%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT085+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 : n028.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 23.58s 3.84s % Output : Proof 29.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT085+1 : TPTP v9.3.1. Bugfixed v9.3.1. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.35 % Computer : n028.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Mon Sep 7 14:21:32 UTC 2026 % 0.09/0.35 % 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. % 0.71/0.70 ________ _____ % 0.71/0.70 ___ __ \_________(_)________________________________ % 0.71/0.70 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.71/0.70 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.71/0.70 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.71/0.70 % 0.71/0.70 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.71/0.70 (2023-06-19) % 0.71/0.70 % 0.71/0.70 (c) Philipp Rümmer, 2009-2023 % 0.71/0.70 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.71/0.70 Amanda Stjerna. % 0.71/0.70 Free software under BSD-3-Clause. % 0.71/0.70 % 0.71/0.70 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.71/0.70 % 0.71/0.71 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.71/0.73 Running up to 7 provers in parallel. % 0.71/0.74 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.71/0.74 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.71/0.74 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.71/0.74 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.71/0.74 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.71/0.74 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.71/0.74 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.00/1.35 Prover 4: Preprocessing ... % 4.00/1.35 Prover 1: Preprocessing ... % 4.75/1.41 Prover 2: Preprocessing ... % 4.75/1.41 Prover 0: Preprocessing ... % 4.75/1.42 Prover 3: Preprocessing ... % 4.75/1.42 Prover 5: Preprocessing ... % 4.75/1.42 Prover 6: Preprocessing ... % 8.65/1.94 Prover 2: Proving ... % 8.65/1.96 Prover 5: Proving ... % 10.02/2.16 Prover 6: Proving ... % 10.79/2.20 Prover 1: Constructing countermodel ... % 10.98/2.27 Prover 3: Constructing countermodel ... % 11.75/2.36 Prover 0: Proving ... % 12.55/2.41 Prover 4: Constructing countermodel ... % 23.58/3.83 Prover 6: proved (3091ms) % 23.58/3.84 % 23.58/3.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 23.58/3.84 % 23.58/3.84 Prover 3: stopped % 23.58/3.85 Prover 2: stopped % 23.58/3.85 Prover 5: stopped % 23.58/3.85 Prover 0: stopped % 23.58/3.86 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 23.58/3.86 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 23.58/3.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 23.58/3.86 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 23.58/3.86 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 24.37/3.91 Prover 7: Preprocessing ... % 24.37/3.95 Prover 11: Preprocessing ... % 24.37/3.98 Prover 8: Preprocessing ... % 24.37/4.00 Prover 13: Preprocessing ... % 24.37/4.02 Prover 10: Preprocessing ... % 25.45/4.07 Prover 13: Warning: ignoring some quantifiers % 25.45/4.08 Prover 13: Constructing countermodel ... % 25.45/4.14 Prover 7: Warning: ignoring some quantifiers % 26.26/4.16 Prover 7: Constructing countermodel ... % 26.77/4.22 Prover 10: Warning: ignoring some quantifiers % 26.77/4.24 Prover 8: Warning: ignoring some quantifiers % 26.77/4.24 Prover 10: Constructing countermodel ... % 26.77/4.25 Prover 8: Constructing countermodel ... % 27.52/4.31 Prover 11: Constructing countermodel ... % 29.06/4.51 Prover 1: Found proof (size 53) % 29.06/4.51 Prover 1: proved (3776ms) % 29.06/4.52 Prover 11: stopped % 29.06/4.52 Prover 8: stopped % 29.06/4.52 Prover 7: stopped % 29.06/4.52 Prover 10: stopped % 29.06/4.52 Prover 13: stopped % 29.06/4.52 Prover 4: stopped % 29.06/4.52 % 29.06/4.