%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO185+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 : 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 23:21:59 EDT 2023 % Result : Theorem 8.45s 1.89s % Output : Proof 10.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO185+3 : TPTP v8.1.2. Released v4.0.0. % 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n022.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Tue Aug 29 23:49:23 EDT 2023 % 0.14/0.34 % CPUTime : % 0.53/0.61 ________ _____ % 0.53/0.61 ___ __ \_________(_)________________________________ % 0.53/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.53/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.53/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.53/0.61 % 0.53/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.53/0.61 (2023-06-19) % 0.53/0.61 % 0.53/0.61 (c) Philipp Rümmer, 2009-2023 % 0.53/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.53/0.61 Amanda Stjerna. % 0.53/0.61 Free software under BSD-3-Clause. % 0.53/0.61 % 0.53/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.53/0.61 % 0.53/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.53/0.62 Running up to 7 provers in parallel. % 0.53/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.53/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.53/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.53/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.53/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.53/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.75/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 3.18/1.16 Prover 1: Preprocessing ... % 3.18/1.16 Prover 4: Preprocessing ... % 3.45/1.20 Prover 5: Preprocessing ... % 3.45/1.20 Prover 6: Preprocessing ... % 3.45/1.20 Prover 3: Preprocessing ... % 3.45/1.20 Prover 0: Preprocessing ... % 3.45/1.20 Prover 2: Preprocessing ... % 6.14/1.55 Prover 5: Proving ... % 6.37/1.59 Prover 2: Proving ... % 7.09/1.69 Prover 1: Constructing countermodel ... % 7.09/1.70 Prover 6: Constructing countermodel ... % 7.09/1.72 Prover 3: Constructing countermodel ... % 8.45/1.89 Prover 3: proved (1250ms) % 8.45/1.89 % 8.45/1.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.45/1.89 % 8.45/1.89 Prover 6: stopped % 8.45/1.89 Prover 2: stopped % 8.45/1.89 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.45/1.90 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.45/1.91 Prover 5: stopped % 8.45/1.91 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.45/1.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.97/1.96 Prover 11: Preprocessing ... % 8.97/1.96 Prover 7: Preprocessing ... % 9.29/1.98 Prover 10: Preprocessing ... % 9.29/1.98 Prover 8: Preprocessing ... % 9.29/2.02 Prover 0: Proving ... % 9.29/2.02 Prover 4: Constructing countermodel ... % 9.82/2.05 Prover 0: stopped % 9.82/2.05 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.82/2.06 Prover 7: Warning: ignoring some quantifiers % 10.04/2.07 Prover 10: Warning: ignoring some quantifiers % 10.04/2.08 Prover 7: Constructing countermodel ... % 10.04/2.08 Prover 13: Preprocessing ... % 10.04/2.09 Prover 1: Found proof (size 48) % 10.04/2.09 Prover 1: proved (1460ms) % 10.04/2.09 Prover 11: stopped % 10.04/2.09 Prover 7: stopped % 10.04/2.10 Prover 4: stopped % 10.04/2.11 Prover 10: Constructing countermodel ... % 10.04/2.11 Prover 10: stopped % 10.04/2.11 Prover 13: stopped % 10.04/2.11 Prover 8: Warning: ignoring some quantifiers % 10.04/2.12 Prover 8: Constructing countermodel ... % 10.44/2.13 Prover 8: stopped % 10.44/2.13 % 10.44/2.