TSTP Solution File: RNG122+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG122+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 03:18:32 EDT 2022
% Result : Theorem 7.00s 4.75s
% Output : Proof 7.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : RNG122+4 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 23:08:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 7.00/4.75 % SZS status Theorem
% 7.00/4.75 % SZS output start Proof
% 7.00/4.75 tff(sdtpldt0_type, type, (
% 7.00/4.75 sdtpldt0: ( $i * $i ) > $i)).
% 7.00/4.75 tff(xr_type, type, (
% 7.00/4.75 xr: $i)).
% 7.00/4.75 tff(sdtasdt0_type, type, (
% 7.00/4.75 sdtasdt0: ( $i * $i ) > $i)).
% 7.00/4.75 tff(xu_type, type, (
% 7.00/4.75 xu: $i)).
% 7.00/4.75 tff(xq_type, type, (
% 7.00/4.75 xq: $i)).
% 7.00/4.75 tff(smndt0_type, type, (
% 7.00/4.75 smndt0: $i > $i)).
% 7.00/4.75 tff(aElement0_type, type, (
% 7.00/4.75 aElement0: $i > $o)).
% 7.00/4.75 tff(aElementOf0_type, type, (
% 7.00/4.75 aElementOf0: ( $i * $i ) > $o)).
% 7.00/4.75 tff(sdtpldt1_type, type, (
% 7.00/4.75 sdtpldt1: ( $i * $i ) > $i)).
% 7.00/4.75 tff(slsdtgt0_type, type, (
% 7.00/4.75 slsdtgt0: $i > $i)).
% 7.00/4.75 tff(xa_type, type, (
% 7.00/4.75 xa: $i)).
% 7.00/4.75 tff(aSet0_type, type, (
% 7.00/4.75 aSet0: $i > $o)).
% 7.00/4.75 tff(xI_type, type, (
% 7.00/4.75 xI: $i)).
% 7.00/4.75 tff(aIdeal0_type, type, (
% 7.00/4.75 aIdeal0: $i > $o)).
% 7.00/4.75 tff(xb_type, type, (
% 7.00/4.75 xb: $i)).
% 7.00/4.75 tff(tptp_fun_W1_38_type, type, (
% 7.00/4.75 tptp_fun_W1_38: $i)).
% 7.00/4.75 tff(tptp_fun_W0_39_type, type, (
% 7.00/4.75 tptp_fun_W0_39: $i)).
% 7.00/4.75 tff(iLess0_type, type, (
% 7.00/4.75 iLess0: ( $i * $i ) > $o)).
% 7.00/4.75 tff(sbrdtbr0_type, type, (
% 7.00/4.75 sbrdtbr0: $i > $i)).
% 7.00/4.75 tff(sz00_type, type, (
% 7.00/4.75 sz00: $i)).
% 7.00/4.75 tff(1,plain,
% 7.00/4.75 (aSet0(xI) <=> aSet0(sdtpldt1(slsdtgt0(xa), slsdtgt0(sdtpldt0(sdtasdt0(xq, xu), xr))))),
% 7.00/4.75 inference(rewrite,[status(thm)],[])).
% 7.00/4.75 tff(2,plain,
% 7.00/4.75 (aSet0(xI) <=> aSet0(xI)),
% 7.00/4.75 inference(rewrite,[status(thm)],[])).
% 7.00/4.75 tff(3,axiom,((((((aSet0(xI) & ![W0: $i] : (aElementOf0(W0, xI) => (![W1: $i] : (aElementOf0(W1, xI) => aElementOf0(sdtpldt0(W0, W1), xI)) & ![W1: $i] : (aElement0(W1) => aElementOf0(sdtasdt0(W1, W0), xI))))) & aIdeal0(xI)) & ![W0: $i] : (aElementOf0(W0, slsdtgt0(xa)) <=> ?[W1: $i] : (aElement0(W1) & (sdtasdt0(xa, W1) = W0)))) & ![W0: $i] : (aElementOf0(W0, slsdtgt0(xb)) <=> ?[W1: $i] : (aElement0(W1) & (sdtasdt0(xb, W1) = W0)))) & ![W0: $i] : (aElementOf0(W0, xI) <=> ?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0)))) & (xI = sdtpldt1(slsdtgt0(xa), slsdtgt0(xb)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2174')).
% 7.00/4.75 tff(4,plain,
% 7.00/4.75 (((((aSet0(xI) & ![W0: $i] : (aElementOf0(W0, xI) => (![W1: $i] : (aElementOf0(W1, xI) => aElementOf0(sdtpldt0(W0, W1), xI)) & ![W1: $i] : (aElement0(W1) => aElementOf0(sdtasdt0(W1, W0), xI))))) & aIdeal0(xI)) & ![W0: $i] : (aElementOf0(W0, slsdtgt0(xa)) <=> ?[W1: $i] : (aElement0(W1) & (sdtasdt0(xa, W1) = W0)))) & ![W0: $i] : (aElementOf0(W0, slsdtgt0(xb)) <=> ?[W1: $i] : (aElement0(W1) & (sdtasdt0(xb, W1) = W0)))) & ![W0: $i] : (aElementOf0(W0, xI) <=> ?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0)))),
% 7.00/4.75 inference(and_elim,[status(thm)],[3])).
% 7.00/4.75 tff(5,plain,
% 7.00/4.75 ((((aSet0(xI) & ![W0: $i] : (aElementOf0(W0, xI) => (![W1: $i] : (aElementOf0(W1, xI) => aElementOf0(sdtpldt0(W0, W1), xI)) & ![W1: $i] : (aElement0(W1) => aElementOf0(sdtasdt0(W1, W0), xI))))) & aIdeal0(xI)) & ![W0: $i] : (aElementOf0(W0, slsdtgt0(xa)) <=> ?[W1: $i] : (aElement0(W1) & (sdtasdt0(xa, W1) = W0)))) & ![W0: $i] : (aElementOf0(W0, slsdtgt0(xb)) <=> ?[W1: $i] : (aElement0(W1) & (sdtasdt0(xb, W1) = W0)))),
% 7.00/4.75 inference(and_elim,[status(thm)],[4])).
