%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO272+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 : n008.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 54.79s 8.09s % Output : Proof 75.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO272+1 : TPTP v8.1.2. Released v4.1.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n008.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Wed Aug 30 00:07:02 EDT 2023 % 0.20/0.34 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 8.66/1.89 Prover 4: Preprocessing ... % 9.01/1.99 Prover 6: Preprocessing ... % 9.59/2.00 Prover 0: Preprocessing ... % 9.59/2.00 Prover 2: Preprocessing ... % 9.59/2.01 Prover 3: Preprocessing ... % 9.59/2.01 Prover 1: Preprocessing ... % 9.59/2.02 Prover 5: Preprocessing ... % 22.56/3.77 Prover 3: Constructing countermodel ... % 22.56/3.78 Prover 1: Constructing countermodel ... % 23.38/3.87 Prover 6: Proving ... % 25.58/4.22 Prover 2: Proving ... % 25.58/4.23 Prover 5: Proving ... % 37.19/5.82 Prover 4: Constructing countermodel ... % 41.29/6.41 Prover 0: Proving ... % 54.79/8.09 Prover 5: proved (7446ms) % 54.79/8.09 % 54.79/8.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 54.79/8.09 % 54.79/8.09 Prover 3: stopped % 54.79/8.10 Prover 6: stopped % 54.79/8.11 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 54.79/8.11 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 54.79/8.12 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 55.29/8.15 Prover 0: stopped % 55.29/8.15 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 57.12/8.47 Prover 8: Preprocessing ... % 57.12/8.50 Prover 10: Preprocessing ... % 57.12/8.50 Prover 11: Preprocessing ... % 57.12/8.51 Prover 7: Preprocessing ... % 61.02/8.88 Prover 10: Warning: ignoring some quantifiers % 61.39/8.93 Prover 10: Constructing countermodel ... % 61.99/9.03 Prover 8: Warning: ignoring some quantifiers % 61.99/9.06 Prover 8: Constructing countermodel ... % 64.74/9.39 Prover 7: Warning: ignoring some quantifiers % 64.74/9.42 Prover 7: Constructing countermodel ... % 70.03/10.13 Prover 4: Found proof (size 29) % 70.03/10.13 Prover 4: proved (9490ms) % 70.03/10.13 Prover 10: stopped % 70.03/10.13 Prover 8: stopped % 70.55/10.13 Prover 7: stopped % 70.55/10.13 Prover 1: stopped % 72.54/10.64 Prover 11: Constructing countermodel ... % 72.54/10.69 Prover 11: stopped % 75.26/12.33 Prover 2: stopped % 75.26/12.33 % 75.26/12.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 75.26/12.33 % 75.26/12.34 % SZS output start Proof for theBenchmark % 75.34/12.36 Assumptions after simplification: % 75.34/12.36 --------------------------------- % 75.34/12.36 % 75.34/12.36 (and(pred(comma_conjunct2(the(212)), 0), and(pred(comma_conjunct1(the(212)), 0), pred(the(212), 0)))) % 75.51/12.41 ron(vd1055, vd1063) = 0 & rcenter(vd1057, vd1063) = 0 & rcircle(vd1063) = 0 & % 75.51/12.41 $i(vd1063) & $i(vd1057) & $i(vd1055) % 75.51/12.41 % 75.51/12.41 (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)))))) % 75.51/12.41 vd1056 = vd1055 & vd1058 = vd1057 & ~ (vd1057 = vd1055) & rpoint(vd1057) = 0 % 75.51/12.41 & rpoint(vd1055) = 0 & $i(vd1057) & $i(vd1055) % 75.51/12.41 % 75.51/12.41 (qu(cond(axiom(182), 0), imp(cond(axiom(182), 0)))) % 75.73/12.