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.44/2.13 % 10.44/2.14 % SZS output start Proof for theBenchmark % 10.44/2.15 Assumptions after simplification: % 10.44/2.15 --------------------------------- % 10.44/2.15 % 10.44/2.15 (a4) % 10.63/2.17 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 10.63/2.17 (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 10.63/2.17 apart_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 10.63/2.17 (incident_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] % 10.63/2.17 : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) % 10.63/2.17 % 10.63/2.17 (apart4) % 10.63/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 10.63/2.18 (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | ~ % 10.63/2.18 $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v1, v2) = 0) % 10.63/2.18 % 10.63/2.18 (ax1) % 10.63/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_points(v0, v1) % 10.63/2.18 = v2) | ~ $i(v1) | ~ $i(v0) | distinct_points(v0, v1) = 0) & ! [v0: $i] % 10.63/2.18 : ! [v1: $i] : ( ~ (equal_points(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 10.63/2.18 [v2: int] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) % 10.63/2.18 % 10.63/2.18 (ceq1) % 10.63/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 10.63/2.18 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | ~ % 10.63/2.18 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v2, v1) = 0) % 10.63/2.18 % 10.63/2.18 (ci3) % 10.63/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 10.63/2.18 v2) | ~ (apart_point_and_line(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 10.63/2.18 [v3: int] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 10.63/2.18 % 10.63/2.18 (ci4) % 10.63/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 10.63/2.18 v2) | ~ (apart_point_and_line(v2, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 10.63/2.18 [v3: int] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 10.63/2.18 % 10.63/2.18 (con) % 10.63/2.19 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 10.63/2.19 any] : ? [v6: any] : (incident_point_and_line(v0, v3) = v6 & % 10.63/2.19 incident_point_and_line(v0, v2) = v5 & equal_points(v0, v4) = 0 & % 10.63/2.19 intersection_point(v2, v3) = v4 & convergent_lines(v2, v3) = 0 & % 10.63/2.19 distinct_points(v0, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( % 10.63/2.19 ~ (v6 = 0) | ~ (v5 = 0))) % 10.63/2.19 % 10.63/2.19 (int1) % 10.63/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 10.63/2.19 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 10.63/2.19 ? [v6: any] : (point(v2) = v6 & line(v1) = v4 & line(v0) = v3 & % 10.63/2.19 convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | % 10.63/2.19 v6 = 0))) % 10.63/2.19 % 10.63/2.19 (function-axioms) % 10.63/2.19 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 10.63/2.19 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 10.63/2.19 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.63/2.19 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.63/2.19 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 10.63/2.19 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.63/2.19 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 10.63/2.19 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.63/2.19 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.63/2.19 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 10.63/2.19 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.63/2.19 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 10.63/2.19 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.63/2.19 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 10.63/2.19 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 10.63/2.19 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 10.63/2.19 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 10.63/2.19 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 10.63/2.19 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 10.63/2.19 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 10.63/2.20 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 10.63/2.20 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 10.63/2.20 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.63/2.20 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.63/2.20 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 10.63/2.20 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.63/2.