% 7.00/4.75 tff(6,plain,
% 7.00/4.75 (((aSet0(xI) & ![W0: $i] : (aElementOf0(W0, xI) => (![W1: $i] : (aElementOf0(W1, xI) => aElementOf0(sdtpldt0(W0, W1), xI)) & ![W1: $i] : (aElement0(W1) => aElementOf0(sdtasdt0(W1, W0), xI))))) & aIdeal0(xI)) & ![W0: $i] : (aElementOf0(W0, slsdtgt0(xa)) <=> ?[W1: $i] : (aElement0(W1) & (sdtasdt0(xa, W1) = W0)))),
% 7.00/4.75 inference(and_elim,[status(thm)],[5])).
% 7.00/4.75 tff(7,plain,
% 7.00/4.75 ((aSet0(xI) & ![W0: $i] : (aElementOf0(W0, xI) => (![W1: $i] : (aElementOf0(W1, xI) => aElementOf0(sdtpldt0(W0, W1), xI)) & ![W1: $i] : (aElement0(W1) => aElementOf0(sdtasdt0(W1, W0), xI))))) & aIdeal0(xI)),
% 7.00/4.75 inference(and_elim,[status(thm)],[6])).
% 7.00/4.75 tff(8,plain,
% 7.00/4.75 (aSet0(xI) & ![W0: $i] : (aElementOf0(W0, xI) => (![W1: $i] : (aElementOf0(W1, xI) => aElementOf0(sdtpldt0(W0, W1), xI)) & ![W1: $i] : (aElement0(W1) => aElementOf0(sdtasdt0(W1, W0), xI))))),
% 7.00/4.75 inference(and_elim,[status(thm)],[7])).
% 7.00/4.75 tff(9,plain,
% 7.00/4.75 (aSet0(xI)),
% 7.00/4.75 inference(and_elim,[status(thm)],[8])).
% 7.00/4.75 tff(10,plain,
% 7.00/4.75 (aSet0(xI)),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[9, 2])).
% 7.00/4.75 tff(11,plain,
% 7.00/4.75 (aSet0(sdtpldt1(slsdtgt0(xa), slsdtgt0(sdtpldt0(sdtasdt0(xq, xu), xr))))),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[10, 1])).
% 7.00/4.75 tff(12,plain,
% 7.00/4.75 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 7.00/4.75 inference(bind,[status(th)],[])).
% 7.00/4.75 tff(13,plain,
% 7.00/4.75 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 7.00/4.75 inference(quant_intro,[status(thm)],[12])).
% 7.00/4.75 tff(14,plain,
% 7.00/4.75 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 7.00/4.75 inference(bind,[status(th)],[])).
% 7.00/4.75 tff(15,plain,
% 7.00/4.75 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 7.00/4.75 inference(quant_intro,[status(thm)],[14])).
% 7.00/4.75 tff(16,plain,
% 7.00/4.75 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 7.00/4.75 inference(transitivity,[status(thm)],[15, 13])).
% 7.00/4.75 tff(17,plain,
% 7.00/4.75 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 7.00/4.75 inference(rewrite,[status(thm)],[])).
% 7.00/4.75 tff(18,plain,
% 7.00/4.75 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, W0) => aElement0(W1)) <=> (aElement0(W1) | (~aElementOf0(W1, W0))))), (![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)) <=> ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))), ((aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> (aSet0(W0) => ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))), rewrite((aSet0(W0) => ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))), ((aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))))),
% 7.00/4.75 inference(bind,[status(th)],[])).
% 7.00/4.75 tff(19,plain,
% 7.00/4.75 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 7.00/4.75 inference(quant_intro,[status(thm)],[18])).
% 7.00/4.75 tff(20,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mEOfElem')).
% 7.00/4.75 tff(21,plain,
% 7.00/4.75 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[20, 19])).
% 7.00/4.75 tff(22,plain,
% 7.00/4.75 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[21, 17])).
% 7.00/4.75 tff(23,plain,(
% 7.00/4.75 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 7.00/4.75 inference(skolemize,[status(sab)],[22])).
% 7.00/4.75 tff(24,plain,
% 7.00/4.75 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[23, 16])).
% 7.00/4.75 tff(25,plain,
% 7.00/4.75 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(sdtpldt1(slsdtgt0(xa), slsdtgt0(sdtpldt0(sdtasdt0(xq, xu), xr))))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(sdtpldt0(sdtasdt0(xq, xu), xr)))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(sdtpldt1(slsdtgt0(xa), slsdtgt0(sdtpldt0(sdtasdt0(xq, xu), xr))))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(sdtpldt0(sdtasdt0(xq, xu), xr)))))))),
% 7.00/4.75 inference(rewrite,[status(thm)],[])).
% 7.00/4.75 tff(26,plain,
% 7.00/4.75 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(sdtpldt1(slsdtgt0(xa), slsdtgt0(sdtpldt0(sdtasdt0(xq, xu), xr))))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(sdtpldt0(sdtasdt0(xq, xu), xr)))))))),
% 7.00/4.75 inference(quant_inst,[status(thm)],[])).
% 7.00/4.75 tff(27,plain,
% 7.00/4.75 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(sdtpldt1(slsdtgt0(xa), slsdtgt0(sdtpldt0(sdtasdt0(xq, xu), xr))))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(sdtpldt0(sdtasdt0(xq, xu), xr))))))),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[26, 25])).
% 7.00/4.75 tff(28,plain,
% 7.00/4.75 (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(sdtpldt0(sdtasdt0(xq, xu), xr))))))),
% 7.00/4.75 inference(unit_resolution,[status(thm)],[27, 24, 11])).
