%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO225+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 : 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 23:22:33 EDT 2023 % Result : Theorem 6.23s 1.70s % Output : Proof 10.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO225+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.33 % Computer : n008.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.33 % CPULimit : 300 % 0.14/0.33 % WCLimit : 300 % 0.14/0.33 % DateTime : Tue Aug 29 21:37:47 EDT 2023 % 0.14/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.66/1.03 Prover 1: Preprocessing ... % 2.66/1.03 Prover 4: Preprocessing ... % 2.66/1.06 Prover 5: Preprocessing ... % 2.66/1.06 Prover 0: Preprocessing ... % 2.66/1.06 Prover 3: Preprocessing ... % 2.66/1.06 Prover 6: Preprocessing ... % 2.66/1.07 Prover 2: Preprocessing ... % 4.79/1.33 Prover 2: Proving ... % 4.79/1.35 Prover 3: Constructing countermodel ... % 4.79/1.35 Prover 5: Proving ... % 4.79/1.35 Prover 1: Constructing countermodel ... % 4.79/1.40 Prover 6: Proving ... % 5.53/1.43 Prover 3: gave up % 5.53/1.43 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.53/1.44 Prover 1: gave up % 5.53/1.44 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.53/1.48 Prover 8: Preprocessing ... % 5.53/1.48 Prover 7: Preprocessing ... % 5.53/1.52 Prover 4: Constructing countermodel ... % 5.53/1.53 Prover 0: Proving ... % 5.53/1.55 Prover 7: Warning: ignoring some quantifiers % 5.53/1.58 Prover 7: Constructing countermodel ... % 6.23/1.63 Prover 8: Warning: ignoring some quantifiers % 6.23/1.64 Prover 8: Constructing countermodel ... % 6.23/1.66 Prover 7: gave up % 6.23/1.66 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 6.23/1.68 Prover 9: Preprocessing ... % 6.23/1.70 Prover 0: proved (1083ms) % 6.23/1.70 % 6.23/1.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.23/1.70 % 7.62/1.71 Prover 6: stopped % 7.62/1.71 Prover 5: stopped % 7.62/1.72 Prover 2: stopped % 7.62/1.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.62/1.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.62/1.72 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.62/1.72 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 7.62/1.72 Prover 8: gave up % 7.62/1.74 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 7.62/1.77 Prover 10: Preprocessing ... % 7.62/1.77 Prover 16: Preprocessing ... % 7.62/1.78 Prover 13: Preprocessing ... % 7.62/1.78 Prover 19: Preprocessing ... % 7.62/1.80 Prover 11: Preprocessing ... % 7.62/1.80 Prover 10: Warning: ignoring some quantifiers % 8.35/1.81 Prover 10: Constructing countermodel ... % 8.35/1.83 Prover 16: Warning: ignoring some quantifiers % 8.35/1.84 Prover 10: gave up % 8.35/1.84 Prover 16: Constructing countermodel ... % 8.35/1.84 Prover 13: Warning: ignoring some quantifiers % 8.35/1.86 Prover 19: Warning: ignoring some quantifiers % 8.35/1.86 Prover 13: Constructing countermodel ... % 8.35/1.87 Prover 9: Constructing countermodel ... % 8.35/1.87 Prover 19: Constructing countermodel ... % 8.35/1.87 Prover 9: stopped % 9.04/1.91 Prover 19: gave up % 9.04/1.93 Prover 4: Found proof (size 69) % 9.04/1.93 Prover 4: proved (1305ms) % 9.04/1.93 Prover 13: stopped % 9.04/1.93 Prover 16: stopped % 9.04/1.96 Prover 11: Constructing countermodel ... % 9.04/1.97 Prover 11: stopped % 9.04/1.97 % 9.04/1.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.04/1.97 % 9.49/1.99 % SZS output start Proof for theBenchmark % 9.49/1.99 Assumptions after simplification: % 9.49/1.99 --------------------------------- % 9.49/1.99 % 9.49/1.99 (ci1) % 9.49/2.