%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO208+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 : n023.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 23:22:20 EDT 2023 % Result : Theorem 7.85s 1.81s % Output : Proof 10.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : GEO208+3 : TPTP v8.1.2. Released v4.0.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n023.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Tue Aug 29 20:33:10 EDT 2023 % 0.13/0.35 % CPUTime : % 0.65/0.66 ________ _____ % 0.65/0.66 ___ __ \_________(_)________________________________ % 0.65/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.65/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.65/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.65/0.66 % 0.65/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.65/0.66 (2023-06-19) % 0.65/0.66 % 0.65/0.66 (c) Philipp Rümmer, 2009-2023 % 0.65/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.65/0.66 Amanda Stjerna. % 0.65/0.66 Free software under BSD-3-Clause. % 0.65/0.66 % 0.65/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.65/0.67 % 0.65/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.65/0.69 Running up to 7 provers in parallel. % 0.80/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.80/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.80/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.80/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.80/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.80/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.80/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.51/1.24 Prover 4: Preprocessing ... % 3.51/1.24 Prover 1: Preprocessing ... % 3.51/1.28 Prover 2: Preprocessing ... % 3.51/1.28 Prover 5: Preprocessing ... % 3.51/1.28 Prover 3: Preprocessing ... % 3.51/1.28 Prover 0: Preprocessing ... % 3.51/1.28 Prover 6: Preprocessing ... % 5.74/1.60 Prover 5: Proving ... % 5.74/1.60 Prover 2: Proving ... % 6.43/1.66 Prover 1: Constructing countermodel ... % 6.43/1.68 Prover 6: Constructing countermodel ... % 7.03/1.71 Prover 3: Constructing countermodel ... % 7.85/1.81 Prover 6: proved (1111ms) % 7.85/1.81 % 7.85/1.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.85/1.81 % 7.85/1.82 Prover 5: stopped % 7.92/1.82 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.92/1.82 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.92/1.82 Prover 2: stopped % 7.92/1.82 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.92/1.82 Prover 3: stopped % 7.92/1.86 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.92/1.87 Prover 8: Preprocessing ... % 7.92/1.87 Prover 10: Preprocessing ... % 7.92/1.89 Prover 7: Preprocessing ... % 7.92/1.90 Prover 11: Preprocessing ... % 8.60/1.97 Prover 1: Found proof (size 28) % 8.60/1.97 Prover 1: proved (1271ms) % 8.60/1.97 Prover 10: Warning: ignoring some quantifiers % 8.60/1.98 Prover 7: Warning: ignoring some quantifiers % 9.23/2.01 Prover 10: Constructing countermodel ... % 9.23/2.01 Prover 7: Constructing countermodel ... % 9.23/2.02 Prover 10: stopped % 9.23/2.02 Prover 7: stopped % 9.23/2.03 Prover 11: stopped % 9.23/2.03 Prover 4: Constructing countermodel ... % 9.23/2.04 Prover 8: Warning: ignoring some quantifiers % 9.23/2.04 Prover 0: Proving ... % 9.23/2.05 Prover 8: Constructing countermodel ... % 9.23/2.05 Prover 0: stopped % 9.23/2.06 Prover 8: stopped % 9.23/2.06 Prover 4: stopped % 9.23/2.06 % 9.23/2.