%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO183+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 : n004.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 23:21:58 EDT 2023 % Result : Theorem 9.39s 1.97s % Output : Proof 11.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.09 % Problem : GEO183+3 : TPTP v8.1.2. Released v4.0.0. % 0.04/0.09 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.28 % Computer : n004.cluster.edu % 0.09/0.28 % Model : x86_64 x86_64 % 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.28 % Memory : 8042.1875MB % 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.28 % CPULimit : 300 % 0.09/0.28 % WCLimit : 300 % 0.09/0.28 % DateTime : Tue Aug 29 22:54:07 EDT 2023 % 0.09/0.28 % CPUTime : % 0.13/0.53 ________ _____ % 0.13/0.53 ___ __ \_________(_)________________________________ % 0.13/0.53 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.13/0.53 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.13/0.53 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.13/0.53 % 0.13/0.53 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.13/0.53 (2023-06-19) % 0.13/0.53 % 0.13/0.53 (c) Philipp Rümmer, 2009-2023 % 0.13/0.53 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.13/0.53 Amanda Stjerna. % 0.13/0.53 Free software under BSD-3-Clause. % 0.13/0.53 % 0.13/0.53 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.13/0.53 % 0.13/0.53 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.13/0.55 Running up to 7 provers in parallel. % 0.13/0.56 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.13/0.56 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.13/0.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.13/0.56 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.13/0.56 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.13/0.56 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.13/0.56 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.92/1.06 Prover 4: Preprocessing ... % 2.92/1.06 Prover 1: Preprocessing ... % 2.92/1.11 Prover 2: Preprocessing ... % 2.92/1.11 Prover 6: Preprocessing ... % 2.92/1.11 Prover 0: Preprocessing ... % 2.92/1.11 Prover 5: Preprocessing ... % 3.52/1.12 Prover 3: Preprocessing ... % 6.49/1.55 Prover 5: Proving ... % 6.49/1.55 Prover 2: Proving ... % 6.94/1.66 Prover 6: Constructing countermodel ... % 7.38/1.69 Prover 3: Constructing countermodel ... % 7.38/1.74 Prover 1: Constructing countermodel ... % 9.39/1.97 Prover 3: proved (1409ms) % 9.39/1.97 % 9.39/1.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.39/1.97 % 9.39/1.97 Prover 5: stopped % 9.39/1.98 Prover 6: stopped % 9.39/1.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 9.39/1.98 Prover 2: stopped % 9.39/1.98 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.39/1.98 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.39/1.98 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.39/2.04 Prover 7: Preprocessing ... % 9.39/2.04 Prover 11: Preprocessing ... % 9.39/2.04 Prover 8: Preprocessing ... % 9.39/2.05 Prover 10: Preprocessing ... % 9.91/2.08 Prover 4: Constructing countermodel ... % 9.91/2.10 Prover 0: Proving ... % 9.91/2.11 Prover 10: Warning: ignoring some quantifiers % 9.91/2.12 Prover 0: stopped % 10.72/2.12 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.72/2.14 Prover 7: Warning: ignoring some quantifiers % 10.72/2.15 Prover 10: Constructing countermodel ... % 10.72/2.15 Prover 1: Found proof (size 43) % 10.72/2.15 Prover 1: proved (1594ms) % 10.72/2.15 Prover 10: stopped % 10.72/2.16 Prover 13: Preprocessing ... % 10.72/2.16 Prover 4: stopped % 10.72/2.16 Prover 7: Constructing countermodel ... % 10.72/2.16 Prover 11: stopped % 10.72/2.17 Prover 7: stopped % 10.72/2.18 Prover 13: stopped % 10.72/2.21 Prover 8: Warning: ignoring some quantifiers % 10.72/2.22 Prover 8: Constructing countermodel ... % 11.35/2.23 Prover 8: stopped % 11.35/2.23 % 11.35/2.