%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO176+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 : n016.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 23:21:52 EDT 2023 % Result : Theorem 7.72s 1.72s % Output : Proof 10.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : GEO176+3 : TPTP v8.1.2. Released v4.0.0. % 0.04/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n016.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Aug 29 20:49:46 EDT 2023 % 0.13/0.34 % CPUTime : % 0.53/0.60 ________ _____ % 0.53/0.60 ___ __ \_________(_)________________________________ % 0.53/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.53/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.53/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.53/0.60 % 0.53/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.53/0.60 (2023-06-19) % 0.53/0.60 % 0.53/0.60 (c) Philipp Rümmer, 2009-2023 % 0.53/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.53/0.60 Amanda Stjerna. % 0.53/0.60 Free software under BSD-3-Clause. % 0.53/0.60 % 0.53/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.53/0.60 % 0.53/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.53/0.61 Running up to 7 provers in parallel. % 0.53/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.53/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.53/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.53/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.53/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.53/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.53/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.16/1.08 Prover 4: Preprocessing ... % 3.16/1.08 Prover 1: Preprocessing ... % 3.16/1.12 Prover 6: Preprocessing ... % 3.16/1.12 Prover 3: Preprocessing ... % 3.16/1.12 Prover 0: Preprocessing ... % 3.16/1.12 Prover 2: Preprocessing ... % 3.16/1.12 Prover 5: Preprocessing ... % 5.94/1.45 Prover 5: Proving ... % 5.94/1.46 Prover 2: Proving ... % 6.65/1.54 Prover 6: Constructing countermodel ... % 6.65/1.54 Prover 3: Constructing countermodel ... % 6.83/1.56 Prover 1: Constructing countermodel ... % 7.72/1.72 Prover 3: proved (1096ms) % 7.72/1.72 % 7.72/1.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.72/1.72 % 7.72/1.72 Prover 5: stopped % 7.72/1.72 Prover 2: stopped % 7.72/1.72 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.72/1.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.72/1.73 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.72/1.73 Prover 6: stopped % 7.72/1.75 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.48/1.78 Prover 7: Preprocessing ... % 8.48/1.80 Prover 11: Preprocessing ... % 8.48/1.81 Prover 10: Preprocessing ... % 8.84/1.83 Prover 8: Preprocessing ... % 8.84/1.84 Prover 1: Found proof (size 34) % 8.84/1.84 Prover 1: proved (1218ms) % 9.02/1.86 Prover 0: Proving ... % 9.02/1.86 Prover 10: Warning: ignoring some quantifiers % 9.02/1.87 Prover 0: stopped % 9.02/1.88 Prover 10: Constructing countermodel ... % 9.02/1.89 Prover 7: Warning: ignoring some quantifiers % 9.02/1.89 Prover 4: Constructing countermodel ... % 9.02/1.90 Prover 10: stopped % 9.02/1.90 Prover 11: stopped % 9.02/1.91 Prover 7: Constructing countermodel ... % 9.02/1.91 Prover 4: stopped % 9.02/1.91 Prover 7: stopped % 9.57/1.97 Prover 8: Warning: ignoring some quantifiers % 9.83/1.97 Prover 8: Constructing countermodel ... % 9.83/1.98 Prover 8: stopped % 9.83/1.98 % 9.83/1.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.83/1.98 % 9.83/1.99 % SZS output start Proof for theBenchmark % 9.83/1.99 Assumptions after simplification: % 9.83/1.99 --------------------------------- % 9.83/1.99 % 9.83/1.99 (ceq1) % 9.83/2.