%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO267+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 : n002.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 23:22:52 EDT 2023 % Result : Theorem 11.66s 2.33s % Output : Proof 14.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO267+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n002.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Tue Aug 29 22:33:35 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.44/1.18 Prover 1: Preprocessing ... % 3.44/1.18 Prover 4: Preprocessing ... % 3.66/1.22 Prover 6: Preprocessing ... % 3.66/1.22 Prover 3: Preprocessing ... % 3.66/1.22 Prover 2: Preprocessing ... % 3.66/1.22 Prover 5: Preprocessing ... % 3.66/1.22 Prover 0: Preprocessing ... % 6.60/1.70 Prover 5: Proving ... % 7.28/1.71 Prover 2: Proving ... % 7.28/1.76 Prover 6: Constructing countermodel ... % 7.28/1.77 Prover 1: Constructing countermodel ... % 7.81/1.79 Prover 3: Constructing countermodel ... % 8.41/1.88 Prover 3: gave up % 8.41/1.88 Prover 6: gave up % 8.46/1.90 Prover 1: gave up % 8.46/1.90 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.46/1.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.46/1.90 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 9.17/2.01 Prover 9: Preprocessing ... % 9.35/2.02 Prover 7: Preprocessing ... % 9.35/2.03 Prover 8: Preprocessing ... % 10.04/2.13 Prover 7: Warning: ignoring some quantifiers % 10.04/2.16 Prover 4: Constructing countermodel ... % 10.04/2.16 Prover 7: Constructing countermodel ... % 10.61/2.24 Prover 0: Proving ... % 11.66/2.33 Prover 0: proved (1695ms) % 11.66/2.33 % 11.66/2.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.66/2.33 % 11.66/2.33 Prover 2: stopped % 11.66/2.33 Prover 5: stopped % 11.66/2.33 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.66/2.33 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.66/2.33 Prover 8: Warning: ignoring some quantifiers % 11.66/2.33 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.66/2.35 Prover 8: Constructing countermodel ... % 11.66/2.36 Prover 7: gave up % 11.66/2.37 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 11.66/2.37 Prover 13: Preprocessing ... % 11.66/2.39 Prover 11: Preprocessing ... % 11.66/2.40 Prover 10: Preprocessing ... % 12.31/2.42 Prover 16: Preprocessing ... % 12.31/2.47 Prover 10: Warning: ignoring some quantifiers % 12.91/2.50 Prover 8: gave up % 12.91/2.50 Prover 4: Found proof (size 31) % 12.91/2.50 Prover 4: proved (1869ms) % 12.91/2.50 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 12.91/2.50 Prover 10: Constructing countermodel ... % 12.91/2.52 Prover 13: Warning: ignoring some quantifiers % 12.91/2.53 Prover 16: Warning: ignoring some quantifiers % 12.91/2.54 Prover 13: Constructing countermodel ... % 12.91/2.54 Prover 11: stopped % 12.91/2.55 Prover 19: Preprocessing ... % 12.91/2.55 Prover 13: stopped % 12.91/2.55 Prover 16: Constructing countermodel ... % 12.91/2.56 Prover 10: stopped % 12.91/2.57 Prover 16: stopped % 12.91/2.57 Prover 9: Constructing countermodel ... % 13.56/2.59 Prover 9: stopped % 13.90/2.67 Prover 19: Warning: ignoring some quantifiers % 14.03/2.68 Prover 19: Constructing countermodel ... % 14.06/2.69 Prover 19: stopped % 14.06/2.69 % 14.06/2.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.06/2.69 % 14.06/2.69 % SZS output start Proof for theBenchmark % 14.06/2.70 Assumptions after simplification: % 14.06/2.70 --------------------------------- % 14.06/2.70 % 14.06/2.70 (a1_defns) % 14.25/2.