%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO271+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 : n032.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 23:22:53 EDT 2023 % Result : Theorem 52.39s 7.54s % Output : Proof 71.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.10 % Problem : GEO271+1 : TPTP v8.1.2. Released v4.1.0. % 0.06/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.30 % Computer : n032.cluster.edu % 0.09/0.30 % Model : x86_64 x86_64 % 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.30 % Memory : 8042.1875MB % 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.30 % CPULimit : 300 % 0.09/0.30 % WCLimit : 300 % 0.09/0.30 % DateTime : Tue Aug 29 20:18:01 EDT 2023 % 0.09/0.30 % CPUTime : % 0.15/0.52 ________ _____ % 0.15/0.52 ___ __ \_________(_)________________________________ % 0.15/0.52 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.15/0.52 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.15/0.52 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.15/0.52 % 0.15/0.52 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.15/0.52 (2023-06-19) % 0.15/0.52 % 0.15/0.52 (c) Philipp Rümmer, 2009-2023 % 0.15/0.52 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.15/0.52 Amanda Stjerna. % 0.15/0.52 Free software under BSD-3-Clause. % 0.15/0.52 % 0.15/0.52 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.15/0.52 % 0.15/0.52 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.15/0.54 Running up to 7 provers in parallel. % 0.15/0.55 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.15/0.55 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.15/0.55 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.15/0.55 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.15/0.55 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.15/0.55 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.15/0.55 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 7.25/1.62 Prover 1: Preprocessing ... % 7.25/1.62 Prover 4: Preprocessing ... % 7.66/1.69 Prover 5: Preprocessing ... % 7.66/1.69 Prover 6: Preprocessing ... % 7.66/1.69 Prover 3: Preprocessing ... % 7.66/1.69 Prover 2: Preprocessing ... % 7.66/1.69 Prover 0: Preprocessing ... % 20.26/3.38 Prover 3: Constructing countermodel ... % 20.26/3.38 Prover 1: Constructing countermodel ... % 20.85/3.41 Prover 6: Proving ... % 21.37/3.52 Prover 2: Proving ... % 22.28/3.65 Prover 5: Proving ... % 30.82/4.73 Prover 4: Constructing countermodel ... % 41.32/6.08 Prover 0: Proving ... % 52.39/7.53 Prover 5: proved (6987ms) % 52.39/7.54 % 52.39/7.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 52.39/7.54 % 52.39/7.54 Prover 3: stopped % 52.39/7.54 Prover 6: stopped % 52.39/7.55 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 52.39/7.55 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 52.39/7.55 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 52.39/7.58 Prover 0: stopped % 52.39/7.60 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 55.07/7.86 Prover 8: Preprocessing ... % 55.07/7.88 Prover 10: Preprocessing ... % 55.64/7.94 Prover 7: Preprocessing ... % 55.64/7.94 Prover 11: Preprocessing ... % 57.01/8.21 Prover 10: Warning: ignoring some quantifiers % 58.11/8.23 Prover 8: Warning: