%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO175+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n026.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 23:21:51 EDT 2023 % Result : Theorem 11.69s 2.32s % Output : Proof 20.90s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO175+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n026.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Aug 29 21:08:50 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.63 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.54/1.08 Prover 4: Preprocessing ... % 2.54/1.08 Prover 1: Preprocessing ... % 2.94/1.13 Prover 3: Preprocessing ... % 2.94/1.13 Prover 0: Preprocessing ... % 2.94/1.13 Prover 2: Preprocessing ... % 2.94/1.13 Prover 6: Preprocessing ... % 2.94/1.13 Prover 5: Preprocessing ... % 4.71/1.36 Prover 5: Proving ... % 4.71/1.36 Prover 2: Proving ... % 4.71/1.37 Prover 1: Constructing countermodel ... % 4.71/1.37 Prover 6: Constructing countermodel ... % 4.71/1.38 Prover 3: Constructing countermodel ... % 5.78/1.52 Prover 3: gave up % 5.78/1.53 Prover 1: gave up % 5.78/1.54 Prover 6: gave up % 5.78/1.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.78/1.54 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.78/1.55 Prover 0: Proving ... % 5.78/1.55 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 5.78/1.56 Prover 4: Constructing countermodel ... % 5.78/1.57 Prover 7: Preprocessing ... % 5.78/1.58 Prover 8: Preprocessing ... % 6.49/1.59 Prover 9: Preprocessing ... % 6.74/1.64 Prover 7: Warning: ignoring some quantifiers % 6.74/1.64 Prover 7: Constructing countermodel ... % 6.74/1.66 Prover 8: Warning: ignoring some quantifiers % 6.74/1.66 Prover 8: Constructing countermodel ... % 7.48/1.73 Prover 7: gave up % 7.48/1.74 Prover 8: gave up % 7.48/1.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.48/1.75 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.48/1.77 Prover 9: Constructing countermodel ... % 7.48/1.77 Prover 10: Preprocessing ... % 7.48/1.78 Prover 11: Preprocessing ... % 8.09/1.80 Prover 10: Warning: ignoring some quantifiers % 8.09/1.81 Prover 10: Constructing countermodel ... % 8.09/1.88 Prover 10: gave up % 8.74/1.88 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 8.87/1.91 Prover 12: Preprocessing ... % 8.99/1.92 Prover 11: Constructing countermodel ... % 8.99/2.01 Prover 12: Proving ... % 11.69/2.32 Prover 0: proved (1682ms) % 11.69/2.32 % 11.69/2.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.69/2.32 % 11.69/2.33 Prover 12: stopped % 11.69/2.33 Prover 9: stopped % 11.69/2.33 Prover 5: stopped % 11.69/2.33 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.69/2.33 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 11.69/2.33 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 11.69/2.33 Prover 2: stopped % 11.69/2.34 Prover 19: Preprocessing ... % 11.69/2.34 Prover 13: Preprocessing ... % 11.69/2.34 Prover 16: Preprocessing ... % 11.69/2.37 Prover 16: Warning: ignoring some quantifiers % 11.69/2.37 Prover 16: Constructing countermodel ... % 11.69/2.38 Prover 13: Warning: ignoring some quantifiers % 11.69/2.38 Prover 13: Constructing countermodel ... % 12.41/2.40 Prover 19: Warning: ignoring some quantifiers % 12.41/2.41 Prover 19: Constructing countermodel ... % 12.55/2.43 Prover 19: gave up % 12.55/2.45 Prover 13: gave up % 12.55/2.50 Prover 16: gave up % 20.90/3.98 Prover 11: Found proof (size 67) % 20.90/3.98 Prover 11: proved (2239ms) % 20.90/3.99 Prover 4: stopped % 20.90/3.99 % 20.90/3.