%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO210+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 : n001.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 23:22:21 EDT 2023 % Result : Theorem 11.45s 2.38s % Output : Proof 14.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEO210+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n001.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Tue Aug 29 20:00:38 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.57 ________ _____ % 0.19/0.57 ___ __ \_________(_)________________________________ % 0.19/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.57 % 0.19/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.57 (2023-06-19) % 0.19/0.57 % 0.19/0.57 (c) Philipp Rümmer, 2009-2023 % 0.19/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.57 Amanda Stjerna. % 0.19/0.57 Free software under BSD-3-Clause. % 0.19/0.57 % 0.19/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.57 % 0.19/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.58 Running up to 7 provers in parallel. % 0.19/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.04/1.22 Prover 4: Preprocessing ... % 3.04/1.23 Prover 1: Preprocessing ... % 3.61/1.28 Prover 0: Preprocessing ... % 3.61/1.28 Prover 5: Preprocessing ... % 3.61/1.28 Prover 6: Preprocessing ... % 3.61/1.28 Prover 3: Preprocessing ... % 3.61/1.28 Prover 2: Preprocessing ... % 7.41/1.79 Prover 5: Proving ... % 7.41/1.84 Prover 2: Proving ... % 8.60/1.96 Prover 6: Constructing countermodel ... % 8.60/2.01 Prover 3: Constructing countermodel ... % 9.28/2.07 Prover 1: Constructing countermodel ... % 11.45/2.37 Prover 3: proved (1778ms) % 11.45/2.37 % 11.45/2.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.45/2.38 % 11.45/2.38 Prover 5: stopped % 11.45/2.38 Prover 2: stopped % 11.45/2.38 Prover 6: stopped % 11.45/2.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.72/2.41 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.72/2.41 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.72/2.41 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.93/2.49 Prover 7: Preprocessing ... % 11.93/2.49 Prover 10: Preprocessing ... % 11.93/2.51 Prover 11: Preprocessing ... % 11.93/2.53 Prover 8: Preprocessing ... % 12.55/2.54 Prover 4: Constructing countermodel ... % 12.55/2.54 Prover 0: Proving ... % 12.55/2.57 Prover 0: stopped % 12.55/2.58 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.98/2.59 Prover 10: Warning: ignoring some quantifiers % 12.98/2.62 Prover 10: Constructing countermodel ... % 12.98/2.64 Prover 13: Preprocessing ... % 12.98/2.65 Prover 7: Warning: ignoring some quantifiers % 13.43/2.67 Prover 7: Constructing countermodel ... % 13.76/2.73 Prover 1: Found proof (size 44) % 13.76/2.73 Prover 1: proved (2135ms) % 13.76/2.73 Prover 10: stopped % 13.76/2.73 Prover 11: stopped % 13.76/2.73 Prover 13: stopped % 13.76/2.73 Prover 7: stopped % 13.76/2.74 Prover 4: stopped % 14.03/2.76 Prover 8: Warning: ignoring some quantifiers % 14.03/2.78 Prover 8: Constructing countermodel ... % 14.03/2.79 Prover 8: stopped % 14.03/2.79 % 14.03/2.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 14.03/2.79 % 14.03/2.80 % SZS output start Proof for theBenchmark % 14.03/2.81 Assumptions after simplification: % 14.03/2.81 --------------------------------- % 14.03/2.81 % 14.03/2.81 (a4) % 14.48/2.85 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 14.48/2.85 (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 14.48/2.85 apart_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 14.48/2.85 (incident_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] % 14.48/2.85 : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) % 