%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO263+1 : TPTP v8.1.2. Bugfixed v6.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n029.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 23:22:51 EDT 2023 % Result : Theorem 253.99s 35.98s % Output : Proof 254.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : GEO263+1 : TPTP v8.1.2. Bugfixed v6.4.0. % 0.08/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.36 % Computer : n029.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Tue Aug 29 22:01:12 EDT 2023 % 0.14/0.36 % CPUTime : % 0.61/0.63 ________ _____ % 0.61/0.63 ___ __ \_________(_)________________________________ % 0.61/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.61/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.61/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.61/0.63 % 0.61/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.61/0.63 (2023-06-19) % 0.61/0.63 % 0.61/0.63 (c) Philipp Rümmer, 2009-2023 % 0.61/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.61/0.63 Amanda Stjerna. % 0.61/0.63 Free software under BSD-3-Clause. % 0.61/0.63 % 0.61/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.61/0.63 % 0.61/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.68/0.64 Running up to 7 provers in parallel. % 0.68/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.68/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.68/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.68/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.68/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.68/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.68/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.98/1.14 Prover 4: Preprocessing ... % 2.98/1.14 Prover 1: Preprocessing ... % 3.57/1.18 Prover 2: Preprocessing ... % 3.57/1.18 Prover 6: Preprocessing ... % 3.57/1.18 Prover 5: Preprocessing ... % 3.57/1.18 Prover 0: Preprocessing ... % 3.57/1.18 Prover 3: Preprocessing ... % 6.30/1.61 Prover 5: Proving ... % 6.95/1.67 Prover 2: Proving ... % 6.95/1.67 Prover 3: Constructing countermodel ... % 6.95/1.68 Prover 6: Constructing countermodel ... % 6.95/1.69 Prover 1: Constructing countermodel ... % 8.45/1.89 Prover 3: gave up % 8.45/1.90 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.06/1.93 Prover 6: gave up % 9.06/1.94 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.06/1.95 Prover 1: gave up % 9.06/1.96 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 9.06/1.96 Prover 7: Preprocessing ... % 9.65/2.01 Prover 8: Preprocessing ... % 9.65/2.02 Prover 4: Constructing countermodel ... % 9.65/2.05 Prover 9: Preprocessing ... % 9.65/2.06 Prover 7: Warning: ignoring some quantifiers % 10.48/2.09 Prover 7: Constructing countermodel ... % 10.72/2.21 Prover 8: Warning: ignoring some quantifiers % 11.40/2.22 Prover 8: Constructing countermodel ... % 11.40/2.30 Prover 0: Proving ... % 12.09/2.38 Prover 7: gave up % 12.09/2.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.89/2.41 Prover 8: gave up % 12.89/2.42 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.89/2.45 Prover 10: Preprocessing ... % 12.89/2.48 Prover 11: Preprocessing ... % 13.65/2.55 Prover 10: Warning: ignoring some quantifiers % 13.65/2.56 Prover 9: Constructing countermodel ... % 13.65/2.57 Prover 10: Constructing countermodel ... % 14.34/2.62 Prover 10: gave up % 14.34/2.62 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 14.34/2.66 Prover 12: Preprocessing ... % 15.09/2.78 Prover 12: Proving ... % 15.99/2.89 Prover 11: Constructing countermodel ... % 37.00/5.54 Prover 12: stopped % 37.00/5.57 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 37.73/5.60 Prover 13: Preprocessing ... % 