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 20.90/3.99 % 20.90/4.00 % SZS output start Proof for theBenchmark % 20.90/4.00 Assumptions after simplification: % 20.90/4.00 --------------------------------- % 20.90/4.00 % 20.90/4.00 (apart3) % 20.90/4.04 ! [v0: $i] : ( ~ (convergent_lines(v0, v0) = 0) | ~ $i(v0)) % 20.90/4.04 % 20.90/4.04 (ceq3) % 20.90/4.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 20.90/4.04 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) % 20.90/4.04 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 20.90/4.04 convergent_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 20.90/4.04 : ! [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ % 20.90/4.04 (convergent_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 20.90/4.04 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 20.90/4.04 [v3: int] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ % 20.90/4.04 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 20.90/4.04 convergent_lines(v0, v2) = 0) % 20.90/4.04 % 20.90/4.04 (ci3) % 20.90/4.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 20.90/4.05 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 20.90/4.05 & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 20.90/4.05 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 20.90/4.05 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 20.90/4.05 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 20.90/4.05 apart_point_and_line(v2, v0) = v3 & $i(v2))) % 20.90/4.05 % 20.90/4.05 (ci4) % 20.90/4.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 20.90/4.05 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 20.90/4.05 & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 20.90/4.05 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 20.90/4.05 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 20.90/4.05 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 20.90/4.05 apart_point_and_line(v2, v1) = v3 & $i(v2))) % 20.90/4.05 % 20.90/4.05 (con) % 20.90/4.05 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 20.90/4.05 int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & intersection_point(v2, % 20.90/4.05 v3) = v4 & apart_point_and_line(v0, v3) = v6 & apart_point_and_line(v0, % 20.90/4.05 v2) = v5 & convergent_lines(v2, v3) = 0 & distinct_points(v0, v4) = 0 & % 20.90/4.05 distinct_points(v0, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 20.90/4.05 % 20.90/4.05 (cu1) % 20.90/4.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 20.90/4.07 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 20.90/4.07 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 20.90/4.07 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 20.90/4.07 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v0, v3) = 0) | (v7 = 0 & % 20.90/4.07 apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, % 20.90/4.07 v3) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 20.90/4.07 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, % 20.90/4.07 v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ % 20.90/4.07 (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 20.90/4.07 | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 