% 7.00/4.75 tff(29,plain,
% 7.00/4.75 (aElementOf0(smndt0(sdtasdt0(xq, xu)), xI) <=> aElementOf0(smndt0(sdtasdt0(xq, xu)), sdtpldt1(slsdtgt0(xa), slsdtgt0(sdtpldt0(sdtasdt0(xq, xu), xr))))),
% 7.00/4.75 inference(rewrite,[status(thm)],[])).
% 7.00/4.75 tff(30,plain,
% 7.00/4.75 (aElementOf0(smndt0(sdtasdt0(xq, xu)), xI) <=> aElementOf0(smndt0(sdtasdt0(xq, xu)), xI)),
% 7.00/4.75 inference(rewrite,[status(thm)],[])).
% 7.00/4.75 tff(31,axiom,(?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb))) & (sdtpldt0(W0, W1) = smndt0(sdtasdt0(xq, xu)))) & aElementOf0(smndt0(sdtasdt0(xq, xu)), xI)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2690')).
% 7.00/4.75 tff(32,plain,
% 7.00/4.75 (aElementOf0(smndt0(sdtasdt0(xq, xu)), xI)),
% 7.00/4.75 inference(and_elim,[status(thm)],[31])).
% 7.00/4.75 tff(33,plain,
% 7.00/4.75 (aElementOf0(smndt0(sdtasdt0(xq, xu)), xI)),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[32, 30])).
% 7.00/4.75 tff(34,plain,
% 7.00/4.75 (aElementOf0(smndt0(sdtasdt0(xq, xu)), sdtpldt1(slsdtgt0(xa), slsdtgt0(sdtpldt0(sdtasdt0(xq, xu), xr))))),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[33, 29])).
% 7.00/4.75 tff(35,plain,
% 7.00/4.75 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(sdtpldt0(sdtasdt0(xq, xu), xr))))))) | (aElement0(smndt0(sdtasdt0(xq, xu))) | (~aElementOf0(smndt0(sdtasdt0(xq, xu)), sdtpldt1(slsdtgt0(xa), slsdtgt0(sdtpldt0(sdtasdt0(xq, xu), xr))))))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(sdtpldt0(sdtasdt0(xq, xu), xr))))))) | aElement0(smndt0(sdtasdt0(xq, xu))) | (~aElementOf0(smndt0(sdtasdt0(xq, xu)), sdtpldt1(slsdtgt0(xa), slsdtgt0(sdtpldt0(sdtasdt0(xq, xu), xr))))))),
% 7.00/4.75 inference(rewrite,[status(thm)],[])).
% 7.00/4.75 tff(36,plain,
% 7.00/4.75 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(sdtpldt0(sdtasdt0(xq, xu), xr))))))) | (aElement0(smndt0(sdtasdt0(xq, xu))) | (~aElementOf0(smndt0(sdtasdt0(xq, xu)), sdtpldt1(slsdtgt0(xa), slsdtgt0(sdtpldt0(sdtasdt0(xq, xu), xr))))))),
% 7.00/4.75 inference(quant_inst,[status(thm)],[])).
% 7.00/4.75 tff(37,plain,
% 7.00/4.75 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, sdtpldt1(slsdtgt0(xa), slsdtgt0(sdtpldt0(sdtasdt0(xq, xu), xr))))))) | aElement0(smndt0(sdtasdt0(xq, xu))) | (~aElementOf0(smndt0(sdtasdt0(xq, xu)), sdtpldt1(slsdtgt0(xa), slsdtgt0(sdtpldt0(sdtasdt0(xq, xu), xr)))))),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[36, 35])).
% 7.00/4.75 tff(38,plain,
% 7.00/4.75 (aElement0(smndt0(sdtasdt0(xq, xu)))),
% 7.00/4.75 inference(unit_resolution,[status(thm)],[37, 34, 28])).
% 7.00/4.75 tff(39,plain,
% 7.00/4.75 (^[W0: $i, W1: $i] : rewrite((aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))) <=> (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1)))))),
% 7.00/4.75 inference(bind,[status(th)],[])).
% 7.00/4.75 tff(40,plain,
% 7.00/4.75 (?[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(sdtpldt0(sdtasdt0(xq, xu), xr), W1))))),
% 7.00/4.75 inference(quant_intro,[status(thm)],[39])).
% 7.00/4.75 tff(41,plain,
% 7.00/4.75 (?[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))))),
% 7.00/4.75 inference(rewrite,[status(thm)],[])).
% 7.00/4.75 tff(42,plain,
% 7.00/4.75 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))) <=> (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 7.00/4.75 inference(bind,[status(th)],[])).
% 7.00/4.75 tff(43,plain,
% 7.00/4.75 (?[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))))),
% 7.00/4.75 inference(quant_intro,[status(thm)],[42])).
% 7.00/4.75 tff(44,axiom,(?[W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2416')).
% 7.00/4.75 tff(45,plain,
% 7.00/4.75 (?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[44, 43])).
% 7.00/4.75 tff(46,plain,
% 7.00/4.75 (?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[45, 41])).
% 7.00/4.75 tff(47,plain,
% 7.00/4.75 (?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1))))),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[46, 40])).
% 7.00/4.75 tff(48,plain,(
% 7.00/4.75 aElement0(W0!39) & aElement0(W1!38) & (xu = sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38)))),
% 7.00/4.75 inference(skolemize,[status(sab)],[47])).
% 7.00/4.75 tff(49,plain,
% 7.00/4.75 (xu = sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))),
% 7.00/4.75 inference(and_elim,[status(thm)],[48])).
% 7.00/4.75 tff(50,plain,
% 7.00/4.75 (sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38)) = xu),
% 7.00/4.75 inference(symmetry,[status(thm)],[49])).
% 7.00/4.75 tff(51,plain,
% 7.00/4.75 (aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))) <=> aElement0(xu)),
% 7.00/4.75 inference(monotonicity,[status(thm)],[50])).
% 7.00/4.75 tff(52,plain,
% 7.00/4.75 (aElement0(W0!39)),
% 7.00/4.75 inference(and_elim,[status(thm)],[48])).