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 29.06/4.52 % 29.06/4.53 % SZS output start Proof for theBenchmark % 29.06/4.54 Assumptions after simplification: % 29.06/4.54 --------------------------------- % 29.06/4.54 % 29.06/4.54 (in_lopen) % 29.06/4.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 29.06/4.59 (in_lopen(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 29.06/4.59 any] : ? [v5: any] : (leq(v0, v2) = v5 & less(v1, v0) = v4 & ( ~ (v5 = 0) % 29.06/4.59 | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 29.06/4.59 (in_lopen(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (leq(v0, % 29.06/4.59 v2) = 0 & less(v1, v0) = 0)) % 29.06/4.59 % 29.06/4.59 (irreflexive) % 29.06/4.60 ! [v0: $i] : ( ~ (less(v0, v0) = 0) | ~ $i(v0)) % 29.06/4.60 % 29.06/4.60 (less_leq_trans) % 29.56/4.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (leq(v1, v2) = 0) | ~ (less(v0, % 29.56/4.60 v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | less(v0, v2) = 0) % 29.56/4.60 % 29.56/4.60 (odrl445) % 29.56/4.60 $i(v400) & $i(v200) & $i(v100) & $i(v50) & $i(v0) & ? [v0: $i] : ? [v1: $i] % 29.56/4.60 : ? [v2: $i] : ? [v3: any] : ? [v4: any] : ? [v5: any] : (in_lopen(v2, v0, % 29.56/4.60 v50) = v5 & in_lopen(v1, v0, v100) = v4 & in_lopen(v0, v0, v200) = v3 & % 29.56/4.60 leq(v400, v0) = 0 & leq(v200, v1) = 0 & leq(v100, v2) = 0 & $i(v2) & $i(v1) % 29.56/4.60 & $i(v0) & (v5 = 0 | v4 = 0 | v3 = 0)) % 29.56/4.60 % 29.56/4.60 (ord_v0_v400) % 29.56/4.61 less(v0, v400) = 0 & $i(v400) & $i(v0) % 29.56/4.61 % 29.56/4.61 (ord_v100_v200) % 29.56/4.61 less(v100, v200) = 0 & $i(v200) & $i(v100) % 29.56/4.61 % 29.56/4.61 (ord_v200_v400) % 29.56/4.61 less(v200, v400) = 0 & $i(v400) & $i(v200) % 29.56/4.61 % 29.56/4.61 (ord_v50_v100) % 29.56/4.61 less(v50, v100) = 0 & $i(v100) & $i(v50) % 29.56/4.61 % 29.56/4.61 (function-axioms) % 29.56/4.62 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 29.56/4.62 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (axis_subsumes(v5, v4, % 29.56/4.62 v3, v2) = v1) | ~ (axis_subsumes(v5, v4, v3, v2) = v0)) & ! [v0: % 29.56/4.62 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 29.56/4.62 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (axis_compatible(v5, v4, v3, v2) = % 29.56/4.62 v1) | ~ (axis_compatible(v5, v4, v3, v2) = v0)) & ! [v0: % 29.56/4.62 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 29.56/4.62 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (axis_conflict(v5, v4, v3, v2) = % 29.56/4.62 v1) | ~ (axis_conflict(v5, v4, v3, v2) = v0)) & ! [v0: % 29.56/4.62 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 29.56/4.62 : ! [v4: $i] : (v1 = v0 | ~ (in_open(v4, v3, v2) = v1) | ~ (in_open(v4, v3, % 29.56/4.62 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 29.56/4.62 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (in_ropen(v4, v3, v2) = % 