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 10.63/2.20 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.63/2.20 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.63/2.20 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 10.63/2.20 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.63/2.20 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 10.63/2.20 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.63/2.20 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 10.63/2.20 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 10.63/2.20 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 10.63/2.20 % 10.63/2.20 Further assumptions not needed in the proof: % 10.63/2.20 -------------------------------------------- % 10.63/2.20 a3, a5, apart1, apart2, apart3, apart5, ax2, ax6, ceq2, ceq3, ci1, ci2, coipo1, % 10.63/2.20 con1, cotno1, couo1, cp1, cp2, cu1, cup1, oac1, occu1, ooc1, ooc2, orth1, ouo1, % 10.63/2.20 p1, par1 % 10.63/2.20 % 10.63/2.20 Those formulas are unsatisfiable: % 10.63/2.20 --------------------------------- % 10.63/2.20 % 10.63/2.20 Begin of proof % 10.63/2.20 | % 10.63/2.20 | ALPHA: (ax1) implies: % 10.63/2.20 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (equal_points(v0, v1) = 0) | ~ $i(v1) % 10.63/2.20 | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & distinct_points(v0, v1) = % 10.63/2.20 | v2)) % 10.63/2.20 | % 10.63/2.20 | ALPHA: (a4) implies: % 10.63/2.20 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 10.63/2.20 | (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 10.63/2.20 | apart_point_and_line(v0, v1) = 0) % 10.63/2.20 | % 10.63/2.20 | ALPHA: (function-axioms) implies: % 10.63/2.20 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.63/2.20 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 10.63/2.20 | (convergent_lines(v3, v2) = v0)) % 10.63/2.20 | % 10.63/2.20 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 10.63/2.20 | all_38_3, all_38_4, all_38_5, all_38_6 gives: % 10.63/2.20 | (4) incident_point_and_line(all_38_6, all_38_3) = all_38_0 & % 10.63/2.20 | incident_point_and_line(all_38_6, all_38_4) = all_38_1 & % 10.63/2.20 | equal_points(all_38_6, all_38_2) = 0 & intersection_point(all_38_4, % 10.63/2.20 | all_38_3) = all_38_2 & convergent_lines(all_38_4, all_38_3) = 0 & % 10.63/2.20 | distinct_points(all_38_6, all_38_5) = 0 & $i(all_38_2) & $i(all_38_3) & % 10.63/2.20 | $i(all_38_4) & $i(all_38_5) & $i(all_38_6) & ( ~ (all_38_0 = 0) | ~ % 10.63/2.20 | (all_38_1 = 0)) % 10.63/2.20 | % 10.63/2.20 | ALPHA: (4) implies: % 10.63/2.20 | (5) $i(all_38_6) % 10.63/2.20 | (6) $i(all_38_5) % 10.63/2.20 | (7) $i(all_38_4) % 10.63/2.20 | (8) $i(all_38_3) % 10.63/2.20 | (9) $i(all_38_2) % 10.63/2.20 | (10) distinct_points(all_38_6, all_38_5) = 0 % 10.63/2.20 | (11) convergent_lines(all_38_4, all_38_3) = 0 % 10.63/2.20 | (12) intersection_point(all_38_4, all_38_3) = all_38_2 % 10.63/2.20 | (13) equal_points(all_38_6, all_38_2) = 0 % 10.63/2.20 | (14) incident_point_and_line(all_38_6, all_38_4) = all_38_1 % 10.63/2.21 | (15) incident_point_and_line(all_38_6, all_38_3) = all_38_0 % 10.63/2.21 | (16) ~ (all_38_0 = 0) | ~ (all_38_1 = 0) % 10.63/2.21 | % 10.63/2.21 | GROUND_INST: instantiating (int1) with all_38_4, all_38_3, all_38_2, % 10.63/2.21 | simplifying with (7), (8), (12) gives: % 10.63/2.21 | (17) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 10.63/2.21 | (point(all_38_2) = v3 & line(all_38_3) = v1 & line(all_38_4) = v0 & % 10.63/2.21 | convergent_lines(all_38_4, all_38_3) = v2 & ( ~ (v2 = 0) | ~ (v1 = % 10.63/2.21 | 0) | ~ (v0 = 0) | v3 = 0)) % 10.63/2.21 | % 