%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO173+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 : n018.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 23:21:50 EDT 2023 % Result : Theorem 7.60s 1.86s % Output : Proof 10.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO173+3 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n018.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 22:42:03 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.65 ________ _____ % 0.20/0.65 ___ __ \_________(_)________________________________ % 0.20/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.65 % 0.20/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.65 (2023-06-19) % 0.20/0.65 % 0.20/0.65 (c) Philipp Rümmer, 2009-2023 % 0.20/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.65 Amanda Stjerna. % 0.20/0.65 Free software under BSD-3-Clause. % 0.20/0.65 % 0.20/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.65 % 0.20/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.67 Running up to 7 provers in parallel. % 0.86/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.86/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.86/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.86/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.86/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.86/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.86/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.23/1.21 Prover 1: Preprocessing ... % 3.23/1.22 Prover 4: Preprocessing ... % 3.23/1.25 Prover 6: Preprocessing ... % 3.23/1.25 Prover 2: Preprocessing ... % 3.23/1.25 Prover 5: Preprocessing ... % 3.23/1.26 Prover 3: Preprocessing ... % 3.23/1.26 Prover 0: Preprocessing ... % 6.03/1.65 Prover 2: Proving ... % 6.57/1.66 Prover 5: Proving ... % 6.99/1.71 Prover 6: Constructing countermodel ... % 6.99/1.71 Prover 1: Constructing countermodel ... % 6.99/1.73 Prover 3: Constructing countermodel ... % 7.60/1.86 Prover 2: proved (1160ms) % 7.60/1.86 Prover 5: proved (1168ms) % 7.60/1.86 % 7.60/1.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.60/1.86 % 7.60/1.86 % 7.60/1.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.60/1.86 % 7.60/1.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.60/1.88 Prover 3: stopped % 7.60/1.88 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.60/1.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.31/1.90 Prover 6: stopped % 8.31/1.91 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.31/1.93 Prover 8: Preprocessing ... % 8.31/1.94 Prover 10: Preprocessing ... % 8.31/1.94 Prover 7: Preprocessing ... % 8.74/1.97 Prover 11: Preprocessing ... % 8.74/2.02 Prover 7: Warning: ignoring some quantifiers % 8.74/2.03 Prover 1: Found proof (size 37) % 8.74/2.03 Prover 1: proved (1347ms) % 8.74/2.04 Prover 7: Constructing countermodel ... % 8.74/2.05 Prover 10: Warning: ignoring some quantifiers % 8.74/2.05 Prover 4: Constructing countermodel ... % 8.74/2.05 Prover 7: stopped % 9.47/2.07 Prover 0: Proving ... % 9.47/2.07 Prover 10: Constructing countermodel ... % 9.47/2.07 Prover 10: stopped % 9.47/2.08 Prover 0: stopped % 9.47/2.08 Prover 4: stopped % 9.47/2.08 Prover 11: stopped % 9.72/2.11 Prover 8: Warning: ignoring some quantifiers % 9.72/2.12 Prover 8: Constructing countermodel ... % 9.72/2.13 Prover 8: stopped % 9.72/2.13 % 9.72/2.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.72/2.13 % 9.93/2.14 % SZS output start Proof for theBenchmark % 9.93/2.14 Assumptions after simplification: % 9.93/2.14 --------------------------------- % 9.93/2.14 % 9.93/2.14 (ci1) % 9.93/2.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 9.93/2.17 ~ (apart_point_and_line(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] % 9.93/2.17 : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 9.93/2.17 % 9.93/2.17 (ci2) % 9.93/2.