% 7.00/4.75 tff(53,plain,
% 7.00/4.75 (aElement0(xa) <=> aElement0(xa)),
% 7.00/4.75 inference(rewrite,[status(thm)],[])).
% 7.00/4.75 tff(54,axiom,(aElement0(xa) & aElement0(xb)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2091')).
% 7.00/4.75 tff(55,plain,
% 7.00/4.75 (aElement0(xa)),
% 7.00/4.75 inference(and_elim,[status(thm)],[54])).
% 7.00/4.75 tff(56,plain,
% 7.00/4.75 (aElement0(xa)),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[55, 53])).
% 7.00/4.75 tff(57,plain,
% 7.00/4.75 (^[W0: $i, W1: $i] : refl((aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 7.00/4.75 inference(bind,[status(th)],[])).
% 7.00/4.75 tff(58,plain,
% 7.00/4.75 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 7.00/4.75 inference(quant_intro,[status(thm)],[57])).
% 7.00/4.75 tff(59,plain,
% 7.00/4.75 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aElement0(W1)) <=> (~((~aElement0(W1)) | (~aElement0(W0))))), ((~(aElement0(W0) & aElement0(W1))) <=> (~(~((~aElement0(W1)) | (~aElement0(W0))))))), rewrite((~(~((~aElement0(W1)) | (~aElement0(W0))))) <=> ((~aElement0(W1)) | (~aElement0(W0)))), ((~(aElement0(W0) & aElement0(W1))) <=> ((~aElement0(W1)) | (~aElement0(W0))))), ((aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> (aElement0(sdtasdt0(W0, W1)) | ((~aElement0(W1)) | (~aElement0(W0)))))), rewrite((aElement0(sdtasdt0(W0, W1)) | ((~aElement0(W1)) | (~aElement0(W0)))) <=> (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))), ((aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))))),
% 7.00/4.75 inference(bind,[status(th)],[])).
% 7.00/4.75 tff(60,plain,
% 7.00/4.75 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 7.00/4.75 inference(quant_intro,[status(thm)],[59])).
% 7.00/4.75 tff(61,plain,
% 7.00/4.75 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 7.00/4.75 inference(rewrite,[status(thm)],[])).
% 7.00/4.75 tff(62,plain,
% 7.00/4.75 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1))) <=> (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))))),
% 7.00/4.75 inference(bind,[status(th)],[])).
% 7.00/4.75 tff(63,plain,
% 7.00/4.75 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 7.00/4.75 inference(quant_intro,[status(thm)],[62])).
% 7.00/4.75 tff(64,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsB_02')).
% 7.00/4.75 tff(65,plain,
% 7.00/4.75 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[64, 63])).
% 7.00/4.75 tff(66,plain,
% 7.00/4.75 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[65, 61])).
% 7.00/4.75 tff(67,plain,(
% 7.00/4.75 ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 7.00/4.75 inference(skolemize,[status(sab)],[66])).
% 7.00/4.75 tff(68,plain,
% 7.00/4.75 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[67, 60])).
% 7.00/4.75 tff(69,plain,
% 7.00/4.75 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[68, 58])).
% 7.00/4.75 tff(70,plain,
% 7.00/4.75 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xa, W0!39)) | (~aElement0(W0!39)) | (~aElement0(xa)))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(xa, W0!39)) | (~aElement0(W0!39)) | (~aElement0(xa)))),
% 7.00/4.75 inference(rewrite,[status(thm)],[])).
% 7.00/4.75 tff(71,plain,
% 7.00/4.75 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xa, W0!39)) | (~aElement0(W0!39)) | (~aElement0(xa)))),
% 7.00/4.75 inference(quant_inst,[status(thm)],[])).
% 7.00/4.75 tff(72,plain,
% 7.00/4.75 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(xa, W0!39)) | (~aElement0(W0!39)) | (~aElement0(xa))),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[71, 70])).
% 7.00/4.75 tff(73,plain,
% 7.00/4.75 (aElement0(sdtasdt0(xa, W0!39))),
% 7.00/4.75 inference(unit_resolution,[status(thm)],[72, 69, 56, 52])).
% 7.00/4.75 tff(74,plain,
% 7.00/4.75 (aElement0(W1!38)),
% 7.00/4.75 inference(and_elim,[status(thm)],[48])).
% 7.00/4.75 tff(75,plain,
% 7.00/4.75 (aElement0(xb) <=> aElement0(sdtpldt0(sdtasdt0(xq, xu), xr))),
% 7.00/4.75 inference(rewrite,[status(thm)],[])).
% 7.00/4.75 tff(76,plain,
% 7.00/4.75 (aElement0(xb) <=> aElement0(xb)),
% 7.00/4.75 inference(rewrite,[status(thm)],[])).
% 7.00/4.75 tff(77,plain,
% 7.00/4.75 (aElement0(xb)),
% 7.00/4.75 inference(and_elim,[status(thm)],[54])).
% 7.00/4.75 tff(78,plain,
% 7.00/4.75 (aElement0(xb)),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[77, 76])).
% 7.00/4.75 tff(79,plain,
% 7.00/4.75 (aElement0(sdtpldt0(sdtasdt0(xq, xu), xr))),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[78, 75])).
% 7.00/4.75 tff(80,plain,
% 7.00/4.75 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(W1!38)) | aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38)))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(W1!38)) | aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38)))),
% 7.00/4.75 inference(rewrite,[status(thm)],[])).
% 7.00/4.75 tff(81,plain,
% 7.00/4.75 ((aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38)) | (~aElement0(W1!38)) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), xr)))) <=> ((~aElement0(sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(W1!38)) | aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38)))),
% 7.00/4.75 inference(rewrite,[status(thm)],[])).
% 7.00/4.75 tff(82,plain,
% 7.00/4.75 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38)) | (~aElement0(W1!38)) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), xr))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(W1!38)) | aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))))),
% 7.00/4.75 inference(monotonicity,[status(thm)],[81])).
