%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO192+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 : n017.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 23:22:05 EDT 2023 % Result : Theorem 19.75s 3.44s % Output : Proof 20.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GEO192+3 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n017.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Tue Aug 29 23:31:29 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 2.95/1.17 Prover 1: Preprocessing ... % 2.95/1.17 Prover 4: Preprocessing ... % 3.11/1.20 Prover 3: Preprocessing ... % 3.11/1.20 Prover 5: Preprocessing ... % 3.11/1.20 Prover 0: Preprocessing ... % 3.11/1.20 Prover 6: Preprocessing ... % 3.11/1.20 Prover 2: Preprocessing ... % 6.22/1.62 Prover 5: Proving ... % 6.80/1.65 Prover 2: Proving ... % 6.80/1.67 Prover 6: Constructing countermodel ... % 6.99/1.71 Prover 3: Constructing countermodel ... % 6.99/1.72 Prover 1: Constructing countermodel ... % 7.59/1.89 Prover 3: gave up % 8.55/1.90 Prover 6: gave up % 8.55/1.91 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.55/1.93 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.55/1.93 Prover 4: Constructing countermodel ... % 8.90/1.97 Prover 7: Preprocessing ... % 8.90/1.97 Prover 1: gave up % 8.90/2.00 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 8.90/2.01 Prover 8: Preprocessing ... % 8.90/2.04 Prover 7: Warning: ignoring some quantifiers % 8.90/2.04 Prover 0: Proving ... % 8.90/2.04 Prover 9: Preprocessing ... % 9.67/2.06 Prover 7: Constructing countermodel ... % 10.36/2.20 Prover 8: Warning: ignoring some quantifiers % 10.36/2.21 Prover 8: Constructing countermodel ... % 11.98/2.38 Prover 8: gave up % 11.98/2.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.98/2.43 Prover 9: Constructing countermodel ... % 12.73/2.46 Prover 10: Preprocessing ... % 13.09/2.51 Prover 10: Warning: ignoring some quantifiers % 13.09/2.53 Prover 10: Constructing countermodel ... % 13.53/2.65 Prover 7: gave up % 13.53/2.66 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.53/2.69 Prover 11: Preprocessing ... % 15.11/2.81 Prover 10: gave up % 15.11/2.83 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391 % 15.84/2.87 Prover 12: Preprocessing ... % 16.40/2.97 Prover 11: Constructing countermodel ... % 17.46/3.08 Prover 12: Proving ... % 19.75/3.44 Prover 11: Found proof (size 70) % 19.75/3.44 Prover 11: proved (780ms) % 19.75/3.44 Prover 9: stopped % 19.75/3.44 Prover 12: stopped % 19.75/3.44 Prover 0: stopped % 19.75/3.44 Prover 5: stopped % 19.75/3.44 Prover 2: stopped % 19.75/3.44 Prover 4: stopped % 19.75/3.44 % 19.75/3.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 19.75/3.44 % 19.75/3.46 % SZS output start Proof for theBenchmark % 19.75/3.46 Assumptions after simplification: % 19.75/3.46 --------------------------------- % 19.75/3.46 % 19.75/3.46 (apart2) % 20.42/3.49 ! [v0: $i] : ( ~ (distinct_lines(v0, v0) = 0) | ~ $i(v0)) % 20.42/3.49 % 20.42/3.49 (apart5) % 20.42/3.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 20.42/3.49 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = % 20.42/3.49 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 20.42/3.49 distinct_lines(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 20.42/3.49 ! [v3: int] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ % 20.42/3.49 (distinct_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 20.42/3.49 distinct_lines(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 20.42/3.49 [v3: int] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ % 20.42/3.49 (distinct_lines(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 20.42/3.49 distinct_lines(v1, v2) = 0) % 20.42/3.49 % 20.42/3.49 (ceq2) % 20.42/3.