm)],[12, 11])).
% 3.19/2.26 tff(14,plain,
% 3.19/2.26 (?[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)))),
% 3.19/2.26 inference(modus_ponens,[status(thm)],[13, 9])).
% 3.19/2.26 tff(15,plain,
% 3.19/2.26 (![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))),
% 3.19/2.26 inference(modus_ponens,[status(thm)],[14, 8])).
% 3.19/2.26 tff(16,plain,
% 3.19/2.26 (![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)))))),
% 3.19/2.26 inference(and_elim,[status(thm)],[15])).
% 3.19/2.26 tff(17,plain,
% 3.19/2.26 (![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)))))))),
% 3.19/2.26 inference(modus_ponens,[status(thm)],[16, 7])).
% 3.19/2.26 tff(18,plain,
% 3.19/2.26 (![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)))))))),
% 3.19/2.26 inference(modus_ponens,[status(thm)],[17, 5])).
% 3.19/2.26 tff(19,plain,
% 3.19/2.26 ((~![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!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W2_33(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W2_33(W1!36)) = W1!36)))))) | (~(aElementOf0(W1!36, slsdtgt0(xb)) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1!36)))))))),
% 3.19/2.26 inference(quant_inst,[status(thm)],[])).
% 3.19/2.26 tff(20,plain,
% 3.19/2.26 (~((~((~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W2_33(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W2_33(W1!36)) = W1!36)))))) | (~(aElementOf0(W1!36, slsdtgt0(xb)) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1!36))))))),
% 3.19/2.26 inference(unit_resolution,[status(thm)],[19, 18])).
% 3.19/2.26 tff(21,plain,
% 3.19/2.26 (((~((~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W2_33(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W2_33(W1!36)) = W1!36)))))) | (~(aElementOf0(W1!36, slsdtgt0(xb)) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xb, W2) = W1!36)))))) | ((~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W2_33(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W2_33(W1!36)) = W1!36)))))),
% 3.19/2.26 inference(tautology,[status(thm)],[])).
% 3.19/2.26 tff(22,plain,
% 3.19/2.26 ((~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W2_33(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W2_33(W1!36)) = W1!36))))),
% 3.19/2.26 inference(unit_resolution,[status(thm)],[21, 20])).
% 3.19/2.26 tff(23,plain,
% 3.19/2.26 (?[W0: $i, W1: $i] : (aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb)) & (sdtpldt0(W0, W1) = xu)) <=> ?[W0: $i, W1: $i] : (aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb)) & (sdtpldt0(W0, W1) = xu))),
% 3.19/2.26 inference(rewrite,[status(thm)],[])).
% 3.19/2.26 tff(24,plain,
% 3.19/2.26 (^[W0: $i, W1: $i] : rewrite(((aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb))) & (sdtpldt0(W0, W1) = xu)) <=> (aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb)) & (sdtpldt0(W0, W1) = xu)))),
% 3.19/2.26 inference(bind,[status(th)],[])).
% 3.19/2.26 tff(25,plain,
% 3.19/2.26 (?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb))) & (sdtpldt0(W0, W1) = xu)) <=> ?[W0: $i, W1: $i] : (aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb)) & (sdtpldt0(W0, W1) = xu))),
% 3.19/2.26 inference(quant_intro,[status(thm)],[24])).
% 3.19/2.26 tff(26,axiom,(((?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb))) & (sdtpldt0(W0, W1) = xu)) & aElementOf0(xu, xI)) & (~(xu = sz00))) & ![W0: $i] : (((?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0)) | aElementOf0(W0, xI)) & (~(W0 = sz00))) => (~iLess0(sbrdtbr0(W0), sbrdtbr0(xu))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2273')).
% 3.19/2.26 tff(27,plain,
% 3.19/2.26 ((?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb))) & (sdtpldt0(W0, W1) = xu)) & aElementOf0(xu, xI)) & (~(xu = sz00))),
% 3.19/2.26 inference(and_elim,[status(thm)],[26])).
