%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT092+1 : TPTP v9.3.1. Bugfixed v9.3.1. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n008.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Tue Sep 8 06:17:30 AM UTC 2026 % Result : Theorem 12.98s 2.41s % Output : Proof 18.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : MGT092+1 : TPTP v9.3.1. Bugfixed v9.3.1. % 0.00/0.03 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.08/0.35 % Computer : n008.cluster.edu % 0.08/0.35 % Model : x86_64 x86_64 % 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.35 % Memory : 8046.5625MB % 0.08/0.35 % OS : Linux 6.8.0-71-generic % 0.08/0.35 % CPULimit : 300 % 0.08/0.35 % WCLimit : 300 % 0.08/0.35 % DateTime : Mon Sep 7 14:24:53 UTC 2026 % 0.08/0.36 % CPUTime : % 0.13/0.37 OpenJDK 64-Bit Server VM warning: Options -Xverify:none and -noverify were deprecated in JDK 13 and will likely be removed in a future release. % 0.57/0.68 ________ _____ % 0.57/0.68 ___ __ \_________(_)________________________________ % 0.57/0.68 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.57/0.68 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.57/0.68 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.57/0.68 % 0.57/0.68 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.57/0.68 (2023-06-19) % 0.57/0.68 % 0.57/0.68 (c) Philipp Rümmer, 2009-2023 % 0.57/0.68 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.57/0.68 Amanda Stjerna. % 0.57/0.68 Free software under BSD-3-Clause. % 0.57/0.68 % 0.57/0.68 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.57/0.68 % 0.57/0.68 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.70/0.70 Running up to 7 provers in parallel. % 0.70/0.71 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.70/0.71 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.70/0.71 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.70/0.71 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.70/0.71 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.70/0.71 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.70/0.71 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.34/1.35 Prover 1: Preprocessing ... % 4.34/1.35 Prover 4: Preprocessing ... % 5.09/1.40 Prover 0: Preprocessing ... % 5.09/1.40 Prover 2: Preprocessing ... % 5.09/1.40 Prover 3: Preprocessing ... % 5.09/1.40 Prover 6: Preprocessing ... % 5.09/1.41 Prover 5: Preprocessing ... % 10.27/2.09 Prover 2: Proving ... % 10.27/2.09 Prover 5: Proving ... % 11.07/2.17 Prover 6: Proving ... % 11.38/2.20 Prover 1: Constructing countermodel ... % 11.38/2.23 Prover 3: Constructing countermodel ... % 12.16/2.35 Prover 4: Constructing countermodel ... % 12.16/2.37 Prover 0: Proving ... % 12.98/2.40 Prover 3: proved (1693ms) % 12.98/2.41 % 12.98/2.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.98/2.41 % 12.98/2.41 Prover 0: stopped % 12.98/2.41 Prover 5: stopped % 12.98/2.42 Prover 6: stopped % 12.98/2.42 Prover 2: stopped % 12.98/2.42 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.98/2.42 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.98/2.42 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.98/2.42 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.98/2.42 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.75/2.54 Prover 11: Preprocessing ... % 13.75/2.57 Prover 8: Preprocessing ... % 13.75/2.59 Prover 10: Preprocessing ... % 14.54/2.60 Prover 13: Preprocessing ... % 14.54/2.61 Prover 7: Preprocessing ... % 15.38/2.75 Prover 1: Found proof (size 55) % 