20.90/4.07 apart_point_and_line(v1, v2) = 0) | (v7 = 0 & apart_point_and_line(v0, % 20.90/4.07 v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 20.90/4.07 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 20.90/4.07 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 20.90/4.07 (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 20.90/4.07 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 20.90/4.07 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 20.90/4.07 apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 20.90/4.07 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 20.90/4.07 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 20.90/4.07 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 20.90/4.07 (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 20.90/4.07 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((v9 = % 20.90/4.07 0 & apart_point_and_line(v1, v3) = 0) | (v8 = 0 & % 20.90/4.07 apart_point_and_line(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, % 20.90/4.07 v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0: % 20.90/4.07 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 20.90/4.07 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ % 20.90/4.07 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ~ % 20.90/4.07 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : % 20.90/4.07 ? [v8: int] : ((v8 = 0 & apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 20.90/4.07 apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, % 20.90/4.07 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 20.90/4.07 ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, % 20.90/4.07 v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ % 20.90/4.07 (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 20.90/4.07 $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 20.90/4.07 apart_point_and_line(v1, v3) = 0) | (v7 = 0 & apart_point_and_line(v1, % 20.90/4.07 v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0: $i] % 20.90/4.07 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (distinct_lines(v2, v3) = 0) | % 20.90/4.07 ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 20.90/4.07 $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 = % 20.90/4.07 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & % 20.90/4.07 apart_point_and_line(v1, v2) = 0) | (v5 = 0 & apart_point_and_line(v0, % 20.90/4.07 v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 20.90/4.07 % 20.90/4.07 (function-axioms) % 20.90/4.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.90/4.07 (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & % 20.90/4.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.90/4.07 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 20.90/4.07 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 20.90/4.07 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 20.90/4.07 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.90/4.07 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.90/4.07 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 20.90/4.07 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 20.90/4.07 $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, % 20.90/4.07 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 20.90/4.07 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 