ignoring some quantifiers % 58.11/8.23 Prover 10: Constructing countermodel ... % 58.11/8.24 Prover 8: Constructing countermodel ... % 59.21/8.44 Prover 7: Warning: ignoring some quantifiers % 59.96/8.48 Prover 7: Constructing countermodel ... % 66.47/9.33 Prover 4: Found proof (size 29) % 66.47/9.34 Prover 4: proved (8789ms) % 66.47/9.34 Prover 8: stopped % 66.47/9.34 Prover 7: stopped % 66.47/9.34 Prover 1: stopped % 66.47/9.34 Prover 10: stopped % 69.82/10.04 Prover 2: stopped % 69.82/10.09 Prover 11: Constructing countermodel ... % 70.37/10.14 Prover 11: stopped % 70.37/10.14 % 70.37/10.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 70.37/10.14 % 70.37/10.15 % SZS output start Proof for theBenchmark % 70.87/10.16 Assumptions after simplification: % 70.87/10.16 --------------------------------- % 70.87/10.17 % 70.87/10.17 (and(pred(comma_conjunct2(the(211)), 0), and(pred(comma_conjunct1(the(211)), 0), pred(the(211), 0)))) % 70.87/10.20 ron(vd1057, vd1061) = 0 & rcenter(vd1055, vd1061) = 0 & rcircle(vd1061) = 0 & % 70.87/10.20 $i(vd1061) & $i(vd1055) & $i(vd1057) % 70.87/10.20 % 70.87/10.20 (and(pred(conjunct2(210), 4), and(holds(conjunct2(210), 1059, 0), and(pred(conjunct2(210), 1), and(pred(conjunct1(210), 2), pred(conjunct1(210), 1)))))) % 70.87/10.20 vd1056 = vd1055 & vd1058 = vd1057 & ~ (vd1055 = vd1057) & rpoint(vd1055) = 0 % 70.87/10.20 & rpoint(vd1057) = 0 & $i(vd1055) & $i(vd1057) % 70.87/10.20 % 70.87/10.20 (qu(cond(axiom(182), 0), imp(cond(axiom(182), 0)))) % 70.87/10.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 70.87/10.22 $i] : (v4 = v3 | ~ (vf(v2, v1) = v5) | ~ (vf(v2, v0) = v5) | ~ % 70.87/10.22 (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (rcenter(v2, v4) = 0) | ~ % 70.87/10.22 (rcenter(v2, v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 70.87/10.22 $i(v0) | ? [v6: any] : ? [v7: any] : (ron(v1, v4) = v6 & ron(v0, v3) = v7 % 70.87/10.22 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 70.87/10.22 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (vf(v2, v1) = v5) | % 70.87/10.22 ~ (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (ron(v1, v4) = 0) | ~ % 70.87/10.22 (ron(v0, v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 70.87/10.22 $i(v0) | ? [v6: $i] : ? [v7: any] : ? [v8: any] : (vf(v2, v0) = v6 & % 70.87/10.22 rcenter(v2, v4) = v7 & rcenter(v2, v3) = v8 & $i(v6) & ( ~ (v8 = 0) | ~ % 70.87/10.22 (v7 = 0) | ~ (v6 = v5)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 70.87/10.22 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (vf(v2, v1) = v5) | ~ % 70.87/10.22 (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (ron(v0, v3) = 0) | ~ % 70.87/10.22 (rcenter(v2, v4) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 70.87/10.22 $i(v0) | ? [v6: $i] : ? [v7: any] : ? [v8: any] : (vf(v2, v0) = v6 & % 70.87/10.22 ron(v1, v4) = v7 & rcenter(v2, v3) = v8 & $i(v6) & ( ~ (v8 = 0) | ~ (v7 = % 70.87/10.22 0) | ~ (v6 = v5)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 70.87/10.22 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (vf(v2, v0) = v5) | ~ % 70.87/10.22 (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (ron(v1, v4) = 0) | ~ (ron(v0, % 70.87/10.22 v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 