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 75.73/12.46 $i] : (v4 = v3 | ~ (vf(v2, v1) = v5) | ~ (vf(v2, v0) = v5) | ~ % 75.73/12.46 (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (rcenter(v2, v4) = 0) | ~ % 75.73/12.46 (rcenter(v2, v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 75.73/12.46 $i(v0) | ? [v6: any] : ? [v7: any] : (ron(v1, v4) = v6 & ron(v0, v3) = v7 % 75.73/12.46 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 75.73/12.46 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (vf(v2, v1) = v5) | % 75.73/12.46 ~ (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (ron(v1, v4) = 0) | ~ % 75.73/12.46 (ron(v0, v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 75.73/12.46 $i(v0) | ? [v6: $i] : ? [v7: any] : ? [v8: any] : (vf(v2, v0) = v6 & % 75.73/12.46 rcenter(v2, v4) = v7 & rcenter(v2, v3) = v8 & $i(v6) & ( ~ (v8 = 0) | ~ % 75.73/12.46 (v7 = 0) | ~ (v6 = v5)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 75.73/12.46 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (vf(v2, v1) = v5) | ~ % 75.73/12.46 (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (ron(v0, v3) = 0) | ~ % 75.73/12.46 (rcenter(v2, v4) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 75.73/12.46 $i(v0) | ? [v6: $i] : ? [v7: any] : ? [v8: any] : (vf(v2, v0) = v6 & % 75.73/12.46 ron(v1, v4) = v7 & rcenter(v2, v3) = v8 & $i(v6) & ( ~ (v8 = 0) | ~ (v7 = % 75.73/12.46 0) | ~ (v6 = v5)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 75.73/12.46 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (vf(v2, v0) = v5) | ~ % 75.73/12.46 (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (ron(v1, v4) = 0) | ~ (ron(v0, % 75.73/12.46 v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 75.73/12.46 ? [v6: $i] : ? [v7: any] : ? [v8: any] : (vf(v2, v1) = v6 & rcenter(v2, % 75.73/12.46 v4) = v7 & rcenter(v2, v3) = v8 & $i(v6) & ( ~ (v8 = 0) | ~ (v7 = 0) | % 75.73/12.46 ~ (v6 = v5)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 75.73/12.46 ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (vf(v2, v0) = v5) | ~ (rpoint(v1) = % 75.73/12.46 0) | ~ (rpoint(v0) = 0) | ~ (ron(v1, v4) = 0) | ~ (rcenter(v2, v3) = 0) % 75.73/12.46 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : % 75.73/12.46 ? [v7: any] : ? [v8: any] : (vf(v2, v1) = v6 & ron(v0, v3) = v7 & % 75.73/12.46 rcenter(v2, v4) = v8 & $i(v6) & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = % 75.73/12.46 v5)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 75.73/12.46 [v4: $i] : (v4 = v3 | ~ (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (ron(v1, % 75.73/12.46 v4) = 0) | ~ (ron(v0, v3) = 0) | ~ (rcenter(v2, v4) = 0) | ~ $i(v4) | % 75.73/12.46 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : % 75.73/12.46 ? [v7: any] : (vf(v2, v1) = v6 & vf(v2, v0) = v5 & rcenter(v2, v3) = v7 & % 75.73/12.46 $i(v6) & $i(v5) & ( ~ (v7 = 0) | ~ (v6 = v5)))) & ! [v0: $i] : ! [v1: % 75.73/12.46 