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 9.83/2.02 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | ~ % 9.83/2.02 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v2, v1) = 0) % 9.83/2.02 % 9.83/2.02 (ci3) % 9.83/2.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 9.83/2.02 v2) | ~ (apart_point_and_line(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 9.83/2.02 [v3: int] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 9.83/2.02 % 9.83/2.02 (ci4) % 9.83/2.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 9.83/2.02 v2) | ~ (apart_point_and_line(v2, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 9.83/2.02 [v3: int] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 9.83/2.02 % 9.83/2.02 (con) % 9.83/2.03 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5: % 9.83/2.03 any] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & intersection_point(v2, % 9.83/2.03 v3) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, % 9.83/2.03 v2) = v4 & convergent_lines(v2, v3) = 0 & distinct_points(v0, v6) = v7 & % 9.83/2.03 distinct_points(v0, v1) = 0 & $i(v6) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 9.83/2.03 (v5 = 0 | v4 = 0)) % 9.83/2.03 % 9.83/2.03 (int1) % 9.83/2.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 9.83/2.03 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 9.83/2.03 ? [v6: any] : (point(v2) = v6 & line(v1) = v4 & line(v0) = v3 & % 9.83/2.03 convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | % 9.83/2.03 v6 = 0))) % 9.83/2.03 % 9.83/2.03 (function-axioms) % 9.83/2.04 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 9.83/2.04 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 9.83/2.04 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.83/2.04 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.83/2.04 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 9.83/2.04 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.83/2.04 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 9.83/2.04 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.83/2.04 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.83/2.04 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 9.83/2.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.83/2.04 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 9.83/2.04 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.83/2.04 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 9.83/2.04 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 9.83/2.04 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 9.83/2.04 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 9.83/2.04 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 9.83/2.04 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 9.83/2.04 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 9.83/2.04 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 9.83/2.04 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 9.83/2.04 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.83/2.04 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.83/2.04 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 9.83/2.04 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.83/2.04 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 9.83/2.04 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.83/2.04 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.83/2.04 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 9.83/2.