70.87/10.22 ? [v6: $i] : ? [v7: any] : ? [v8: any] : (vf(v2, v1) = v6 & rcenter(v2, % 70.87/10.22 v4) = v7 & rcenter(v2, v3) = v8 & $i(v6) & ( ~ (v8 = 0) | ~ (v7 = 0) | % 70.87/10.22 ~ (v6 = v5)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 70.87/10.22 ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (vf(v2, v0) = v5) | ~ (rpoint(v1) = % 70.87/10.22 0) | ~ (rpoint(v0) = 0) | ~ (ron(v1, v4) = 0) | ~ (rcenter(v2, v3) = 0) % 70.87/10.22 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : % 70.87/10.22 ? [v7: any] : ? [v8: any] : (vf(v2, v1) = v6 & ron(v0, v3) = v7 & % 70.87/10.22 rcenter(v2, v4) = v8 & $i(v6) & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = % 70.87/10.22 v5)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 70.87/10.22 [v4: $i] : (v4 = v3 | ~ (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (ron(v1, % 70.87/10.22 v4) = 0) | ~ (ron(v0, v3) = 0) | ~ (rcenter(v2, v4) = 0) | ~ $i(v4) | % 70.87/10.22 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : % 70.87/10.22 ? [v7: any] : (vf(v2, v1) = v6 & vf(v2, v0) = v5 & rcenter(v2, v3) = v7 & % 70.87/10.22 $i(v6) & $i(v5) & ( ~ (v7 = 0) | ~ (v6 = v5)))) & ! [v0: $i] : ! [v1: % 70.87/10.22 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (rpoint(v1) = % 70.87/10.22 0) | ~ (rpoint(v0) = 0) | ~ (ron(v1, v4) = 0) | ~ (ron(v0, v3) = 0) | % 70.87/10.22 ~ (rcenter(v2, v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 70.87/10.22 $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: any] : (vf(v2, v1) = v6 & % 70.87/10.22 vf(v2, v0) = v5 & rcenter(v2, v4) = v7 & $i(v6) & $i(v5) & ( ~ (v7 = 0) | % 70.87/10.22 ~ (v6 = v5)))) % 70.87/10.22 % 70.87/10.22 (qu(cond(axiom(184), 0), imp(cond(axiom(184), 0)))) % 70.87/10.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 70.87/10.22 $i] : ( ~ (vf(v1, v3) = v5) | ~ (vf(v1, v0) = v4) | ~ (rpoint(v3) = 0) | % 70.87/10.22 ~ (rpoint(v0) = 0) | ~ (rcenter(v1, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 70.87/10.22 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : (ron(v3, v2) = v6 & % 70.87/10.22 ron(v0, v2) = v7 & ( ~ (v6 = 0) | (( ~ (v7 = 0) | v5 = v4) & ( ~ (v5 = v4) % 70.87/10.22 | v7 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 70.87/10.22 $i] : ! [v4: $i] : ! [v5: any] : ( ~ (vf(v1, v3) = v4) | ~ (rpoint(v3) = % 70.87/10.22 0) | ~ (rpoint(v0) = 0) | ~ (ron(v0, v2) = v5) | ~ $i(v3) | ~ $i(v2) | % 70.87/10.22 ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : (vf(v1, % 70.87/10.22 v0) = v8 & ron(v3, v2) = v6 & rcenter(v1, v2) = v7 & $i(v8) & ( ~ (v7 = % 70.87/10.22 0) | ~ (v6 = 0) | (( ~ (v8 = v4) | v5 = 0) & ( ~ (v5 = 0) | v8 = % 70.87/10.23 v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 70.87/10.23 [v4: $i] : ( ~ (vf(v1, v0) = v4) | ~ (rpoint(v3) = 0) | ~ (rpoint(v0) = 0) | % 70.87/10.23 ~ (ron(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 70.87/10.23 [v5: any] : ? [v6: $i] : ? [v7: any] : (vf(v1, v3) = v6 & ron(v0, v2) = v7 % 70.87/10.23 & rcenter(v1, v2) = v5 & $i(v6) & ( ~ (v5 = 0) | (( ~ (v7 = 0) | v6 = v4) % 70.87/10.23 & ( ~ (v6 = v4) | v7 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 70.87/10.23 $i] : ! [v3: $i] : ! [v4: any] : ( ~ (rpoint(v3) = 0) | ~ (rpoint(v0) = % 70.87/10.23 0) | ~ (ron(v3, v2) = 0) | ~ (ron(v0, v2) = v4) | ~ (rcenter(v1, v2) = % 70.87/10.23 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: % 70.87/10.23 $i] : (vf(v1, v3) = v6 & vf(v1, v0) = v5 & $i(v6) & $i(v5) & ( ~ (v6 = v5) % 70.87/10.23 | v4 = 0) & ( ~ (v4 = 0) | v6 = v5))) % 70.87/10.23 % 70.87/10.23 (qu(theu(the(211), 1), imp(the(211)))) % 70.87/10.23 $i(vd1061) & $i(vd1055) & $i(vd1057) & ? [v0: $i] : ( ~ (v0 = vd1061) & % 70.87/10.23 ron(vd1057, v0) = 0 & rcenter(vd1055, v0) = 0 & rcircle(v0) = 0 & $i(v0)) % 70.87/10.23 % 70.87/10.23 (function-axioms) % 70.87/10.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 70.87/10.23 | ~ (vtriangle(v4, v3, v2) = v1) | ~ (vtriangle(v4, v3, v2) = v0)) & ! % 70.87/10.23 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 70.87/10.23 ~ (vg(v4, v3, v2) = v1) | ~ (vg(v4, v3, v2) = v0)) & ! [v0: % 70.87/10.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 70.87/10.23 : ! [v4: $i] : (v1 = v0 | ~ (rS(v4, v3, v2) = v1) | ~ (rS(v4, v3, v2) = % 70.87/10.23 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 70.87/10.23 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (rR(v4, v3, v2) = v1) | ~ % 70.87/10.23 (rR(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 70.87/10.23 $i] : ! [v4: $i] : (v1 = v0 | ~ (vangle(v4, v3, v2) = v1) | ~ (vangle(v4, % 70.87/10.23 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 70.87/10.23 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (rleq(v3, v2) = v1) | ~ (rleq(v3, % 70.87/10.23 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 70.87/10.23 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (rgeq(v3, v2) = v1) | ~ (rgeq(v3, % 70.87/10.23 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 70.87/10.23 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (rinside(v3, v2) = v1) | ~ % 70.87/10.23 (rinside(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 70.87/10.23 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (rless(v3, % 70.87/10.23 v2) = v1) | ~ (rless(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 70.87/10.23 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 70.87/10.23 (rintersect(v3, v2) = v1) | ~ (rintersect(v3, v2) = v0)) & ! [v0: $i] : ! % 70.87/10.23 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ % 70.87/10.23 (vplus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 70.87/10.23 $i] : (v1 = v0 | ~ (vf(v3, v2) = v1) | ~ (vf(v3, v2) = v0)) & ! [v0: % 70.87/10.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 70.87/10.23 : (v1 = v0 | ~ (ron(v3, v2) = v1) | ~ (ron(v3, v2) = v0)) & ! [v0: % 70.87/10.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 70.87/10.23 : (v1 = v0 | ~ (rcenter(v3, v2) = v1) | ~ (rcenter(v3, v2) = v0)) & ! [v0: % 70.87/10.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 70.87/10.23 ~ (rtriangle(v2) = v1) | ~ (rtriangle(v2) = v0)) & ! [v0: % 70.87/10.