%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : GEO238+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 : n021.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 23:22:39 EDT 2023 % Result : Theorem 8.80s 1.88s % Output : Proof 11.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.13 % Problem : GEO238+3 : TPTP v8.1.2. Released v4.0.0. % 0.09/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.36 % Computer : n021.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Tue Aug 29 19:24:44 EDT 2023 % 0.14/0.36 % CPUTime : % 0.50/0.62 ________ _____ % 0.50/0.62 ___ __ \_________(_)________________________________ % 0.50/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.50/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.50/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.50/0.62 % 0.50/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.50/0.62 (2023-06-19) % 0.50/0.62 % 0.50/0.62 (c) Philipp Rümmer, 2009-2023 % 0.50/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.50/0.62 Amanda Stjerna. % 0.50/0.62 Free software under BSD-3-Clause. % 0.50/0.62 % 0.50/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.50/0.62 % 0.50/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.50/0.63 Running up to 7 provers in parallel. % 0.50/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.50/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.50/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.50/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.50/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.50/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.50/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.93/1.15 Prover 4: Preprocessing ... % 2.93/1.15 Prover 1: Preprocessing ... % 3.62/1.18 Prover 3: Preprocessing ... % 3.62/1.18 Prover 5: Preprocessing ... % 3.62/1.18 Prover 0: Preprocessing ... % 3.62/1.18 Prover 2: Preprocessing ... % 3.62/1.18 Prover 6: Preprocessing ... % 7.57/1.71 Prover 5: Proving ... % 7.57/1.72 Prover 2: Proving ... % 7.57/1.75 Prover 6: Constructing countermodel ... % 7.57/1.75 Prover 1: Constructing countermodel ... % 7.57/1.77 Prover 3: Constructing countermodel ... % 8.80/1.88 Prover 5: proved (1236ms) % 8.80/1.88 % 8.80/1.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.80/1.88 % 8.80/1.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.80/1.89 Prover 6: stopped % 8.80/1.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.80/1.90 Prover 2: stopped % 8.80/1.91 Prover 3: stopped % 8.80/1.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.80/1.92 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.47/1.99 Prover 8: Preprocessing ... % 9.47/1.99 Prover 10: Preprocessing ... % 9.47/1.99 Prover 7: Preprocessing ... % 9.47/2.02 Prover 1: Found proof (size 27) % 9.47/2.02 Prover 1: proved (1374ms) % 9.90/2.03 Prover 11: Preprocessing ... % 10.12/2.05 Prover 10: stopped % 10.12/2.05 Prover 7: stopped % 10.12/2.12 Prover 4: Constructing countermodel ... % 10.70/2.15 Prover 4: stopped % 10.70/2.15 Prover 0: Proving ... % 10.70/2.16 Prover 8: Warning: ignoring some quantifiers % 10.70/2.16 Prover 0: stopped % 10.70/2.17 Prover 8: Constructing countermodel ... % 11.03/2.18 Prover 8: stopped % 11.03/2.19 Prover 11: stopped % 11.03/2.19 % 11.03/2.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.03/2.19 % 11.03/2.20 % SZS output start Proof for theBenchmark % 11.03/2.20 Assumptions after simplification: % 11.03/2.20 --------------------------------- % 11.03/2.20 % 11.03/2.20 (a8_defns) % 11.03/2.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 11.03/2.23 (divides_points(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 11.03/2.23 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 11.03/2.23 (left_apart_point(v1, v2) = v7 & left_apart_point(v0, v2) = v4 & % 11.03/2.23 right_apart_point(v1, v2) = v5 & right_apart_point(v0, v2) = v6 & ( ~ (v7 % 11.03/2.23 = 0) | ~ (v6 = 0)) & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! % 11.03/2.23 [v1: $i] : ! [v2: $i] : ( ~ (divides_points(v2, v0, v1) = 0) | ~ $i(v2) | ~ % 11.03/2.23 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: % 11.03/2.23 any] : (left_apart_point(v1, v2) = v6 & left_apart_point(v0, v2) = v3 & % 11.03/2.23 right_apart_point(v1, v2) = v4 & right_apart_point(v0, v2) = v5 & ((v6 = 0 % 11.03/2.23 & v5 = 0) | (v4 = 0 & v3 = 0)))) % 11.03/2.23 % 11.03/2.23 (ax10_basics) % 11.03/2.