37.92/5.69 Prover 13: Warning: ignoring some quantifiers % 38.64/5.71 Prover 13: Constructing countermodel ... % 38.64/5.76 Prover 13: gave up % 38.64/5.77 Prover 14: Options: -triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=414236379 % 39.30/5.83 Prover 14: Preprocessing ... % 41.08/6.06 Prover 14: Proving ... % 58.87/8.33 Prover 2: stopped % 58.87/8.34 Prover 15: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=723048181 % 58.87/8.36 Prover 15: Preprocessing ... % 60.03/8.45 Prover 15: Proving ... % 103.05/13.98 Prover 5: stopped % 103.05/13.99 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 103.39/14.02 Prover 16: Preprocessing ... % 103.53/14.07 Prover 16: Warning: ignoring some quantifiers % 103.53/14.07 Prover 16: Constructing countermodel ... % 105.37/14.31 Prover 16: gave up % 105.67/14.33 Prover 17: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=642448422 % 105.81/14.35 Prover 17: Preprocessing ... % 105.81/14.40 Prover 17: Constructing countermodel ... % 105.81/14.41 Prover 17: gave up % 106.43/14.43 Prover 18: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-219651170 % 106.43/14.46 Prover 18: Preprocessing ... % 106.94/14.50 Prover 18: Warning: ignoring some quantifiers % 106.94/14.50 Prover 18: Constructing countermodel ... % 106.94/14.56 Prover 18: gave up % 107.65/14.58 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 107.81/14.62 Prover 19: Preprocessing ... % 108.71/14.70 Prover 19: Warning: ignoring some quantifiers % 108.71/14.72 Prover 19: Constructing countermodel ... % 110.53/15.00 Prover 19: gave up % 111.08/15.01 Prover 20: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=2065050644 % 111.65/15.08 Prover 20: Preprocessing ... % 112.34/15.17 Prover 20: Proving ... % 203.82/28.03 Prover 4: stopped % 203.82/28.04 Prover 21: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=201956991 % 204.19/28.09 Prover 21: Preprocessing ... % 205.09/28.22 Prover 21: Proving ... % 206.60/28.47 Prover 9: stopped % 229.41/31.85 Prover 14: stopped % 253.74/35.91 Prover 11: Found proof (size 37) % 253.74/35.91 Prover 11: proved (33488ms) % 253.74/35.91 Prover 15: stopped % 253.74/35.91 Prover 21: stopped % 253.74/35.91 Prover 20: stopped % 253.99/35.98 Prover 0: stopped % 253.99/35.98 % 253.99/35.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 253.99/35.98 % 253.99/35.98 % SZS output start Proof for theBenchmark % 253.99/35.99 Assumptions after simplification: % 253.99/35.99 --------------------------------- % 253.99/35.99 % 253.99/35.99 (bet_def) % 254.16/36.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 254.16/36.02 | ~ (between_on_line(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 254.16/36.02 $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: % 254.16/36.02 int] : ((( ~ (v8 = 0) & before_on_line(v0, v2, v1) = v8) | ( ~ (v7 = 0) & % 254.16/36.02 before_on_line(v0, v3, v2) = v7)) & (( ~ (v6 = 0) & before_on_line(v0, % 254.16/36.02 v2, v3) = v6) | ( ~ (v5 = 0) & before_on_line(v0, v1, v2) = v5)))) & % 254.16/36.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 254.16/36.02 (between_on_line(v0, v1, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 254.16/36.02 ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ((v7 % 254.16/36.02 = 0 & v6 = 0 & before_on_line(v0, v3, v2) = 0 & before_on_line(v0, v2, % 254.16/36.02 v1) = 0) | (v5 = 0 & v4 = 0 & before_on_line(v0, v2, v3) = 0 & % 254.16/36.02 before_on_line(v0, v1, v2) = 0))) % 254.16/36.02 % 254.16/36.02 (con) % 254.16/36.03 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 254.16/36.03 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 254.16/36.03 ? [v11: $i] : ? [v12: int] : ( ~ (v12 = 