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3 | ~ (rpoint(v1) = % 75.73/12.46 0) | ~ (rpoint(v0) = 0) | ~ (ron(v1, v4) = 0) | ~ (ron(v0, v3) = 0) | % 75.73/12.46 ~ (rcenter(v2, v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 75.73/12.46 $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: any] : (vf(v2, v1) = v6 & % 75.73/12.46 vf(v2, v0) = v5 & rcenter(v2, v4) = v7 & $i(v6) & $i(v5) & ( ~ (v7 = 0) | % 75.73/12.46 ~ (v6 = v5)))) % 75.73/12.46 % 75.73/12.46 (qu(cond(axiom(184), 0), imp(cond(axiom(184), 0)))) % 75.73/12.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 75.73/12.48 $i] : ( ~ (vf(v1, v3) = v5) | ~ (vf(v1, v0) = v4) | ~ (rpoint(v3) = 0) | % 75.73/12.48 ~ (rpoint(v0) = 0) | ~ (rcenter(v1, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 75.73/12.48 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : (ron(v3, v2) = v6 & % 75.73/12.48 ron(v0, v2) = v7 & ( ~ (v6 = 0) | (( ~ (v7 = 0) | v5 = v4) & ( ~ (v5 = v4) % 75.73/12.48 | v7 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 75.73/12.48 $i] : ! [v4: $i] : ! [v5: any] : ( ~ (vf(v1, v3) = v4) | ~ (rpoint(v3) = % 75.73/12.48 0) | ~ (rpoint(v0) = 0) | ~ (ron(v0, v2) = v5) | ~ $i(v3) | ~ $i(v2) | % 75.73/12.48 ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: $i] : (vf(v1, % 75.73/12.48 v0) = v8 & ron(v3, v2) = v6 & rcenter(v1, v2) = v7 & $i(v8) & ( ~ (v7 = % 75.73/12.48 0) | ~ (v6 = 0) | (( ~ (v8 = v4) | v5 = 0) & ( ~ (v5 = 0) | v8 = % 75.73/12.48 v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 75.73/12.48 [v4: $i] : ( ~ (vf(v1, v0) = v4) | ~ (rpoint(v3) = 0) | ~ (rpoint(v0) = 0) | % 75.73/12.48 ~ (ron(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 75.73/12.48 [v5: any] : ? [v6: $i] : ? [v7: any] : (vf(v1, v3) = v6 & ron(v0, v2) = v7 % 75.73/12.48 & rcenter(v1, v2) = v5 & $i(v6) & ( ~ (v5 = 0) | (( ~ (v7 = 0) | v6 = v4) % 75.73/12.48 & ( ~ (v6 = v4) | v7 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 75.73/12.48 $i] : ! [v3: $i] : ! [v4: any] : ( ~ (rpoint(v3) = 0) | ~ (rpoint(v0) = % 75.73/12.48 0) | ~ (ron(v3, v2) = 0) | ~ (ron(v0, v2) = v4) | ~ (rcenter(v1, v2) = % 75.73/12.48 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: % 75.73/12.48 $i] : (vf(v1, v3) = v6 & vf(v1, v0) = v5 & $i(v6) & $i(v5) & ( ~ (v6 = v5) % 75.73/12.48 | v4 = 0) & ( ~ (v4 = 0) | v6 = v5))) % 75.73/12.48 % 75.73/12.48 (qu(theu(the(212), 1), imp(the(212)))) % 75.73/12.48 $i(vd1063) & $i(vd1057) & $i(vd1055) & ? [v0: $i] : ( ~ (v0 = vd1063) & % 75.73/12.48 ron(vd1055, v0) = 0 & rcenter(vd1057, v0) = 0 & rcircle(v0) = 0 & $i(v0)) % 75.73/12.48 % 75.73/12.48 (function-axioms) % 75.73/12.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 75.73/12.49 | ~ (vtriangle(v4, v3, v2) = v1) | ~ (vtriangle(v4, v3, v2) = v0)) & ! % 75.73/12.49 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 75.73/12.49 ~ (vg(v4, v3, v2) = v1) | ~ (vg(v4, v3, v2) = v0)) & ! [v0: % 75.73/12.