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.23/2.06 % 9.23/2.07 % SZS output start Proof for theBenchmark % 9.23/2.07 Assumptions after simplification: % 9.23/2.07 --------------------------------- % 9.23/2.07 % 9.23/2.07 (a3) % 9.89/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (parallel_lines(v0, % 9.89/2.10 v1) = v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v1) = 0) & ! % 9.89/2.10 [v0: $i] : ! [v1: $i] : ( ~ (parallel_lines(v0, v1) = 0) | ~ $i(v1) | ~ % 9.89/2.10 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) % 9.89/2.10 % 9.89/2.10 (a4) % 9.89/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 9.89/2.10 (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 9.89/2.10 apart_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 9.89/2.10 (incident_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] % 9.89/2.10 : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) % 9.89/2.10 % 9.89/2.10 (ax2) % 9.89/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_lines(v0, v1) = % 9.89/2.10 v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v0, v1) = 0) & ! [v0: $i] : % 9.89/2.10 ! [v1: $i] : ( ~ (equal_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 9.89/2.10 int] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) % 9.89/2.10 % 9.89/2.10 (con) % 9.89/2.10 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 9.89/2.10 incident_point_and_line(v0, v2) = 0 & incident_point_and_line(v0, v1) = 0 & % 9.89/2.10 parallel_lines(v1, v2) = 0 & equal_lines(v1, v2) = v3 & $i(v2) & $i(v1) & % 9.89/2.10 $i(v0)) % 9.89/2.10 % 9.89/2.10 (cup1) % 9.89/2.10 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 9.89/2.10 (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ~ % 9.89/2.10 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 9.89/2.10 (apart_point_and_line(v0, v2) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0 % 9.89/2.10 | v4 = 0))) % 9.89/2.10 % 9.89/2.10 (p1) % 9.99/2.11 ! [v0: $i] : ! [v1: $i] : ( ~ (distinct_lines(v0, v1) = 0) | ~ $i(v1) | ~ % 9.99/2.11 $i(v0) | convergent_lines(v0, v1) = 0) % 9.99/2.11 % 9.99/2.11 (function-axioms) % 9.99/2.11 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 9.99/2.11 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 9.99/2.11 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.99/2.11 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.99/2.11 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 9.99/2.11 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.99/2.11 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 9.99/2.11 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.99/2.11 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.99/2.11 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 9.99/2.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.99/2.11 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 9.99/2.11 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.99/2.11 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 9.99/2.11 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 9.99/2.11 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 9.99/2.11 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 9.99/2.11 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 9.99/2.11 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 9.99/2.11 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 9.99/2.11 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 9.99/2.11 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 9.99/2.11 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.99/2.11 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.99/2.11 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 9.99/2.11 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.99/2.11 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 9.99/2.11 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.99/2.11 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.99/2.11 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 9.99/2.