0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.12 % Command : vampire_hol --schedule thf_2019 --mode portfolio --time_limit %ds %s 0.12/0.33 % Computer : n015.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 180 0.12/0.33 % DateTime : Thu Aug 29 14:39:37 EDT 2019 0.12/0.33 % CPUTime : 0.18/0.40 % lrs-3_4:1_cunif=on:en=on:foolp=on:holcelim=on:holscev=on:combelim=inference_rules:afea=on:afp=1000:afq=1.4:amm=sco:fde=none:gs=on:lcm=reverse:lma=on:nwc=1.5:stl=30:sd=1:ss=axioms:sp=reverse_arity:urr=on:updr=off:uhcvi=on_11 on theBenchmark 1.54/1.70 % Time limit reached! 1.54/1.70 % ------------------------------ 1.54/1.70 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 1.54/1.70 % Termination reason: Time limit 1.54/1.70 % Termination phase: Saturation 1.54/1.70 1.54/1.70 % Memory used [KB]: 46566 1.54/1.70 % Time elapsed: 1.300 s 1.54/1.70 % ------------------------------ 1.54/1.70 % ------------------------------ 1.54/1.73 % lrs+1011_5:4_anc=none:bsr=on:ccuc=small_ones:irw=on:stl=300d:fde=unused:holscev=on:sp=reverse_arity:sos=on:foolp=on:acc=on:afp=10000:gs=on:nwc=1.2:holcelim=on:updr=off:sac=on:afea=on:newcnf=on:gsem=off:cond=on:add=large:en=on:combelim=inference_rules:gsaa=from_current:amm=off:nm=2:afq=2:cunif=on_38 on theBenchmark 5.64/5.73 % Time limit reached! 5.64/5.73 % ------------------------------ 5.64/5.73 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 5.64/5.73 % Termination reason: Time limit 5.64/5.73 % Termination phase: Saturation 5.64/5.73 5.64/5.73 % Memory used [KB]: 73303 5.64/5.73 % Time elapsed: 4.0000 s 5.64/5.73 % ------------------------------ 5.64/5.73 % ------------------------------ 5.64/5.76 % ott+11_16_cunif=on:en=on:foolp=on:holcelim=on:holscev=on:combelim=inference_rules:afea=on:av=off:gs=on:gsem=on:irw=on:lma=on:nm=64:newcnf=on:nwc=1.3:sas=z3:sp=reverse_arity_16 on theBenchmark 7.42/7.56 % Time limit reached! 7.42/7.56 % ------------------------------ 7.42/7.56 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 7.42/7.56 % Termination reason: Time limit 7.42/7.56 % Termination phase: Saturation 7.42/7.56 7.42/7.56 % Memory used [KB]: 38634 7.42/7.56 % Time elapsed: 1.800 s 7.42/7.56 % ------------------------------ 7.42/7.56 % ------------------------------ 7.42/7.58 % lrs+1011_7_anc=none:stl=300d:holscev=on:sp=reverse_arity:foolp=on:lma=on:urr=on:afp=40000:nwc=2.5:holcelim=on:flr=on:updr=off:afea=on:cond=on:add=large:en=on:combelim=both:amm=off:nm=4:fsr=off:afq=1.4:afr=on:er=known:cunif=on_2 on theBenchmark 8.03/8.08 % Time limit reached! 8.03/8.08 % ------------------------------ 8.03/8.08 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 8.03/8.08 % Termination reason: Time limit 8.03/8.08 % Termination phase: Saturation 8.03/8.08 8.03/8.08 % Memory used [KB]: 25585 8.03/8.08 % Time elapsed: 0.500 s 8.03/8.08 % ------------------------------ 8.03/8.08 % ------------------------------ 8.03/8.11 % ott+11_16_sas=z3:irw=on:e2e=off:holscev=on:sp=reverse_arity:foolp=on:addc=user:lma=on:gs=on:nwc=1.3:holcelim=on:afea=on:newcnf=on:gsem=on:en=on:combelim=inference_rules:nm=64:av=off_16 on theBenchmark 9.87/9.91 % Time limit reached! 9.87/9.91 % ------------------------------ 9.87/9.91 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 9.87/9.91 % Termination reason: Time limit 9.87/9.91 % Termination phase: Saturation 9.87/9.91 9.87/9.91 % Memory used [KB]: 46566 9.87/9.91 % Time elapsed: 1.800 s 9.87/9.91 % ------------------------------ 9.87/9.91 % ------------------------------ 9.87/9.93 % lrs+1011_7_anc=none:stl=300d:holscev=on:foolp=on:lma=on:afp=4000:nwc=2.5:holcelim=on:updr=off:afea=on:cond=on:add=large:combelim=inference_rules:amm=off:bd=off:nm=4:fsr=off:csl=3:afq=1.4:afr=on:er=known_2 on theBenchmark 9.91/10.43 % Time limit reached! 9.91/10.43 % ------------------------------ 9.91/10.43 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 9.91/10.43 % Termination reason: Time limit 9.91/10.43 % Termination phase: Saturation 9.91/10.43 9.91/10.43 % Memory used [KB]: 29295 9.91/10.43 % Time elapsed: 0.500 s 9.91/10.43 % ------------------------------ 9.91/10.43 % ------------------------------ 9.91/10.46 % lrs+1011_7_cunif=on:en=on:foolp=on:holcelim=on:holscev=on:combelim=inference_rules:afea=on:add=large:afr=on:afp=40000:afq=1.4:amm=off:anc=none:cond=on:er=known:fsr=off:lma=on:nm=4:nwc=2.5:stl=30:sp=reverse_arity:updr=off_2 on theBenchmark 10.90/10.96 % Time limit reached! 10.90/10.96 % ------------------------------ 10.90/10.96 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 10.90/10.96 % Termination reason: Time limit 10.90/10.96 % Termination phase: Saturation 10.90/10.96 10.90/10.96 % Memory used [KB]: 42600 10.90/10.96 % Time elapsed: 0.500 s 10.90/10.96 % ------------------------------ 10.90/10.96 % ------------------------------ 10.90/10.99 % ott+1011_1024_anc=none:e2e=off:holscev=on:foolp=on:abs=on:acc=on:urr=on:nwc=1.5:holcelim=on:updr=off:sac=on:afea=on:newcnf=on:cond=on:add=off:combelim=both:amm=off:nm=32:afq=1:afr=on_300 on theBenchmark 41.67/41.19 % Time limit reached! 41.67/41.19 % ------------------------------ 41.67/41.19 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 41.67/41.19 % Termination reason: Time limit 41.67/41.19 % Termination phase: Saturation 41.67/41.19 41.67/41.19 % Memory used [KB]: 1012435 41.67/41.19 % Time elapsed: 30.200 s 41.67/41.19 % ------------------------------ 41.67/41.19 % ------------------------------ 41.71/41.29 % dis+10_4_cunif=on:en=on:foolp=on:holcelim=on:holscev=on:combelim=inference_rules:afea=on:av=off:bsr=on:cond=fast:er=filter:fde=none:gsp=input_only:lcm=reverse:lma=on:nwc=4:sp=occurrence:urr=on_8 on theBenchmark 42.90/42.39 % Time limit reached! 42.90/42.39 % ------------------------------ 42.90/42.39 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 42.90/42.39 % Termination reason: Time limit 42.90/42.39 % Termination phase: Saturation 42.90/42.39 42.90/42.39 % Memory used [KB]: 20084 42.90/42.39 % Time elapsed: 1.100 s 42.90/42.39 % ------------------------------ 42.90/42.39 % ------------------------------ 42.91/42.42 % lrs+1011_7_cunif=on:en=on:foolp=on:holcelim=on:holscev=on:combelim=inference_rules:afea=on:add=large:afr=on:afp=40000:afq=1.4:amm=off:anc=none:cond=on:er=known:fsr=off:lma=on:nm=4:nwc=2.5:stl=30:sp=reverse_arity:updr=off_2 on theBenchmark 43.42/42.92 % Time limit reached! 43.42/42.92 % ------------------------------ 43.42/42.92 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 43.42/42.92 % Termination reason: Time limit 43.42/42.92 % Termination phase: Saturation 43.42/42.92 43.42/42.92 % Memory used [KB]: 38506 43.42/42.92 % Time elapsed: 0.500 s 43.42/42.92 % ------------------------------ 43.42/42.92 % ------------------------------ 43.42/42.95 % ott+11_2:1_cunif=on:en=on:foolp=on:holcelim=on:holscev=on:combelim=inference_rules:afea=on:add=large:afp=40000:afq=2.0:amm=sco:anc=none:br=off:cond=on:irw=on:nwc=1:sd=2:ss=axioms:st=2.0:sos=all:urr=on:updr=off_111 on theBenchmark 54.82/54.25 % Time limit reached! 54.82/54.25 % ------------------------------ 54.82/54.25 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 54.82/54.25 % Termination reason: Time limit 54.82/54.25 % Termination phase: Saturation 54.82/54.25 54.82/54.25 % Memory used [KB]: 166948 54.82/54.25 % Time elapsed: 11.300 s 54.82/54.25 % ------------------------------ 54.82/54.25 % ------------------------------ 54.87/54.29 % ott+1011_10_bsr=on:erd=off:sas=vampire:fde=none:sp=reverse_arity:sos=all:foolp=on:addc=user:acc=on:afp=4000:fd=off:updr=off:cond=fast:lcm=reverse:add=large:nocto=10:ep=R:nm=16:fsr=off:aup=on:afq=1.1_300 on theBenchmark 85.25/84.47 % Time limit reached! 85.25/84.47 % ------------------------------ 85.25/84.47 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 85.25/84.47 % Termination reason: Time limit 85.25/84.47 % Termination phase: Saturation 85.25/84.47 85.25/84.47 % Memory used [KB]: 460035 85.25/84.47 % Time elapsed: 30.200 s 85.25/84.47 % ------------------------------ 85.25/84.47 % ------------------------------ 85.36/84.52 % lrs-3_4:1_stl=300d:fde=none:holscev=on:sp=reverse_arity:foolp=on:lma=on:urr=on:afp=1000:gs=on:nwc=2:updr=off:afea=on:lcm=reverse:en=on:sd=7:amm=sco:bd=off:csl=3:afq=1.4:uhcvi=on:ss=axioms_11 on theBenchmark 86.70/85.82 % Time limit reached! 86.70/85.82 % ------------------------------ 86.70/85.82 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 86.70/85.82 % Termination reason: Time limit 86.70/85.82 % Termination phase: Saturation 86.70/85.82 86.70/85.82 % Memory used [KB]: 54242 86.70/85.82 % Time elapsed: 1.300 s 86.70/85.82 % ------------------------------ 86.70/85.82 % ------------------------------ 86.70/85.85 % lrs-3_4:1_cunif=on:en=on:foolp=on:holcelim=on:holscev=on:combelim=inference_rules:afea=on:afp=1000:afq=1.4:amm=sco:fde=none:gs=on:lcm=reverse:lma=on:nwc=1.5:stl=30:sd=1:ss=axioms:sp=reverse_arity:urr=on:updr=off:uhcvi=on_11 on theBenchmark 88.02/87.15 % Time limit reached! 