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 70.87/10.23 ~ (rreal(v2) = v1) | ~ (rreal(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 70.87/10.23 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (rline(v2) = v1) | ~ % 70.87/10.23 (rline(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 70.87/10.23 : ! [v2: $i] : (v1 = v0 | ~ (rpoint(v2) = v1) | ~ (rpoint(v2) = v0)) & ! % 70.87/10.23 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 70.87/10.23 | ~ (rcircle(v2) = v1) | ~ (rcircle(v2) = v0)) % 70.87/10.23 % 70.87/10.23 Further assumptions not needed in the proof: % 70.87/10.23 -------------------------------------------- % 70.87/10.24 ass(cond(156, 0), 0), pred(axiom(137), 1), pred(axiom(137), 2), pred(axiom(5), % 70.87/10.24 0), qu(cond(axiom(1), 0), imp(cond(axiom(1), 0))), qu(cond(axiom(101), 0), % 70.87/10.24 imp(cond(axiom(101), 0))), qu(cond(axiom(103), 0), imp(cond(axiom(103), 0))), % 70.87/10.24 qu(cond(axiom(105), 0), imp(cond(axiom(105), 0))), qu(cond(axiom(107), 0), % 70.87/10.24 imp(cond(axiom(107), 0))), qu(cond(axiom(109), 0), imp(cond(axiom(109), 0))), % 70.87/10.24 qu(cond(axiom(11), 0), imp(cond(axiom(11), 0))), qu(cond(axiom(111), 0), % 70.87/10.24 imp(cond(axiom(111), 0))), qu(cond(axiom(113), 0), imp(cond(axiom(113), 0))), % 70.87/10.24 qu(cond(axiom(115), 0), imp(cond(axiom(115), 0))), qu(cond(axiom(117), 0), % 70.87/10.24 imp(cond(axiom(117), 0))), qu(cond(axiom(119), 0), imp(cond(axiom(119), 0))), % 70.87/10.24 qu(cond(axiom(121), 0), imp(cond(axiom(121), 0))), qu(cond(axiom(123), 0), % 70.87/10.24 imp(cond(axiom(123), 0))), qu(cond(axiom(125), 0), imp(cond(axiom(125), 0))), % 70.87/10.24 qu(cond(axiom(127), 0), imp(cond(axiom(127), 0))), qu(cond(axiom(129), 0), % 70.87/10.24 imp(cond(axiom(129), 0))), qu(cond(axiom(13), 0), imp(cond(axiom(13), 0))), % 70.87/10.24 qu(cond(axiom(131), 0), imp(cond(axiom(131), 0))), qu(cond(axiom(133), 0), % 70.87/10.24 imp(cond(axiom(133), 0))), qu(cond(axiom(135), 0), imp(cond(axiom(135), 0))), % 70.87/10.24 qu(cond(axiom(139), 0), imp(cond(axiom(139), 0))), qu(cond(axiom(141), 0), % 70.87/10.24 imp(cond(axiom(141), 0))), qu(cond(axiom(143), 0), imp(cond(axiom(143), 0))), % 70.87/10.24 qu(cond(axiom(145), 0), imp(cond(axiom(145), 0))), qu(cond(axiom(147), 0), % 70.87/10.24 imp(cond(axiom(147), 0))), qu(cond(axiom(149), 0), imp(cond(axiom(149), 0))), % 70.87/10.24 qu(cond(axiom(15), 0), imp(cond(axiom(15), 0))), qu(cond(axiom(151), 0), % 70.87/10.24 imp(cond(axiom(151), 0))), qu(cond(axiom(153), 0), imp(cond(axiom(153), 0))), % 70.87/10.24 qu(cond(axiom(160), 0), imp(cond(axiom(160), 0))), qu(cond(axiom(162), 0), % 70.87/10.24 imp(cond(axiom(162), 0))), qu(cond(axiom(164), 0), imp(cond(axiom(164), 0))), % 70.87/10.24 qu(cond(axiom(166), 0), imp(cond(axiom(166), 0))), qu(cond(axiom(168), 0), % 70.87/10.24 imp(cond(axiom(168), 0))), qu(cond(axiom(17), 0), imp(cond(axiom(17), 0))), % 70.87/10.24 qu(cond(axiom(170), 0), imp(cond(axiom(170), 0))), qu(cond(axiom(172), 0), % 70.87/10.24 imp(cond(axiom(172), 0))), qu(cond(axiom(174), 0), imp(cond(axiom(174), 0))), % 70.87/10.24 qu(cond(axiom(176), 0), imp(cond(axiom(176), 0))), qu(cond(axiom(178), 0), % 70.87/10.24 imp(cond(axiom(178), 0))), qu(cond(axiom(180), 0), imp(cond(axiom(180), 0))), % 70.87/10.24 qu(cond(axiom(186), 0), imp(cond(axiom(186), 0))), qu(cond(axiom(188), 0), % 70.87/10.24 imp(cond(axiom(188), 0))), qu(cond(axiom(19), 0), imp(cond(axiom(19), 0))), % 70.87/10.24 qu(cond(axiom(190), 0), imp(cond(axiom(190), 0))), qu(cond(axiom(192), 0), % 70.87/10.24 imp(cond(axiom(192), 0))), qu(cond(axiom(194), 0), imp(cond(axiom(194), 0))), % 70.87/10.24 qu(cond(axiom(196), 