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 14.25/2.73 (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | ~ % 14.25/2.73 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & % 14.25/2.73 unequally_directed_opposite_lines(v0, v1) = v4)) & ! [v0: $i] : ! [v1: % 14.25/2.73 $i] : ! [v2: int] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) % 14.25/2.73 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) % 14.25/2.73 & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4 & $i(v3))) % 14.25/2.73 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (reverse_line(v1) = v2) | ~ % 14.25/2.73 (unequally_directed_lines(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | % 14.25/2.73 unequally_directed_opposite_lines(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : % 14.25/2.73 ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 14.25/2.73 ? [v2: $i] : (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0 & % 14.25/2.73 $i(v2))) % 14.25/2.73 % 14.25/2.73 (ax7_basics) % 14.25/2.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 14.25/2.75 any] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ % 14.25/2.75 (unequally_directed_lines(v1, v4) = v5) | ~ (unequally_directed_lines(v0, % 14.25/2.75 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 14.25/2.75 any] : ? [v8: any] : ? [v9: any] : (unequally_directed_lines(v1, v2) = % 14.25/2.75 v9 & unequally_directed_lines(v0, v4) = v8 & unequally_directed_lines(v0, % 14.25/2.75 v2) = v7 & unequally_directed_lines(v0, v1) = v6 & ( ~ (v6 = 0) | (v9 = % 14.25/2.75 0 & v5 = 0) | (v8 = 0 & v7 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 14.25/2.75 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (reverse_line(v2) = % 14.25/2.75 v4) | ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v4) = % 14.25/2.75 v5) | ~ (unequally_directed_lines(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | % 14.25/2.75 ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: any] : % 14.25/2.75 (unequally_directed_lines(v1, v4) = v9 & unequally_directed_lines(v1, v2) = % 14.25/2.75 v8 & unequally_directed_lines(v0, v2) = v7 & unequally_directed_lines(v0, % 14.25/2.75 v1) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v8 = 0) | (v7 = 0 & v5 = 0)))) & ! % 14.25/2.75 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: $i] : ! [v5: % 14.25/2.75 any] : ( ~ (reverse_line(v2) = v4) | ~ (unequally_directed_lines(v1, v4) = % 14.25/2.75 v5) | ~ (unequally_directed_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 14.25/2.75 ~ $i(v0) | ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: any] : ? % 14.25/2.75 [v10: any] : (reverse_line(v1) = v7 & unequally_directed_lines(v1, v2) = v10 % 14.25/2.75 & unequally_directed_lines(v0, v7) = v8 & unequally_directed_lines(v0, v4) % 14.25/2.75 = v9 & unequally_directed_lines(v0, v1) = v6 & $i(v7) & ( ~ (v8 = 0) | ~ % 14.25/2.75 (v6 = 0) | (v10 = 0 & v5 = 0) | (v9 = 0 & v3 = 0)))) & ! [v0: $i] : ! % 14.25/2.75 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ! [v5: any] : ( ~ % 14.25/2.75 (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v3) = v5) | ~ % 14.25/2.75 (unequally_directed_lines(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 14.25/2.75 | ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: any] : ? [v10: any] : % 14.25/2.75 (reverse_line(v1) = v7 & unequally_directed_lines(v1, v2) = v10 & % 14.25/2.75 unequally_directed_lines(v0, v7) = v8 & unequally_directed_lines(v0, v2) = % 14.25/2.75 v9 & unequally_directed_lines(v0, v1) = v6 & $i(v7) & ( ~ (v8 = 0) | ~ % 14.25/2.75 (v6 = 0) | (v10 = 0 & v5 = 0) | (v9 = 0 & v4 = 0)))) & ! [v0: $i] : ! % 14.25/2.75 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ! [v5: any] : ( ~ % 14.25/2.75 (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v2) = v5) | ~ % 14.25/2.75 (unequally_directed_lines(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 14.25/2.75 | ? [v6: any] : ? [v7: $i] : ? [v8: any] : ? [v9: any] : ? [v10: any] : % 14.25/2.75 (reverse_line(v1) = v7 & unequally_directed_lines(v1, v3) = v10 & % 14.25/2.75 unequally_directed_lines(v0, v7) = v8 & unequally_directed_lines(v0, v2) = % 14.25/2.75 v9 & unequally_directed_lines(v0, v1) = v6 & $i(v7) & ( ~ (v8 = 0) | ~ % 14.25/2.75 (v6 = 0) | (v10 = 0 & v5 = 0) | (v9 = 0 & v4 = 0)))) & ! [v0: $i] : ! % 14.25/2.75 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ (reverse_line(v2) = % 14.25/2.75 v3) | ~ (unequally_directed_lines(v1, v3) = v4) | ~ % 14.25/2.75 (unequally_directed_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 14.25/2.75 ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: any] : % 14.25/2.75 (reverse_line(v1) = v5 & unequally_directed_lines(v1, v2) = v9 & % 14.25/2.75 unequally_directed_lines(v0, v5) = v6 & unequally_directed_lines(v0, v3) = % 14.25/2.75 v8 & unequally_directed_lines(v0, v2) = v7 & $i(v5) & ( ~ (v6 = 0) | (v9 = % 14.25/2.75 0 & v4 = 0) | (v8 = 0 & v7 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 14.25/2.75 [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ (reverse_line(v2) = v3) | ~ % 14.25/2.75 (unequally_directed_lines(v0, v3) = v4) | ~ (unequally_directed_lines(v0, % 14.25/2.75 v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: % 14.25/2.75 any] : ? [v7: any] : ? [v8: any] : ? [v9: any] : (reverse_line(v1) = v5 % 14.25/2.75 & unequally_directed_lines(v1, v3) = v9 & unequally_directed_lines(v1, v2) % 14.25/2.75 = v8 & unequally_directed_lines(v0, v5) = v6 & % 14.25/2.75 unequally_directed_lines(v0, v2) = v7 & $i(v5) & ( ~ (v6 = 0) | (v9 = 0 & % 14.25/2.75 v8 = 0) | (v7 = 0 & v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 14.25/2.75 $i] : ! [v3: $i] : ! [v4: any] : ( ~ (reverse_line(v1) = v3) | ~ % 14.25/2.75 (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, % 14.25/2.75 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 14.25/2.75 any] : ? [v7: $i] : ? [v8: any] : ? [v9: any] : (reverse_line(v2) = v7 % 14.25/2.75 & unequally_directed_lines(v1, v7) = v9 & unequally_directed_lines(v0, v7) % 14.25/2.75 = v8 & unequally_directed_lines(v0, v2) = v6 & % 14.25/2.75 unequally_directed_lines(v0, v1) = v5 & $i(v7) & ( ~ (v5 = 0) | (v9 = 0 & % 14.25/2.75 v4 = 0) | (v8 = 0 & v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 14.25/2.75 $i] : ! [v3: $i] : ! [v4: any] : ( ~ (reverse_line(v1) = v3) | ~ % 14.25/2.75 (unequally_directed_lines(v0, v3) = 0) | ~ (unequally_directed_lines(v0, % 14.25/2.75 v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 14.25/2.75 $i] : ? [v7: any] : ? [v8: any] : ? [v9: any] : (reverse_line(v2) = v6 % 14.25/2.75 & unequally_directed_lines(v1, v6) = v9 & unequally_directed_lines(v1, v2) % 14.25/2.75 = v8 & unequally_directed_lines(v0, v6) = v7 & % 14.25/2.75 unequally_directed_lines(v0, v1) = v5 & $i(v6) & ( ~ (v5 = 0) | (v9 = 0 & % 14.25/2.75 v8 = 0) | (v7 = 0 & v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 14.25/2.75 $i] : ! [v3: any] : ! [v4: any] : ( ~ (unequally_directed_lines(v1, v2) = % 14.25/2.75 v4) | ~ (unequally_directed_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 14.25/2.75 ~ $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? % 14.25/2.75 [v9: any] : ? [v10: any] : (reverse_line(v2) = v8 & reverse_line(v1) = v6 & % 14.25/2.75 unequally_directed_lines(v1, v8) = v10 & unequally_directed_lines(v0, v8) % 14.25/2.75 = v9 & unequally_directed_lines(v0, v6) = v7 & % 14.25/2.75 unequally_directed_lines(v0, v1) = v5 & $i(v8) & $i(v6) & ( ~ (v7 = 0) | % 14.25/2.75 ~ (v5 = 0) | (v10 = 0 & v4 = 0) | (v9 = 0 & v3 = 0)))) & ! [v0: $i] : % 14.25/2.75 ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (unequally_directed_lines(v1, % 14.25/2.75 