88.02/87.15 % ------------------------------ 88.02/87.15 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 88.02/87.15 % Termination reason: Time limit 88.02/87.15 % Termination phase: Saturation 88.02/87.15 88.02/87.15 % Memory used [KB]: 47333 88.02/87.15 % Time elapsed: 1.300 s 88.02/87.15 % ------------------------------ 88.02/87.15 % ------------------------------ 88.02/87.19 % lrs+10_3:1_cunif=on:en=on:foolp=on:holcelim=on:holscev=on:combelim=inference_rules:afea=on:av=off:bsr=on:cond=on:er=known:gs=on:lcm=reverse:nm=32:nwc=4:stl=30:sp=occurrence:urr=on:updr=off_73 on theBenchmark 95.63/94.68 % Time limit reached! 95.63/94.68 % ------------------------------ 95.63/94.68 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 95.63/94.68 % Termination reason: Time limit 95.63/94.68 % Termination phase: Saturation 95.63/94.68 95.63/94.68 % Memory used [KB]: 224772 95.63/94.68 % Time elapsed: 7.500 s 95.63/94.68 % ------------------------------ 95.63/94.68 % ------------------------------ 95.73/94.72 % lrs-3_4:1_anc=all_dependent:stl=300d:fde=none:holscev=on:sp=reverse_arity:foolp=on:lma=on:urr=on:afp=1000:gs=on:nwc=1.5:holcelim=on:updr=off:afea=on:lcm=reverse:en=on:combelim=inference_rules:sd=1:amm=sco:csl=2:afq=1.4:uhcvi=on:ss=axioms_11 on theBenchmark 97.04/96.02 % Time limit reached! 97.04/96.02 % ------------------------------ 97.04/96.02 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 97.04/96.02 % Termination reason: Time limit 97.04/96.02 % Termination phase: Saturation 97.04/96.02 97.04/96.02 % Memory used [KB]: 55393 97.04/96.02 % Time elapsed: 1.300 s 97.04/96.02 % ------------------------------ 97.04/96.02 % ------------------------------ 97.04/96.05 % lrs+1011_3:1_sas=vampire:holscev=on:sp=reverse_arity:sos=all:foolp=on:afp=10000:holcelim=on:updr=off:afea=on:cond=on:add=off:en=on:combelim=both:ep=R:amm=off:nm=16:fsr=off:afq=1.1_300 on theBenchmark 120.10/118.75 % Refutation found. Thanks to Tanya! 120.10/118.75 % SZS status Theorem for theBenchmark 120.10/118.75 % SZS output start Proof for theBenchmark 120.10/118.75 184. breln = ^[X3 : $i, X4 : $i, X5 : $i] : ((subset @ X5) @ ((cartprod @ X3) @ X4)) [input] 120.10/118.75 201. (brelnall1 = ! [X3,X4,X13] : ((((breln @ X3) @ X4) @ X13) => ! [X0 : ($i > $o)] : (! [X1] : (((in @ X1) @ X3) => ! [X2] : (((in @ X2) @ X4) => (((in @ ((kpair @ X1) @ X2)) @ X13) => (X0 @ ((kpair @ X1) @ X2))))) => ! [X1] : (((in @ X1) @ X13) => (X0 @ X1))))) [input] 120.10/118.75 288. breln1 = ^[X3 : $i, X13 : $i] : (((breln @ X3) @ X3) @ X13) [input] 120.10/118.75 293. setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => ! [X3,X13] : (((breln1 @ X3) @ X13) => ! [X0 : ($i > $o)] : (! [X1] : (((in @ X1) @ X3) => ! [X2] : (((in @ X2) @ X3) => (((in @ ((kpair @ X1) @ X2)) @ X13) => (X0 @ ((kpair @ X1) @ X2))))) => ! [X1] : (((in @ X1) @ X13) => (X0 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [input] 120.10/118.75 294. ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => ! [X3,X13] : (((breln1 @ X3) @ X13) => ! [X0 : ($i > $o)] : (! [X1] : (((in @ X1) @ X3) => ! [X2] : (((in @ X2) @ X3) => (((in @ ((kpair @ X1) @ X2)) @ X13) => (X0 @ ((kpair @ X1) @ X2))))) => ! [X1] : (((in @ X1) @ X13) => (X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [negated conjecture 293] 120.10/118.75 296. ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => ! [X0,X1] : (((breln1 @ X0) @ X1) => ! [X2 : ($i > $o)] : (! [X3] : (((in @ X3) @ X0) => ! [X4] : (((in @ X4) @ X0) => (((in @ ((kpair @ X3) @ X4)) @ X1) => (X2 @ ((kpair @ X3) @ X4))))) => ! [X5] : (((in @ X5) @ X1) => (X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [rectify 294] 120.10/118.75 297. ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ((funcGraphProp4 = $true) => ((subbreln = $true) => ((eqbreln = $true) => ((funcext = $true) => ((funcext2 = $true) => ((ap2apEq1 = $true) => ((ap2apEq2 = $true) => ((beta1 = $true) => ((eta1 = $true) => ((lam2lamEq = $true) => ((beta2 = $true) => ((eta2 = $true) => ((iffalseProp1 = $true) => ((iffalseProp2 = $true) => ((iftrueProp1 = $true) => ((iftrueProp2 = $true) => ((ifSingleton = $true) => ((ifp = $true) => ((theeq = $true) => ((iftrue = $true) => ((iffalse = $true) => ((iftrueorfalse = $true) => ((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((powersetT_lem = $true) => ((setminusT_lem = $true) => ((complementT_lem = $true) => ((setextT = $true) => ((subsetTI = $true) => ((powersetTI1 = $true) => ((powersetTE1 = $true) => ((complementTI1 = $true) => ((complementTE1 = $true) => ((binintersectTELcontra = $true) => ((binintersectTERcontra = $true) => ((contrasubsetT = $true) => ((contrasubsetT1 = $true) => ((contrasubsetT2 = $true) => ((contrasubsetT3 = $true) => ((doubleComplementI1 = $true) => ((doubleComplementE1 = $true) => ((doubleComplementSub1 = $true) => ((doubleComplementSub2 = $true) => ((doubleComplementEq = $true) => ((complementTnotintersectT = $true) => ((complementImpComplementIntersect = $true) => ((complementSubsetComplementIntersect = $true) => ((complementInPowersetComplementIntersect = $true) => ((contraSubsetComplement = $true) => ((complementTcontraSubset = $true) => ((binunionTILcontra = $true) => ((binunionTIRcontra = $true) => ((inIntersectImpInUnion = $true) => ((inIntersectImpInUnion2 = $true) => ((inIntersectImpInIntersectUnions = $true) => ((intersectInPowersetIntersectUnions = $true) => ((inComplementUnionImpNotIn1 = $true) => ((inComplementUnionImpInComplement1 = $true) => ((binunionTE = $true) => ((binunionTEcontra = $true) => ((demorgan2a1 = $true) => ((complementUnionInPowersetComplement = $true) => ((demorgan2a2 = $true) => ((demorgan1a = $true) => ((demorgan1b = $true) => ((demorgan1 = $true) => ((demorgan2a = $true) => ((demorgan2b2 = $true) => ((demorgan2b = $true) => ((demorgan2 = $true) => ((woz13rule0 = $true) => ((woz13rule1 = $true) => ((woz13rule2 = $true) => ((woz13rule3 = $true) => ((woz13rule4 = $true) => ((woz1_1 = $true) => ((woz1_2 = $true) => ((woz1_3 = $true) => ((woz1_4 = $true) => ((woz1_5 = $true) => ((breln1all2 = $true) => ((breln1SetBreln1 = $true) => ((choice2fnsingleton = $true) => ((setOfPairsIsBReln1 = $true) => ! [X0,X1] : (($true = breln1 @ X0 @ X1) => ! [X2 : ($i > $o)] : (! [X3] : (($true = in @ X3 @ X0) => ! [X4] : (($true = in @ X4 @ X0) => (($true = in @ (kpair @ X3 @ X4) @ X1) => ($true = X2 @ (kpair @ X3 @ X4))))) => ! [X5] : (($true = in @ X5 @ X1) => ($true = X2 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [fool elimination 296] 120.10/118.75 825. (brelnall1 = ! [X0,X1,X2] : ((((breln @ X0) @ X1) @ X2) => ! [X3 : ($i > $o)] : (! [X4] : (((in @ X4) @ X0) => ! [X5] : (((in @ X5) @ X1) => (((in @ ((kpair @ X4) @ X5)) @ X2) => (X3 @ ((kpair @ X4) @ X5))))) => ! [X6] : (((in @ X6) @ X2) => (X3 @ X6))))) [rectify 201] 120.10/118.75 826. (brelnall1 = $true) <=> ! [X0,X1,X2] : (($true = breln @ X0 @ X1 @ X2) => ! [X3 : ($i > $o)] : (! [X4] : (($true = in @ X4 @ X0) => ! [X5] : (($true = in @ X5 @ X1) => (($true = in @ (kpair @ X4 @ X5) @ X2) => ($true = X3 @ (kpair @ X4 @ X5))))) => ! [X6] : (($true = in @ X6 @ X2) => ($true = X3 @ X6)))) [fool elimination 825] 120.10/118.75 885. breln1 = ^[X0 : $i, X1 : $i] : (((breln @ X0) @ X0) @ X1) [rectify 288] 120.10/118.75 888. breln1 = sCOMB_47 @ breln @ iCOMB_8 [fool elimination 885] 120.10/118.75 889. breln = ^[X0 : $i, X1 : $i, X2 : $i] : ((subset @ X2) @ ((cartprod @ X0) @ X1)) [rectify 184] 120.10/118.75 890. breln = bCOMB_40 @ (bCOMB_28 @ (cCOMB_29 @ subset)) @ cartprod [fool elimination 889] 120.10/118.75 980. (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0,X1] : (? [X2 : ($i > $o)] : (? [X5] : (($true != X2 @ X5) & ($true = in @ X5 @ X1)) & ! [X3] : (! [X4] : ((($true = X2 @ (kpair @ X3 @ X4)) | ($true != in @ (kpair @ X3 @ X4) @ X1)) | ($true != in @ X4 @ X0)) | ($true != in @ X3 @ X0))) & ($true = breln1 @ X0 @ X1)) & (setOfPairsIsBReln1 = $true)) & (choice2fnsingleton = $true)) & (breln1SetBreln1 = $true)) & (breln1all2 = $true)) & (woz1_5 = $true)) & (woz1_4 = $true)) & (woz1_3 = $true)) & (woz1_2 = $true)) & (woz1_1 = $true)) & (woz13rule4 = $true)) & (woz13rule3 = $true)) & (woz13rule2 = $true)) & (woz13rule1 = $true)) & (woz13rule0 = $true)) & (demorgan2 = $true)) & (demorgan2b = $true)) & (demorgan2b2 = $true)) & (demorgan2a = $true)) & (demorgan1 = $true)) & (demorgan1b = $true)) & (demorgan1a = $true)) & (demorgan2a2 = $true)) & (complementUnionInPowersetComplement = $true)) & (demorgan2a1 = $true)) & (binunionTEcontra = $true)) & (binunionTE = $true)) & (inComplementUnionImpInComplement1 = $true)) & (inComplementUnionImpNotIn1 = $true)) & (intersectInPowersetIntersectUnions = $true)) & (inIntersectImpInIntersectUnions = $true)) & (inIntersectImpInUnion2 = $true)) & (inIntersectImpInUnion = $true)) & (binunionTIRcontra = $true)) & (binunionTILcontra = $true)) & (complementTcontraSubset = $true)) & (contraSubsetComplement = $true)) & (complementInPowersetComplementIntersect = $true)) & (complementSubsetComplementIntersect = $true)) & (complementImpComplementIntersect = $true)) & (complementTnotintersectT = $true)) & (doubleComplementEq = $true)) & (doubleComplementSub2 = $true)) & (doubleComplementSub1 = $true)) & (doubleComplementE1 = $true)) & (doubleComplementI1 = $true)) & (contrasubsetT3 = $true)) & (contrasubsetT2 = $true)) & (contrasubsetT1 = $true)) & (contrasubsetT = $true)) & (binintersectTERcontra = $true)) & (binintersectTELcontra = $true)) & (complementTE1 = $true)) & (complementTI1 = $true)) & (powersetTE1 = $true)) & (powersetTI1 = $true)) & (subsetTI = $true)) & (setextT = $true)) & (complementT_lem = $true)) & (setminusT_lem = $true)) & (powersetT_lem = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)) & (iftrueorfalse = $true)) & (iffalse = $true)) & (iftrue = $true)) & (theeq = $true)) & (ifp = $true)) & (ifSingleton = $true)) & (iftrueProp2 = $true)) & (iftrueProp1 = $true)) & (iffalseProp2 = $true)) & (iffalseProp1 = $true)) & (eta2 = $true)) & (beta2 = $true)) & (lam2lamEq = $true)) & (eta1 = $true)) & (beta1 = $true)) & (ap2apEq2 = $true)) & (ap2apEq1 = $true)) & (funcext2 = $true)) & (funcext = $true)) & (eqbreln = $true)) & (subbreln = $true)) & (funcGraphProp4 = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true) [ennf transformation 297] 120.10/118.75 981. ? [X0,X1] : (? [X2 : ($i > $o)] : (? [X5] : (($true != X2 @ X5) & ($true = in @ X5 @ X1)) & ! [X3] : (! [X4] : (($true = X2 @ (kpair @ X3 @ X4)) | ($true != in @ (kpair @ X3 @ X4) @ X1) | ($true != in @ X4 @ X0)) | ($true != in @ X3 @ X0))) & ($true = breln1 @ X0 @ X1)) & (setOfPairsIsBReln1 = $true) & (choice2fnsingleton = $true) & (breln1SetBreln1 = $true) & (breln1all2 = $true) & (woz1_5 = $true) & (woz1_4 = $true) & (woz1_3 = $true) & (woz1_2 = $true) & (woz1_1 = $true) & (woz13rule4 = $true) & (woz13rule3 = $true) & (woz13rule2 = $true) & (woz13rule1 = $true) & (woz13rule0 = $true) & (demorgan2 = $true) & (demorgan2b = $true) & (demorgan2b2 = $true) & (demorgan2a = $true) & (demorgan1 = $true) & (demorgan1b = $true) & (demorgan1a = $true) & (demorgan2a2 = $true) & (complementUnionInPowersetComplement = $true) & (demorgan2a1 = $true) & (binunionTEcontra = $true) & (binunionTE = $true) & (inComplementUnionImpInComplement1 = $true) & (inComplementUnionImpNotIn1 = $true) & (intersectInPowersetIntersectUnions = $true) & (inIntersectImpInIntersectUnions = $true) & (inIntersectImpInUnion2 = $true) & (inIntersectImpInUnion = $true) & (binunionTIRcontra = $true) & (binunionTILcontra = $true) & (complementTcontraSubset = $true) & (contraSubsetComplement = $true) & (complementInPowersetComplementIntersect = $true) & (complementSubsetComplementIntersect = $true) & (complementImpComplementIntersect = $true) & (complementTnotintersectT = $true) & (doubleComplementEq = $true) & (doubleComplementSub2 = $true) & (doubleComplementSub1 = $true) & (doubleComplementE1 = $true) & (doubleComplementI1 = $true) & (contrasubsetT3 = $true) & (contrasubsetT2 = $true) & (contrasubsetT1 = $true) & (contrasubsetT = $true) & (binintersectTERcontra = $true) & (binintersectTELcontra = $true) & (complementTE1 = $true) & (complementTI1 = $true) & (powersetTE1 = $true) & (powersetTI1 = $true) & (subsetTI = $true) & (setextT = $true) & (complementT_lem = $true) & (setminusT_lem = $true) & (powersetT_lem = $true) & (binunionT_lem = $true) & (binintersectT_lem = $true) & (iftrueorfalse = $true) & (iffalse = $true) & (iftrue = $true) & (theeq = $true) & (ifp = $true) & (ifSingleton = $true) & (iftrueProp2 = $true) & (iftrueProp1 = $true) & (iffalseProp2 = $true) & (iffalseProp1 = $true) & (eta2 = $true) & (beta2 = $true) & (lam2lamEq = $true) & (eta1 = $true) & (beta1 = $true) & (ap2apEq2 = $true) & (ap2apEq1 = $true) & (funcext2 = $true) & (funcext = $true) & (eqbreln = $true) & (subbreln = $true) & (funcGraphProp4 = $true) & (funcextLem = $true) & (funcGraphProp2 = $true) & (funcGraphProp3 = $true) & (funcGraphProp1 = $true) & (ex1E2 = $true) & (brelnall2 = $true) & (brelnall1 = $true) & (lam2p = $true) & (lamp = $true) & (lamProp = $true) & (funcinfuncset = $true) & (ap2p = $true) & (infuncsetfunc = $true) & (app = $true) & (apProp = $true) & (funcImageSingleton = $true) & (dpsetconstrER = $true) & (dpsetconstrEL2 = $true) & (dpsetconstrEL1 = $true) & (dpsetconstrERa = $true) & (setOfPairsIsBReln = $true) & (dpsetconstrSub = $true) & (dpsetconstrI = $true) & (cartprodpairsurjEq = $true) & (cartprodsndpairEq = $true) & (cartprodfstpairEq = $true) & (cartprodmempaircEq = $true) & (cartprodpairmemER = $true) & (cartprodpairmemEL = $true) & (cartprodsndin = $true) & (kpairsurjEq = $true) & (ksndpairEq = $true) & (ksndsingleton = $true) & (setukpairinjR = $true) & (setukpairinjR2 = $true) & (upairequniteq = $true) & (setukpairinjR1 = $true) & (setukpairinjR12 = $true) & (setukpairinjR11 = $true) & (setukpairinjL = $true) & (setukpairinjL2 = $true) & (cartprodfstin = $true) & (kfstpairEq = $true) & (theprop = $true) & (kfstsingleton = $true) & (setukpairinjL1 = $true) & (singletonsuniq = $true) & (ex1I2 = $true) & (ex1I = $true) & (ex1E1 = $true) & (singletonprop = $true) & (setunionsingleton = $true) & (setunionsingleton2 = $true) & (setunionsingleton1 = $true) & (setunionE2 = $true) & (cartprodmempair = $true) & (cartprodmempair1 = $true) & (cartprodpairin = $true) & (ubforcartprodlem3 = $true) & (ubforcartprodlem2 = $true) & (ubforcartprodlem1 = $true) & (upairinpowunion = $true) & (upairsubunion = $true) & (upairset2E = $true) & (singletoninpowunion = $true) & (singletoninpowerset = $true) & (singletonsubset = $true) & (kpairp = $true) & (kpairiskpair = $true) & (setukpairIR = $true) & (setukpairIL = $true) & (secondinupair = $true) & (symdiffIneg2 = $true) & (symdiffIneg1 = $true) & (symdiffI2 = $true) & (symdiffI1 = $true) & (symdiffE = $true) & (setminusSubset1 = $true) & (setminusLsub = $true) & (setminusIRneg = $true) & (setminusILneg = $true) & (setminusELneg = $true) & (setminusERneg = $true) & (setminusSubset2 = $true) & (setminusER = $true) & (setminusEL = $true) & (setminusI = $true) & (bs114d = $true) & (binintersectSubset1 = $true) & (binintersectSubset4 = $true) & (binintersectRsub = $true) & (disjointsetsI1 = $true) & (binintersectER = $true) & (binintersectSubset3 = $true) & (binintersectSubset2 = $true) & (binintersectLsub = $true) & (binintersectEL = $true) & (binintersectSubset5 = $true) & (binintersectI = $true) & (binunionRsub = $true) & (binunionLsub = $true) & (binunionE = $true) & (binunionEcases = $true) & (binunionIR = $true) & (upairset2IR = $true) & (binunionIL = $true) & (sepSubset = $true) & (sepInPowerset = $true) & (powersetsubset = $true) & (inPowerset = $true) & (powersetE1 = $true) & (powersetI1 = $true) & (subsetemptysetimpeq = $true) & (setextsub = $true) & (subset2powerset = $true) & (setadjoinSub2 = $true) & (setadjoinSub = $true) & (subsetTrans = $true) & (subsetRefl = $true) & (notequalI2 = $true) & (notequalI1 = $true) & (notsubsetI = $true) & (subsetE2 = $true) & (subsetE = $true) & (emptysetsubset = $true) & (subsetI2 = $true) & (eqimpsubset1 = $true) & (eqimpsubset2 = $true) & (subsetI1 = $true) & (dsetconstr__Cong = $true) & (descr__Cong = $true) & (exuEu = $true) & (omega__Cong = $true) & (setunion__Cong = $true) & (powerset__Cong = $true) & (setadjoin__Cong = $true) & (emptyset__Cong = $true) & (exu__Cong = $true) & (exuE3u = $true) & (in__Cong = $true) & (inCongP = $true) & (exuI2 = $true) & (exuI3 = $true) & (exuI1 = $true) & (notdallE = $true) & (notdexE = $true) & (prop2set2propI = $true) & (prop2setI = $true) & (quantDeMorgan4 = $true) & (quantDeMorgan3 = $true) & (quantDeMorgan2 = $true) & (quantDeMorgan1 = $true) & (vacuousDall = $true) & (emptyE1 = $true) & (upairsetIR = $true) & (upairsetIL = $true) & (upairsetE = $true) & (singletonsswitch = $true) & (eqinunit = $true) & (notinsingleton = $true) & (uniqinunit = $true) & (nonemptyImpWitness = $true) & (exuE2 = $true) & (subPowSU = $true) & (setunionE = $true) & (setunionI = $true) & (powersetE = $true) & (emptyInPowerset = $true) & (emptyinPowerset = $true) & (powersetI = $true) & (setoftrueEq = $true) & (setadjoinOr = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (emptyinunitempty = $true) & (setadjoinIL = $true) & (nonemptyI1 = $true) & (nonemptyI = $true) & (nonemptyE1 = $true) & (setbeta = $true) & (noeltsimpempty = $true) & (emptyI = $true) & (setext = $true) & (exuE3e = $true) & (notinemptyset = $true) & (emptysetimpfalse = $true) & (emptysetE = $true) & (prop2setE = $true) & (exuE1 = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (dsetconstrI = $true) & (descrp = $true) & (wellorderingAx = $true) & (foundationAx = $true) & (replAx = $true) & (omegaIndAx = $true) & (omegaSAx = $true) & (omega0Ax = $true) & (setunionAx = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (emptysetAx = $true) & (setextAx = $true) [flattening 980] 120.10/118.75 1292. (brelnall1 = $true) <=> ! [X0,X1,X2] : (! [X3 : ($i > $o)] : (! [X6] : (($true = X3 @ X6) | ($true != in @ X6 @ X2)) | ? [X4] : (? [X5] : ((($true != X3 @ (kpair @ X4 @ X5)) & ($true = in @ (kpair @ X4 @ X5) @ X2)) & ($true = in @ X5 @ X1)) & ($true = in @ X4 @ X0))) | ($true != breln @ X0 @ X1 @ X2)) [ennf transformation 826] 120.10/118.75 1293. (brelnall1 = $true) <=> ! [X0,X1,X2] : (! [X3 : ($i > $o)] : (! [X6] : (($true = X3 @ X6) | ($true != in @ X6 @ X2)) | ? [X4] : (? [X5] : (($true != X3 @ (kpair @ X4 @ X5)) & ($true = in @ (kpair @ X4 @ X5) @ X2) & ($true = in @ X5 @ X1)) & ($true = in @ X4 @ X0))) | ($true != breln @ X0 @ X1 @ X2)) [flattening 1292] 120.10/118.75 1362. ? [X0,X1] : (? [X2 : ($i > $o)] : (? [X3] : (($true != X2 @ X3) & ($true = in @ X3 @ X1)) & ! [X4] : (! [X5] : (($true = X2 @ (kpair @ X4 @ X5)) | ($true != in @ (kpair @ X4 @ X5) @ X1) | ($true != in @ X5 @ X0)) | ($true != in @ X4 @ X0))) & ($true = breln1 @ X0 @ X1)) & (setOfPairsIsBReln1 = $true) & (choice2fnsingleton = $true) & (breln1SetBreln1 = $true) & (breln1all2 = $true) & (woz1_5 = $true) & (woz1_4 = $true) & (woz1_3 = $true) & (woz1_2 = $true) & (woz1_1 = $true) & (woz13rule4 = $true) & (woz13rule3 = $true) & (woz13rule2 = $true) & (woz13rule1 = $true) & (woz13rule0 = $true) & (demorgan2 = $true) & (demorgan2b = $true) & (demorgan2b2 = $true) & (demorgan2a = $true) & (demorgan1 = $true) & (demorgan1b = $true) & (demorgan1a = $true) & (demorgan2a2 = $true) & (complementUnionInPowersetComplement = $true) & (demorgan2a1 = $true) & (binunionTEcontra = $true) & (binunionTE = $true) & (inComplementUnionImpInComplement1 = $true) & (inComplementUnionImpNotIn1 = $true) & (intersectInPowersetIntersectUnions = $true) & (inIntersectImpInIntersectUnions = $true) & (inIntersectImpInUnion2 = $true) & (inIntersectImpInUnion = $true) & (binunionTIRcontra = $true) & (binunionTILcontra = $true) & (complementTcontraSubset = $true) & (contraSubsetComplement = $true) & (complementInPowersetComplementIntersect = $true) & (complementSubsetComplementIntersect = $true) & (complementImpComplementIntersect = $true) & (complementTnotintersectT = $true) & (doubleComplementEq = $true) & (doubleComplementSub2 = $true) & (doubleComplementSub1 = $true) & (doubleComplementE1 = $true) & (doubleComplementI1 = $true) & (contrasubsetT3 = $true) & (contrasubsetT2 = $true) & (contrasubsetT1 = $true) & (contrasubsetT = $true) & (binintersectTERcontra = $true) & (binintersectTELcontra = $true) & (complementTE1 = $true) & (complementTI1 = $true) & (powersetTE1 = $true) & (powersetTI1 = $true) & (subsetTI = $true) & (setextT = $true) & (complementT_lem = $true) & (setminusT_lem = $true) & (powersetT_lem = $true) & (binunionT_lem = $true) & (binintersectT_lem = $true) & (iftrueorfalse = $true) & (iffalse = $true) & (iftrue = $true) & (theeq = $true) & (ifp = $true) & (ifSingleton = $true) & (iftrueProp2 = $true) & (iftrueProp1 = $true) & (iffalseProp2 = $true) & (iffalseProp1 = $true) & (eta2 = $true) & (beta2 = $true) & (lam2lamEq = $true) & (eta1 = $true) & (beta1 = $true) & (ap2apEq2 = $true) & (ap2apEq1 = $true) & (funcext2 = $true) & (funcext = $true) & (eqbreln = $true) & (subbreln = $true) & (funcGraphProp4 = $true) & (funcextLem = $true) & (funcGraphProp2 = $true) & (funcGraphProp3 = $true) & (funcGraphProp1 = $true) & (ex1E2 = $true) & (brelnall2 = $true) & (brelnall1 = $true) & (lam2p = $true) & (lamp = $true) & (lamProp = $true) & (funcinfuncset = $true) & (ap2p = $true) & (infuncsetfunc = $true) & (app = $true) & (apProp = $true) & (funcImageSingleton = $true) & (dpsetconstrER = $true) & (dpsetconstrEL2 = $true) & (dpsetconstrEL1 = $true) & (dpsetconstrERa = $true) & (setOfPairsIsBReln = $true) & (dpsetconstrSub = $true) & (dpsetconstrI = $true) & (cartprodpairsurjEq = $true) & (cartprodsndpairEq = $true) & (cartprodfstpairEq = $true) & (cartprodmempaircEq = $true) & (cartprodpairmemER = $true) & (cartprodpairmemEL = $true) & (cartprodsndin = $true) & (kpairsurjEq = $true) & (ksndpairEq = $true) & (ksndsingleton = $true) & (setukpairinjR = $true) & (setukpairinjR2 = $true) & (upairequniteq = $true) & (setukpairinjR1 = $true) & (setukpairinjR12 = $true) & (setukpairinjR11 = $true) & (setukpairinjL = $true) & (setukpairinjL2 = $true) & (cartprodfstin = $true) & (kfstpairEq = $true) & (theprop = $true) & (kfstsingleton = $true) & (setukpairinjL1 = $true) & (singletonsuniq = $true) & (ex1I2 = $true) & (ex1I = $true) & (ex1E1 = $true) & (singletonprop = $true) & (setunionsingleton = $true) & (setunionsingleton2 = $true) & (setunionsingleton1 = $true) & (setunionE2 = $true) & (cartprodmempair = $true) & (cartprodmempair1 = $true) & (cartprodpairin = $true) & (ubforcartprodlem3 = $true) & (ubforcartprodlem2 = $true) & (ubforcartprodlem1 = $true) & (upairinpowunion = $true) & (upairsubunion = $true) & (upairset2E = $true) & (singletoninpowunion = $true) & (singletoninpowerset = $true) & (singletonsubset = $true) & (kpairp = $true) & (kpairiskpair = $true) & (setukpairIR = $true) & (setukpairIL = $true) & (secondinupair = $true) & (symdiffIneg2 = $true) & (symdiffIneg1 = $true) & (symdiffI2 = $true) & (symdiffI1 = $true) & (symdiffE = $true) & (setminusSubset1 = $true) & (setminusLsub = $true) & (setminusIRneg = $true) & (setminusILneg = $true) & (setminusELneg = $true) & (setminusERneg = $true) & (setminusSubset2 = $true) & (setminusER = $true) & (setminusEL = $true) & (setminusI = $true) & (bs114d = $true) & (binintersectSubset1 = $true) & (binintersectSubset4 = $true) & (binintersectRsub = $true) & (disjointsetsI1 = $true) & (binintersectER = $true) & (binintersectSubset3 = $true) & (binintersectSubset2 = $true) & (binintersectLsub = $true) & (binintersectEL = $true) & (binintersectSubset5 = $true) & (binintersectI = $true) & (binunionRsub = $true) & (binunionLsub = $true) & (binunionE = $true) & (binunionEcases = $true) & (binunionIR = $true) & (upairset2IR = $true) & (binunionIL = $true) & (sepSubset = $true) & (sepInPowerset = $true) & (powersetsubset = $true) & (inPowerset = $true) & (powersetE1 = $true) & (powersetI1 = $true) & (subsetemptysetimpeq = $true) & (setextsub = $true) & (subset2powerset = $true) & (setadjoinSub2 = $true) & (setadjoinSub = $true) & (subsetTrans = $true) & (subsetRefl = $true) & (notequalI2 = $true) & (notequalI1 = $true) & (notsubsetI = $true) & (subsetE2 = $true) & (subsetE = $true) & (emptysetsubset = $true) & (subsetI2 = $true) & (eqimpsubset1 = $true) & (eqimpsubset2 = $true) & (subsetI1 = $true) & (dsetconstr__Cong = $true) & (descr__Cong = $true) & (exuEu = $true) & (omega__Cong = $true) & (setunion__Cong = $true) & (powerset__Cong = $true) & (setadjoin__Cong = $true) & (emptyset__Cong = $true) & (exu__Cong = $true) & (exuE3u = $true) & (in__Cong = $true) & (inCongP = $true) & (exuI2 = $true) & (exuI3 = $true) & (exuI1 = $true) & (notdallE = $true) & (notdexE = $true) & (prop2set2propI = $true) & (prop2setI = $true) & (quantDeMorgan4 = $true) & (quantDeMorgan3 = $true) & (quantDeMorgan2 = $true) & (quantDeMorgan1 = $true) & (vacuousDall = $true) & (emptyE1 = $true) & (upairsetIR = $true) & (upairsetIL = $true) & (upairsetE = $true) & (singletonsswitch = $true) & (eqinunit = $true) & (notinsingleton = $true) & (uniqinunit = $true) & (nonemptyImpWitness = $true) & (exuE2 = $true) & (subPowSU = $true) & (setunionE = $true) & (setunionI = $true) & (powersetE = $true) & (emptyInPowerset = $true) & (emptyinPowerset = $true) & (powersetI = $true) & (setoftrueEq = $true) & (setadjoinOr = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (emptyinunitempty = $true) & (setadjoinIL = $true) & (nonemptyI1 = $true) & (nonemptyI = $true) & (nonemptyE1 = $true) & (setbeta = $true) & (noeltsimpempty = $true) & (emptyI = $true) & (setext = $true) & (exuE3e = $true) & (notinemptyset = $true) & (emptysetimpfalse = $true) & (emptysetE = $true) & (prop2setE = $true) & (exuE1 = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (dsetconstrI = $true) & (descrp = $true) & (wellorderingAx = $true) & (foundationAx = $true) & (replAx = $true) & (omegaIndAx = $true) & (omegaSAx = $true) & (omega0Ax = $true) & (setunionAx = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (emptysetAx = $true) & (setextAx = $true) [rectify 981] 120.10/118.75 1363. ? [X0,X1] : (? [X2 : ($i > $o)] : (? [X3] : (($true != X2 @ X3) & ($true = in @ X3 @ X1)) & ! [X4] : (! [X5] : (($true = X2 @ (kpair @ X4 @ X5)) | ($true != in @ (kpair @ X4 @ X5) @ X1) | ($true != in @ X5 @ X0)) | ($true != in @ X4 @ X0))) & ($true = breln1 @ X0 @ X1)) => (? [X2 : ($i > $o)] : (? [X3] : (($true != X2 @ X3) & ($true = in @ X3 @ sK19)) & ! [X4] : (! [X5] : (($true = X2 @ (kpair @ X4 @ X5)) | ($true != in @ (kpair @ X4 @ X5) @ sK19) | ($true != in @ X5 @ sK18)) | ($true != in @ X4 @ sK18))) & ($true = breln1 @ sK18 @ sK19)) [choice axiom] 120.10/118.75 1364. ? [X2 : ($i > $o)] : (? [X3] : (($true != X2 @ X3) & ($true = in @ X3 @ X1)) & ! [X4] : (! [X5] : (($true = X2 @ (kpair @ X4 @ X5)) | ($true != in @ (kpair @ X4 @ X5) @ X1) | ($true != in @ X5 @ X0)) | ($true != in @ X4 @ X0))) => (? [X3] : (($true != sK20 @ X3) & ($true = in @ X3 @ X1)) & ! [X4] : (! [X5] : (($true = sK20 @ (kpair @ X4 @ X5)) | ($true != in @ (kpair @ X4 @ X5) @ X1) | ($true != in @ X5 @ X0)) | ($true != in @ X4 @ X0))) [choice axiom] 120.10/118.75 1365. ? [X3] : (($true != X2 @ X3) & ($true = in @ X3 @ X1)) => (($true != X2 @ sK21) & ($true = in @ sK21 @ X1)) [choice axiom] 120.10/118.75 1366. (((($true != sK20 @ sK21) & ($true = in @ sK21 @ sK19)) & ! [X4] : (! [X5] : (($true = sK20 @ (kpair @ X4 @ X5)) | ($true != in @ (kpair @ X4 @ X5) @ sK19) | ($true != in @ X5 @ sK18)) | ($true != in @ X4 @ sK18))) & ($true = breln1 @ sK18 @ sK19)) & (setOfPairsIsBReln1 = $true) & (choice2fnsingleton = $true) & (breln1SetBreln1 = $true) & (breln1all2 = $true) & (woz1_5 = $true) & (woz1_4 = $true) & (woz1_3 = $true) & (woz1_2 = $true) & (woz1_1 = $true) & (woz13rule4 = $true) & (woz13rule3 = $true) & (woz13rule2 = $true) & (woz13rule1 = $true) & (woz13rule0 = $true) & (demorgan2 = $true) & (demorgan2b = $true) & (demorgan2b2 = $true) & (demorgan2a = $true) & (demorgan1 = $true) & (demorgan1b = $true) & (demorgan1a = $true) & (demorgan2a2 = $true) & (complementUnionInPowersetComplement = $true) & (demorgan2a1 = $true) & (binunionTEcontra = $true) & (binunionTE = $true) & (inComplementUnionImpInComplement1 = $true) & (inComplementUnionImpNotIn1 = $true) & (intersectInPowersetIntersectUnions = $true) & (inIntersectImpInIntersectUnions = $true) & (inIntersectImpInUnion2 = $true) & (inIntersectImpInUnion = $true) & (binunionTIRcontra = $true) & (binunionTILcontra = $true) & (complementTcontraSubset = $true) & (contraSubsetComplement = $true) & (complementInPowersetComplementIntersect = $true) & (complementSubsetComplementIntersect = $true) & (complementImpComplementIntersect = $true) & (complementTnotintersectT = $true) & (doubleComplementEq = $true) & (doubleComplementSub2 = $true) & (doubleComplementSub1 = $true) & (doubleComplementE1 = $true) & (doubleComplementI1 = $true) & (contrasubsetT3 = $true) & (contrasubsetT2 = $true) & (contrasubsetT1 = $true) & (contrasubsetT = $true) & (binintersectTERcontra = $true) & (binintersectTELcontra = $true) & (complementTE1 = $true) & (complementTI1 = $true) & (powersetTE1 = $true) & (powersetTI1 = $true) & (subsetTI = $true) & (setextT = $true) & (complementT_lem = $true) & (setminusT_lem = $true) & (powersetT_lem = $true) & (binunionT_lem = $true) & (binintersectT_lem = $true) & (iftrueorfalse = $true) & (iffalse = $true) & (iftrue = $true) & (theeq = $true) & (ifp = $true) & (ifSingleton = $true) & (iftrueProp2 = $true) & (iftrueProp1 = $true) & (iffalseProp2 = $true) & (iffalseProp1 = $true) & (eta2 = $true) & (beta2 = $true) & (lam2lamEq = $true) & (eta1 = $true) & (beta1 = $true) & (ap2apEq2 = $true) & (ap2apEq1 = $true) & (funcext2 = $true) & (funcext = $true) & (eqbreln = $true) & (subbreln = $true) & (funcGraphProp4 = $true) & (funcextLem = $true) & (funcGraphProp2 = $true) & (funcGraphProp3 = $true) & (funcGraphProp1 = $true) & (ex1E2 = $true) & (brelnall2 = $true) & (brelnall1 = $true) & (lam2p = $true) & (lamp = $true) & (lamProp = $true) & (funcinfuncset = $true) & (ap2p = $true) & (infuncsetfunc = $true) & (app = $true) & (apProp = $true) & (funcImageSingleton = $true) & (dpsetconstrER = $true) & (dpsetconstrEL2 = $true) & (dpsetconstrEL1 = $true) & (dpsetconstrERa = $true) & (setOfPairsIsBReln = $true) & (dpsetconstrSub = $true) & (dpsetconstrI = $true) & (cartprodpairsurjEq = $true) & (cartprodsndpairEq = $true) & (cartprodfstpairEq = $true) & (cartprodmempaircEq = $true) & (cartprodpairmemER = $true) & (cartprodpairmemEL = $true) & (cartprodsndin = $true) & (kpairsurjEq = $true) & (ksndpairEq = $true) & (ksndsingleton = $true) & (setukpairinjR = $true) & (setukpairinjR2 = $true) & (upairequniteq = $true) & (setukpairinjR1 = $true) & (setukpairinjR12 = $true) & (setukpairinjR11 = $true) & (setukpairinjL = $true) & (setukpairinjL2 = $true) & (cartprodfstin = $true) & (kfstpairEq = $true) & (theprop = $true) & (kfstsingleton = $true) & (setukpairinjL1 = $true) & (singletonsuniq = $true) & (ex1I2 = $true) & (ex1I = $true) & (ex1E1 = $true) & (singletonprop = $true) & (setunionsingleton = $true) & (setunionsingleton2 = $true) & (setunionsingleton1 = $true) & (setunionE2 = $true) & (cartprodmempair = $true) & (cartprodmempair1 = $true) & (cartprodpairin = $true) & (ubforcartprodlem3 = $true) & (ubforcartprodlem2 = $true) & (ubforcartprodlem1 = $true) & (upairinpowunion = $true) & (upairsubunion = $true) & (upairset2E = $true) & (singletoninpowunion = $true) & (singletoninpowerset = $true) & (singletonsubset = $true) & (kpairp = $true) & (kpairiskpair = $true) & (setukpairIR = $true) & (setukpairIL = $true) & (secondinupair = $true) & (symdiffIneg2 = $true) & (symdiffIneg1 = $true) & (symdiffI2 = $true) & (symdiffI1 = $true) & (symdiffE = $true) & (setminusSubset1 = $true) & (setminusLsub = $true) & (setminusIRneg = $true) & (setminusILneg = $true) & (setminusELneg = $true) & (setminusERneg = $true) & (setminusSubset2 = $true) & (setminusER = $true) & (setminusEL = $true) & (setminusI = $true) & (bs114d = $true) & (binintersectSubset1 = $true) & (binintersectSubset4 = $true) & (binintersectRsub = $true) & (disjointsetsI1 = $true) & (binintersectER = $true) & (binintersectSubset3 = $true) & (binintersectSubset2 = $true) & (binintersectLsub = $true) & (binintersectEL = $true) & (binintersectSubset5 = $true) & (binintersectI = $true) & (binunionRsub = $true) & (binunionLsub = $true) & (binunionE = $true) & (binunionEcases = $true) & (binunionIR = $true) & (upairset2IR = $true) & (binunionIL = $true) & (sepSubset = $true) & (sepInPowerset = $true) & (powersetsubset = $true) & (inPowerset = $true) & (powersetE1 = $true) & (powersetI1 = $true) & (subsetemptysetimpeq = $true) & (setextsub = $true) & (subset2powerset = $true) & (setadjoinSub2 = $true) & (setadjoinSub = $true) & (subsetTrans = $true) & (subsetRefl = $true) & (notequalI2 = $true) & (notequalI1 = $true) & (notsubsetI = $true) & (subsetE2 = $true) & (subsetE = $true) & (emptysetsubset = $true) & (subsetI2 = $true) & (eqimpsubset1 = $true) & (eqimpsubset2 = $true) & (subsetI1 = $true) & (dsetconstr__Cong = $true) & (descr__Cong = $true) & (exuEu = $true) & (omega__Cong = $true) & (setunion__Cong = $true) & (powerset__Cong = $true) & (setadjoin__Cong = $true) & (emptyset__Cong = $true) & (exu__Cong = $true) & (exuE3u = $true) & (in__Cong = $true) & (inCongP = $true) & (exuI2 = $true) & (exuI3 = $true) & (exuI1 = $true) & (notdallE = $true) & (notdexE = $true) & (prop2set2propI = $true) & (prop2setI = $true) & (quantDeMorgan4 = $true) & (quantDeMorgan3 = $true) & (quantDeMorgan2 = $true) & (quantDeMorgan1 = $true) & (vacuousDall = $true) & (emptyE1 = $true) & (upairsetIR = $true) & (upairsetIL = $true) & (upairsetE = $true) & (singletonsswitch = $true) & (eqinunit = $true) & (notinsingleton = $true) & (uniqinunit = $true) & (nonemptyImpWitness = $true) & (exuE2 = $true) & (subPowSU = $true) & (setunionE = $true) & (setunionI = $true) & (powersetE = $true) & (emptyInPowerset = $true) & (emptyinPowerset = $true) & (powersetI = $true) & (setoftrueEq = $true) & (setadjoinOr = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (emptyinunitempty = $true) & (setadjoinIL = $true) & (nonemptyI1 = $true) & (nonemptyI = $true) & (nonemptyE1 = $true) & (setbeta = $true) & (noeltsimpempty = $true) & (emptyI = $true) & (setext = $true) & (exuE3e = $true) & (notinemptyset = $true) & (emptysetimpfalse = $true) & (emptysetE = $true) & (prop2setE = $true) & (exuE1 = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (dsetconstrI = $true) & (descrp = $true) & (wellorderingAx = $true) & (foundationAx = $true) & (replAx = $true) & (omegaIndAx = $true) & (omegaSAx = $true) & (omega0Ax = $true) & (setunionAx = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (emptysetAx = $true) & (setextAx = $true) [skolemisation 1362,1365,1364,1363] 120.10/118.75 2631. ((brelnall1 = $true) | ? [X0,X1,X2] : (? [X3 : ($i > $o)] : (? [X6] : (($true != X3 @ X6) & ($true = in @ X6 @ X2)) & ! [X4] : (! [X5] : (($true = X3 @ (kpair @ X4 @ X5)) | ($true != in @ (kpair @ X4 @ X5) @ X2) | ($true != in @ X5 @ X1)) | ($true != in @ X4 @ X0))) & ($true = breln @ X0 @ X1 @ X2))) & (! [X0,X1,X2] : (! [X3 : ($i > $o)] : (! [X6] : (($true = X3 @ X6) | ($true != in @ X6 @ X2)) | ? [X4] : (? [X5] : (($true != X3 @ (kpair @ X4 @ X5)) & ($true = in @ (kpair @ X4 @ X5) @ X2) & ($true = in @ X5 @ X1)) & ($true = in @ X4 @ X0))) | ($true != breln @ X0 @ X1 @ X2)) | (brelnall1 != $true)) [nnf transformation 1293] 120.10/118.75 2632. ((brelnall1 = $true) | ? [X0,X1,X2] : (? [X3 : ($i > $o)] : (? [X4] : (($true != X3 @ X4) & ($true = in @ X4 @ X2)) & ! [X5] : (! [X6] : (($true = X3 @ (kpair @ X5 @ X6)) | ($true != in @ (kpair @ X5 @ X6) @ X2) | ($true != in @ X6 @ X1)) | ($true != in @ X5 @ X0))) & ($true = breln @ X0 @ X1 @ X2))) & (! [X7,X8,X9] : (! [X10 : ($i > $o)] : (! [X11] : (($true = X10 @ X11) | ($true != in @ X11 @ X9)) | ? [X12] : (? [X13] : (($true != X10 @ (kpair @ X12 @ X13)) & ($true = in @ (kpair @ X12 @ X13) @ X9) & ($true = in @ X13 @ X8)) & ($true = in @ X12 @ X7))) | ($true != breln @ X7 @ X8 @ X9)) | (brelnall1 != $true)) [rectify 2631] 120.10/118.75 2633. ? [X0,X1,X2] : (? [X3 : ($i > $o)] : (? [X4] : (($true != X3 @ X4) & ($true = in @ X4 @ X2)) & ! [X5] : (! [X6] : (($true = X3 @ (kpair @ X5 @ X6)) | ($true != in @ (kpair @ X5 @ X6) @ X2) | ($true != in @ X6 @ X1)) | ($true != in @ X5 @ X0))) & ($true = breln @ X0 @ X1 @ X2)) => (? [X3 : ($i > $o)] : (? [X4] : (($true != X3 @ X4) & ($true = in @ X4 @ sK821)) & ! [X5] : (! [X6] : (($true = X3 @ (kpair @ X5 @ X6)) | ($true != in @ (kpair @ X5 @ X6) @ sK821) | ($true != in @ X6 @ sK820)) | ($true != in @ X5 @ sK819))) & ($true = breln @ sK819 @ sK820 @ sK821)) [choice axiom] 120.10/118.75 2634. ? [X3 : ($i > $o)] : (? [X4] : (($true != X3 @ X4) & ($true = in @ X4 @ X2)) & ! [X5] : (! [X6] : (($true = X3 @ (kpair @ X5 @ X6)) | ($true != in @ (kpair @ X5 @ X6) @ X2) | ($true != in @ X6 @ X1)) | ($true != in @ X5 @ X0))) => (? [X4] : (($true != sK822 @ X4) & ($true = in @ X4 @ X2)) & ! [X5] : (! [X6] : (($true = sK822 @ (kpair @ X5 @ X6)) | ($true != in @ (kpair @ X5 @ X6) @ X2) | ($true != in @ X6 @ X1)) | ($true != in @ X5 @ X0))) [choice axiom] 120.10/118.75 2635. ? [X4] : (($true != X3 @ X4) & ($true = in @ X4 @ X2)) => (($true != X3 @ sK823) & ($true = in @ sK823 @ X2)) [choice axiom] 120.10/118.75 2636. ! [X10 : ($i > $o),X9,X8,X7] : (? [X12] : (? [X13] : (($true != X10 @ (kpair @ X12 @ X13)) & ($true = in @ (kpair @ X12 @ X13) @ X9) & ($true = in @ X13 @ X8)) & ($true = in @ X12 @ X7)) => (? [X13] : (($true != X10 @ (kpair @ (sK824 @ X10 @ X9 @ X8 @ X7) @ X13)) & ($true = in @ (kpair @ (sK824 @ X10 @ X9 @ X8 @ X7) @ X13) @ X9) & ($true = in @ X13 @ X8)) & ($true = in @ (sK824 @ X10 @ X9 @ X8 @ X7) @ X7))) [choice axiom] 120.10/118.75 2637. ! [X10 : ($i > $o),X9,X8,X7] : (? [X13] : (($true != X10 @ (kpair @ X12 @ X13)) & ($true = in @ (kpair @ X12 @ X13) @ X9) & ($true = in @ X13 @ X8)) => (($true != X10 @ (kpair @ X12 @ (sK825 @ X10 @ X9 @ X8 @ X7))) & ($true = in @ (kpair @ X12 @ (sK825 @ X10 @ X9 @ X8 @ X7)) @ X9) & ($true = in @ (sK825 @ X10 @ X9 @ X8 @ X7) @ X8))) [choice axiom] 120.10/118.75 2638. ((brelnall1 = $true) | (((($true != sK822 @ sK823) & ($true = in @ sK823 @ sK821)) & ! [X5] : (! [X6] : (($true = sK822 @ (kpair @ X5 @ X6)) | ($true != in @ (kpair @ X5 @ X6) @ sK821) | ($true != in @ X6 @ sK820)) | ($true != in @ X5 @ sK819))) & ($true = breln @ sK819 @ sK820 @ sK821))) & (! [X7,X8,X9] : (! [X10 : ($i > $o)] : (! [X11] : (($true = X10 @ X11) | ($true != in @ X11 @ X9)) | ((($true != X10 @ (kpair @ (sK824 @ X10 @ X9 @ X8 @ X7) @ (sK825 @ X10 @ X9 @ X8 @ X7))) & ($true = in @ (kpair @ (sK824 @ X10 @ X9 @ X8 @ X7) @ (sK825 @ X10 @ X9 @ X8 @ X7)) @ X9) & ($true = in @ (sK825 @ X10 @ X9 @ X8 @ X7) @ X8)) & ($true = in @ (sK824 @ X10 @ X9 @ X8 @ X7) @ X7))) | ($true != breln @ X7 @ X8 @ X9)) | (brelnall1 != $true)) [skolemisation 2632,2637,2636,2635,2634,2633] 120.10/118.75 3008. (brelnall1 = $true) [cnf transformation 1366] 120.10/118.75 3099. ($true = breln1 @ sK18 @ sK19) [cnf transformation 1366] 120.10/118.75 3100. ($true = sK20 @ (kpair @ X4 @ X5)) | ($true != in @ (kpair @ X4 @ X5) @ sK19) | ($true != in @ X5 @ sK18) | ($true != in @ X4 @ sK18) [cnf transformation 1366] 120.10/118.75 3101. ($true = in @ sK21 @ sK19) [cnf transformation 1366] 120.10/118.75 3102. ($true != sK20 @ sK21) [cnf transformation 1366] 120.10/118.75 4228. ($true = X10 @ X11) | ($true != in @ X11 @ X9) | ($true = in @ (sK824 @ X10 @ X9 @ X8 @ X7) @ X7) | ($true != breln @ X7 @ X8 @ X9) | (brelnall1 != $true) [cnf transformation 2638] 120.10/118.75 4229. ($true = X10 @ X11) | ($true != in @ X11 @ X9) | ($true = in @ (sK825 @ X10 @ X9 @ X8 @ X7) @ X8) | ($true != breln @ X7 @ X8 @ X9) | (brelnall1 != $true) [cnf transformation 2638] 120.10/118.75 4230. ($true = X10 @ X11) | ($true != in @ X11 @ X9) | ($true = in @ (kpair @ (sK824 @ X10 @ X9 @ X8 @ X7) @ (sK825 @ X10 @ X9 @ X8 @ X7)) @ X9) | ($true != breln @ X7 @ X8 @ X9) | (brelnall1 != $true) [cnf transformation 2638] 120.10/118.75 4231. ($true = X10 @ X11) | ($true != in @ X11 @ X9) | ($true != X10 @ (kpair @ (sK824 @ X10 @ X9 @ X8 @ X7) @ (sK825 @ X10 @ X9 @ X8 @ X7))) | ($true != breln @ X7 @ X8 @ X9) | (brelnall1 != $true) [cnf transformation 2638] 120.10/118.75 4374. breln1 = sCOMB_47 @ breln @ iCOMB_8 [cnf transformation 888] 120.10/118.75 4375. breln = bCOMB_40 @ (bCOMB_28 @ (cCOMB_29 @ subset)) @ cartprod [cnf transformation 890] 120.10/118.75 4377. breln1 = sCOMB_47 @ (bCOMB_40 @ (bCOMB_28 @ (cCOMB_29 @ subset)) @ cartprod) @ iCOMB_8 [definition unfolding 4374,4375] 120.10/118.75 4378. ($true = sCOMB_47 @ (bCOMB_40 @ (bCOMB_28 @ (cCOMB_29 @ subset)) @ cartprod) @ iCOMB_8 @ sK18 @ sK19) [definition unfolding 3099,4377] 120.10/118.75 5466. ($true = X10 @ X11) | ($true != in @ X11 @ X9) | ($true != X10 @ (kpair @ (sK824 @ X10 @ X9 @ X8 @ X7) @ (sK825 @ X10 @ X9 @ X8 @ X7))) | ($true != bCOMB_40 @ (bCOMB_28 @ (cCOMB_29 @ subset)) @ cartprod @ X7 @ X8 @ X9) | ($true != $true) [definition unfolding 4231,4375,3008] 120.10/118.75 5467. ($true = X10 @ X11) | ($true != in @ X11 @ X9) | ($true = in @ (kpair @ (sK824 @ X10 @ X9 @ X8 @ X7) @ (sK825 @ X10 @ X9 @ X8 @ X7)) @ X9) | ($true != bCOMB_40 @ (bCOMB_28 @ (cCOMB_29 @ subset)) @ cartprod @ X7 @ X8 @ X9) | ($true != $true) [definition unfolding 4230,4375,3008] 120.10/118.75 5468. ($true = X10 @ X11) | ($true != in @ X11 @ X9) | ($true = in @ (sK825 @ X10 @ X9 @ X8 @ X7) @ X8) | ($true != bCOMB_40 @ (bCOMB_28 @ (cCOMB_29 @ subset)) @ cartprod @ X7 @ X8 @ X9) | ($true != $true) [definition unfolding 4229,4375,3008] 120.10/118.75 5469. ($true = X10 @ X11) | ($true != in @ X11 @ X9) | ($true = in @ (sK824 @ X10 @ X9 @ X8 @ X7) @ X7) | ($true != bCOMB_40 @ (bCOMB_28 @ (cCOMB_29 @ subset)) @ cartprod @ X7 @ X8 @ X9) | ($true != $true) [definition unfolding 4228,4375,3008] 120.10/118.75 5679. ! [X1 : $o,X0 : $o] : (sQ967_eqProxy(X0,X1) <=> (X0 = X1)) [equality proxy definition] 120.10/118.75 5709. ~sQ967_eqProxy($true,vAPP_5_0(sK20,sK21)) [equality proxy replacement 3102,5679] 120.10/118.75 5710. sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,sK21),sK19)) [equality proxy replacement 3101,5679] 120.10/118.75 5711. sQ967_eqProxy($true,vAPP_5_0(sK20,vAPP_8_0(vAPP_9_0(kpair,X4),X5))) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(kpair,X4),X5)),sK19)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X5),sK18)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X4),sK18)) [equality proxy replacement 3100,5679,5679,5679,5679] 120.10/118.75 5712. sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(vAPP_27_8(vAPP_47_14(sCOMB_47,vAPP_39_9(vAPP_40_27(bCOMB_40,vAPP_28_6(bCOMB_28,vAPP_29_6(cCOMB_29,subset))),cartprod)),iCOMB_8),sK18),sK19)) [equality proxy replacement 4378,5679] 120.10/118.75 