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 9.49/2.02 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 9.49/2.02 (apart_point_and_line(v0, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 % 9.49/2.02 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 9.49/2.02 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 9.49/2.02 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 9.49/2.02 apart_point_and_line(v0, v2) = v3 & $i(v2))) % 9.49/2.02 % 9.49/2.02 (ci2) % 9.49/2.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 9.49/2.03 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 9.49/2.03 (apart_point_and_line(v1, v2) = v4 & distinct_points(v0, v1) = v3 & ( ~ (v4 % 9.49/2.03 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 9.49/2.03 (distinct_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 9.49/2.03 [v3: int] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & % 9.49/2.03 apart_point_and_line(v1, v2) = v3 & $i(v2))) % 9.49/2.03 % 9.49/2.03 (con) % 9.49/2.03 ? [v0: $i] : ? [v1: $i] : (point(v1) = 0 & point(v0) = 0 & % 9.49/2.03 distinct_points(v0, v1) = 0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: int] : % 9.49/2.03 (v3 = 0 | ~ (line(v2) = v3) | ~ $i(v2)) & ! [v2: $i] : ! [v3: int] : (v3 % 9.49/2.03 = 0 | ~ (apart_point_and_line(v1, v2) = v3) | ~ $i(v2) | % 9.49/2.03 apart_point_and_line(v0, v2) = 0) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | % 9.49/2.03 ~ (apart_point_and_line(v0, v2) = v3) | ~ $i(v2) | % 9.49/2.03 apart_point_and_line(v1, v2) = 0)) % 9.49/2.03 % 9.49/2.03 (con1) % 9.49/2.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 9.49/2.04 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: % 9.49/2.04 any] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & % 9.49/2.04 distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | % 9.49/2.04 v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = % 9.49/2.04 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : % 9.49/2.04 ? [v5: any] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & % 9.49/2.04 line_connecting(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v5 = % 9.49/2.04 0))) % 9.49/2.04 % 9.49/2.04 (cu1) % 9.49/2.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 9.49/2.05 int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ % 9.49/2.05 (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 9.49/2.05 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 9.49/2.05 ? [v8: any] : (apart_point_and_line(v0, v3) = v8 & apart_point_and_line(v0, % 9.49/2.05 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 9.49/2.05 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 9.49/2.05 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = % 9.49/2.05 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) % 9.49/2.05 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 9.49/2.05 [v7: any] : ? [v8: any] : (apart_point_and_line(v1, v2) = v8 & % 9.49/2.05 apart_point_and_line(v0, v2) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v6 % 9.49/2.05 = 0) | v8 = 0 | v7 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 9.49/2.05 ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 9.49/2.05 (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 9.49/2.05 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 9.49/2.05 any] : ? [v8: any] : ? [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 9.49/2.05 apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 9.49/2.05 distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = % 9.49/2.05 