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 20.42/3.50 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, % 20.42/3.50 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = % 20.42/3.50 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 20.42/3.50 ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | % 20.42/3.50 ~ (apart_point_and_line(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 20.42/3.50 distinct_lines(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 20.42/3.50 [v3: int] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ % 20.42/3.50 (distinct_lines(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 20.42/3.50 apart_point_and_line(v0, v2) = 0) % 20.42/3.50 % 20.42/3.50 (ci3) % 20.42/3.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 20.42/3.50 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 20.42/3.50 & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 20.42/3.50 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 20.42/3.50 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 20.42/3.50 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 20.42/3.50 apart_point_and_line(v2, v0) = v3 & $i(v2))) % 20.42/3.50 % 20.42/3.50 (ci4) % 20.42/3.50 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, v1) = % 20.42/3.50 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v4 = 0) % 20.42/3.50 & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 20.42/3.50 convergent_lines(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 20.42/3.50 (convergent_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? % 20.42/3.50 [v3: int] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & % 20.42/3.50 apart_point_and_line(v2, v1) = v3 & $i(v2))) % 20.42/3.50 % 20.42/3.50 (con) % 20.42/3.51 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: % 20.42/3.51 int] : (intersection_point(v0, v1) = v3 & apart_point_and_line(v3, v2) = 0 & % 20.42/3.51 convergent_lines(v0, v1) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (( ~ (v5 % 20.42/3.51 = 0) & distinct_lines(v1, v2) = v5) | ( ~ (v4 = 0) & % 20.42/3.51 distinct_lines(v0, v2) = v4))) % 20.42/3.51 % 20.42/3.51 (function-axioms) % 20.56/3.52 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 20.56/3.52 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 20.56/3.52 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.56/3.52 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.56/3.52 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 20.56/3.52 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 20.56/3.52 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 20.56/3.52 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.56/3.52 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.56/3.52 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 20.56/3.