% 7.00/4.75 tff(83,plain,
% 7.00/4.75 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38)) | (~aElement0(W1!38)) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), xr))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(W1!38)) | aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38)))),
% 7.00/4.75 inference(transitivity,[status(thm)],[82, 80])).
% 7.00/4.75 tff(84,plain,
% 7.00/4.75 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38)) | (~aElement0(W1!38)) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), xr))))),
% 7.00/4.75 inference(quant_inst,[status(thm)],[])).
% 7.00/4.75 tff(85,plain,
% 7.00/4.75 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(W1!38)) | aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[84, 83])).
% 7.00/4.75 tff(86,plain,
% 7.00/4.75 (aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))),
% 7.00/4.75 inference(unit_resolution,[status(thm)],[85, 69, 79, 74])).
% 7.00/4.75 tff(87,plain,
% 7.00/4.75 (^[W0: $i, W1: $i] : refl((aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 7.00/4.75 inference(bind,[status(th)],[])).
% 7.00/4.75 tff(88,plain,
% 7.00/4.75 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 7.00/4.75 inference(quant_intro,[status(thm)],[87])).
% 7.00/4.75 tff(89,plain,
% 7.00/4.75 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aElement0(W1)) <=> (~((~aElement0(W1)) | (~aElement0(W0))))), ((~(aElement0(W0) & aElement0(W1))) <=> (~(~((~aElement0(W1)) | (~aElement0(W0))))))), rewrite((~(~((~aElement0(W1)) | (~aElement0(W0))))) <=> ((~aElement0(W1)) | (~aElement0(W0)))), ((~(aElement0(W0) & aElement0(W1))) <=> ((~aElement0(W1)) | (~aElement0(W0))))), ((aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> (aElement0(sdtpldt0(W0, W1)) | ((~aElement0(W1)) | (~aElement0(W0)))))), rewrite((aElement0(sdtpldt0(W0, W1)) | ((~aElement0(W1)) | (~aElement0(W0)))) <=> (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))), ((aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))))),
% 7.00/4.75 inference(bind,[status(th)],[])).
% 7.00/4.75 tff(90,plain,
% 7.00/4.75 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 7.00/4.75 inference(quant_intro,[status(thm)],[89])).
% 7.00/4.75 tff(91,plain,
% 7.00/4.75 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 7.00/4.75 inference(rewrite,[status(thm)],[])).
% 7.00/4.75 tff(92,plain,
% 7.00/4.75 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1))) <=> (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))))),
% 7.00/4.75 inference(bind,[status(th)],[])).
% 7.00/4.75 tff(93,plain,
% 7.00/4.75 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 7.00/4.75 inference(quant_intro,[status(thm)],[92])).
% 7.00/4.75 tff(94,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsB')).
% 7.00/4.75 tff(95,plain,
% 7.00/4.75 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[94, 93])).
% 7.00/4.75 tff(96,plain,
% 7.00/4.75 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[95, 91])).
% 7.00/4.75 tff(97,plain,(
% 7.00/4.75 ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 7.00/4.75 inference(skolemize,[status(sab)],[96])).
% 7.00/4.75 tff(98,plain,
% 7.00/4.75 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[97, 90])).
% 7.00/4.75 tff(99,plain,
% 7.00/4.75 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[98, 88])).
% 7.00/4.75 tff(100,plain,
% 7.00/4.75 (((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))))),
% 7.00/4.75 inference(rewrite,[status(thm)],[])).
% 7.00/4.75 tff(101,plain,
% 7.00/4.75 ((aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))) | (~aElement0(sdtasdt0(xa, W0!39)))) <=> ((~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))))),
% 7.00/4.75 inference(rewrite,[status(thm)],[])).
% 7.00/4.75 tff(102,plain,
% 7.00/4.75 (((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38)))))),
% 7.00/4.75 inference(monotonicity,[status(thm)],[101])).
% 7.00/4.75 tff(103,plain,
% 7.00/4.75 (((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))))),
% 7.00/4.75 inference(transitivity,[status(thm)],[102, 100])).
% 7.00/4.75 tff(104,plain,
% 7.00/4.75 ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))))),
% 7.00/4.75 inference(quant_inst,[status(thm)],[])).
% 7.00/4.75 tff(105,plain,
% 7.00/4.75 ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38)))),
% 7.00/4.75 inference(modus_ponens,[status(thm)],[104, 103])).
% 7.00/4.75 tff(106,plain,
% 7.00/4.75 ((~aElement0(sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38)))),
% 7.00/4.76 inference(unit_resolution,[status(thm)],[105, 99])).
% 7.00/4.76 tff(107,plain,
% 7.00/4.76 (aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(sdtpldt0(sdtasdt0(xq, xu), xr), W1!38)))),
% 7.00/4.76 inference(unit_resolution,[status(thm)],[106, 86, 73])).
% 7.00/4.76 tff(108,plain,
% 7.00/4.76 (aElement0(xu)),
% 7.00/4.76 inference(modus_ponens,[status(thm)],[107, 51])).
% 7.00/4.76 tff(109,plain,
% 7.00/4.76 (aElement0(xq) <=> aElement0(xq)),
% 7.00/4.76 inference(rewrite,[status(thm)],[])).
% 7.00/4.76 tff(110,axiom,(((aElement0(xq) & aElement0(xr)) & (xb = sdtpldt0(sdtasdt0(xq, xu), xr))) & ((xr = sz00) | iLess0(sbrdtbr0(xr), sbrdtbr0(xu)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2666')).
% 7.00/4.76 tff(111,plain,
% 7.00/4.76 ((aElement0(xq) & aElement0(xr)) & (xb = sdtpldt0(sdtasdt0(xq, xu), xr))),
% 7.00/4.76 inference(and_elim,[status(thm)],[110])).