15.38/2.76 Prover 1: proved (2046ms) % 15.38/2.76 Prover 4: stopped % 15.38/2.78 Prover 7: Warning: ignoring some quantifiers % 15.38/2.79 Prover 10: Warning: ignoring some quantifiers % 16.14/2.80 Prover 7: Constructing countermodel ... % 16.14/2.81 Prover 13: Warning: ignoring some quantifiers % 16.14/2.81 Prover 10: Constructing countermodel ... % 16.14/2.83 Prover 7: stopped % 16.14/2.83 Prover 13: Constructing countermodel ... % 16.14/2.84 Prover 10: stopped % 16.14/2.84 Prover 8: Warning: ignoring some quantifiers % 16.14/2.85 Prover 13: stopped % 16.14/2.86 Prover 8: Constructing countermodel ... % 16.14/2.89 Prover 8: stopped % 16.82/3.01 Prover 11: Constructing countermodel ... % 17.46/3.04 Prover 11: stopped % 17.46/3.04 % 17.46/3.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 17.46/3.04 % 17.46/3.06 % SZS output start Proof for theBenchmark % 17.46/3.07 Assumptions after simplification: % 17.46/3.07 --------------------------------- % 17.46/3.07 % 17.46/3.07 (completion_conflict) % 17.96/3.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 17.96/3.13 | ~ (completion_conflict(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 17.96/3.13 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: % 17.96/3.13 any] : ? [v9: any] : (leq(v2, v1) = v7 & leq(v2, v0) = v5 & leq(v1, v3) = % 17.96/3.13 v8 & leq(v0, v3) = v6 & less(v0, v1) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0) | % 17.96/3.13 ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)))) % 17.96/3.13 % 17.96/3.13 (leq_trans) % 17.96/3.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (leq(v0, % 17.96/3.14 v2) = v3) | ~ (leq(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 17.96/3.14 ? [v4: int] : ( ~ (v4 = 0) & leq(v1, v2) = v4)) % 17.96/3.14 % 17.96/3.14 (less_implies_leq) % 17.96/3.14 ! [v0: $i] : ! [v1: $i] : ( ~ (less(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 17.96/3.14 leq(v0, v1) = 0) % 17.96/3.14 % 17.96/3.14 (odrl633) % 17.96/3.14 $i(v1200) & $i(v800) & $i(v400) & $i(v0) & ? [v0: int] : ( ~ (v0 = 0) & % 17.96/3.14 completion_conflict(v400, v800, v0, v1200) = v0) % 17.96/3.14 % 17.96/3.14 (ord_v0_v400) % 17.96/3.14 less(v0, v400) = 0 & $i(v400) & $i(v0) % 17.96/3.14 % 17.96/3.14 (ord_v400_v800) % 17.96/3.14 less(v400, v800) = 0 & $i(v800) & $i(v400) % 17.96/3.14 % 17.96/3.14 (ord_v800_v1200) % 17.96/3.15 less(v800, v1200) = 0 & $i(v1200) & $i(v800) % 17.96/3.15 % 17.96/3.15 (sharpness_conflict) % 17.96/3.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 17.96/3.15 | ~ (completion_conflict(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ % 17.96/3.15 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: % 17.96/3.15 any] : (leq(v2, v0) = v5 & leq(v1, v3) = v8 & leq(v0, v3) = v6 & less(v0, % 17.96/3.15 v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)))) % 17.96/3.15 % 17.96/3.15 (function-axioms) % 17.96/3.17 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 17.96/3.17 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (axis_compatible(v5, v4, % 17.96/3.17 v3, v2) = v1) | ~ (axis_compatible(v5, v4, v3, v2) = v0)) & ! [v0: % 17.96/3.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.96/3.17 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (axis_subsumes(v5, v4, v3, v2) = % 17.96/3.17 v1) | ~ (axis_subsumes(v5, v4, v3, v2) = v0)) & ! [v0: % 17.96/3.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.96/3.17 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (axis_conflict(v5, v4, v3, v2) = % 17.96/3.17 v1) | ~ (axis_conflict(v5, v4, v3, v2) = v0)) & ! [v0: % 17.96/3.