20.90/4.07 (distinct_points(v3, v2) = v0)) % 20.90/4.07 % 20.90/4.07 Further assumptions not needed in the proof: % 20.90/4.07 -------------------------------------------- % 20.90/4.08 apart1, apart2, apart4, apart5, ax6, ceq1, ceq2, ci1, ci2 % 20.90/4.08 % 20.90/4.08 Those formulas are unsatisfiable: % 20.90/4.08 --------------------------------- % 20.90/4.08 % 20.90/4.08 Begin of proof % 20.90/4.08 | % 20.90/4.08 | ALPHA: (ci3) implies: % 20.90/4.08 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 20.90/4.08 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 20.90/4.08 | (( ~ (v4 = 0) & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 20.90/4.08 | convergent_lines(v0, v1) = v3))) % 20.90/4.08 | % 20.90/4.08 | ALPHA: (ci4) implies: % 20.90/4.08 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 20.90/4.08 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 20.90/4.08 | (( ~ (v4 = 0) & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 20.90/4.08 | convergent_lines(v0, v1) = v3))) % 20.90/4.08 | % 20.90/4.08 | ALPHA: (cu1) implies: % 20.90/4.08 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 20.90/4.08 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) % 20.90/4.08 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, % 20.90/4.08 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 20.90/4.08 | [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & % 20.90/4.08 | apart_point_and_line(v1, v3) = 0) | (v7 = 0 & % 20.90/4.08 | apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & % 20.90/4.08 | distinct_lines(v2, v3) = v6))) % 20.90/4.08 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 20.90/4.08 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 20.90/4.08 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 20.90/4.08 | $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? % 20.90/4.08 | [v9: int] : ((v9 = 0 & apart_point_and_line(v1, v2) = 0) | (v8 = 0 & % 20.90/4.08 | apart_point_and_line(v0, v3) = 0) | ( ~ (v7 = 0) & % 20.90/4.08 | distinct_lines(v2, v3) = v7) | ( ~ (v6 = 0) & distinct_points(v0, % 20.90/4.08 | v1) = v6))) % 20.90/4.08 | % 20.90/4.08 | ALPHA: (ceq3) implies: % 20.90/4.09 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 20.90/4.09 | (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | % 20.90/4.09 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v2) = 0) % 20.90/4.09 | % 20.90/4.09 | ALPHA: (function-axioms) implies: % 20.90/4.09 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.90/4.09 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 20.90/4.09 | (convergent_lines(v3, v2) = v0)) % 20.90/4.09 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.90/4.09 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 20.90/4.09 | (apart_point_and_line(v3, v2) = v0)) % 20.90/4.09 | % 20.90/4.09 | DELTA: instantiating (con) with fresh symbols all_17_0, all_17_1, all_17_2, % 20.90/4.09 | all_17_3, all_17_4, all_17_5, all_17_6 gives: % 20.90/4.09 | (8) ~ (all_17_0 = 0) & ~ (all_17_1 = 0) & intersection_point(all_17_4, % 20.90/4.09 | all_17_3) = all_17_2 & apart_point_and_line(all_17_6, all_17_3) = % 20.90/4.09 | all_17_0 & apart_point_and_line(all_17_6, all_17_4) = all_17_1 & % 20.90/4.09 | convergent_lines(all_17_4, all_17_3) = 0 & distinct_points(all_17_6, % 20.90/4.09 | all_17_2) = 0 & distinct_points(all_17_6, all_17_5) = 