v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ~ $i(v2) | ~ % 14.25/2.75 $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: $i] % 14.25/2.75 : ? [v8: any] : ? [v9: any] : (reverse_line(v2) = v7 & reverse_line(v1) = % 14.25/2.75 v4 & unequally_directed_lines(v1, v7) = v9 & unequally_directed_lines(v0, % 14.25/2.75 v7) = v8 & unequally_directed_lines(v0, v4) = v5 & % 14.25/2.75 unequally_directed_lines(v0, v2) = v6 & $i(v7) & $i(v4) & ( ~ (v5 = 0) | % 14.25/2.75 (v9 = 0 & v3 = 0) | (v8 = 0 & v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : % 14.25/2.75 ! [v2: $i] : ! [v3: any] : ( ~ (unequally_directed_lines(v0, v2) = v3) | ~ % 14.25/2.75 (unequally_directed_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 14.25/2.75 ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: any] : ? % 14.25/2.75 [v9: any] : (reverse_line(v2) = v6 & reverse_line(v1) = v4 & % 14.25/2.75 unequally_directed_lines(v1, v6) = v9 & unequally_directed_lines(v1, v2) = % 14.25/2.75 v8 & unequally_directed_lines(v0, v6) = v7 & unequally_directed_lines(v0, % 14.25/2.75 v4) = v5 & $i(v6) & $i(v4) & ( ~ (v5 = 0) | (v9 = 0 & v8 = 0) | (v7 = 0 % 14.25/2.75 & v3 = 0)))) % 14.25/2.75 % 14.25/2.75 (ax8_basics) % 14.25/2.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 14.25/2.75 (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | ~ % 14.25/2.75 $i(v1) | ~ $i(v0) | unequally_directed_lines(v0, v1) = 0) & ! [v0: $i] : % 14.25/2.75 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = % 14.25/2.75 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (reverse_line(v1) = v3 & % 14.25/2.75 unequally_directed_lines(v0, v3) = 0 & $i(v3))) % 14.25/2.75 % 14.25/2.75 (con) % 14.25/2.76 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int] : ( ~ % 14.25/2.76 (v4 = 0) & ~ (v3 = 0) & unequally_directed_lines(v1, v2) = v4 & % 14.25/2.76 unequally_directed_opposite_lines(v1, v2) = v3 & % 14.25/2.76 unequally_directed_opposite_lines(v0, v1) = 0 & $i(v2) & $i(v1) & $i(v0)) % 14.25/2.76 % 14.25/2.76 (function-axioms) % 14.25/2.76 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 14.25/2.76 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_on_line(v5, v4, % 14.25/2.76 v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) & ! [v0: % 14.25/2.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.25/2.76 : ! [v4: $i] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~ % 14.25/2.76 (before_on_line(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.25/2.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 14.25/2.76 (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) & % 14.25/2.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.25/2.76 (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = % 14.25/2.76 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 14.25/2.76 ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 14.25/2.76 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 14.25/2.76 [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 14.25/2.76 (distinct_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 14.25/2.76 ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 14.25/2.76 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.25/2.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.25/2.76 (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! % 14.25/2.76 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 14.25/2.76 $i] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ % 14.25/2.76 (incident_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 14.25/2.76 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.25/2.76 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 14.25/2.76 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 14.25/2.76 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 14.25/2.76 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.25/2.