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.56/3.52 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 20.56/3.52 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.56/3.52 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 20.56/3.52 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 20.56/3.52 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 20.56/3.52 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 20.56/3.52 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 20.56/3.52 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 20.56/3.52 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 20.56/3.52 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 20.56/3.52 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 20.56/3.52 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.56/3.52 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.56/3.52 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 20.56/3.52 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 20.56/3.52 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 20.56/3.52 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 20.56/3.52 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.56/3.52 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 20.56/3.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.56/3.52 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 20.56/3.52 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 20.56/3.52 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 20.56/3.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 20.56/3.52 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 20.56/3.52 % 20.56/3.52 Further assumptions not needed in the proof: % 20.56/3.52 -------------------------------------------- % 20.56/3.52 a3, a4, a5, apart1, apart3, apart4, ax1, ax2, ax6, ceq1, ceq3, ci1, ci2, coipo1, % 20.56/3.52 con1, cotno1, couo1, cp1, cp2, cu1, cup1, int1, oac1, occu1, ooc1, ooc2, orth1, % 20.56/3.52 ouo1, p1, par1 % 20.56/3.52 % 20.56/3.52 Those formulas are unsatisfiable: % 20.56/3.52 --------------------------------- % 20.56/3.52 % 20.56/3.52 Begin of proof % 20.56/3.52 | % 20.56/3.52 | ALPHA: (apart5) implies: % 20.62/3.53 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 20.62/3.53 | (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | ~ % 20.62/3.53 | $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v0, v2) = 0) % 20.62/3.53 | % 20.62/3.53 | ALPHA: (ci3) implies: % 20.62/3.53 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 20.62/3.53 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 20.62/3.53 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3 % 20.62/3.53 | & $i(v2))) % 20.62/3.53 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 20.62/3.53 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 20.62/3.53 | (( ~ (v4 = 0) & apart_point_and_line(v2, v0) = v4) | ( ~ (v3 = 0) & % 20.62/3.53 | convergent_lines(v0, v1) = v3))) % 20.62/3.53 | % 20.62/3.53 | ALPHA: (ci4) implies: % 20.62/3.53 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (convergent_lines(v0, v1) = 0) | ~ % 20.62/3.53 | $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 20.62/3.53 | intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3 % 20.62/3.53 | & $i(v2))) % 20.62/3.53 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection_point(v0, % 20.62/3.53 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 20.62/3.53 | (( ~ (v4 = 0) & apart_point_and_line(v2, v1) = v4) | ( ~ (v3 = 0) & % 20.62/3.53 | convergent_lines(v0, v1) = v3))) % 20.62/3.53 | % 20.62/3.53 | ALPHA: (ceq2) implies: % 20.62/3.53 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 