0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.12 % Command : vampire_hol --schedule thf_2019 --mode portfolio --time_limit %ds %s 0.12/0.33 % Computer : n006.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 13:13:09 EDT 2019 0.12/0.33 % CPUTime : 0.12/0.41 % 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 1.55/1.71 % Time limit reached! 1.55/1.71 % ------------------------------ 1.55/1.71 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 1.55/1.71 % Termination reason: Time limit 1.55/1.71 % Termination phase: Saturation 1.55/1.71 1.55/1.71 % Memory used [KB]: 44519 1.55/1.71 % Time elapsed: 1.300 s 1.55/1.71 % ------------------------------ 1.55/1.71 % ------------------------------ 1.55/1.77 % 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 5.61/5.77 % Time limit reached! 5.61/5.77 % ------------------------------ 5.61/5.77 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 5.61/5.77 % Termination reason: Time limit 5.61/5.77 % Termination phase: Saturation 5.61/5.77 5.61/5.77 % Memory used [KB]: 74583 5.61/5.77 % Time elapsed: 4.0000 s 5.61/5.77 % ------------------------------ 5.61/5.77 % ------------------------------ 5.71/5.83 % 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 7.54/7.63 % Time limit reached! 7.54/7.63 % ------------------------------ 7.54/7.63 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 7.54/7.63 % Termination reason: Time limit 7.54/7.63 % Termination phase: Saturation 7.54/7.63 7.54/7.63 % Memory used [KB]: 30958 7.54/7.63 % Time elapsed: 1.800 s 7.54/7.63 % ------------------------------ 7.54/7.63 % ------------------------------ 7.57/7.69 % 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 8.12/8.18 % Time limit reached! 8.12/8.18 % ------------------------------ 8.12/8.18 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 8.12/8.18 % Termination reason: Time limit 8.12/8.18 % Termination phase: Saturation 8.12/8.18 8.12/8.18 % Memory used [KB]: 20980 8.12/8.18 % Time elapsed: 0.500 s 8.12/8.18 % ------------------------------ 8.12/8.18 % ------------------------------ 8.12/8.21 % 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 9.96/10.01 % Time limit reached! 9.96/10.01 % ------------------------------ 9.96/10.01 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 9.96/10.01 % Termination reason: Time limit 9.96/10.01 % Termination phase: Saturation 9.96/10.01 9.96/10.01 % Memory used [KB]: 33133 9.96/10.01 % Time elapsed: 1.800 s 9.96/10.01 % ------------------------------ 9.96/10.01 % ------------------------------ 9.96/10.04 % 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 10.49/10.54 % Time limit reached! 10.49/10.54 % ------------------------------ 10.49/10.54 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 10.49/10.54 % Termination reason: Time limit 10.49/10.54 % Termination phase: Saturation 10.49/10.54 10.49/10.54 % Memory used [KB]: 27632 10.49/10.54 % Time elapsed: 0.500 s 10.49/10.54 % ------------------------------ 10.49/10.54 % ------------------------------ 10.49/10.57 % 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 10.53/11.07 % Time limit reached! 10.53/11.07 % ------------------------------ 10.53/11.07 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 10.53/11.07 % Termination reason: Time limit 10.53/11.07 % Termination phase: Saturation 10.53/11.07 10.53/11.07 % Memory used [KB]: 40297 10.53/11.07 % Time elapsed: 0.500 s 10.53/11.07 % ------------------------------ 10.53/11.07 % ------------------------------ 11.06/11.10 % 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 41.76/41.30 % Time limit reached! 