%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO238+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 : n022.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 23:22:39 EDT 2023 % Result : Theorem 10.64s 2.28s % Output : Proof 16.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : GEO238+1 : TPTP v8.1.2. Bugfixed v6.4.0. % 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n022.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Tue Aug 29 22:21:38 EDT 2023 % 0.12/0.35 % CPUTime : % 0.63/0.64 ________ _____ % 0.63/0.64 ___ __ \_________(_)________________________________ % 0.63/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.63/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.63/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.63/0.64 % 0.63/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.63/0.64 (2023-06-19) % 0.63/0.64 % 0.63/0.64 (c) Philipp Rümmer, 2009-2023 % 0.63/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.63/0.64 Amanda Stjerna. % 0.63/0.64 Free software under BSD-3-Clause. % 0.63/0.64 % 0.63/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.63/0.64 % 0.63/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.70/0.65 Running up to 7 provers in parallel. % 0.70/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.70/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.70/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.70/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.70/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.70/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.70/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.17/1.19 Prover 4: Preprocessing ... % 3.17/1.20 Prover 1: Preprocessing ... % 3.42/1.24 Prover 6: Preprocessing ... % 3.42/1.24 Prover 0: Preprocessing ... % 3.42/1.24 Prover 5: Preprocessing ... % 3.42/1.24 Prover 2: Preprocessing ... % 3.42/1.24 Prover 3: Preprocessing ... % 6.85/1.73 Prover 5: Proving ... % 7.73/1.83 Prover 6: Constructing countermodel ... % 8.01/1.86 Prover 3: Constructing countermodel ... % 8.01/1.89 Prover 2: Proving ... % 8.01/1.92 Prover 6: gave up % 8.01/1.93 Prover 1: Constructing countermodel ... % 8.01/1.93 Prover 3: gave up % 8.60/1.94 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.60/1.95 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.90/2.02 Prover 1: gave up % 8.90/2.04 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 9.38/2.06 Prover 7: Preprocessing ... % 9.38/2.10 Prover 8: Preprocessing ... % 9.81/2.13 Prover 9: Preprocessing ... % 10.64/2.24 Prover 7: Warning: ignoring some quantifiers % 10.64/2.27 Prover 2: proved (1603ms) % 10.64/2.28 % 10.64/2.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.64/2.28 % 10.64/2.28 Prover 5: stopped % 11.00/2.30 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.00/2.30 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.00/2.31 Prover 7: Constructing countermodel ... % 11.00/2.35 Prover 11: Preprocessing ... % 11.00/2.35 Prover 10: Preprocessing ... % 11.61/2.40 Prover 4: Constructing countermodel ... % 11.61/2.41 Prover 8: Warning: ignoring some quantifiers % 11.90/2.42 Prover 8: Constructing countermodel ... % 11.90/2.42 Prover 7: gave up % 12.07/2.44 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.07/2.44 Prover 10: Warning: ignoring some quantifiers % 12.07/2.48 Prover 13: Preprocessing ... % 12.07/2.48 Prover 10: Constructing countermodel ... % 12.69/2.54 Prover 0: Proving ... % 12.69/2.55 Prover 0: stopped % 12.69/2.55 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 12.69/2.57 Prover 10: gave up % 12.69/2.57 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 13.18/2.60 Prover 8: gave up % 13.18/2.60 Prover 16: Preprocessing ... % 13.18/2.61 Prover 13: Warning: ignoring some quantifiers % 13.18/2.63 Prover 19: Preprocessing ... % 13.18/2.65 Prover 13: Constructing countermodel ... % 13.82/2.69 Prover 16: Warning: ignoring some quantifiers % 14.11/2.71 Prover 16: Constructing countermodel ... % 14.28/2.80 Prover 9: Constructing countermodel ... % 14.28/2.81 Prover 13: gave up % 14.28/2.82 Prover 9: stopped % 14.92/2.84 Prover 19: Warning: ignoring some quantifiers % 14.92/2.86 Prover 19: Constructing countermodel ... % 14.92/2.88 Prover 11: Constructing countermodel ... % 14.92/2.88 Prover 16: gave up % 16.29/3.05 Prover 11: Found proof (size 28) % 16.29/3.05 Prover 11: proved (751ms) % 16.29/3.05 Prover 4: stopped % 16.29/3.05 Prover 19: stopped % 16.29/3.05 % 16.29/3.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.29/3.05 % 16.29/3.06 % SZS output start Proof for theBenchmark % 16.29/3.06 Assumptions after simplification: % 16.29/3.06 --------------------------------- % 16.29/3.06 % 16.29/3.06 (con) % 16.29/3.09 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (divides_points(v3, % 16.29/3.09 v1, v2) = 0 & divides_points(v3, v0, v2) = 0 & divides_points(v3, v0, v1) % 16.29/3.09 = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 16.29/3.09 % 16.29/3.09 (div_def) % 16.29/3.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 16.29/3.09 (divides_points(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 16.29/3.09 [v4: int] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ((( ~ % 16.29/3.09 (v8 = 0) & left_apart_point(v1, v2) = v8) | ( ~ (v7 = 0) & % 16.29/3.09 reverse_line(v2) = v5 & left_apart_point(v0, v5) = v7 & $i(v5))) & (( % 16.29/3.09 ~ (v6 = 0) & reverse_line(v2) = v5 & left_apart_point(v1, v5) = v6 & % 16.29/3.09 $i(v5)) | ( ~ (v4 = 0) & left_apart_point(v0, v2) = v4)))) & ! [v0: % 16.29/3.09 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (divides_points(v2, v0, v1) = 0) | ~ % 16.29/3.09 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : % 16.29/3.09 ? [v6: int] : ? [v7: int] : (reverse_line(v2) = v4 & $i(v4) & ((v7 = 0 & % 16.29/3.09 v6 = 0 & left_apart_point(v1, v2) = 0 & left_apart_point(v0, v4) = 0) % 16.29/3.09 | (v5 = 0 & v3 = 0 & left_apart_point(v1, v4) = 0 & left_apart_point(v0, % 16.29/3.09 v2) = 0)))) % 16.29/3.09 % 16.29/3.09 (oag10) % 16.29/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (reverse_line(v1) = v2) | ~ % 16.29/3.10 (left_apart_point(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! % 16.29/3.10 [v1: $i] : ( ~ (left_apart_point(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)) % 16.29/3.10 % 16.29/3.10 (function-axioms) % 16.29/3.10 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 16.29/3.10 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_on_line(v5, v4, % 16.29/3.10 v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) & ! [v0: % 16.29/3.10 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 16.29/3.10 : ! [v4: $i] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~ % 16.29/3.10 (before_on_line(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.29/3.10 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 16.29/3.10 (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) & % 16.29/3.