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.96/3.17 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (completion_conflict(v5, v4, v3, % 17.96/3.17 v2) = v1) | ~ (completion_conflict(v5, v4, v3, v2) = v0)) & ! [v0: % 17.96/3.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.96/3.17 : ! [v4: $i] : (v1 = v0 | ~ (in_open(v4, v3, v2) = v1) | ~ (in_open(v4, v3, % 17.96/3.17 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 17.96/3.17 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (in_ropen(v4, v3, v2) = % 17.96/3.17 v1) | ~ (in_ropen(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 17.96/3.17 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 17.96/3.17 ~ (in_lopen(v4, v3, v2) = v1) | ~ (in_lopen(v4, v3, v2) = v0)) & ! [v0: % 17.96/3.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.96/3.17 : ! [v4: $i] : (v1 = v0 | ~ (in_closed(v4, v3, v2) = v1) | ~ (in_closed(v4, % 17.96/3.17 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 17.96/3.17 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 17.96/3.17 (completion_compatible(v4, v3, v2) = v1) | ~ (completion_compatible(v4, v3, % 17.96/3.17 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 % 17.96/3.17 = v0 | ~ (box_verdict(v3, v2) = v1) | ~ (box_verdict(v3, v2) = v0)) & ! % 17.96/3.17 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 17.96/3.17 $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 17.96/3.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.96/3.17 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0: % 17.96/3.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 17.96/3.17 ~ (val(v2) = v1) | ~ (val(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 17.96/3.17 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (is_verdict(v2) = v1) | ~ % 17.96/3.17 (is_verdict(v2) = v0)) % 17.96/3.17 % 17.96/3.17 Further assumptions not needed in the proof: % 17.96/3.17 -------------------------------------------- % 17.96/3.17 axis_compatible_def, axis_conflict_def, axis_subsumes_def, box_compatible, % 17.96/3.17 box_conflict, box_unknown, box_verdict_total, compatible_is_verdict, % 17.96/3.17 completion_compat, conflict_is_verdict, distinct, in_closed, in_lopen, in_open, % 17.96/3.17 in_ropen, irreflexive, leq_antisym, leq_def, leq_less_trans, less_leq_trans, % 17.96/3.17 monotone_conflict, redundancy, sharpness_compat, transitive, trichotomy, % 17.96/3.17 unknown_is_verdict, val_v0, val_v1200, val_v400, val_v800, verdict_enum, % 17.96/3.17 verdicts_distinct_cf_cp, verdicts_distinct_cf_un, verdicts_distinct_cp_un % 17.96/3.17 % 17.96/3.17 Those formulas are unsatisfiable: % 17.96/3.17 --------------------------------- % 17.96/3.17 % 17.96/3.17 Begin of proof % 17.96/3.17 | % 17.96/3.17 | ALPHA: (ord_v0_v400) implies: % 17.96/3.18 | (1) less(v0, v400) = 0 % 17.96/3.18 | % 17.96/3.18 | ALPHA: (ord_v400_v800) implies: % 17.96/3.18 | (2) less(v400, v800) = 0 % 17.96/3.18 | % 17.96/3.18 | ALPHA: (ord_v800_v1200) implies: % 17.96/3.18 | (3) less(v800, v1200) = 0 % 17.96/3.18 | % 17.96/3.18 | ALPHA: (odrl633) implies: % 17.96/3.18 | (4) $i(v0) % 17.96/3.18 | (5) $i(v400) % 17.96/3.18 | (6) $i(v800) % 17.96/3.18 | (7) $i(v1200) % 17.96/3.18 | (8) ? [v0: int] : ( ~ (v0 = 0) & completion_conflict(v400, v800, v0, % 17.96/3.18 | v1200) = v0) % 17.96/3.18 | % 17.96/3.18 | ALPHA: (function-axioms) implies: % 17.96/3.18 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 17.96/3.18 | ! [v3: $i] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = % 17.96/3.18 | v0)) % 17.96/3.18 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 17.96/3.18 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = % 17.96/3.18 | v0)) % 17.96/3.18 | % 17.96/3.18 | DELTA: instantiating (8) with fresh symbol all_31_0 gives: % 17.96/3.19 | (11) ~ (all_31_0 = 0) & completion_conflict(v400, v800, v0, v1200) = % 17.96/3.19 | all_31_0 % 17.96/3.19 | % 17.96/3.19 | ALPHA: (11) implies: % 17.96/3.19 | (12) ~ (all_31_0 = 0) % 17.96/3.19 | (13) completion_conflict(v400, v800, v0, v1200) = all_31_0 % 17.96/3.19 | % 17.96/3.19 | GROUND_INST: instantiating (less_implies_leq) with v0, v400, simplifying with % 17.96/3.19 | (1), (4), (5) gives: % 17.96/3.19 | (14) leq(v0, v400) = 0 % 17.96/3.19 | % 17.96/3.19 | GROUND_INST: instantiating (less_implies_leq) with v400, v800, simplifying % 17.96/3.19 | with (2), (5), (6) gives: % 17.96/3.19 | (15) leq(v400, v800) = 0 % 17.96/3.19 | % 17.96/3.19 | GROUND_INST: instantiating (less_implies_leq) with v800, v1200, simplifying % 17.96/3.19 | with (3), (6), (7) gives: % 17.96/3.19 | (16) leq(v800, v1200) = 0 % 17.96/3.19 | % 17.96/3.19 | GROUND_INST: instantiating (completion_conflict) with v400, v800, v0, v1200, % 17.96/3.19 | all_31_0, simplifying with (4), (5), (6), (7), (13) gives: % 17.96/3.19 | (17) all_31_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 17.96/3.19 | any] : ? [v4: any] : (leq(v800, v1200) = v3 & leq(v400, v1200) = v1 % 17.96/3.19 | & leq(v0, v800) = v2 & leq(v0, v400) = v0 & less(v400, v800) = v4 & % 17.96/3.19 | ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 17.96/3.19 | 0))) % 17.96/3.19 | % 17.96/3.20 | GROUND_INST: instantiating (sharpness_conflict) with v400, v800, v0, v1200, % 17.96/3.20 | all_31_0, simplifying with (4), (5), (6), (7), (13) gives: % 18.28/3.20 | (18) all_31_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 18.28/3.20 | any] : (leq(v800, v1200) = v3 & leq(v400, v1200) = v1 & leq(v0, % 18.28/3.20 | v400) = v0 & less(v400, v800) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | % 18.28/3.20 | ~ (v1 = 0) | ~ (v0 = 0))) % 18.28/3.20 | % 18.28/3.20 | BETA: splitting (18) gives: % 18.28/3.20 | % 18.28/3.20 | Case 1: % 18.28/3.20 | | % 18.28/3.20 | | (19) all_31_0 = 0 % 18.28/3.20 | | % 18.28/3.20 | | REDUCE: (12), (19) imply: % 18.28/3.20 | | (20) $false % 18.28/3.20 | | % 18.28/3.20 | | CLOSE: (20) is inconsistent. % 18.28/3.20 | | % 18.28/3.20 | Case 2: % 18.28/3.20 | | % 18.28/3.20 | | (21) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 18.28/3.20 | | (leq(v800, v1200) = v3 & leq(v400, v1200) = v1 & leq(v0, v400) = v0 % 18.28/3.20 | | & less(v400, v800) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) % 18.28/3.20 | | | ~ (v0 = 0))) % 18.28/3.20 | | % 18.28/3.20 | | DELTA: instantiating (21) with fresh symbols all_43_0, all_43_1, all_43_2, % 18.28/3.20 | | all_43_3 gives: % 18.28/3.20 | | (22) leq(v800, v1200) = all_43_0 & leq(v400, v1200) = all_43_2 & leq(v0, % 18.28/3.20 | | v400) = all_43_3 & less(v400, v800) = all_43_1 & ( ~ (all_43_0 = % 18.28/3.20 | | 0) | ~ (all_43_1 = 0) | ~ (all_43_2 = 0) | ~ (all_43_3 = 0)) % 18.28/3.20 | | % 18.28/3.20 | | ALPHA: (22) implies: % 18.28/3.21 | | (23) less(v400, v800) = all_43_1 % 18.28/3.21 | | (24) leq(v0, v400) = all_43_3 % 18.28/3.21 | | (25) leq(v400, v1200) = all_43_2 % 18.28/3.21 | | (26) leq(v800, v1200) = all_43_0 % 18.28/3.21 | | (27) ~ (all_43_0 = 0) | ~ (all_43_1 = 0) | ~ (all_43_2 = 0) | ~ % 18.28/3.21 | | (all_43_3 = 0) % 18.28/3.21 | | % 