41.76/41.30 % ------------------------------ 41.76/41.30 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 41.76/41.30 % Termination reason: Time limit 41.76/41.30 % Termination phase: Saturation 41.76/41.30 41.76/41.30 % Memory used [KB]: 970346 41.76/41.30 % Time elapsed: 30.200 s 41.76/41.30 % ------------------------------ 41.76/41.30 % ------------------------------ 41.77/41.37 % 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 42.90/42.47 % Time limit reached! 42.90/42.47 % ------------------------------ 42.90/42.47 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 42.90/42.47 % Termination reason: Time limit 42.90/42.47 % Termination phase: Saturation 42.90/42.47 42.90/42.47 % Memory used [KB]: 17142 42.90/42.47 % Time elapsed: 1.100 s 42.90/42.47 % ------------------------------ 42.90/42.47 % ------------------------------ 42.95/42.53 % 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 43.46/43.03 % Time limit reached! 43.46/43.03 % ------------------------------ 43.46/43.03 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 43.46/43.03 % Termination reason: Time limit 43.46/43.03 % Termination phase: Saturation 43.46/43.03 43.46/43.03 % Memory used [KB]: 42856 43.46/43.03 % Time elapsed: 0.500 s 43.46/43.03 % ------------------------------ 43.46/43.03 % ------------------------------ 43.53/43.06 % 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 45.62/45.14 % Refutation found. Thanks to Tanya! 45.62/45.14 % SZS status Theorem for theBenchmark 45.62/45.14 % SZS output start Proof for theBenchmark 45.62/45.14 140. kpair = ^[X1 : $i, X2 : $i] : ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) [input] 45.62/45.14 168. (kfstpairEq = ! [X1,X2] : (kfst @ ((kpair @ X1) @ X2)) = X1) [input] 45.62/45.14 176. (setukpairinjR2 = ! [X1,X2,X8,X10] : (((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X8) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X8) @ ((setadjoin @ X10) @ emptyset))) @ emptyset)) => X2 = X10)) [input] 45.62/45.14 177. 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 => ! [X1,X2,X8,X10] : (((kpair @ X1) @ X2) = ((kpair @ X8) @ X10) => X2 = X10)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [input] 45.62/45.14 178. ~(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 => ! [X1,X2,X8,X10] : (((kpair @ X1) @ X2) = ((kpair @ X8) @ X10) => X2 = X10))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [negated conjecture 177] 45.62/45.14 180. ~(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 => ! [X0,X1,X2,X3] : (((kpair @ X0) @ X1) = ((kpair @ X2) @ X3) => X1 = X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [rectify 178] 45.62/45.14 181. ~((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) => ! [X0,X1,X2,X3] : (kpair @ X0 @ X1 = kpair @ X2 @ X3 => X1 = X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [fool elimination 180] 45.62/45.14 258. (kfstpairEq = ! [X0,X1] : (kfst @ ((kpair @ X0) @ X1)) = X0) [rectify 168] 45.62/45.14 259. (kfstpairEq = $true) <=> ! [X0,X1] : kfst @ (kpair @ X0 @ X1) = X0 [fool elimination 258] 45.62/45.14 510. (setukpairinjR2 = ! [X0,X1,X2,X3] : (((setadjoin @ ((setadjoin @ X0) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X0) @ ((setadjoin @ X1) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X2) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X2) @ ((setadjoin @ X3) @ emptyset))) @ emptyset)) => X1 = X3)) [rectify 176] 45.62/45.14 511. (setukpairinjR2 = $true) <=> ! [X0,X1,X2,X3] : (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset) = setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset) => X1 = X3) [fool elimination 510] 45.62/45.14 526. kpair = ^[X0 : $i, X1 : $i] : ((setadjoin @ ((setadjoin @ X0) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X0) @ ((setadjoin @ X1) @ emptyset))) @ emptyset)) [rectify 140] 45.62/45.14 527. kpair = sCOMB_66 @ (bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset))) @ (cCOMB_64 @ (bCOMB_65 @ cCOMB_15 @ (bCOMB_63 @ (bCOMB_56 @ setadjoin) @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset)))) @ emptyset) [fool elimination 526] 45.62/45.14 577. (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0,X1,X2,X3] : (X1 != X3 & kpair @ X0 @ X1 = kpair @ X2 @ X3) & (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 181] 45.62/45.14 578. ? [X0,X1,X2,X3] : (X1 != X3 & kpair @ X0 @ X1 = kpair @ X2 @ X3) & (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 577] 45.62/45.14 581. (setukpairinjR2 = $true) <=> ! [X0,X1,X2,X3] : (X1 = X3 | setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset) != setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) [ennf transformation 511] 45.62/45.14 774. ? [X0,X1,X2,X3] : (X1 != X3 & kpair @ X0 @ X1 = kpair @ X2 @ X3) => (sK9 != sK11 & kpair @ sK8 @ sK9 = kpair @ sK10 @ sK11) [choice axiom] 45.62/45.14 775. (sK9 != sK11 & kpair @ sK8 @ sK9 = kpair @ sK10 @ sK11) & (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 578,774] 45.62/45.14 780. ((setukpairinjR2 = $true) | ? [X0,X1,X2,X3] : (X1 != X3 & setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset) = setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))) & (! [X0,X1,X2,X3] : (X1 = X3 | setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset) != setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) | (setukpairinjR2 != $true)) [nnf transformation 581] 45.62/45.14 781. ((setukpairinjR2 = $true) | ? [X0,X1,X2,X3] : (X1 != X3 & setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset) = setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))) & (! [X4,X5,X6,X7] : (X5 = X7 | setadjoin @ (setadjoin @ X4 @ emptyset) @ (setadjoin @ (setadjoin @ X4 @ (setadjoin @ X5 @ emptyset)) @ emptyset) != setadjoin @ (setadjoin @ X6 @ emptyset) @ (setadjoin @ (setadjoin @ X6 @ (setadjoin @ X7 @ emptyset)) @ emptyset)) | (setukpairinjR2 != $true)) [rectify 780] 45.62/45.14 782. ? [X0,X1,X2,X3] : (X1 != X3 & setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset) = setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) => (sK15 != sK17 & setadjoin @ (setadjoin @ sK14 @ emptyset) @ (setadjoin @ (setadjoin @ sK14 @ (setadjoin @ sK15 @ emptyset)) @ emptyset) = setadjoin @ (setadjoin @ sK16 @ emptyset) @ (setadjoin @ (setadjoin @ sK16 @ (setadjoin @ sK17 @ emptyset)) @ emptyset)) [choice axiom] 45.62/45.14 783. ((setukpairinjR2 = $true) | (sK15 != sK17 & setadjoin @ (setadjoin @ sK14 @ emptyset) @ (setadjoin @ (setadjoin @ sK14 @ (setadjoin @ sK15 @ emptyset)) @ emptyset) = setadjoin @ (setadjoin @ sK16 @ emptyset) @ (setadjoin @ (setadjoin @ sK16 @ (setadjoin @ sK17 @ emptyset)) @ emptyset))) & (! [X4,X5,X6,X7] : (X5 = X7 | setadjoin @ (setadjoin @ X4 @ emptyset) @ (setadjoin @ (setadjoin @ X4 @ (setadjoin @ X5 @ emptyset)) @ emptyset) != setadjoin @ (setadjoin @ X6 @ emptyset) @ (setadjoin @ (setadjoin @ X6 @ (setadjoin @ X7 @ emptyset)) @ emptyset)) | (setukpairinjR2 != $true)) [skolemisation 781,782] 45.62/45.14 812. ((kfstpairEq = $true) | ? [X0,X1] : kfst @ (kpair @ X0 @ X1) != X0) & (! [X0,X1] : kfst @ (kpair @ X0 @ X1) = X0 | (kfstpairEq != $true)) [nnf transformation 259] 45.62/45.14 813. ((kfstpairEq = $true) | ? [X0,X1] : kfst @ (kpair @ X0 @ X1) != X0) & (! [X2,X3] : kfst @ (kpair @ X2 @ X3) = X2 | (kfstpairEq != $true)) [rectify 812] 45.62/45.14 814. ? [X0,X1] : kfst @ (kpair @ X0 @ X1) != X0 => kfst @ (kpair @ sK40 @ sK41) != sK40 [choice axiom] 45.62/45.14 815. ((kfstpairEq = $true) | kfst @ (kpair @ sK40 @ sK41) != sK40) & (! [X2,X3] : kfst @ (kpair @ X2 @ X3) = X2 | (kfstpairEq != $true)) [skolemisation 813,814] 45.62/45.14 1739. (kfstpairEq = $true) [cnf transformation 775] 45.62/45.14 1747. (setukpairinjR2 = $true) [cnf transformation 775] 45.62/45.14 1748. kpair @ sK8 @ sK9 = kpair @ sK10 @ sK11 [cnf transformation 775] 45.62/45.14 1749. sK9 != sK11 [cnf transformation 775] 45.62/45.14 1752. X5 = X7 | setadjoin @ (setadjoin @ X4 @ emptyset) @ (setadjoin @ (setadjoin @ X4 @ (setadjoin @ X5 @ emptyset)) @ emptyset) != setadjoin @ (setadjoin @ X6 @ emptyset) @ (setadjoin @ (setadjoin @ X6 @ (setadjoin @ X7 @ emptyset)) @ emptyset) | (setukpairinjR2 != $true) [cnf transformation 783] 45.62/45.14 1777. kfst @ (kpair @ X2 @ X3) = X2 | (kfstpairEq != $true) [cnf transformation 815] 45.62/45.14 2411. kpair = sCOMB_66 @ (bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset))) @ (cCOMB_64 @ (bCOMB_65 @ cCOMB_15 @ (bCOMB_63 @ (bCOMB_56 @ setadjoin) @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset)))) @ emptyset) [cnf transformation 527] 45.62/45.14 2417. sCOMB_66 @ (bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset))) @ (cCOMB_64 @ (bCOMB_65 @ cCOMB_15 @ (bCOMB_63 @ (bCOMB_56 @ setadjoin) @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset)))) @ emptyset) @ sK8 @ sK9 = sCOMB_66 @ (bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset))) @ (cCOMB_64 @ (bCOMB_65 @ cCOMB_15 @ (bCOMB_63 @ (bCOMB_56 @ setadjoin) @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset)))) @ emptyset) @ sK10 @ sK11 [definition unfolding 1748,2411,2411] 45.62/45.14 2420. X5 = X7 | setadjoin @ (setadjoin @ X4 @ emptyset) @ (setadjoin @ (setadjoin @ X4 @ (setadjoin @ X5 @ emptyset)) @ emptyset) != setadjoin @ (setadjoin @ X6 @ emptyset) @ (setadjoin @ (setadjoin @ X6 @ (setadjoin @ X7 @ emptyset)) @ emptyset) | ($true != $true) [definition unfolding 1752,1747] 45.62/45.14 2444. kfst @ (sCOMB_66 @ (bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset))) @ (cCOMB_64 @ (bCOMB_65 @ cCOMB_15 @ (bCOMB_63 @ (bCOMB_56 @ setadjoin) @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset)))) @ emptyset) @ X2 @ X3) = X2 | ($true != $true) [definition unfolding 1777,2411,1739] 45.62/45.14 3430. kfst @ (sCOMB_66 @ (bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset))) @ (cCOMB_64 @ (bCOMB_65 @ cCOMB_15 @ (bCOMB_63 @ (bCOMB_56 @ setadjoin) @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset)))) @ emptyset) @ X2 @ X3) = X2 [trivial inequality removal 2444] 45.62/45.14 3431. kfst @ (bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ X2 @ (cCOMB_64 @ (bCOMB_65 @ cCOMB_15 @ (bCOMB_63 @ (bCOMB_56 @ setadjoin) @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset)))) @ emptyset @ X2) @ X3) = X2 [S combinator elimination 3430] 45.62/45.14 3432. kfst @ (bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ X2 @ (bCOMB_65 @ cCOMB_15 @ (bCOMB_63 @ (bCOMB_56 @ setadjoin) @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset))) @ X2 @ emptyset) @ X3) = X2 [C combinator elimination 3431] 45.62/45.14 3433. kfst @ (bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ X2 @ (cCOMB_15 @ (bCOMB_63 @ (bCOMB_56 @ setadjoin) @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset)) @ X2) @ emptyset) @ X3) = X2 [B combinator elimination 3432] 45.62/45.14 3434. kfst @ (bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ X2 @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset) @ X2)) @ emptyset) @ X3) = X2 [B combinator elimination 3433] 45.62/45.14 3435. kfst @ (bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ X2 @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (bCOMB_60 @ bCOMB_54 @ setadjoin @ X2 @ (cCOMB_15 @ setadjoin @ emptyset))) @ emptyset) @ X3) = X2 [C combinator elimination 3434] 45.62/45.14 3436. kfst @ (bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ X2 @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (bCOMB_54 @ (setadjoin @ X2) @ (cCOMB_15 @ setadjoin @ emptyset))) @ emptyset) @ X3) = X2 [B combinator elimination 3435] 45.62/45.14 3437. kfst @ (bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ X2) @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (bCOMB_54 @ (setadjoin @ X2) @ (cCOMB_15 @ setadjoin @ emptyset))) @ emptyset) @ X3) = X2 [B combinator elimination 3436] 45.62/45.14 3438. kfst @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ X2 @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (bCOMB_54 @ (setadjoin @ X2) @ (cCOMB_15 @ setadjoin @ emptyset))) @ emptyset @ X3)) = X2 [B combinator elimination 3437] 45.62/45.14 3439. kfst @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ X2 @ (bCOMB_56 @ setadjoin @ (bCOMB_54 @ (setadjoin @ X2) @ (cCOMB_15 @ setadjoin @ emptyset)) @ X3 @ emptyset)) = X2 [C combinator elimination 3438] 45.62/45.14 3440. kfst @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ X2 @ (setadjoin @ (bCOMB_54 @ (setadjoin @ X2) @ (cCOMB_15 @ setadjoin @ emptyset) @ X3) @ emptyset)) = X2 [B combinator elimination 3439] 45.62/45.14 3441. kfst @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ X2 @ (setadjoin @ (setadjoin @ X2 @ (cCOMB_15 @ setadjoin @ emptyset @ X3)) @ emptyset)) = X2 [B combinator elimination 3440] 45.62/45.14 3442. kfst @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ X2 @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) = X2 [C combinator elimination 3441] 45.62/45.14 3443. kfst @ (setadjoin @ (cCOMB_15 @ setadjoin @ emptyset @ X2) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) = X2 [B combinator elimination 3442] 45.62/45.14 3444. kfst @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) = X2 [C combinator elimination 3443] 45.62/45.14 3480. setadjoin @ (setadjoin @ X4 @ emptyset) @ (setadjoin @ (setadjoin @ X4 @ (setadjoin @ X5 @ emptyset)) @ emptyset) != setadjoin @ (setadjoin @ X6 @ emptyset) @ (setadjoin @ (setadjoin @ X6 @ (setadjoin @ X7 @ emptyset)) @ emptyset) | X5 = X7 [trivial inequality removal 2420] 45.62/45.14 3481. sCOMB_66 @ (bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset))) @ (cCOMB_64 @ (bCOMB_65 @ cCOMB_15 @ (bCOMB_63 @ (bCOMB_56 @ setadjoin) @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset)))) @ emptyset) @ sK8 @ sK9 = bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK10 @ (cCOMB_64 @ (bCOMB_65 @ cCOMB_15 @ (bCOMB_63 @ (bCOMB_56 @ setadjoin) @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset)))) @ emptyset @ sK10) @ sK11 [S combinator elimination 2417] 45.62/45.14 3482. bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK10 @ (bCOMB_65 @ cCOMB_15 @ (bCOMB_63 @ (bCOMB_56 @ setadjoin) @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset))) @ sK10 @ emptyset) @ sK11 = sCOMB_66 @ (bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset))) @ (cCOMB_64 @ (bCOMB_65 @ cCOMB_15 @ (bCOMB_63 @ (bCOMB_56 @ setadjoin) @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset)))) @ emptyset) @ sK8 @ sK9 [C combinator elimination 3481] 45.62/45.14 3483. bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK10 @ (bCOMB_65 @ cCOMB_15 @ (bCOMB_63 @ (bCOMB_56 @ setadjoin) @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset))) @ sK10 @ emptyset) @ sK11 = bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK8 @ (cCOMB_64 @ (bCOMB_65 @ cCOMB_15 @ (bCOMB_63 @ (bCOMB_56 @ setadjoin) @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset)))) @ emptyset @ sK8) @ sK9 [S combinator elimination 3482] 45.62/45.14 3484. bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK8 @ (bCOMB_65 @ cCOMB_15 @ (bCOMB_63 @ (bCOMB_56 @ setadjoin) @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset))) @ sK8 @ emptyset) @ sK9 = bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK10 @ (bCOMB_65 @ cCOMB_15 @ (bCOMB_63 @ (bCOMB_56 @ setadjoin) @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset))) @ sK10 @ emptyset) @ sK11 [C combinator elimination 3483] 45.62/45.14 3485. bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK10 @ (cCOMB_15 @ (bCOMB_63 @ (bCOMB_56 @ setadjoin) @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK10) @ emptyset) @ sK11 = bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK8 @ (bCOMB_65 @ cCOMB_15 @ (bCOMB_63 @ (bCOMB_56 @ setadjoin) @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset))) @ sK8 @ emptyset) @ sK9 [B combinator elimination 3484] 45.62/45.14 3486. bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK8 @ (cCOMB_15 @ (bCOMB_63 @ (bCOMB_56 @ setadjoin) @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK8) @ emptyset) @ sK9 = bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK10 @ (cCOMB_15 @ (bCOMB_63 @ (bCOMB_56 @ setadjoin) @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK10) @ emptyset) @ sK11 [B combinator elimination 3485] 45.62/45.14 3487. bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK10 @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset) @ sK10)) @ emptyset) @ sK11 = bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK8 @ (cCOMB_15 @ (bCOMB_63 @ (bCOMB_56 @ setadjoin) @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK8) @ emptyset) @ sK9 [B combinator elimination 3486] 45.62/45.14 3488. bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK8 @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset) @ sK8)) @ emptyset) @ sK9 = bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK10 @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset) @ sK10)) @ emptyset) @ sK11 [B combinator elimination 3487] 45.62/45.14 3489. bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK10 @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (bCOMB_60 @ bCOMB_54 @ setadjoin @ sK10 @ (cCOMB_15 @ setadjoin @ emptyset))) @ emptyset) @ sK11 = bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK8 @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (cCOMB_61 @ (bCOMB_60 @ bCOMB_54 @ setadjoin) @ (cCOMB_15 @ setadjoin @ emptyset) @ sK8)) @ emptyset) @ sK9 [C combinator elimination 3488] 45.62/45.14 3490. bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK8 @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (bCOMB_60 @ bCOMB_54 @ setadjoin @ sK8 @ (cCOMB_15 @ setadjoin @ emptyset))) @ emptyset) @ sK9 = bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK10 @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (bCOMB_60 @ bCOMB_54 @ setadjoin @ sK10 @ (cCOMB_15 @ setadjoin @ emptyset))) @ emptyset) @ sK11 [C combinator elimination 3489] 45.62/45.14 3491. bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK10 @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (bCOMB_54 @ (setadjoin @ sK10) @ (cCOMB_15 @ setadjoin @ emptyset))) @ emptyset) @ sK11 = bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK8 @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (bCOMB_60 @ bCOMB_54 @ setadjoin @ sK8 @ (cCOMB_15 @ setadjoin @ emptyset))) @ emptyset) @ sK9 [B combinator elimination 3490] 45.62/45.14 3492. bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK8 @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (bCOMB_54 @ (setadjoin @ sK8) @ (cCOMB_15 @ setadjoin @ emptyset))) @ emptyset) @ sK9 = bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK10 @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (bCOMB_54 @ (setadjoin @ sK10) @ (cCOMB_15 @ setadjoin @ emptyset))) @ emptyset) @ sK11 [B combinator elimination 3491] 45.62/45.14 3493. bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK10) @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (bCOMB_54 @ (setadjoin @ sK10) @ (cCOMB_15 @ setadjoin @ emptyset))) @ emptyset) @ sK11 = bCOMB_60 @ bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK8 @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (bCOMB_54 @ (setadjoin @ sK8) @ (cCOMB_15 @ setadjoin @ emptyset))) @ emptyset) @ sK9 [B combinator elimination 3492] 45.62/45.14 3494. bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK8) @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (bCOMB_54 @ (setadjoin @ sK8) @ (cCOMB_15 @ setadjoin @ emptyset))) @ emptyset) @ sK9 = bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK10) @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (bCOMB_54 @ (setadjoin @ sK10) @ (cCOMB_15 @ setadjoin @ emptyset))) @ emptyset) @ sK11 [B combinator elimination 3493] 45.62/45.14 3495. bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK10 @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (bCOMB_54 @ (setadjoin @ sK10) @ (cCOMB_15 @ setadjoin @ emptyset))) @ emptyset @ sK11) = bCOMB_54 @ (bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK8) @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (bCOMB_54 @ (setadjoin @ sK8) @ (cCOMB_15 @ setadjoin @ emptyset))) @ emptyset) @ sK9 [B combinator elimination 3494] 45.62/45.14 3496. bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK8 @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (bCOMB_54 @ (setadjoin @ sK8) @ (cCOMB_15 @ setadjoin @ emptyset))) @ emptyset @ sK9) = bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK10 @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (bCOMB_54 @ (setadjoin @ sK10) @ (cCOMB_15 @ setadjoin @ emptyset))) @ emptyset @ sK11) [B combinator elimination 3495] 45.62/45.14 3497. bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK10 @ (bCOMB_56 @ setadjoin @ (bCOMB_54 @ (setadjoin @ sK10) @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK11 @ emptyset) = bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK8 @ (cCOMB_15 @ (bCOMB_56 @ setadjoin @ (bCOMB_54 @ (setadjoin @ sK8) @ (cCOMB_15 @ setadjoin @ emptyset))) @ emptyset @ sK9) [C combinator elimination 3496] 45.62/45.14 3498. bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK8 @ (bCOMB_56 @ setadjoin @ (bCOMB_54 @ (setadjoin @ sK8) @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK9 @ emptyset) = bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK10 @ (bCOMB_56 @ setadjoin @ (bCOMB_54 @ (setadjoin @ sK10) @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK11 @ emptyset) [C combinator elimination 3497] 45.62/45.14 3499. bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK10 @ (setadjoin @ (bCOMB_54 @ (setadjoin @ sK10) @ (cCOMB_15 @ setadjoin @ emptyset) @ sK11) @ emptyset) = bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK8 @ (bCOMB_56 @ setadjoin @ (bCOMB_54 @ (setadjoin @ sK8) @ (cCOMB_15 @ setadjoin @ emptyset)) @ sK9 @ emptyset) [B combinator elimination 3498] 45.62/45.14 3500. bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK8 @ (setadjoin @ (bCOMB_54 @ (setadjoin @ sK8) @ (cCOMB_15 @ setadjoin @ emptyset) @ sK9) @ emptyset) = bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK10 @ (setadjoin @ (bCOMB_54 @ (setadjoin @ sK10) @ (cCOMB_15 @ setadjoin @ emptyset) @ sK11) @ emptyset) [B combinator elimination 3499] 45.62/45.14 