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.29/3.10 (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = % 16.29/3.10 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 16.29/3.10 ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 16.29/3.10 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 16.29/3.10 [v3: $i] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~ % 16.29/3.10 (left_convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.29/3.10 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.29/3.10 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 16.29/3.10 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.29/3.10 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 16.29/3.10 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 16.29/3.10 $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, % 16.29/3.10 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 16.29/3.10 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 16.29/3.10 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 16.29/3.10 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.29/3.10 (unequally_directed_lines(v3, v2) = v1) | ~ (unequally_directed_lines(v3, % 16.29/3.10 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 16.29/3.10 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | % 16.29/3.10 ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 16.29/3.10 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.29/3.10 (left_apart_point(v3, v2) = v1) | ~ (left_apart_point(v3, v2) = v0)) & ! % 16.29/3.10 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 16.29/3.10 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: MultipleValueBool] : % 16.29/3.10 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (line(v2) = v1) | ~ % 16.29/3.10 (line(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 16.29/3.10 (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) % 16.29/3.10 % 16.29/3.10 Further assumptions not needed in the proof: % 16.29/3.10 -------------------------------------------- % 16.29/3.11 apt_def, bet_def, bf_def, con_def, oag1, oag11, oag2, oag3, oag4, oag5, oag6, % 16.29/3.11 oag7, oag8, oag9, oagco1, oagco10, oagco2, oagco3, oagco4, oagco5, oagco6, % 16.29/3.11 oagco7, oagco8, oagco9, oagsub1, oagsub2, oagsub3, oaguc1, oaguc2 % 16.29/3.11 % 16.29/3.11 Those formulas are unsatisfiable: % 16.29/3.11 --------------------------------- % 16.29/3.11 % 16.29/3.11 Begin of proof % 16.29/3.11 | % 16.29/3.11 | ALPHA: (div_def) implies: % 16.29/3.11 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (divides_points(v2, v0, % 16.29/3.11 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? % 16.29/3.11 | [v4: $i] : ? [v5: int] : ? [v6: int] : ? [v7: int] : % 16.29/3.11 | (reverse_line(v2) = v4 & $i(v4) & ((v7 = 0 & v6 = 0 & % 16.29/3.11 | left_apart_point(v1, v2) = 0 & left_apart_point(v0, v4) = 0) | % 16.29/3.11 | (v5 = 0 & v3 = 0 & left_apart_point(v1, v4) = 0 & % 16.29/3.11 | left_apart_point(v0, v2) = 0)))) % 16.29/3.11 | % 16.29/3.11 | ALPHA: (oag10) implies: % 16.29/3.11 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (left_apart_point(v0, v1) = 0) | ~ % 16.29/3.11 | $i(v1) | ~ $i(v0)) % 16.29/3.11 | % 16.29/3.11 | ALPHA: (function-axioms) implies: % 16.29/3.11 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 