14.48/2.85 % 14.48/2.85 (a5) % 14.48/2.85 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (orthogonal_lines(v0, % 14.48/2.85 v1) = v2) | ~ $i(v1) | ~ $i(v0) | unorthogonal_lines(v0, v1) = 0) & ! % 14.48/2.85 [v0: $i] : ! [v1: $i] : ( ~ (orthogonal_lines(v0, v1) = 0) | ~ $i(v1) | ~ % 14.48/2.85 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) % 14.48/2.85 % 14.48/2.85 (ax2) % 14.48/2.85 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_lines(v0, v1) = % 14.48/2.85 v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v0, v1) = 0) & ! [v0: $i] : % 14.48/2.85 ! [v1: $i] : ( ~ (equal_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 14.48/2.85 int] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) % 14.48/2.85 % 14.48/2.86 (con) % 14.48/2.86 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 14.48/2.86 = 0) & orthogonal_lines(v1, v2) = 0 & incident_point_and_line(v0, v1) = 0 % 14.48/2.86 & equal_lines(v1, v3) = v4 & orthogonal_through_point(v2, v0) = v3 & $i(v3) % 14.48/2.86 & $i(v2) & $i(v1) & $i(v0)) % 14.48/2.86 % 14.48/2.86 (cup1) % 14.48/2.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 14.48/2.86 (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ~ % 14.48/2.86 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 14.48/2.86 (apart_point_and_line(v0, v2) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0 % 14.48/2.86 | v4 = 0))) % 14.48/2.86 % 14.48/2.86 (ooc1) % 14.48/2.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (orthogonal_through_point(v1, % 14.48/2.86 v0) = v2) | ~ (unorthogonal_lines(v2, v1) = 0) | ~ $i(v1) | ~ $i(v0)) % 14.48/2.86 % 14.48/2.86 (ooc2) % 14.48/2.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (orthogonal_through_point(v1, % 14.48/2.86 v0) = v2) | ~ (apart_point_and_line(v0, v2) = 0) | ~ $i(v1) | ~ % 14.48/2.86 $i(v0)) % 14.48/2.86 % 14.48/2.86 (ouo1) % 14.48/2.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 14.48/2.87 int] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ % 14.48/2.87 (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ~ % 14.48/2.87 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 14.48/2.87 (unorthogonal_lines(v2, v3) = v7 & apart_point_and_line(v0, v2) = v6 & (v7 = % 14.48/2.87 0 | v6 = 0))) % 14.48/2.87 % 14.48/2.87 (function-axioms) % 14.48/2.88 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 14.48/2.88 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 14.48/2.88 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.48/2.88 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.48/2.88 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 14.48/2.88 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 14.48/2.88 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 14.48/2.88 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.48/2.88 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.48/2.88 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 14.48/2.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.48/2.88 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 14.48/2.88 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.48/2.88 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 14.48/2.88 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 14.48/2.88 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 14.48/2.88 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 14.48/2.88 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 14.48/2.88 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 14.48/2.88 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 14.48/2.88 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 14.48/2.88 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 14.48/2.88 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.48/2.88 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.48/2.88 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 14.48/2.88 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 14.48/2.88 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 14.48/2.88 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 14.48/2.88 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.48/2.88 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 14.48/2.