%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO220+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 : n011.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 23:22:29 EDT 2023 % Result : Theorem 8.15s 1.86s % Output : Proof 10.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : GEO220+3 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n011.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 19:49:26 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.63 ________ _____ % 0.21/0.63 ___ __ \_________(_)________________________________ % 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.64 Running up to 7 provers in parallel. % 0.21/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.08/1.19 Prover 1: Preprocessing ... % 3.08/1.19 Prover 4: Preprocessing ... % 3.58/1.23 Prover 3: Preprocessing ... % 3.58/1.23 Prover 0: Preprocessing ... % 3.58/1.23 Prover 2: Preprocessing ... % 3.58/1.23 Prover 6: Preprocessing ... % 3.58/1.23 Prover 5: Preprocessing ... % 6.48/1.63 Prover 5: Proving ... % 6.48/1.64 Prover 2: Proving ... % 6.86/1.69 Prover 1: Constructing countermodel ... % 6.86/1.69 Prover 6: Constructing countermodel ... % 7.65/1.78 Prover 3: Constructing countermodel ... % 8.15/1.86 Prover 6: proved (1192ms) % 8.15/1.86 % 8.15/1.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.15/1.86 % 8.15/1.86 Prover 5: stopped % 8.15/1.86 Prover 2: stopped % 8.15/1.87 Prover 3: stopped % 8.15/1.87 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.15/1.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.15/1.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.15/1.87 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.15/1.94 Prover 10: Preprocessing ... % 8.15/1.96 Prover 11: Preprocessing ... % 8.15/1.98 Prover 7: Preprocessing ... % 8.15/1.98 Prover 8: Preprocessing ... % 8.15/1.99 Prover 10: Warning: ignoring some quantifiers % 8.84/2.02 Prover 10: Constructing countermodel ... % 8.84/2.05 Prover 7: Warning: ignoring some quantifiers % 9.52/2.07 Prover 7: Constructing countermodel ... % 9.52/2.10 Prover 1: Found proof (size 36) % 9.52/2.10 Prover 1: proved (1443ms) % 9.52/2.10 Prover 7: stopped % 9.52/2.10 Prover 10: stopped % 9.52/2.11 Prover 4: Constructing countermodel ... % 9.52/2.11 Prover 11: stopped % 9.52/2.13 Prover 0: Proving ... % 9.52/2.13 Prover 4: stopped % 9.52/2.13 Prover 8: Warning: ignoring some quantifiers % 10.11/2.13 Prover 0: stopped % 10.11/2.14 Prover 8: Constructing countermodel ... % 10.11/2.15 Prover 8: stopped % 10.11/2.15 % 10.11/2.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.11/2.15 % 10.11/2.16 % SZS output start Proof for theBenchmark % 10.11/2.16 Assumptions after simplification: % 10.11/2.16 --------------------------------- % 10.11/2.16 % 10.11/2.16 (a3) % 10.33/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (parallel_lines(v0, % 10.33/2.19 v1) = v2) | ~ $i(v1) | ~ $i(v0) | convergent_lines(v0, v1) = 0) & ! % 10.33/2.19 [v0: $i] : ! [v1: $i] : ( ~ (parallel_lines(v0, v1) = 0) | ~ $i(v1) | ~ % 10.33/2.19 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) % 10.33/2.19 % 10.33/2.19 (a5) % 10.33/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (orthogonal_lines(v0, % 10.33/2.19 v1) = v2) | ~ $i(v1) | ~ $i(v0) | unorthogonal_lines(v0, v1) = 0) & ! % 10.33/2.19 [v0: $i] : ! [v1: $i] : ( ~ (orthogonal_lines(v0, v1) = 0) | ~ $i(v1) | ~ % 10.33/2.19 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) % 10.33/2.19 % 10.33/2.19 (con) % 10.33/2.19 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 10.33/2.19 orthogonal_lines(v0, v2) = 0 & orthogonal_lines(v0, v1) = 0 & % 10.33/2.19 parallel_lines(v1, v2) = v3 & $i(v2) & $i(v1) & $i(v0)) % 10.33/2.19 % 10.33/2.19 (cotno1) % 10.33/2.