% 3.19/2.26 tff(28,plain,
% 3.19/2.26 (?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb))) & (sdtpldt0(W0, W1) = xu)) & aElementOf0(xu, xI)),
% 3.19/2.26 inference(and_elim,[status(thm)],[27])).
% 3.19/2.26 tff(29,plain,
% 3.19/2.26 (?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb))) & (sdtpldt0(W0, W1) = xu))),
% 3.19/2.26 inference(and_elim,[status(thm)],[28])).
% 3.19/2.26 tff(30,plain,
% 3.19/2.26 (?[W0: $i, W1: $i] : (aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb)) & (sdtpldt0(W0, W1) = xu))),
% 3.19/2.26 inference(modus_ponens,[status(thm)],[29, 25])).
% 3.19/2.26 tff(31,plain,
% 3.19/2.26 (?[W0: $i, W1: $i] : (aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb)) & (sdtpldt0(W0, W1) = xu))),
% 3.19/2.26 inference(modus_ponens,[status(thm)],[30, 23])).
% 3.19/2.26 tff(32,plain,(
% 3.19/2.26 aElementOf0(W0!37, slsdtgt0(xa)) & aElementOf0(W1!36, slsdtgt0(xb)) & (sdtpldt0(W0!37, W1!36) = xu)),
% 3.19/2.26 inference(skolemize,[status(sab)],[31])).
% 3.19/2.26 tff(33,plain,
% 3.19/2.26 (aElementOf0(W1!36, slsdtgt0(xb))),
% 3.19/2.26 inference(and_elim,[status(thm)],[32])).
% 3.19/2.26 tff(34,plain,
% 3.19/2.26 ((~((~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W2_33(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W2_33(W1!36)) = W1!36)))))) | (~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W2_33(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W2_33(W1!36)) = W1!36))))),
% 3.19/2.26 inference(tautology,[status(thm)],[])).
% 3.19/2.26 tff(35,plain,
% 3.19/2.26 ((~((~aElementOf0(W1!36, slsdtgt0(xb))) | (~((~aElement0(tptp_fun_W2_33(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W2_33(W1!36)) = W1!36)))))) | (~((~aElement0(tptp_fun_W2_33(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W2_33(W1!36)) = W1!36))))),
% 3.19/2.27 inference(unit_resolution,[status(thm)],[34, 33])).
% 3.19/2.27 tff(36,plain,
% 3.19/2.27 (~((~aElement0(tptp_fun_W2_33(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W2_33(W1!36)) = W1!36)))),
% 3.19/2.27 inference(unit_resolution,[status(thm)],[35, 22])).
% 3.19/2.27 tff(37,plain,
% 3.19/2.27 (((~aElement0(tptp_fun_W2_33(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W2_33(W1!36)) = W1!36))) | (sdtasdt0(xb, tptp_fun_W2_33(W1!36)) = W1!36)),
% 3.19/2.27 inference(tautology,[status(thm)],[])).
% 3.19/2.27 tff(38,plain,
% 3.19/2.27 (sdtasdt0(xb, tptp_fun_W2_33(W1!36)) = W1!36),
% 3.19/2.27 inference(unit_resolution,[status(thm)],[37, 36])).
% 3.19/2.27 tff(39,plain,
% 3.19/2.27 (^[W1: $i] : refl((~((~((~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))))))) <=> (~((~((~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))))))))),
% 3.19/2.27 inference(bind,[status(th)],[])).
% 3.19/2.27 tff(40,plain,
% 3.19/2.27 (![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(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)))))))),
% 3.19/2.27 inference(quant_intro,[status(thm)],[39])).
% 3.19/2.27 tff(41,plain,
% 3.19/2.27 (^[W1: $i] : rewrite((~((~((~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))))))) <=> (~((~((~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))))))))),
% 3.19/2.27 inference(bind,[status(th)],[])).