% 7.00/4.76 tff(112,plain,
% 7.00/4.76 (aElement0(xq) & aElement0(xr)),
% 7.00/4.76 inference(and_elim,[status(thm)],[111])).
% 7.00/4.76 tff(113,plain,
% 7.00/4.76 (aElement0(xq)),
% 7.00/4.76 inference(and_elim,[status(thm)],[112])).
% 7.00/4.76 tff(114,plain,
% 7.00/4.76 (aElement0(xq)),
% 7.00/4.76 inference(modus_ponens,[status(thm)],[113, 109])).
% 7.00/4.76 tff(115,plain,
% 7.00/4.76 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(xu)) | (~aElement0(xq)) | aElement0(sdtasdt0(xq, xu)))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xu)) | (~aElement0(xq)) | aElement0(sdtasdt0(xq, xu)))),
% 7.00/4.76 inference(rewrite,[status(thm)],[])).
% 7.00/4.76 tff(116,plain,
% 7.00/4.76 ((aElement0(sdtasdt0(xq, xu)) | (~aElement0(xu)) | (~aElement0(xq))) <=> ((~aElement0(xu)) | (~aElement0(xq)) | aElement0(sdtasdt0(xq, xu)))),
% 7.00/4.76 inference(rewrite,[status(thm)],[])).
% 7.00/4.76 tff(117,plain,
% 7.00/4.76 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xq, xu)) | (~aElement0(xu)) | (~aElement0(xq)))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(xu)) | (~aElement0(xq)) | aElement0(sdtasdt0(xq, xu))))),
% 7.00/4.76 inference(monotonicity,[status(thm)],[116])).
% 7.00/4.76 tff(118,plain,
% 7.00/4.76 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xq, xu)) | (~aElement0(xu)) | (~aElement0(xq)))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xu)) | (~aElement0(xq)) | aElement0(sdtasdt0(xq, xu)))),
% 7.00/4.76 inference(transitivity,[status(thm)],[117, 115])).
% 7.00/4.76 tff(119,plain,
% 7.00/4.76 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xq, xu)) | (~aElement0(xu)) | (~aElement0(xq)))),
% 7.00/4.76 inference(quant_inst,[status(thm)],[])).
% 7.00/4.76 tff(120,plain,
% 7.00/4.76 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xu)) | (~aElement0(xq)) | aElement0(sdtasdt0(xq, xu))),
% 7.00/4.76 inference(modus_ponens,[status(thm)],[119, 118])).
% 7.00/4.76 tff(121,plain,
% 7.00/4.76 ((~aElement0(xu)) | aElement0(sdtasdt0(xq, xu))),
% 7.00/4.76 inference(unit_resolution,[status(thm)],[120, 69, 114])).
% 7.00/4.76 tff(122,plain,
% 7.00/4.76 (aElement0(sdtasdt0(xq, xu))),
% 7.00/4.76 inference(unit_resolution,[status(thm)],[121, 108])).
% 7.00/4.76 tff(123,plain,
% 7.00/4.76 (aElement0(xr) <=> aElement0(xr)),
% 7.00/4.76 inference(rewrite,[status(thm)],[])).
% 7.00/4.76 tff(124,plain,
% 7.00/4.76 (aElement0(xr)),
% 7.00/4.76 inference(and_elim,[status(thm)],[112])).
% 7.00/4.76 tff(125,plain,
% 7.00/4.76 (aElement0(xr)),
% 7.00/4.76 inference(modus_ponens,[status(thm)],[124, 123])).
% 7.00/4.76 tff(126,plain,
% 7.00/4.76 (^[W0: $i, W1: $i, W2: $i] : refl(((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 7.00/4.76 inference(bind,[status(th)],[])).
% 7.00/4.76 tff(127,plain,
% 7.00/4.76 (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 7.00/4.76 inference(quant_intro,[status(thm)],[126])).
% 7.00/4.76 tff(128,plain,
% 7.00/4.76 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aElement0(W1) & aElement0(W2)) <=> (~((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))))), ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) <=> (~(~((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))))))), rewrite((~(~((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))))) <=> ((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))), ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) <=> ((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))))), (((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> (((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))))), rewrite((((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))), (((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))))),
% 7.00/4.76 inference(bind,[status(th)],[])).
% 7.00/4.76 tff(129,plain,
% 7.00/4.76 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 7.00/4.76 inference(quant_intro,[status(thm)],[128])).
% 7.00/4.76 tff(130,plain,
% 7.00/4.76 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 7.00/4.76 inference(rewrite,[status(thm)],[])).
% 7.00/4.76 tff(131,plain,
% 7.00/4.76 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aElement0(W0) & aElement0(W1)) & aElement0(W2)) <=> (aElement0(W0) & aElement0(W1) & aElement0(W2))), ((((aElement0(W0) & aElement0(W1)) & aElement0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((aElement0(W0) & aElement0(W1) & aElement0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))))), rewrite(((aElement0(W0) & aElement0(W1) & aElement0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))), ((((aElement0(W0) & aElement0(W1)) & aElement0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))))),
% 7.00/4.76 inference(bind,[status(th)],[])).
% 7.00/4.76 tff(132,plain,
% 7.00/4.76 (![W0: $i, W1: $i, W2: $i] : (((aElement0(W0) & aElement0(W1)) & aElement0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 7.00/4.76 inference(quant_intro,[status(thm)],[131])).
% 7.00/4.76 tff(133,axiom,(![W0: $i, W1: $i, W2: $i] : (((aElement0(W0) & aElement0(W1)) & aElement0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mAddAsso')).
% 7.00/4.76 tff(134,plain,
% 7.00/4.76 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 7.00/4.76 inference(modus_ponens,[status(thm)],[133, 132])).
% 7.00/4.76 tff(135,plain,
% 7.00/4.76 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 7.00/4.76 inference(modus_ponens,[status(thm)],[134, 130])).
% 7.00/4.76 tff(136,plain,(
% 7.00/4.76 ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 7.00/4.76 inference(skolemize,[status(sab)],[135])).
