%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO275+1 : TPTP v8.1.2. Released v4.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n012.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 23:22:54 EDT 2023 % Result : Theorem 103.88s 15.84s % Output : Proof 104.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : GEO275+1 : TPTP v8.1.2. Released v4.1.0. % 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n012.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 : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Tue Aug 29 22:39:38 EDT 2023 % 0.12/0.33 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.63 Running up to 7 provers in parallel. % 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 9.30/1.96 Prover 1: Preprocessing ... % 9.36/1.99 Prover 4: Preprocessing ... % 9.36/2.00 Prover 3: Preprocessing ... % 9.36/2.00 Prover 2: Preprocessing ... % 9.36/2.00 Prover 5: Preprocessing ... % 9.36/2.00 Prover 6: Preprocessing ... % 9.36/2.00 Prover 0: Preprocessing ... % 22.93/3.86 Prover 1: Constructing countermodel ... % 22.93/3.88 Prover 3: Constructing countermodel ... % 23.92/3.93 Prover 6: Proving ... % 26.15/4.28 Prover 5: Proving ... % 26.90/4.33 Prover 2: Proving ... % 37.55/5.89 Prover 4: Constructing countermodel ... % 42.66/6.40 Prover 0: Proving ... % 99.79/13.98 Prover 5: stopped % 99.79/13.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 99.79/13.99 Prover 4: Found proof (size 39) % 99.79/14.00 Prover 4: proved (13351ms) % 99.79/14.00 Prover 6: stopped % 99.79/14.00 Prover 3: stopped % 100.22/14.00 Prover 1: stopped % 100.22/14.02 Prover 0: stopped % 101.02/14.25 Prover 7: Preprocessing ... % 101.98/14.33 Prover 7: stopped % 103.88/15.84 Prover 2: stopped % 103.88/15.84 % 103.88/15.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 103.88/15.84 % 103.88/15.86 % SZS output start Proof for theBenchmark % 104.04/15.88 Assumptions after simplification: % 104.04/15.88 --------------------------------- % 104.04/15.88 % 104.04/15.88 (and(pred(comma_conjunct2(the(228)), 0), and(pred(comma_conjunct1(the(228)), 0), pred(the(228), 0)))) % 104.04/15.92 ron(vd1081, vd1095) = 0 & rcenter(vd1080, vd1095) = 0 & rcircle(vd1095) = 0 & % 104.04/15.92 $i(vd1095) & $i(vd1080) & $i(vd1081) % 104.04/15.92 % 104.04/15.93 (pred(224, 5)) % 104.04/15.93 ~ (vd1080 = vd1081) & $i(vd1080) & $i(vd1081) % 104.04/15.93 % 104.04/15.93 (pred(226, 0)) % 104.04/15.93 rpoint(vd1089) = 0 & $i(vd1089) % 104.04/15.93 % 104.04/15.93 (qe(s1(plural(224)))) % 104.04/15.93 rpoint(vd1080) = 0 & $i(vd1080) % 104.04/15.93 % 104.04/15.93 (qe(s2(plural(224)))) % 104.04/15.93 rpoint(vd1081) = 0 & $i(vd1081) % 104.04/15.93 % 104.04/15.93 (qu(cond(axiom(119), 0), imp(cond(axiom(119), 0)))) % 104.57/15.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 104.57/15.99 int] : (v5 = 0 | v2 = v1 | ~ (rinside(v0, v4) = 0) | ~ (rR(v0, v1, v2) = % 104.57/15.99 v5) | ~ (rpoint(v2) = 0) | ~ (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ % 104.57/15.99 (rline(v3) = 0) | ~ (ron(v2, v3) = 0) | ~ (rcircle(v4) = 0) | ~ $i(v4) | % 104.57/15.99 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 104.57/15.99 ? [v8: any] : ? [v9: any] : (ron(v2, v4) = v6 & ron(v1, v4) = v7 & ron(v1, % 104.57/15.99 v3) = v8 & ron(v0, v3) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | % 104.57/15.99 ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 104.57/15.99 ! [v4: $i] : ! [v5: int] : (v5 = 0 | v2 = v1 | ~ (rinside(v0, v4) = 0) | ~ % 104.57/15.99 (rR(v0, v1, v2) = v5) | ~ (rpoint(v2) = 0) | ~ (rpoint(v1) = 0) | ~ % 104.57/15.99 (rpoint(v0) = 0) | ~ (rline(v3) = 0) | ~ (ron(v1, v3) = 0) | ~ % 104.57/15.99 (rcircle(v4) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 104.57/15.99 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: any] : % 104.57/15.99 (ron(v2, v4) = v6 & ron(v2, v3) = v8 & ron(v1, v4) = v7 & ron(v0, v3) = v9 & % 104.57/15.99 ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : % 104.57/15.99 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 % 104.57/15.99 | v2 = v1 | ~ (rinside(v0, v4) = 0) | ~ (rR(v0, v1, v2) = v5) | ~ % 104.57/15.99 (rpoint(v2) = 0) | ~ (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (rline(v3) % 104.57/15.99 = 0) | ~ (ron(v0, v3) = 0) | ~ (rcircle(v4) = 0) | ~ $i(v4) | ~ $i(v3) % 104.57/15.99 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: % 104.57/15.99 any] : ? [v9: any] : (ron(v2, v4) = v6 & ron(v2, v3) = v8 & ron(v1, v4) = % 104.57/15.99 v7 & ron(v1, v3) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 % 104.57/15.99 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 