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.48/2.88 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 14.48/2.88 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 14.48/2.88 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 14.48/2.88 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 14.48/2.88 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 14.48/2.88 % 14.48/2.88 Further assumptions not needed in the proof: % 14.48/2.88 -------------------------------------------- % 14.48/2.88 a3, apart1, apart2, apart3, apart4, apart5, ax1, ax6, ceq1, ceq2, ceq3, ci1, % 14.48/2.88 ci2, ci3, ci4, coipo1, con1, cotno1, couo1, cp1, cp2, cu1, int1, oac1, occu1, % 14.48/2.88 orth1, p1, par1 % 14.48/2.88 % 14.48/2.88 Those formulas are unsatisfiable: % 14.48/2.88 --------------------------------- % 14.48/2.88 % 14.48/2.88 Begin of proof % 14.48/2.88 | % 14.48/2.88 | ALPHA: (ax2) implies: % 14.48/2.88 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 14.48/2.89 | (equal_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 14.48/2.89 | distinct_lines(v0, v1) = 0) % 14.48/2.89 | % 14.48/2.89 | ALPHA: (a4) implies: % 14.48/2.89 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (incident_point_and_line(v0, v1) = 0) | % 14.48/2.89 | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 14.48/2.89 | apart_point_and_line(v0, v1) = v2)) % 14.48/2.89 | % 14.48/2.89 | ALPHA: (a5) implies: % 14.48/2.89 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (orthogonal_lines(v0, v1) = 0) | ~ % 14.48/2.89 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 14.48/2.89 | unorthogonal_lines(v0, v1) = v2)) % 14.48/2.89 | % 14.48/2.89 | ALPHA: (function-axioms) implies: % 14.48/2.89 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 14.48/2.89 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 14.48/2.89 | (apart_point_and_line(v3, v2) = v0)) % 14.48/2.89 | % 14.48/2.89 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 14.48/2.89 | all_38_3, all_38_4 gives: % 14.48/2.90 | (5) ~ (all_38_0 = 0) & orthogonal_lines(all_38_3, all_38_2) = 0 & % 14.48/2.90 | incident_point_and_line(all_38_4, all_38_3) = 0 & equal_lines(all_38_3, % 14.48/2.90 | all_38_1) = all_38_0 & orthogonal_through_point(all_38_2, all_38_4) = % 14.48/2.90 | all_38_1 & $i(all_38_1) & $i(all_38_2) & $i(all_38_3) & $i(all_38_4) % 14.48/2.90 | % 14.48/2.90 | ALPHA: (5) implies: % 14.48/2.90 | (6) ~ (all_38_0 = 0) % 14.48/2.90 | (7) $i(all_38_4) % 14.48/2.90 | (8) $i(all_38_3) % 14.48/2.90 | (9) $i(all_38_2) % 14.48/2.90 | (10) $i(all_38_1) % 14.48/2.90 | (11) orthogonal_through_point(all_38_2, all_38_4) = all_38_1 % 14.48/2.90 | (12) equal_lines(all_38_3, all_38_1) = all_38_0 % 14.48/2.90 | (13) incident_point_and_line(all_38_4, all_38_3) = 0 % 14.48/2.90 | (14) orthogonal_lines(all_38_3, all_38_2) = 0 % 14.48/2.90 | % 14.48/2.90 | GROUND_INST: instantiating (1) with all_38_3, all_38_1, all_38_0, simplifying % 14.48/2.90 | with (8), (10), (12) gives: % 14.48/2.90 | (15) all_38_0 = 0 | distinct_lines(all_38_3, all_38_1) = 0 % 14.48/2.90 | % 14.48/2.90 | GROUND_INST: instantiating (2) with all_38_4, all_38_3, simplifying