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ! [v4: any] : ( ~ % 10.33/2.20 (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | % 10.33/2.20 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: % 10.33/2.20 any] : ? [v8: any] : (unorthogonal_lines(v1, v2) = v8 & % 10.33/2.20 convergent_lines(v1, v2) = v7 & convergent_lines(v0, v2) = v6 & % 10.33/2.20 convergent_lines(v0, v1) = v5 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v6 = 0 & v4 % 10.33/2.20 = 0) | (v5 = 0 & v3 = 0)))) % 10.33/2.20 % 10.33/2.20 (couo1) % 10.33/2.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: int] : (v4 = % 10.33/2.20 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ % 10.33/2.20 (unorthogonal_lines(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 10.33/2.20 [v5: int] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) % 10.33/2.20 % 10.33/2.20 (function-axioms) % 10.33/2.21 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 10.33/2.21 [v3: $i] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ % 10.33/2.21 (orthogonal_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.33/2.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.33/2.21 (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) % 10.33/2.21 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.33/2.21 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ % 10.33/2.21 (parallel_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.33/2.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.33/2.21 (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0: % 10.33/2.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.33/2.21 : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 10.33/2.21 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.33/2.21 (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, % 10.33/2.21 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 10.33/2.21 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | % 10.33/2.21 ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 10.33/2.21 $i] : ! [v3: $i] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ % 10.33/2.21 (parallel_through_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 10.33/2.21 $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ % 10.33/2.21 (intersection_point(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 10.33/2.21 : ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 10.33/2.21 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.33/2.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.33/2.21 (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = % 10.33/2.21 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.33/2.21 $i] : ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 10.33/2.21 (convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 10.33/2.21 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.33/2.21 (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0: % 10.33/2.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.33/2.21 : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = % 10.33/2.21 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 10.33/2.21 $i] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: % 10.33/2.21 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 10.33/2.21 ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 10.33/2.21 % 10.33/2.21 Further assumptions not needed in the proof: % 10.33/2.21 -------------------------------------------- % 10.33/2.21 a4, apart1, apart2, apart3, apart4, apart5, ax1, ax2, ax6, ceq1, ceq2, ceq3, % 10.33/2.21 ci1, ci2, ci3, ci4, coipo1, con1, cp1, cp2, cu1, cup1, int1, oac1, occu1, ooc1, % 10.33/2.21 ooc2, orth1, ouo1, p1, par1 % 10.33/2.21 % 10.33/2.21 Those formulas are unsatisfiable: % 10.33/2.21 --------------------------------- % 10.33/2.21 % 10.33/2.21 