104.57/15.99 [v4: $i] : ! [v5: int] : (v5 = 0 | v2 = v1 | ~ (rR(v0, v1, v2) = v5) | ~ % 104.57/15.99 (rpoint(v2) = 0) | ~ (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (rline(v3) % 104.57/15.99 = 0) | ~ (ron(v2, v4) = 0) | ~ (ron(v2, v3) = 0) | ~ (rcircle(v4) = 0) % 104.57/15.99 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : % 104.57/15.99 ? [v7: any] : ? [v8: any] : ? [v9: any] : (rinside(v0, v4) = v7 & ron(v1, % 104.57/15.99 v4) = v6 & ron(v1, v3) = v8 & ron(v0, v3) = v9 & ( ~ (v9 = 0) | ~ (v8 = % 104.57/15.99 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 104.57/15.99 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | v2 = v1 | ~ % 104.57/15.99 (rR(v0, v1, v2) = v5) | ~ (rpoint(v2) = 0) | ~ (rpoint(v1) = 0) | ~ % 104.57/15.99 (rpoint(v0) = 0) | ~ (rline(v3) = 0) | ~ (ron(v2, v4) = 0) | ~ (ron(v1, % 104.57/15.99 v3) = 0) | ~ (rcircle(v4) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 104.57/15.99 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: % 104.57/15.99 any] : (rinside(v0, v4) = v7 & ron(v2, v3) = v8 & ron(v1, v4) = v6 & % 104.57/15.99 ron(v0, v3) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = % 104.57/15.99 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 104.57/15.99 [v4: $i] : ! [v5: int] : (v5 = 0 | v2 = v1 | ~ (rR(v0, v1, v2) = v5) | ~ % 104.57/15.99 (rpoint(v2) = 0) | ~ (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (rline(v3) % 104.57/15.99 = 0) | ~ (ron(v2, v4) = 0) | ~ (ron(v0, v3) = 0) | ~ (rcircle(v4) = 0) % 104.57/15.99 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : % 104.57/15.99 ? [v7: any] : ? [v8: any] : ? [v9: any] : (rinside(v0, v4) = v7 & ron(v2, % 104.57/15.99 v3) = v8 & ron(v1, v4) = v6 & ron(v1, v3) = v9 & ( ~ (v9 = 0) | ~ (v8 = % 104.57/15.99 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 104.57/15.99 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | v2 = v1 | ~ % 104.57/15.99 (rR(v0, v1, v2) = v5) | ~ (rpoint(v2) = 0) | ~ (rpoint(v1) = 0) | ~ % 104.57/15.99 (rpoint(v0) = 0) | ~ (rline(v3) = 0) | ~ (ron(v2, v3) = 0) | ~ (ron(v1, % 104.57/15.99 v4) = 0) | ~ (rcircle(v4) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 104.57/15.99 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: % 104.57/15.99 any] : (rinside(v0, v4) = v7 & ron(v2, v4) = v6 & ron(v1, v3) = v8 & % 104.57/15.99 ron(v0, v3) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = % 104.57/15.99 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 104.57/15.99 [v4: $i] : ! [v5: int] : (v5 = 0 | v2 = v1 | ~ (rR(v0, v1, v2) = v5) | ~ % 104.57/15.99 (rpoint(v2) = 0) | ~ (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (rline(v3) % 104.57/15.99 = 0) | ~ (ron(v1, v4) = 0) | ~ (ron(v1, v3) = 0) | ~ (rcircle(v4) = 0) % 104.57/15.99 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : % 104.57/15.99 ? [v7: any] : ? [v8: any] : ? [v9: any] : (rinside(v0, v4) = v7 & ron(v2, % 104.57/15.99 v4) = v6 & ron(v2, v3) = v8 & ron(v0, v3) = v9 & ( ~ (v9 = 0) | ~ (v8 = % 104.57/15.99 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 104.57/15.99 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | v2 = v1 | ~ % 104.57/15.99 (rR(v0, v1, v2) = v5) | ~ (rpoint(v2) = 0) | ~ (rpoint(v1) = 0) | ~ % 104.57/15.99 (rpoint(v0) = 0) | ~ (rline(v3) = 0) | ~ (ron(v1, v4) = 0) | ~ (ron(v0, % 104.57/15.99 v3) = 0) | ~ (rcircle(v4) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 104.57/15.99 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: % 104.57/15.99 any] : (rinside(v0, v4) = v7 & ron(v2, v4) = v6 & ron(v2, v3) = v8 & % 104.57/15.99 ron(v1, v3) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = % 104.57/15.99 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 104.57/15.99 [v4: $i] : (v2 = v1 | ~ (rinside(v0, v4) = 0) | ~ (rpoint(v2) = 0) | ~ % 104.57/15.99 (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (rline(v3) = 0) | ~ (ron(v2, % 104.57/15.99 v4) = 0) | ~ (ron(v1, v3) = 0) | ~ (rcircle(v4) = 0) | ~ $i(v4) | ~ % 104.57/15.99 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 104.57/15.99 ? [v7: any] : ? [v8: any] : (rR(v0, v1, v2) = v8 & ron(v2, v3) = v6 & % 104.57/15.99 ron(v1, v4) = v5 & ron(v0, v3) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 % 104.57/15.99 = 0) | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 104.57/15.99 $i] : ! [v4: $i] : (v2 = v1 | ~ (rinside(v0, v4) = 0) | ~ (rpoint(v2) = % 104.57/15.99 0) | ~ (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (rline(v3) = 0) | ~ % 104.57/15.99 (ron(v2, v3) = 0) | ~ (ron(v1, v4) = 0) | ~ (rcircle(v4) = 0) | ~ $i(v4) % 104.57/15.99 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 