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 9.49/2.05 int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = % 9.49/2.05 v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 9.49/2.05 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: % 9.49/2.05 any] : (apart_point_and_line(v1, v3) = v9 & apart_point_and_line(v0, v2) = % 9.49/2.05 v8 & distinct_lines(v2, v3) = v7 & distinct_points(v0, v1) = v6 & ( ~ (v7 % 9.49/2.05 = 0) | ~ (v6 = 0) | v9 = 0 | v8 = 0))) & ! [v0: $i] : ! [v1: $i] : % 9.49/2.05 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] : (v5 = 0 | v4 = 0 | ~ % 9.49/2.05 (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) % 9.49/2.05 | ~ (distinct_lines(v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 9.49/2.05 $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 9.49/2.05 (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v0, v3) = v7 & % 9.49/2.05 distinct_points(v0, v1) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) & ! [v0: % 9.49/2.05 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: int] % 9.49/2.05 : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ % 9.49/2.05 (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ~ % 9.49/2.05 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 9.49/2.05 ? [v8: any] : (apart_point_and_line(v1, v3) = v8 & apart_point_and_line(v1, % 9.49/2.05 v2) = v7 & distinct_lines(v2, v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = % 9.49/2.05 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 9.49/2.05 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) % 9.49/2.05 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 9.49/2.05 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 & % 9.49/2.05 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & % 9.49/2.05 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 9.49/2.05 % 9.49/2.05 (function-axioms) % 9.49/2.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.49/2.06 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 9.49/2.06 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 9.49/2.06 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 9.49/2.06 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 9.49/2.06 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 9.49/2.06 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 9.49/2.06 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 9.49/2.06 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.49/2.06 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.49/2.06 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 9.49/2.06 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.49/2.06 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 9.49/2.06 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.49/2.06 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.49/2.06 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 9.49/2.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.49/2.06 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 9.49/2.06 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.49/2.06 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 9.49/2.06 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 9.49/2.06 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 9.49/2.06 % 9.49/2.06 Further assumptions not needed in the proof: % 9.49/2.06 -------------------------------------------- % 9.49/2.06 apart1, apart2, apart3, apart4, apart5, ax6, ceq1, ceq2, ceq3, ci3, ci4, int1, % 9.49/2.06 orth1, par1 % 9.49/2.06 % 9.49/2.06 Those formulas are unsatisfiable: % 9.49/2.06 --------------------------------- % 9.49/2.06 % 9.49/2.06 Begin of proof % 9.49/2.06 | % 9.49/2.06 | ALPHA: (ci1) implies: % 9.49/2.06 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 9.49/2.06 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 9.49/2.06 | line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3 & % 9.49/2.06 | $i(v2))) % 9.49/2.06 | % 9.49/2.06 | ALPHA: (ci2) implies: % 9.49/2.06 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 9.49/2.06 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 9.49/2.06 | line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3 & % 9.49/2.06 | $i(v2))) % 9.49/2.06 | % 9.49/2.06 | ALPHA: (cu1) implies: % 9.49/2.06 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 9.49/2.06 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 9.49/2.06 | | ~ (apart_point_and_line(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 9.49/2.06 | $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? % 9.49/2.06 | [v9: any] : (apart_point_and_line(v1, v2) = v9 & % 9.49/2.06 | apart_point_and_line(v0, v3) = v8 & distinct_lines(v2, v3) = v7 & % 9.49/2.06 | distinct_points(v0, v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = 0 % 9.49/2.06 | | v8 = 0))) % 9.49/2.06 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 9.49/2.06 | ! [v5: int] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) % 9.49/2.06 | | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, % 9.49/2.06 | v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 9.49/2.07 | [v6: any] : ? [v7: any] : ? [v8: any] : (apart_point_and_line(v0, % 9.49/2.07 | v3) = v8 & apart_point_and_line(v0, v2) = v7 & distinct_lines(v2, % 9.49/2.07 | v3) = v6 & ( ~ (v6 = 0) | v8 = 0 | v7 = 0))) % 9.49/2.07 | % 9.49/2.07 | ALPHA: (con1) implies: % 9.49/2.07 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_points(v0, v1) = 0) | ~ % 9.49/2.07 | $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? % 9.49/2.07 | [v5: any] : (point(v1) = v3 & point(v0) = v2 & line(v4) = v5 & % 9.49/2.07 | line_connecting(v0, v1) = v4 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) % 9.49/2.07 | | v5 = 0))) % 9.49/2.07 | % 9.49/2.07 | ALPHA: (function-axioms) implies: % 9.49/2.07 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.49/2.07 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 9.49/2.07 | (apart_point_and_line(v3, v2) = v0)) % 9.49/2.07 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.49/2.07 | (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 9.49/2.07 | % 9.49/2.07 | DELTA: instantiating (con) with fresh symbols all_21_0, all_21_1 gives: % 9.49/2.07 | (8) point(all_21_0) = 0 & point(all_21_1) = 0 & distinct_points(all_21_1, % 9.49/2.07 | all_21_0) = 0 & $i(all_21_0) & $i(all_21_1) & ! [v0: $i] : ! [v1: % 9.49/2.07 | int] : (v1 = 0 | ~ (line(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ! % 9.49/2.07 | [v1: int] : (v1 = 0 | ~ (apart_point_and_line(all_21_0, v0) = v1) | ~ % 9.49/2.07 | $i(v0) | apart_point_and_line(all_21_1, v0) = 0) & ! [v0: $i] : ! % 9.49/2.07 | [v1: int] : (v1 = 0 | ~ (apart_point_and_line(all_21_1, v0) = v1) | ~ % 9.49/2.07 | $i(v0) | apart_point_and_line(all_21_0, v0) = 0) % 9.49/2.07 | % 9.49/2.07 | ALPHA: (8) implies: % 9.49/2.07 | (9) $i(all_21_1) % 9.49/2.07 | (10) $i(all_21_0) % 9.49/2.07 | (11) distinct_points(all_21_1, all_21_0) = 0 % 9.49/2.07 | (12) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 9.49/2.07 | (apart_point_and_line(all_21_0, v0) = v1) | ~ $i(v0) | % 9.49/2.07 | apart_point_and_line(all_21_1, v0) = 0) % 9.49/2.07 | % 9.49/2.07 | GROUND_INST: instantiating (5) with all_21_1, all_21_0, simplifying with (9), % 9.49/2.07 | (10), (11) gives: % 9.49/2.07 | (13) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : % 9.49/2.07 | (point(all_21_0) = v1 & point(all_21_1) = v0 & line(v2) = v3 & % 9.49/2.07 | line_connecting(all_21_1, all_21_0) = v2 & $i(v2) & ( ~ (v1 = 0) | % 9.49/2.07 | ~ (v0 = 0) | v3 = 0)) % 9.49/2.07 | % 9.49/2.07 | GROUND_INST: instantiating (2) with all_21_1, all_21_0, simplifying with (9), % 9.49/2.07 | (10), (11) gives: % 9.49/2.08 | (14) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_21_1, % 9.49/2.08 | all_21_0) = v0 & apart_point_and_line(all_21_0, v0) = v1 & $i(v0)) % 9.49/2.08 | % 9.49/2.08 | GROUND_INST: instantiating (1) with all_21_1, all_21_0, simplifying with (9), % 9.49/2.08 | (10), (11) gives: % 9.49/2.08 | (15) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & line_connecting(all_21_1, % 9.49/2.08 | all_21_0) = v0 & apart_point_and_line(all_21_1, v0) = v1 & $i(v0)) % 9.49/2.08 | % 9.49/2.08 | DELTA: instantiating (15) with fresh symbols all_29_0, all_29_1 gives: % 9.49/2.08 | (16) ~ (all_29_0 = 0) & line_connecting(all_21_1, all_21_0) = all_29_1 & % 9.49/2.08 | apart_point_and_line(all_21_1, all_29_1) = all_29_0 & $i(all_29_1) % 9.49/2.08 | % 9.49/2.08 | ALPHA: (16) implies: % 9.49/2.08 | (17) ~ (all_29_0 = 0) % 9.49/2.08 | (18) apart_point_and_line(all_21_1, all_29_1) = all_29_0 % 9.49/2.08 | (19) line_connecting(all_21_1, all_21_0) = all_29_1 % 9.49/2.08 | % 9.49/2.08 | DELTA: instantiating (14) with fresh symbols all_31_0, all_31_1 gives: % 9.49/2.08 | (20) ~ (all_31_0 = 0) & line_connecting(all_21_1, all_21_0) = all_31_1 & % 9.49/2.08 | apart_point_and_line(all_21_0, all_31_1) = all_31_0 & $i(all_31_1) % 9.49/2.08 | % 9.49/2.08 | ALPHA: (20) implies: % 9.49/2.08 | (21) ~ (all_31_0 = 0) % 9.49/2.08 | (22) $i(all_31_1) % 9.49/2.08 | (23) apart_point_and_line(all_21_0, all_31_1) = all_31_0 % 9.49/2.08 | (24) line_connecting(all_21_1, all_21_0) = all_31_1 % 9.49/2.08 | % 9.49/2.08 | DELTA: instantiating (13) with fresh symbols all_33_0, all_33_1, all_33_2, % 9.49/2.08 | all_33_3 gives: % 9.49/2.08 | (25) point(all_21_0) = all_33_2 & point(all_21_1) = all_33_3 & % 9.49/2.08 | line(all_33_1) = all_33_0 & line_connecting(all_21_1, all_21_0) = % 9.49/2.08 | all_33_1 & $i(all_33_1) & ( ~ (all_33_2 = 0) | ~ (all_33_3 = 0) | % 9.49/2.08 | all_33_0 = 0) % 9.49/2.08 | % 9.49/2.08 | ALPHA: (25) implies: % 9.49/2.08 | (26) line_connecting(all_21_1, all_21_0) = all_33_1 % 9.49/2.08 | % 9.49/2.08 | GROUND_INST: instantiating (7) with all_31_1, all_33_1, all_21_0, all_21_1, % 9.49/2.08 | simplifying with (24), (26) gives: % 9.49/2.08 | (27) all_33_1 = all_31_1 % 9.49/2.08 | % 9.49/2.08 | GROUND_INST: instantiating (7) with all_29_1, all_33_1, all_21_0, all_21_1, % 9.49/2.08 | simplifying with (19), (26) gives: % 9.49/2.08 | (28) all_33_1 = all_29_1 % 9.49/2.08 | % 9.49/2.08 | COMBINE_EQS: (27), (28) imply: % 9.49/2.08 | (29) all_31_1 = all_29_1 % 9.49/2.08 | % 9.49/2.08 | REDUCE: (23), (29) imply: % 9.49/2.08 | (30) apart_point_and_line(all_21_0, all_29_1) = all_31_0 % 9.49/2.08 | % 9.49/2.08 | REDUCE: (22), (29) imply: % 9.49/2.08 | (31) $i(all_29_1) % 9.49/2.08 | % 9.49/2.08 | GROUND_INST: instantiating (3) with all_21_1, all_21_1, all_29_1, all_29_1, % 9.49/2.08 | all_29_0, all_29_0, simplifying with (9), (18), (31) gives: % 9.49/2.08 | (32) all_29_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 9.49/2.08 | any] : (apart_point_and_line(all_21_1, all_29_1) = v3 & % 9.49/2.08 | apart_point_and_line(all_21_1, all_29_1) = v2 & % 9.49/2.08 | distinct_lines(all_29_1, all_29_1) = v1 & distinct_points(all_21_1, % 9.49/2.08 | all_21_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 9.49/2.08 | % 9.49/2.08 | GROUND_INST: instantiating (4) with all_21_1, all_21_0, all_29_1, all_29_1, % 9.49/2.08 | all_31_0, all_31_0, simplifying with (9), (10), (11), (30), (31) % 9.49/2.08 | gives: % 9.49/2.09 | (33) all_31_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 9.49/2.09 | (apart_point_and_line(all_21_1, all_29_1) = v2 & % 9.49/2.09 | apart_point_and_line(all_21_1, all_29_1) = v1 & % 9.49/2.09 | distinct_lines(all_29_1, all_29_1) = v0 & ( ~ (v0 = 0) | v2 = 0 | v1 % 9.49/2.09 | = 0)) % 9.49/2.09 | % 9.49/2.09 | GROUND_INST: instantiating (3) with all_21_0, all_21_1, all_29_1, all_29_1, % 9.49/2.09 | all_31_0, all_29_0, simplifying with (9), (10), (18), (30), (31) % 9.49/2.09 | gives: % 9.49/2.09 | (34) all_31_0 = 0 | all_29_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: % 9.49/2.09 | any] : ? [v3: any] : (apart_point_and_line(all_21_0, all_29_1) = v2 % 9.49/2.09 | & apart_point_and_line(all_21_1, all_29_1) = v3 & % 9.49/2.09 | distinct_lines(all_29_1, all_29_1) = v1 & distinct_points(all_21_0, % 9.49/2.09 | all_21_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 9.49/2.09 | % 9.49/2.09 | GROUND_INST: instantiating (12) with all_29_1, all_31_0, simplifying with % 9.49/2.09 | (30), (31) gives: % 9.49/2.09 | (35) all_31_0 = 0 | apart_point_and_line(all_21_1, all_29_1) = 0 % 9.49/2.09 | % 9.49/2.09 | BETA: splitting (35) gives: % 9.49/2.09 | % 9.98/2.09 | Case 1: % 9.98/2.09 | | % 9.98/2.09 | | (36) apart_point_and_line(all_21_1, all_29_1) = 0 % 9.98/2.09 | | % 9.98/2.09 | | BETA: splitting (33) gives: % 9.98/2.09 | | % 9.98/2.09 | | Case 1: % 9.98/2.09 | | | % 9.98/2.09 | | | (37) all_31_0 = 0 % 9.98/2.09 | | | % 9.98/2.09 | | | REDUCE: (21), (37) imply: % 9.98/2.09 | | | (38) $false % 9.98/2.09 | | | % 9.98/2.09 | | | CLOSE: (38) is inconsistent. % 9.98/2.09 | | | % 9.98/2.09 | | Case 2: % 9.98/2.09 | | | % 9.98/2.09 | | | (39) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 9.98/2.09 | | | (apart_point_and_line(all_21_1, all_29_1) = v2 & % 9.98/2.09 | | | apart_point_and_line(all_21_1, all_29_1) = v1 & % 9.98/2.09 | | | distinct_lines(all_29_1, all_29_1) = v0 & ( ~ (v0 = 0) | v2 = 0 % 9.98/2.09 | | | | v1 = 0)) % 9.98/2.09 | | | % 9.98/2.09 | | | DELTA: instantiating (39) with fresh symbols all_67_0, all_67_1, all_67_2 % 9.98/2.09 | | | gives: % 9.98/2.09 | | | (40) apart_point_and_line(all_21_1, all_29_1) = all_67_0 & % 9.98/2.09 | | | apart_point_and_line(all_21_1, all_29_1) = all_67_1 & % 9.98/2.09 | | | distinct_lines(all_29_1, all_29_1) = all_67_2 & ( ~ (all_67_2 = 0) % 9.98/2.09 | | | | all_67_0 = 0 | all_67_1 = 0) % 9.98/2.09 | | | % 9.98/2.09 | | | ALPHA: (40) implies: % 9.98/2.09 | | | (41) apart_point_and_line(all_21_1, all_29_1) = all_67_1 % 9.98/2.09 | | | (42) apart_point_and_line(all_21_1, all_29_1) = all_67_0 % 9.98/2.09 | | | % 9.98/2.09 | | | BETA: splitting (32) gives: % 9.98/2.09 | | | % 9.98/2.09 | | | Case 1: % 9.98/2.09 | | | | % 9.98/2.09 | | | | (43) all_29_0 = 0 % 9.98/2.09 | | | | % 9.98/2.09 | | | | REDUCE: (17), (43) imply: % 9.98/2.09 | | | | (44) $false % 9.98/2.09 | | | | % 9.98/2.09 | | | | CLOSE: (44) is inconsistent. % 9.98/2.09 | | | | % 9.98/2.09 | | | Case 2: % 9.98/2.09 | | | | % 9.98/2.09 | | | | (45) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 9.98/2.09 | | | | (apart_point_and_line(all_21_1, all_29_1) = v3 & % 9.98/2.10 | | | | apart_point_and_line(all_21_1, all_29_1) = v2 & % 