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.35/2.23 % 11.35/2.24 % SZS output start Proof for theBenchmark % 11.35/2.24 Assumptions after simplification: % 11.35/2.24 --------------------------------- % 11.35/2.24 % 11.35/2.24 (a4) % 11.35/2.26 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 11.35/2.27 (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 11.35/2.27 apart_point_and_line(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 11.35/2.27 (incident_point_and_line(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] % 11.35/2.27 : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) % 11.35/2.27 % 11.35/2.27 (ax2) % 11.35/2.27 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_lines(v0, v1) = % 11.35/2.27 v2) | ~ $i(v1) | ~ $i(v0) | distinct_lines(v0, v1) = 0) & ! [v0: $i] : % 11.35/2.27 ! [v1: $i] : ( ~ (equal_lines(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 11.35/2.27 int] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) % 11.35/2.27 % 11.35/2.27 (ceq2) % 11.35/2.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 11.35/2.27 (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | ~ % 11.35/2.27 $i(v2) | ~ $i(v1) | ~ $i(v0) | apart_point_and_line(v0, v2) = 0) % 11.35/2.27 % 11.35/2.27 (ci1) % 11.35/2.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 11.35/2.27 ~ (apart_point_and_line(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] % 11.35/2.27 : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 11.35/2.27 % 11.35/2.27 (ci2) % 11.35/2.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 11.35/2.27 ~ (apart_point_and_line(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] % 11.35/2.27 : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) % 11.35/2.27 % 11.35/2.27 (con) % 11.35/2.28 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 11.35/2.28 any] : ? [v6: any] : (incident_point_and_line(v1, v2) = v6 & % 11.35/2.28 incident_point_and_line(v0, v2) = v5 & equal_lines(v2, v4) = 0 & % 11.35/2.28 line_connecting(v0, v1) = v4 & convergent_lines(v2, v3) = 0 & % 11.35/2.28 distinct_points(v0, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( % 11.35/2.28 ~ (v6 = 0) | ~ (v5 = 0))) % 11.35/2.28 % 11.35/2.28 (con1) % 11.35/2.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (line_connecting(v0, v1) = v2) | % 11.35/2.28 ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: % 11.35/2.28 any] : (point(v1) = v4 & point(v0) = v3 & line(v2) = v6 & % 11.35/2.28 distinct_points(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | % 11.35/2.28 v6 = 0))) % 11.35/2.28 % 11.35/2.28 (function-axioms) % 11.35/2.29 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 11.35/2.29 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 11.35/2.29 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.35/2.29 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.35/2.29 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 11.35/2.29 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 11.35/2.29 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 11.35/2.29 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.35/2.29 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.35/2.29 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 11.35/2.29 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 11.35/2.29 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 11.35/2.29 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.35/2.29 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 11.35/2.29 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 