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 75.73/12.49 : ! [v4: $i] : (v1 = v0 | ~ (rS(v4, v3, v2) = v1) | ~ (rS(v4, v3, v2) = % 75.73/12.49 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 75.73/12.49 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (rR(v4, v3, v2) = v1) | ~ % 75.73/12.49 (rR(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 75.73/12.49 $i] : ! [v4: $i] : (v1 = v0 | ~ (vangle(v4, v3, v2) = v1) | ~ (vangle(v4, % 75.73/12.49 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 75.73/12.49 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (rleq(v3, v2) = v1) | ~ (rleq(v3, % 75.73/12.49 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 75.73/12.49 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (rgeq(v3, v2) = v1) | ~ (rgeq(v3, % 75.73/12.49 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 75.73/12.49 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (rinside(v3, v2) = v1) | ~ % 75.73/12.49 (rinside(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 75.73/12.49 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (rless(v3, % 75.73/12.49 v2) = v1) | ~ (rless(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 75.73/12.49 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 75.73/12.49 (rintersect(v3, v2) = v1) | ~ (rintersect(v3, v2) = v0)) & ! [v0: $i] : ! % 75.73/12.49 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (vplus(v3, v2) = v1) | ~ % 75.73/12.49 (vplus(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 75.73/12.49 $i] : (v1 = v0 | ~ (vf(v3, v2) = v1) | ~ (vf(v3, v2) = v0)) & ! [v0: % 75.73/12.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 75.73/12.49 : (v1 = v0 | ~ (ron(v3, v2) = v1) | ~ (ron(v3, v2) = v0)) & ! [v0: % 75.73/12.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 75.73/12.49 : (v1 = v0 | ~ (rcenter(v3, v2) = v1) | ~ (rcenter(v3, v2) = v0)) & ! [v0: % 75.73/12.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 75.73/12.49 ~ (rtriangle(v2) = v1) | ~ (rtriangle(v2) = v0)) & ! [v0: % 75.73/12.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 75.73/12.49 ~ (rreal(v2) = v1) | ~ (rreal(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 75.73/12.49 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (rline(v2) = v1) | ~ % 75.73/12.49 (rline(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 75.73/12.49 : ! [v2: $i] : (v1 = v0 | ~ (rpoint(v2) = v1) | ~ (rpoint(v2) = v0)) & ! % 75.73/12.49 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 75.73/12.49 | ~ (rcircle(v2) = v1) | ~ (rcircle(v2) = v0)) % 75.73/12.49 % 75.73/12.49 Further assumptions not needed in the proof: % 75.73/12.49 -------------------------------------------- % 75.73/12.49 ass(cond(156, 0), 0), pred(axiom(137), 1), pred(axiom(137), 2), pred(axiom(5), % 75.73/12.49 0), qu(cond(axiom(1), 0), imp(cond(axiom(1), 0))), qu(cond(axiom(101), 0), % 75.73/12.50 imp(cond(axiom(101), 0))), qu(cond(axiom(103), 0), imp(cond(axiom(103), 0))), % 75.73/12.50 qu(cond(axiom(105), 0), imp(cond(axiom(105), 0))), qu(cond(axiom(107), 0), % 75.73/12.50 imp(cond(axiom(107), 0))), qu(cond(axiom(109), 0), imp(cond(axiom(109), 0))), % 75.73/12.50 qu(cond(axiom(11), 0), imp(cond(axiom(11), 0))), qu(cond(axiom(111), 0), % 75.73/12.50 imp(cond(axiom(111), 0))), qu(cond(axiom(113), 