0 & % 20.90/4.09 | $i(all_17_2) & $i(all_17_3) & $i(all_17_4) & $i(all_17_5) & % 20.90/4.09 | $i(all_17_6) % 20.90/4.09 | % 20.90/4.09 | ALPHA: (8) implies: % 20.90/4.09 | (9) ~ (all_17_1 = 0) % 20.90/4.09 | (10) ~ (all_17_0 = 0) % 20.90/4.09 | (11) $i(all_17_6) % 20.90/4.09 | (12) $i(all_17_4) % 20.90/4.09 | (13) $i(all_17_3) % 20.90/4.09 | (14) $i(all_17_2) % 20.90/4.09 | (15) distinct_points(all_17_6, all_17_2) = 0 % 20.90/4.09 | (16) convergent_lines(all_17_4, all_17_3) = 0 % 20.90/4.09 | (17) apart_point_and_line(all_17_6, all_17_4) = all_17_1 % 20.90/4.09 | (18) apart_point_and_line(all_17_6, all_17_3) = all_17_0 % 20.90/4.09 | (19) intersection_point(all_17_4, all_17_3) = all_17_2 % 20.90/4.09 | % 20.90/4.09 | GROUND_INST: instantiating (3) with all_17_6, all_17_2, all_17_3, all_17_4, % 20.90/4.09 | all_17_0, all_17_1, simplifying with (11), (12), (13), (14), % 20.90/4.09 | (15), (17), (18) gives: % 20.90/4.09 | (20) all_17_0 = 0 | all_17_1 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 20.90/4.09 | int] : ((v2 = 0 & apart_point_and_line(all_17_2, all_17_4) = 0) | % 20.90/4.09 | (v1 = 0 & apart_point_and_line(all_17_2, all_17_3) = 0) | ( ~ (v0 = % 20.90/4.09 | 0) & distinct_lines(all_17_3, all_17_4) = v0)) % 20.90/4.09 | % 20.90/4.09 | GROUND_INST: instantiating (4) with all_17_6, all_17_6, all_17_3, all_17_4, % 20.90/4.09 | all_17_0, all_17_1, simplifying with (11), (12), (13), (17), (18) % 20.90/4.09 | gives: % 20.90/4.09 | (21) all_17_0 = 0 | all_17_1 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: % 20.90/4.09 | int] : ? [v3: int] : ((v3 = 0 & apart_point_and_line(all_17_6, % 20.90/4.09 | all_17_3) = 0) | (v2 = 0 & apart_point_and_line(all_17_6, % 20.90/4.09 | all_17_4) = 0) | ( ~ (v1 = 0) & distinct_lines(all_17_3, % 20.90/4.09 | all_17_4) = v1) | ( ~ (v0 = 0) & distinct_points(all_17_6, % 20.90/4.09 | all_17_6) = v0)) % 20.90/4.09 | % 20.90/4.10 | GROUND_INST: instantiating (2) with all_17_4, all_17_3, all_17_2, simplifying % 20.90/4.10 | with (12), (13), (19) gives: % 20.90/4.10 | (22) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 20.90/4.10 | apart_point_and_line(all_17_2, all_17_3) = v1) | ( ~ (v0 = 0) & % 20.90/4.10 | convergent_lines(all_17_4, all_17_3) = v0)) % 20.90/4.10 | % 20.90/4.10 | GROUND_INST: instantiating (1) with all_17_4, all_17_3, all_17_2, simplifying % 20.90/4.10 | with (12), (13), (19) gives: % 20.90/4.10 | (23) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 20.90/4.10 | apart_point_and_line(all_17_2, all_17_4) = v1) | ( ~ (v0 = 0) & % 20.90/4.10 | convergent_lines(all_17_4, all_17_3) = v0)) % 20.90/4.10 | % 20.90/4.10 | DELTA: instantiating (23) with fresh symbols all_24_0, all_24_1 gives: % 20.90/4.10 | (24) ( ~ (all_24_0 = 0) & apart_point_and_line(all_17_2, all_17_4) = % 20.90/4.10 | all_24_0) | ( ~ (all_24_1 = 0) & convergent_lines(all_17_4, % 20.90/4.10 | all_17_3) = all_24_1) % 20.90/4.10 | % 20.90/4.10 | DELTA: instantiating (22) with fresh symbols all_25_0, all_25_1 gives: % 20.90/4.10 | (25) ( ~ (all_25_0 = 0) & apart_point_and_line(all_17_2, all_17_3) = % 20.90/4.10 | all_25_0) | ( ~ (all_25_1 = 0) & convergent_lines(all_17_4, % 20.90/4.10 | all_17_3) = all_25_1) % 20.90/4.10 | % 20.90/4.10 | BETA: splitting (24) gives: % 20.90/4.10 | % 20.90/4.10 | Case 1: % 20.90/4.10 | | % 20.90/4.10 | | (26) ~ (all_24_0 = 