%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO244+3 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n018.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 23:22:42 EDT 2023 % Result : Theorem 8.89s 1.92s % Output : Proof 15.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : GEO244+3 : TPTP v8.1.2. Released v4.0.0. % 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n018.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Tue Aug 29 23:54:03 EDT 2023 % 0.14/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.99/1.12 Prover 4: Preprocessing ... % 2.99/1.12 Prover 1: Preprocessing ... % 2.99/1.16 Prover 5: Preprocessing ... % 2.99/1.16 Prover 2: Preprocessing ... % 2.99/1.17 Prover 6: Preprocessing ... % 2.99/1.17 Prover 0: Preprocessing ... % 2.99/1.17 Prover 3: Preprocessing ... % 7.20/1.69 Prover 5: Proving ... % 7.51/1.72 Prover 2: Proving ... % 7.77/1.76 Prover 3: Constructing countermodel ... % 7.77/1.77 Prover 6: Constructing countermodel ... % 7.77/1.78 Prover 1: Constructing countermodel ... % 8.49/1.86 Prover 6: gave up % 8.49/1.86 Prover 3: gave up % 8.49/1.87 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.49/1.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.49/1.88 Prover 1: gave up % 8.49/1.90 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 8.89/1.92 Prover 2: proved (1280ms) % 8.89/1.92 % 8.89/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.89/1.92 % 8.89/1.93 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.89/1.93 Prover 5: stopped % 8.89/1.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.33/1.98 Prover 8: Preprocessing ... % 9.33/1.99 Prover 9: Preprocessing ... % 9.33/1.99 Prover 7: Preprocessing ... % 9.33/2.01 Prover 11: Preprocessing ... % 9.33/2.02 Prover 10: Preprocessing ... % 10.09/2.09 Prover 7: Warning: ignoring some quantifiers % 10.41/2.12 Prover 10: Warning: ignoring some quantifiers % 10.41/2.12 Prover 4: Constructing countermodel ... % 10.41/2.12 Prover 7: Constructing countermodel ... % 10.74/2.15 Prover 10: Constructing countermodel ... % 10.74/2.16 Prover 0: Proving ... % 10.74/2.17 Prover 8: Warning: ignoring some quantifiers % 10.74/2.17 Prover 0: stopped % 10.74/2.18 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.74/2.19 Prover 8: Constructing countermodel ... % 10.74/2.21 Prover 13: Preprocessing ... % 10.74/2.29 Prover 10: gave up % 10.74/2.30 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 10.74/2.31 Prover 13: Warning: ignoring some quantifiers % 10.74/2.32 Prover 8: gave up % 10.74/2.32 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 10.74/2.33 Prover 13: Constructing countermodel ... % 11.81/2.39 Prover 19: Preprocessing ... % 11.81/2.39 Prover 16: Preprocessing ... % 13.09/2.46 Prover 16: Warning: ignoring some quantifiers % 13.09/2.47 Prover 16: Constructing countermodel ... % 13.85/2.55 Prover 9: Constructing countermodel ... % 13.85/2.57 Prover 19: Warning: ignoring some quantifiers % 13.85/2.57 Prover 9: stopped % 13.85/2.57 Prover 11: Constructing countermodel ... % 13.85/2.58 Prover 19: Constructing countermodel ... % 15.39/2.79 Prover 4: Found proof (size 51) % 15.39/2.79 Prover 4: proved (2138ms) % 15.39/2.79 Prover 11: stopped % 15.39/2.79 Prover 7: stopped % 15.39/2.79 Prover 19: stopped % 15.39/2.79 Prover 13: stopped % 15.39/2.79 Prover 16: stopped % 15.39/2.79 % 15.39/2.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.39/2.79 % 15.72/2.81 % SZS output start Proof for theBenchmark % 15.72/2.81 Assumptions after simplification: % 15.72/2.81 --------------------------------- % 15.72/2.81 % 15.72/2.81 (a2_defns) % 15.72/2.