11.35/2.29 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 11.35/2.29 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 11.35/2.29 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 11.35/2.29 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 11.35/2.29 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 11.35/2.29 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 11.35/2.29 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 11.35/2.29 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.35/2.29 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.35/2.29 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 11.35/2.29 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 11.35/2.29 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 11.35/2.29 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.35/2.29 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.35/2.29 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 11.35/2.29 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 11.35/2.29 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 11.35/2.29 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 11.35/2.29 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 11.35/2.29 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 11.35/2.29 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 11.35/2.29 % 11.35/2.29 Further assumptions not needed in the proof: % 11.35/2.29 -------------------------------------------- % 11.35/2.29 a3, a5, apart1, apart2, apart3, apart4, apart5, ax1, ax6, ceq1, ceq3, ci3, ci4, % 11.35/2.29 coipo1, cotno1, couo1, cp1, cp2, cu1, cup1, int1, oac1, occu1, ooc1, ooc2, % 11.35/2.29 orth1, ouo1, p1, par1 % 11.35/2.29 % 11.35/2.29 Those formulas are unsatisfiable: % 11.35/2.29 --------------------------------- % 11.35/2.29 % 11.35/2.29 Begin of proof % 11.35/2.29 | % 11.35/2.29 | ALPHA: (ax2) implies: % 11.35/2.29 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (equal_lines(v0, v1) = 0) | ~ $i(v1) | % 11.35/2.29 | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = % 11.35/2.29 | v2)) % 11.35/2.29 | % 11.35/2.29 | ALPHA: (a4) implies: % 11.35/2.29 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 11.35/2.29 | (incident_point_and_line(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 11.35/2.29 | apart_point_and_line(v0, v1) = 0) % 11.35/2.29 | % 11.35/2.29 | ALPHA: (function-axioms) implies: % 11.35/2.30 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 11.35/2.30 | ! [v3: $i] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ % 11.35/2.30 | (distinct_points(v3, v2) = v0)) % 11.35/2.30 | % 11.35/2.30 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 11.35/2.30 | all_38_3, all_38_4, all_38_5, all_38_6 gives: % 11.35/2.30 | (4) incident_point_and_line(all_38_5, all_38_4) = all_38_0 & % 11.35/2.30 | incident_point_and_line(all_38_6, all_38_4) = all_38_1 & % 11.35/2.30 | equal_lines(all_38_4, all_38_2) = 0 & line_connecting(all_38_6, % 11.35/2.30 | all_38_5) = all_38_2 & convergent_lines(all_38_4, all_38_3) = 0 & % 11.35/2.30 | distinct_points(all_38_6, all_38_5) = 0 & $i(all_38_2) & $i(all_38_3) & % 11.35/2.30 | $i(all_38_4) & $i(all_38_5) & $i(all_38_6) & ( ~ (all_38_0 = 0) | ~ % 11.35/2.30 | (all_38_1 = 0)) % 11.35/2.30 | % 11.35/2.30 | ALPHA: (4) implies: % 11.74/2.30 | (5) $i(all_38_6) % 11.74/2.30 | (6) $i(all_38_5) % 11.74/2.30 | (7) $i(all_38_4) % 11.74/2.30 | (8) $i(all_38_2) % 11.74/2.30 | (9) distinct_points(all_38_6, all_38_5) = 0 % 11.74/2.30 | (10) line_connecting(all_38_6, all_38_5) = all_38_2 % 11.74/2.30 | (11) equal_lines(all_38_4, all_38_2) = 0 % 11.74/2.30 | (12) incident_point_and_line(all_38_6, all_38_4) = all_38_1 % 11.74/2.30 | (13) incident_point_and_line(all_38_5, all_38_4) = all_38_0 % 11.74/2.30 | (14) ~ (all_38_0 = 0) | ~ (all_38_1 = 0) % 11.74/2.30 | % 11.74/2.30 | GROUND_INST: instantiating (con1) with all_38_6, all_38_5, all_38_2, % 11.74/2.30 | simplifying with (5), (6), (10) gives: % 11.74/2.30 | (15) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 11.74/2.30 | (point(all_38_5) = v1 & point(all_38_6) = v0 & line(all_38_2) = v3 & % 11.74/2.30 | distinct_points(all_38_6, all_38_5) = v2 & ( ~ (v2 = 0) | ~ (v1 = % 11.74/2.30 | 0) | ~ (v0 = 0) | v3 = 0)) % 11.74/2.30 | % 11.74/2.30 | GROUND_INST: instantiating (1) with all_38_4, all_38_2, simplifying with (7), % 11.74/2.30 | (8), (11) gives: % 11.74/2.30 | (16) ? [v0: int] : ( ~ (v0 = 0) & distinct_lines(all_38_4, all_38_2) = v0) % 11.74/2.30 | % 11.74/2.30 | GROUND_INST: instantiating (2) with all_38_6, all_38_4, all_38_1, simplifying % 11.74/2.30 | with (5), (7), (12) gives: % 11.74/2.30 | (17) all_38_1 = 0 | apart_point_and_line(all_38_6, all_38_4) = 0 % 11.74/2.30 | % 11.74/2.30 | GROUND_INST: instantiating (2) with all_38_5, all_38_4, all_38_0, simplifying % 11.74/2.30 | with (6), (7), (13) gives: % 11.74/2.30 | (18) all_38_0 = 0 | apart_point_and_line(all_38_5, all_38_4) = 0 % 11.74/2.30 | % 11.74/2.30 | DELTA: instantiating (16) with fresh symbol all_45_0 gives: % 11.74/2.30 | (19) ~ (all_45_0 = 0) & distinct_lines(all_38_4, all_38_2) = all_45_0 % 11.74/2.31 | % 11.74/2.31 | ALPHA: (19) implies: % 11.74/2.31 | (20) ~ (all_45_0 = 0) % 11.74/2.31 | (21) distinct_lines(all_38_4, all_38_2) = all_45_0 % 11.74/2.31 | % 11.74/2.31 | DELTA: instantiating (15) with fresh symbols all_47_0, all_47_1, all_47_2, % 11.74/2.31 | all_47_3 gives: % 11.74/2.31 | (22) point(all_38_5) = all_47_2 & point(all_38_6) = all_47_3 & % 11.74/2.31 | line(all_38_2) = all_47_0 & distinct_points(all_38_6, all_38_5) = % 11.74/2.31 | all_47_1 & ( ~ (all_47_1 = 0) | ~ (all_47_2 = 0) | ~ (all_47_3 = 0) % 11.74/2.31 | | all_47_0 = 0) % 11.74/2.31 | % 11.74/2.31 | ALPHA: (22) implies: % 11.74/2.31 | (23) distinct_points(all_38_6, all_38_5) = all_47_1 % 11.74/2.31 | % 11.74/2.31 | GROUND_INST: instantiating (3) with 0, all_47_1, all_38_5, all_38_6, % 11.74/2.31 | simplifying with (9), (23) gives: % 11.74/2.31 | (24) all_47_1 = 0 % 11.74/2.31 | % 11.74/2.31 | BETA: splitting (14) gives: % 11.74/2.31 | % 11.74/2.31 | Case 1: % 11.74/2.31 | | % 11.74/2.31 | | (25) ~ (all_38_0 = 0) % 11.74/2.31 | | % 11.74/2.31 | | BETA: splitting (18) gives: % 11.74/2.31 | | % 11.74/2.31 | | Case 1: % 11.74/2.31 | | | % 11.74/2.31 | | | (26) apart_point_and_line(all_38_5, all_38_4) = 0 % 11.74/2.31 | | | % 11.74/2.31 | | | GROUND_INST: instantiating (ceq2) with all_38_5, all_38_4, all_38_2, % 11.74/2.31 | | | all_45_0, simplifying with (6), (7), (8), (21), (26) gives: % 11.74/2.31 | | | (27) all_45_0 = 0 | apart_point_and_line(all_38_5, all_38_2) = 0 % 11.74/2.31 | | | % 11.74/2.31 | | | BETA: splitting (27) gives: % 11.74/2.31 | | | % 11.74/2.31 | | | Case 1: % 11.74/2.31 | | | | % 11.74/2.31 | | | | (28) apart_point_and_line(all_38_5, all_38_2) = 0 % 11.74/2.31 | | | | % 11.74/2.31 | | | | GROUND_INST: instantiating (ci2) with all_38_6, all_38_5, all_38_2, % 11.74/2.31 | | | | simplifying with (5), (6), (10), (28) gives: % 11.74/2.31 | | | | (29) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_38_6, % 11.74/2.31 | | | | all_38_5) = v0) % 11.74/2.31 | | | | % 11.74/2.31 | | | | DELTA: instantiating (29) with fresh symbol all_82_0 gives: % 11.74/2.31 | | | | (30) ~ (all_82_0 = 0) & distinct_points(all_38_6, all_38_5) = % 11.74/2.31 | | | | all_82_0 % 11.74/2.31 | | | | % 11.74/2.31 | | | | ALPHA: (30) implies: % 11.74/2.31 | | | | (31) ~ (all_82_0 = 0) % 11.74/2.31 | | | | (32) distinct_points(all_38_6, all_38_5) = all_82_0 % 11.74/2.31 | | | | % 11.74/2.31 | | | | GROUND_INST: instantiating (3) with 0, all_82_0, all_38_5, all_38_6, % 11.74/2.31 | | | | simplifying with (9), (32) gives: % 11.74/2.31 | | | | (33) all_82_0 = 0 % 11.74/2.31 | | | | % 11.74/2.31 | | | | REDUCE: (31), (33) imply: % 11.74/2.31 | | | | (34) $false % 11.74/2.31 | | | | % 11.74/2.31 | | | | CLOSE: (34) is inconsistent. % 11.74/2.31 | | | | % 11.74/2.31 | | | Case 2: % 11.74/2.31 | | | | % 11.74/2.31 | | | | (35) all_45_0 = 0 % 11.74/2.31 | | | | % 11.74/2.31 | | | | REDUCE: (20), (35) imply: % 11.74/2.31 | | | | (36) $false % 11.74/2.31 | | | | % 11.74/2.31 | | | | CLOSE: (36) is inconsistent. % 11.74/2.31 | | | | % 11.74/2.31 | | | End of split % 11.74/2.31 | | | % 11.74/2.31 | | Case 2: % 11.74/2.31 | | | % 11.74/2.31 | | | (37) all_38_0 = 0 % 11.74/2.31 | | | % 11.74/2.31 | | | REDUCE: (25), (37) imply: % 11.74/2.31 | | | (38) $false % 11.74/2.31 | | | % 11.74/2.31 | | | CLOSE: (38) is inconsistent. % 11.74/2.31 | | | % 11.74/2.31 | | End of split % 11.74/2.31 | | % 11.74/2.31 | Case 2: % 11.74/2.31 | | % 11.74/2.31 | | (39) ~ (all_38_1 = 0) % 11.74/2.31 | | % 11.74/2.31 | | BETA: splitting (17) gives: % 11.74/2.31 | | % 11.74/2.31 | | Case 1: % 11.74/2.31 | | | % 11.74/2.31 | | | (40) apart_point_and_line(all_38_6, all_38_4) = 0 % 11.74/2.31 | | | % 11.74/2.31 | | | GROUND_INST: instantiating (ceq2) with all_38_6, all_38_4, all_38_2, % 11.74/2.31 | | | all_45_0, simplifying with (5), (7), (8), (21), (40) gives: % 11.74/2.31 | | | (41) all_45_0 = 0 | apart_point_and_line(all_38_6, all_38_2) = 0 % 11.74/2.32 | | | % 11.74/2.32 | | | BETA: splitting (41) gives: % 11.74/2.32 | | | % 11.74/2.32 | | | Case 1: % 11.74/2.32 | | | | % 11.74/2.32 | | | | (42) apart_point_and_line(all_38_6, all_38_2) = 0 % 11.74/2.32 | | | | % 11.74/2.32 | | | | GROUND_INST: instantiating (ci1) with all_38_6, all_38_5, all_38_2, % 11.74/2.32 | | | | simplifying with (5), (6), (10), (42) gives: % 11.74/2.32 | | | | (43) ? [v0: int] : ( ~ (v0 = 0) & distinct_points(all_38_6, % 11.74/2.32 | | | | all_38_5) = v0) % 11.74/2.32 | | | | % 11.74/2.32 | | | | DELTA: instantiating (43) with fresh symbol all_80_0 gives: % 11.74/2.32 | | | | (44) ~ (all_80_0 = 0) & distinct_points(all_38_6, all_38_5) = % 11.74/2.32 | | | | all_80_0 % 11.74/2.32 | | | | % 11.74/2.32 | | | | ALPHA: (44) implies: % 11.74/2.32 | | | | (45) ~ (all_80_0 = 0) % 11.74/2.32 | | | | (46) distinct_points(all_38_6, all_38_5) = all_80_0 % 11.74/2.32 | | | | % 11.74/2.32 | | | | GROUND_INST: instantiating (3) with 0, all_80_0, all_38_5, all_38_6, % 11.74/2.32 | | | | simplifying with (9), (46) gives: % 11.74/2.32 | | | | (47) all_80_0 = 0 % 11.74/2.32 | | | | % 11.74/2.32 | | | | REDUCE: (45), (47) imply: % 11.74/2.32 | | | | (48) $false % 11.74/2.32 | | | | % 11.74/2.32 | | | | CLOSE: (48) is inconsistent. % 11.74/2.32 | | | | % 11.74/2.32 | | | Case 2: % 11.74/2.32 | | | | % 11.74/2.32 | | | | (49) all_45_0 = 0 % 11.74/2.32 | | | | % 11.74/2.32 | | | | REDUCE: (20), (49) imply: % 11.74/2.32 | | | | (50) $false % 11.74/2.32 | | | | % 11.74/2.32 | | | | CLOSE: (50) is inconsistent. % 11.74/2.32 | | | | % 11.74/2.32 | | | End of split % 11.74/2.32 | | | % 11.74/2.32 | | Case 2: % 11.74/2.32 | | | % 11.74/2.32 | | | (51) all_38_1 = 0 % 11.74/2.32 | | | % 11.74/2.32 | | | REDUCE: (39), (51) imply: % 11.74/2.32 | | | (52) $false % 11.74/2.32 | | | % 11.74/2.32 | | | CLOSE: (52) is inconsistent. % 11.74/2.32 | | | % 11.74/2.32 | | End of split % 11.74/2.32 | | % 11.74/2.32 | End of split % 11.74/2.32 | % 11.74/2.32 End of proof % 11.74/2.32 % SZS output end Proof for theBenchmark % 11.74/2.32 % 11.74/2.32 1786ms %------------------------------------------------------------------------------