% 7.00/4.76 tff(137,plain,
% 7.00/4.76 (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 7.00/4.76 inference(modus_ponens,[status(thm)],[136, 129])).
% 7.00/4.76 tff(138,plain,
% 7.00/4.76 (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 7.00/4.76 inference(modus_ponens,[status(thm)],[137, 127])).
% 7.00/4.76 tff(139,plain,
% 7.00/4.76 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))))),
% 7.00/4.76 inference(rewrite,[status(thm)],[])).
% 7.00/4.76 tff(140,plain,
% 7.00/4.76 (((sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(smndt0(sdtasdt0(xq, xu))))) <=> ((~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))))),
% 7.00/4.76 inference(rewrite,[status(thm)],[])).
% 7.00/4.76 tff(141,plain,
% 7.00/4.76 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(smndt0(sdtasdt0(xq, xu))))))),
% 7.00/4.76 inference(monotonicity,[status(thm)],[140])).
% 7.00/4.76 tff(142,plain,
% 7.00/4.76 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))))),
% 7.00/4.76 inference(transitivity,[status(thm)],[141, 139])).
% 7.00/4.76 tff(143,plain,
% 7.00/4.76 ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))))),
% 7.00/4.76 inference(quant_inst,[status(thm)],[])).
% 7.00/4.76 tff(144,plain,
% 7.00/4.76 ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(smndt0(sdtasdt0(xq, xu))))),
% 7.00/4.76 inference(modus_ponens,[status(thm)],[143, 142])).
% 7.00/4.76 tff(145,plain,
% 7.00/4.76 ((~aElement0(sdtasdt0(xq, xu))) | (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(smndt0(sdtasdt0(xq, xu))))),
% 7.00/4.76 inference(unit_resolution,[status(thm)],[144, 138, 125])).
% 7.00/4.76 tff(146,plain,
% 7.00/4.76 (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))),
% 7.00/4.76 inference(unit_resolution,[status(thm)],[145, 122, 38])).
% 7.00/4.76 tff(147,plain,
% 7.00/4.76 (^[W0: $i] : refl(((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0)))))) <=> ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0)))))))),
% 7.00/4.76 inference(bind,[status(th)],[])).
% 7.00/4.76 tff(148,plain,
% 7.00/4.76 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0)))))) <=> ![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))),
% 7.00/4.76 inference(quant_intro,[status(thm)],[147])).
% 7.00/4.76 tff(149,plain,
% 7.00/4.76 (^[W0: $i] : rewrite(((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0)))))))),
% 7.00/4.76 inference(bind,[status(th)],[])).
% 7.00/4.76 tff(150,plain,
% 7.00/4.76 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))),
% 7.00/4.76 inference(quant_intro,[status(thm)],[149])).
% 7.00/4.76 tff(151,plain,
% 7.00/4.76 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 7.00/4.76 inference(rewrite,[status(thm)],[])).
% 7.00/4.76 tff(152,plain,
% 7.00/4.76 (^[W0: $i] : rewrite((aElement0(W0) => ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))))),
% 7.00/4.76 inference(bind,[status(th)],[])).
% 7.00/4.76 tff(153,plain,
% 7.00/4.76 (![W0: $i] : (aElement0(W0) => ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 7.00/4.76 inference(quant_intro,[status(thm)],[152])).
% 7.00/4.76 tff(154,axiom,(![W0: $i] : (aElement0(W0) => ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mAddInvr')).
% 7.00/4.76 tff(155,plain,
% 7.00/4.76 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 7.00/4.76 inference(modus_ponens,[status(thm)],[154, 153])).
% 7.00/4.76 tff(156,plain,
% 7.00/4.76 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 7.00/4.76 inference(modus_ponens,[status(thm)],[155, 151])).
% 7.00/4.76 tff(157,plain,(
% 7.00/4.76 ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 7.00/4.76 inference(skolemize,[status(sab)],[156])).
% 7.00/4.76 tff(158,plain,
% 7.00/4.76 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))),
% 7.00/4.76 inference(modus_ponens,[status(thm)],[157, 150])).
% 7.00/4.76 tff(159,plain,
% 7.00/4.76 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))),
% 7.00/4.76 inference(modus_ponens,[status(thm)],[158, 148])).
% 7.00/4.76 tff(160,plain,
% 7.00/4.76 (((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | ((~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), smndt0(sdtasdt0(xq, xu))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)))))))) <=> ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | (~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), smndt0(sdtasdt0(xq, xu))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)))))))),
% 7.00/4.76 inference(rewrite,[status(thm)],[])).
% 7.00/4.76 tff(161,plain,
% 7.00/4.76 ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | ((~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), smndt0(sdtasdt0(xq, xu))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)))))))),
% 7.00/4.76 inference(quant_inst,[status(thm)],[])).
% 7.00/4.76 tff(162,plain,
% 7.00/4.76 ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | (~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), smndt0(sdtasdt0(xq, xu))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu))))))),
% 7.00/4.76 inference(modus_ponens,[status(thm)],[161, 160])).
% 7.00/4.76 tff(163,plain,
% 7.00/4.76 ((~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), smndt0(sdtasdt0(xq, xu))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu))))))),
% 7.00/4.76 inference(unit_resolution,[status(thm)],[162, 159])).
% 7.00/4.76 tff(164,plain,
% 7.00/4.76 (~((~(sdtpldt0(sdtasdt0(xq, xu), smndt0(sdtasdt0(xq, xu))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)))))),
% 7.00/4.76 inference(unit_resolution,[status(thm)],[163, 122])).
% 7.00/4.76 tff(165,plain,
% 7.00/4.76 (((~(sdtpldt0(sdtasdt0(xq, xu), smndt0(sdtasdt0(xq, xu))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu))))) | (sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)))),
% 7.00/4.76 inference(tautology,[status(thm)],[])).
% 7.00/4.76 tff(166,plain,
% 7.00/4.76 (sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu))),
% 7.00/4.76 inference(unit_resolution,[status(thm)],[165, 164])).