104.57/15.99 any] : ? [v7: any] : ? [v8: any] : (rR(v0, v1, v2) = v8 & ron(v2, v4) = % 104.57/15.99 v5 & ron(v1, v3) = v6 & ron(v0, v3) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ % 104.57/15.99 (v5 = 0) | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 104.57/15.99 $i] : ! [v4: $i] : (v2 = v1 | ~ (rinside(v0, v4) = 0) | ~ (rpoint(v2) = % 104.57/15.99 0) | ~ (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (rline(v3) = 0) | ~ % 104.57/15.99 (ron(v2, v3) = 0) | ~ (ron(v1, v3) = 0) | ~ (rcircle(v4) = 0) | ~ $i(v4) % 104.57/15.99 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 104.57/15.99 any] : ? [v7: any] : ? [v8: any] : (rR(v0, v1, v2) = v8 & ron(v2, v4) = % 104.57/15.99 v5 & ron(v1, v4) = v6 & ron(v0, v3) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ % 104.57/15.99 (v5 = 0) | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 104.57/15.99 $i] : ! [v4: $i] : (v2 = v1 | ~ (rpoint(v2) = 0) | ~ (rpoint(v1) = 0) | % 104.57/15.99 ~ (rpoint(v0) = 0) | ~ (rline(v3) = 0) | ~ (ron(v2, v4) = 0) | ~ (ron(v1, % 104.57/15.99 v4) = 0) | ~ (ron(v0, v3) = 0) | ~ (rcircle(v4) = 0) | ~ $i(v4) | ~ % 104.57/15.99 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 104.57/15.99 ? [v7: any] : ? [v8: any] : (rinside(v0, v4) = v5 & rR(v0, v1, v2) = v8 & % 104.57/15.99 ron(v2, v3) = v6 & ron(v1, v3) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 % 104.57/15.99 = 0) | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 104.57/15.99 $i] : ! [v4: $i] : (v2 = v1 | ~ (rpoint(v2) = 0) | ~ (rpoint(v1) = 0) | % 104.57/15.99 ~ (rpoint(v0) = 0) | ~ (rline(v3) = 0) | ~ (ron(v2, v4) = 0) | ~ (ron(v1, % 104.57/15.99 v3) = 0) | ~ (ron(v0, v3) = 0) | ~ (rcircle(v4) = 0) | ~ $i(v4) | ~ % 104.57/15.99 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 104.57/15.99 ? [v7: any] : ? [v8: any] : (rinside(v0, v4) = v6 & rR(v0, v1, v2) = v8 & % 104.57/15.99 ron(v2, v3) = v7 & ron(v1, v4) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 % 104.57/15.99 = 0) | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 104.57/15.99 $i] : ! [v4: $i] : (v2 = v1 | ~ (rpoint(v2) = 0) | ~ (rpoint(v1) = 0) | % 104.57/15.99 ~ (rpoint(v0) = 0) | ~ (rline(v3) = 0) | ~ (ron(v2, v3) = 0) | ~ (ron(v1, % 104.57/15.99 v4) = 0) | ~ (ron(v0, v3) = 0) | ~ (rcircle(v4) = 0) | ~ $i(v4) | ~ % 104.57/15.99 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 104.57/15.99 ? [v7: any] : ? [v8: any] : (rinside(v0, v4) = v6 & rR(v0, v1, v2) = v8 & % 104.57/15.99 ron(v2, v4) = v5 & ron(v1, v3) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 % 104.57/15.99 = 0) | v8 = 0))) % 104.57/15.99 % 104.57/15.99 (qu(cond(axiom(182), 0), imp(cond(axiom(182), 0)))) % 104.57/16.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 104.57/16.00 $i] : (v4 = v3 | ~ (vf(v2, v1) = v5) | ~ (vf(v2, v0) = v5) | ~ % 104.57/16.00 (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (rcenter(v2, v4) = 0) | ~ % 104.57/16.00 (rcenter(v2, v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 104.57/16.00 $i(v0) | ? [v6: any] : ? [v7: any] : (ron(v1, v4) = v6 & ron(v0, v3) = v7 % 104.57/16.00 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 104.57/16.00 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (vf(v2, v1) = v5) | % 104.57/16.00 ~ (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (ron(v1, v4) = 0) | ~ % 104.57/16.00 (ron(v0, v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 104.57/16.00 $i(v0) | ? [v6: $i] : ? [v7: any] : ? [v8: any] : (vf(v2, v0) = v6 & % 104.57/16.00 rcenter(v2, v4) = v7 & rcenter(v2, v3) = v8 & $i(v6) & ( ~ (v8 = 0) | ~ % 104.57/16.00 (v7 = 0) | ~ (v6 = v5)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 104.57/16.00 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (vf(v2, v1) = v5) | ~ % 104.57/16.00 (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (ron(v0, v3) = 0) | ~ % 104.57/16.00 (rcenter(v2, v4) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 104.57/16.00 $i(v0) | ? [v6: $i] : ? [v7: any] : ? [v8: any] : (vf(v2, v0) = v6 & % 104.57/16.00 ron(v1, v4) = v7 & rcenter(v2, v3) = v8 & $i(v6) & ( ~ (v8 = 0) | ~ (v7 = % 104.57/16.00 0) | ~ (v6 = v5)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 104.57/16.00 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (vf(v2, v0) = v5) | ~ % 104.57/16.00 (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (ron(v1, v4) = 0) | ~ (ron(v0, % 104.57/16.00 v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 104.57/16.00 ? [v6: $i] : ? [v7: any] : ? [v8: any] : (vf(v2, v1) = v6 & rcenter(v2, % 104.57/16.00 v4) = v7 & rcenter(v2, v3) = v8 & $i(v6) & ( ~ (v8 = 0) | ~ (v7 = 0) | % 104.57/16.00 ~ (v6 = v5)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 104.57/16.00 ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (vf(v2, v0) = v5) | ~ (rpoint(v1) = % 104.57/16.00 0) | ~ (rpoint(v0) = 0) | ~ (ron(v1, v4) = 0) | ~ (rcenter(v2, v3) = 0) % 104.57/16.00 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : % 104.57/16.00 ? [v7: any] : ? [v8: any] : (vf(v2, v1) = v6 & ron(v0, v3) = v7 & % 104.57/16.00 rcenter(v2, v4) = v8 & $i(v6) & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = % 104.57/16.00 v5)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 104.57/16.00 [v4: $i] : (v4 = v3 | ~ (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (ron(v1, % 104.57/16.00 v4) = 0) | ~ (ron(v0, v3) = 0) | ~ (rcenter(v2, v4) = 0) | ~ $i(v4) | % 104.57/16.01 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : % 104.57/16.01 ? [v7: any] : (vf(v2, v1) = v6 & vf(v2, v0) = v5 & rcenter(v2, v3) = v7 & % 104.57/16.01 $i(v6) & $i(v5) & ( ~ (v7 = 0) | ~ (v6 = v5)))) & ! [v0: $i] : ! [v1: % 104.57/16.01 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (rpoint(v1) = % 104.57/16.01 0) | ~ (rpoint(v0) = 0) | ~ (ron(v1, v4) = 0) | ~ (ron(v0, v3) = 0) | % 104.57/16.01 ~ (rcenter(v2, v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 104.57/16.01 $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: any] : (vf(v2, v1) = v6 & % 104.57/16.01 vf(v2, v0) = v5 & rcenter(v2, v4) = v7 & $i(v6) & $i(v5) & ( ~ (v7 = 0) | % 104.57/16.01 ~ (v6 = v5)))) % 104.57/16.01 % 104.57/16.01 (qu(cond(axiom(184), 0), imp(cond(axiom(184), 0)))) % 104.57/16.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 104.57/16.01 $i] : ( ~ (vf(v1, v3) = v5) | ~ (vf(v1, v0) = v4) | ~ (rpoint(v3) = 0) | % 104.57/16.01 ~ (rpoint(v0) = 0) | ~ (rcenter(v1, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 104.57/16.01 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : (ron(v3, v2) = v6 & % 104.57/16.01 ron(v0, v2) = v7 & ( ~ (v6 = 0) | (( ~ (v7 = 0) | v5 = v4) & ( ~ (v5 = v4) % 104.57/16.01 | v7 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 104.57/16.01 $i] : ! [v4: $i] : ! [v5: any] : ( ~ (vf(v1, v3) = v4) | ~ (rpoint(v3) = % 104.57/16.01 0) | ~ (rpoint(v0) = 0) | ~ (ron(v0, v2) = v5) | ~ $i(v3) | ~ $i(v2) | % 104.57/16.01 ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : (vf(v1, % 104.57/16.01 v0) = v8 & ron(v3, v2) = v6 & rcenter(v1, v2) = v7 & $i(v8) & ( ~ (v7 = % 104.57/16.01 0) | ~ (v6 = 0) | (( ~ (v8 = v4) | v5 = 0) & ( ~ (v5 = 0) | v8 = % 104.57/16.01 v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 104.57/16.01 [v4: $i] : ( ~ (vf(v1, v0) = v4) | ~ (rpoint(v3) = 0) | ~ (rpoint(v0) = 0) | % 104.57/16.01 ~ (ron(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 104.57/16.01 [v5: any] : ? [v6: $i] : ? [v7: any] : (vf(v1, v3) = v6 & ron(v0, v2) = v7 % 104.57/16.01 & rcenter(v1, v2) = v5 & $i(v6) & ( ~ (v5 = 0) | (( ~ (v7 = 0) | v6 = v4) % 104.57/16.01 & ( ~ (v6 = v4) | v7 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 104.57/16.01 $i] : ! [v3: $i] : ! [v4: any] : ( ~ (rpoint(v3) = 0) | ~ (rpoint(v0) = % 104.57/16.01 0) | ~ (ron(v3, v2) = 0) | ~ (ron(v0, v2) = v4) | ~ (rcenter(v1, v2) = % 104.57/16.01 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: % 104.57/16.01 $i] : (vf(v1, v3) = v6 & vf(v1, v0) = v5 & $i(v6) & $i(v5) & ( ~ (v6 = v5) % 104.57/16.01 | v4 = 0) & ( ~ (v4 = 0) | v6 = v5))) % 104.57/16.01 % 104.57/16.01 (qu(theu(the(228), 1), imp(the(228)))) % 104.57/16.01 $i(vd1095) & $i(vd1080) & $i(vd1081) & ? [v0: $i] : ( ~ (v0 = vd1095) & % 104.57/16.01 ron(vd1081, v0) = 0 & rcenter(vd1080, v0) = 0 & rcircle(v0) = 0 & $i(v0)) % 104.57/16.01 % 104.57/16.01 (replace(replace(and(pred(s2(plural(the(227))), 0), and(pred(s1(plural(the(227))), 0), pred(the(227), 0)))))) % 104.57/16.01 rline(vskolem1092) = 0 & ron(vd1089, vskolem1092) = 0 & ron(vd1080, % 104.57/16.01 vskolem1092) = 0 & $i(vd1089) & $i(vskolem1092) & $i(vd1080) % 104.57/16.01 % 104.57/16.01 (function-axioms) % 104.74/16.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 104.74/16.02 $i] : (v1 = v0 | ~ (vskolem1052(v5, v4, v3, v2) = v1) | ~ (vskolem1052(v5, % 104.74/16.02 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 104.74/16.02 $i] : ! [v4: $i] : (v1 = v0 | ~ (vtriangle(v4, v3, v2) = v1) | ~ % 104.74/16.02 (vtriangle(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 104.74/16.02 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vg(v4, v3, v2) = v1) | ~ (vg(v4, v3, % 104.74/16.02 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 104.74/16.02 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (rS(v4, v3, v2) = v1) | % 104.74/16.02 ~ (rS(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 104.74/16.02 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (vangle(v4, v3, v2) = v1) | ~ % 104.74/16.02 (vangle(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 104.74/16.