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.99/2.11 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 9.99/2.11 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.99/2.11 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 9.99/2.11 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 9.99/2.11 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 9.99/2.11 % 9.99/2.11 Further assumptions not needed in the proof: % 9.99/2.11 -------------------------------------------- % 9.99/2.11 a5, apart1, apart2, apart3, apart4, apart5, ax1, ax6, ceq1, ceq2, ceq3, ci1, % 9.99/2.11 ci2, ci3, ci4, coipo1, con1, cotno1, couo1, cp1, cp2, cu1, int1, oac1, occu1, % 9.99/2.11 ooc1, ooc2, orth1, ouo1, par1 % 9.99/2.11 % 9.99/2.11 Those formulas are unsatisfiable: % 9.99/2.11 --------------------------------- % 9.99/2.11 % 9.99/2.11 Begin of proof % 10.04/2.12 | % 10.04/2.12 | ALPHA: (ax2) implies: % 10.04/2.12 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 10.04/2.12 | (equal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 10.04/2.12 | distinct_lines(v0, v1) = 0) % 10.04/2.12 | % 10.04/2.12 | ALPHA: (a3) implies: % 10.04/2.12 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (parallel_lines(v0, v1) = 0) | ~ % 10.04/2.12 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 10.04/2.12 | convergent_lines(v0, v1) = v2)) % 10.04/2.12 | % 10.04/2.12 | ALPHA: (a4) implies: % 10.04/2.12 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (incident_point_and_line(v0, v1) = 0) | % 10.04/2.12 | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 10.04/2.12 | apart_point_and_line(v0, v1) = v2)) % 10.04/2.12 | % 10.04/2.12 | ALPHA: (function-axioms) implies: % 10.04/2.12 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.04/2.12 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 10.04/2.12 | (convergent_lines(v3, v2) = v0)) % 10.04/2.12 | % 10.04/2.12 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 10.04/2.12 | all_38_3 gives: % 10.04/2.12 | (5) ~ (all_38_0 = 0) & incident_point_and_line(all_38_3, all_38_1) = 0 & % 10.04/2.12 | incident_point_and_line(all_38_3, all_38_2) = 0 & % 10.04/2.12 | parallel_lines(all_38_2, all_38_1) = 0 & equal_lines(all_38_2, % 10.04/2.12 | all_38_1) = all_38_0 & $i(all_38_1) & $i(all_38_2) & $i(all_38_3) % 10.04/2.12 | % 10.04/2.12 | ALPHA: (5) implies: % 10.04/2.12 | (6) ~ (all_38_0 = 0) % 10.04/2.12 | (7) $i(all_38_3) % 10.04/2.12 | (8) $i(all_38_2) % 10.04/2.12 | (9) $i(all_38_1) % 10.04/2.12 | (10) equal_lines(all_38_2, all_38_1) = all_38_0 % 10.04/2.12 | (11) parallel_lines(all_38_2, all_38_1) = 0 % 10.04/2.12 | (12) incident_point_and_line(all_38_3, all_38_2) = 0 % 10.04/2.12 | % 10.04/2.12 | GROUND_INST: instantiating (1) with all_38_2, all_38_1, all_38_0, simplifying % 10.04/2.12 | with (8), (9), (10) gives: % 10.04/2.13 | (13) all_38_0 = 0 | distinct_lines(all_38_2, all_38_1) = 0 % 10.04/2.13 | % 10.04/2.13 | GROUND_INST: instantiating (2) with all_38_2, all_38_1, simplifying with (8), % 10.04/2.13 | (9), (11) gives: % 10.04/2.13 | (14) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_2, all_38_1) = % 10.04/2.13 | v0) % 10.04/2.13 | % 10.04/2.13 | GROUND_INST: instantiating (3) with all_38_3, all_38_2, simplifying with (7), % 10.04/2.13 | (8), (12) gives: % 10.04/2.13 | (15) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_38_3, all_38_2) % 10.04/2.13 | = v0) % 10.04/2.13 | % 10.04/2.13 | DELTA: instantiating (14) with