20.62/3.53 | (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, % 20.62/3.54 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v1, % 20.62/3.54 | v2) = 0) % 20.62/3.54 | % 20.62/3.54 | ALPHA: (function-axioms) implies: % 20.62/3.54 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.62/3.54 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 20.62/3.54 | (convergent_lines(v3, v2) = v0)) % 20.62/3.54 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 20.62/3.54 | ! [v3: $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 20.62/3.54 | (apart_point_and_line(v3, v2) = v0)) % 20.62/3.54 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.62/3.54 | (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = % 20.62/3.54 | v0)) % 20.62/3.54 | % 20.62/3.54 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 20.62/3.54 | all_38_3, all_38_4, all_38_5 gives: % 20.62/3.54 | (10) intersection_point(all_38_5, all_38_4) = all_38_2 & % 20.62/3.54 | apart_point_and_line(all_38_2, all_38_3) = 0 & % 20.62/3.54 | convergent_lines(all_38_5, all_38_4) = 0 & $i(all_38_2) & $i(all_38_3) % 20.62/3.54 | & $i(all_38_4) & $i(all_38_5) & (( ~ (all_38_0 = 0) & % 20.62/3.54 | distinct_lines(all_38_4, all_38_3) = all_38_0) | ( ~ (all_38_1 = % 20.62/3.54 | 0) & distinct_lines(all_38_5, all_38_3) = all_38_1)) % 20.62/3.54 | % 20.62/3.54 | ALPHA: (10) implies: % 20.62/3.54 | (11) $i(all_38_5) % 20.62/3.54 | (12) $i(all_38_4) % 20.62/3.54 | (13) $i(all_38_3) % 20.62/3.54 | (14) convergent_lines(all_38_5, all_38_4) = 0 % 20.62/3.54 | (15) apart_point_and_line(all_38_2, all_38_3) = 0 % 20.62/3.54 | (16) intersection_point(all_38_5, all_38_4) = all_38_2 % 20.62/3.54 | (17) ( ~ (all_38_0 = 0) & distinct_lines(all_38_4, all_38_3) = all_38_0) | % 20.62/3.54 | ( ~ (all_38_1 = 0) & distinct_lines(all_38_5, all_38_3) = all_38_1) % 20.62/3.54 | % 20.62/3.54 | GROUND_INST: instantiating (4) with all_38_5, all_38_4, simplifying with (11), % 20.62/3.54 | (12), (14) gives: % 20.62/3.54 | (18) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 20.62/3.54 | intersection_point(all_38_5, all_38_4) = v0 & % 20.62/3.54 | apart_point_and_line(v0, all_38_4) = v1 & $i(v0)) % 20.62/3.54 | % 20.62/3.54 | GROUND_INST: instantiating (2) with all_38_5, all_38_4, simplifying with (11), % 20.62/3.54 | (12), (14) gives: % 20.62/3.54 | (19) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 20.62/3.54 | intersection_point(all_38_5, all_38_4) = v0 & % 20.62/3.54 | apart_point_and_line(v0, all_38_5) = v1 & $i(v0)) % 20.62/3.54 | % 20.62/3.54 | GROUND_INST: instantiating (5) with all_38_5, all_38_4, all_38_2, simplifying % 20.62/3.54 | with (11), (12), (16) gives: % 20.62/3.55 | (20) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 20.62/3.55 | apart_point_and_line(all_38_2, all_38_4) = v1) | ( ~ (v0 = 0) & % 20.62/3.55 | convergent_lines(all_38_5, all_38_4) = v0)) % 20.62/3.55 | % 20.62/3.55 | GROUND_INST: instantiating (3) with all_38_5, all_38_4, all_38_2, simplifying % 20.62/3.55 | with (11), (12), (16) gives: % 20.62/3.55 | (21) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) & % 20.62/3.55 | apart_point_and_line(all_38_2, all_38_5) = v1) | ( ~ (v0 = 0) & % 20.62/3.55 | convergent_lines(all_38_5, all_38_4) = v0)) % 20.62/3.55 | % 20.62/3.55 | DELTA: instantiating (20) with fresh symbols all_49_0, all_49_1 gives: % 20.62/3.55 | (22) ( ~ (all_49_0 = 0) & apart_point_and_line(all_38_2, all_38_4) = % 