0), imp(cond(axiom(113), 0))), % 75.73/12.50 qu(cond(axiom(115), 0), imp(cond(axiom(115), 0))), qu(cond(axiom(117), 0), % 75.73/12.50 imp(cond(axiom(117), 0))), qu(cond(axiom(119), 0), imp(cond(axiom(119), 0))), % 75.73/12.50 qu(cond(axiom(121), 0), imp(cond(axiom(121), 0))), qu(cond(axiom(123), 0), % 75.73/12.50 imp(cond(axiom(123), 0))), qu(cond(axiom(125), 0), imp(cond(axiom(125), 0))), % 75.73/12.50 qu(cond(axiom(127), 0), imp(cond(axiom(127), 0))), qu(cond(axiom(129), 0), % 75.73/12.50 imp(cond(axiom(129), 0))), qu(cond(axiom(13), 0), imp(cond(axiom(13), 0))), % 75.73/12.50 qu(cond(axiom(131), 0), imp(cond(axiom(131), 0))), qu(cond(axiom(133), 0), % 75.73/12.50 imp(cond(axiom(133), 0))), qu(cond(axiom(135), 0), imp(cond(axiom(135), 0))), % 75.73/12.50 qu(cond(axiom(139), 0), imp(cond(axiom(139), 0))), qu(cond(axiom(141), 0), % 75.73/12.50 imp(cond(axiom(141), 0))), qu(cond(axiom(143), 0), imp(cond(axiom(143), 0))), % 75.73/12.50 qu(cond(axiom(145), 0), imp(cond(axiom(145), 0))), qu(cond(axiom(147), 0), % 75.73/12.50 imp(cond(axiom(147), 0))), qu(cond(axiom(149), 0), imp(cond(axiom(149), 0))), % 75.73/12.50 qu(cond(axiom(15), 0), imp(cond(axiom(15), 0))), qu(cond(axiom(151), 0), % 75.73/12.50 imp(cond(axiom(151), 0))), qu(cond(axiom(153), 0), imp(cond(axiom(153), 0))), % 75.73/12.50 qu(cond(axiom(160), 0), imp(cond(axiom(160), 0))), qu(cond(axiom(162), 0), % 75.73/12.50 imp(cond(axiom(162), 0))), qu(cond(axiom(164), 0), imp(cond(axiom(164), 0))), % 75.73/12.50 qu(cond(axiom(166), 0), imp(cond(axiom(166), 0))), qu(cond(axiom(168), 0), % 75.73/12.50 imp(cond(axiom(168), 0))), qu(cond(axiom(17), 0), imp(cond(axiom(17), 0))), % 75.73/12.50 qu(cond(axiom(170), 0), imp(cond(axiom(170), 0))), qu(cond(axiom(172), 0), % 75.73/12.50 imp(cond(axiom(172), 0))), qu(cond(axiom(174), 0), imp(cond(axiom(174), 0))), % 75.73/12.50 qu(cond(axiom(176), 0), imp(cond(axiom(176), 0))), qu(cond(axiom(178), 0), % 75.73/12.50 imp(cond(axiom(178), 0))), qu(cond(axiom(180), 0), imp(cond(axiom(180), 0))), % 75.73/12.50 qu(cond(axiom(186), 0), imp(cond(axiom(186), 0))), qu(cond(axiom(188), 0), % 75.73/12.50 imp(cond(axiom(188), 0))), qu(cond(axiom(19), 0), imp(cond(axiom(19), 0))), % 75.73/12.50 qu(cond(axiom(190), 0), imp(cond(axiom(190), 0))), qu(cond(axiom(192), 0), % 75.73/12.50 imp(cond(axiom(192), 0))), qu(cond(axiom(194), 0), imp(cond(axiom(194), 0))), % 75.73/12.50 qu(cond(axiom(196), 0), imp(cond(axiom(196), 0))), qu(cond(axiom(198), 0), % 75.73/12.50 imp(cond(axiom(198), 0))), qu(cond(axiom(200), 0), imp(cond(axiom(200), 0))), % 75.73/12.50 qu(cond(axiom(202), 0), imp(cond(axiom(202), 0))), qu(cond(axiom(204), 0), % 75.73/12.50 imp(cond(axiom(204), 0))), qu(cond(axiom(21), 0), imp(cond(axiom(21), 0))), % 75.73/12.50 qu(cond(axiom(23), 0), imp(cond(axiom(23), 0))), qu(cond(axiom(25), 0), % 75.73/12.50 imp(cond(axiom(25), 0))), qu(cond(axiom(27), 0), imp(cond(axiom(27), 0))), % 75.73/12.50 qu(cond(axiom(29), 0), imp(cond(axiom(29), 0))), qu(cond(axiom(3), 0), % 75.73/12.50 imp(cond(axiom(3), 0))), qu(cond(axiom(31), 0), imp(cond(axiom(31), 0))), % 75.73/12.50 qu(cond(axiom(33), 