fresh symbol all_47_0 gives: % 10.04/2.13 | (16) ~ (all_47_0 = 0) & convergent_lines(all_38_2, all_38_1) = all_47_0 % 10.04/2.13 | % 10.04/2.13 | ALPHA: (16) implies: % 10.04/2.13 | (17) ~ (all_47_0 = 0) % 10.04/2.13 | (18) convergent_lines(all_38_2, all_38_1) = all_47_0 % 10.04/2.13 | % 10.04/2.13 | DELTA: instantiating (15) with fresh symbol all_49_0 gives: % 10.04/2.13 | (19) ~ (all_49_0 = 0) & apart_point_and_line(all_38_3, all_38_2) = % 10.04/2.13 | all_49_0 % 10.04/2.13 | % 10.04/2.13 | ALPHA: (19) implies: % 10.04/2.13 | (20) ~ (all_49_0 = 0) % 10.04/2.13 | (21) apart_point_and_line(all_38_3, all_38_2) = all_49_0 % 10.04/2.13 | % 10.04/2.13 | BETA: splitting (13) gives: % 10.04/2.13 | % 10.04/2.13 | Case 1: % 10.04/2.13 | | % 10.04/2.13 | | (22) distinct_lines(all_38_2, all_38_1) = 0 % 10.04/2.13 | | % 10.04/2.13 | | GROUND_INST: instantiating (p1) with all_38_2, all_38_1, simplifying with % 10.04/2.13 | | (8), (9), (22) gives: % 10.04/2.13 | | (23) convergent_lines(all_38_2, all_38_1) = 0 % 10.04/2.13 | | % 10.04/2.13 | | GROUND_INST: instantiating (cup1) with all_38_3, all_38_2, all_38_1, % 10.04/2.13 | | all_49_0, simplifying with (7), (8), (9), (21), (22) gives: % 10.04/2.13 | | (24) all_49_0 = 0 | ? [v0: any] : ? [v1: any] : % 10.04/2.13 | | (apart_point_and_line(all_38_3, all_38_1) = v0 & % 10.04/2.13 | | convergent_lines(all_38_2, all_38_1) = v1 & (v1 = 0 | v0 = 0)) % 10.04/2.13 | | % 10.04/2.13 | | BETA: splitting (24) gives: % 10.04/2.13 | | % 10.04/2.13 | | Case 1: % 10.04/2.13 | | | % 10.04/2.13 | | | (25) all_49_0 = 0 % 10.04/2.13 | | | % 10.04/2.13 | | | REDUCE: (20), (25) imply: % 10.04/2.13 | | | (26) $false % 10.04/2.13 | | | % 10.04/2.13 | | | CLOSE: (26) is inconsistent. % 10.04/2.13 | | | % 10.04/2.13 | | Case 2: % 10.04/2.13 | | | % 10.04/2.13 | | | (27) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_3, % 10.04/2.13 | | | all_38_1) = v0 & convergent_lines(all_38_2, all_38_1) = v1 & % 10.04/2.13 | | | (v1 = 0 | v0 = 0)) % 10.04/2.13 | | | % 10.04/2.13 | | | DELTA: instantiating (27) with fresh symbols all_65_0, all_65_1 gives: % 10.04/2.13 | | | (28) apart_point_and_line(all_38_3, all_38_1) = all_65_1 & % 10.04/2.13 | | | convergent_lines(all_38_2, all_38_1) = all_65_0 & (all_65_0 = 0 | % 10.04/2.13 | | | all_65_1 = 0) % 10.04/2.13 | | | % 10.04/2.13 | | | ALPHA: (28) implies: % 10.04/2.13 | | | (29) convergent_lines(all_38_2, all_38_1) = all_65_0 % 10.04/2.13 | | | % 10.04/2.13 | | | GROUND_INST: instantiating (4) with all_47_0, all_65_0, all_38_1, % 10.04/2.13 | | | all_38_2, simplifying with (18), (29) gives: % 10.04/2.13 | | | (30) all_65_0 = all_47_0 % 10.04/2.13 | | | % 10.04/2.13 | | | GROUND_INST: instantiating (4) with 0, all_65_0, all_38_1, all_38_2, % 10.04/2.14 | | | simplifying with (23), (29) gives: % 10.04/2.14 | | | (31) all_65_0 = 0 % 10.04/2.14 | | | % 10.04/2.14 | | | COMBINE_EQS: (30), (31) imply: % 10.04/2.14 | | | (32) all_47_0 = 0 % 10.04/2.14 | | | % 10.04/2.14 | | | REDUCE: (17), (32) imply: % 10.04/2.14 | | | (33) $false % 10.04/2.14 | | | % 10.04/2.14 | | | CLOSE: (33) is inconsistent. % 10.04/2.14 | | | % 10.04/2.14 | | End of split % 10.04/2.14 | | % 10.04/2.14 | Case 2: % 10.04/2.14 | | % 10.04/2.14 | | (34) all_38_0 = 0 % 10.04/2.14 | | % 10.04/2.14 | | REDUCE: (6), (34) imply: % 10.04/2.14 | | (35) $false % 10.04/2.14 | | % 10.04/2.14 | | CLOSE: (35) is inconsistent. % 10.04/2.14 | | % 10.04/2.14 | End of split % 10.04/2.14 | % 10.04/2.14 End of proof % 10.04/2.14 % SZS output end Proof for theBenchmark % 10.04/2.14 % 10.04/2.14 1470ms %------------------------------------------------------------------------------