% 3.19/2.27 tff(42,plain,
% 3.19/2.27 (![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(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)))))))),
% 3.19/2.27 inference(quant_intro,[status(thm)],[41])).
% 3.19/2.27 tff(43,plain,
% 3.19/2.27 (![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(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)))))))),
% 3.19/2.27 inference(transitivity,[status(thm)],[42, 40])).
% 3.19/2.27 tff(44,plain,
% 3.19/2.27 (^[W1: $i] : trans(monotonicity(rewrite(((~aElementOf0(W1, slsdtgt0(xa))) | (aElement0(tptp_fun_W2_32(W1)) & (sdtasdt0(xa, tptp_fun_W2_32(W1)) = W1))) <=> ((~aElementOf0(W1, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W2_32(W1))) | (~(sdtasdt0(xa, tptp_fun_W2_32(W1)) = W1)))))), rewrite((aElementOf0(W1, slsdtgt0(xa)) | ![W2: $i] : (~(aElement0(W2) & (sdtasdt0(xa, W2) = W1)))) <=> (aElementOf0(W1, slsdtgt0(xa)) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W1))))), ((((~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))))) <=> (((~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))))))), rewrite((((~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))))) <=> (~((~((~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)))))))), ((((~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))))) <=> (~((~((~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)))))))))),
% 3.19/2.27 inference(bind,[status(th)],[])).
% 3.19/2.27 tff(45,plain,
% 3.19/2.27 (![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(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)))))))),
% 3.19/2.27 inference(quant_intro,[status(thm)],[44])).
% 3.19/2.27 tff(46,plain,
% 3.19/2.27 (![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)))))),
% 3.19/2.27 inference(and_elim,[status(thm)],[15])).
% 3.19/2.27 tff(47,plain,
% 3.19/2.27 (![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)))))))),
% 3.19/2.27 inference(modus_ponens,[status(thm)],[46, 45])).
% 3.19/2.27 tff(48,plain,
% 3.19/2.27 (![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)))))))),
% 3.19/2.27 inference(modus_ponens,[status(thm)],[47, 43])).
% 3.19/2.27 tff(49,plain,
% 3.19/2.27 ((~![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)))))))) | (~((~((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W2_32(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W2_32(W0!37)) = W0!37)))))) | (~(aElementOf0(W0!37, slsdtgt0(xa)) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0!37)))))))),
% 3.19/2.27 inference(quant_inst,[status(thm)],[])).
% 3.19/2.27 tff(50,plain,
% 3.19/2.27 (~((~((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W2_32(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W2_32(W0!37)) = W0!37)))))) | (~(aElementOf0(W0!37, slsdtgt0(xa)) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0!37))))))),
% 3.19/2.27 inference(unit_resolution,[status(thm)],[49, 48])).
% 3.19/2.27 tff(51,plain,
% 3.19/2.27 (((~((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W2_32(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W2_32(W0!37)) = W0!37)))))) | (~(aElementOf0(W0!37, slsdtgt0(xa)) | ![W2: $i] : ((~aElement0(W2)) | (~(sdtasdt0(xa, W2) = W0!37)))))) | ((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W2_32(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W2_32(W0!37)) = W0!37)))))),
% 3.19/2.27 inference(tautology,[status(thm)],[])).
% 3.19/2.27 tff(52,plain,
% 3.19/2.27 ((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W2_32(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W2_32(W0!37)) = W0!37))))),
% 3.19/2.27 inference(unit_resolution,[status(thm)],[51, 50])).
% 3.19/2.27 tff(53,plain,
% 3.19/2.27 (aElementOf0(W0!37, slsdtgt0(xa))),
% 3.19/2.27 inference(and_elim,[status(thm)],[32])).
% 3.19/2.27 tff(54,plain,
% 3.19/2.27 ((~((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W2_32(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W2_32(W0!37)) = W0!37)))))) | (~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W2_32(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W2_32(W0!37)) = W0!37))))),
% 3.19/2.27 inference(tautology,[status(thm)],[])).