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 104.74/16.02 (rR(v4, v3, v2) = v1) | ~ (rR(v4, v3, v2) = v0)) & ! [v0: % 104.74/16.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 104.74/16.02 : (v1 = v0 | ~ (rgeq(v3, v2) = v1) | ~ (rgeq(v3, v2) = v0)) & ! [v0: % 104.74/16.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 104.74/16.02 : (v1 = v0 | ~ (rintersect(v3, v2) = v1) | ~ (rintersect(v3, v2) = v0)) & ! % 104.74/16.02 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 104.74/16.02 $i] : (v1 = v0 | ~ (rless(v3, v2) = v1) | ~ (rless(v3, v2) = v0)) & ! % 104.74/16.02 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 104.74/16.02 $i] : (v1 = v0 | ~ (rleq(v3, v2) = v1) | ~ (rleq(v3, v2) = v0)) & ! [v0: % 104.74/16.02 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) % 104.74/16.03 = v1) | ~ (vplus(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 104.74/16.03 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (rinside(v3, % 104.74/16.03 v2) = v1) | ~ (rinside(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 104.74/16.03 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vf(v3, v2) = v1) | ~ (vf(v3, v2) = % 104.74/16.03 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 104.74/16.03 $i] : ! [v3: $i] : (v1 = v0 | ~ (ron(v3, v2) = v1) | ~ (ron(v3, v2) = % 104.74/16.03 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 104.74/16.03 $i] : ! [v3: $i] : (v1 = v0 | ~ (rcenter(v3, v2) = v1) | ~ (rcenter(v3, % 104.74/16.03 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 104.74/16.03 ! [v2: $i] : (v1 = v0 | ~ (rtriangle(v2) = v1) | ~ (rtriangle(v2) = v0)) & % 104.74/16.03 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 104.74/16.03 v0 | ~ (rreal(v2) = v1) | ~ (rreal(v2) = v0)) & ! [v0: MultipleValueBool] % 104.74/16.03 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (rpoint(v2) = v1) | % 104.74/16.03 ~ (rpoint(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 104.74/16.03 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (rline(v2) = v1) | ~ % 104.74/16.03 (rline(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 104.74/16.03 : ! [v2: $i] : (v1 = v0 | ~ (rcircle(v2) = v1) | ~ (rcircle(v2) = v0)) % 104.74/16.03 % 104.74/16.03 Further assumptions not needed in the proof: % 104.74/16.03 -------------------------------------------- % 104.74/16.03 ass(cond(156, 0), 0), ass(cond(goal(206), 0), 0), ass(cond(goal(206), 0), 1), % 104.74/16.03 ass(cond(goal(206), 0), 2), holds(226, 1090, 0), holds(226, 1090, 1), % 104.74/16.03 holds(conjunct1(225), 1087, 0), holds(conjunct2(225), 1088, 0), pred(225, 1), % 104.74/16.03 pred(225, 4), pred(axiom(137), 1), pred(axiom(137), 2), pred(axiom(5), 0), % 104.74/16.03 qu(cond(axiom(1), 0), imp(cond(axiom(1), 0))), qu(cond(axiom(101), 0), % 104.74/16.03 imp(cond(axiom(101), 0))), qu(cond(axiom(103), 0), imp(cond(axiom(103), 0))), % 104.74/16.03 qu(cond(axiom(105), 0), imp(cond(axiom(105), 0))), qu(cond(axiom(107), 0), % 104.74/16.03 imp(cond(axiom(107), 0))), qu(cond(axiom(109), 0), imp(cond(axiom(109), 0))), % 104.74/16.03 qu(cond(axiom(11), 0), imp(cond(axiom(11), 0))), qu(cond(axiom(111), 0), % 104.74/16.03 imp(cond(axiom(111), 0))), qu(cond(axiom(113), 0), imp(cond(axiom(113), 0))), % 104.74/16.03 qu(cond(axiom(115), 0), imp(cond(axiom(115), 0))), qu(cond(axiom(117), 0), % 104.74/16.03 imp(cond(axiom(117), 0))), qu(cond(axiom(121), 0), imp(cond(axiom(121), 0))), % 104.74/16.03 qu(cond(axiom(123), 0), imp(cond(axiom(123), 0))), qu(cond(axiom(125), 0), % 104.74/16.03 imp(cond(axiom(125), 0))), qu(cond(axiom(127), 0), imp(cond(axiom(127), 0))), % 104.74/16.03 qu(cond(axiom(129), 0), imp(cond(axiom(129), 0))), qu(cond(axiom(13), 0), % 104.74/16.03 imp(cond(axiom(13), 0))), qu(cond(axiom(131), 0), imp(cond(axiom(131), 0))), % 104.74/16.03 qu(cond(axiom(133), 0), imp(cond(axiom(133), 0))), qu(cond(axiom(135), 0), % 104.74/16.03 imp(cond(axiom(135), 0))), qu(cond(axiom(139), 0), imp(cond(axiom(139), 0))), % 104.74/16.03 qu(cond(axiom(141), 0), imp(cond(axiom(141), 0))), qu(cond(axiom(143), 0), % 104.74/16.03 imp(cond(axiom(143), 0))), qu(cond(axiom(145), 0), imp(cond(axiom(145), 0))), % 104.74/16.03 qu(cond(axiom(147), 0), imp(cond(axiom(147), 0))), qu(cond(axiom(149), 0), % 104.74/16.03 imp(cond(axiom(149), 0))), qu(cond(axiom(15), 0), imp(cond(axiom(15), 