9.98/2.10 | | | | distinct_lines(all_29_1, all_29_1) = v1 & % 9.98/2.10 | | | | distinct_points(all_21_1, all_21_1) = v0 & ( ~ (v1 = 0) | ~ % 9.98/2.10 | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 9.98/2.10 | | | | % 9.98/2.10 | | | | DELTA: instantiating (45) with fresh symbols all_77_0, all_77_1, % 9.98/2.10 | | | | all_77_2, all_77_3 gives: % 9.98/2.10 | | | | (46) apart_point_and_line(all_21_1, all_29_1) = all_77_0 & % 9.98/2.10 | | | | apart_point_and_line(all_21_1, all_29_1) = all_77_1 & % 9.98/2.10 | | | | distinct_lines(all_29_1, all_29_1) = all_77_2 & % 9.98/2.10 | | | | distinct_points(all_21_1, all_21_1) = all_77_3 & ( ~ (all_77_2 = % 9.98/2.10 | | | | 0) | ~ (all_77_3 = 0) | all_77_0 = 0 | all_77_1 = 0) % 9.98/2.10 | | | | % 9.98/2.10 | | | | ALPHA: (46) implies: % 9.98/2.10 | | | | (47) apart_point_and_line(all_21_1, all_29_1) = all_77_1 % 9.98/2.10 | | | | (48) apart_point_and_line(all_21_1, all_29_1) = all_77_0 % 9.98/2.10 | | | | % 9.98/2.10 | | | | BETA: splitting (34) gives: % 9.98/2.10 | | | | % 9.98/2.10 | | | | Case 1: % 9.98/2.10 | | | | | % 9.98/2.10 | | | | | (49) all_31_0 = 0 % 9.98/2.10 | | | | | % 9.98/2.10 | | | | | REDUCE: (21), (49) imply: % 9.98/2.10 | | | | | (50) $false % 9.98/2.10 | | | | | % 9.98/2.10 | | | | | CLOSE: (50) is inconsistent. % 9.98/2.10 | | | | | % 9.98/2.10 | | | | Case 2: % 9.98/2.10 | | | | | % 10.02/2.10 | | | | | (51) all_29_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 10.02/2.10 | | | | | [v3: any] : (apart_point_and_line(all_21_0, all_29_1) = v2 & % 10.02/2.10 | | | | | apart_point_and_line(all_21_1, all_29_1) = v3 & % 10.02/2.10 | | | | | distinct_lines(all_29_1, all_29_1) = v1 & % 10.02/2.10 | | | | | distinct_points(all_21_0, all_21_1) = v0 & ( ~ (v1 = 0) | ~ % 10.02/2.10 | | | | | (v0 = 0) | v3 = 0 | v2 = 0)) % 10.02/2.10 | | | | | % 10.02/2.10 | | | | | BETA: splitting (51) gives: % 10.02/2.10 | | | | | % 10.02/2.10 | | | | | Case 1: % 10.02/2.10 | | | | | | % 10.02/2.10 | | | | | | (52) all_29_0 = 0 % 10.02/2.10 | | | | | | % 10.02/2.10 | | | | | | REDUCE: (17), (52) imply: % 10.02/2.10 | | | | | | (53) $false % 10.02/2.10 | | | | | | % 10.02/2.10 | | | | | | CLOSE: (53) is inconsistent. % 10.02/2.10 | | | | | | % 10.02/2.10 | | | | | Case 2: % 10.02/2.10 | | | | | | % 10.02/2.10 | | | | | | (54) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 10.02/2.10 | | | | | | (apart_point_and_line(all_21_0, all_29_1) = v2 & % 10.02/2.10 | | | | | | apart_point_and_line(all_21_1, all_29_1) = v3 & % 10.02/2.10 | | | | | | distinct_lines(all_29_1, all_29_1) = v1 & % 10.02/2.10 | | | | | | distinct_points(all_21_0, all_21_1) = v0 & ( ~ (v1 = 0) | % 10.02/2.10 | | | | | | ~ (v0 = 0) | v3 = 0 | v2 = 0)) % 10.02/2.10 | | | | | | % 10.02/2.10 | | | | | | DELTA: instantiating (54) with fresh symbols all_89_0, all_89_1, % 10.02/2.10 | | | | | | all_89_2, all_89_3 gives: % 10.02/2.10 | | | | | | (55) apart_point_and_line(all_21_0, all_29_1) = all_89_1 & % 10.02/2.10 | | | | | | apart_point_and_line(all_21_1, all_29_1) = all_89_0 & % 10.02/2.10 | | | | | | distinct_lines(all_29_1, all_29_1) = all_89_2 & % 10.02/2.10 | | | | | | distinct_points(all_21_0, all_21_1) = all_89_3 & ( ~ % 10.02/2.10 | | | | | | (all_89_2 = 0) | ~ (all_89_3 = 0) | all_89_0 = 0 | % 10.02/2.10 | | | | | | all_89_1 = 0) % 10.02/2.10 | | | | | | % 10.02/2.10 | | | | | | ALPHA: (55) implies: % 10.02/2.10 | | | | | | (56) apart_point_and_line(all_21_1, all_29_1) = all_89_0 % 10.02/2.10 | | | | | | % 10.02/2.10 | | | | | | GROUND_INST: instantiating (6) with all_29_0, all_77_1, all_29_1, % 