0) & parallel_through_point(v2, v5) % 254.16/36.03 = v10 & parallel_through_point(v2, v4) = v8 & parallel_through_point(v2, v3) % 254.16/36.03 = v6 & intersection_point(v1, v10) = v11 & intersection_point(v1, v8) = v9 & % 254.16/36.03 intersection_point(v1, v6) = v7 & between_on_line(v1, v7, v9, v11) = v12 & % 254.16/36.03 between_on_line(v0, v3, v4, v5) = 0 & convergent_lines(v1, v2) = 0 & % 254.16/36.03 convergent_lines(v0, v2) = 0 & convergent_lines(v0, v1) = 0 & $i(v11) & % 254.16/36.03 $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 254.16/36.03 $i(v2) & $i(v1) & $i(v0)) % 254.16/36.03 % 254.16/36.03 (con_def) % 254.16/36.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ % 254.16/36.04 (unequally_directed_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ~ % 254.16/36.04 $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ((v5 = 0 & v3 = 0 & % 254.16/36.04 unequally_directed_lines(v0, v1) = 0) | ( ~ (v4 = 0) & % 254.16/36.04 convergent_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 254.16/36.04 int] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 254.16/36.04 | ? [v3: int] : ? [v4: $i] : ? [v5: int] : (( ~ (v5 = 0) & % 254.16/36.04 unequally_directed_lines(v0, v4) = v5 & reverse_line(v1) = v4 & $i(v4)) % 254.16/36.04 | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0: $i] : % 254.16/36.04 ! [v1: $i] : ! [v2: $i] : ( ~ (unequally_directed_lines(v0, v2) = 0) | ~ % 254.16/36.04 (reverse_line(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: % 254.16/36.04 int] : ((v4 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & % 254.16/36.04 unequally_directed_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : % 254.16/36.04 ! [v2: any] : ( ~ (unequally_directed_lines(v0, v1) = v2) | ~ $i(v1) | ~ % 254.16/36.04 $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ((v5 = 0 & v2 = 0 & % 254.16/36.04 unequally_directed_lines(v0, v4) = 0 & reverse_line(v1) = v4 & $i(v4)) | % 254.16/36.04 ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: % 254.16/36.04 $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 254.16/36.04 $i] : (unequally_directed_lines(v0, v2) = 0 & unequally_directed_lines(v0, % 254.16/36.04 v1) = 0 & reverse_line(v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : % 254.16/36.04 ( ~ (unequally_directed_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 254.16/36.04 $i] : ? [v3: int] : ? [v4: int] : ((v4 = 0 & convergent_lines(v0, v1) = % 254.16/36.04 0) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v2) = v3 & % 254.16/36.04 reverse_line(v1) = v2 & $i(v2)))) % 254.16/36.04 % 254.16/36.04 (oag11) % 254.16/36.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (left_convergent_lines(v0, v2) = % 254.16/36.04 0) | ~ (reverse_line(v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : % 254.16/36.04 ! [v1: $i] : ( ~ (left_convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)) % 254.16/36.04 % 254.16/36.04 (oag9) % 254.16/36.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 254.16/36.04 (left_convergent_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ~ % 254.16/36.04 $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ((v6 = 0 & % 254.16/36.04 left_convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & % 254.16/36.04 unequally_directed_lines(v0, v2) = v5) | ( ~ (v4 = 0) & % 254.16/36.04 unequally_directed_lines(v0, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : % 254.16/36.04 ! [v2: int] : (v2 = 0 | ~ (left_convergent_lines(v0, v1) = v2) | ~ $i(v1) | % 254.16/36.04 ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ? [v6: int] : ((v6 = % 254.16/36.04 0 & left_convergent_lines(v0, v4) = 0 & reverse_line(v1) = v4 & $i(v4)) % 254.16/36.04 | ( ~ (v5 = 