0))), % 104.74/16.03 qu(cond(axiom(151), 0), imp(cond(axiom(151), 0))), qu(cond(axiom(153), 0), % 104.74/16.03 imp(cond(axiom(153), 0))), qu(cond(axiom(160), 0), imp(cond(axiom(160), 0))), % 104.74/16.03 qu(cond(axiom(162), 0), imp(cond(axiom(162), 0))), qu(cond(axiom(164), 0), % 104.74/16.03 imp(cond(axiom(164), 0))), qu(cond(axiom(166), 0), imp(cond(axiom(166), 0))), % 104.74/16.03 qu(cond(axiom(168), 0), imp(cond(axiom(168), 0))), qu(cond(axiom(17), 0), % 104.74/16.03 imp(cond(axiom(17), 0))), qu(cond(axiom(170), 0), imp(cond(axiom(170), 0))), % 104.74/16.03 qu(cond(axiom(172), 0), imp(cond(axiom(172), 0))), qu(cond(axiom(174), 0), % 104.74/16.03 imp(cond(axiom(174), 0))), qu(cond(axiom(176), 0), imp(cond(axiom(176), 0))), % 104.74/16.03 qu(cond(axiom(178), 0), imp(cond(axiom(178), 0))), qu(cond(axiom(180), 0), % 104.74/16.03 imp(cond(axiom(180), 0))), qu(cond(axiom(186), 0), imp(cond(axiom(186), 0))), % 104.74/16.03 qu(cond(axiom(188), 0), imp(cond(axiom(188), 0))), qu(cond(axiom(19), 0), % 104.74/16.03 imp(cond(axiom(19), 0))), qu(cond(axiom(190), 0), imp(cond(axiom(190), 0))), % 104.74/16.03 qu(cond(axiom(192), 0), imp(cond(axiom(192), 0))), qu(cond(axiom(194), 0), % 104.74/16.03 imp(cond(axiom(194), 0))), qu(cond(axiom(196), 0), imp(cond(axiom(196), 0))), % 104.74/16.03 qu(cond(axiom(198), 0), imp(cond(axiom(198), 0))), qu(cond(axiom(200), 0), % 104.74/16.03 imp(cond(axiom(200), 0))), qu(cond(axiom(202), 0), imp(cond(axiom(202), 0))), % 104.74/16.03 qu(cond(axiom(204), 0), imp(cond(axiom(204), 0))), qu(cond(axiom(21), 0), % 104.74/16.03 imp(cond(axiom(21), 0))), qu(cond(axiom(23), 0), imp(cond(axiom(23), 0))), % 104.74/16.03 qu(cond(axiom(25), 0), imp(cond(axiom(25), 0))), qu(cond(axiom(27), 0), % 104.74/16.03 imp(cond(axiom(27), 0))), qu(cond(axiom(29), 0), imp(cond(axiom(29), 0))), % 104.74/16.03 qu(cond(axiom(3), 0), imp(cond(axiom(3), 0))), qu(cond(axiom(31), 0), % 104.74/16.03 imp(cond(axiom(31), 0))), qu(cond(axiom(33), 0), imp(cond(axiom(33), 0))), % 104.74/16.03 qu(cond(axiom(35), 0), imp(cond(axiom(35), 0))), qu(cond(axiom(37), 0), % 104.74/16.03 imp(cond(axiom(37), 0))), qu(cond(axiom(39), 0), imp(cond(axiom(39), 0))), % 104.74/16.03 qu(cond(axiom(41), 0), imp(cond(axiom(41), 0))), qu(cond(axiom(43), 0), % 104.74/16.03 imp(cond(axiom(43), 0))), qu(cond(axiom(45), 0), imp(cond(axiom(45), 0))), % 104.74/16.03 qu(cond(axiom(47), 0), imp(cond(axiom(47), 0))), qu(cond(axiom(49), 0), % 104.74/16.03 imp(cond(axiom(49), 0))), qu(cond(axiom(51), 0), imp(cond(axiom(51), 0))), % 104.74/16.03 qu(cond(axiom(53), 0), imp(cond(axiom(53), 0))), qu(cond(axiom(55), 0), % 104.74/16.03 imp(cond(axiom(55), 0))), qu(cond(axiom(57), 0), imp(cond(axiom(57), 0))), % 104.74/16.03 qu(cond(axiom(59), 0), imp(cond(axiom(59), 0))), qu(cond(axiom(61), 0), % 104.74/16.03 imp(cond(axiom(61), 0))), qu(cond(axiom(63), 0), imp(cond(axiom(63), 0))), % 104.74/16.03 qu(cond(axiom(65), 0), imp(cond(axiom(65), 0))), qu(cond(axiom(67), 0), % 104.74/16.03 imp(cond(axiom(67), 0))), qu(cond(axiom(69), 0), imp(cond(axiom(69), 0))), % 104.74/16.03 qu(cond(axiom(7), 0), imp(cond(axiom(7), 0))), qu(cond(axiom(71), 0), % 104.74/16.03 imp(cond(axiom(71), 0))), qu(cond(axiom(73), 0), imp(cond(axiom(73), 0))), % 104.74/16.03 qu(cond(axiom(75), 0), imp(cond(axiom(75), 0))), qu(cond(axiom(77), 0), % 104.74/16.03 imp(cond(axiom(77), 0))), qu(cond(axiom(79), 0), imp(cond(axiom(79), 0))), % 104.74/16.03 qu(cond(axiom(81), 0), imp(cond(axiom(81), 0))), qu(cond(axiom(83), 0), % 104.74/16.03 imp(cond(axiom(83), 0))), qu(cond(axiom(85), 0), imp(cond(axiom(85), 0))), % 104.74/16.03 qu(cond(axiom(87), 0), imp(cond(axiom(87), 0))), qu(cond(axiom(89), 0), % 104.74/16.03 imp(cond(axiom(89), 0))), qu(cond(axiom(9), 0), imp(cond(axiom(9), 0))), % 104.74/16.03 qu(cond(axiom(91), 0), imp(cond(axiom(91), 0))), qu(cond(axiom(93), 0), % 104.74/16.03 imp(cond(axiom(93), 0))), qu(cond(axiom(95), 0), imp(cond(axiom(95), 0))), % 104.74/16.03 qu(cond(axiom(97), 0), imp(cond(axiom(97), 0))), qu(cond(axiom(99), 0), % 104.74/16.03 imp(cond(axiom(99), 0))), replace(pred(227, 2)), replace(qu(theu(the(227), 1), % 104.74/16.03 imp(the(227)))) % 104.74/16.03 % 104.74/16.03 Those formulas are unsatisfiable: % 104.74/16.03 --------------------------------- % 104.74/16.03 % 104.74/16.03 Begin of proof % 104.74/16.03 | % 104.74/16.03 | ALPHA: (and(pred(comma_conjunct2(the(228)), 0), % 104.74/16.03 | and(pred(comma_conjunct1(the(228)), 0), pred(the(228), 0)))) % 104.74/16.03 | implies: % 104.74/16.03 | (1) rcenter(vd1080, vd1095) = 0 % 104.74/16.03 | (2) ron(vd1081, vd1095) = 0 % 