10.63/2.21 | GROUND_INST: instantiating (1) with all_38_6, all_38_2, simplifying with (5), % 10.63/2.21 | (9), (13) gives: % 10.63/2.21 | (18) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_38_6, all_38_2) = % 10.63/2.21 | v0) % 10.63/2.21 | % 10.63/2.21 | GROUND_INST: instantiating (2) with all_38_6, all_38_4, all_38_1, simplifying % 10.63/2.21 | with (5), (7), (14) gives: % 10.63/2.21 | (19) all_38_1 = 0 | apart_point_and_line(all_38_6, all_38_4) = 0 % 10.63/2.21 | % 10.63/2.21 | GROUND_INST: instantiating (2) with all_38_6, all_38_3, all_38_0, simplifying % 10.63/2.21 | with (5), (8), (15) gives: % 10.63/2.21 | (20) all_38_0 = 0 | apart_point_and_line(all_38_6, all_38_3) = 0 % 10.63/2.21 | % 10.63/2.21 | DELTA: instantiating (18) with fresh symbol all_45_0 gives: % 10.63/2.21 | (21) ~ (all_45_0 = 0) & distinct_points(all_38_6, all_38_2) = all_45_0 % 10.63/2.21 | % 10.63/2.21 | ALPHA: (21) implies: % 10.63/2.21 | (22) ~ (all_45_0 = 0) % 10.63/2.21 | (23) distinct_points(all_38_6, all_38_2) = all_45_0 % 10.63/2.21 | % 10.63/2.21 | DELTA: instantiating (17) with fresh symbols all_47_0, all_47_1, all_47_2, % 10.63/2.21 | all_47_3 gives: % 10.63/2.21 | (24) point(all_38_2) = all_47_0 & line(all_38_3) = all_47_2 & % 10.63/2.21 | line(all_38_4) = all_47_3 & convergent_lines(all_38_4, all_38_3) = % 10.63/2.21 | all_47_1 & ( ~ (all_47_1 = 0) | ~ (all_47_2 = 0) | ~ (all_47_3 = 0) % 10.63/2.21 | | all_47_0 = 0) % 10.63/2.21 | % 10.63/2.21 | ALPHA: (24) implies: % 10.63/2.21 | (25) convergent_lines(all_38_4, all_38_3) = all_47_1 % 10.63/2.21 | % 10.63/2.21 | GROUND_INST: instantiating (3) with 0, all_47_1, all_38_3, all_38_4, % 10.63/2.21 | simplifying with (11), (25) gives: % 10.63/2.21 | (26) all_47_1 = 0 % 10.63/2.21 | % 10.63/2.21 | GROUND_INST: instantiating (apart4) with all_38_6, all_38_5, all_38_2, % 10.63/2.21 | all_45_0, simplifying with (5), (6), (9), (10), (23) gives: % 10.63/2.21 | (27) all_45_0 = 0 | distinct_points(all_38_5, all_38_2) = 0 % 10.63/2.21 | % 10.63/2.21 | BETA: splitting (16) gives: % 10.63/2.21 | % 10.63/2.21 | Case 1: % 10.63/2.21 | | % 10.63/2.21 | | (28) ~ (all_38_0 = 0) % 10.63/2.21 | | % 10.63/2.21 | | BETA: splitting (20) gives: % 10.63/2.21 | | % 10.63/2.21 | | Case 1: % 10.63/2.21 | | | % 10.63/2.21 | | | (29) apart_point_and_line(all_38_6, all_38_3) = 0 % 10.63/2.21 | | | % 10.63/2.21 | | | BETA: splitting (27) gives: % 10.63/2.21 | | | % 10.63/2.21 | | | Case 1: % 10.63/2.21 | | | | % 10.63/2.21 | | | | % 10.63/2.21 | | | | GROUND_INST: instantiating (ceq1) with all_38_6, all_38_3, all_38_2, % 10.63/2.21 | | | | all_45_0, simplifying with (5), (8), (9), (23), (29) gives: % 10.63/2.21 | | | | (30) all_45_0 = 0 | apart_point_and_line(all_38_2, all_38_3) = 0 % 10.63/2.21 | | | | % 10.63/2.21 | | | | BETA: splitting (30) gives: % 10.63/2.21 | | | | % 10.63/2.21 | | | | Case 1: % 10.63/2.21 | | | | | % 10.63/2.22 | | | | | (31) apart_point_and_line(all_38_2, all_38_3) = 0 % 10.63/2.22 | | | | | % 10.63/2.22 | | | | | GROUND_INST: instantiating (ci4) with all_38_4, all_38_3, all_38_2, % 10.63/2.22 | | | | | simplifying with (7), (8), (12), (31) gives: % 10.63/2.22 | | | | | (32) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_4, % 10.63/2.22 | | | | | all_38_3) = v0) % 10.63/2.22 | | | | | % 10.63/2.22 | | | | | DELTA: instantiating (32) with fresh symbol all_86_0 gives: % 10.63/2.22 | | | | | (33) ~ (all_86_0 = 0) & convergent_lines(all_38_4, all_38_3) = % 10.63/2.22 | | | | | all_86_0 % 10.63/2.22 | | | | | % 10.63/2.22 | | | | | ALPHA: (33) implies: % 10.63/2.22 | | | | | (34) ~ (all_86_0 = 0) % 10.63/2.22 | | | | | (35) convergent_lines(all_38_4, all_38_3) = all_86_0 % 10.63/2.22 | | | | | % 10.63/2.22 | | | | | GROUND_INST: instantiating (3) with 0, all_86_0, all_38_3, all_38_4, % 10.63/2.22 | | | | | simplifying with (11), (35) gives: % 10.63/2.22 | | | | | (36) all_86_0 = 0 % 10.63/2.22 | | | | | % 10.63/2.22 | | | | | REDUCE: (34), (36) imply: % 10.63/2.22 | | | | | (37) $false % 10.63/2.22 | | | | | % 10.63/2.22 | | | | | CLOSE: (37) is inconsistent. % 10.63/2.22 | | | | | % 10.63/2.22 | | | | Case 2: % 10.63/2.22 | | | | | % 10.63/2.22 | | | | | (38) all_45_0 = 0 % 10.63/2.22 | | | | | % 10.63/2.22 | | | | | REDUCE: (22), (38) imply: % 10.63/2.22 | | | | | (39) $false % 10.63/2.22 | | | | | % 10.63/2.22 | | | | | CLOSE: (39) is inconsistent. % 10.63/2.22 | | | | | % 10.63/2.22 | | | | End of split % 10.63/2.22 | | | | % 10.63/2.22 | | | Case 2: % 10.63/2.22 | | | | % 10.63/2.22 | | | | (40) all_45_0 = 0 % 10.63/2.22 | | | | % 10.63/2.22 | | | | REDUCE: (22), (40) imply: % 10.63/2.22 | | | | (41) $false % 10.63/2.22 | | | | % 10.63/2.22 | | | | CLOSE: (41) is inconsistent. % 10.63/2.22 | | | | % 10.63/2.22 | | | End of split % 10.63/2.22 | | | % 10.63/2.22 | | Case 2: % 10.63/2.22 | | | % 10.63/2.22 | | | (42) all_38_0 = 0 % 10.63/2.22 | | | % 10.63/2.22 | | | REDUCE: (28), (42) imply: % 10.63/2.22 | | | (43) $false % 10.63/2.22 | | | % 10.63/2.22 | | | CLOSE: (43) is inconsistent. % 10.63/2.22 | | | % 10.63/2.22 | | End of split % 10.63/2.22 | | % 10.63/2.22 | Case 2: % 10.63/2.22 | | % 10.63/2.22 | | (44) ~ (all_38_1 = 0) % 10.63/2.22 | | % 10.63/2.22 | | BETA: splitting (19) gives: % 10.63/2.22 | | % 10.63/2.22 | | Case 1: % 10.63/2.22 | | | % 10.63/2.22 | | | (45) apart_point_and_line(all_38_6, all_38_4) = 0 % 10.63/2.22 | | | % 10.63/2.22 | | | GROUND_INST: instantiating (ceq1) with all_38_6, all_38_4, all_38_2, % 10.63/2.22 | | | all_45_0, simplifying with (5), (7), (9), (23), (45) gives: % 10.63/2.22 | | | (46) all_45_0 = 0 | apart_point_and_line(all_38_2, all_38_4) = 0 % 10.63/2.22 | | | % 10.63/2.22 | | | BETA: splitting (46) gives: % 10.63/2.22 | | | % 10.63/2.22 | | | Case 1: % 10.63/2.22 | | | | % 10.63/2.22 | | | | (47) apart_point_and_line(all_38_2, all_38_4) = 0 % 10.63/2.22 | | | | % 10.63/2.22 | | | | GROUND_INST: instantiating (ci3) with all_38_4, all_38_3, all_38_2, % 10.63/2.22 | | | | simplifying with (7), (8), (12), (47) gives: % 10.63/2.22 | | | | (48) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_4, % 10.63/2.22 | | | | all_38_3) = v0) % 10.63/2.22 | | | | % 10.63/2.22 | | | | DELTA: instantiating (48) with fresh symbol all_84_0 gives: % 10.63/2.22 | | | | (49) ~ (all_84_0 = 0) & convergent_lines(all_38_4, all_38_3) = % 10.63/2.22 | | | | all_84_0 % 10.63/2.22 | | | | % 10.63/2.22 | | | | ALPHA: (49) implies: % 10.63/2.22 | | | | (50) ~ (all_84_0 = 0) % 10.63/2.22 | | | | (51) convergent_lines(all_38_4, all_38_3) = all_84_0 % 10.63/2.22 | | | | % 10.63/2.22 | | | | GROUND_INST: instantiating (3) with 0, all_84_0, all_38_3, all_38_4, % 10.63/2.22 | | | | simplifying with (11), (51) gives: % 10.63/2.22 | | | | (52) all_84_0 = 0 % 10.63/2.22 | | | | % 10.63/2.22 | | | | REDUCE: (50), (52) imply: % 10.63/2.22 | | | | (53) $false % 10.63/2.22 | | | | % 10.63/2.22 | | | | CLOSE: (53) is inconsistent. % 10.63/2.22 | | | | % 10.63/2.23 | | | Case 2: % 10.63/2.23 | | | | % 10.63/2.23 | | | | (54) all_45_0 = 0 % 10.63/2.23 | | | | % 10.63/2.23 | | | | REDUCE: (22), (54) imply: % 10.63/2.23 | | | | (55) $false % 10.63/2.23 | | | | % 10.63/2.23 | | | | CLOSE: (55) is inconsistent. % 10.63/2.23 | | | | % 10.63/2.23 | | | End of split % 10.63/2.23 | | | % 10.63/2.23 | | Case 2: % 10.63/2.23 | | | % 10.63/2.23 | | | (56) all_38_1 = 0 % 10.63/2.23 | | | % 10.63/2.23 | | | REDUCE: (44), (56) imply: % 10.63/2.23 | | | (57) $false % 10.63/2.23 | | | % 10.63/2.23 | | | CLOSE: (57) is inconsistent. % 10.63/2.23 | | | % 10.63/2.23 | | End of split % 10.63/2.23 | | % 10.63/2.23 | End of split % 10.63/2.23 | % 10.63/2.23 End of proof % 10.63/2.23 % SZS output end Proof for theBenchmark % 10.63/2.23 % 10.63/2.23 1615ms %------------------------------------------------------------------------------