%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO258+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 : n012.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 23:22:49 EDT 2023 % Result : Theorem 7.87s 1.83s % Output : Proof 10.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : GEO258+1 : TPTP v8.1.2. Bugfixed v6.4.0. % 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n012.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Tue Aug 29 21:48:53 EDT 2023 % 0.13/0.33 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.94/1.10 Prover 4: Preprocessing ... % 2.94/1.10 Prover 1: Preprocessing ... % 3.22/1.14 Prover 6: Preprocessing ... % 3.22/1.14 Prover 3: Preprocessing ... % 3.22/1.14 Prover 2: Preprocessing ... % 3.22/1.14 Prover 0: Preprocessing ... % 3.22/1.14 Prover 5: Preprocessing ... % 6.55/1.62 Prover 5: Proving ... % 7.08/1.69 Prover 2: Proving ... % 7.08/1.71 Prover 1: Constructing countermodel ... % 7.08/1.71 Prover 3: Constructing countermodel ... % 7.56/1.73 Prover 6: Constructing countermodel ... % 7.87/1.83 Prover 6: proved (1181ms) % 7.87/1.83 % 7.87/1.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.87/1.83 % 7.87/1.84 Prover 5: stopped % 7.87/1.84 Prover 3: stopped % 8.50/1.85 Prover 2: stopped % 8.50/1.86 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.50/1.86 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.50/1.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.50/1.86 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.76/1.95 Prover 7: Preprocessing ... % 8.76/1.97 Prover 11: Preprocessing ... % 8.76/1.98 Prover 8: Preprocessing ... % 8.76/2.00 Prover 10: Preprocessing ... % 9.29/2.02 Prover 1: Found proof (size 39) % 9.29/2.02 Prover 1: proved (1410ms) % 9.85/2.07 Prover 4: Constructing countermodel ... % 9.85/2.07 Prover 7: Warning: ignoring some quantifiers % 9.85/2.07 Prover 10: Warning: ignoring some quantifiers % 9.85/2.09 Prover 10: Constructing countermodel ... % 9.85/2.09 Prover 11: stopped % 9.85/2.10 Prover 7: Constructing countermodel ... % 10.37/2.10 Prover 10: stopped % 10.37/2.11 Prover 7: stopped % 10.37/2.11 Prover 4: stopped % 10.37/2.14 Prover 8: Warning: ignoring some quantifiers % 10.37/2.16 Prover 8: Constructing countermodel ... % 10.37/2.16 Prover 0: Proving ... % 10.77/2.16 Prover 8: stopped % 10.77/2.17 Prover 0: stopped % 10.77/2.17 % 10.77/2.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.77/2.17 % 10.77/2.17 % SZS output start Proof for theBenchmark % 10.77/2.18 Assumptions after simplification: % 10.77/2.18 --------------------------------- % 10.77/2.18 % 10.77/2.18 (bet_def) % 10.77/2.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 10.77/2.20 | ~ (between_on_line(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 10.77/2.20 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: % 10.77/2.20 any] : (before_on_line(v0, v3, v2) = v7 & before_on_line(v0, v2, v3) = v6 % 10.77/2.21 & before_on_line(v0, v2, v1) = v8 & before_on_line(v0, v1, v2) = v5 & ( ~ % 10.77/2.21 (v8 = 0) | ~ (v7 = 0)) & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : % 10.77/2.21 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (between_on_line(v0, v1, v2, v3) % 10.77/2.21 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? % 10.77/2.21 [v5: any] : ? [v6: any] : ? [v7: any] : (before_on_line(v0, v3, v2) = v6 & % 10.77/2.21 before_on_line(v0, v2, v3) = v5 & before_on_line(v0, v2, v1) = v7 & % 10.77/2.21 before_on_line(v0, v1, v2) = v4 & ((v7 = 0 & v6 = 0) | (v5 = 0 & v4 = % 10.77/2.21 0)))) % 10.77/2.21 % 10.77/2.21 (con) % 10.77/2.21 