6840. sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9)) | ~sQ967_eqProxy($true,vAPP_5_0(X10,vAPP_8_0(vAPP_9_0(kpair,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,X10),X9),X8),X7)),vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,X10),X9),X8),X7)))) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(vAPP_14_0(vAPP_39_9(vAPP_40_27(bCOMB_40,vAPP_28_6(bCOMB_28,vAPP_29_6(cCOMB_29,subset))),cartprod),X7),X8),X9)) | ~sQ967_eqProxy($true,$true) [equality proxy replacement 5466,5679,5679,5679,5679,5679] 120.10/118.75 6841. sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9)) | sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(kpair,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,X10),X9),X8),X7)),vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,X10),X9),X8),X7))),X9)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(vAPP_14_0(vAPP_39_9(vAPP_40_27(bCOMB_40,vAPP_28_6(bCOMB_28,vAPP_29_6(cCOMB_29,subset))),cartprod),X7),X8),X9)) | ~sQ967_eqProxy($true,$true) [equality proxy replacement 5467,5679,5679,5679,5679,5679] 120.10/118.75 6842. sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9)) | sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,X10),X9),X8),X7)),X8)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(vAPP_14_0(vAPP_39_9(vAPP_40_27(bCOMB_40,vAPP_28_6(bCOMB_28,vAPP_29_6(cCOMB_29,subset))),cartprod),X7),X8),X9)) | ~sQ967_eqProxy($true,$true) [equality proxy replacement 5468,5679,5679,5679,5679,5679] 120.10/118.75 6843. sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9)) | sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,X10),X9),X8),X7)),X7)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(vAPP_14_0(vAPP_39_9(vAPP_40_27(bCOMB_40,vAPP_28_6(bCOMB_28,vAPP_29_6(cCOMB_29,subset))),cartprod),X7),X8),X9)) | ~sQ967_eqProxy($true,$true) [equality proxy replacement 5469,5679,5679,5679,5679,5679] 120.10/118.75 6982. sQ967_eqProxy(X0,X0) [equality proxy axiom 5679] 120.10/118.75 7167. sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9)) | sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,X10),X9),X8),X7)),X7)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(vAPP_27_8(vAPP_28_6(bCOMB_28,vAPP_29_6(cCOMB_29,subset)),vAPP_9_0(cartprod,X7)),X8),X9)) | ~sQ967_eqProxy($true,$true) [B combinator elimination 6843] 120.10/118.75 7168. sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9)) | sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,X10),X9),X8),X7)),X7)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(vAPP_29_6(cCOMB_29,subset),vAPP_8_0(vAPP_9_0(cartprod,X7),X8)),X9)) | ~sQ967_eqProxy($true,$true) [B combinator elimination 7167] 120.10/118.75 7169. sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9)) | sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,X10),X9),X8),X7)),X7)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(subset,X9),vAPP_8_0(vAPP_9_0(cartprod,X7),X8))) | ~sQ967_eqProxy($true,$true) [C combinator elimination 7168] 120.10/118.75 7170. sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9)) | sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,X10),X9),X8),X7)),X8)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(vAPP_27_8(vAPP_28_6(bCOMB_28,vAPP_29_6(cCOMB_29,subset)),vAPP_9_0(cartprod,X7)),X8),X9)) | ~sQ967_eqProxy($true,$true) [B combinator elimination 6842] 120.10/118.75 7171. sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9)) | sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,X10),X9),X8),X7)),X8)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(vAPP_29_6(cCOMB_29,subset),vAPP_8_0(vAPP_9_0(cartprod,X7),X8)),X9)) | ~sQ967_eqProxy($true,$true) [B combinator elimination 7170] 120.10/118.75 7172. sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9)) | sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,X10),X9),X8),X7)),X8)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(subset,X9),vAPP_8_0(vAPP_9_0(cartprod,X7),X8))) | ~sQ967_eqProxy($true,$true) [C combinator elimination 7171] 120.10/118.75 7173. sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9)) | sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(kpair,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,X10),X9),X8),X7)),vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,X10),X9),X8),X7))),X9)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(vAPP_27_8(vAPP_28_6(bCOMB_28,vAPP_29_6(cCOMB_29,subset)),vAPP_9_0(cartprod,X7)),X8),X9)) | ~sQ967_eqProxy($true,$true) [B combinator elimination 6841] 120.10/118.75 7174. sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9)) | sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(kpair,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,X10),X9),X8),X7)),vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,X10),X9),X8),X7))),X9)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(vAPP_29_6(cCOMB_29,subset),vAPP_8_0(vAPP_9_0(cartprod,X7),X8)),X9)) | ~sQ967_eqProxy($true,$true) [B combinator elimination 7173] 120.10/118.75 7175. sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9)) | sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(kpair,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,X10),X9),X8),X7)),vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,X10),X9),X8),X7))),X9)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(subset,X9),vAPP_8_0(vAPP_9_0(cartprod,X7),X8))) | ~sQ967_eqProxy($true,$true) [C combinator elimination 7174] 120.10/118.75 7176. sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9)) | ~sQ967_eqProxy($true,vAPP_5_0(X10,vAPP_8_0(vAPP_9_0(kpair,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,X10),X9),X8),X7)),vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,X10),X9),X8),X7)))) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(vAPP_27_8(vAPP_28_6(bCOMB_28,vAPP_29_6(cCOMB_29,subset)),vAPP_9_0(cartprod,X7)),X8),X9)) | ~sQ967_eqProxy($true,$true) [B combinator elimination 6840] 120.10/118.75 7177. sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9)) | ~sQ967_eqProxy($true,vAPP_5_0(X10,vAPP_8_0(vAPP_9_0(kpair,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,X10),X9),X8),X7)),vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,X10),X9),X8),X7)))) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(vAPP_29_6(cCOMB_29,subset),vAPP_8_0(vAPP_9_0(cartprod,X7),X8)),X9)) | ~sQ967_eqProxy($true,$true) [B combinator elimination 7176] 120.10/118.75 7178. sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9)) | ~sQ967_eqProxy($true,vAPP_5_0(X10,vAPP_8_0(vAPP_9_0(kpair,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,X10),X9),X8),X7)),vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,X10),X9),X8),X7)))) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(subset,X9),vAPP_8_0(vAPP_9_0(cartprod,X7),X8))) | ~sQ967_eqProxy($true,$true) [C combinator elimination 7177] 120.10/118.75 7537. sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(vAPP_14_0(vAPP_39_9(vAPP_40_27(bCOMB_40,vAPP_28_6(bCOMB_28,vAPP_29_6(cCOMB_29,subset))),cartprod),sK18),vAPP_8_0(iCOMB_8,sK18)),sK19)) [S combinator elimination 5712] 120.10/118.75 7538. sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(vAPP_14_0(vAPP_39_9(vAPP_40_27(bCOMB_40,vAPP_28_6(bCOMB_28,vAPP_29_6(cCOMB_29,subset))),cartprod),sK18),sK18),sK19)) [I combinator elimination 7537] 120.10/118.75 7539. sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(vAPP_27_8(vAPP_28_6(bCOMB_28,vAPP_29_6(cCOMB_29,subset)),vAPP_9_0(cartprod,sK18)),sK18),sK19)) [B combinator elimination 7538] 120.10/118.75 7540. sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(vAPP_29_6(cCOMB_29,subset),vAPP_8_0(vAPP_9_0(cartprod,sK18),sK18)),sK19)) [B combinator elimination 7539] 120.10/118.75 7541. sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(subset,sK19),vAPP_8_0(vAPP_9_0(cartprod,sK18),sK18))) [C combinator elimination 7540] 120.10/118.75 7546. 1 <=> ~sQ967_eqProxy($true,$true) [avatar definition] 120.10/118.75 7547. ~sQ967_eqProxy($true,$true) <- {1} [avatar component clause 7546] 120.10/118.75 8780. 596 <=> ! [X9,X11,X7,X8,X10 : ($i > $o)] : (sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(subset,X9),vAPP_8_0(vAPP_9_0(cartprod,X7),X8))) | ~sQ967_eqProxy($true,vAPP_5_0(X10,vAPP_8_0(vAPP_9_0(kpair,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,X10),X9),X8),X7)),vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,X10),X9),X8),X7)))) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9))) [avatar definition] 120.10/118.75 8781. ~sQ967_eqProxy($true,vAPP_5_0(X10,vAPP_8_0(vAPP_9_0(kpair,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,X10),X9),X8),X7)),vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,X10),X9),X8),X7)))) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(subset,X9),vAPP_8_0(vAPP_9_0(cartprod,X7),X8))) | sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9)) <- {596} [avatar component clause 8780] 120.10/118.75 8782. ~1 | 596 [avatar split clause 7178,8780,7546] 120.10/118.75 8784. 