0) & apart_point_and_line(all_17_2, all_17_4) = % 20.90/4.10 | | all_24_0 % 20.90/4.10 | | % 20.90/4.10 | | ALPHA: (26) implies: % 20.90/4.10 | | (27) ~ (all_24_0 = 0) % 20.90/4.10 | | (28) apart_point_and_line(all_17_2, all_17_4) = all_24_0 % 20.90/4.10 | | % 20.90/4.10 | | BETA: splitting (21) gives: % 20.90/4.10 | | % 20.90/4.10 | | Case 1: % 20.90/4.10 | | | % 20.90/4.10 | | | (29) all_17_0 = 0 % 20.90/4.10 | | | % 20.90/4.10 | | | REDUCE: (10), (29) imply: % 20.90/4.10 | | | (30) $false % 20.90/4.10 | | | % 20.90/4.10 | | | CLOSE: (30) is inconsistent. % 20.90/4.10 | | | % 20.90/4.10 | | Case 2: % 20.90/4.10 | | | % 20.90/4.10 | | | (31) all_17_1 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ? % 20.90/4.10 | | | [v3: int] : ((v3 = 0 & apart_point_and_line(all_17_6, all_17_3) = % 20.90/4.10 | | | 0) | (v2 = 0 & apart_point_and_line(all_17_6, all_17_4) = 0) | % 20.90/4.10 | | | ( ~ (v1 = 0) & distinct_lines(all_17_3, all_17_4) = v1) | ( ~ % 20.90/4.10 | | | (v0 = 0) & distinct_points(all_17_6, all_17_6) = v0)) % 20.90/4.10 | | | % 20.90/4.10 | | | BETA: splitting (20) gives: % 20.90/4.10 | | | % 20.90/4.10 | | | Case 1: % 20.90/4.10 | | | | % 20.90/4.10 | | | | (32) all_17_0 = 0 % 20.90/4.10 | | | | % 20.90/4.10 | | | | REDUCE: (10), (32) imply: % 20.90/4.10 | | | | (33) $false % 20.90/4.10 | | | | % 20.90/4.10 | | | | CLOSE: (33) is inconsistent. % 20.90/4.10 | | | | % 20.90/4.10 | | | Case 2: % 20.90/4.10 | | | | % 20.90/4.10 | | | | (34) all_17_1 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 % 20.90/4.10 | | | | = 0 & apart_point_and_line(all_17_2, all_17_4) = 0) | (v1 = % 20.90/4.10 | | | | 0 & apart_point_and_line(all_17_2, all_17_3) = 0) | ( ~ (v0 % 20.90/4.10 | | | | = 0) & distinct_lines(all_17_3, all_17_4) = v0)) % 20.90/4.10 | | | | % 20.90/4.10 | | | | BETA: splitting (25) gives: % 20.90/4.10 | | | | % 20.90/4.10 | | | | Case 1: % 20.90/4.10 | | | | | % 20.90/4.10 | | | | | (35) ~ (all_25_0 = 0) & apart_point_and_line(all_17_2, all_17_3) = % 20.90/4.10 | | | | | all_25_0 % 20.90/4.10 | | | | | % 20.90/4.10 | | | | | ALPHA: (35) implies: % 20.90/4.10 | | | | | (36) ~ (all_25_0 = 0) % 20.90/4.10 | | | | | (37) apart_point_and_line(all_17_2, all_17_3) = all_25_0 % 20.90/4.10 | | | | | % 20.90/4.10 | | | | | BETA: splitting (34) gives: % 20.90/4.10 | | | | | % 20.90/4.10 | | | | | Case 1: % 20.90/4.10 | | | | | | % 20.90/4.10 | | | | | | (38) all_17_1 = 0 % 20.90/4.10 | | | | | | % 20.90/4.10 | | | | | | REDUCE: (9), (38) imply: % 20.90/4.10 | | | | | | (39) $false % 20.90/4.10 | | | | | | % 20.90/4.10 | | | | | | CLOSE: (39) is inconsistent. % 20.90/4.10 | | | | | | % 20.90/4.10 | | | | | Case 2: % 20.90/4.10 | | | | | | % 20.90/4.11 | | | | | | (40) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & % 20.90/4.11 | | | | | | apart_point_and_line(all_17_2, all_17_4) = 0) | (v1 = 0 % 20.90/4.11 | | | | | | & apart_point_and_line(all_17_2, all_17_3) = 0) | ( ~ % 20.90/4.11 | | | | | | (v0 = 0) & distinct_lines(all_17_3, all_17_4) = v0)) % 20.90/4.11 | | | | | | % 20.90/4.11 | | | | | | DELTA: instantiating (40) with fresh symbols all_113_0, all_113_1, % 20.90/4.11 | | | | | | all_113_2 gives: % 20.90/4.11 | | | | | | (41) (all_113_0 = 0 & apart_point_and_line(all_17_2, all_17_4) = % 20.90/4.11 | | | | | | 0) | (all_113_1 = 0 & apart_point_and_line(all_17_2, % 20.90/4.11 | | | | | | all_17_3) = 