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 15.72/2.84 (left_apart_point(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ~ $i(v1) | % 15.72/2.84 ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & right_apart_point(v0, v1) = v4)) & % 15.72/2.84 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (right_apart_point(v0, % 15.72/2.84 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 15.72/2.84 = 0) & left_apart_point(v0, v3) = v4 & reverse_line(v1) = v3 & $i(v3))) % 15.72/2.84 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (left_apart_point(v0, v2) = 0) % 15.72/2.84 | ~ (reverse_line(v1) = v2) | ~ $i(v1) | ~ $i(v0) | right_apart_point(v0, % 15.72/2.84 v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (right_apart_point(v0, v1) = 0) % 15.72/2.84 | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (left_apart_point(v0, v2) = 0 & % 15.72/2.84 reverse_line(v1) = v2 & $i(v2))) % 15.72/2.84 % 15.72/2.84 (ax10_basics) % 15.72/2.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (left_apart_point(v0, v2) = 0) | % 15.72/2.84 ~ (reverse_line(v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: % 15.72/2.84 $i] : ( ~ (left_apart_point(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)) % 15.72/2.84 % 15.72/2.84 (ax1_cons_objs) % 15.72/2.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 15.72/2.84 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: % 15.72/2.84 any] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & % 15.72/2.84 distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | % 15.72/2.84 v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = % 15.72/2.84 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : % 15.72/2.84 ? [v5: any] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & % 15.72/2.84 line_connecting(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = % 15.72/2.84 0))) % 15.72/2.84 % 15.72/2.84 (ax5_cons_objs) % 15.72/2.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 15.72/2.85 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 15.72/2.85 (distinct_points(v0, v1) = v3 & apart_point_and_line(v1, v2) = v5 & % 15.72/2.85 apart_point_and_line(v0, v2) = v4 & ( ~ (v3 = 0) | ( ~ (v5 = 0) & ~ (v4 = % 15.72/2.85 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = % 15.72/2.85 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ? [v4: int] : ( % 15.72/2.85 ~ (v4 = 0) & ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 15.72/2.85 apart_point_and_line(v1, v2) = v4 & apart_point_and_line(v0, v2) = v3 & % 15.72/2.85 $i(v2))) % 15.72/2.85 % 15.72/2.85 (ax9_cons_objs) % 15.72/2.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v1, v0) = v2) | % 15.72/2.85 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6: % 15.72/2.85 any] : (line_connecting(v0, v1) = v4 & distinct_points(v0, v1) = v3 & % 15.72/2.85 equally_directed_lines(v4, v5) = v6 & reverse_line(v2) = v5 & $i(v5) & % 15.72/2.85 $i(v4) & ( ~ (v3 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 15.72/2.85 $i] : ( ~ (line_connecting(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 15.72/2.85 any] : ? [v4: $i] : ? [v5: $i] : ? [v6: any] : (line_connecting(v1, v0) % 15.72/2.85 = v4 & distinct_points(v0, v1) = v3 & equally_directed_lines(v2, v5) = v6 % 15.72/2.85 & reverse_line(v4) = v5 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 = 0))) & ! % 15.72/2.85 [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ % 15.72/2.85 $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (line_connecting(v1, v0) % 15.72/2.85 = v3 & line_connecting(v0, v1) = v2 & equally_directed_lines(v2, v4) = 0 & % 15.72/2.85 reverse_line(v3) = v4 & $i(v4) & $i(v3) & $i(v2))) % 