18.28/3.21 | | BETA: splitting (17) gives: % 18.28/3.21 | | % 18.28/3.21 | | Case 1: % 18.28/3.21 | | | % 18.28/3.21 | | | (28) all_31_0 = 0 % 18.28/3.21 | | | % 18.28/3.21 | | | REDUCE: (12), (28) imply: % 18.28/3.21 | | | (29) $false % 18.28/3.21 | | | % 18.28/3.21 | | | CLOSE: (29) is inconsistent. % 18.28/3.21 | | | % 18.28/3.21 | | Case 2: % 18.28/3.21 | | | % 18.28/3.21 | | | (30) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? % 18.28/3.21 | | | [v4: any] : (leq(v800, v1200) = v3 & leq(v400, v1200) = v1 & % 18.28/3.21 | | | leq(v0, v800) = v2 & leq(v0, v400) = v0 & less(v400, v800) = v4 % 18.28/3.21 | | | & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ % 18.28/3.21 | | | (v0 = 0))) % 18.28/3.21 | | | % 18.28/3.21 | | | DELTA: instantiating (30) with fresh symbols all_48_0, all_48_1, all_48_2, % 18.28/3.21 | | | all_48_3, all_48_4 gives: % 18.28/3.21 | | | (31) leq(v800, v1200) = all_48_1 & leq(v400, v1200) = all_48_3 & % 18.28/3.21 | | | leq(v0, v800) = all_48_2 & leq(v0, v400) = all_48_4 & less(v400, % 18.28/3.21 | | | v800) = all_48_0 & ( ~ (all_48_0 = 0) | ~ (all_48_1 = 0) | ~ % 18.28/3.21 | | | (all_48_2 = 0) | ~ (all_48_3 = 0) | ~ (all_48_4 = 0)) % 18.28/3.21 | | | % 18.28/3.21 | | | ALPHA: (31) implies: % 18.28/3.21 | | | (32) less(v400, v800) = all_48_0 % 18.28/3.21 | | | (33) leq(v0, v400) = all_48_4 % 18.28/3.21 | | | (34) leq(v400, v1200) = all_48_3 % 18.28/3.21 | | | (35) leq(v800, v1200) = all_48_1 % 18.28/3.21 | | | % 18.28/3.21 | | | GROUND_INST: instantiating (9) with 0, all_48_0, v800, v400, simplifying % 18.28/3.21 | | | with (2), (32) gives: % 18.28/3.22 | | | (36) all_48_0 = 0 % 18.28/3.22 | | | % 18.28/3.22 | | | GROUND_INST: instantiating (9) with all_43_1, all_48_0, v800, v400, % 18.28/3.22 | | | simplifying with (23), (32) gives: % 18.28/3.22 | | | (37) all_48_0 = all_43_1 % 18.28/3.22 | | | % 18.28/3.22 | | | GROUND_INST: instantiating (10) with all_43_3, all_48_4, v400, v0, % 18.28/3.22 | | | simplifying with (24), (33) gives: % 18.28/3.22 | | | (38) all_48_4 = all_43_3 % 18.28/3.22 | | | % 18.28/3.22 | | | GROUND_INST: instantiating (10) with 0, all_48_4, v400, v0, simplifying % 18.28/3.22 | | | with (14), (33) gives: % 18.28/3.22 | | | (39) all_48_4 = 0 % 18.28/3.22 | | | % 18.28/3.22 | | | GROUND_INST: instantiating (10) with all_43_2, all_48_3, v1200, v400, % 18.28/3.22 | | | simplifying with (25), (34) gives: % 18.28/3.22 | | | (40) all_48_3 = all_43_2 % 18.28/3.22 | | | % 18.28/3.22 | | | GROUND_INST: instantiating (10) with all_43_0, all_48_1, v1200, v800, % 18.28/3.22 | | | simplifying with (26), (35) gives: % 18.28/3.22 | | | (41) all_48_1 = all_43_0 % 18.28/3.22 | | | % 18.28/3.22 | | | GROUND_INST: instantiating (10) with 0, all_48_1, v1200, v800, simplifying % 18.28/3.22 | | | with (16), (35) gives: % 18.28/3.22 | | | (42) all_48_1 = 0 % 18.28/3.22 | | | % 18.28/3.22 | | | COMBINE_EQS: (36), (37) imply: % 18.28/3.22 | | | (43) all_43_1 = 0 % 18.28/3.22 | | | % 18.28/3.22 | | | SIMP: (43) implies: % 18.28/3.22 | | | (44) all_43_1 = 0 % 18.28/3.22 | | | % 18.28/3.22 | | | COMBINE_EQS: (41), (42) imply: % 18.28/3.22 | | | (45) all_43_0 = 0 % 18.28/3.22 | | | % 18.28/3.22 | | | COMBINE_EQS: (38), (39) imply: % 18.28/3.22 | | | (46) all_43_3 = 0 % 18.28/3.22 | | | % 18.28/3.22 | | | BETA: splitting (27) gives: % 18.28/3.22 | | | % 18.28/3.22 | | | Case 1: % 18.28/3.22 | | | | % 18.28/3.22 | | | | (47) ~ (all_43_0 = 0) % 18.28/3.22 | | | | % 18.28/3.22 | | | | REDUCE: (45), (47) imply: % 18.28/3.22 | | | | (48) $false % 18.28/3.22 | | | | % 18.28/3.22 | | | | CLOSE: (48) is inconsistent. % 18.28/3.22 | | | | % 18.28/3.22 | | | Case 2: % 18.28/3.22 | | | | % 18.28/3.22 | | | | (49) ~ (all_43_1 = 0) | ~ (all_43_2 = 0) | ~ (all_43_3 = 0) % 18.28/3.22 | | | | % 18.28/3.22 | | | | BETA: splitting (49) gives: % 18.28/3.22 | | | | % 18.28/3.22 | | | | Case 1: % 18.28/3.22 | | | | | % 18.28/3.22 | | | | | (50) ~ (all_43_1 = 0) % 18.28/3.22 | | | | | % 18.28/3.22 | | | | | REDUCE: (44), (50) imply: % 18.28/3.22 | | | | | (51) $false % 18.28/3.23 | | | | | % 18.28/3.23 | | | | | CLOSE: (51) is inconsistent. % 18.28/3.23 | | | | | % 18.28/3.23 | | | | Case 2: % 18.28/3.23 | | | | | % 18.28/3.23 | | | | | (52) ~ (all_43_2 = 0) | ~ (all_43_3 = 0) % 18.28/3.23 | | | | | % 18.28/3.23 | | | | | BETA: splitting (52) gives: % 18.28/3.23 | | | | | % 18.28/3.23 | | | | | Case 1: % 18.28/3.23 | | | | | | % 18.28/3.23 | | | | | | (53) ~ (all_43_2 = 0) % 18.28/3.23 | | | | | | % 18.28/3.23 | | | | | | GROUND_INST: instantiating (leq_trans) with v400, v800, v1200, % 18.28/3.23 | | | | | | all_43_2, simplifying with (5), (6), (7), (15), (25) % 18.28/3.23 | | | | | | gives: % 18.28/3.23 | | | | | | (54) all_43_2 = 0 | ? [v0: int] : ( ~ (v0 = 0) & leq(v800, % 18.28/3.23 | | | | | | v1200) = v0) % 18.28/3.23 | | | | | | % 18.28/3.23 | | | | | | BETA: splitting (54) gives: % 18.28/3.23 | | | | | | % 18.28/3.23 | | | | | | Case 1: % 18.28/3.23 | | | | | | | % 18.28/3.23 | | | | | | | (55) all_43_2 = 0 % 18.28/3.23 | | | | | | | % 18.28/3.23 | | | | | | | REDUCE: (53), (55) imply: % 18.28/3.23 | | | | | | | (56) $false % 18.28/3.23 | | | | | | | % 18.28/3.23 | | | | | | | CLOSE: (56) is inconsistent. % 18.28/3.23 | | | | | | | % 18.28/3.23 | | | | | | Case 2: % 18.28/3.23 | | | | | | | % 18.28/3.23 | | | | | | | (57) ? [v0: int] : ( ~ (v0 = 0) & leq(v800, v1200) = v0) % 18.28/3.23 | | | | | | | % 18.28/3.23 | | | | | | | DELTA: instantiating (57) with fresh symbol all_79_0 gives: % 18.28/3.23 | | | | | | | (58) ~ (all_79_0 = 0) & leq(v800, v1200) = all_79_0 % 18.28/3.23 | | | | | | | % 18.28/3.23 | | | | | | | ALPHA: (58) implies: % 18.28/3.23 | | | | | | | (59) ~ (all_79_0 = 0) % 18.28/3.23 | | | | | | | (60) leq(v800, v1200) = all_79_0 % 18.28/3.23 | | | | | | | % 18.28/3.23 | | | | | | | GROUND_INST: instantiating (10) with 0, all_79_0, v1200, v800, % 18.28/3.23 | | | | | | | simplifying with (16), (60) gives: % 18.28/3.23 | | | | | | | (61) all_79_0 = 0 % 18.28/3.23 | | | | | | | % 18.28/3.23 | | | | | | | REDUCE: (59), (61) imply: % 18.28/3.23 | | | | | | | (62) $false % 18.28/3.23 | | | | | | | % 18.28/3.23 | | | | | | | CLOSE: (62) is inconsistent. % 18.28/3.23 | | | | | | | % 18.28/3.23 | | | | | | End of split % 18.28/3.23 | | | | | | % 18.28/3.23 | | | | | Case 2: % 18.28/3.23 | | | | | | % 18.28/3.23 | | | | | | (63) ~ (all_43_3 = 0) % 18.28/3.23 | | | | | | % 18.28/3.23 | | | | | | REDUCE: (46), (63) imply: % 18.28/3.23 | | | | | | (64) $false % 18.28/3.23 | | | | | | % 18.28/3.23 | | | | | | CLOSE: (64) is inconsistent. % 18.28/3.23 | | | | | | % 18.28/3.23 | | | | | End of split % 18.28/3.23 | | | | | % 18.28/3.23 | | | | End of split % 18.28/3.23 | | | | % 18.28/3.23 | | | End of split % 18.28/3.23 | | | % 18.28/3.23 | | End of split % 18.28/3.23 | | % 18.28/3.23 | End of split % 18.28/3.23 | % 18.28/3.23 End of proof % 18.28/3.24 % SZS output end Proof for theBenchmark % 18.28/3.24 % 18.28/3.24 2555ms %------------------------------------------------------------------------------