% 3.19/2.27 tff(55,plain,
% 3.19/2.27 ((~((~aElementOf0(W0!37, slsdtgt0(xa))) | (~((~aElement0(tptp_fun_W2_32(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W2_32(W0!37)) = W0!37)))))) | (~((~aElement0(tptp_fun_W2_32(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W2_32(W0!37)) = W0!37))))),
% 3.19/2.27 inference(unit_resolution,[status(thm)],[54, 53])).
% 3.19/2.27 tff(56,plain,
% 3.19/2.27 (~((~aElement0(tptp_fun_W2_32(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W2_32(W0!37)) = W0!37)))),
% 3.19/2.27 inference(unit_resolution,[status(thm)],[55, 52])).
% 3.19/2.27 tff(57,plain,
% 3.19/2.27 (((~aElement0(tptp_fun_W2_32(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W2_32(W0!37)) = W0!37))) | (sdtasdt0(xa, tptp_fun_W2_32(W0!37)) = W0!37)),
% 3.19/2.27 inference(tautology,[status(thm)],[])).
% 3.19/2.27 tff(58,plain,
% 3.19/2.27 (sdtasdt0(xa, tptp_fun_W2_32(W0!37)) = W0!37),
% 3.19/2.27 inference(unit_resolution,[status(thm)],[57, 56])).
% 3.19/2.27 tff(59,plain,
% 3.19/2.27 (sdtpldt0(sdtasdt0(xa, tptp_fun_W2_32(W0!37)), sdtasdt0(xb, tptp_fun_W2_33(W1!36))) = sdtpldt0(W0!37, W1!36)),
% 3.19/2.27 inference(monotonicity,[status(thm)],[58, 38])).
% 3.19/2.27 tff(60,plain,
% 3.19/2.27 (sdtpldt0(W0!37, W1!36) = sdtpldt0(sdtasdt0(xa, tptp_fun_W2_32(W0!37)), sdtasdt0(xb, tptp_fun_W2_33(W1!36)))),
% 3.19/2.27 inference(symmetry,[status(thm)],[59])).
% 3.19/2.27 tff(61,plain,
% 3.19/2.27 (sdtpldt0(W0!37, W1!36) = xu),
% 3.19/2.27 inference(and_elim,[status(thm)],[32])).
% 3.19/2.27 tff(62,plain,
% 3.19/2.27 (xu = sdtpldt0(W0!37, W1!36)),
% 3.19/2.27 inference(symmetry,[status(thm)],[61])).
% 3.19/2.27 tff(63,plain,
% 3.19/2.27 (xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W2_32(W0!37)), sdtasdt0(xb, tptp_fun_W2_33(W1!36)))),
% 3.19/2.27 inference(transitivity,[status(thm)],[62, 60])).
% 3.19/2.27 tff(64,plain,
% 3.19/2.27 (((~aElement0(tptp_fun_W2_33(W1!36))) | (~(sdtasdt0(xb, tptp_fun_W2_33(W1!36)) = W1!36))) | aElement0(tptp_fun_W2_33(W1!36))),
% 3.19/2.27 inference(tautology,[status(thm)],[])).
% 3.19/2.27 tff(65,plain,
% 3.19/2.27 (aElement0(tptp_fun_W2_33(W1!36))),
% 3.19/2.27 inference(unit_resolution,[status(thm)],[64, 36])).
% 3.19/2.27 tff(66,plain,
% 3.19/2.27 (((~aElement0(tptp_fun_W2_32(W0!37))) | (~(sdtasdt0(xa, tptp_fun_W2_32(W0!37)) = W0!37))) | aElement0(tptp_fun_W2_32(W0!37))),
% 3.19/2.27 inference(tautology,[status(thm)],[])).