598 <=> ! [X9,X11,X7,X8,X10 : ($i > $o)] : (sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(subset,X9),vAPP_8_0(vAPP_9_0(cartprod,X7),X8))) | sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(kpair,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,X10),X9),X8),X7)),vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,X10),X9),X8),X7))),X9)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9))) [avatar definition] 120.10/118.75 8785. ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(subset,X9),vAPP_8_0(vAPP_9_0(cartprod,X7),X8))) | sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(kpair,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,X10),X9),X8),X7)),vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,X10),X9),X8),X7))),X9)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9)) <- {598} [avatar component clause 8784] 120.10/118.75 8786. ~1 | 598 [avatar split clause 7175,8784,7546] 120.10/118.75 8788. 600 <=> ! [X9,X11,X7,X8,X10 : ($i > $o)] : (sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(subset,X9),vAPP_8_0(vAPP_9_0(cartprod,X7),X8))) | sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,X10),X9),X8),X7)),X8)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9))) [avatar definition] 120.10/118.75 8789. ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(subset,X9),vAPP_8_0(vAPP_9_0(cartprod,X7),X8))) | sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,X10),X9),X8),X7)),X8)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9)) <- {600} [avatar component clause 8788] 120.10/118.75 8790. ~1 | 600 [avatar split clause 7172,8788,7546] 120.10/118.75 8792. 602 <=> ! [X9,X11,X7,X8,X10 : ($i > $o)] : (sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(subset,X9),vAPP_8_0(vAPP_9_0(cartprod,X7),X8))) | sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,X10),X9),X8),X7)),X7)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9))) [avatar definition] 120.10/118.75 8793. ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(subset,X9),vAPP_8_0(vAPP_9_0(cartprod,X7),X8))) | sQ967_eqProxy($true,vAPP_5_0(X10,X11)) | sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,X10),X9),X8),X7)),X7)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X11),X9)) <- {602} [avatar component clause 8792] 120.10/118.75 8794. ~1 | 602 [avatar split clause 7169,8792,7546] 120.10/118.75 23637. sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,X9),sK19),sK18),sK18)),sK18)) | sQ967_eqProxy($true,vAPP_5_0(X9,X10)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X10),sK19)) <- {600} [resolution 8789,7541] 120.10/118.75 23661. sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,X9),sK19),sK18),sK18)),sK18)) | sQ967_eqProxy($true,vAPP_5_0(X9,X10)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X10),sK19)) <- {602} [resolution 8793,7541] 120.10/118.75 25488. ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(kpair,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,sK20),X98),X100),X99)),vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,sK20),X98),X100),X99))),sK19)) | sQ967_eqProxy($true,vAPP_5_0(sK20,X101)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X101),X98)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(subset,X98),vAPP_8_0(vAPP_9_0(cartprod,X99),X100))) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,sK20),X98),X100),X99)),sK18)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,sK20),X98),X100),X99)),sK18)) <- {596} [resolution 8781,5711] 120.10/118.75 25609. sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(kpair,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,X9),sK19),sK18),sK18)),vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,X9),sK19),sK18),sK18))),sK19)) | sQ967_eqProxy($true,vAPP_5_0(X9,X10)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X10),sK19)) <- {598} [resolution 8785,7541] 120.10/118.75 69696. 14682 <=> ! [X92] : (sQ967_eqProxy($true,vAPP_5_0(sK20,X92)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X92),sK19))) [avatar definition] 120.10/118.75 69697. sQ967_eqProxy($true,vAPP_5_0(sK20,X92)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X92),sK19)) <- {14682} [avatar component clause 69696] 120.10/118.75 70003. ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,sK21),sK19)) <- {14682} [resolution 69697,5709] 120.10/118.75 70213. $false <- {14682} [resolution 70003,5710] 120.10/118.75 70218. ~14682 [avatar contradiction clause 70213] 120.10/118.75 92284. $false <- {1} [resolution 7547,6982] 120.10/118.75 92285. 1 [avatar contradiction clause 92284] 120.10/118.75 228851. sQ967_eqProxy($true,vAPP_5_0(sK20,X0)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X0),sK19)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(subset,sK19),vAPP_8_0(vAPP_9_0(cartprod,sK18),sK18))) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,sK20),sK19),sK18),sK18)),sK18)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,sK20),sK19),sK18),sK18)),sK18)) | sQ967_eqProxy($true,vAPP_5_0(sK20,X1)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X1),sK19)) <- {596, 598} [resolution 25488,25609] 120.10/118.75 228856. sQ967_eqProxy($true,vAPP_5_0(sK20,X0)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X0),sK19)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(subset,sK19),vAPP_8_0(vAPP_9_0(cartprod,sK18),sK18))) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,sK20),sK19),sK18),sK18)),sK18)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,sK20),sK19),sK18),sK18)),sK18)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X0),sK19)) <- {596, 598} [condensation 228851] 120.10/118.75 228857. sQ967_eqProxy($true,vAPP_5_0(sK20,X0)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X0),sK19)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(subset,sK19),vAPP_8_0(vAPP_9_0(cartprod,sK18),sK18))) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,sK20),sK19),sK18),sK18)),sK18)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,sK20),sK19),sK18),sK18)),sK18)) <- {596, 598} [duplicate literal removal 228856] 120.10/118.75 228866. 36301 <=> ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,sK20),sK19),sK18),sK18)),sK18)) [avatar definition] 120.10/118.75 228867. ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK824,sK20),sK19),sK18),sK18)),sK18)) <- {36301} [avatar component clause 228866] 120.10/118.75 228872. 36303 <=> ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,sK20),sK19),sK18),sK18)),sK18)) [avatar definition] 120.10/118.75 228873. ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,vAPP_8_0(vAPP_9_0(vAPP_18_0(vAPP_94_5(sK825,sK20),sK19),sK18),sK18)),sK18)) <- {36303} [avatar component clause 228872] 120.10/118.75 228878. 36305 <=> ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(subset,sK19),vAPP_8_0(vAPP_9_0(cartprod,sK18),sK18))) [avatar definition] 120.10/118.75 228879. ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(subset,sK19),vAPP_8_0(vAPP_9_0(cartprod,sK18),sK18))) <- {36305} [avatar component clause 228878] 120.10/118.75 228880. ~36301 | ~36303 | ~36305 | 14682 | ~596 | ~598 [avatar split clause 228857,8784,8780,69696,228878,228872,228866] 120.10/118.75 244151. sQ967_eqProxy($true,vAPP_5_0(sK20,X0)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X0),sK19)) <- {602, 36301} [resolution 228867,23661] 120.10/118.75 244161. 14682 | ~602 | 36301 [avatar split clause 244151,228866,8792,69696] 120.10/118.75 244265. $false <- {36305} [resolution 228879,7541] 120.10/118.75 244270. 36305 [avatar contradiction clause 244265] 120.10/118.75 244551. sQ967_eqProxy($true,vAPP_5_0(sK20,X0)) | ~sQ967_eqProxy($true,vAPP_5_0(vAPP_6_0(in,X0),sK19)) <- {600, 36303} [resolution 228873,23637] 120.10/118.75 244561. 14682 | ~600 | 36303 [avatar split clause 244551,228872,8788,69696] 120.10/118.75 244562. $false [avatar sat refutation 244561,8790,92285,70218,228880,8782,8786,244161,8794,244270] 120.10/118.75 % SZS output end Proof for theBenchmark 120.10/118.75 % ------------------------------ 120.10/118.75 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 120.10/118.75 % Termination reason: Refutation 120.10/118.75 120.10/118.75 % Memory used [KB]: 293726 120.10/118.75 % Time elapsed: 22.715 s 120.10/118.75 % ------------------------------ 120.10/118.75 % ------------------------------ 120.10/118.78 % Success in time 118.432 s 120.10/118.78 EOF