0) & unequally_directed_lines(v0, v4) = v5 & reverse_line(v1) % 254.16/36.04 = v4 & $i(v4)) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) % 254.16/36.04 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unequally_directed_lines(v0, % 254.16/36.04 v2) = 0) | ~ (reverse_line(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 254.16/36.04 int] : ? [v4: int] : ? [v5: int] : ((v5 = 0 & left_convergent_lines(v0, % 254.16/36.04 v2) = 0) | (v4 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) % 254.16/36.04 & unequally_directed_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : % 254.16/36.04 ( ~ (unequally_directed_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 254.16/36.04 $i] : ? [v3: int] : ? [v4: int] : ? [v5: int] : ((v5 = 0 & % 254.16/36.04 left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2 & $i(v2)) | % 254.16/36.04 (v4 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & % 254.16/36.04 unequally_directed_lines(v0, v2) = v3 & reverse_line(v1) = v2 & % 254.16/36.04 $i(v2)))) % 254.16/36.04 % 254.16/36.04 (function-axioms) % 254.16/36.05 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 254.16/36.05 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_on_line(v5, v4, % 254.16/36.05 v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) & ! [v0: % 254.16/36.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 254.16/36.05 : ! [v4: $i] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~ % 254.16/36.05 (before_on_line(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 254.16/36.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 254.16/36.05 (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) & % 254.16/36.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 254.16/36.05 (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = % 254.16/36.05 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 254.16/36.05 ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 254.16/36.05 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 254.16/36.05 [v3: $i] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~ % 254.16/36.05 (left_convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 254.16/36.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 254.16/36.05 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 254.16/36.05 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 254.16/36.05 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 254.16/36.05 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 254.16/36.05 $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, % 254.16/36.05 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 254.16/36.05 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 254.16/36.05 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 254.16/36.05 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 254.16/36.05 (unequally_directed_lines(v3, v2) = v1) | ~ (unequally_directed_lines(v3, % 254.16/36.05 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 254.16/36.05 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | % 254.16/36.05 ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 254.16/36.05 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 254.16/36.05 (left_apart_point(v3, v2) = v1) | ~ (left_apart_point(v3, v2) = v0)) & ! % 254.16/36.05 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 254.16/36.05 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: MultipleValueBool] : % 254.16/36.05 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (line(v2) = v1) | ~ % 254.16/36.05 (line(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 254.16/36.05 (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) % 254.16/36.05 % 254.16/36.05 