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.25/2.76 (equally_directed_opposite_lines(v3, v2) = v1) | ~ % 14.25/2.76 (equally_directed_opposite_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] % 14.25/2.76 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.25/2.76 (equally_directed_lines(v3, v2) = v1) | ~ (equally_directed_lines(v3, v2) = % 14.25/2.76 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 14.25/2.76 $i] : ! [v3: $i] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~ % 14.25/2.76 (left_convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.25/2.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.25/2.76 (right_convergent_lines(v3, v2) = v1) | ~ (right_convergent_lines(v3, v2) = % 14.25/2.76 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 14.25/2.76 $i] : ! [v3: $i] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~ % 14.25/2.76 (left_apart_point(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.25/2.76 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.25/2.76 (right_apart_point(v3, v2) = v1) | ~ (right_apart_point(v3, v2) = v0)) & ! % 14.25/2.76 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 14.25/2.76 $i] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | ~ % 14.25/2.76 (unequally_directed_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 14.25/2.76 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.25/2.76 (unequally_directed_opposite_lines(v3, v2) = v1) | ~ % 14.25/2.76 (unequally_directed_opposite_lines(v3, v2) = v0)) & ! [v0: % 14.25/2.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 14.25/2.76 ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 14.25/2.76 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (line(v2) = v1) | ~ % 14.25/2.76 (line(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 14.25/2.76 (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) % 14.25/2.76 % 14.25/2.76 Further assumptions not needed in the proof: % 14.25/2.76 -------------------------------------------- % 14.25/2.76 a2_defns, a3_defns, a4_defns, a5_defns, a6_defns, a7_defns, a8_defns, a9_defns, % 14.25/2.76 ax10_basics, ax10_cons_objs, ax11_basics, ax1_basics, ax1_cons_objs, ax1_subs, % 14.25/2.76 ax1_uniq_cons, ax2_basics, ax2_cons_objs, ax2_subs, ax2_uniq_cons, ax3_basics, % 14.25/2.76 ax3_cons_objs, ax3_subs, ax4_basics, ax4_cons_objs, ax4_defns, ax5_basics, % 14.25/2.76 ax5_cons_objs, ax6_basics, ax6_cons_objs, ax7_cons_objs, ax8_cons_objs, % 14.25/2.76 ax9_basics, ax9_cons_objs % 14.25/2.76 % 14.25/2.76 Those formulas are unsatisfiable: % 14.25/2.76 --------------------------------- % 14.25/2.76 % 14.25/2.76 Begin of proof % 14.25/2.77 | % 14.25/2.77 | ALPHA: (a1_defns) implies: % 14.25/2.77 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 14.25/2.77 | (unequally_directed_opposite_lines(v0, v1) = v2) | ~ $i(v1) | ~ % 14.25/2.77 | $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & reverse_line(v1) % 14.25/2.77 | = v3 & unequally_directed_lines(v0, v3) = v4 & $i(v3))) % 14.25/2.77 | % 14.25/2.77 | ALPHA: (ax7_basics) implies: % 14.25/2.77 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : % 14.25/2.77 | ( ~ (unequally_directed_lines(v1, v2) = v4) | ~ % 14.25/2.77 | (unequally_directed_lines(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 14.25/2.77 | $i(v0) | ? [v5: any] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? % 14.25/2.77 | [v9: any] : ? [v10: any] : (reverse_line(v2) = v8 & reverse_line(v1) % 14.25/2.77 | = v6 & unequally_directed_lines(v1, v8) = v10 & % 14.25/2.77 | unequally_directed_lines(v0, v8) = v9 & % 14.25/2.77 | unequally_directed_lines(v0, v6) = v7 & % 14.25/2.77 | unequally_directed_lines(v0, v1) = v5 & $i(v8) & $i(v6) & ( ~ (v7 = % 14.25/2.77 | 0) | ~ (v5 = 0) | (v10 = 0 & v4 = 0) | (v9 = 0 & v3 = 0)))) % 14.25/2.77 | % 14.25/2.77 | ALPHA: (ax8_basics) implies: % 14.25/2.77 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 14.25/2.77 | (unequally_directed_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? % 14.25/2.77 | [v3: $i] : (reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) % 14.25/2.77 | = 0 & $i(v3))) % 14.25/2.77 | % 14.25/2.77 | ALPHA: (function-axioms) implies: % 14.25/2.77 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 14.25/2.77 | (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) % 14.25/2.77 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 14.25/2.77 | ! [v3: $i] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | % 14.25/2.77 | ~ (unequally_directed_lines(v3, v2) = v0)) % 14.25/2.77 | % 14.25/2.77 | DELTA: instantiating (con) with fresh symbols all_39_0, all_39_1, all_39_2, % 14.25/2.77 | all_39_3, all_39_4 gives: % 14.25/2.77 | (6) ~ (all_39_0 = 0) & ~ (all_39_1 = 0) & % 14.25/2.77 | unequally_directed_lines(all_39_3, all_39_2) = all_39_0 & % 14.25/2.77 | unequally_directed_opposite_lines(all_39_3, all_39_2) = all_39_1 & % 14.25/2.77 | unequally_directed_opposite_lines(all_39_4, all_39_3) = 0 & % 14.25/2.77 | $i(all_39_2) & $i(all_39_3) & $i(all_39_4) % 14.25/2.77 | % 14.25/2.77 | ALPHA: (6) implies: % 14.25/2.77 | (7) ~ (all_39_1 = 0) % 14.25/2.77 | (8) ~ (all_39_0 = 0) % 14.25/2.77 | (9) $i(all_39_3) % 14.25/2.77 | (10) $i(all_39_2) % 14.25/2.77 | (11) unequally_directed_opposite_lines(all_39_3, all_39_2) = all_39_1 % 14.25/2.77 | (12) unequally_directed_lines(all_39_3, all_39_2) = all_39_0 % 14.25/2.77 | % 14.25/2.78 | GROUND_INST: instantiating (1) with all_39_3, all_39_2, all_39_1, simplifying % 14.25/2.78 | with (9), (10), (11) gives: % 14.25/2.78 | (13) all_39_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 14.25/2.78 | reverse_line(all_39_2) = v0 & unequally_directed_lines(all_39_3, v0) % 14.25/2.78 | = v1 & $i(v0)) % 14.25/2.78 | % 14.25/2.78 | GROUND_INST: instantiating (2) with all_39_3, all_39_3, all_39_2, all_39_0, % 14.25/2.78 | all_39_0, simplifying with (9), (10), (12) gives: % 14.25/2.78 | (14) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: any] % 14.25/2.78 | : ? [v5: any] : (reverse_line(all_39_2) = v3 & reverse_line(all_39_3) % 14.25/2.78 | = v1 & unequally_directed_lines(all_39_3, v3) = v5 & % 14.25/2.78 | unequally_directed_lines(all_39_3, v3) = v4 & % 14.25/2.78 | unequally_directed_lines(all_39_3, v1) = v2 & % 14.25/2.78 | unequally_directed_lines(all_39_3, all_39_3) = v0 & $i(v3) & $i(v1) % 14.25/2.78 | & ( ~ (v2 = 0) | ~ (v0 = 0) | (v5 = 0 & all_39_0 = 0) | (v4 = 0 & % 14.25/2.78 | all_39_0 = 0))) % 14.25/2.78 | % 14.25/2.78 | GROUND_INST: instantiating (3) with all_39_3, all_39_2, all_39_0, simplifying % 14.25/2.78 | with (9), (10), (12) gives: % 14.25/2.78 | (15) all_39_0 = 0 | ? [v0: $i] : (reverse_line(all_39_2) = v0 & % 14.25/2.78 | unequally_directed_lines(all_39_3, v0) = 0 & $i(v0)) % 14.25/2.78 | % 14.25/2.78 | DELTA: instantiating (14) with fresh symbols all_58_0, all_58_1, all_58_2, % 14.25/2.78 | all_58_3, all_58_4, all_58_5 gives: % 14.25/2.78 | (16) reverse_line(all_39_2) = all_58_2 & reverse_line(all_39_3) = all_58_4 % 14.25/2.78 | & unequally_directed_lines(all_39_3, all_58_2) = all_58_0 & % 14.25/2.78 | unequally_directed_lines(all_39_3, all_58_2) = all_58_1 & % 14.25/2.78 | unequally_directed_lines(all_39_3, all_58_4) = all_58_3 & % 14.25/2.78 | unequally_directed_lines(all_39_3, all_39_3) = all_58_5 & $i(all_58_2) % 14.25/2.78 | & $i(all_58_4) & ( ~ (all_58_3 = 0) | ~ (all_58_5 = 0) | (all_58_0 = % 14.25/2.78 | 0 & all_39_0 = 0) | (all_58_1 = 0 & all_39_0 = 0)) % 14.25/2.78 | % 14.25/2.78 | ALPHA: (16) implies: % 14.25/2.78 | (17) reverse_line(all_39_2) = all_58_2 % 14.25/2.78 | % 14.25/2.78 | BETA: splitting (13) gives: % 14.25/2.78 | % 14.25/2.78 | Case 1: % 14.25/2.78 | | % 14.25/2.78 | | (18) all_39_1 = 0 % 14.25/2.78 | | % 14.25/2.78 | | REDUCE: (7), (18) imply: % 14.25/2.78 | | (19) $false % 14.25/2.78 | | % 14.25/2.78 | | CLOSE: (19) is inconsistent. % 14.25/2.78 | | % 14.25/2.78 | Case 2: % 14.25/2.78 | | % 14.25/2.78 | | (20) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & reverse_line(all_39_2) = % 14.25/2.78 | | v0 & unequally_directed_lines(all_39_3, v0) = v1 & $i(v0)) % 14.25/2.78 | | % 14.25/2.78 | | DELTA: instantiating (20) with fresh symbols all_64_0, all_64_1 gives: % 14.25/2.78 | | (21) ~ (all_64_0 = 0) & reverse_line(all_39_2) = all_64_1 & % 14.25/2.78 | | unequally_directed_lines(all_39_3, all_64_1) = all_64_0 & % 14.25/2.78 | | $i(all_64_1) % 14.25/2.78 | | % 14.25/2.78 | | ALPHA: (21) implies: % 14.25/2.78 | | (22) ~ (all_64_0 = 0) % 14.25/2.78 | | (23) unequally_directed_lines(all_39_3, all_64_1) = all_64_0 % 14.25/2.78 | | (24) reverse_line(all_39_2) = all_64_1 % 14.25/2.78 | | % 14.25/2.78 | | BETA: splitting (15) gives: % 14.25/2.78 | | % 14.25/2.78 | | Case 1: % 14.25/2.78 | | | % 14.25/2.78 | | | (25) all_39_0 = 0 % 14.25/2.78 | | | % 14.25/2.78 | | | REDUCE: (8), (25) imply: % 14.25/2.78 | | | (26) $false % 14.25/2.78 | | | % 14.25/2.78 | | | CLOSE: (26) is inconsistent. % 14.25/2.78 | | | % 14.25/2.78 | | Case 2: % 14.25/2.78 | | | % 14.25/2.79 | | | (27) ? [v0: $i] : (reverse_line(all_39_2) = v0 & % 14.25/2.79 | | | unequally_directed_lines(all_39_3, v0) = 0 & $i(v0)) % 14.25/2.79 | | | % 14.25/2.79 | | | DELTA: instantiating (27) with fresh symbol all_70_0 gives: % 14.25/2.79 | | | (28) reverse_line(all_39_2) = all_70_0 & % 14.25/2.79 | | | unequally_directed_lines(all_39_3, all_70_0) = 0 & $i(all_70_0) % 14.25/2.79 | | | % 14.25/2.79 | | | ALPHA: (28) implies: % 14.25/2.79 | | | (29) unequally_directed_lines(all_39_3, all_70_0) = 0 % 14.25/2.79 | | | (30) reverse_line(all_39_2) = all_70_0 % 14.25/2.79 | | | % 14.25/2.79 | | | GROUND_INST: instantiating (4) with all_64_1, all_70_0, all_39_2, % 14.25/2.79 | | | simplifying with (24), (30) gives: % 14.25/2.79 | | | (31) all_70_0 = all_64_1 % 14.25/2.79 | | | % 14.25/2.79 | | | GROUND_INST: instantiating (4) with all_58_2, all_70_0, all_39_2, % 14.25/2.79 | | | simplifying with (17), (30) gives: % 14.25/2.79 | | | (32) all_70_0 = all_58_2 % 14.25/2.79 | | | % 14.25/2.79 | | | COMBINE_EQS: (31), (32) imply: % 14.25/2.79 | | | (33) all_64_1 = all_58_2 % 14.25/2.79 | | | % 14.25/2.79 | | | SIMP: (33) implies: % 14.25/2.79 | | | (34) all_64_1 = all_58_2 % 14.25/2.79 | | | % 14.25/2.79 | | | REDUCE: (29), (32) imply: % 14.25/2.79 | | | (35) unequally_directed_lines(all_39_3, all_58_2) = 0 % 14.25/2.79 | | | % 14.25/2.79 | | | REDUCE: (23), (34) imply: % 14.25/2.79 | | | (36) unequally_directed_lines(all_39_3, all_58_2) = all_64_0 % 14.25/2.79 | | | % 14.25/2.79 | | | GROUND_INST: instantiating (5) with 0, all_64_0, all_58_2, all_39_3, % 14.25/2.79 | | | simplifying with (35), (36) gives: % 14.25/2.79 | | | (37) all_64_0 = 0 % 14.25/2.79 | | | % 14.25/2.79 | | | REDUCE: (22), (37) imply: % 14.25/2.79 | | | (38) $false % 14.25/2.79 | | | % 14.25/2.79 | | | CLOSE: (38) is inconsistent. % 14.25/2.79 | | | % 14.25/2.79 | | End of split % 14.25/2.79 | | % 14.25/2.79 | End of split % 14.25/2.79 | % 14.25/2.79 End of proof % 14.25/2.79 % SZS output end Proof for theBenchmark % 14.25/2.79 % 14.25/2.79 2181ms %------------------------------------------------------------------------------