104.74/16.03 | % 104.74/16.03 | ALPHA: (replace(replace(and(pred(s2(plural(the(227))), 0), % 104.74/16.03 | and(pred(s1(plural(the(227))), 0), pred(the(227), 0)))))) % 104.74/16.03 | implies: % 104.74/16.03 | (3) $i(vskolem1092) % 104.74/16.03 | (4) ron(vd1080, vskolem1092) = 0 % 104.74/16.03 | (5) ron(vd1089, vskolem1092) = 0 % 104.74/16.03 | (6) rline(vskolem1092) = 0 % 104.74/16.03 | % 104.74/16.03 | ALPHA: (pred(224, 5)) implies: % 104.74/16.03 | (7) ~ (vd1080 = vd1081) % 104.74/16.03 | % 104.74/16.03 | ALPHA: (qe(s2(plural(224)))) implies: % 104.74/16.03 | (8) rpoint(vd1081) = 0 % 104.74/16.03 | % 104.74/16.04 | ALPHA: (qe(s1(plural(224)))) implies: % 104.74/16.04 | (9) rpoint(vd1080) = 0 % 104.74/16.04 | % 104.74/16.04 | ALPHA: (pred(226, 0)) implies: % 104.74/16.04 | (10) $i(vd1089) % 104.74/16.04 | (11) rpoint(vd1089) = 0 % 104.74/16.04 | % 104.74/16.04 | ALPHA: (qu(cond(axiom(119), 0), imp(cond(axiom(119), 0)))) implies: % 104.74/16.04 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 104.74/16.04 | (v2 = v1 | ~ (rpoint(v2) = 0) | ~ (rpoint(v1) = 0) | ~ (rpoint(v0) % 104.74/16.04 | = 0) | ~ (rline(v3) = 0) | ~ (ron(v2, v3) = 0) | ~ (ron(v1, v4) % 104.74/16.04 | = 0) | ~ (ron(v0, v3) = 0) | ~ (rcircle(v4) = 0) | ~ $i(v4) | % 104.74/16.04 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? % 104.74/16.04 | [v6: any] : ? [v7: any] : ? [v8: any] : (rinside(v0, v4) = v6 & % 104.74/16.04 | rR(v0, v1, v2) = v8 & ron(v2, v4) = v5 & ron(v1, v3) = v7 & ( ~ % 104.74/16.04 | (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v8 = 0))) % 104.74/16.04 | % 104.74/16.04 | ALPHA: (qu(cond(axiom(184), 0), imp(cond(axiom(184), 0)))) implies: % 104.74/16.04 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 104.74/16.04 | ( ~ (rpoint(v3) = 0) | ~ (rpoint(v0) = 0) | ~ (ron(v3, v2) = 0) | ~ % 104.74/16.04 | (ron(v0, v2) = v4) | ~ (rcenter(v1, v2) = 0) | ~ $i(v3) | ~ % 104.74/16.04 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (vf(v1, % 104.74/16.04 | v3) = v6 & vf(v1, v0) = v5 & $i(v6) & $i(v5) & ( ~ (v6 = v5) | % 104.74/16.04 | v4 = 0) & ( ~ (v4 = 0) | v6 = v5))) % 104.74/16.04 | % 104.74/16.04 | ALPHA: (qu(cond(axiom(182), 0), imp(cond(axiom(182), 0)))) implies: % 104.74/16.04 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 104.74/16.04 | (v4 = v3 | ~ (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (ron(v1, v4) % 104.74/16.04 | = 0) | ~ (ron(v0, v3) = 0) | ~ (rcenter(v2, v3) = 0) | ~ $i(v4) % 104.74/16.04 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? % 104.74/16.04 | [v6: $i] : ? [v7: any] : (vf(v2, v1) = v6 & vf(v2, v0) = v5 & % 104.74/16.04 | rcenter(v2, v4) = v7 & $i(v6) & $i(v5) & ( ~ (v7 = 0) | ~ (v6 = % 104.74/16.04 | v5)))) % 104.74/16.04 | % 104.74/16.04 | ALPHA: (qu(theu(the(228), 1), imp(the(228)))) implies: % 104.74/16.04 | (15) $i(vd1081) % 104.74/16.04 | (16) $i(vd1080) % 104.74/16.04 | (17) $i(vd1095) % 104.74/16.05 | (18) ? [v0: $i] : ( ~ (v0 = vd1095) & ron(vd1081, v0) = 0 & % 104.74/16.05 | rcenter(vd1080, v0) = 0 & rcircle(v0) = 0 & $i(v0)) % 104.74/16.05 | % 104.74/16.05 | ALPHA: (function-axioms) implies: % 104.74/16.05 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 104.74/16.05 | : ! [v3: $i] : (v1 = v0 | ~ (rcenter(v3, v2) = v1) | ~ (rcenter(v3, % 104.74/16.05 | v2) = v0)) % 104.74/16.05 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 104.74/16.05 | (vf(v3, v2) = v1) | ~ (vf(v3, v2) = v0)) % 104.74/16.05 | % 104.74/16.05 | DELTA: instantiating (18) with fresh symbol all_109_0 gives: % 104.74/16.05 | (21) ~ (all_109_0 = vd1095) & ron(vd1081, all_109_0) = 0 & rcenter(vd1080, % 104.74/16.05 | all_109_0) = 0 & rcircle(all_109_0) = 0 & $i(all_109_0) % 104.74/16.05 | % 104.74/16.05 | ALPHA: (21) implies: % 104.74/16.05 | (22) ~ (all_109_0 = vd1095) % 104.74/16.05 | (23) $i(all_109_0) % 104.74/16.05 | (24) rcircle(all_109_0) = 0 % 104.74/16.05 | (25) rcenter(vd1080, all_109_0) = 0 % 104.74/16.05 | (26) ron(vd1081, all_109_0) = 0 % 104.74/16.05 | % 104.74/16.05 | GROUND_INST: instantiating (14) with vd1081, vd1081, vd1080, vd1095, % 104.74/16.05 | all_109_0, simplifying with (1), (2), (8), (15), (16), (17), % 104.74/16.06 | (23), (26) gives: % 104.74/16.06 | (27) all_109_0 = vd1095 | ? [v0: $i] : ? [v1: $i] : ? [v2: any] : % 104.74/16.06 | (vf(vd1080, vd1081) = v1 & vf(vd1080, vd1081) = v0 & rcenter(vd1080, % 104.74/16.06 | all_109_0) = v2 & $i(v1) & $i(v0) & ( ~ (v2 = 0) | ~ (v1 = v0))) % 104.74/16.06 | % 104.74/16.06 | GROUND_INST: instantiating (13) with vd1081, vd1080, vd1095, vd1081, 0, % 104.74/16.06 | simplifying with (1), (2), (8), (15), (16), (17) gives: % 