15.72/2.85 % 15.72/2.85 (con) % 15.72/2.86 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 15.72/2.86 int] : ( ~ (v5 = 0) & line_connecting(v1, v0) = v4 & line_connecting(v0, v1) % 15.72/2.86 = v3 & distinct_points(v0, v1) = 0 & left_apart_point(v2, v4) = v5 & % 15.72/2.86 right_apart_point(v2, v3) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 15.72/2.86 % 15.72/2.86 (function-axioms) % 15.72/2.87 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.72/2.87 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_on_line(v5, v4, % 15.72/2.87 v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) & ! [v0: % 15.72/2.87 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.72/2.87 : ! [v4: $i] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~ % 15.72/2.87 (before_on_line(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.72/2.87 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 15.72/2.87 (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) & % 15.72/2.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.72/2.87 (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = % 15.72/2.87 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 15.72/2.87 ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 15.72/2.87 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.72/2.87 [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 15.72/2.87 (distinct_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.72/2.87 ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 15.72/2.87 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.72/2.87 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.72/2.87 (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! % 15.72/2.87 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 15.72/2.87 $i] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ % 15.72/2.87 (incident_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.72/2.87 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.72/2.87 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 15.72/2.87 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 15.72/2.87 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 15.72/2.87 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.72/2.87 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.72/2.87 (equally_directed_opposite_lines(v3, v2) = v1) | ~ % 15.72/2.87 (equally_directed_opposite_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] % 15.72/2.87 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.72/2.87 (equally_directed_lines(v3, v2) = v1) | ~ (equally_directed_lines(v3, v2) = % 15.72/2.87 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.72/2.87 $i] : ! [v3: $i] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~ % 15.72/2.87 (left_convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.72/2.87 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.72/2.87 (right_convergent_lines(v3, v2) = v1) | ~ (right_convergent_lines(v3, v2) = % 15.72/2.87 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 15.72/2.87 $i] : ! [v3: $i] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~ % 15.72/2.87 (left_apart_point(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 15.72/2.87 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.72/2.87 (right_apart_point(v3, v2) = v1) | ~ (right_apart_point(v3, v2) = v0)) & ! % 15.72/2.87 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 15.72/2.87 $i] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | ~ % 15.72/2.87 (unequally_directed_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.72/2.87 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.72/2.87 (unequally_directed_opposite_lines(v3, v2) = v1) | ~ % 15.72/2.87 (unequally_directed_opposite_lines(v3, v2) = v0)) & ! [v0: % 15.72/2.87 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 15.72/2.87 ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.72/2.87 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (line(v2) = v1) | ~ % 15.72/2.87 (line(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 15.72/2.87 (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) % 15.72/2.87 % 15.72/2.87 Further assumptions not needed in the proof: % 15.72/2.87 -------------------------------------------- % 15.72/2.87 a1_defns, a3_defns, a4_defns, a5_defns, a6_defns, a7_defns, a8_defns, a9_defns, % 15.72/2.87 ax10_cons_objs, ax11_basics, ax1_basics, ax1_subs, ax1_uniq_cons, ax2_basics, % 15.72/2.87 ax2_cons_objs, ax2_subs, ax2_uniq_cons, ax3_basics, ax3_cons_objs, ax3_subs, % 15.72/2.87 ax4_basics, ax4_cons_objs, ax4_defns, ax5_basics, ax6_basics, ax6_cons_objs, % 15.72/2.87 ax7_basics, ax7_cons_objs, ax8_basics, ax8_cons_objs, ax9_basics % 15.72/2.87 % 15.72/2.87 Those formulas are unsatisfiable: % 15.72/2.87 --------------------------------- % 15.72/2.87 % 15.72/2.87 Begin of proof % 15.72/2.87 | % 15.72/2.87 | ALPHA: (a2_defns) implies: % 15.72/2.87 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (right_apart_point(v0, v1) = 0) | ~ % 15.72/2.87 | $i(v1) | ~ $i(v0) | ? [v2: $i] : (left_apart_point(v0, v2) = 0 & % 15.72/2.87 | reverse_line(v1) = v2 & $i(v2))) % 15.72/2.87 | % 15.72/2.87 | ALPHA: (ax10_basics) implies: % 15.72/2.87 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (left_apart_point(v0, v1) = 0) | ~ % 15.72/2.87 | $i(v1) | ~ $i(v0)) % 15.72/2.87 | % 15.72/2.87 | ALPHA: (ax1_cons_objs) implies: % 15.72/2.88 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 15.72/2.88 | $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? % 15.72/2.88 | [v5: any] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & % 15.72/2.88 | line_connecting(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) % 15.72/2.88 | | v5 = 0))) % 15.72/2.88 | % 15.72/2.88 | ALPHA: (ax5_cons_objs) implies: % 15.72/2.88 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 15.72/2.88 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ? [v4: int] : ( ~ % 15.72/2.88 | (v4 = 0) & ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 15.72/2.88 | apart_point_and_line(v1, v2) = v4 & apart_point_and_line(v0, v2) = % 15.72/2.88 | v3 & $i(v2))) % 15.72/2.88 | % 15.72/2.88 | ALPHA: (ax9_cons_objs) implies: % 15.72/2.88 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 15.72/2.88 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 15.72/2.88 | (line_connecting(v1, v0) = v3 & line_connecting(v0, v1) = v2 & % 15.72/2.88 | equally_directed_lines(v2, v4) = 0 & reverse_line(v3) = v4 & $i(v4) % 15.72/2.88 | & $i(v3) & $i(v2))) % 15.72/2.88 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) % 15.72/2.88 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? % 15.72/2.88 | [v5: $i] : ? [v6: any] : (line_connecting(v1, v0) = v4 & % 15.72/2.88 | distinct_points(v0, v1) = v3 & equally_directed_lines(v2, v5) = v6 % 15.72/2.88 | & reverse_line(v4) = v5 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 = % 15.72/2.88 | 0))) % 15.72/2.88 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v1, v0) % 15.72/2.88 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? % 15.72/2.88 | [v5: $i] : ? [v6: any] : (line_connecting(v0, v1) = v4 & % 15.72/2.88 | distinct_points(v0, v1) = v3 & equally_directed_lines(v4, v5) = v6 % 15.72/2.88 | & reverse_line(v2) = v5 