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.83/2.04 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 9.83/2.04 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.83/2.04 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 9.83/2.04 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 9.83/2.04 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 9.83/2.04 % 9.83/2.04 Further assumptions not needed in the proof: % 9.83/2.04 -------------------------------------------- % 9.83/2.05 a3, a4, a5, apart1, apart2, apart3, apart4, apart5, ax1, ax2, ax6, ceq2, ceq3, % 9.83/2.05 ci1, ci2, coipo1, con1, cotno1, couo1, cp1, cp2, cu1, cup1, oac1, occu1, ooc1, % 9.83/2.05 ooc2, orth1, ouo1, p1, par1 % 9.83/2.05 % 9.83/2.05 Those formulas are unsatisfiable: % 9.83/2.05 --------------------------------- % 9.83/2.05 % 9.83/2.05 Begin of proof % 9.83/2.05 | % 9.83/2.05 | ALPHA: (function-axioms) implies: % 10.21/2.05 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.21/2.05 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 10.21/2.05 | (convergent_lines(v3, v2) = v0)) % 10.21/2.05 | % 10.21/2.05 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 10.21/2.05 | all_38_3, all_38_4, all_38_5, all_38_6, all_38_7 gives: % 10.21/2.05 | (2) ~ (all_38_0 = 0) & intersection_point(all_38_5, all_38_4) = all_38_1 & % 10.21/2.05 | apart_point_and_line(all_38_7, all_38_4) = all_38_2 & % 10.21/2.05 | apart_point_and_line(all_38_7, all_38_5) = all_38_3 & % 10.21/2.05 | convergent_lines(all_38_5, all_38_4) = 0 & distinct_points(all_38_7, % 10.21/2.05 | all_38_1) = all_38_0 & distinct_points(all_38_7, all_38_6) = 0 & % 10.21/2.05 | $i(all_38_1) & $i(all_38_4) & $i(all_38_5) & $i(all_38_6) & % 10.21/2.05 | $i(all_38_7) & (all_38_2 = 0 | all_38_3 = 0) % 10.21/2.05 | % 10.21/2.05 | ALPHA: (2) implies: % 10.21/2.05 | (3) ~ (all_38_0 = 0) % 10.21/2.05 | (4) $i(all_38_7) % 10.21/2.05 | (5) $i(all_38_5) % 10.21/2.05 | (6) $i(all_38_4) % 10.21/2.05 | (7) $i(all_38_1) % 10.21/2.05 | (8) distinct_points(all_38_7, all_38_1) = all_38_0 % 10.21/2.05 | (9) convergent_lines(all_38_5, all_38_4) = 0 % 10.21/2.05 | (10) apart_point_and_line(all_38_7, all_38_5) = all_38_3 % 10.21/2.05 | (11) apart_point_and_line(all_38_7, all_38_4) = all_38_2 % 10.21/2.05 | (12) intersection_point(all_38_5, all_38_4) = all_38_1 % 10.21/2.05 | (13) all_38_2 = 0 | all_38_3 = 0 % 10.21/2.05 | % 10.21/2.05 | GROUND_INST: instantiating (int1) with all_38_5, all_38_4, all_38_1, % 10.21/2.05 | simplifying with (5), (6), (12) gives: % 10.21/2.06 | (14) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 10.21/2.06 | (point(all_38_1) = v3 & line(all_38_4) = v1 & line(all_38_5) = v0 & % 10.21/2.06 | convergent_lines(all_38_5, all_38_4) = v2 & ( ~ (v2 = 0) | ~ (v1 = % 10.21/2.06 | 0) | ~ (v0 = 0) | v3 = 0)) % 10.21/2.06 | % 10.21/2.06 | DELTA: instantiating (14) with fresh symbols all_45_0, all_45_1, all_45_2, % 10.21/2.06 | all_45_3 gives: % 10.21/2.06 | (15) point(all_38_1) = all_45_0 & line(all_38_4) = all_45_2 & % 10.21/2.06 | line(all_38_5) = all_45_3 & convergent_lines(all_38_5, all_38_4) = % 10.21/2.06 | all_45_1 & ( ~ (all_45_1 = 0) | ~ (all_45_2 = 0) | ~ (all_45_3 = 0) % 10.21/2.06 | | all_45_0 = 0) % 10.21/2.06 | % 10.21/2.06 | ALPHA: (15) implies: % 10.21/2.06 | (16) convergent_lines(all_38_5, all_38_4) = all_45_1 % 10.21/2.06 | % 10.21/2.06 | GROUND_INST: instantiating (1) with 0, all_45_1, all_38_4, all_38_5, % 10.21/2.06 | simplifying with (9), (16) gives: % 10.21/2.06 | (17) all_45_1 = 0 % 10.21/2.06 | % 10.21/2.06 | BETA: splitting (13) gives: % 10.21/2.06 | % 10.21/2.06 | Case 1: % 10.21/2.06 | | % 10.21/2.06 | | (18) all_38_2 = 0 % 10.21/2.06 | | % 10.21/2.06 | | REDUCE: (11), (18) imply: % 10.21/2.06 | | (19) apart_point_and_line(all_38_7, all_38_4) = 0 % 10.21/2.06 | | % 10.21/2.06 | | GROUND_INST: instantiating (ceq1) with all_38_7, all_38_4, all_38_1, % 10.21/2.06 | | all_38_0, simplifying with (4), (6), (7), (8), (19) gives: % 10.21/2.06 | | (20) all_38_0 = 0 | apart_point_and_line(all_38_1, all_38_4) = 0 % 10.21/2.06 | | % 10.21/2.06 | | BETA: splitting (20) gives: % 10.21/2.06 | | % 10.21/2.06 | | Case 1: % 10.21/2.06 | | | % 10.21/2.06 | | | (21) apart_point_and_line(all_38_1, all_38_4) = 0 % 10.21/2.06 | | | % 10.21/2.06 | | | GROUND_INST: instantiating (ci4) with all_38_5, all_38_4, all_38_1, % 10.21/2.06 | | | simplifying with (5), (6), (12), (21) gives: % 10.21/2.06 | | | (22) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_5, all_38_4) % 10.21/2.06 | | | = v0) % 10.21/2.06 | | | % 10.21/2.06 | | | DELTA: instantiating (22) with fresh symbol all_78_0 gives: % 10.21/2.06 | | | (23) ~ (all_78_0 = 0) & convergent_lines(all_38_5, all_38_4) = % 10.21/2.06 | | | all_78_0 % 10.21/2.06 | | | % 10.21/2.06 | | | ALPHA: (23) implies: % 10.21/2.06 | | | (24) ~ (all_78_0 = 0) % 10.21/2.06 | | | (25) convergent_lines(all_38_5, all_38_4) = all_78_0 % 10.21/2.06 | | | % 10.21/2.06 | | | GROUND_INST: instantiating (1) with 0, all_78_0, all_38_4, all_38_5, % 10.21/2.06 | | | simplifying with (9), (25) gives: % 10.21/2.06 | | | (26) all_78_0 = 0 % 10.21/2.06 | | | % 10.21/2.06 | | | REDUCE: (24), (26) imply: % 10.21/2.06 | | | (27) $false % 10.21/2.06 | | | % 10.21/2.06 | | | CLOSE: (27) is inconsistent. % 10.21/2.06 | | | % 10.21/2.06 | | Case 2: % 10.21/2.06 | | | % 10.21/2.06 | | | (28) all_38_0 = 0 % 10.21/2.06 | | | % 10.21/2.06 | | | REDUCE: (3), (28) imply: % 10.21/2.06 | | | (29) $false % 10.21/2.06 | | | % 10.21/2.06 | | | CLOSE: (29) is inconsistent. % 10.21/2.06 | | | % 10.21/2.06 | | End of split % 10.21/2.06 | | % 10.21/2.06 | Case 2: % 10.21/2.06 | | % 10.21/2.07 | | (30) all_38_3 = 0 % 10.21/2.07 | | % 10.21/2.07 | | REDUCE: (10), (30) imply: % 10.21/2.07 | | (31) apart_point_and_line(all_38_7, all_38_5) = 0 % 10.21/2.07 | | % 10.21/2.07 | | GROUND_INST: instantiating (ceq1) with all_38_7, all_38_5, all_38_1, % 10.21/2.07 | | all_38_0, simplifying with (4), (5), (7), (8), (31) gives: % 10.21/2.07 | | (32) all_38_0 = 0 | apart_point_and_line(all_38_1, all_38_5) = 0 % 10.21/2.07 | | % 10.21/2.07 | | BETA: splitting (32) gives: % 10.21/2.07 | | % 10.21/2.07 | | Case 1: % 10.21/2.07 | | | % 10.21/2.07 | | | (33) apart_point_and_line(all_38_1, all_38_5) = 0 % 10.21/2.07 | | | % 10.21/2.07 | | | GROUND_INST: instantiating (ci3) with all_38_5, all_38_4, all_38_1, % 10.21/2.07 | | | simplifying with (5), (6), (12), (33) gives: % 10.21/2.07 | | | (34) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_5, all_38_4) % 10.21/2.07 | | | = v0) % 10.21/2.07 | | | % 10.21/2.07 | | | DELTA: instantiating (34) with fresh symbol all_78_0 gives: % 10.21/2.07 | | | (35) ~ (all_78_0 = 0) & convergent_lines(all_38_5, all_38_4) = % 10.21/2.07 | | | all_78_0 % 10.21/2.07 | | | % 10.21/2.07 | | | ALPHA: (35) implies: % 10.21/2.07 | | | (36) ~ (all_78_0 = 0) % 10.21/2.07 | | | (37) convergent_lines(all_38_5, all_38_4) = all_78_0 % 10.21/2.07 | | | % 10.21/2.07 | | | GROUND_INST: instantiating (1) with 0, all_78_0, all_38_4, all_38_5, % 10.21/2.07 | | | simplifying with (9), (37) gives: % 10.21/2.07 | | | (38) all_78_0 = 0 % 10.21/2.07 | | | % 10.21/2.07 | | | REDUCE: (36), (38) imply: % 10.21/2.07 | | | (39) $false % 10.21/2.07 | | | % 10.21/2.07 | | | CLOSE: (39) is inconsistent. % 10.21/2.07 | | | % 10.21/2.07 | | Case 2: % 10.21/2.07 | | | % 10.21/2.07 | | | (40) all_38_0 = 0 % 10.21/2.07 | | | % 10.21/2.07 | | | REDUCE: (3), (40) imply: % 10.21/2.07 | | | (41) $false % 10.21/2.07 | | | % 10.21/2.07 | | | CLOSE: (41) is inconsistent. % 10.21/2.07 | | | % 10.21/2.07 | | End of split % 10.21/2.07 | | % 10.21/2.07 | End of split % 10.21/2.07 | % 10.21/2.07 End of proof % 10.21/2.07 % SZS output end Proof for theBenchmark % 10.21/2.07 % 10.21/2.07 1471ms %------------------------------------------------------------------------------