Begin of proof % 10.33/2.21 | % 10.33/2.21 | ALPHA: (a3) implies: % 10.33/2.21 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ % 10.33/2.21 | (parallel_lines(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 10.33/2.21 | convergent_lines(v0, v1) = 0) % 10.33/2.21 | % 10.33/2.21 | ALPHA: (a5) implies: % 10.33/2.21 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (orthogonal_lines(v0, v1) = 0) | ~ % 10.33/2.21 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 10.33/2.21 | unorthogonal_lines(v0, v1) = v2)) % 10.33/2.21 | % 10.33/2.21 | ALPHA: (function-axioms) implies: % 10.33/2.21 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.33/2.21 | ! [v3: $i] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ % 10.33/2.21 | (convergent_lines(v3, v2) = v0)) % 10.33/2.21 | % 10.33/2.21 | DELTA: instantiating (con) with fresh symbols all_38_0, all_38_1, all_38_2, % 10.33/2.21 | all_38_3 gives: % 10.33/2.22 | (4) ~ (all_38_0 = 0) & orthogonal_lines(all_38_3, all_38_1) = 0 & % 10.33/2.22 | orthogonal_lines(all_38_3, all_38_2) = 0 & parallel_lines(all_38_2, % 10.33/2.22 | all_38_1) = all_38_0 & $i(all_38_1) & $i(all_38_2) & $i(all_38_3) % 10.33/2.22 | % 10.33/2.22 | ALPHA: (4) implies: % 10.33/2.22 | (5) ~ (all_38_0 = 0) % 10.33/2.22 | (6) $i(all_38_3) % 10.33/2.22 | (7) $i(all_38_2) % 10.33/2.22 | (8) $i(all_38_1) % 10.33/2.22 | (9) parallel_lines(all_38_2, all_38_1) = all_38_0 % 10.33/2.22 | (10) orthogonal_lines(all_38_3, all_38_2) = 0 % 10.33/2.22 | (11) orthogonal_lines(all_38_3, all_38_1) = 0 % 10.33/2.22 | % 10.33/2.22 | GROUND_INST: instantiating (1) with all_38_2, all_38_1, all_38_0, simplifying % 10.33/2.22 | with (7), (8), (9) gives: % 10.33/2.22 | (12) all_38_0 = 0 | convergent_lines(all_38_2, all_38_1) = 0 % 10.33/2.22 | % 10.33/2.22 | GROUND_INST: instantiating (2) with all_38_3, all_38_2, simplifying with (6), % 10.33/2.22 | (7), (10) gives: % 10.33/2.22 | (13) ? [v0: int] : ( ~ (v0 = 0) & unorthogonal_lines(all_38_3, all_38_2) = % 10.33/2.22 | v0) % 10.33/2.22 | % 10.33/2.22 | GROUND_INST: instantiating (2) with all_38_3, all_38_1, simplifying with (6), % 10.33/2.22 | (8), (11) gives: % 10.33/2.22 | (14) ? [v0: int] : ( ~ (v0 = 0) & unorthogonal_lines(all_38_3, all_38_1) = % 10.33/2.22 | v0) % 10.33/2.22 | % 10.33/2.22 | DELTA: instantiating (14) with fresh symbol all_45_0 gives: % 10.33/2.22 | (15) ~ (all_45_0 = 0) & unorthogonal_lines(all_38_3, all_38_1) = all_45_0 % 10.33/2.22 | % 10.33/2.22 | ALPHA: (15) implies: % 10.33/2.22 | (16) ~ (all_45_0 = 0) % 10.33/2.22 | (17) unorthogonal_lines(all_38_3, all_38_1) = all_45_0 % 10.33/2.22 | % 10.33/2.22 | DELTA: instantiating (13) with fresh symbol all_47_0 gives: % 10.33/2.22 | (18) ~ (all_47_0 = 0) & unorthogonal_lines(all_38_3, all_38_2) = all_47_0 % 10.33/2.22 | % 10.33/2.22 | ALPHA: (18) implies: % 10.33/2.22 | (19) ~ (all_47_0 = 0) % 10.33/2.22 | (20) unorthogonal_lines(all_38_3, all_38_2) = all_47_0 % 10.33/2.22 | % 10.33/2.22 | BETA: splitting (12) gives: % 10.33/2.22 | % 10.33/2.22 | Case 1: % 10.33/2.22 | | % 10.33/2.22 | | (21) convergent_lines(all_38_2, all_38_1) = 0 % 10.33/2.22 | | % 10.33/2.22 | | GROUND_INST: instantiating (couo1) with all_38_3, all_38_2, all_38_1, % 10.33/2.22 | | all_47_0, all_45_0, simplifying with (6), (7), (8), (17), (20) % 10.33/2.22 | | gives: % 10.33/2.22 | | (22) all_47_0 = 0 | all_45_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 10.33/2.22 | | convergent_lines(all_38_2, all_38_1) = v0) % 10.33/2.22 | | % 10.33/2.22 | | GROUND_INST: instantiating (cotno1) with all_38_3, all_38_2, all_38_1, % 10.33/2.22 | | all_47_0, all_45_0, simplifying with (6), (7), (8), (17), (20) % 10.33/2.22 | | gives: % 10.33/2.23 | | (23) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 10.33/2.23 | | (unorthogonal_lines(all_38_2, all_38_1) = v3 & % 10.33/2.23 | | convergent_lines(all_38_2, all_38_1) = v2 & % 10.33/2.23 | | convergent_lines(all_38_3, all_38_1) = v1 & % 10.33/2.23 | | convergent_lines(all_38_3, all_38_2) = v0 & ( ~ (v3 = 0) | ~ (v2 % 10.33/2.23 | | = 0) | (v1 = 0 & all_45_0 = 0) | (v0 = 0 & all_47_0 = 0))) % 10.33/2.23 | | % 10.33/2.23 | | DELTA: instantiating (23) with fresh symbols all_60_0, all_60_1, all_60_2, % 10.33/2.23 | | all_60_3 gives: % 10.33/2.23 | | (24) unorthogonal_lines(all_38_2, all_38_1) = all_60_0 & % 10.33/2.23 | | convergent_lines(all_38_2, all_38_1) = all_60_1 & % 10.33/2.23 | | convergent_lines(all_38_3, all_38_1) = all_60_2 & % 10.33/2.23 | | convergent_lines(all_38_3, all_38_2) = all_60_3 & ( ~ (all_60_0 = 0) % 10.33/2.23 | | | ~ (all_60_1 = 0) | (all_60_2 = 0 & all_45_0 = 0) | (all_60_3 = % 10.33/2.23 | | 0 & all_47_0 = 0)) % 10.33/2.23 | | % 10.33/2.23 | | ALPHA: (24) implies: % 10.33/2.23 | | (25) convergent_lines(all_38_2, all_38_1) = all_60_1 % 10.33/2.23 | | % 10.33/2.23 | | BETA: splitting (22) gives: % 10.33/2.23 | | % 10.33/2.23 | | Case 1: % 10.33/2.23 | | | % 10.33/2.23 | | | (26) all_47_0 = 0 % 10.33/2.23 | | | % 10.33/2.23 | | | REDUCE: (19), (26) imply: % 10.33/2.23 | | | (27) $false % 10.33/2.23 | | | % 10.33/2.23 | | | CLOSE: (27) is inconsistent. % 10.33/2.23 | | | % 10.33/2.23 | | Case 2: % 10.33/2.23 | | | % 10.33/2.23 | | | (28) all_45_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 10.33/2.23 | | | convergent_lines(all_38_2, all_38_1) = v0) % 10.33/2.23 | | | % 10.33/2.23 | | | BETA: splitting (28) gives: % 10.33/2.23 | | | % 10.33/2.23 | | | Case 1: % 10.33/2.23 | | | | % 10.33/2.23 | | | | (29) all_45_0 = 0 % 10.33/2.23 | | | | % 10.33/2.23 | | | | REDUCE: (16), (29) imply: % 10.33/2.23 | | | | (30) $false % 10.33/2.23 | | | | % 10.33/2.23 | | | | CLOSE: (30) is inconsistent. % 10.33/2.23 | | | | % 10.33/2.23 | | | Case 2: % 10.33/2.23 | | | | % 10.33/2.23 | | | | (31) ? [v0: int] : ( ~ (v0 = 0) & convergent_lines(all_38_2, % 10.33/2.23 | | | | all_38_1) = v0) % 10.33/2.23 | | | | % 10.33/2.23 | | | | DELTA: instantiating (31) with fresh symbol all_98_0 gives: % 10.33/2.23 | | | | (32) ~ (all_98_0 = 0) & convergent_lines(all_38_2, all_38_1) = % 10.33/2.23 | | | | all_98_0 % 10.33/2.23 | | | | % 10.33/2.23 | | | | ALPHA: (32) implies: % 10.33/2.23 | | | | (33) ~ (all_98_0 = 0) % 10.33/2.23 | | | | (34) convergent_lines(all_38_2, all_38_1) = all_98_0 % 10.33/2.23 | | | | % 10.33/2.23 | | | | GROUND_INST: instantiating (3) with 0, all_98_0, all_38_1, all_38_2, % 10.33/2.23 | | | | simplifying with (21), (34) gives: % 10.33/2.23 | | | | (35) all_98_0 = 0 % 10.33/2.23 | | | | % 10.33/2.23 | | | | GROUND_INST: instantiating (3) with all_60_1, all_98_0, all_38_1, % 10.33/2.23 | | | | all_38_2, simplifying with (25), (34) gives: % 10.33/2.23 | | | | (36) all_98_0 = all_60_1 % 10.33/2.23 | | | | % 10.33/2.23 | | | | COMBINE_EQS: (35), (36) imply: % 10.33/2.23 | | | | (37) all_60_1 = 0 % 10.33/2.23 | | | | % 10.33/2.23 | | | | REDUCE: (33), (35) imply: % 10.33/2.23 | | | | (38) $false % 10.33/2.23 | | | | % 10.33/2.23 | | | | CLOSE: (38) is inconsistent. % 10.33/2.23 | | | | % 10.33/2.23 | | | End of split % 10.33/2.23 | | | % 10.33/2.23 | | End of split % 10.33/2.23 | | % 10.33/2.23 | Case 2: % 10.33/2.23 | | % 10.33/2.23 | | (39) all_38_0 = 0 % 10.33/2.23 | | % 10.33/2.23 | | REDUCE: (5), (39) imply: % 10.33/2.23 | | (40) $false % 10.33/2.23 | | % 10.33/2.23 | | CLOSE: (40) is inconsistent. % 10.33/2.23 | | % 10.33/2.23 | End of split % 10.33/2.23 | % 10.33/2.23 End of proof % 10.33/2.23 % SZS output end Proof for theBenchmark % 10.33/2.23 % 10.33/2.23 1602ms %------------------------------------------------------------------------------