16.29/3.11 | (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) % 16.29/3.11 | % 16.29/3.11 | DELTA: instantiating (con) with fresh symbols all_34_0, all_34_1, all_34_2, % 16.29/3.11 | all_34_3 gives: % 16.29/3.11 | (4) divides_points(all_34_0, all_34_2, all_34_1) = 0 & % 16.29/3.11 | divides_points(all_34_0, all_34_3, all_34_1) = 0 & % 16.29/3.11 | divides_points(all_34_0, all_34_3, all_34_2) = 0 & $i(all_34_0) & % 16.29/3.11 | $i(all_34_1) & $i(all_34_2) & $i(all_34_3) % 16.29/3.11 | % 16.29/3.11 | ALPHA: (4) implies: % 16.29/3.11 | (5) $i(all_34_3) % 16.29/3.11 | (6) $i(all_34_2) % 16.29/3.11 | (7) $i(all_34_1) % 16.29/3.11 | (8) $i(all_34_0) % 16.29/3.11 | (9) divides_points(all_34_0, all_34_3, all_34_2) = 0 % 16.29/3.11 | (10) divides_points(all_34_0, all_34_3, all_34_1) = 0 % 16.29/3.11 | (11) divides_points(all_34_0, all_34_2, all_34_1) = 0 % 16.29/3.11 | % 16.29/3.12 | GROUND_INST: instantiating (1) with all_34_3, all_34_2, all_34_0, simplifying % 16.29/3.12 | with (5), (6), (8), (9) gives: % 16.29/3.12 | (12) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : ? [v4: % 16.29/3.12 | int] : (reverse_line(all_34_0) = v1 & $i(v1) & ((v4 = 0 & v3 = 0 & % 16.29/3.12 | left_apart_point(all_34_2, all_34_0) = 0 & % 16.29/3.12 | left_apart_point(all_34_3, v1) = 0) | (v2 = 0 & v0 = 0 & % 16.29/3.12 | left_apart_point(all_34_2, v1) = 0 & left_apart_point(all_34_3, % 16.29/3.12 | all_34_0) = 0))) % 16.29/3.12 | % 16.29/3.12 | GROUND_INST: instantiating (1) with all_34_3, all_34_1, all_34_0, simplifying % 16.29/3.12 | with (5), (7), (8), (10) gives: % 16.29/3.12 | (13) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : ? [v4: % 16.29/3.12 | int] : (reverse_line(all_34_0) = v1 & $i(v1) & ((v4 = 0 & v3 = 0 & % 16.29/3.12 | left_apart_point(all_34_1, all_34_0) = 0 & % 16.29/3.12 | left_apart_point(all_34_3, v1) = 0) | (v2 = 0 & v0 = 0 & % 16.29/3.12 | left_apart_point(all_34_1, v1) = 0 & left_apart_point(all_34_3, % 16.82/3.12 | all_34_0) = 0))) % 16.82/3.12 | % 16.82/3.12 | GROUND_INST: instantiating (1) with all_34_2, all_34_1, all_34_0, simplifying % 16.82/3.12 | with (6), (7), (8), (11) gives: % 16.82/3.12 | (14) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : ? [v4: % 16.82/3.12 | int] : (reverse_line(all_34_0) = v1 & $i(v1) & ((v4 = 0 & v3 = 0 & % 16.82/3.12 | left_apart_point(all_34_1, all_34_0) = 0 & % 16.82/3.12 | left_apart_point(all_34_2, v1) = 0) | (v2 = 0 & v0 = 0 & % 16.82/3.12 | left_apart_point(all_34_1, v1) = 0 & left_apart_point(all_34_2, % 16.82/3.12 | all_34_0) = 0))) % 16.82/3.12 | % 16.82/3.12 | DELTA: instantiating (14) with fresh symbols all_41_0, all_41_1, all_41_2, % 16.82/3.12 | all_41_3, all_41_4 gives: % 16.82/3.12 | (15) reverse_line(all_34_0) = all_41_3 & $i(all_41_3) & ((all_41_0 = 0 & % 16.82/3.12 | all_41_1 = 0 & left_apart_point(all_34_1, all_34_0) = 0 & % 16.82/3.12 | left_apart_point(all_34_2, all_41_3) = 0) | (all_41_2 = 0 & % 16.82/3.12 | all_41_4 = 0 & left_apart_point(all_34_1, all_41_3) = 0 & % 16.82/3.12 | left_apart_point(all_34_2, all_34_0) = 0)) % 16.82/3.12 | % 16.82/3.12 | ALPHA: (15) implies: % 16.82/3.12 | (16) reverse_line(all_34_0) = all_41_3 % 16.82/3.12 | (17) (all_41_0 = 0 & all_41_1 = 0 & left_apart_point(all_34_1, all_34_0) = % 16.82/3.12 | 0 & left_apart_point(all_34_2, all_41_3) = 0) | (all_41_2 = 0 & % 16.82/3.12 | all_41_4 = 0 & left_apart_point(all_34_1, all_41_3) = 0 & % 