0), imp(cond(axiom(33), 0))), qu(cond(axiom(35), 0), % 75.73/12.50 imp(cond(axiom(35), 0))), qu(cond(axiom(37), 0), imp(cond(axiom(37), 0))), % 75.73/12.50 qu(cond(axiom(39), 0), imp(cond(axiom(39), 0))), qu(cond(axiom(41), 0), % 75.73/12.50 imp(cond(axiom(41), 0))), qu(cond(axiom(43), 0), imp(cond(axiom(43), 0))), % 75.73/12.50 qu(cond(axiom(45), 0), imp(cond(axiom(45), 0))), qu(cond(axiom(47), 0), % 75.73/12.50 imp(cond(axiom(47), 0))), qu(cond(axiom(49), 0), imp(cond(axiom(49), 0))), % 75.73/12.50 qu(cond(axiom(51), 0), imp(cond(axiom(51), 0))), qu(cond(axiom(53), 0), % 75.73/12.50 imp(cond(axiom(53), 0))), qu(cond(axiom(55), 0), imp(cond(axiom(55), 0))), % 75.73/12.50 qu(cond(axiom(57), 0), imp(cond(axiom(57), 0))), qu(cond(axiom(59), 0), % 75.73/12.50 imp(cond(axiom(59), 0))), qu(cond(axiom(61), 0), imp(cond(axiom(61), 0))), % 75.73/12.50 qu(cond(axiom(63), 0), imp(cond(axiom(63), 0))), qu(cond(axiom(65), 0), % 75.73/12.50 imp(cond(axiom(65), 0))), qu(cond(axiom(67), 0), imp(cond(axiom(67), 0))), % 75.73/12.50 qu(cond(axiom(69), 0), imp(cond(axiom(69), 0))), qu(cond(axiom(7), 0), % 75.73/12.50 imp(cond(axiom(7), 0))), qu(cond(axiom(71), 0), imp(cond(axiom(71), 0))), % 75.73/12.50 qu(cond(axiom(73), 0), imp(cond(axiom(73), 0))), qu(cond(axiom(75), 0), % 75.73/12.50 imp(cond(axiom(75), 0))), qu(cond(axiom(77), 0), imp(cond(axiom(77), 0))), % 75.73/12.50 qu(cond(axiom(79), 0), imp(cond(axiom(79), 0))), qu(cond(axiom(81), 0), % 75.73/12.50 imp(cond(axiom(81), 0))), qu(cond(axiom(83), 0), imp(cond(axiom(83), 0))), % 75.73/12.50 qu(cond(axiom(85), 0), imp(cond(axiom(85), 0))), qu(cond(axiom(87), 0), % 75.73/12.50 imp(cond(axiom(87), 0))), qu(cond(axiom(89), 0), imp(cond(axiom(89), 0))), % 75.73/12.50 qu(cond(axiom(9), 0), imp(cond(axiom(9), 0))), qu(cond(axiom(91), 0), % 75.73/12.50 imp(cond(axiom(91), 0))), qu(cond(axiom(93), 0), imp(cond(axiom(93), 0))), % 75.73/12.50 qu(cond(axiom(95), 0), imp(cond(axiom(95), 0))), qu(cond(axiom(97), 0), % 75.73/12.50 imp(cond(axiom(97), 0))), qu(cond(axiom(99), 0), imp(cond(axiom(99), 0))), % 75.73/12.50 replace(pred(211, 2)), replace(qu(theu(the(211), 1), imp(the(211)))), % 75.73/12.50 replace(replace(and(pred(comma_conjunct2(the(211)), 0), % 75.73/12.50 and(pred(comma_conjunct1(the(211)), 0), pred(the(211), 0))))) % 75.73/12.50 % 75.73/12.50 Those formulas are unsatisfiable: % 75.73/12.50 --------------------------------- % 75.73/12.50 % 75.73/12.50 Begin of proof % 75.73/12.50 | % 75.73/12.50 | ALPHA: (and(pred(comma_conjunct2(the(212)), 0), % 75.73/12.50 | and(pred(comma_conjunct1(the(212)), 0), pred(the(212), 0)))) % 75.73/12.50 | implies: % 75.73/12.50 | (1) rcenter(vd1057, vd1063) = 0 % 75.73/12.50 | (2) ron(vd1055, vd1063) = 0 % 75.73/12.50 | % 75.73/12.50 | ALPHA: (and(pred(conjunct2(210), 4), and(holds(conjunct2(210), 1059, 0), % 75.73/12.50 | and(pred(conjunct2(210), 1), and(pred(conjunct1(210), 2), % 75.73/12.50 | pred(conjunct1(210), 1)))))) implies: % 75.73/12.50 | (3) rpoint(vd1055) = 0 % 75.73/12.50 | % 75.73/12.50 | ALPHA: (qu(cond(axiom(184), 0), imp(cond(axiom(184), 0)))) implies: % 75.73/12.50 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 75.73/12.50 | ( ~ (rpoint(v3) = 0) | ~ (rpoint(v0) = 0) | ~ (ron(v3, v2) = 0) | ~ % 75.73/12.50 | (ron(v0, v2) = v4) | ~ (rcenter(v1, v2) = 0) | ~ $i(v3) | ~ $i(v2) % 75.73/12.50 | | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : (vf(v1, v3) = % 75.73/12.50 | v6 & vf(v1, v0) = v5 & $i(v6) & $i(v5) & ( ~ (v6 = v5) | v4 = 0) & % 75.73/12.50 | ( ~ (v4 = 0) | v6 = v5))) % 75.73/12.50 | % 75.73/12.50 | ALPHA: (qu(cond(axiom(182), 0), imp(cond(axiom(182), 0)))) implies: % 75.73/12.50 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 75.73/12.50 | (v4 = v3 | ~ (rpoint(v1) = 0) | ~ (rpoint(v0) = 0) | ~ (ron(v1, v4) % 75.73/12.51 | = 0) | ~ (ron(v0, v3) = 0) | ~ (rcenter(v2, v4) = 0) | ~ $i(v4) % 75.73/12.51 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? % 75.73/12.51 | [v6: $i] : ? [v7: any] : (vf(v2, v1) = v6 & vf(v2, v0) = v5 & % 75.73/12.51 | rcenter(v2, v3) = v7 & $i(v6) & $i(v5) & ( ~ (v7 = 0) | ~ (v6 = % 75.73/12.51 | v5)))) % 75.73/12.51 | % 75.73/12.51 | ALPHA: (qu(theu(the(212), 1), imp(the(212)))) implies: % 75.73/12.51 | (6) $i(vd1055) % 75.73/12.51 | (7) $i(vd1057) % 75.73/12.51 | (8) $i(vd1063) % 75.73/12.51 | (9) ? [v0: $i] : ( ~ (v0 = vd1063) & ron(vd1055, v0) = 0 & rcenter(vd1057, % 75.73/12.51 | v0) = 0 & rcircle(v0) = 0 & $i(v0)) % 75.73/12.51 | % 75.73/12.51 | ALPHA: (function-axioms) implies: % 75.73/12.51 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 75.73/12.51 | : ! [v3: $i] : (v1 = v0 | ~ (rcenter(v3, v2) = v1) | ~ (rcenter(v3, % 75.73/12.51 | v2) = v0)) % 75.73/12.51 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 75.73/12.51 | (vf(v3, v2) = v1) | ~ (vf(v3, v2) = v0)) % 75.73/12.51 | % 75.73/12.51 | DELTA: instantiating (9) with fresh symbol all_102_0 gives: % 75.73/12.51 | (12) ~ (all_102_0 = vd1063) & ron(vd1055, all_102_0) = 0 & rcenter(vd1057, % 75.73/12.51 | all_102_0) = 0 & rcircle(all_102_0) = 0 & $i(all_102_0) % 75.73/12.51 | % 75.73/12.51 | ALPHA: (12) implies: % 75.73/12.51 | (13) ~ (all_102_0 = vd1063) % 75.73/12.51 | (14) $i(all_102_0) % 75.73/12.51 | (15) rcenter(vd1057, all_102_0) = 0 % 75.73/12.51 | (16) ron(vd1055, all_102_0) = 0 % 75.73/12.51 | % 75.73/12.51 | GROUND_INST: instantiating (5) with vd1055, vd1055, vd1057, vd1063, all_102_0, % 75.73/12.51 | simplifying with (2), (3), (6), (7), (8), (14), (15), (16) gives: % 75.73/12.51 | (17) all_102_0 = vd1063 | ? [v0: $i] : ? [v1: $i] : ? [v2: any] : % 75.73/12.51 | (vf(vd1057, vd1055) = v1 & vf(vd1057, vd1055) = v0 & rcenter(vd1057, % 75.73/12.51 | vd1063) = v2 & $i(v1) & $i(v0) & ( ~ (v2 = 0) | ~ (v1 = v0))) % 75.73/12.51 | % 75.73/12.52 | GROUND_INST: instantiating (4) with vd1055, vd1057, vd1063, vd1055, 0, % 75.73/12.52 | simplifying with (1), (2), (3), (6), (7), (8) gives: % 75.73/12.52 | (18) ? [v0: $i] : (vf(vd1057, vd1055) = v0 & $i(v0)) % 75.73/12.52 | % 75.73/12.52 | DELTA: instantiating (18) with fresh symbol all_122_0 gives: % 75.73/12.52 | (19) vf(vd1057, vd1055) = all_122_0 & $i(all_122_0) % 75.73/12.52 | % 75.73/12.52 | ALPHA: (19) implies: % 