104.74/16.06 | (28) ? [v0: $i] : (vf(vd1080, vd1081) = v0 & $i(v0)) % 104.74/16.06 | % 104.74/16.06 | GROUND_INST: instantiating (12) with vd1089, vd1081, vd1080, vskolem1092, % 104.74/16.06 | all_109_0, simplifying with (3), (4), (5), (6), (8), (9), (10), % 104.74/16.06 | (11), (15), (16), (23), (24), (26) gives: % 104.74/16.06 | (29) vd1080 = vd1081 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 104.74/16.06 | any] : (rinside(vd1089, all_109_0) = v1 & rR(vd1089, vd1081, vd1080) % 104.74/16.06 | = v3 & ron(vd1080, all_109_0) = v0 & ron(vd1081, vskolem1092) = v2 & % 104.74/16.06 | ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0)) % 104.74/16.06 | % 104.74/16.06 | DELTA: instantiating (28) with fresh symbol all_129_0 gives: % 104.74/16.06 | (30) vf(vd1080, vd1081) = all_129_0 & $i(all_129_0) % 104.74/16.06 | % 104.74/16.06 | ALPHA: (30) implies: % 104.74/16.06 | (31) vf(vd1080, vd1081) = all_129_0 % 104.74/16.06 | % 104.74/16.06 | BETA: splitting (27) gives: % 104.74/16.06 | % 104.74/16.06 | Case 1: % 104.74/16.06 | | % 104.74/16.06 | | (32) all_109_0 = vd1095 % 104.74/16.06 | | % 104.74/16.06 | | REDUCE: (22), (32) imply: % 104.74/16.07 | | (33) $false % 104.74/16.07 | | % 104.74/16.07 | | CLOSE: (33) is inconsistent. % 104.74/16.07 | | % 104.74/16.07 | Case 2: % 104.74/16.07 | | % 104.74/16.07 | | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : (vf(vd1080, vd1081) = v1 % 104.74/16.07 | | & vf(vd1080, vd1081) = v0 & rcenter(vd1080, all_109_0) = v2 & % 104.74/16.07 | | $i(v1) & $i(v0) & ( ~ (v2 = 0) | ~ (v1 = v0))) % 104.74/16.07 | | % 104.74/16.07 | | DELTA: instantiating (34) with fresh symbols all_361_0, all_361_1, all_361_2 % 104.74/16.07 | | gives: % 104.74/16.07 | | (35) vf(vd1080, vd1081) = all_361_1 & vf(vd1080, vd1081) = all_361_2 & % 104.74/16.07 | | rcenter(vd1080, all_109_0) = all_361_0 & $i(all_361_1) & % 104.74/16.07 | | $i(all_361_2) & ( ~ (all_361_0 = 0) | ~ (all_361_1 = all_361_2)) % 104.74/16.07 | | % 104.74/16.07 | | ALPHA: (35) implies: % 104.74/16.07 | | (36) rcenter(vd1080, all_109_0) = all_361_0 % 104.74/16.07 | | (37) vf(vd1080, vd1081) = all_361_2 % 104.74/16.07 | | (38) vf(vd1080, vd1081) = all_361_1 % 104.74/16.07 | | (39) ~ (all_361_0 = 0) | ~ (all_361_1 = all_361_2) % 104.74/16.07 | | % 104.74/16.07 | | BETA: splitting (29) gives: % 104.74/16.07 | | % 104.74/16.07 | | Case 1: % 104.74/16.07 | | | % 104.74/16.07 | | | (40) vd1080 = vd1081 % 104.74/16.07 | | | % 104.74/16.07 | | | REDUCE: (7), (40) imply: % 104.74/16.07 | | | (41) $false % 104.74/16.07 | | | % 104.74/16.07 | | | CLOSE: (41) is inconsistent. % 104.74/16.07 | | | % 104.74/16.07 | | Case 2: % 104.74/16.07 | | | % 104.74/16.07 | | | % 104.74/16.07 | | | GROUND_INST: instantiating (19) with 0, all_361_0, all_109_0, vd1080, % 104.74/16.07 | | | simplifying with (25), (36) gives: % 104.74/16.07 | | | (42) all_361_0 = 0 % 104.74/16.07 | | | % 104.74/16.07 | | | GROUND_INST: instantiating (20) with all_361_2, all_361_1, vd1081, vd1080, % 104.74/16.07 | | | simplifying with (37), (38) gives: % 104.74/16.07 | | | (43) all_361_1 = all_361_2 % 104.74/16.07 | | | % 104.74/16.07 | | | GROUND_INST: instantiating (20) with all_129_0, all_361_1, vd1081, vd1080, % 104.74/16.07 | | | simplifying with (31), (38) gives: % 104.74/16.07 | | | (44) all_361_1 = all_129_0 % 104.74/16.07 | | | % 104.74/16.07 | | | COMBINE_EQS: (43), (44) imply: % 104.74/16.07 | | | (45) all_361_2 = all_129_0 % 104.74/16.07 | | | % 104.74/16.07 | | | SIMP: (45) implies: % 104.74/16.07 | | | (46) all_361_2 = all_129_0 % 104.74/16.07 | | | % 104.74/16.07 | | | BETA: splitting (39) gives: % 104.74/16.07 | | | % 104.74/16.07 | | | Case 1: % 104.74/16.07 | | | | % 104.74/16.07 | | | | (47) ~ (all_361_0 = 0) % 104.74/16.07 | | | | % 104.74/16.07 | | | | REDUCE: (42), (47) imply: % 104.74/16.07 | | | | (48) $false % 104.74/16.07 | | | | % 104.74/16.07 | | | | CLOSE: (48) is inconsistent. % 104.74/16.07 | | | | % 104.74/16.07 | | | Case 2: % 104.74/16.07 | | | | % 104.74/16.07 | | | | (49) ~ (all_361_1 = all_361_2) % 104.74/16.07 | | | | % 104.74/16.07 | | | | REDUCE: (44), (46), (49) imply: % 104.74/16.07 | | | | (50) $false % 104.74/16.07 | | | | % 104.74/16.07 | | | | CLOSE: (50) is inconsistent. % 104.74/16.07 | | | | % 104.74/16.08 | | | End of split % 104.74/16.08 | | | % 104.74/16.08 | | End of split % 104.74/16.08 | | % 104.74/16.08 | End of split % 104.74/16.08 | % 104.74/16.08 End of proof % 104.74/16.08 % SZS output end Proof for theBenchmark % 104.74/16.08 % 104.74/16.08 15466ms %------------------------------------------------------------------------------