% 3.19/2.27 tff(67,plain,
% 3.19/2.27 (aElement0(tptp_fun_W2_32(W0!37))),
% 3.19/2.27 inference(unit_resolution,[status(thm)],[66, 56])).
% 3.19/2.27 tff(68,plain,
% 3.19/2.27 (^[W0: $i, W1: $i] : refl(((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))) <=> ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))))),
% 3.19/2.27 inference(bind,[status(th)],[])).
% 3.19/2.27 tff(69,plain,
% 3.19/2.27 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))) <=> ![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 3.19/2.27 inference(quant_intro,[status(thm)],[68])).
% 3.19/2.27 tff(70,plain,
% 3.19/2.27 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite((aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))) <=> (~((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))))), ((~(aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))) <=> (~(~((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))))))), rewrite((~(~((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))))) <=> ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))), ((~(aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))) <=> ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))))),
% 3.19/2.27 inference(bind,[status(th)],[])).
% 3.19/2.27 tff(71,plain,
% 3.19/2.27 (![W0: $i, W1: $i] : (~(aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))) <=> ![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 3.19/2.28 inference(quant_intro,[status(thm)],[70])).
% 3.19/2.28 tff(72,plain,
% 3.19/2.28 ((~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))) <=> (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 3.19/2.28 inference(rewrite,[status(thm)],[])).
% 3.19/2.28 tff(73,plain,
% 3.19/2.28 ((~?[W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))) <=> (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 3.19/2.28 inference(rewrite,[status(thm)],[])).
% 3.19/2.28 tff(74,axiom,(~?[W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 3.19/2.28 tff(75,plain,
% 3.19/2.28 (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 3.19/2.28 inference(modus_ponens,[status(thm)],[74, 73])).
% 3.19/2.28 tff(76,plain,
% 3.19/2.28 (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 3.19/2.28 inference(modus_ponens,[status(thm)],[75, 72])).
% 3.19/2.28 tff(77,plain,
% 3.19/2.28 (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 3.19/2.28 inference(modus_ponens,[status(thm)],[76, 72])).
% 3.19/2.28 tff(78,plain,
% 3.19/2.28 (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 3.19/2.28 inference(modus_ponens,[status(thm)],[77, 72])).
% 3.19/2.28 tff(79,plain,
% 3.19/2.28 (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 3.19/2.28 inference(modus_ponens,[status(thm)],[78, 72])).
% 3.19/2.28 tff(80,plain,
% 3.19/2.28 (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 3.19/2.28 inference(modus_ponens,[status(thm)],[79, 72])).
% 3.19/2.28 tff(81,plain,
% 3.19/2.28 (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 3.19/2.28 inference(modus_ponens,[status(thm)],[80, 72])).
% 3.19/2.28 tff(82,plain,
% 3.19/2.28 (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 3.19/2.28 inference(modus_ponens,[status(thm)],[81, 72])).
% 3.19/2.28 tff(83,plain,
% 3.19/2.28 (^[W0: $i, W1: $i] : refl($oeq((~(aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))), (~(aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))))),
% 3.19/2.28 inference(bind,[status(th)],[])).
% 3.19/2.28 tff(84,plain,(
% 3.19/2.28 ![W0: $i, W1: $i] : (~(aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 3.19/2.28 inference(nnf-neg,[status(sab)],[82, 83])).
% 3.19/2.28 tff(85,plain,
% 3.19/2.28 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 3.19/2.28 inference(modus_ponens,[status(thm)],[84, 71])).
% 3.19/2.28 tff(86,plain,
% 3.19/2.28 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 3.19/2.28 inference(modus_ponens,[status(thm)],[85, 69])).