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 9.93/2.17 ~ (apart_point_and_line(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] % 9.93/2.17 : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 9.93/2.17 % 9.93/2.17 (con) % 9.93/2.17 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 9.93/2.17 int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & line_connecting(v0, v1) = % 9.93/2.17 v4 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v2) = v5 & % 9.93/2.17 convergent_lines(v2, v3) = 0 & distinct_lines(v2, v4) = 0 & % 9.93/2.17 distinct_points(v0, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 9.93/2.17 % 9.93/2.17 (con1) % 9.93/2.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 9.93/2.17 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: % 9.93/2.17 any] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & % 9.93/2.17 distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | % 9.93/2.17 v6 = 0))) % 9.93/2.17 % 9.93/2.17 (cu1) % 9.93/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 9.93/2.18 (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ~ $i(v3) % 9.93/2.18 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 9.93/2.18 any] : ? [v7: any] : (apart_point_and_line(v1, v3) = v7 & % 9.93/2.18 apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & % 9.93/2.18 apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) % 9.93/2.18 % 9.93/2.18 (function-axioms) % 9.93/2.18 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 9.93/2.18 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 9.93/2.18 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.93/2.18 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.93/2.18 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 9.93/2.18 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.93/2.18 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 9.93/2.18 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.93/2.18 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.93/2.18 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 9.93/2.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.93/2.18 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 9.93/2.18 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.93/2.19 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 9.93/2.19 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 9.93/2.19 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 9.93/2.19 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 9.93/2.19 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 9.93/2.19 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 9.93/2.19 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 9.93/2.19 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 9.93/2.19 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 9.93/2.19 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.93/2.19 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.93/2.19 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 9.93/2.19 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.93/2.19 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 9.93/2.19 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.93/2.19 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.93/2.19 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 9.93/2.19 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.93/2.19 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 9.93/2.19 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.93/2.19 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 9.93/2.19 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 9.93/2.19 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 9.93/2.19 % 9.93/2.19 Further assumptions not needed in the proof: % 9.93/2.19 -------------------------------------------- % 9.93/2.19 a3, a4, a5, apart1, apart2, apart3, apart4, apart5, ax1, ax2, ax6, ceq1, ceq2, % 9.93/2.19 ceq3, ci3, ci4, coipo1, cotno1, couo1, cp1, cp2, cup1, int1, oac1, occu1, ooc1, % 9.93/2.19 ooc2, orth1, ouo1, p1, par1 % 9.93/2.19 % 9.93/2.19 Those formulas are unsatisfiable: % 9.93/2.19 --------------------------------- % 9.93/2.19 % 9.93/2.19 Begin of proof % 9.93/2.19 | % 9.93/2.19 | ALPHA: (function-axioms) implies: % 9.93/2.19 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.93/2.19 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 9.93/2.19 | (distinct_points(v3, v2) = v0)) % 9.93/2.19 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.93/2.19 