3501. bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK10 @ (setadjoin @ (setadjoin @ sK10 @ (cCOMB_15 @ setadjoin @ emptyset @ sK11)) @ emptyset) = bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK8 @ (setadjoin @ (bCOMB_54 @ (setadjoin @ sK8) @ (cCOMB_15 @ setadjoin @ emptyset) @ sK9) @ emptyset) [B combinator elimination 3500] 45.62/45.14 3502. bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK8 @ (setadjoin @ (setadjoin @ sK8 @ (cCOMB_15 @ setadjoin @ emptyset @ sK9)) @ emptyset) = bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK10 @ (setadjoin @ (setadjoin @ sK10 @ (cCOMB_15 @ setadjoin @ emptyset @ sK11)) @ emptyset) [B combinator elimination 3501] 45.62/45.14 3503. bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK10 @ (setadjoin @ (setadjoin @ sK10 @ (setadjoin @ sK11 @ emptyset)) @ emptyset) = bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK8 @ (setadjoin @ (setadjoin @ sK8 @ (cCOMB_15 @ setadjoin @ emptyset @ sK9)) @ emptyset) [C combinator elimination 3502] 45.62/45.14 3504. bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK8 @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ sK9 @ emptyset)) @ emptyset) = bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK10 @ (setadjoin @ (setadjoin @ sK10 @ (setadjoin @ sK11 @ emptyset)) @ emptyset) [C combinator elimination 3503] 45.62/45.14 3505. setadjoin @ (cCOMB_15 @ setadjoin @ emptyset @ sK10) @ (setadjoin @ (setadjoin @ sK10 @ (setadjoin @ sK11 @ emptyset)) @ emptyset) = bCOMB_56 @ setadjoin @ (cCOMB_15 @ setadjoin @ emptyset) @ sK8 @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ sK9 @ emptyset)) @ emptyset) [B combinator elimination 3504] 45.62/45.14 3506. setadjoin @ (cCOMB_15 @ setadjoin @ emptyset @ sK8) @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ sK9 @ emptyset)) @ emptyset) = setadjoin @ (cCOMB_15 @ setadjoin @ emptyset @ sK10) @ (setadjoin @ (setadjoin @ sK10 @ (setadjoin @ sK11 @ emptyset)) @ emptyset) [B combinator elimination 3505] 45.62/45.14 3507. setadjoin @ (setadjoin @ sK10 @ emptyset) @ (setadjoin @ (setadjoin @ sK10 @ (setadjoin @ sK11 @ emptyset)) @ emptyset) = setadjoin @ (cCOMB_15 @ setadjoin @ emptyset @ sK8) @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ sK9 @ emptyset)) @ emptyset) [C combinator elimination 3506] 45.62/45.14 3508. setadjoin @ (setadjoin @ sK8 @ emptyset) @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ sK9 @ emptyset)) @ emptyset) = setadjoin @ (setadjoin @ sK10 @ emptyset) @ (setadjoin @ (setadjoin @ sK10 @ (setadjoin @ sK11 @ emptyset)) @ emptyset) [C combinator elimination 3507] 45.62/45.14 39099. kfst @ (setadjoin @ (setadjoin @ sK8 @ emptyset) @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ sK9 @ emptyset)) @ emptyset)) = sK10 [superposition 3444,3508] 45.62/45.14 39119. sK8 = sK10 [forward demodulation 39099,3444] 45.62/45.14 39122. setadjoin @ (setadjoin @ sK8 @ emptyset) @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ sK9 @ emptyset)) @ emptyset) = setadjoin @ (setadjoin @ sK8 @ emptyset) @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ sK11 @ emptyset)) @ emptyset) [backward demodulation 39119,3508] 45.62/45.14 44314. $false [unit resulting resolution 1749,39122,3480] 45.62/45.14 % SZS output end Proof for theBenchmark 45.62/45.14 % ------------------------------ 45.62/45.14 % Version: Vampire 4.2.2 (commit 9d3eacc on 2019-04-30 12:01:32 +0100) 45.62/45.14 % Termination reason: Refutation 45.62/45.14 45.62/45.14 % Memory used [KB]: 54753 45.62/45.14 % Time elapsed: 2.085 s 45.62/45.14 % ------------------------------ 45.62/45.14 % ------------------------------ 45.62/45.14 % Success in time 44.8 s 45.62/45.15 EOF