with (7), % 14.48/2.90 | (8), (13) gives: % 14.48/2.90 | (16) ? [v0: int] : ( ~ (v0 = 0) & apart_point_and_line(all_38_4, all_38_3) % 14.48/2.90 | = v0) % 14.48/2.90 | % 14.48/2.90 | GROUND_INST: instantiating (3) with all_38_3, all_38_2, simplifying with (8), % 14.48/2.90 | (9), (14) gives: % 14.48/2.90 | (17) ? [v0: int] : ( ~ (v0 = 0) & unorthogonal_lines(all_38_3, all_38_2) = % 14.48/2.90 | v0) % 14.48/2.90 | % 14.48/2.90 | DELTA: instantiating (17) with fresh symbol all_45_0 gives: % 14.48/2.90 | (18) ~ (all_45_0 = 0) & unorthogonal_lines(all_38_3, all_38_2) = all_45_0 % 14.48/2.90 | % 14.48/2.90 | ALPHA: (18) implies: % 14.48/2.91 | (19) ~ (all_45_0 = 0) % 14.48/2.91 | (20) unorthogonal_lines(all_38_3, all_38_2) = all_45_0 % 14.48/2.91 | % 14.48/2.91 | DELTA: instantiating (16) with fresh symbol all_47_0 gives: % 14.48/2.91 | (21) ~ (all_47_0 = 0) & apart_point_and_line(all_38_4, all_38_3) = % 14.48/2.91 | all_47_0 % 14.48/2.91 | % 14.48/2.91 | ALPHA: (21) implies: % 14.48/2.91 | (22) ~ (all_47_0 = 0) % 14.48/2.91 | (23) apart_point_and_line(all_38_4, all_38_3) = all_47_0 % 14.48/2.91 | % 14.48/2.91 | BETA: splitting (15) gives: % 14.48/2.91 | % 14.48/2.91 | Case 1: % 14.48/2.91 | | % 14.48/2.91 | | (24) distinct_lines(all_38_3, all_38_1) = 0 % 14.48/2.91 | | % 14.48/2.91 | | GROUND_INST: instantiating (cup1) with all_38_4, all_38_3, all_38_1, % 14.48/2.91 | | all_47_0, simplifying with (7), (8), (10), (23), (24) gives: % 14.48/2.91 | | (25) all_47_0 = 0 | ? [v0: any] : ? [v1: any] : % 14.48/2.91 | | (apart_point_and_line(all_38_4, all_38_1) = v0 & % 14.48/2.91 | | convergent_lines(all_38_3, all_38_1) = v1 & (v1 = 0 | v0 = 0)) % 14.48/2.91 | | % 14.48/2.91 | | GROUND_INST: instantiating (ouo1) with all_38_4, all_38_3, all_38_1, % 14.48/2.91 | | all_38_2, all_47_0, all_45_0, simplifying with (7), (8), (9), % 14.48/2.91 | | (10), (20), (23), (24) gives: % 14.48/2.91 | | (26) all_47_0 = 0 | all_45_0 = 0 | ? [v0: any] : ? [v1: any] : % 14.48/2.91 | | (unorthogonal_lines(all_38_1, all_38_2) = v1 & % 14.48/2.91 | | apart_point_and_line(all_38_4, all_38_1) = v0 & (v1 = 0 | v0 = 0)) % 14.48/2.91 | | % 14.48/2.91 | | BETA: splitting (25) gives: % 14.48/2.91 | | % 14.48/2.91 | | Case 1: % 14.48/2.91 | | | % 14.48/2.91 | | | (27) all_47_0 = 0 % 14.48/2.91 | | | % 14.48/2.91 | | | REDUCE: (22), (27) imply: % 14.48/2.91 | | | (28) $false % 14.48/2.92 | | | % 14.48/2.92 | | | CLOSE: (28) is inconsistent. % 14.48/2.92 | | | % 14.48/2.92 | | Case 2: % 14.48/2.92 | | | % 14.48/2.92 | | | (29) ? [v0: any] : ? [v1: any] : (apart_point_and_line(all_38_4, % 14.48/2.92 | | | all_38_1) = v0 & convergent_lines(all_38_3, all_38_1) = v1 & % 14.48/2.92 | | | (v1 = 0 | v0 = 0)) % 14.48/2.92 | | | % 14.48/2.92 | | | DELTA: instantiating (29) with fresh symbols all_77_0, all_77_1 gives: % 14.48/2.92 | | | (30) apart_point_and_line(all_38_4, all_38_1) = all_77_1 & % 14.48/2.92 | | | convergent_lines(all_38_3, all_38_1) = all_77_0 & (all_77_0 = 0 | % 14.48/2.92 | | | all_77_1 = 0) % 14.48/2.92 | | | % 14.48/2.92 | | | ALPHA: (30) implies: % 14.48/2.92 | | | (31) apart_point_and_line(all_38_4, all_38_1) = all_77_1 % 14.48/2.92 | | | % 14.48/2.92 | | | BETA: splitting (26) gives: % 14.48/2.92 | | | % 14.48/2.92 | | | Case 1: % 14.48/2.92 | | | | % 14.48/2.92 | | | | (32) all_47_0 = 0 % 14.48/2.92 | | | | % 14.48/2.92 | | | | REDUCE: (22), (32) imply: % 14.48/2.92 | | | | (33) $false % 14.48/2.92 | | | | % 14.48/2.92 | | | | CLOSE: (33) is inconsistent. % 14.48/2.92 | | | | % 14.48/2.92 | | | Case 2: % 14.48/2.92 | | | | % 14.48/2.92 | | | | (34) all_45_0 = 0 | ? [v0: any] : ? [v1: any] : % 14.48/2.92 | | | | (unorthogonal_lines(all_38_1, all_38_2) = v1 & % 14.48/2.92 | | | | apart_point_and_line(all_38_4, all_38_1) = v0 & (v1 = 0 | v0 = % 14.48/2.92 | | | | 0)) % 14.48/2.92 | | | | % 14.48/2.92 | | | | BETA: splitting (34) gives: % 14.48/2.92 | | | | % 14.48/2.92 | | | | Case 1: % 14.48/2.92 | | | | | % 14.48/2.92 | | | | | (35) all_45_0 = 0 % 14.48/2.92 | | | | | % 14.48/2.92 | | | | | REDUCE: (19), (35) imply: % 14.48/2.92 | | | | | (36) $false % 14.48/2.92 | | | | | % 14.48/2.92 | | | | | CLOSE: (36) is inconsistent. % 14.48/2.92 | | | | | % 14.48/2.92 | | | | Case 2: % 14.48/2.92 | | | | | % 14.48/2.92 | | | | | (37) ? [v0: any] : ? [v1: any] : (unorthogonal_lines(all_38_1, % 14.48/2.92 | | | | | all_38_2) = v1 & apart_point_and_line(all_38_4, all_38_1) % 14.48/2.92 | | | | | = v0 & (v1 = 0 | v0 = 0)) % 14.48/2.92 | | | | | % 14.48/2.92 | | | | | DELTA: instantiating (37) with fresh symbols all_86_0, all_86_1 gives: % 14.48/2.92 | | | | | (38) unorthogonal_lines(all_38_1, all_38_2) = all_86_0 & % 14.48/2.92 | | | | | apart_point_and_line(all_38_4, all_38_1) = all_86_1 & % 14.48/2.92 | | | | | (all_86_0 = 0 | all_86_1 = 0) % 14.48/2.92 | | | | | % 14.48/2.92 | | | | | ALPHA: (38) implies: % 14.48/2.92 | | | | | (39) apart_point_and_line(all_38_4, all_38_1) = all_86_1 % 14.48/2.92 | | | | | (40) unorthogonal_lines(all_38_1, all_38_2) = all_86_0 % 14.48/2.92 | | | | | (41) all_86_0 = 0 | all_86_1 = 0 % 14.48/2.92 | | | | | % 14.48/2.93 | | | | | GROUND_INST: instantiating (4) with all_77_1, all_86_1, all_38_1, % 14.48/2.93 | | | | | all_38_4, simplifying with (31), (39) gives: % 14.48/2.93 | | | | | (42) all_86_1 = all_77_1 % 14.48/2.93 | | | | | % 14.48/2.93 | | | | | BETA: splitting (41) gives: % 14.48/2.93 | | | | | % 14.48/2.93 | | | | | Case 1: % 14.48/2.93 | | | | | | % 14.48/2.93 | | | | | | (43) all_86_0 = 0 % 14.48/2.93 | | | | | | % 14.48/2.93 | | | | | | REDUCE: (40), (43) imply: % 14.48/2.93 | | | | | | (44) unorthogonal_lines(all_38_1, all_38_2) = 0 % 14.48/2.93 | | | | | | % 14.48/2.93 | | | | | | GROUND_INST: instantiating (ooc1) with all_38_4, all_38_2, all_38_1, % 14.48/2.93 | | | | | | simplifying with (7), (9), (11), (44) gives: % 14.48/2.93 | | | | | | (45) $false % 14.48/2.93 | | | | | | % 14.48/2.93 | | | | | | CLOSE: (45) is inconsistent. % 14.48/2.93 | | | | | | % 14.48/2.93 | | | | | Case 2: % 14.48/2.93 | | | | | | % 14.48/2.93 | | | | | | (46) all_86_1 = 0 % 14.48/2.93 | | | | | | % 14.48/2.93 | | | | | | COMBINE_EQS: (42), (46) imply: % 14.48/2.93 | | | | | | (47) all_77_1 = 0 % 14.48/2.93 | | | | | | % 14.48/2.93 | | | | | | REDUCE: (31), (47) imply: % 14.48/2.93 | | | | | | (48) apart_point_and_line(all_38_4, all_38_1) = 0 % 14.48/2.93 | | | | | | % 14.48/2.93 | | | | | | GROUND_INST: instantiating (ooc2) with all_38_4, all_38_2, all_38_1, % 14.48/2.93 | | | | | | simplifying with (7), (9), (11), (48) gives: % 14.48/2.93 | | | | | | (49) $false % 14.48/2.93 | | | | | | % 14.48/2.93 | | | | | | CLOSE: (49) is inconsistent. % 14.48/2.93 | | | | | | % 14.48/2.93 | | | | | End of split % 14.48/2.93 | | | | | % 14.48/2.93 | | | | End of split % 14.48/2.93 | | | | % 14.48/2.93 | | | End of split % 14.48/2.93 | | | % 14.48/2.93 | | End of split % 14.48/2.93 | | % 14.48/2.93 | Case 2: % 14.48/2.93 | | % 14.48/2.93 | | (50) all_38_0 = 0 % 14.48/2.93 | | % 14.48/2.93 | | REDUCE: (6), (50) imply: % 14.48/2.93 | | (51) $false % 14.48/2.93 | | % 14.48/2.93 | | CLOSE: (51) is inconsistent. % 14.48/2.93 | | % 14.48/2.93 | End of split % 14.48/2.93 | % 14.48/2.93 End of proof % 14.48/2.93 % SZS output end Proof for theBenchmark % 14.48/2.93 % 14.48/2.93 2362ms %------------------------------------------------------------------------------