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 10.77/2.21 = 0) & between_on_line(v0, v3, v2, v1) = v4 & between_on_line(v0, v1, v2, % 10.77/2.21 v3) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 10.77/2.21 % 10.77/2.21 (function-axioms) % 10.77/2.22 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 10.77/2.22 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_on_line(v5, v4, % 10.77/2.22 v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) & ! [v0: % 10.77/2.22 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.77/2.22 : ! [v4: $i] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~ % 10.77/2.22 (before_on_line(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.77/2.22 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 10.77/2.22 (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) & % 10.77/2.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.77/2.22 (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = % 10.77/2.22 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 10.77/2.22 ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 10.77/2.22 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 10.77/2.22 [v3: $i] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~ % 10.77/2.22 (left_convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.77/2.22 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.77/2.22 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 10.77/2.22 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.77/2.22 (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! % 10.77/2.22 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 10.77/2.22 $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, % 10.77/2.22 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 10.77/2.22 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 10.77/2.22 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.77/2.22 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.77/2.22 (unequally_directed_lines(v3, v2) = v1) | ~ (unequally_directed_lines(v3, % 10.77/2.22 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 10.77/2.22 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | % 10.77/2.22 ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 10.77/2.22 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.77/2.22 (left_apart_point(v3, v2) = v1) | ~ (left_apart_point(v3, v2) = v0)) & ! % 10.77/2.22 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 10.77/2.22 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: MultipleValueBool] : % 10.77/2.22 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (line(v2) = v1) | ~ % 10.77/2.22 (line(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 10.77/2.22 (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) % 10.77/2.22 % 10.77/2.22 Further assumptions not needed in the proof: % 10.77/2.22 -------------------------------------------- % 10.77/2.22 apt_def, bf_def, con_def, div_def, oag1, oag10, oag11, oag2, oag3, oag4, oag5, % 10.77/2.22 oag6, oag7, oag8, oag9, oagco1, oagco10, oagco2, oagco3, oagco4, oagco5, oagco6, % 10.77/2.22 oagco7, oagco8, oagco9, oagsub1, oagsub2, oagsub3, oaguc1, oaguc2 % 10.77/2.22 % 10.77/2.22 Those formulas are unsatisfiable: % 10.77/2.22 --------------------------------- % 10.77/2.22 % 10.77/2.22 Begin of proof % 10.77/2.22 | % 10.77/2.22 | ALPHA: (bet_def) implies: % 10.77/2.22 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 10.77/2.22 | (between_on_line(v0, v1, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 10.77/2.22 | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? % 10.77/2.22 | [v7: any] : (before_on_line(v0, v3, v2) = v6 & before_on_line(v0, v2, % 10.77/2.22 | v3) = v5 & before_on_line(v0, v2, v1) = v7 & before_on_line(v0, % 10.77/2.22 | v1, v2) = v4 & ((v7 = 0 & v6 = 0) | (v5 = 0 & v4 = 0)))) % 10.77/2.22 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 10.77/2.22 | (v4 = 0 | ~ (between_on_line(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ % 10.77/2.22 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? % 10.77/2.22 | [v7: any] : ? [v8: any] : (before_on_line(v0, v3, v2) = v7 & % 10.77/2.22 | before_on_line(v0, v2, v3) = v6 & before_on_line(v0, v2, v1) = v8 & % 10.77/2.22 | before_on_line(v0, v1, v2) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0)) & ( ~ % 10.77/2.22 | (v6 = 0) | ~ (v5 = 0)))) % 10.77/2.22 | % 10.77/2.22 | ALPHA: (function-axioms) implies: % 10.77/2.22 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.77/2.22 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = % 10.77/2.22 | v1) | ~ (before_on_line(v4, v3, v2) = v0)) % 10.77/2.22 | % 10.77/2.22 | DELTA: instantiating (con) with fresh symbols all_34_0, all_34_1, all_34_2, % 10.77/2.22 | all_34_3, all_34_4 gives: % 10.77/2.22 | (4) ~ (all_34_0 = 0) & between_on_line(all_34_4, all_34_1, all_34_2, % 10.77/2.22 | all_34_3) = all_34_0 & between_on_line(all_34_4, all_34_3, all_34_2, % 10.77/2.22 | all_34_1) = 0 & $i(all_34_1) & $i(all_34_2) & $i(all_34_3) & % 10.77/2.22 | $i(all_34_4) % 10.77/2.22 | % 10.77/2.23 | ALPHA: (4) implies: % 10.77/2.23 | (5) ~ (all_34_0 = 0) % 10.77/2.23 | (6) $i(all_34_4) % 10.77/2.23 | (7) $i(all_34_3) % 10.77/2.23 | (8) $i(all_34_2) % 10.77/2.23 | (9) $i(all_34_1) % 10.77/2.23 | (10) between_on_line(all_34_4, all_34_3, all_34_2, all_34_1) = 0 % 10.77/2.23 | (11) between_on_line(all_34_4, all_34_1, all_34_2, all_34_3) = all_34_0 % 10.77/2.23 | % 10.77/2.23 | GROUND_INST: instantiating (1) with all_34_4, all_34_3, all_34_2, all_34_1, % 10.77/2.23 | simplifying with (6), (7), (8), (9), (10) gives: % 10.77/2.23 | (12) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 10.77/2.23 | (before_on_line(all_34_4, all_34_1, all_34_2) = v2 & % 10.77/2.23 | before_on_line(all_34_4, all_34_2, all_34_1) = v1 & % 10.77/2.23 | before_on_line(all_34_4, all_34_2, all_34_3) = v3 & % 10.77/2.23 | before_on_line(all_34_4, all_34_3, all_34_2) = v0 & ((v3 = 0 & v2 = % 10.77/2.23 | 0) | (v1 = 0 & v0 = 0))) % 10.77/2.23 | % 10.77/2.23 | GROUND_INST: instantiating (2) with all_34_4, all_34_1, all_34_2, all_34_3, % 10.77/2.23 | all_34_0, simplifying with (6), (7), (8), (9), (11) gives: % 10.77/2.23 | (13) all_34_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 10.77/2.23 | any] : (before_on_line(all_34_4, all_34_1, all_34_2) = v0 & % 10.77/2.23 | before_on_line(all_34_4, all_34_2, all_34_1) = v3 & % 10.77/2.23 | before_on_line(all_34_4, all_34_2, all_34_3) = v1 & % 10.77/2.23 | before_on_line(all_34_4, all_34_3, all_34_2) = v2 & ( ~ (v3 = 0) | % 10.77/2.23 | ~ (v2 = 0)) & ( ~ (v1 = 0) | ~ (v0 = 0))) % 10.77/2.23 | % 10.77/2.23 | DELTA: instantiating (12) with fresh symbols all_41_0, all_41_1, all_41_2, % 10.77/2.23 | all_41_3 gives: % 10.77/2.23 | (14) before_on_line(all_34_4, all_34_1, all_34_2) = all_41_1 & % 10.77/2.23 | before_on_line(all_34_4, all_34_2, all_34_1) = all_41_2 & % 10.77/2.23 | before_on_line(all_34_4, all_34_2, all_34_3) = all_41_0 & % 10.77/2.23 | before_on_line(all_34_4, all_34_3, all_34_2) = all_41_3 & ((all_41_0 = % 10.77/2.23 | 0 & all_41_1 = 0) | (all_41_2 = 0 & all_41_3 = 0)) % 10.77/2.23 | % 10.77/2.23 | ALPHA: (14) implies: % 10.77/2.23 | (15) before_on_line(all_34_4, all_34_3, all_34_2) = all_41_3 % 10.77/2.23 | (16) before_on_line(all_34_4, all_34_2, all_34_3) = all_41_0 % 10.77/2.23 | (17) before_on_line(all_34_4, all_34_2, all_34_1) = all_41_2 % 10.77/2.23 | (18) before_on_line(all_34_4, all_34_1, all_34_2) = all_41_1 % 10.77/2.23 | (19) (all_41_0 = 0 & all_41_1 = 0) | (all_41_2 = 0 & all_41_3 = 0) % 10.77/2.23 | % 10.77/2.23 | BETA: splitting (19) gives: % 10.77/2.23 | % 10.77/2.23 | Case 1: % 10.77/2.23 | | % 10.77/2.23 | | (20) all_41_0 = 0 & all_41_1 = 0 % 10.77/2.23 | | % 10.77/2.23 | | ALPHA: (20) implies: % 10.77/2.23 | | (21) all_41_1 = 0 % 10.77/2.23 | | (22) all_41_0 = 0 % 10.77/2.23 | | % 10.77/2.23 | | REDUCE: (18), (21) imply: % 10.77/2.23 | | (23) before_on_line(all_34_4, all_34_1, all_34_2) = 0 % 10.77/2.23 | | % 10.77/2.23 | | REDUCE: (16), (22) imply: % 10.77/2.23 | | (24) before_on_line(all_34_4, all_34_2, all_34_3) = 0 % 10.77/2.23 | | % 10.77/2.23 | | BETA: splitting (13) gives: % 10.77/2.23 | | % 10.77/2.23 | | Case 1: % 10.77/2.23 | | | % 10.77/2.23 | | | (25) all_34_0 = 0 % 10.77/2.23 | | | % 10.77/2.23 | | | REDUCE: (5), (25) imply: % 10.77/2.23 | | | (26) $false % 10.77/2.24 | | | % 10.77/2.24 | | | CLOSE: (26) is inconsistent. % 10.77/2.24 | | | % 10.77/2.24 | | Case 2: % 10.77/2.24 | | | % 10.77/2.24 | | | (27) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 10.77/2.24 | | | (before_on_line(all_34_4, all_34_1, all_34_2) = v0 & % 10.77/2.24 | | | before_on_line(all_34_4, all_34_2, all_34_1) = v3 & % 10.77/2.24 | | | before_on_line(all_34_4, all_34_2, all_34_3) = v1 & % 10.77/2.24 | | | before_on_line(all_34_4, all_34_3, all_34_2) = v2 & ( ~ (v3 = 0) % 10.77/2.24 | | | | ~ (v2 = 0)) & ( ~ (v1 = 0) | ~ (v0 = 0))) % 10.77/2.24 | | | % 10.77/2.24 | | | DELTA: instantiating (27) with fresh symbols all_54_0, all_54_1, all_54_2, % 10.77/2.24 | | | all_54_3 gives: % 10.77/2.24 | | | (28) before_on_line(all_34_4, all_34_1, all_34_2) = all_54_3 & % 10.77/2.24 | | | before_on_line(all_34_4, all_34_2, all_34_1) = all_54_0 & % 10.77/2.24 | | | before_on_line(all_34_4, all_34_2, all_34_3) = all_54_2 & % 10.77/2.24 | | | before_on_line(all_34_4, all_34_3, all_34_2) = all_54_1 & ( ~ % 10.77/2.24 | | | (all_54_0 = 0) | ~ (all_54_1 = 0)) & ( ~ (all_54_2 = 0) | ~ % 10.77/2.24 | | | (all_54_3 = 0)) % 10.77/2.24 | | | % 10.77/2.24 | | | ALPHA: (28) implies: % 10.77/2.24 | | | (29) before_on_line(all_34_4, all_34_2, all_34_3) = all_54_2 % 10.77/2.24 | | | (30) before_on_line(all_34_4, all_34_1, all_34_2) = all_54_3 % 10.77/2.24 | | | (31) ~ (all_54_2 = 0) | ~ (all_54_3 = 0) % 10.77/2.24 | | | % 10.77/2.24 | | | GROUND_INST: instantiating (3) with 0, all_54_2, all_34_3, all_34_2, % 10.77/2.24 | | | all_34_4, simplifying with (24), (29) gives: % 10.77/2.24 | | | (32) all_54_2 = 0 % 10.77/2.24 | | | % 10.77/2.24 | | | GROUND_INST: instantiating (3) with 0, all_54_3, all_34_2, all_34_1, % 10.77/2.24 | | | all_34_4, simplifying with (23), (30) gives: % 10.77/2.24 | | | (33) all_54_3 = 0 % 10.77/2.24 | | | % 10.77/2.24 | | | BETA: splitting (31) gives: % 10.77/2.24 | | | % 10.77/2.24 | | | Case 1: % 10.77/2.24 | | | | % 10.77/2.24 | | | | (34) ~ (all_54_2 = 0) % 10.77/2.24 | | | | % 10.77/2.24 | | | | REDUCE: (32), (34) imply: % 10.77/2.24 | | | | (35) $false % 10.77/2.24 | | | | % 10.77/2.24 | | | | CLOSE: (35) is inconsistent. % 10.77/2.24 | | | | % 10.77/2.24 | | | Case 2: % 10.77/2.24 | | | | % 10.77/2.24 | | | | (36) ~ (all_54_3 = 0) % 10.77/2.24 | | | | % 10.77/2.24 | | | | REDUCE: (33), (36) imply: % 10.77/2.24 | | | | (37) $false % 10.77/2.24 | | | | % 10.77/2.24 | | | | CLOSE: (37) is inconsistent. % 10.77/2.24 | | | | % 10.77/2.24 | | | End of split % 10.77/2.24 | | | % 10.77/2.24 | | End of split % 10.77/2.24 | | % 10.77/2.24 | Case 2: % 10.77/2.24 | | % 10.77/2.24 | | (38) all_41_2 = 0 & all_41_3 = 0 % 10.77/2.24 | | % 10.77/2.24 | | ALPHA: (38) implies: % 10.77/2.24 | | (39) all_41_3 = 0 % 10.77/2.24 | | (40) all_41_2 = 0 % 10.77/2.24 | | % 10.77/2.24 | | REDUCE: (17), (40) imply: % 10.77/2.24 | | (41) before_on_line(all_34_4, all_34_2, all_34_1) = 0 % 10.77/2.24 | | % 10.77/2.24 | | REDUCE: (15), (39) imply: % 10.77/2.24 | | (42) before_on_line(all_34_4, all_34_3, all_34_2) = 0 % 10.77/2.24 | | % 10.77/2.24 | | BETA: splitting (13) gives: % 10.77/2.24 | | % 10.77/2.24 | | Case 1: % 10.77/2.24 | | | % 10.77/2.24 | | | (43) all_34_0 = 0 % 10.77/2.24 | | | % 10.77/2.24 | | | REDUCE: (5), (43) imply: % 10.77/2.24 | | | (44) $false % 10.77/2.24 | | | % 10.77/2.24 | | | CLOSE: (44) is inconsistent. % 10.77/2.24 | | | % 10.77/2.24 | | Case 2: % 10.77/2.24 | | | % 10.77/2.24 | | | (45) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 10.77/2.24 | | | (before_on_line(all_34_4, all_34_1, all_34_2) = v0 & % 10.77/2.24 | | | before_on_line(all_34_4, all_34_2, all_34_1) = v3 & % 10.77/2.24 | | | before_on_line(all_34_4, all_34_2, all_34_3) = v1 & % 10.77/2.24 | | | before_on_line(all_34_4, all_34_3, all_34_2) = v2 & ( ~ (v3 = 0) % 10.77/2.24 | | | | ~ (v2 = 0)) & ( ~ (v1 = 0) | ~ (v0 = 0))) % 10.77/2.24 | | | % 10.77/2.24 | | | DELTA: instantiating (45) with fresh symbols all_54_0, all_54_1, all_54_2, % 10.77/2.24 | | | all_54_3 gives: % 10.77/2.24 | | | (46) before_on_line(all_34_4, all_34_1, all_34_2) = all_54_3 & % 10.77/2.24 | | | before_on_line(all_34_4, all_34_2, all_34_1) = all_54_0 & % 10.77/2.24 | | | before_on_line(all_34_4, all_34_2, all_34_3) = all_54_2 & % 10.77/2.24 | | | before_on_line(all_34_4, all_34_3, all_34_2) = all_54_1 & ( ~ % 10.77/2.24 | | | (all_54_0 = 0) | ~ (all_54_1 = 0)) & ( ~ (all_54_2 = 0) | ~ % 10.77/2.24 | | | (all_54_3 = 0)) % 10.77/2.24 | | | % 10.77/2.24 | | | ALPHA: (46) implies: % 10.77/2.25 | | | (47) before_on_line(all_34_4, all_34_3, all_34_2) = all_54_1 % 10.77/2.25 | | | (48) before_on_line(all_34_4, all_34_2, all_34_1) = all_54_0 % 10.77/2.25 | | | (49) ~ (all_54_0 = 0) | ~ (all_54_1 = 0) % 10.77/2.25 | | | % 10.77/2.25 | | | GROUND_INST: instantiating (3) with 0, all_54_1, all_34_2, all_34_3, % 10.77/2.25 | | | all_34_4, simplifying with (42), (47) gives: % 10.77/2.25 | | | (50) all_54_1 = 0 % 10.77/2.25 | | | % 10.77/2.25 | | | GROUND_INST: instantiating (3) with 0, all_54_0, all_34_1, all_34_2, % 10.77/2.25 | | | all_34_4, simplifying with (41), (48) gives: % 10.77/2.25 | | | (51) all_54_0 = 0 % 10.77/2.25 | | | % 10.77/2.25 | | | BETA: splitting (49) gives: % 10.77/2.25 | | | % 10.77/2.25 | | | Case 1: % 10.77/2.25 | | | | % 10.77/2.25 | | | | (52) ~ (all_54_0 = 0) % 10.77/2.25 | | | | % 10.77/2.25 | | | | REDUCE: (51), (52) imply: % 10.77/2.25 | | | | (53) $false % 10.77/2.25 | | | | % 10.77/2.25 | | | | CLOSE: (53) is inconsistent. % 10.77/2.25 | | | | % 10.77/2.25 | | | Case 2: % 10.77/2.25 | | | | % 10.77/2.25 | | | | (54) ~ (all_54_1 = 0) % 10.77/2.25 | | | | % 10.77/2.25 | | | | REDUCE: (50), (54) imply: % 10.77/2.25 | | | | (55) $false % 10.77/2.25 | | | | % 10.77/2.25 | | | | CLOSE: (55) is inconsistent. % 10.77/2.25 | | | | % 10.77/2.25 | | | End of split % 10.77/2.25 | | | % 10.77/2.25 | | End of split % 10.77/2.25 | | % 10.77/2.25 | End of split % 10.77/2.25 | % 10.77/2.25 End of proof % 10.77/2.25 % SZS output end Proof for theBenchmark % 10.77/2.25 % 10.77/2.25 1654ms %------------------------------------------------------------------------------