Further assumptions not needed in the proof: % 254.16/36.05 -------------------------------------------- % 254.16/36.05 apt_def, bf_def, div_def, oag1, oag10, oag2, oag3, oag4, oag5, oag6, oag7, oag8, % 254.16/36.05 oagco1, oagco10, oagco2, oagco3, oagco4, oagco5, oagco6, oagco7, oagco8, oagco9, % 254.16/36.05 oagsub1, oagsub2, oagsub3, oaguc1, oaguc2 % 254.16/36.05 % 254.16/36.05 Those formulas are unsatisfiable: % 254.16/36.05 --------------------------------- % 254.16/36.05 % 254.16/36.05 Begin of proof % 254.16/36.05 | % 254.16/36.05 | ALPHA: (con_def) implies: % 254.16/36.05 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 254.16/36.05 | $i(v1) | ~ $i(v0) | ? [v2: $i] : (unequally_directed_lines(v0, v2) % 254.16/36.05 | = 0 & unequally_directed_lines(v0, v1) = 0 & reverse_line(v1) = v2 % 254.16/36.05 | & $i(v2))) % 254.16/36.05 | % 254.16/36.05 | ALPHA: (bet_def) implies: % 254.16/36.06 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 254.16/36.06 | (v4 = 0 | ~ (between_on_line(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ % 254.16/36.06 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? % 254.16/36.06 | [v7: int] : ? [v8: int] : ((( ~ (v8 = 0) & before_on_line(v0, v2, % 254.16/36.06 | v1) = v8) | ( ~ (v7 = 0) & before_on_line(v0, v3, v2) = v7)) % 254.16/36.06 | & (( ~ (v6 = 0) & before_on_line(v0, v2, v3) = v6) | ( ~ (v5 = 0) & % 254.16/36.06 | before_on_line(v0, v1, v2) = v5)))) % 254.16/36.06 | % 254.16/36.06 | ALPHA: (oag9) implies: % 254.16/36.06 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 254.16/36.06 | (unequally_directed_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | % 254.16/36.06 | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ? [v5: int] : % 254.16/36.06 | ((v5 = 0 & left_convergent_lines(v0, v2) = 0) | (v4 = 0 & % 254.16/36.06 | left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & % 254.16/36.06 | unequally_directed_lines(v0, v1) = v3))) % 254.16/36.06 | % 254.16/36.06 | ALPHA: (oag11) implies: % 254.16/36.06 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (left_convergent_lines(v0, v1) = 0) | % 254.16/36.06 | ~ $i(v1) | ~ $i(v0)) % 254.16/36.06 | % 254.16/36.06 | ALPHA: (function-axioms) implies: % 254.16/36.06 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 254.16/36.06 | (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) % 254.16/36.06 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 254.16/36.06 | ! [v3: $i] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | % 254.16/36.06 | ~ (unequally_directed_lines(v3, v2) = v0)) % 254.16/36.06 | % 254.16/36.06 | DELTA: instantiating (con) with fresh symbols all_34_0, all_34_1, all_34_2, % 254.16/36.06 | all_34_3, all_34_4, all_34_5, all_34_6, all_34_7, all_34_8, all_34_9, % 254.16/36.06 | all_34_10, all_34_11, all_34_12 gives: % 254.16/36.06 | (7) ~ (all_34_0 = 0) & parallel_through_point(all_34_10, all_34_7) = % 254.16/36.06 | all_34_2 & parallel_through_point(all_34_10, all_34_8) = all_34_4 & % 254.16/36.06 | parallel_through_point(all_34_10, all_34_9) = all_34_6 & % 254.16/36.06 | intersection_point(all_34_11, all_34_2) = all_34_1 & % 254.16/36.06 | intersection_point(all_34_11, all_34_4) = all_34_3 & % 254.16/36.06 | intersection_point(all_34_11, all_34_6) = all_34_5 & % 254.16/36.06 | between_on_line(all_34_11, all_34_5, all_34_3, all_34_1) = all_34_0 & % 254.16/36.06 | between_on_line(all_34_12, all_34_9, all_34_8, all_34_7) = 0 & % 254.16/36.06 | convergent_lines(all_34_11, all_34_10) = 0 & % 254.16/36.06 | convergent_lines(all_34_12, all_34_10) = 0 & % 254.16/36.06 | convergent_lines(all_34_12, all_34_11) = 0 & $i(all_34_1) & % 254.16/36.06 | $i(all_34_2) & $i(all_34_3) & $i(all_34_4) & $i(all_34_5) & % 