0), imp(cond(axiom(196), 0))), qu(cond(axiom(198), 0), % 70.87/10.24 imp(cond(axiom(198), 0))), qu(cond(axiom(200), 0), imp(cond(axiom(200), 0))), % 70.87/10.24 qu(cond(axiom(202), 0), imp(cond(axiom(202), 0))), qu(cond(axiom(204), 0), % 70.87/10.24 imp(cond(axiom(204), 0))), qu(cond(axiom(21), 0), imp(cond(axiom(21), 0))), % 70.87/10.24 qu(cond(axiom(23), 0), imp(cond(axiom(23), 0))), qu(cond(axiom(25), 0), % 70.87/10.24 imp(cond(axiom(25), 0))), qu(cond(axiom(27), 0), imp(cond(axiom(27), 0))), % 70.87/10.24 qu(cond(axiom(29), 0), imp(cond(axiom(29), 0))), qu(cond(axiom(3), 0), % 70.87/10.24 imp(cond(axiom(3), 0))), qu(cond(axiom(31), 0), imp(cond(axiom(31), 0))), % 70.87/10.24 qu(cond(axiom(33), 0), imp(cond(axiom(33), 0))), qu(cond(axiom(35), 0), % 70.87/10.24 imp(cond(axiom(35), 0))), qu(cond(axiom(37), 0), imp(cond(axiom(37), 0))), % 70.87/10.24 qu(cond(axiom(39), 0), imp(cond(axiom(39), 0))), qu(cond(axiom(41), 0), % 70.87/10.24 imp(cond(axiom(41), 0))), qu(cond(axiom(43), 0), imp(cond(axiom(43), 0))), % 70.87/10.24 qu(cond(axiom(45), 0), imp(cond(axiom(45), 0))), qu(cond(axiom(47), 0), % 70.87/10.24 imp(cond(axiom(47), 0))), qu(cond(axiom(49), 0), imp(cond(axiom(49), 0))), % 70.87/10.24 qu(cond(axiom(51), 0), imp(cond(axiom(51), 0))), qu(cond(axiom(53), 0), % 70.87/10.24 imp(cond(axiom(53), 0))), qu(cond(axiom(55), 0), imp(cond(axiom(55), 0))), % 70.87/10.24 qu(cond(axiom(57), 0), imp(cond(axiom(57), 0))), qu(cond(axiom(59), 0), % 70.87/10.24 imp(cond(axiom(59), 0))), qu(cond(axiom(61), 0), imp(cond(axiom(61), 0))), % 70.87/10.24 qu(cond(axiom(63), 0), imp(cond(axiom(63), 0))), qu(cond(axiom(65), 0), % 70.87/10.24 imp(cond(axiom(65), 0))), qu(cond(axiom(67), 0), imp(cond(axiom(67), 0))), % 70.87/10.24 qu(cond(axiom(69), 0), imp(cond(axiom(69), 0))), qu(cond(axiom(7), 0), % 70.87/10.24 imp(cond(axiom(7), 0))), qu(cond(axiom(71), 0), imp(cond(axiom(71), 0))), % 70.87/10.24 qu(cond(axiom(73), 0), imp(cond(axiom(73), 0))), qu(cond(axiom(75), 0), % 70.87/10.24 imp(cond(axiom(75), 0))), qu(cond(axiom(77), 0), imp(cond(axiom(77), 0))), % 70.87/10.24 qu(cond(axiom(79), 0), imp(cond(axiom(79), 0))), qu(cond(axiom(81), 0), % 70.87/10.24 imp(cond(axiom(81), 0))), qu(cond(axiom(83), 0), imp(cond(axiom(83), 0))), % 70.87/10.24 qu(cond(axiom(85), 0), imp(cond(axiom(85), 0))), qu(cond(axiom(87), 0), % 70.87/10.24 imp(cond(axiom(87), 0))), qu(cond(axiom(89), 0), imp(cond(axiom(89), 0))), % 70.87/10.24 qu(cond(axiom(9), 0), imp(cond(axiom(9), 0))), qu(cond(axiom(91), 0), % 70.87/10.24 imp(cond(axiom(91), 0))), qu(cond(axiom(93), 0), imp(cond(axiom(93), 0))), % 70.87/10.24 qu(cond(axiom(95), 0), imp(cond(axiom(95), 0))), qu(cond(axiom(97), 0), % 70.87/10.24 imp(cond(axiom(97), 0))), qu(cond(axiom(99), 0), imp(cond(axiom(99), 0))) % 70.87/10.24 % 70.87/10.24 Those formulas are unsatisfiable: % 70.87/10.24 --------------------------------- % 70.87/10.24 % 70.87/10.24 Begin of proof % 70.87/10.24 | % 70.87/10.24 | ALPHA: (and(pred(comma_conjunct2(the(211)), 0), % 70.87/10.24 | and(pred(comma_conjunct1(the(211)), 0), pred(the(211), 0)))) % 70.87/10.24 | implies: % 71.25/10.24 | (1) rcenter(vd1055, vd1061) = 0 % 71.25/10.24 | (2) ron(vd1057, vd1061) = 0 % 71.25/10.24 | % 71.25/10.24 | ALPHA: (and(pred(conjunct2(210), 