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (left_apart_point(v0, v2) = 0) | % 11.03/2.23 ~ (reverse_line(v1) = v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: % 11.03/2.23 $i] : ( ~ (left_apart_point(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)) % 11.03/2.23 % 11.03/2.23 (con) % 11.03/2.23 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (divides_points(v3, % 11.03/2.23 v1, v2) = 0 & divides_points(v3, v0, v2) = 0 & divides_points(v3, v0, v1) % 11.03/2.23 = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 11.03/2.23 % 11.03/2.23 (function-axioms) % 11.03/2.24 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 11.03/2.24 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (between_on_line(v5, v4, % 11.03/2.24 v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) & ! [v0: % 11.03/2.24 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 11.03/2.24 : ! [v4: $i] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~ % 11.03/2.24 (before_on_line(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.03/2.24 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 11.03/2.24 (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) & % 11.03/2.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.03/2.24 (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = % 11.03/2.24 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 11.03/2.24 ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 11.03/2.24 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 11.03/2.24 [v3: $i] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ % 11.03/2.24 (distinct_lines(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 11.03/2.24 ! [v3: $i] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ % 11.03/2.24 (line_connecting(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.03/2.24 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.03/2.24 (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! % 11.03/2.24 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 11.03/2.24 $i] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ % 11.03/2.24 (incident_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 11.03/2.24 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.03/2.24 (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! % 11.03/2.24 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 11.03/2.24 $i] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ % 11.03/2.24 (apart_point_and_line(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.03/2.24 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.03/2.24 (equally_directed_opposite_lines(v3, v2) = v1) | ~ % 11.03/2.24 (equally_directed_opposite_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] % 11.03/2.24 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.03/2.24 (equally_directed_lines(v3, v2) = v1) | ~ (equally_directed_lines(v3, v2) = % 11.03/2.24 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 11.03/2.24 $i] : ! [v3: $i] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~ % 11.03/2.24 (left_convergent_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.03/2.24 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.03/2.24 (right_convergent_lines(v3, v2) = v1) | ~ (right_convergent_lines(v3, v2) = % 11.03/2.24 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 11.03/2.24 $i] : ! [v3: $i] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~ % 11.03/2.24 (left_apart_point(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.03/2.24 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.03/2.24 (right_apart_point(v3, v2) = v1) | ~ (right_apart_point(v3, v2) = v0)) & ! % 11.03/2.24 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 11.03/2.24 $i] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | ~ % 11.03/2.24 (unequally_directed_lines(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 11.03/2.24 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.03/2.24 (unequally_directed_opposite_lines(v3, v2) = v1) | ~ % 11.03/2.24 (unequally_directed_opposite_lines(v3, v2) = v0)) & ! [v0: % 11.03/2.24 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 11.03/2.24 ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 11.03/2.24 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (line(v2) = v1) | ~ % 11.03/2.24 (line(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 11.03/2.24 (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) % 11.03/2.24 % 11.03/2.24 Further assumptions not needed in the proof: % 11.03/2.24 -------------------------------------------- % 11.03/2.24 a1_defns, a2_defns, a3_defns, a4_defns, a5_defns, a6_defns, a7_defns, a9_defns, % 11.03/2.24 ax10_cons_objs, ax11_basics, ax1_basics, ax1_cons_objs, ax1_subs, ax1_uniq_cons, % 11.03/2.24 ax2_basics, ax2_cons_objs, ax2_subs, ax2_uniq_cons, ax3_basics, ax3_cons_objs, % 11.03/2.24 ax3_subs, ax4_basics, ax4_cons_objs, ax4_defns, ax5_basics, ax5_cons_objs, % 11.03/2.24 ax6_basics, ax6_cons_objs, ax7_basics, ax7_cons_objs, ax8_basics, ax8_cons_objs, % 11.03/2.24 ax9_basics, ax9_cons_objs % 11.03/2.24 % 11.03/2.24 Those formulas are unsatisfiable: % 11.03/2.24 --------------------------------- % 11.03/2.24 % 11.03/2.24 Begin of proof % 11.37/2.24 | % 11.37/2.24 | ALPHA: (a8_defns) implies: % 11.37/2.25 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (divides_points(v2, v0, % 11.37/2.25 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? % 11.37/2.25 | [v4: any] : ? [v5: any] : ? [v6: any] : (left_apart_point(v1, v2) = % 11.37/2.25 | v6 & left_apart_point(v0, v2) = v3 & right_apart_point(v1, v2) = v4 % 11.37/2.25 | & right_apart_point(v0, v2) = v5 & ((v6 = 0 & v5 = 0) | (v4 = 0 & % 11.37/2.25 | v3 = 0)))) % 11.37/2.25 | % 11.37/2.25 | ALPHA: (ax10_basics) implies: % 11.37/2.25 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (left_apart_point(v0, v1) = 0) | ~ % 11.37/2.25 | $i(v1) | ~ $i(v0)) % 11.37/2.25 | % 11.37/2.25 | ALPHA: (function-axioms) implies: % 11.37/2.25 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 11.37/2.25 | ! [v3: $i] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~ % 11.37/2.25 | (left_apart_point(v3, v2) = v0)) % 11.37/2.25 | % 11.37/2.25 | DELTA: instantiating (con) with fresh symbols all_39_0, all_39_1, all_39_2, % 11.37/2.25 | all_39_3 gives: % 11.37/2.25 | (4) divides_points(all_39_0, all_39_2, all_39_1) = 0 & % 11.37/2.25 | divides_points(all_39_0, all_39_3, all_39_1) = 0 & % 11.37/2.25 | divides_points(all_39_0, all_39_3, all_39_2) = 0 & $i(all_39_0) & % 11.37/2.25 | $i(all_39_1) & $i(all_39_2) & $i(all_39_3) % 11.37/2.25 | % 11.37/2.25 | ALPHA: (4) implies: % 11.37/2.25 | (5) $i(all_39_3) % 11.37/2.25 | (6) $i(all_39_2) % 11.37/2.25 | (7) $i(all_39_1) % 11.37/2.25 | (8) $i(all_39_0) % 11.37/2.25 | (9) divides_points(all_39_0, all_39_3, all_39_2) = 0 % 11.37/2.25 | (10) divides_points(all_39_0, all_39_3, all_39_1) = 0 % 11.37/2.25 | (11) divides_points(all_39_0, all_39_2, all_39_1) = 0 % 11.37/2.25 | % 11.37/2.25 | GROUND_INST: instantiating (1) with all_39_3, all_39_2, all_39_0, simplifying % 11.37/2.25 | with (5), (6), (8), (9) gives: % 11.37/2.25 | (12) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 11.37/2.25 | (left_apart_point(all_39_2, all_39_0) = v3 & % 11.37/2.25 | left_apart_point(all_39_3, all_39_0) = v0 & % 11.37/2.25 | right_apart_point(all_39_2, all_39_0) = v1 & % 11.37/2.25 | right_apart_point(all_39_3, all_39_0) = v2 & ((v3 = 0 & v2 = 0) | % 11.37/2.25 | (v1 = 0 & v0 = 0))) % 11.37/2.25 | % 11.37/2.25 | GROUND_INST: instantiating (1) with all_39_3, all_39_1, all_39_0, simplifying % 11.37/2.25 | with (5), (7), (8), (10) gives: % 11.37/2.25 | (13) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 11.37/2.25 | (left_apart_point(all_39_1, all_39_0) = v3 & % 11.37/2.25 | left_apart_point(all_39_3, all_39_0) = v0 & % 11.37/2.25 | right_apart_point(all_39_1, all_39_0) = v1 & % 11.37/2.25 | right_apart_point(all_39_3, all_39_0) = v2 & ((v3 = 0 & v2 = 0) | % 11.37/2.25 | (v1 = 0 & v0 = 0))) % 11.37/2.25 | % 11.37/2.25 | GROUND_INST: instantiating (1) with all_39_2, all_39_1, all_39_0, simplifying % 11.37/2.25 | with (6), (7), (8), (11) gives: % 11.37/2.25 | (14) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 11.37/2.25 | (left_apart_point(all_39_1, all_39_0) = v3 & % 11.37/2.25 | left_apart_point(all_39_2, all_39_0) = v0 & % 11.37/2.25 | right_apart_point(all_39_1, all_39_0) = v1 & % 11.37/2.25 | right_apart_point(all_39_2, all_39_0) = v2 & ((v3 = 0 & v2 = 0) | % 11.37/2.25 | (v1 = 0 & v0 = 0))) % 11.37/2.25 | % 11.37/2.25 | DELTA: instantiating (14) with fresh symbols all_46_0, all_46_1, all_46_2, % 11.37/2.25 | all_46_3 gives: % 11.37/2.26 | (15) left_apart_point(all_39_1, all_39_0) = all_46_0 & % 11.37/2.26 | left_apart_point(all_39_2, all_39_0) = all_46_3 & % 11.37/2.26 | right_apart_point(all_39_1, all_39_0) = all_46_2 & % 11.37/2.26 | right_apart_point(all_39_2, all_39_0) = all_46_1 & ((all_46_0 = 0 & % 11.37/2.26 | all_46_1 = 0) | (all_46_2 = 0 & all_46_3 = 0)) % 11.37/2.26 | % 11.37/2.26 | ALPHA: (15) implies: % 11.37/2.26 | (16) left_apart_point(all_39_2, all_39_0) = all_46_3 % 11.37/2.26 | (17) left_apart_point(all_39_1, all_39_0) = all_46_0 % 11.37/2.26 | (18) (all_46_0 = 0 & all_46_1 = 0) | (all_46_2 = 0 & all_46_3 = 0) % 11.37/2.26 | % 11.37/2.26 | DELTA: instantiating (13) with fresh symbols all_48_0, all_48_1, all_48_2, % 11.37/2.26 | all_48_3 gives: % 11.37/2.26 | (19) left_apart_point(all_39_1, all_39_0) = all_48_0 & % 11.37/2.26 | left_apart_point(all_39_3, all_39_0) = all_48_3 & % 11.37/2.26 | right_apart_point(all_39_1, all_39_0) = all_48_2 & % 11.37/2.26 | right_apart_point(all_39_3, all_39_0) = all_48_1 & ((all_48_0 = 0 & % 11.37/2.26 | all_48_1 = 0) | (all_48_2 = 0 & all_48_3 = 0)) % 11.37/2.26 | % 11.37/2.26 | ALPHA: (19) implies: % 11.37/2.26 | (20) left_apart_point(all_39_1, all_39_0) = all_48_0 % 11.37/2.26 | % 11.37/2.26 | DELTA: instantiating (12) with fresh symbols all_50_0, all_50_1, all_50_2, % 11.37/2.26 | all_50_3 gives: % 11.37/2.26 | (21) left_apart_point(all_39_2, all_39_0) = all_50_0 & % 11.37/2.26 | left_apart_point(all_39_3, all_39_0) = all_50_3 & % 11.37/2.26 | right_apart_point(all_39_2, all_39_0) = all_50_2 & % 11.37/2.26 | right_apart_point(all_39_3, all_39_0) = all_50_1 & ((all_50_0 = 0 & % 11.37/2.26 | all_50_1 = 0) | (all_50_2 = 0 & all_50_3 = 0)) % 11.37/2.26 | % 11.37/2.26 | ALPHA: (21) implies: % 11.37/2.26 | (22) left_apart_point(all_39_2, all_39_0) = all_50_0 % 11.37/2.26 | % 11.37/2.26 | GROUND_INST: instantiating (3) with all_46_3, all_50_0, all_39_0, all_39_2, % 11.37/2.26 | simplifying with (16), (22) gives: % 11.37/2.26 | (23) all_50_0 = all_46_3 % 11.37/2.26 | % 11.37/2.26 | GROUND_INST: instantiating (3) with all_46_0, all_48_0, all_39_0, all_39_1, % 11.37/2.26 | simplifying with (17), (20) gives: % 11.37/2.26 | (24) all_48_0 = all_46_0 % 11.37/2.26 | % 11.37/2.26 | BETA: splitting (18) gives: % 11.37/2.26 | % 11.37/2.26 | Case 1: % 11.37/2.26 | | % 11.37/2.26 | | (25) all_46_0 = 0 & all_46_1 = 0 % 11.37/2.26 | | % 11.37/2.26 | | ALPHA: (25) implies: % 11.37/2.26 | | (26) all_46_0 = 0 % 11.37/2.26 | | % 11.37/2.26 | | REDUCE: (17), (26) imply: % 11.37/2.26 | | (27) left_apart_point(all_39_1, all_39_0) = 0 % 11.37/2.26 | | % 11.37/2.26 | | GROUND_INST: instantiating (2) with all_39_1, all_39_0, simplifying with % 11.37/2.26 | | (7), (8), (27) gives: % 11.37/2.26 | | (28) $false % 11.37/2.26 | | % 11.37/2.26 | | CLOSE: (28) is inconsistent. % 11.37/2.26 | | % 11.37/2.26 | Case 2: % 11.37/2.26 | | % 11.37/2.26 | | (29) all_46_2 = 0 & all_46_3 = 0 % 11.37/2.26 | | % 11.37/2.26 | | ALPHA: (29) implies: % 11.37/2.26 | | (30) all_46_3 = 0 % 11.37/2.26 | | % 11.37/2.26 | | REDUCE: (16), (30) imply: % 11.37/2.26 | | (31) left_apart_point(all_39_2, all_39_0) = 0 % 11.37/2.26 | | % 11.37/2.26 | | GROUND_INST: instantiating (2) with all_39_2, all_39_0, simplifying with % 11.37/2.26 | | (6), (8), (31) gives: % 11.37/2.26 | | (32) $false % 11.37/2.26 | | % 11.37/2.26 | | CLOSE: (32) is inconsistent. % 11.37/2.26 | | % 11.37/2.26 | End of split % 11.37/2.26 | % 11.37/2.26 End of proof % 11.37/2.26 % SZS output end Proof for theBenchmark % 11.37/2.26 % 11.37/2.26 1640ms %------------------------------------------------------------------------------