254.16/36.06 | $i(all_34_6) & $i(all_34_7) & $i(all_34_8) & $i(all_34_9) & % 254.16/36.06 | $i(all_34_10) & $i(all_34_11) & $i(all_34_12) % 254.16/36.06 | % 254.16/36.06 | ALPHA: (7) implies: % 254.16/36.06 | (8) ~ (all_34_0 = 0) % 254.16/36.06 | (9) $i(all_34_12) % 254.16/36.06 | (10) $i(all_34_11) % 254.16/36.06 | (11) $i(all_34_10) % 254.16/36.06 | (12) $i(all_34_5) % 254.16/36.06 | (13) $i(all_34_3) % 254.16/36.06 | (14) $i(all_34_1) % 254.16/36.06 | (15) convergent_lines(all_34_12, all_34_10) = 0 % 254.16/36.06 | (16) convergent_lines(all_34_11, all_34_10) = 0 % 254.16/36.06 | (17) between_on_line(all_34_11, all_34_5, all_34_3, all_34_1) = all_34_0 % 254.16/36.06 | % 254.16/36.07 | GROUND_INST: instantiating (1) with all_34_12, all_34_10, simplifying with % 254.16/36.07 | (9), (11), (15) gives: % 254.16/36.07 | (18) ? [v0: $i] : (unequally_directed_lines(all_34_12, v0) = 0 & % 254.16/36.07 | unequally_directed_lines(all_34_12, all_34_10) = 0 & % 254.16/36.07 | reverse_line(all_34_10) = v0 & $i(v0)) % 254.16/36.07 | % 254.16/36.07 | GROUND_INST: instantiating (1) with all_34_11, all_34_10, simplifying with % 254.16/36.07 | (10), (11), (16) gives: % 254.16/36.07 | (19) ? [v0: $i] : (unequally_directed_lines(all_34_11, v0) = 0 & % 254.16/36.07 | unequally_directed_lines(all_34_11, all_34_10) = 0 & % 254.16/36.07 | reverse_line(all_34_10) = v0 & $i(v0)) % 254.16/36.07 | % 254.16/36.07 | GROUND_INST: instantiating (2) with all_34_11, all_34_5, all_34_3, all_34_1, % 254.16/36.07 | all_34_0, simplifying with (10), (12), (13), (14), (17) gives: % 254.16/36.07 | (20) all_34_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: % 254.16/36.07 | int] : ((( ~ (v3 = 0) & before_on_line(all_34_11, all_34_3, % 254.16/36.07 | all_34_5) = v3) | ( ~ (v2 = 0) & before_on_line(all_34_11, % 254.16/36.07 | all_34_1, all_34_3) = v2)) & (( ~ (v1 = 0) & % 254.16/36.07 | before_on_line(all_34_11, all_34_3, all_34_1) = v1) | ( ~ (v0 = % 254.16/36.07 | 0) & before_on_line(all_34_11, all_34_5, all_34_3) = v0))) % 254.16/36.07 | % 254.16/36.07 | DELTA: instantiating (19) with fresh symbol all_53_0 gives: % 254.16/36.07 | (21) unequally_directed_lines(all_34_11, all_53_0) = 0 & % 254.16/36.07 | unequally_directed_lines(all_34_11, all_34_10) = 0 & % 254.16/36.07 | reverse_line(all_34_10) = all_53_0 & $i(all_53_0) % 254.16/36.07 | % 254.16/36.07 | ALPHA: (21) implies: % 254.16/36.07 | (22) reverse_line(all_34_10) = all_53_0 % 254.16/36.07 | (23) unequally_directed_lines(all_34_11, all_34_10) = 0 % 254.16/36.07 | (24) unequally_directed_lines(all_34_11, all_53_0) = 0 % 254.16/36.07 | % 254.16/36.07 | DELTA: instantiating (18) with fresh symbol all_55_0 gives: % 254.16/36.07 | (25) unequally_directed_lines(all_34_12, all_55_0) = 0 & % 254.16/36.07 | unequally_directed_lines(all_34_12, all_34_10) = 0 & % 254.16/36.07 | reverse_line(all_34_10) = all_55_0 & $i(all_55_0) % 254.16/36.07 | % 254.16/36.07 | ALPHA: (25) implies: % 254.16/36.07 | (26) $i(all_55_0) % 254.16/36.07 | (27) reverse_line(all_34_10) = all_55_0 % 254.16/36.07 | % 254.16/36.07 | BETA: splitting (20) gives: % 254.16/36.07 | % 254.16/36.07 | Case 1: % 254.16/36.07 | | % 254.16/36.07 | | (28) all_34_0 = 0 % 254.16/36.07 | | % 254.16/36.07 | | REDUCE: (8), (28) imply: % 254.16/36.07 | | (29) $false % 254.47/36.07 | | % 254.47/36.07 | | CLOSE: (29) is inconsistent. % 254.47/36.07 | | % 254.47/36.07 | Case 2: % 254.47/36.07 | | % 254.47/36.07 | | % 254.47/36.07 | | GROUND_INST: instantiating (5) with all_53_0, all_55_0, all_34_10, % 254.47/36.07 | | simplifying with (22), (27) gives: % 254.47/36.07 | | (30) all_55_0 = all_53_0 % 254.47/36.07 | | % 254.47/36.07 | | REDUCE: (26), (30) imply: % 254.47/36.07 | | (31) $i(all_53_0) % 254.47/36.07 | | % 254.47/36.07 | | GROUND_INST: instantiating (3) with all_34_11, all_34_10, all_53_0, % 254.47/36.07 | | simplifying with (10), (11), (22), (24) gives: % 254.47/36.08 | | (32) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & % 254.47/36.08 | | left_convergent_lines(all_34_11, all_53_0) = 0) | (v1 = 0 & % 254.47/36.08 | | left_convergent_lines(all_34_11, all_34_10) = 0) | ( ~ (v0 = 0) % 254.47/36.08 | | & unequally_directed_lines(all_34_11, all_34_10) = v0)) % 254.47/36.08 | | % 254.47/36.08 | | DELTA: instantiating (32) with fresh symbols all_94_0, all_94_1, all_94_2 % 254.47/36.08 | | gives: % 254.47/36.08 | | (33) (all_94_0 = 0 & left_convergent_lines(all_34_11, all_53_0) = 0) | % 254.47/36.08 | | (all_94_1 = 0 & left_convergent_lines(all_34_11, all_34_10) = 0) | ( % 254.47/36.08 | | ~ (all_94_2 = 0) & unequally_directed_lines(all_34_11, all_34_10) % 254.47/36.08 | | = all_94_2) % 254.47/36.08 | | % 254.47/36.08 | | BETA: splitting (33) gives: % 254.47/36.08 | | % 254.47/36.08 | | Case 1: % 254.47/36.08 | | | % 254.47/36.08 | | | (34) all_94_0 = 0 & left_convergent_lines(all_34_11, all_53_0) = 0 % 254.47/36.08 | | | % 254.47/36.08 | | | ALPHA: (34) implies: % 254.47/36.08 | | | (35) left_convergent_lines(all_34_11, all_53_0) = 0 % 254.47/36.08 | | | % 254.47/36.08 | | | GROUND_INST: instantiating (4) with all_34_11, all_53_0, simplifying with % 254.47/36.08 | | | (10), (31), (35) gives: % 254.47/36.08 | | | (36) $false % 254.47/36.08 | | | % 254.47/36.08 | | | CLOSE: (36) is inconsistent. % 254.47/36.08 | | | % 254.47/36.08 | | Case 2: % 254.47/36.08 | | | % 254.47/36.08 | | | (37) (all_94_1 = 0 & left_convergent_lines(all_34_11, all_34_10) = 0) | % 254.47/36.08 | | | ( ~ (all_94_2 = 0) & unequally_directed_lines(all_34_11, % 254.47/36.08 | | | all_34_10) = all_94_2) % 254.47/36.08 | | | % 254.47/36.08 | | | BETA: splitting (37) gives: % 254.47/36.08 | | | % 254.47/36.08 | | | Case 1: % 254.47/36.08 | | | | % 254.47/36.08 | | | | (38) all_94_1 = 0 & left_convergent_lines(all_34_11, all_34_10) = 0 % 254.47/36.08 | | | | % 254.47/36.08 | | | | ALPHA: (38) implies: % 254.47/36.08 | | | | (39) left_convergent_lines(all_34_11, all_34_10) = 0 % 254.47/36.08 | | | | % 254.47/36.08 | | | | GROUND_INST: instantiating (4) with all_34_11, all_34_10, simplifying % 254.47/36.08 | | | | with (10), (11), (39) gives: % 254.47/36.08 | | | | (40) $false % 254.47/36.08 | | | | % 254.47/36.08 | | | | CLOSE: (40) is inconsistent. % 254.47/36.08 | | | | % 254.47/36.08 | | | Case 2: % 254.47/36.08 | | | | % 254.47/36.08 | | | | (41) ~ (all_94_2 = 0) & unequally_directed_lines(all_34_11, % 254.47/36.08 | | | | all_34_10) = all_94_2 % 254.47/36.08 | | | | % 254.47/36.08 | | | | ALPHA: (41) implies: % 254.47/36.08 | | | | (42) ~ (all_94_2 = 0) % 254.47/36.08 | | | | (43) unequally_directed_lines(all_34_11, all_34_10) = all_94_2 % 254.47/36.08 | | | | % 254.47/36.08 | | | | GROUND_INST: instantiating (6) with 0, all_94_2, all_34_10, all_34_11, % 254.47/36.08 | | | | simplifying with (23), (43) gives: % 254.47/36.08 | | | | (44) all_94_2 = 0 % 254.47/36.08 | | | | % 254.47/36.08 | | | | REDUCE: (42), (44) imply: % 254.47/36.08 | | | | (45) $false % 254.47/36.08 | | | | % 254.47/36.08 | | | | CLOSE: (45) is inconsistent. % 254.47/36.08 | | | | % 254.47/36.08 | | | End of split % 254.47/36.08 | | | % 254.47/36.08 | | End of split % 254.47/36.08 | | % 254.47/36.08 | End of split % 254.47/36.08 | % 254.47/36.08 End of proof % 254.47/36.08 % SZS output end Proof for theBenchmark % 254.47/36.08 % 254.47/36.08 35450ms %------------------------------------------------------------------------------