4), and(holds(conjunct2(210), 1059, 0), % 71.25/10.24 | and(pred(conjunct2(210), 1), and(pred(conjunct1(210), 2), % 71.25/10.24 | pred(conjunct1(210), 1)))))) implies: % 71.25/10.24 | (3) rpoint(vd1057) = 0 % 71.25/10.24 | % 71.25/10.24 | ALPHA: (qu(cond(axiom(184), 0), imp(cond(axiom(184), 0)))) implies: % 71.25/10.24 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 71.25/10.24 | ( ~ (rpoint(v3) = 0) | ~ (rpoint(v0) = 0) | ~ (ron(v3, v2) = 0) | ~ % 71.25/10.24 | (ron(v0, v2) = v4) | ~ (rcenter(v1, v2) = 0) | ~ $i(v3) | ~ $i(v2) % 71.25/10.24 | | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (vf(v1, v3) = % 71.25/10.24 | v6 & vf(v1, v0) = v5 & $i(v6) & $i(v5) & ( ~ (v6 = v5) | v4 = 0) & % 71.25/10.24 | ( ~ (v4 = 0) | v6 = v5))) % 71.25/10.24 | % 71.25/10.24 | ALPHA: (qu(cond(axiom(182), 0), imp(cond(axiom(182), 0)))) implies: % 71.25/10.24 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 71.25/10.24 | (v4 = v3 | ~ (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (ron(v1, v4) % 71.25/10.24 | = 0) | ~ (ron(v0, v3) = 0) | ~ (rcenter(v2, v3) = 0) | ~ $i(v4) % 71.25/10.24 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? % 71.25/10.24 | [v6: $i] : ? [v7: any] : (vf(v2, v1) = v6 & vf(v2, v0) = v5 & % 71.25/10.24 | rcenter(v2, v4) = v7 & $i(v6) & $i(v5) & ( ~ (v7 = 0) | ~ (v6 = % 71.25/10.24 | v5)))) % 71.25/10.24 | % 71.25/10.24 | ALPHA: (qu(theu(the(211), 1), imp(the(211)))) implies: % 71.25/10.24 | (6) $i(vd1057) % 71.25/10.24 | (7) $i(vd1055) % 71.25/10.24 | (8) $i(vd1061) % 71.25/10.25 | (9) ? [v0: $i] : ( ~ (v0 = vd1061) & ron(vd1057, v0) = 0 & rcenter(vd1055, % 71.25/10.25 | v0) = 0 & rcircle(v0) = 0 & $i(v0)) % 71.25/10.25 | % 71.25/10.25 | ALPHA: (function-axioms) implies: % 71.25/10.25 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 71.25/10.25 | : ! [v3: $i] : (v1 = v0 | ~ (rcenter(v3, v2) = v1) | ~ (rcenter(v3, % 71.25/10.25 | v2) = v0)) % 71.25/10.25 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 71.25/10.25 | (vf(v3, v2) = v1) | ~ (vf(v3, v2) = v0)) % 71.25/10.25 | % 71.25/10.25 | DELTA: instantiating (9) with fresh symbol all_101_0 gives: % 71.25/10.25 | (12) ~ (all_101_0 = vd1061) & ron(vd1057, all_101_0) = 0 & rcenter(vd1055, % 71.25/10.25 | all_101_0) = 0 & rcircle(all_101_0) = 0 & $i(all_101_0) % 71.25/10.25 | % 71.25/10.25 | ALPHA: (12) implies: % 71.25/10.25 | (13) ~ (all_101_0 = vd1061) % 71.25/10.25 | (14) $i(all_101_0) % 71.25/10.25 | (15) rcenter(vd1055, all_101_0) = 0 % 71.25/10.25 | (16) ron(vd1057, all_101_0) = 0 % 71.25/10.25 | % 71.25/10.25 | GROUND_INST: instantiating (5) with vd1057, vd1057, vd1055, vd1061, all_101_0, % 71.25/10.25 | simplifying with (1), (2), (3), (6), (7), (8), (14), (16) gives: % 71.25/10.25 | (17) all_101_0 = vd1061 | ? [v0: $i] : ? [v1: $i] : ? [v2: any] : % 71.25/10.25 | (vf(vd1055, vd1057) = v1 & vf(vd1055, vd1057) = v0 & rcenter(vd1055, % 71.25/10.25 | all_101_0) = v2 & $i(v1) & $i(v0) & ( ~ (v2 = 0) | ~ (v1 = v0))) % 71.25/10.25 | % 71.25/10.25 | GROUND_INST: instantiating (4) with vd1057, vd1055, vd1061, vd1057, 0, % 71.25/10.25 | simplifying with (1), (2), (3), (6), (7), (8) gives: % 71.25/10.25 | (18) ? [v0: $i] : (vf(vd1055, vd1057) = v0 & $i(v0)) % 71.25/10.25 | % 71.25/10.25 | DELTA: instantiating (18) with fresh