20.62/3.55 | all_49_0) | ( ~ (all_49_1 = 0) & convergent_lines(all_38_5, % 20.62/3.55 | all_38_4) = all_49_1) % 20.62/3.55 | % 20.62/3.55 | DELTA: instantiating (21) with fresh symbols all_50_0, all_50_1 gives: % 20.62/3.55 | (23) ( ~ (all_50_0 = 0) & apart_point_and_line(all_38_2, all_38_5) = % 20.62/3.55 | all_50_0) | ( ~ (all_50_1 = 0) & convergent_lines(all_38_5, % 20.62/3.55 | all_38_4) = all_50_1) % 20.62/3.55 | % 20.62/3.55 | DELTA: instantiating (19) with fresh symbols all_51_0, all_51_1 gives: % 20.62/3.55 | (24) ~ (all_51_0 = 0) & intersection_point(all_38_5, all_38_4) = all_51_1 % 20.62/3.55 | & apart_point_and_line(all_51_1, all_38_5) = all_51_0 & $i(all_51_1) % 20.62/3.55 | % 20.62/3.55 | ALPHA: (24) implies: % 20.62/3.55 | (25) ~ (all_51_0 = 0) % 20.62/3.55 | (26) $i(all_51_1) % 20.62/3.55 | (27) apart_point_and_line(all_51_1, all_38_5) = all_51_0 % 20.62/3.55 | (28) intersection_point(all_38_5, all_38_4) = all_51_1 % 20.62/3.55 | % 20.62/3.55 | DELTA: instantiating (18) with fresh symbols all_53_0, all_53_1 gives: % 20.62/3.55 | (29) ~ (all_53_0 = 0) & intersection_point(all_38_5, all_38_4) = all_53_1 % 20.62/3.55 | & apart_point_and_line(all_53_1, all_38_4) = all_53_0 & $i(all_53_1) % 20.62/3.55 | % 20.62/3.55 | ALPHA: (29) implies: % 20.62/3.55 | (30) ~ (all_53_0 = 0) % 20.62/3.55 | (31) apart_point_and_line(all_53_1, all_38_4) = all_53_0 % 20.62/3.55 | (32) intersection_point(all_38_5, all_38_4) = all_53_1 % 20.62/3.55 | % 20.62/3.55 | BETA: splitting (22) gives: % 20.62/3.55 | % 20.62/3.55 | Case 1: % 20.62/3.55 | | % 20.62/3.55 | | (33) ~ (all_49_0 = 0) & apart_point_and_line(all_38_2, all_38_4) = % 20.62/3.55 | | all_49_0 % 20.62/3.55 | | % 20.62/3.55 | | ALPHA: (33) implies: % 20.62/3.55 | | (34) apart_point_and_line(all_38_2, all_38_4) = all_49_0 % 20.62/3.55 | | % 20.62/3.55 | | BETA: splitting (23) gives: % 20.62/3.55 | | % 20.62/3.55 | | Case 1: % 20.62/3.55 | | | % 20.62/3.55 | | | (35) ~ (all_50_0 = 0) & apart_point_and_line(all_38_2, all_38_5) = % 20.62/3.55 | | | all_50_0 % 20.62/3.55 | | | % 20.62/3.55 | | | ALPHA: (35) implies: % 20.62/3.55 | | | (36) apart_point_and_line(all_38_2, all_38_5) = all_50_0 % 20.62/3.55 | | | % 20.62/3.55 | | | GROUND_INST: instantiating (9) with all_38_2, all_53_1, all_38_4, % 20.62/3.55 | | | all_38_5, simplifying with (16), (32) gives: % 20.62/3.55 | | | (37) all_53_1 = all_38_2 % 20.62/3.55 | | | % 20.62/3.55 | | | GROUND_INST: instantiating (9) with all_51_1, all_53_1, all_38_4, % 20.62/3.55 | | | all_38_5, simplifying with (28), (32) gives: % 20.62/3.55 | | | (38) all_53_1 = all_51_1 % 20.62/3.55 | | | % 20.62/3.55 | | | COMBINE_EQS: (37), (38) imply: % 20.62/3.55 | | | (39) all_51_1 = all_38_2 % 20.62/3.55 | | | % 20.62/3.55 | | | REDUCE: (31), (37) imply: % 20.62/3.56 | | | (40) apart_point_and_line(all_38_2, all_38_4) = all_53_0 % 20.62/3.56 | | | % 20.62/3.56 | | | REDUCE: (27), (39) imply: % 20.62/3.56 | | | (41) apart_point_and_line(all_38_2, all_38_5) = all_51_0 % 20.62/3.56 | | | % 20.62/3.56 | | | REDUCE: (26), (39) imply: % 20.62/3.56 | | | (42) $i(all_38_2) % 20.62/3.56 | | | % 20.62/3.56 | | | GROUND_INST: instantiating (8) with all_50_0, all_51_0, all_38_5, % 20.62/3.56 | | | all_38_2, simplifying with (36), (41) gives: % 20.62/3.56 | | | (43) all_51_0 = all_50_0 % 20.62/3.56 | | | % 20.62/3.56 | | | GROUND_INST: instantiating (8) with