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 9.93/2.19 | (apart_point_and_line(v3, v2) = v0)) % 9.93/2.19 | % 9.93/2.19 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 9.93/2.19 | all_38_3, all_38_4, all_38_5, all_38_6 gives: % 9.93/2.19 | (3) ~ (all_38_0 = 0) & ~ (all_38_1 = 0) & line_connecting(all_38_6, % 9.93/2.19 | all_38_5) = all_38_2 & apart_point_and_line(all_38_5, all_38_4) = % 9.93/2.19 | all_38_0 & apart_point_and_line(all_38_6, all_38_4) = all_38_1 & % 9.93/2.19 | convergent_lines(all_38_4, all_38_3) = 0 & distinct_lines(all_38_4, % 9.93/2.19 | all_38_2) = 0 & distinct_points(all_38_6, all_38_5) = 0 & % 9.93/2.19 | $i(all_38_2) & $i(all_38_3) & $i(all_38_4) & $i(all_38_5) & % 9.93/2.19 | $i(all_38_6) % 9.93/2.19 | % 9.93/2.19 | ALPHA: (3) implies: % 9.93/2.19 | (4) ~ (all_38_1 = 0) % 9.93/2.19 | (5) ~ (all_38_0 = 0) % 9.93/2.19 | (6) $i(all_38_6) % 9.93/2.19 | (7) $i(all_38_5) % 9.93/2.19 | (8) $i(all_38_4) % 9.93/2.19 | (9) $i(all_38_2) % 9.93/2.19 | (10) distinct_points(all_38_6, all_38_5) = 0 % 9.93/2.19 | (11) distinct_lines(all_38_4, all_38_2) = 0 % 9.93/2.19 | (12) apart_point_and_line(all_38_6, all_38_4) = all_38_1 % 9.93/2.19 | (13) apart_point_and_line(all_38_5, all_38_4) = all_38_0 % 9.93/2.19 | (14) line_connecting(all_38_6, all_38_5) = all_38_2 % 9.93/2.19 | % 9.93/2.20 | GROUND_INST: instantiating (cu1) with all_38_6, all_38_5, all_38_4, all_38_2, % 9.93/2.20 | simplifying with (6), (7), (8), (9), (10), (11) gives: % 9.93/2.20 | (15) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 9.93/2.20 | (apart_point_and_line(all_38_5, all_38_2) = v3 & % 9.93/2.20 | apart_point_and_line(all_38_5, all_38_4) = v2 & % 9.93/2.20 | apart_point_and_line(all_38_6, all_38_2) = v1 & % 9.93/2.20 | apart_point_and_line(all_38_6, all_38_4) = v0 & (v3 = 0 | v2 = 0 | % 9.93/2.20 | v1 = 0 | v0 = 0)) % 9.93/2.20 | % 9.93/2.20 | GROUND_INST: instantiating (con1) with all_38_6, all_38_5, all_38_2, % 9.93/2.20 | simplifying with (6), (7), (14) gives: % 9.93/2.20 | (16) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 9.93/2.20 | (point(all_38_5) = v1 & point(all_38_6) = v0 & line(all_38_2) = v3 & % 9.93/2.20 | distinct_points(all_38_6, all_38_5) = v2 & ( ~ (v2 = 0) | ~ (v1 = % 9.93/2.20 | 0) | ~ (v0 = 0) | v3 = 0)) % 9.93/2.20 | % 10.23/2.20 | DELTA: instantiating (16) with fresh symbols all_46_0, all_46_1, all_46_2, % 10.23/2.20 | all_46_3 gives: % 10.23/2.20 | (17) point(all_38_5) = all_46_2 & point(all_38_6) = all_46_3 & % 10.23/2.20 | line(all_38_2) = all_46_0 & distinct_points(all_38_6, all_38_5) = % 10.23/2.20 | all_46_1 & ( ~ (all_46_1 = 0) | ~ (all_46_2 = 0) | ~ (all_46_3 = 0) % 10.23/2.20 | | all_46_0 = 0) % 10.23/2.20 | % 10.23/2.20 | ALPHA: (17) implies: % 10.23/2.20 | (18) distinct_points(all_38_6, all_38_5) = all_46_1 % 10.23/2.20 | % 10.23/2.20 | DELTA: instantiating (15) with fresh symbols all_48_0, all_48_1, all_48_2, % 10.23/2.20 | all_48_3 gives: % 10.23/2.20 | (19) apart_point_and_line(all_38_5, all_38_2) = all_48_0 & % 10.23/2.20 | apart_point_and_line(all_38_5, all_38_4) = all_48_1 & % 10.23/2.20 | apart_point_and_line(all_38_6, all_38_2) = all_48_2 & % 10.23/2.20 | apart_point_and_line(all_38_6, all_38_4) = all_48_3 & (all_48_0 = 0 | % 10.23/2.20 | all_48_1 = 0 | all_48_2 = 0 | all_48_3 = 0) % 10.23/2.20 | % 10.23/2.20 | ALPHA: (19) implies: % 10.23/2.20 | (20) apart_point_and_line(all_38_6, all_38_4) = all_48_3 % 10.23/2.20 | (21) apart_point_and_line(all_38_6, all_38_2) = all_48_2 % 10.23/2.20 | (22) apart_point_and_line(all_38_5, all_38_4) = all_48_1 % 10.23/2.20 | (23) apart_point_and_line(all_38_5, all_38_2) = all_48_0 % 10.23/2.20 | (24) all_48_0 = 0 | all_48_1 = 0 | all_48_2 = 0 | all_48_3 = 0 % 10.23/2.20 | % 10.23/2.20 | GROUND_INST: instantiating (1) with 0, all_46_1, all_38_5, all_38_6, % 10.23/2.20 | simplifying with (10), (18) gives: % 10.23/2.20 | (25) all_46_1 = 0 % 10.23/2.20 | % 10.23/2.20 | GROUND_INST: instantiating (2) with all_38_1, all_48_3, all_38_4, all_38_6, % 10.23/2.20 | simplifying with (12), (20) gives: % 10.23/2.20 | (26) all_48_3 = all_38_1 % 10.23/2.20 | % 10.23/2.20 | GROUND_INST: instantiating (2) with all_38_0, all_48_1, all_38_4, all_38_5, % 10.23/2.20 | simplifying