symbol all_119_0 gives: % 71.25/10.25 | (19) vf(vd1055, vd1057) = all_119_0 & $i(all_119_0) % 71.25/10.25 | % 71.25/10.25 | ALPHA: (19) implies: % 71.25/10.25 | (20) vf(vd1055, vd1057) = all_119_0 % 71.25/10.25 | % 71.25/10.25 | BETA: splitting (17) gives: % 71.25/10.25 | % 71.25/10.25 | Case 1: % 71.25/10.25 | | % 71.25/10.25 | | (21) all_101_0 = vd1061 % 71.25/10.25 | | % 71.25/10.25 | | REDUCE: (13), (21) imply: % 71.25/10.25 | | (22) $false % 71.25/10.25 | | % 71.25/10.25 | | CLOSE: (22) is inconsistent. % 71.25/10.25 | | % 71.25/10.26 | Case 2: % 71.25/10.26 | | % 71.25/10.26 | | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : (vf(vd1055, vd1057) = v1 % 71.25/10.26 | | & vf(vd1055, vd1057) = v0 & rcenter(vd1055, all_101_0) = v2 & % 71.25/10.26 | | $i(v1) & $i(v0) & ( ~ (v2 = 0) | ~ (v1 = v0))) % 71.25/10.26 | | % 71.25/10.26 | | DELTA: instantiating (23) with fresh symbols all_177_0, all_177_1, all_177_2 % 71.25/10.26 | | gives: % 71.25/10.26 | | (24) vf(vd1055, vd1057) = all_177_1 & vf(vd1055, vd1057) = all_177_2 & % 71.25/10.26 | | rcenter(vd1055, all_101_0) = all_177_0 & $i(all_177_1) & % 71.25/10.26 | | $i(all_177_2) & ( ~ (all_177_0 = 0) | ~ (all_177_1 = all_177_2)) % 71.25/10.26 | | % 71.25/10.26 | | ALPHA: (24) implies: % 71.25/10.26 | | (25) rcenter(vd1055, all_101_0) = all_177_0 % 71.25/10.26 | | (26) vf(vd1055, vd1057) = all_177_2 % 71.25/10.26 | | (27) vf(vd1055, vd1057) = all_177_1 % 71.25/10.26 | | (28) ~ (all_177_0 = 0) | ~ (all_177_1 = all_177_2) % 71.25/10.26 | | % 71.25/10.26 | | GROUND_INST: instantiating (10) with 0, all_177_0, all_101_0, vd1055, % 71.25/10.26 | | simplifying with (15), (25) gives: % 71.25/10.26 | | (29) all_177_0 = 0 % 71.25/10.26 | | % 71.25/10.26 | | GROUND_INST: instantiating (11) with all_177_2, all_177_1, vd1057, vd1055, % 71.25/10.26 | | simplifying with (26), (27) gives: % 71.25/10.26 | | (30) all_177_1 = all_177_2 % 71.25/10.26 | | % 71.25/10.26 | | GROUND_INST: instantiating (11) with all_119_0, all_177_1, vd1057, vd1055, % 71.25/10.26 | | simplifying with (20), (27) gives: % 71.25/10.26 | | (31) all_177_1 = all_119_0 % 71.25/10.26 | | % 71.25/10.26 | | COMBINE_EQS: (30), (31) imply: % 71.25/10.26 | | (32) all_177_2 = all_119_0 % 71.25/10.26 | | % 71.25/10.26 | | SIMP: (32) implies: % 71.25/10.26 | | (33) all_177_2 = all_119_0 % 71.25/10.26 | | % 71.25/10.26 | | BETA: splitting (28) gives: % 71.25/10.26 | | % 71.25/10.26 | | Case 1: % 71.25/10.26 | | | % 71.25/10.26 | | | (34) ~ (all_177_0 = 0) % 71.25/10.26 | | | % 71.25/10.26 | | | REDUCE: (29), (34) imply: % 71.25/10.26 | | | (35) $false % 71.25/10.26 | | | % 71.25/10.26 | | | CLOSE: (35) is inconsistent. % 71.25/10.26 | | | % 71.25/10.26 | | Case 2: % 71.25/10.26 | | | % 71.25/10.26 | | | (36) ~ (all_177_1 = all_177_2) % 71.25/10.26 | | | % 71.25/10.26 | | | REDUCE: (31), (33), (36) imply: % 71.25/10.26 | | | (37) $false % 71.25/10.26 | | | % 71.25/10.26 | | | CLOSE: (37) is inconsistent. % 71.25/10.26 | | | % 71.25/10.26 | | End of split % 71.25/10.26 | | % 71.25/10.26 | End of split % 71.25/10.26 | % 71.25/10.26 End of proof % 71.25/10.26 % SZS output end Proof for theBenchmark % 71.25/10.26 % 71.25/10.26 9736ms %------------------------------------------------------------------------------