10.02/2.10 | | | | | | all_21_1, simplifying with (18), (47) gives: % 10.02/2.10 | | | | | | (57) all_77_1 = all_29_0 % 10.02/2.10 | | | | | | % 10.02/2.10 | | | | | | GROUND_INST: instantiating (6) with 0, all_77_1, all_29_1, all_21_1, % 10.02/2.10 | | | | | | simplifying with (36), (47) gives: % 10.02/2.10 | | | | | | (58) all_77_1 = 0 % 10.02/2.10 | | | | | | % 10.02/2.10 | | | | | | GROUND_INST: instantiating (6) with all_77_1, all_77_0, all_29_1, % 10.02/2.10 | | | | | | all_21_1, simplifying with (47), (48) gives: % 10.02/2.10 | | | | | | (59) all_77_0 = all_77_1 % 10.02/2.10 | | | | | | % 10.02/2.10 | | | | | | GROUND_INST: instantiating (6) with all_67_0, all_77_0, all_29_1, % 10.02/2.10 | | | | | | all_21_1, simplifying with (42), (48) gives: % 10.02/2.10 | | | | | | (60) all_77_0 = all_67_0 % 10.02/2.10 | | | | | | % 10.02/2.10 | | | | | | GROUND_INST: instantiating (6) with all_77_1, all_89_0, all_29_1, % 10.02/2.10 | | | | | | all_21_1, simplifying with (47), (56) gives: % 10.02/2.10 | | | | | | (61) all_89_0 = all_77_1 % 10.02/2.10 | | | | | | % 10.02/2.10 | | | | | | GROUND_INST: instantiating (6) with all_67_1, all_89_0, all_29_1, % 10.02/2.10 | | | | | | all_21_1, simplifying with (41), (56) gives: % 10.02/2.10 | | | | | | (62) all_89_0 = all_67_1 % 10.02/2.10 | | | | | | % 10.02/2.10 | | | | | | COMBINE_EQS: (61), (62) imply: % 10.02/2.10 | | | | | | (63) all_77_1 = all_67_1 % 10.02/2.10 | | | | | | % 10.02/2.11 | | | | | | SIMP: (63) implies: % 10.02/2.11 | | | | | | (64) all_77_1 = all_67_1 % 10.02/2.11 | | | | | | % 10.02/2.11 | | | | | | COMBINE_EQS: (59), (60) imply: % 10.02/2.11 | | | | | | (65) all_77_1 = all_67_0 % 10.02/2.11 | | | | | | % 10.02/2.11 | | | | | | SIMP: (65) implies: % 10.02/2.11 | | | | | | (66) all_77_1 = all_67_0 % 10.06/2.11 | | | | | | % 10.06/2.11 | | | | | | COMBINE_EQS: (57), (66) imply: % 10.06/2.11 | | | | | | (67) all_67_0 = all_29_0 % 10.06/2.11 | | | | | | % 10.06/2.11 | | | | | | COMBINE_EQS: (58), (66) imply: % 10.06/2.11 | | | | | | (68) all_67_0 = 0 % 10.06/2.11 | | | | | | % 10.06/2.11 | | | | | | COMBINE_EQS: (64), (66) imply: % 10.06/2.11 | | | | | | (69) all_67_0 = all_67_1 % 10.06/2.11 | | | | | | % 10.06/2.11 | | | | | | COMBINE_EQS: (68), (69) imply: % 10.06/2.11 | | | | | | (70) all_67_1 = 0 % 10.06/2.11 | | | | | | % 10.06/2.11 | | | | | | COMBINE_EQS: (67), (69) imply: % 10.06/2.11 | | | | | | (71) all_67_1 = all_29_0 % 10.06/2.11 | | | | | | % 10.06/2.11 | | | | | | COMBINE_EQS: (70), (71) imply: % 10.06/2.11 | | | | | | (72) all_29_0 = 0 % 10.06/2.11 | | | | | | % 10.06/2.11 | | | | | | SIMP: (72) implies: % 10.06/2.11 | | | | | | (73) all_29_0 = 0 % 10.06/2.11 | | | | | | % 10.06/2.11 | | | | | | REDUCE: (17), (73) imply: % 10.06/2.11 | | | | | | (74) $false % 10.06/2.11 | | | | | | % 10.06/2.11 | | | | | | CLOSE: (74) is inconsistent. % 10.06/2.11 | | | | | | % 10.06/2.11 | | | | | End of split % 10.06/2.11 | | | | | % 10.06/2.11 | | | | End of split % 10.06/2.11 | | | | % 10.06/2.11 | | | End of split % 10.06/2.11 | | | % 10.06/2.11 | | End of split % 10.06/2.11 | | % 10.06/2.11 | Case 2: % 10.06/2.11 | | % 10.06/2.11 | | (75) all_31_0 = 0 % 10.06/2.11 | | % 10.06/2.11 | | REDUCE: (21), (75) imply: % 10.06/2.11 | | (76) $false % 10.06/2.11 | | % 10.06/2.11 | | CLOSE: (76) is inconsistent. % 10.06/2.11 | | % 10.06/2.11 | End of split % 10.06/2.11 | % 10.06/2.11 End of proof % 10.06/2.11 % SZS output end Proof for theBenchmark % 10.06/2.11 % 10.06/2.11 1511ms %------------------------------------------------------------------------------