with (13), (22) gives: % 10.23/2.20 | (27) all_48_1 = all_38_0 % 10.23/2.20 | % 10.23/2.20 | BETA: splitting (24) gives: % 10.23/2.20 | % 10.23/2.20 | Case 1: % 10.23/2.20 | | % 10.23/2.20 | | (28) all_48_0 = 0 % 10.23/2.20 | | % 10.23/2.20 | | REDUCE: (23), (28) imply: % 10.23/2.20 | | (29) apart_point_and_line(all_38_5, all_38_2) = 0 % 10.23/2.20 | | % 10.23/2.20 | | GROUND_INST: instantiating (ci2) with all_38_6, all_38_5, all_38_2, % 10.23/2.20 | | simplifying with (6), (7), (14), (29) gives: % 10.23/2.20 | | (30) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_38_6, all_38_5) = % 10.23/2.20 | | v0) % 10.23/2.20 | | % 10.23/2.20 | | DELTA: instantiating (30) with fresh symbol all_66_0 gives: % 10.23/2.21 | | (31) ~ (all_66_0 = 0) & distinct_points(all_38_6, all_38_5) = all_66_0 % 10.23/2.21 | | % 10.23/2.21 | | ALPHA: (31) implies: % 10.23/2.21 | | (32) ~ (all_66_0 = 0) % 10.23/2.21 | | (33) distinct_points(all_38_6, all_38_5) = all_66_0 % 10.23/2.21 | | % 10.23/2.21 | | GROUND_INST: instantiating (1) with 0, all_66_0, all_38_5, all_38_6, % 10.23/2.21 | | simplifying with (10), (33) gives: % 10.23/2.21 | | (34) all_66_0 = 0 % 10.23/2.21 | | % 10.23/2.21 | | REDUCE: (32), (34) imply: % 10.23/2.21 | | (35) $false % 10.23/2.21 | | % 10.23/2.21 | | CLOSE: (35) is inconsistent. % 10.23/2.21 | | % 10.23/2.21 | Case 2: % 10.23/2.21 | | % 10.23/2.21 | | (36) all_48_1 = 0 | all_48_2 = 0 | all_48_3 = 0 % 10.23/2.21 | | % 10.23/2.21 | | BETA: splitting (36) gives: % 10.23/2.21 | | % 10.23/2.21 | | Case 1: % 10.23/2.21 | | | % 10.23/2.21 | | | (37) all_48_1 = 0 % 10.23/2.21 | | | % 10.23/2.21 | | | COMBINE_EQS: (27), (37) imply: % 10.23/2.21 | | | (38) all_38_0 = 0 % 10.23/2.21 | | | % 10.23/2.21 | | | REDUCE: (5), (38) imply: % 10.23/2.21 | | | (39) $false % 10.23/2.21 | | | % 10.23/2.21 | | | CLOSE: (39) is inconsistent. % 10.23/2.21 | | | % 10.23/2.21 | | Case 2: % 10.23/2.21 | | | % 10.23/2.21 | | | (40) all_48_2 = 0 | all_48_3 = 0 % 10.23/2.21 | | | % 10.23/2.21 | | | BETA: splitting (40) gives: % 10.23/2.21 | | | % 10.23/2.21 | | | Case 1: % 10.23/2.21 | | | | % 10.23/2.21 | | | | (41) all_48_2 = 0 % 10.23/2.21 | | | | % 10.23/2.21 | | | | REDUCE: (21), (41) imply: % 10.23/2.21 | | | | (42) apart_point_and_line(all_38_6, all_38_2) = 0 % 10.23/2.21 | | | | % 10.23/2.21 | | | | GROUND_INST: instantiating (ci1) with all_38_6, all_38_5, all_38_2, % 10.23/2.21 | | | | simplifying with (6), (7), (14), (42) gives: % 10.23/2.21 | | | | (43) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_38_6, % 10.23/2.21 | | | | all_38_5) = v0) % 10.23/2.21 | | | | % 10.23/2.21 | | | | DELTA: instantiating (43) with fresh symbol all_74_0 gives: % 10.23/2.21 | | | | (44) ~ (all_74_0 = 0) & distinct_points(all_38_6, all_38_5) = % 10.23/2.21 | | | | all_74_0 % 10.23/2.21 | | | | % 10.23/2.21 | | | | ALPHA: (44) implies: % 10.23/2.21 | | | | (45) ~ (all_74_0 = 0) % 10.23/2.21 | | | | (46) distinct_points(all_38_6, all_38_5) = all_74_0 % 10.23/2.21 | | | | % 10.23/2.21 | | | | GROUND_INST: instantiating (1) with 0, all_74_0, all_38_5, all_38_6, % 10.23/2.21 | | | | simplifying with (10), (46) gives: % 10.23/2.21 | | | | (47) all_74_0 = 0 % 10.23/2.21 | | | | % 10.23/2.21 | | | | REDUCE: (45), (47) imply: % 10.23/2.21 | | | | (48) $false % 10.23/2.21 | | | | % 10.23/2.21 | | | | CLOSE: (48) is inconsistent. % 10.23/2.21 | | | | % 10.23/2.21 | | | Case 2: % 10.23/2.21 | | | | % 10.23/2.21 | | | | (49) all_48_3 = 0 % 10.23/2.21 | | | | % 10.23/2.21 | | | | COMBINE_EQS: (26), (49) imply: % 10.23/2.21 | | | | (50) all_38_1 = 0 % 10.23/2.21 | | | | % 10.23/2.21 | | | | SIMP: (50) implies: % 10.23/2.21 | | | | (51) all_38_1 = 0 % 10.23/2.21 | | | | % 10.23/2.21 | | | | REDUCE: (4), (51) imply: % 10.23/2.21 | | | | (52) $false % 10.23/2.21 | | | | % 10.23/2.21 | | | | CLOSE: (52) is inconsistent. % 10.23/2.21 | | | | % 10.23/2.21 | | | End of split % 10.23/2.21 | | | % 10.23/2.21 | | End of split % 10.23/2.21 | | % 10.23/2.21 | End of split % 10.23/2.21 | % 10.23/2.21 End of proof % 10.23/2.21 % SZS output end Proof for theBenchmark % 10.23/2.21 % 10.23/2.21 1559ms %------------------------------------------------------------------------------