75.73/12.52 | (20) vf(vd1057, vd1055) = all_122_0 % 75.73/12.52 | % 75.73/12.52 | BETA: splitting (17) gives: % 75.73/12.52 | % 75.73/12.52 | Case 1: % 75.73/12.52 | | % 75.73/12.52 | | (21) all_102_0 = vd1063 % 75.73/12.52 | | % 75.73/12.52 | | REDUCE: (13), (21) imply: % 75.73/12.52 | | (22) $false % 75.73/12.52 | | % 75.73/12.52 | | CLOSE: (22) is inconsistent. % 75.73/12.52 | | % 75.73/12.52 | Case 2: % 75.73/12.52 | | % 75.73/12.52 | | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : (vf(vd1057, vd1055) = v1 % 75.73/12.52 | | & vf(vd1057, vd1055) = v0 & rcenter(vd1057, vd1063) = v2 & $i(v1) % 75.73/12.52 | | & $i(v0) & ( ~ (v2 = 0) | ~ (v1 = v0))) % 75.73/12.52 | | % 75.73/12.52 | | DELTA: instantiating (23) with fresh symbols all_202_0, all_202_1, all_202_2 % 75.73/12.52 | | gives: % 75.73/12.52 | | (24) vf(vd1057, vd1055) = all_202_1 & vf(vd1057, vd1055) = all_202_2 & % 75.73/12.52 | | rcenter(vd1057, vd1063) = all_202_0 & $i(all_202_1) & $i(all_202_2) % 75.73/12.52 | | & ( ~ (all_202_0 = 0) | ~ (all_202_1 = all_202_2)) % 75.73/12.52 | | % 75.73/12.52 | | ALPHA: (24) implies: % 75.73/12.52 | | (25) rcenter(vd1057, vd1063) = all_202_0 % 75.73/12.52 | | (26) vf(vd1057, vd1055) = all_202_2 % 75.73/12.52 | | (27) vf(vd1057, vd1055) = all_202_1 % 75.73/12.52 | | (28) ~ (all_202_0 = 0) | ~ (all_202_1 = all_202_2) % 75.73/12.52 | | % 75.73/12.52 | | GROUND_INST: instantiating (10) with 0, all_202_0, vd1063, vd1057, % 75.73/12.52 | | simplifying with (1), (25) gives: % 75.73/12.52 | | (29) all_202_0 = 0 % 75.73/12.52 | | % 75.73/12.52 | | GROUND_INST: instantiating (11) with all_202_2, all_202_1, vd1055, vd1057, % 75.73/12.52 | | simplifying with (26), (27) gives: % 75.73/12.52 | | (30) all_202_1 = all_202_2 % 75.73/12.52 | | % 75.73/12.52 | | GROUND_INST: instantiating (11) with all_122_0, all_202_1, vd1055, vd1057, % 75.73/12.52 | | simplifying with (20), (27) gives: % 75.73/12.52 | | (31) all_202_1 = all_122_0 % 75.73/12.52 | | % 75.73/12.52 | | COMBINE_EQS: (30), (31) imply: % 75.73/12.52 | | (32) all_202_2 = all_122_0 % 75.73/12.52 | | % 75.73/12.52 | | SIMP: (32) implies: % 75.73/12.52 | | (33) all_202_2 = all_122_0 % 75.73/12.52 | | % 75.73/12.52 | | BETA: splitting (28) gives: % 75.73/12.52 | | % 75.73/12.52 | | Case 1: % 75.73/12.52 | | | % 75.73/12.52 | | | (34) ~ (all_202_0 = 0) % 75.73/12.52 | | | % 75.73/12.52 | | | REDUCE: (29), (34) imply: % 75.73/12.52 | | | (35) $false % 75.73/12.52 | | | % 75.73/12.52 | | | CLOSE: (35) is inconsistent. % 75.73/12.52 | | | % 75.73/12.52 | | Case 2: % 75.73/12.52 | | | % 75.73/12.52 | | | (36) ~ (all_202_1 = all_202_2) % 75.73/12.52 | | | % 75.73/12.52 | | | REDUCE: (31), (33), (36) imply: % 75.73/12.52 | | | (37) $false % 75.73/12.52 | | | % 75.73/12.52 | | | CLOSE: (37) is inconsistent. % 75.73/12.52 | | | % 75.73/12.52 | | End of split % 75.73/12.52 | | % 75.73/12.52 | End of split % 75.73/12.52 | % 75.73/12.52 End of proof % 75.73/12.53 % SZS output end Proof for theBenchmark % 75.73/12.53 % 75.73/12.53 11916ms %------------------------------------------------------------------------------