all_49_0, all_53_0, all_38_4, % 20.62/3.56 | | | all_38_2, simplifying with (34), (40) gives: % 20.62/3.56 | | | (44) all_53_0 = all_49_0 % 20.62/3.56 | | | % 20.62/3.56 | | | REDUCE: (30), (44) imply: % 20.62/3.56 | | | (45) ~ (all_49_0 = 0) % 20.62/3.56 | | | % 20.62/3.56 | | | REDUCE: (25), (43) imply: % 20.62/3.56 | | | (46) ~ (all_50_0 = 0) % 20.62/3.56 | | | % 20.62/3.56 | | | GROUND_INST: instantiating (6) with all_38_2, all_38_3, all_38_5, % 20.62/3.56 | | | all_50_0, simplifying with (11), (13), (15), (36), (42) % 20.62/3.56 | | | gives: % 20.62/3.56 | | | (47) all_50_0 = 0 | distinct_lines(all_38_3, all_38_5) = 0 % 20.62/3.56 | | | % 20.62/3.56 | | | GROUND_INST: instantiating (6) with all_38_2, all_38_3, all_38_4, % 20.62/3.56 | | | all_49_0, simplifying with (12), (13), (15), (34), (42) % 20.62/3.56 | | | gives: % 20.62/3.56 | | | (48) all_49_0 = 0 | distinct_lines(all_38_3, all_38_4) = 0 % 20.62/3.56 | | | % 20.62/3.56 | | | BETA: splitting (17) gives: % 20.62/3.56 | | | % 20.62/3.56 | | | Case 1: % 20.62/3.56 | | | | % 20.62/3.56 | | | | (49) ~ (all_38_0 = 0) & distinct_lines(all_38_4, all_38_3) = % 20.62/3.56 | | | | all_38_0 % 20.62/3.56 | | | | % 20.62/3.56 | | | | ALPHA: (49) implies: % 20.62/3.56 | | | | (50) ~ (all_38_0 = 0) % 20.62/3.56 | | | | (51) distinct_lines(all_38_4, all_38_3) = all_38_0 % 20.62/3.56 | | | | % 20.62/3.56 | | | | BETA: splitting (48) gives: % 20.62/3.56 | | | | % 20.62/3.56 | | | | Case 1: % 20.62/3.56 | | | | | % 20.62/3.56 | | | | | (52) distinct_lines(all_38_3, all_38_4) = 0 % 20.62/3.56 | | | | | % 20.62/3.56 | | | | | GROUND_INST: instantiating (1) with all_38_3, all_38_4, all_38_3, % 20.62/3.56 | | | | | all_38_0, simplifying with (12), (13), (51), (52) gives: % 20.62/3.56 | | | | | (53) all_38_0 = 0 | distinct_lines(all_38_3, all_38_3) = 0 % 20.62/3.56 | | | | | % 20.62/3.56 | | | | | BETA: splitting (53) gives: % 20.62/3.56 | | | | | % 20.62/3.56 | | | | | Case 1: % 20.62/3.56 | | | | | | % 20.62/3.56 | | | | | | (54) distinct_lines(all_38_3, all_38_3) = 0 % 20.62/3.56 | | | | | | % 20.62/3.56 | | | | | | GROUND_INST: instantiating (apart2) with all_38_3, simplifying with % 20.62/3.56 | | | | | | (13), (54) gives: % 20.62/3.56 | | | | | | (55) $false % 20.62/3.56 | | | | | | % 20.62/3.56 | | | | | | CLOSE: (55) is inconsistent. % 20.62/3.56 | | | | | | % 20.62/3.56 | | | | | Case 2: % 20.62/3.56 | | | | | | % 20.62/3.56 | | | | | | (56) all_38_0 = 0 % 20.62/3.56 | | | | | | % 20.62/3.56 | | | | | | REDUCE: (50), (56) imply: % 20.62/3.56 | | | | | | (57) $false % 20.62/3.56 | | | | | | % 20.62/3.56 | | | | | | CLOSE: (57) is inconsistent. % 20.62/3.56 | | | | | | % 20.62/3.56 | | | | | End of split % 20.62/3.56 | | | | | % 20.62/3.56 | | | | Case 2: % 20.62/3.56 | | | | | % 20.62/3.56 | | | | | (58) all_49_0 = 0 % 20.62/3.56 | | | | | % 20.62/3.56 | | | | | REDUCE: (45), (58) imply: % 20.62/3.56 | | | | | (59) $false % 20.62/3.56 | | | | | % 20.62/3.56 | | | | | CLOSE: (59) is inconsistent. % 20.62/3.56 | | | | | % 20.62/3.56 | | | | End of split % 20.62/3.56 | | | | % 20.62/3.56 | | | Case 2: % 20.62/3.56 | | | | % 20.62/3.56 | | | | (60) ~ (all_38_1 = 0) & distinct_lines(all_38_5, all_38_3) = % 20.62/3.56 | | | | all_38_1 % 20.62/3.56 | | | | % 20.62/3.56 | | | | ALPHA: (60) implies: % 20.62/3.56 | | | | (61) ~ (all_38_1 = 0) % 20.62/3.56 | | | | (62) distinct_lines(all_38_5, all_38_3) = all_38_1 % 20.62/3.56 | | | | % 20.62/3.56 | | | | BETA: splitting (47) gives: % 20.62/3.56 | | | | % 20.62/3.56 | | | | Case 1: % 20.62/3.56 | | | | | % 20.62/3.56 | | | | | (63) distinct_lines(all_38_3, all_38_5) = 0 % 20.62/3.56 | | | | | % 20.62/3.56 | | | | | GROUND_INST: instantiating (1) with all_38_3, all_38_5, all_38_3, % 20.62/3.56 | | | | | all_38_1, simplifying with (11), (13), (62), (63) gives: % 20.62/3.56 | | | | | (64) all_38_1 = 0 | distinct_lines(all_38_3, all_38_3) = 0 % 20.62/3.57 | | | | | % 20.62/3.57 | | | | | BETA: splitting (64) gives: % 20.62/3.57 | | | | | % 20.62/3.57 | | | | | Case 1: % 20.62/3.57 | | | | | | % 20.62/3.57 | | | | | | (65) distinct_lines(all_38_3, all_38_3) = 0 % 20.62/3.57 | | | | | | % 20.62/3.57 | | | | | | GROUND_INST: instantiating (apart2) with all_38_3, simplifying with % 20.62/3.57 | | | | | | (13), (65) gives: % 20.62/3.57 | | | | | | (66) $false % 20.62/3.57 | | | | | | % 20.62/3.57 | | | | | | CLOSE: (66) is inconsistent. % 20.62/3.57 | | | | | | % 20.62/3.57 | | | | | Case 2: % 20.62/3.57 | | | | | | % 20.62/3.57 | | | | | | (67) all_38_1 = 0 % 20.62/3.57 | | | | | | % 20.62/3.57 | | | | | | REDUCE: (61), (67) imply: % 20.62/3.57 | | | | | | (68) $false % 20.62/3.57 | | | | | | % 20.62/3.57 | | | | | | CLOSE: (68) is inconsistent. % 20.62/3.57 | | | | | | % 20.62/3.57 | | | | | End of split % 20.62/3.57 | | | | | % 20.62/3.57 | | | | Case 2: % 20.62/3.57 | | | | | % 20.62/3.57 | | | | | (69) all_50_0 = 0 % 20.62/3.57 | | | | | % 20.62/3.57 | | | | | REDUCE: (46), (69) imply: % 20.62/3.57 | | | | | (70) $false % 20.62/3.57 | | | | | % 20.62/3.57 | | | | | CLOSE: (70) is inconsistent. % 20.62/3.57 | | | | | % 20.62/3.57 | | | | End of split % 20.62/3.57 | | | | % 20.62/3.57 | | | End of split % 20.62/3.57 | | | % 20.62/3.57 | | Case 2: % 20.62/3.57 | | | % 20.62/3.57 | | | (71) ~ (all_50_1 = 0) & convergent_lines(all_38_5, all_38_4) = % 20.62/3.57 | | | all_50_1 % 20.62/3.57 | | | % 20.62/3.57 | | | ALPHA: (71) implies: % 20.62/3.57 | | | (72) ~ (all_50_1 = 0) % 20.62/3.57 | | | (73) convergent_lines(all_38_5, all_38_4) = all_50_1 % 20.62/3.57 | | | % 20.62/3.57 | | | GROUND_INST: instantiating (7) with 0, all_50_1, all_38_4, all_38_5, % 20.62/3.57 | | | simplifying with (14), (73) gives: % 20.62/3.57 | | | (74) all_50_1 = 0 % 20.62/3.57 | | | % 20.62/3.57 | | | REDUCE: (72), (74) imply: % 20.62/3.57 | | | (75) $false % 20.62/3.57 | | | % 20.62/3.57 | | | CLOSE: (75) is inconsistent. % 20.62/3.57 | | | % 20.62/3.57 | | End of split % 20.62/3.57 | | % 20.62/3.57 | Case 2: % 20.62/3.57 | | % 20.62/3.57 | | (76) ~ (all_49_1 = 0) & convergent_lines(all_38_5, all_38_4) = all_49_1 % 20.62/3.57 | | % 20.62/3.57 | | ALPHA: (76) implies: % 20.62/3.57 | | (77) ~ (all_49_1 = 0) % 20.62/3.57 | | (78) convergent_lines(all_38_5, all_38_4) = all_49_1 % 20.62/3.57 | | % 20.62/3.57 | | GROUND_INST: instantiating (7) with 0, all_49_1, all_38_4, all_38_5, % 20.62/3.57 | | simplifying with (14), (78) gives: % 20.62/3.57 | | (79) all_49_1 = 0 % 20.62/3.57 | | % 20.62/3.57 | | REDUCE: (77), (79) imply: % 20.62/3.57 | | (80) $false % 20.62/3.57 | | % 20.62/3.57 | | CLOSE: (80) is inconsistent. % 20.62/3.57 | | % 20.62/3.57 | End of split % 20.62/3.57 | % 20.62/3.57 End of proof % 20.62/3.57 % SZS output end Proof for theBenchmark % 20.62/3.57 % 20.62/3.57 2961ms %------------------------------------------------------------------------------