0) | ( ~ (all_113_2 = 0) & % 20.90/4.11 | | | | | | distinct_lines(all_17_3, all_17_4) = all_113_2) % 20.90/4.11 | | | | | | % 20.90/4.11 | | | | | | BETA: splitting (41) gives: % 20.90/4.11 | | | | | | % 20.90/4.11 | | | | | | Case 1: % 20.90/4.11 | | | | | | | % 20.90/4.11 | | | | | | | (42) all_113_0 = 0 & apart_point_and_line(all_17_2, all_17_4) = % 20.90/4.11 | | | | | | | 0 % 20.90/4.11 | | | | | | | % 20.90/4.11 | | | | | | | ALPHA: (42) implies: % 20.90/4.11 | | | | | | | (43) apart_point_and_line(all_17_2, all_17_4) = 0 % 20.90/4.11 | | | | | | | % 20.90/4.11 | | | | | | | GROUND_INST: instantiating (7) with 0, all_24_0, all_17_4, % 20.90/4.11 | | | | | | | all_17_2, simplifying with (28), (43) gives: % 20.90/4.11 | | | | | | | (44) all_24_0 = 0 % 20.90/4.11 | | | | | | | % 20.90/4.11 | | | | | | | REDUCE: (27), (44) imply: % 20.90/4.11 | | | | | | | (45) $false % 20.90/4.11 | | | | | | | % 20.90/4.11 | | | | | | | CLOSE: (45) is inconsistent. % 20.90/4.11 | | | | | | | % 20.90/4.11 | | | | | | Case 2: % 20.90/4.11 | | | | | | | % 20.90/4.11 | | | | | | | (46) (all_113_1 = 0 & apart_point_and_line(all_17_2, all_17_3) % 20.90/4.11 | | | | | | | = 0) | ( ~ (all_113_2 = 0) & distinct_lines(all_17_3, % 20.90/4.11 | | | | | | | all_17_4) = all_113_2) % 20.90/4.11 | | | | | | | % 20.90/4.11 | | | | | | | BETA: splitting (46) gives: % 20.90/4.11 | | | | | | | % 20.90/4.11 | | | | | | | Case 1: % 20.90/4.11 | | | | | | | | % 20.90/4.11 | | | | | | | | (47) all_113_1 = 0 & apart_point_and_line(all_17_2, all_17_3) % 20.90/4.11 | | | | | | | | = 0 % 20.90/4.11 | | | | | | | | % 20.90/4.11 | | | | | | | | ALPHA: (47) implies: % 20.90/4.11 | | | | | | | | (48) apart_point_and_line(all_17_2, all_17_3) = 0 % 20.90/4.11 | | | | | | | | % 20.90/4.11 | | | | | | | | GROUND_INST: instantiating (7) with 0, all_25_0, all_17_3, % 20.90/4.11 | | | | | | | | all_17_2, simplifying with (37), (48) gives: % 20.90/4.11 | | | | | | | | (49) all_25_0 = 0 % 20.90/4.11 | | | | | | | | % 20.90/4.11 | | | | | | | | REDUCE: (36), (49) imply: % 20.90/4.11 | | | | | | | | (50) $false % 20.90/4.11 | | | | | | | | % 20.90/4.11 | | | | | | | | CLOSE: (50) is inconsistent. % 20.90/4.11 | | | | | | | | % 20.90/4.11 | | | | | | | Case 2: % 20.90/4.11 | | | | | | | | % 20.90/4.11 | | | | | | | | (51) ~ (all_113_2 = 0) & distinct_lines(all_17_3, all_17_4) % 20.90/4.11 | | | | | | | | = all_113_2 % 20.90/4.11 | | | | | | | | % 20.90/4.11 | | | | | | | | ALPHA: (51) implies: % 20.90/4.11 | | | | | | | | (52) ~ (all_113_2 = 0) % 20.90/4.11 | | | | | | | | (53) distinct_lines(all_17_3, all_17_4) = all_113_2 % 20.90/4.11 | | | | | | | | % 20.90/4.11 | | | | | | | | BETA: splitting (31) gives: % 20.90/4.11 | | | | | | | | % 20.90/4.11 | | | | | | | | Case 1: % 20.90/4.11 | | | | | | | | | % 20.90/4.11 | | | | | | | | | (54) all_17_1 = 0 % 20.90/4.11 | | | | | | | | | % 20.90/4.11 | | | | | | | | | REDUCE: (9), (54) imply: % 20.90/4.11 | | | | | | | | | (55) $false % 20.90/4.11 | | | | | | | | | % 20.90/4.11 | | | | | | | | | CLOSE: (55) is inconsistent. % 20.90/4.11 | | | | | | | | | % 20.90/4.11 | | | | | | | | Case 2: % 20.90/4.11 | | | | | | | | | % 20.90/4.11 | | | | | | | | | % 20.90/4.11 | | | | | | | | | GROUND_INST: instantiating (5) with all_17_4, all_17_3, % 20.90/4.11 | | | | | | | | | all_17_4, all_113_2, simplifying