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 = % 15.72/2.88 | 0))) % 15.72/2.88 | % 15.72/2.88 | ALPHA: (function-axioms) implies: % 15.72/2.88 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 15.72/2.88 | (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) % 15.72/2.88 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.72/2.88 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 15.72/2.88 | % 15.72/2.89 | DELTA: instantiating (con) with fresh symbols all_39_0, all_39_1, all_39_2, % 15.72/2.89 | all_39_3, all_39_4, all_39_5 gives: % 15.72/2.89 | (10) ~ (all_39_0 = 0) & line_connecting(all_39_4, all_39_5) = all_39_1 & % 15.72/2.89 | line_connecting(all_39_5, all_39_4) = all_39_2 & % 15.72/2.89 | distinct_points(all_39_5, all_39_4) = 0 & left_apart_point(all_39_3, % 15.72/2.89 | all_39_1) = all_39_0 & right_apart_point(all_39_3, all_39_2) = 0 & % 15.72/2.89 | $i(all_39_1) & $i(all_39_2) & $i(all_39_3) & $i(all_39_4) & % 15.72/2.89 | $i(all_39_5) % 15.72/2.89 | % 15.72/2.89 | ALPHA: (10) implies: % 15.72/2.89 | (11) $i(all_39_5) % 15.72/2.89 | (12) $i(all_39_4) % 15.72/2.89 | (13) $i(all_39_3) % 15.72/2.89 | (14) $i(all_39_2) % 15.72/2.89 | (15) right_apart_point(all_39_3, all_39_2) = 0 % 15.72/2.89 | (16) distinct_points(all_39_5, all_39_4) = 0 % 15.72/2.89 | (17) line_connecting(all_39_5, all_39_4) = all_39_2 % 15.72/2.89 | (18) line_connecting(all_39_4, all_39_5) = all_39_1 % 15.72/2.89 | % 15.72/2.89 | GROUND_INST: instantiating (1) with all_39_3, all_39_2, simplifying with (13), % 15.72/2.89 | (14), (15) gives: % 15.72/2.89 | (19) ? [v0: $i] : (left_apart_point(all_39_3, v0) = 0 & % 15.72/2.89 | reverse_line(all_39_2) = v0 & $i(v0)) % 15.72/2.89 | % 15.72/2.89 | GROUND_INST: instantiating (3) with all_39_5, all_39_4, simplifying with (11), % 15.72/2.89 | (12), (16) gives: % 15.72/2.89 | (20) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 15.72/2.89 | (point(all_39_4) = v1 & point(all_39_5) = v0 & line(v2) = v3 & % 15.72/2.89 | line_connecting(all_39_5, all_39_4) = v2 & $i(v2) & ( ~ (v1 = 0) | % 15.72/2.89 | ~ (v0 = 0) | v3 = 0)) % 15.72/2.89 | % 15.72/2.89 | GROUND_INST: instantiating (4) with all_39_5, all_39_4, simplifying with (11), % 15.72/2.89 | (12), (16) gives: % 15.72/2.89 | (21) ? [v0: $i] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = 0) & ~ (v1 = 0) % 15.72/2.89 | & line_connecting(all_39_5, all_39_4) = v0 & % 15.72/2.89 | apart_point_and_line(all_39_4, v0) = v2 & % 15.72/2.89 | apart_point_and_line(all_39_5, v0) = v1 & $i(v0)) % 15.72/2.89 | % 15.72/2.89 | GROUND_INST: instantiating (5) with all_39_5, all_39_4, simplifying with (11), % 15.72/2.89 | (12), (16) gives: % 15.72/2.89 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (line_connecting(all_39_4, % 15.72/2.89 | all_39_5) = v1 & line_connecting(all_39_5, all_39_4) = v0 & % 15.72/2.89 | equally_directed_lines(v0, v2) = 0 & reverse_line(v1) = v2 & $i(v2) % 15.72/2.89 | & $i(v1) & $i(v0)) % 15.72/2.89 | % 15.72/2.89 | GROUND_INST: instantiating (7) with all_39_4, all_39_5, all_39_2, simplifying % 15.72/2.89 | with (11), (12), (17) gives: % 15.72/2.89 | (23) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : % 15.72/2.89 | (line_connecting(all_39_4, all_39_5) = v1 & distinct_points(all_39_4, % 15.72/2.89 | all_39_5) = v0 & equally_directed_lines(v1, v2) = v3 & % 15.72/2.89 | reverse_line(all_39_2) = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) | v3 = % 15.72/2.89 | 0)) % 15.72/2.89 | % 15.72/2.90 | GROUND_INST: instantiating (7) with all_39_5, all_39_4, all_39_1, simplifying % 15.72/2.90 | with (11), (12), (18) gives: % 15.72/2.90 | (24) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : % 15.72/2.90 | (line_connecting(all_39_5, all_39_4) = v1 & distinct_points(all_39_5, % 15.72/2.90 | all_39_4) = v0 & equally_directed_lines(v1, v2) = v3 & % 15.72/2.90 | reverse_line(all_39_1) = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) | v3 = % 15.72/2.90 | 0)) % 15.72/2.90 | % 15.72/2.90 | GROUND_INST: instantiating (6) with all_39_4, all_39_5, all_39_1, simplifying % 15.72/2.90 | with (11), (12), (18) gives: % 15.72/2.90 | (25) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : % 15.72/2.90 | (line_connecting(all_39_5, all_39_4) = v1 & distinct_points(all_39_4, % 15.72/2.90 | all_39_5) = v0 & equally_directed_lines(all_39_1, v2) = v3 & % 15.72/2.90 | reverse_line(v1) = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) | v3 = 0)) % 15.72/2.90 | % 15.72/2.90 | DELTA: instantiating (19) with fresh symbol all_48_0 gives: % 15.72/2.90 | (26) left_apart_point(all_39_3, all_48_0) = 0 & reverse_line(all_39_2) = % 15.72/2.90 | all_48_0 & $i(all_48_0) % 15.72/2.90 | % 15.72/2.90 | ALPHA: (26) implies: % 15.72/2.90 | (27) reverse_line(all_39_2) = all_48_0 % 15.72/2.90 | (28) left_apart_point(all_39_3, all_48_0) = 0 % 15.72/2.90 | % 15.72/2.90 | DELTA: instantiating (21) with fresh symbols all_56_0, all_56_1, all_56_2 % 15.72/2.90 | gives: % 15.72/2.90 | (29) ~ (all_56_0 = 0) & ~ (all_56_1 = 0) & line_connecting(all_39_5, % 15.72/2.90 | all_39_4) = all_56_2 & apart_point_and_line(all_39_4, all_56_2) = % 15.72/2.90 | all_56_0 & apart_point_and_line(all_39_5, all_56_2) = all_56_1 & % 15.72/2.90 | $i(all_56_2) % 15.72/2.90 | % 15.72/2.90 | ALPHA: (29) implies: % 15.72/2.90 | (30) line_connecting(all_39_5, all_39_4) = all_56_2 % 15.72/2.90 | % 15.72/2.90 | DELTA: instantiating (22) with fresh symbols all_58_0, all_58_1, all_58_2 % 15.72/2.90 | gives: % 15.72/2.90 | (31) line_connecting(all_39_4, all_39_5) = all_58_1 & % 15.72/2.90 | line_connecting(all_39_5, all_39_4) = all_58_2 & % 15.72/2.90 | equally_directed_lines(all_58_2, all_58_0) = 0 & % 15.72/2.90 | reverse_line(all_58_1) = all_58_0 & $i(all_58_0) & $i(all_58_1) & % 15.72/2.90 | $i(all_58_2) % 15.72/2.90 | % 15.72/2.90 | ALPHA: (31) implies: % 15.72/2.90 | (32) line_connecting(all_39_5, all_39_4) = all_58_2 % 15.72/2.90 | % 15.72/2.90 | DELTA: instantiating (25) with fresh symbols all_60_0, all_60_1, all_60_2, % 15.72/2.90 | all_60_3 gives: % 15.72/2.90 | (33) line_connecting(all_39_5, all_39_4) = all_60_2 & % 15.72/2.90 | distinct_points(all_39_4, all_39_5) = all_60_3 & % 15.72/2.90 | equally_directed_lines(all_39_1, all_60_1) = all_60_0 & % 15.72/2.90 | reverse_line(all_60_2) = all_60_1 & $i(all_60_1) & $i(all_60_2) & ( ~ % 15.72/2.90 | (all_60_3 = 0) | all_60_0 = 0) % 15.72/2.90 | % 15.72/2.90 | ALPHA: (33) implies: % 15.72/2.90 | (34) $i(all_60_1) % 15.72/2.90 | (35) reverse_line(all_60_2) = all_60_1 % 15.72/2.90 | (36) line_connecting(all_39_5, all_39_4) = all_60_2 % 15.72/2.90 | % 15.72/2.90 | DELTA: instantiating (23) with fresh symbols all_64_0, all_64_1, all_64_2, % 15.72/2.90 | all_64_3 gives: % 15.72/2.90 | (37) line_connecting(all_39_4, all_39_5) = all_64_2 & % 15.72/2.90 | distinct_points(all_39_4, all_39_5) = all_64_3 & % 15.72/2.90 | equally_directed_lines(all_64_2, all_64_1) = all_64_0 & % 15.72/2.90 | reverse_line(all_39_2) = all_64_1 & $i(all_64_1) & $i(all_64_2) & ( ~ % 15.72/2.90 | (all_64_3 = 0) | all_64_0 = 0) % 15.72/2.90 | % 15.72/2.90 | ALPHA: (37) implies: % 15.72/2.90 | (38) reverse_line(all_39_2) = all_64_1 % 15.72/2.90 | % 15.72/2.90 | DELTA: instantiating (24) with fresh symbols all_68_0, all_68_1, all_68_2, % 15.72/2.90 | all_68_3 gives: % 15.72/2.90 | (39) line_connecting(all_39_5, all_39_4) = all_68_2 & % 15.72/2.90 | distinct_points(all_39_5, all_39_4) = all_68_3 & % 15.72/2.90 | equally_directed_lines(all_68_2, all_68_1) = all_68_0 & % 15.72/2.90 | reverse_line(all_39_1) = all_68_1 & $i(all_68_1) & $i(all_68_2) & ( ~ % 15.72/2.90 | (all_68_3 = 0) | all_68_0 = 0) % 15.72/2.90 | % 15.72/2.90 | ALPHA: (39) implies: % 15.72/2.90 | (40) line_connecting(all_39_5, all_39_4) = all_68_2 % 15.72/2.90 | % 15.72/2.90 | DELTA: instantiating (20) with fresh symbols all_72_0, all_72_1, all_72_2, % 15.72/2.90 | all_72_3 gives: % 15.72/2.91 | (41) point(all_39_4) = all_72_2 & point(all_39_5) = all_72_3 & % 15.72/2.91 | line(all_72_1) = all_72_0 & line_connecting(all_39_5, all_39_4) = % 15.72/2.91 | all_72_1 & $i(all_72_1) & ( ~ (all_72_2 = 0) | ~ (all_72_3 = 0) | % 15.72/2.91 | all_72_0 = 0) % 15.72/2.91 | % 15.72/2.91 | ALPHA: (41) implies: % 15.72/2.91 | (42) line_connecting(all_39_5, all_39_4) = all_72_1 % 15.72/2.91 | % 15.72/2.91 | GROUND_INST: instantiating (8) with all_48_0, all_64_1, all_39_2, simplifying % 15.72/2.91 | with (27), (38) gives: % 15.72/2.91 | (43) all_64_1 = all_48_0 % 15.72/2.91 | % 15.72/2.91 | GROUND_INST: instantiating (9) with all_39_2, all_60_2, all_39_4, all_39_5, % 15.72/2.91 | simplifying with (17), (36) gives: % 15.72/2.91 | (44) all_60_2 = all_39_2 % 15.72/2.91 | % 15.72/2.91 | GROUND_INST: instantiating (9) with all_56_2, all_60_2, all_39_4, all_39_5, % 15.72/2.91 | simplifying with (30), (36) gives: % 15.72/2.91 | (45) all_60_2 = all_56_2 % 15.72/2.91 | % 15.72/2.91 | GROUND_INST: instantiating (9) with all_68_2, all_72_1, all_39_4, all_39_5, % 15.72/2.91 | simplifying with (40), (42) gives: % 15.72/2.91 | (46) all_72_1 = all_68_2 % 15.72/2.91 | % 15.72/2.91 | GROUND_INST: instantiating (9) with all_60_2, all_72_1, all_39_4, all_39_5, % 15.72/2.91 | simplifying with (36), (42) gives: % 15.72/2.91 | (47) all_72_1 = all_60_2 % 15.72/2.91 | % 15.72/2.91 | GROUND_INST: instantiating (9) with all_58_2, all_72_1, all_39_4, all_39_5, % 15.72/2.91 | simplifying with (32), (42) gives: % 15.72/2.91 | (48) all_72_1 = all_58_2 % 15.72/2.91 | % 15.72/2.91 | COMBINE_EQS: (46), (48) imply: % 15.72/2.91 | (49) all_68_2 = all_58_2 % 15.72/2.91 | % 15.72/2.91 | COMBINE_EQS: (46), (47) imply: % 15.72/2.91 | (50) all_68_2 = all_60_2 % 15.72/2.91 | % 15.72/2.91 | COMBINE_EQS: (49), (50) imply: % 15.72/2.91 | (51) all_60_2 = all_58_2 % 15.72/2.91 | % 15.72/2.91 | SIMP: (51) implies: % 15.72/2.91 | (52) all_60_2 = all_58_2 % 15.72/2.91 | % 15.72/2.91 | COMBINE_EQS: (45), (52) imply: % 15.72/2.91 | (53) all_58_2 = all_56_2 % 15.72/2.91 | % 15.72/2.91 | COMBINE_EQS: (44), (52) imply: % 15.72/2.91 | (54) all_58_2 = all_39_2 % 15.72/2.91 | % 15.72/2.91 | COMBINE_EQS: (53), (54) imply: % 15.72/2.91 | (55) all_56_2 = all_39_2 % 15.72/2.91 | % 15.72/2.91 | REDUCE: (35), (44) imply: % 15.72/2.91 | (56) reverse_line(all_39_2) = all_60_1 % 15.72/2.91 | % 15.72/2.91 | GROUND_INST: instantiating (8) with all_48_0, all_60_1, all_39_2, simplifying % 15.72/2.91 | with (27), (56) gives: % 15.72/2.91 | (57) all_60_1 = all_48_0 % 15.72/2.91 | % 15.72/2.91 | REDUCE: (34), (57) imply: % 15.72/2.91 | (58) $i(all_48_0) % 15.72/2.91 | % 15.72/2.91 | GROUND_INST: instantiating (2) with all_39_3, all_48_0, simplifying with (13), % 15.72/2.91 | (28), (58) gives: % 15.72/2.91 | (59) $false % 15.72/2.91 | % 15.72/2.91 | CLOSE: (59) is inconsistent. % 15.72/2.91 | % 15.72/2.91 End of proof % 15.72/2.91 % SZS output end Proof for theBenchmark % 15.72/2.91 % 15.72/2.91 2292ms %------------------------------------------------------------------------------