% 3.19/2.28 tff(87,plain,
% 3.19/2.28 (((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | ((~aElement0(tptp_fun_W2_32(W0!37))) | (~aElement0(tptp_fun_W2_33(W1!36))) | (~(xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W2_32(W0!37)), sdtasdt0(xb, tptp_fun_W2_33(W1!36))))))) <=> ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | (~aElement0(tptp_fun_W2_32(W0!37))) | (~aElement0(tptp_fun_W2_33(W1!36))) | (~(xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W2_32(W0!37)), sdtasdt0(xb, tptp_fun_W2_33(W1!36))))))),
% 3.19/2.28 inference(rewrite,[status(thm)],[])).
% 3.19/2.28 tff(88,plain,
% 3.19/2.28 (((~aElement0(tptp_fun_W2_33(W1!36))) | (~aElement0(tptp_fun_W2_32(W0!37))) | (~(xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W2_32(W0!37)), sdtasdt0(xb, tptp_fun_W2_33(W1!36)))))) <=> ((~aElement0(tptp_fun_W2_32(W0!37))) | (~aElement0(tptp_fun_W2_33(W1!36))) | (~(xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W2_32(W0!37)), sdtasdt0(xb, tptp_fun_W2_33(W1!36))))))),
% 3.19/2.28 inference(rewrite,[status(thm)],[])).
% 3.19/2.28 tff(89,plain,
% 3.19/2.28 (((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | ((~aElement0(tptp_fun_W2_33(W1!36))) | (~aElement0(tptp_fun_W2_32(W0!37))) | (~(xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W2_32(W0!37)), sdtasdt0(xb, tptp_fun_W2_33(W1!36))))))) <=> ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | ((~aElement0(tptp_fun_W2_32(W0!37))) | (~aElement0(tptp_fun_W2_33(W1!36))) | (~(xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W2_32(W0!37)), sdtasdt0(xb, tptp_fun_W2_33(W1!36)))))))),
% 3.19/2.28 inference(monotonicity,[status(thm)],[88])).
% 3.19/2.28 tff(90,plain,
% 3.19/2.28 (((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | ((~aElement0(tptp_fun_W2_33(W1!36))) | (~aElement0(tptp_fun_W2_32(W0!37))) | (~(xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W2_32(W0!37)), sdtasdt0(xb, tptp_fun_W2_33(W1!36))))))) <=> ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | (~aElement0(tptp_fun_W2_32(W0!37))) | (~aElement0(tptp_fun_W2_33(W1!36))) | (~(xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W2_32(W0!37)), sdtasdt0(xb, tptp_fun_W2_33(W1!36))))))),
% 3.19/2.28 inference(transitivity,[status(thm)],[89, 87])).
% 3.19/2.28 tff(91,plain,
% 3.19/2.28 ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | ((~aElement0(tptp_fun_W2_33(W1!36))) | (~aElement0(tptp_fun_W2_32(W0!37))) | (~(xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W2_32(W0!37)), sdtasdt0(xb, tptp_fun_W2_33(W1!36))))))),
% 3.19/2.28 inference(quant_inst,[status(thm)],[])).
% 3.19/2.28 tff(92,plain,
% 3.19/2.28 ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))) | (~aElement0(tptp_fun_W2_32(W0!37))) | (~aElement0(tptp_fun_W2_33(W1!36))) | (~(xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W2_32(W0!37)), sdtasdt0(xb, tptp_fun_W2_33(W1!36)))))),
% 3.19/2.28 inference(modus_ponens,[status(thm)],[91, 90])).
% 3.19/2.28 tff(93,plain,
% 3.19/2.28 (~(xu = sdtpldt0(sdtasdt0(xa, tptp_fun_W2_32(W0!37)), sdtasdt0(xb, tptp_fun_W2_33(W1!36))))),
% 3.19/2.28 inference(unit_resolution,[status(thm)],[92, 86, 67, 65])).
% 3.19/2.28 tff(94,plain,
% 3.19/2.28 ($false),
% 3.19/2.28 inference(unit_resolution,[status(thm)],[93, 63])).
% 3.19/2.28 % SZS output end Proof
%------------------------------------------------------------------------------