with (12), (13), % 20.90/4.11 | | | | | | | | | (16), (53) gives: % 20.90/4.11 | | | | | | | | | (56) all_113_2 = 0 | convergent_lines(all_17_4, all_17_4) = % 20.90/4.11 | | | | | | | | | 0 % 20.90/4.11 | | | | | | | | | % 20.90/4.11 | | | | | | | | | BETA: splitting (56) gives: % 20.90/4.11 | | | | | | | | | % 20.90/4.11 | | | | | | | | | Case 1: % 20.90/4.11 | | | | | | | | | | % 20.90/4.11 | | | | | | | | | | (57) convergent_lines(all_17_4, all_17_4) = 0 % 20.90/4.11 | | | | | | | | | | % 20.90/4.11 | | | | | | | | | | GROUND_INST: instantiating (apart3) with all_17_4, simplifying % 20.90/4.11 | | | | | | | | | | with (12), (57) gives: % 20.90/4.11 | | | | | | | | | | (58) $false % 20.90/4.11 | | | | | | | | | | % 20.90/4.11 | | | | | | | | | | CLOSE: (58) is inconsistent. % 20.90/4.11 | | | | | | | | | | % 20.90/4.11 | | | | | | | | | Case 2: % 20.90/4.11 | | | | | | | | | | % 20.90/4.11 | | | | | | | | | | (59) all_113_2 = 0 % 20.90/4.11 | | | | | | | | | | % 20.90/4.11 | | | | | | | | | | REDUCE: (52), (59) imply: % 20.90/4.11 | | | | | | | | | | (60) $false % 20.90/4.11 | | | | | | | | | | % 20.90/4.11 | | | | | | | | | | CLOSE: (60) is inconsistent. % 20.90/4.11 | | | | | | | | | | % 20.90/4.11 | | | | | | | | | End of split % 20.90/4.11 | | | | | | | | | % 20.90/4.11 | | | | | | | | End of split % 20.90/4.11 | | | | | | | | % 20.90/4.11 | | | | | | | End of split % 20.90/4.11 | | | | | | | % 20.90/4.11 | | | | | | End of split % 20.90/4.11 | | | | | | % 20.90/4.11 | | | | | End of split % 20.90/4.11 | | | | | % 20.90/4.11 | | | | Case 2: % 20.90/4.11 | | | | | % 20.90/4.11 | | | | | (61) ~ (all_25_1 = 0) & convergent_lines(all_17_4, all_17_3) = % 20.90/4.11 | | | | | all_25_1 % 20.90/4.11 | | | | | % 20.90/4.11 | | | | | ALPHA: (61) implies: % 20.90/4.11 | | | | | (62) ~ (all_25_1 = 0) % 20.90/4.11 | | | | | (63) convergent_lines(all_17_4, all_17_3) = all_25_1 % 20.90/4.11 | | | | | % 20.90/4.11 | | | | | GROUND_INST: instantiating (6) with 0, all_25_1, all_17_3, all_17_4, % 20.90/4.11 | | | | | simplifying with (16), (63) gives: % 20.90/4.11 | | | | | (64) all_25_1 = 0 % 20.90/4.12 | | | | | % 20.90/4.12 | | | | | REDUCE: (62), (64) imply: % 20.90/4.12 | | | | | (65) $false % 20.90/4.12 | | | | | % 20.90/4.12 | | | | | CLOSE: (65) is inconsistent. % 20.90/4.12 | | | | | % 20.90/4.12 | | | | End of split % 20.90/4.12 | | | | % 20.90/4.12 | | | End of split % 20.90/4.12 | | | % 20.90/4.12 | | End of split % 20.90/4.12 | | % 20.90/4.12 | Case 2: % 20.90/4.12 | | % 20.90/4.12 | | (66) ~ (all_24_1 = 0) & convergent_lines(all_17_4, all_17_3) = all_24_1 % 20.90/4.12 | | % 20.90/4.12 | | ALPHA: (66) implies: % 20.90/4.12 | | (67) ~ (all_24_1 = 0) % 20.90/4.12 | | (68) convergent_lines(all_17_4, all_17_3) = all_24_1 % 20.90/4.12 | | % 20.90/4.12 | | GROUND_INST: instantiating (6) with 0, all_24_1, all_17_3, all_17_4, % 20.90/4.12 | | simplifying with (16), (68) gives: % 20.90/4.12 | | (69) all_24_1 = 0 % 20.90/4.12 | | % 20.90/4.12 | | REDUCE: (67), (69) imply: % 20.90/4.12 | | (70) $false % 20.90/4.12 | | % 20.90/4.12 | | CLOSE: (70) is inconsistent. % 20.90/4.12 | | % 20.90/4.12 | End of split % 20.90/4.12 | % 20.90/4.12 End of proof % 20.90/4.12 % SZS output end Proof for theBenchmark % 20.90/4.12 % 20.90/4.12 3494ms %------------------------------------------------------------------------------