16.82/3.12 | left_apart_point(all_34_2, all_34_0) = 0) % 16.82/3.12 | % 16.82/3.12 | DELTA: instantiating (13) with fresh symbols all_43_0, all_43_1, all_43_2, % 16.82/3.12 | all_43_3, all_43_4 gives: % 16.82/3.12 | (18) reverse_line(all_34_0) = all_43_3 & $i(all_43_3) & ((all_43_0 = 0 & % 16.82/3.12 | all_43_1 = 0 & left_apart_point(all_34_1, all_34_0) = 0 & % 16.82/3.12 | left_apart_point(all_34_3, all_43_3) = 0) | (all_43_2 = 0 & % 16.82/3.13 | all_43_4 = 0 & left_apart_point(all_34_1, all_43_3) = 0 & % 16.82/3.13 | left_apart_point(all_34_3, all_34_0) = 0)) % 16.82/3.13 | % 16.82/3.13 | ALPHA: (18) implies: % 16.82/3.13 | (19) $i(all_43_3) % 16.82/3.13 | (20) reverse_line(all_34_0) = all_43_3 % 16.82/3.13 | % 16.82/3.13 | DELTA: instantiating (12) with fresh symbols all_45_0, all_45_1, all_45_2, % 16.82/3.13 | all_45_3, all_45_4 gives: % 16.82/3.13 | (21) reverse_line(all_34_0) = all_45_3 & $i(all_45_3) & ((all_45_0 = 0 & % 16.82/3.13 | all_45_1 = 0 & left_apart_point(all_34_2, all_34_0) = 0 & % 16.82/3.13 | left_apart_point(all_34_3, all_45_3) = 0) | (all_45_2 = 0 & % 16.82/3.13 | all_45_4 = 0 & left_apart_point(all_34_2, all_45_3) = 0 & % 16.82/3.13 | left_apart_point(all_34_3, all_34_0) = 0)) % 16.82/3.13 | % 16.82/3.13 | ALPHA: (21) implies: % 16.82/3.13 | (22) reverse_line(all_34_0) = all_45_3 % 16.82/3.13 | % 16.82/3.13 | GROUND_INST: instantiating (3) with all_43_3, all_45_3, all_34_0, simplifying % 16.82/3.13 | with (20), (22) gives: % 16.82/3.13 | (23) all_45_3 = all_43_3 % 16.82/3.13 | % 16.82/3.13 | GROUND_INST: instantiating (3) with all_41_3, all_45_3, all_34_0, simplifying % 16.82/3.13 | with (16), (22) gives: % 16.82/3.13 | (24) all_45_3 = all_41_3 % 16.82/3.13 | % 16.82/3.13 | COMBINE_EQS: (23), (24) imply: % 16.82/3.13 | (25) all_43_3 = all_41_3 % 16.82/3.13 | % 16.82/3.13 | SIMP: (25) implies: % 16.82/3.13 | (26) all_43_3 = all_41_3 % 16.82/3.13 | % 16.82/3.13 | REDUCE: (19), (26) imply: % 16.82/3.13 | (27) $i(all_41_3) % 16.82/3.13 | % 16.82/3.13 | BETA: splitting (17) gives: % 16.82/3.13 | % 16.82/3.13 | Case 1: % 16.82/3.13 | | % 16.82/3.13 | | (28) all_41_0 = 0 & all_41_1 = 0 & left_apart_point(all_34_1, all_34_0) = % 16.82/3.13 | | 0 & left_apart_point(all_34_2, all_41_3) = 0 % 16.82/3.13 | | % 16.82/3.13 | | ALPHA: (28) implies: % 16.82/3.13 | | (29) left_apart_point(all_34_1, all_34_0) = 0 % 16.82/3.13 | | % 16.82/3.13 | | GROUND_INST: instantiating (2) with all_34_1, all_34_0, simplifying with % 16.82/3.13 | | (7), (8), (29) gives: % 16.82/3.13 | | (30) $false % 16.82/3.13 | | % 16.82/3.13 | | CLOSE: (30) is inconsistent. % 16.82/3.13 | | % 16.82/3.13 | Case 2: % 16.82/3.13 | | % 16.82/3.13 | | (31) all_41_2 = 0 & all_41_4 = 0 & left_apart_point(all_34_1, all_41_3) = % 16.82/3.13 | | 0 & left_apart_point(all_34_2, all_34_0) = 0 % 16.82/3.13 | | % 16.82/3.13 | | ALPHA: (31) implies: % 16.82/3.13 | | (32) left_apart_point(all_34_1, all_41_3) = 0 % 16.82/3.13 | | % 16.82/3.13 | | GROUND_INST: instantiating (2) with all_34_1, all_41_3, simplifying with % 16.82/3.13 | | (7), (27), (32) gives: % 16.82/3.13 | | (33) $false % 16.82/3.13 | | % 16.82/3.13 | | CLOSE: (33) is inconsistent. % 16.82/3.13 | | % 16.82/3.13 | End of split % 16.82/3.13 | % 16.82/3.13 End of proof % 16.82/3.13 % SZS output end Proof for theBenchmark % 16.82/3.13 % 16.82/3.13 2493ms %------------------------------------------------------------------------------