% 7.00/4.76 tff(167,plain,
% 7.00/4.76 (sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)) = sz00),
% 7.00/4.76 inference(symmetry,[status(thm)],[166])).
% 7.00/4.76 tff(168,plain,
% 7.00/4.76 (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(sz00, xr)),
% 7.00/4.76 inference(monotonicity,[status(thm)],[167])).
% 7.00/4.76 tff(169,plain,
% 7.00/4.76 (sdtpldt0(sz00, xr) = sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr)),
% 7.00/4.76 inference(symmetry,[status(thm)],[168])).
% 7.00/4.76 tff(170,plain,
% 7.00/4.76 (^[W0: $i] : refl(((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))) <=> ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))))),
% 7.00/4.76 inference(bind,[status(th)],[])).
% 7.00/4.76 tff(171,plain,
% 7.00/4.76 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))) <=> ![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 7.00/4.76 inference(quant_intro,[status(thm)],[170])).
% 7.00/4.76 tff(172,plain,
% 7.00/4.76 (^[W0: $i] : rewrite(((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))))),
% 7.00/4.76 inference(bind,[status(th)],[])).
% 7.00/4.76 tff(173,plain,
% 7.00/4.76 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 7.00/4.76 inference(quant_intro,[status(thm)],[172])).
% 7.00/4.76 tff(174,plain,
% 7.00/4.76 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 7.00/4.76 inference(rewrite,[status(thm)],[])).
% 7.00/4.76 tff(175,plain,
% 7.00/4.76 (^[W0: $i] : rewrite((aElement0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))))),
% 7.00/4.76 inference(bind,[status(th)],[])).
% 7.00/4.76 tff(176,plain,
% 7.00/4.76 (![W0: $i] : (aElement0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 7.00/4.76 inference(quant_intro,[status(thm)],[175])).
% 7.00/4.76 tff(177,axiom,(![W0: $i] : (aElement0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mAddZero')).
% 7.00/4.76 tff(178,plain,
% 7.00/4.76 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 7.00/4.76 inference(modus_ponens,[status(thm)],[177, 176])).
% 7.00/4.76 tff(179,plain,
% 7.00/4.76 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 7.00/4.76 inference(modus_ponens,[status(thm)],[178, 174])).
% 7.00/4.76 tff(180,plain,(
% 7.00/4.76 ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 7.00/4.76 inference(skolemize,[status(sab)],[179])).
% 7.00/4.76 tff(181,plain,
% 7.00/4.76 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 7.00/4.76 inference(modus_ponens,[status(thm)],[180, 173])).
% 7.00/4.76 tff(182,plain,
% 7.00/4.76 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 7.00/4.76 inference(modus_ponens,[status(thm)],[181, 171])).
% 7.00/4.76 tff(183,plain,
% 7.00/4.76 (((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aElement0(xr)) | (~((~(sdtpldt0(xr, sz00) = xr)) | (~(xr = sdtpldt0(sz00, xr))))))) <=> ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aElement0(xr)) | (~((~(sdtpldt0(xr, sz00) = xr)) | (~(xr = sdtpldt0(sz00, xr))))))),
% 7.00/4.76 inference(rewrite,[status(thm)],[])).
% 7.00/4.76 tff(184,plain,
% 7.00/4.76 ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aElement0(xr)) | (~((~(sdtpldt0(xr, sz00) = xr)) | (~(xr = sdtpldt0(sz00, xr))))))),
% 7.00/4.76 inference(quant_inst,[status(thm)],[])).
% 7.00/4.76 tff(185,plain,
% 7.00/4.76 ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aElement0(xr)) | (~((~(sdtpldt0(xr, sz00) = xr)) | (~(xr = sdtpldt0(sz00, xr)))))),
% 7.00/4.76 inference(modus_ponens,[status(thm)],[184, 183])).
% 7.00/4.76 tff(186,plain,
% 7.00/4.76 (~((~(sdtpldt0(xr, sz00) = xr)) | (~(xr = sdtpldt0(sz00, xr))))),
% 7.00/4.76 inference(unit_resolution,[status(thm)],[185, 182, 125])).
% 7.00/4.76 tff(187,plain,
% 7.00/4.76 (((~(sdtpldt0(xr, sz00) = xr)) | (~(xr = sdtpldt0(sz00, xr)))) | (xr = sdtpldt0(sz00, xr))),
% 7.00/4.76 inference(tautology,[status(thm)],[])).
% 7.00/4.76 tff(188,plain,
% 7.00/4.76 (xr = sdtpldt0(sz00, xr)),
% 7.00/4.76 inference(unit_resolution,[status(thm)],[187, 186])).
% 7.00/4.76 tff(189,plain,
% 7.00/4.76 (xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))),
% 7.00/4.76 inference(transitivity,[status(thm)],[188, 169, 146])).
% 7.00/4.76 tff(190,plain,
% 7.00/4.76 ((~(xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb))) <=> (~(xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))))),
% 7.00/4.76 inference(rewrite,[status(thm)],[])).
% 7.00/4.76 tff(191,plain,
% 7.00/4.76 ((~(xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb))) <=> (~(xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb)))),
% 7.00/4.76 inference(rewrite,[status(thm)],[])).
% 7.00/4.76 tff(192,axiom,(~(xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 7.00/4.76 tff(193,plain,
% 7.00/4.76 (~(xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb))),
% 7.00/4.76 inference(modus_ponens,[status(thm)],[192, 191])).
% 7.00/4.76 tff(194,plain,
% 7.00/4.76 (~(xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr)))),
% 7.00/4.76 inference(modus_ponens,[status(thm)],[193, 190])).
% 7.00/4.78 tff(195,plain,
% 7.00/4.78 ($false),
% 7.00/4.78 inference(unit_resolution,[status(thm)],[194, 189])).
% 7.00/4.78 % SZS output end Proof
%------------------------------------------------------------------------------