29.56/4.62 v1) | ~ (in_ropen(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 29.56/4.62 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 29.56/4.62 ~ (in_lopen(v4, v3, v2) = v1) | ~ (in_lopen(v4, v3, v2) = v0)) & ! [v0: % 29.56/4.62 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 29.56/4.62 : ! [v4: $i] : (v1 = v0 | ~ (in_closed(v4, v3, v2) = v1) | ~ (in_closed(v4, % 29.56/4.62 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 29.56/4.62 (v1 = v0 | ~ (box_verdict(v3, v2) = v1) | ~ (box_verdict(v3, v2) = v0)) & ! % 29.56/4.62 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 29.56/4.62 $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 29.56/4.62 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 29.56/4.62 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0: % 29.56/4.62 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 29.56/4.62 ~ (val(v2) = v1) | ~ (val(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 29.56/4.62 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (is_verdict(v2) = v1) | ~ % 29.56/4.62 (is_verdict(v2) = v0)) % 29.56/4.62 % 29.56/4.62 Further assumptions not needed in the proof: % 29.56/4.62 -------------------------------------------- % 29.56/4.62 axis_compatible_def, axis_conflict_def, axis_subsumes_def, box_compatible, % 29.56/4.62 box_conflict, box_unknown, box_verdict_total, compatible_is_verdict, % 29.56/4.62 conflict_is_verdict, distinct, in_closed, in_open, in_ropen, leq_antisym, % 29.56/4.62 leq_def, leq_less_trans, leq_trans, less_implies_leq, ord_v0_v100, ord_v0_v200, % 29.56/4.62 ord_v0_v50, ord_v100_v400, ord_v50_v200, ord_v50_v400, transitive, trichotomy, % 29.56/4.62 unknown_is_verdict, val_v0, val_v100, val_v200, val_v400, val_v50, verdict_enum, % 29.56/4.62 verdicts_distinct_cf_cp, verdicts_distinct_cf_un, verdicts_distinct_cp_un % 29.56/4.62 % 29.56/4.62 Those formulas are unsatisfiable: % 29.56/4.62 --------------------------------- % 29.56/4.62 % 29.56/4.62 Begin of proof % 29.56/4.63 | % 29.56/4.63 | ALPHA: (in_lopen) implies: % 29.56/4.63 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (in_lopen(v0, v1, v2) = % 29.56/4.63 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (leq(v0, v2) = 0 & % 29.56/4.63 | less(v1, v0) = 0)) % 29.56/4.63 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 29.56/4.63 | (in_lopen(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 29.56/4.63 | [v4: any] : ? [v5: any] : (leq(v0, v2) = v5 & less(v1, v0) = v4 & ( % 29.56/4.63 | ~ (v5 = 0) | ~ (v4 = 0)))) % 29.56/4.63 | % 29.56/4.63 | ALPHA: (ord_v0_v400) implies: % 29.56/4.63 | (3) less(v0, v400) = 0 % 29.56/4.63 | % 29.56/4.63 | ALPHA: (ord_v50_v100) implies: % 29.56/4.63 | (4) less(v50, v100) = 0 % 29.56/4.63 | % 29.56/4.63 | ALPHA: (ord_v100_v200) implies: % 29.56/4.63 | (5) less(v100, v200) = 0 % 29.56/4.63 | % 29.56/4.63 | ALPHA: (ord_v200_v400) implies: % 29.56/4.63 | (6) less(v200, v400) = 0 % 29.56/4.63 | % 29.56/4.63 | ALPHA: (odrl445) implies: % 29.56/4.64 | (7) $i(v0) % 29.56/4.64 | (8) $i(v50) % 29.56/4.64 | (9) $i(v100) % 29.56/4.64 | (10) $i(v200) % 29.56/4.64 | (11) $i(v400) % 29.56/4.64 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: any] % 29.56/4.64 | : ? [v5: any] : (in_lopen(v2, v0, v50) = v5 & in_lopen(v1, v0, v100) % 29.56/4.64 | = v4 & in_lopen(v0, v0, v200) = v3 & leq(v400, v0) = 0 & leq(v200, % 29.56/4.64 | v1) = 0 & leq(v100, v2) = 0 & $i(v2) & $i(v1) & $i(v0) & (v5 = 0 | % 29.56/4.64 | v4 = 0 | v3 = 0)) % 29.56/4.64 | % 29.56/4.64 | ALPHA: (function-axioms) implies: % 29.56/4.64 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 29.56/4.64 | : ! [v3: $i] : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = % 29.56/4.64 | v0)) % 29.56/4.64 | % 29.56/4.64 | DELTA: instantiating (12) with fresh symbols all_25_0, all_25_1, all_25_2, % 29.56/4.64 | all_25_3, all_25_4, all_25_5 gives: % 29.56/4.64 | (14) in_lopen(all_25_3, v0, v50) = all_25_0 & in_lopen(all_25_4, v0, v100) % 29.56/4.64 | = all_25_1 & in_lopen(all_25_5, v0, v200) = all_25_2 & leq(v400, % 29.56/4.64 | all_25_5) = 0 & leq(v200, all_25_4) = 0 & leq(v100, all_25_3) = 0 & % 29.56/4.64 | $i(all_25_3) & $i(all_25_4) & $i(all_25_5) & (all_25_0 = 0 | all_25_1 % 29.56/4.64 | = 0 | all_25_2 = 0) % 29.56/4.64 | % 29.56/4.64 | ALPHA: (14) implies: % 29.56/4.64 | (15) $i(all_25_5) % 29.56/4.64 | (16) $i(all_25_4) % 29.56/4.64 | (17) $i(all_25_3) % 29.56/4.64 | (18) leq(v100, all_25_3) = 0 % 29.56/4.64 | (19) leq(v200, all_25_4) = 0 % 29.56/4.65 | (20) leq(v400, all_25_5) = 0 % 29.56/4.65 | (21) in_lopen(all_25_5, v0, v200) = all_25_2 % 29.56/4.65 | (22) in_lopen(all_25_4, v0, v100) = all_25_1 % 29.56/4.65 | (23) in_lopen(all_25_3, v0, v50) = all_25_0 % 29.56/4.65 | (24) all_25_0 = 0 | all_25_1 = 0 | all_25_2 = 0 % 29.56/4.65 | % 29.56/4.65 | GROUND_INST: instantiating (less_leq_trans) with v50, v100, all_25_3, % 29.56/4.65 | simplifying with (4), (8), (9), (17), (18) gives: % 29.56/4.65 | (25) less(v50, all_25_3) = 0 % 29.56/4.65 | % 29.56/4.65 | GROUND_INST: instantiating (less_leq_trans) with v100, v200, all_25_4, % 29.56/4.65 | simplifying with (5), (9), (10), (16), (19) gives: % 29.56/4.65 | (26) less(v100, all_25_4) = 0 % 29.56/4.65 | % 29.56/4.65 | GROUND_INST: instantiating (less_leq_trans) with v200, v400, all_25_5, % 29.56/4.65 | simplifying with (6), (10), (11), (15), (20) gives: % 29.56/4.65 | (27) less(v200, all_25_5) = 0 % 29.56/4.65 | % 29.56/4.65 | GROUND_INST: instantiating (less_leq_trans) with v0, v400, all_25_5, % 29.56/4.65 | simplifying with (3), (7), (11), (15), (20) gives: % 29.56/4.65 | (28) less(v0, all_25_5) = 0 % 29.56/4.65 | % 29.56/4.65 | GROUND_INST: instantiating (2) with all_25_5, v0, v200, all_25_2, simplifying % 29.56/4.65 | with (7), (10), (15), (21) gives: % 29.56/4.66 | (29) all_25_2 = 0 | ? [v0: any] : ? [v1: any] : (leq(all_25_5, v200) = v1 % 29.56/4.66 | & less(v0, all_25_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 29.56/4.66 | % 29.56/4.66 | GROUND_INST: instantiating (2) with all_25_3, v0, v50, all_25_0, simplifying % 29.56/4.66 | with (7), (8), (17), (23) gives: % 29.56/4.66 | (30) all_25_0 = 0 | ? [v0: any] : ? [v1: any] : (leq(all_25_3, v50) = v1 % 29.56/4.66 | & less(v0, all_25_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 29.56/4.66 | % 29.56/4.66 | BETA: splitting (30) gives: % 29.56/4.66 | % 29.56/4.66 | Case 1: % 29.56/4.66 | | % 29.56/4.66 | | (31) all_25_0 = 0 % 29.56/4.66 | | % 29.56/4.66 | | REDUCE: (23), (31) imply: % 29.56/4.66 | | (32) in_lopen(all_25_3, v0, v50) = 0 % 29.56/4.66 | | % 29.56/4.66 | | GROUND_INST: instantiating (1) with all_25_3, v0, v50, simplifying with (7), % 29.56/4.66 | | (8), (17), (32) gives: % 29.56/4.66 | | (33) leq(all_25_3, v50) = 0 & less(v0, all_25_3) = 0 % 29.56/4.66 | | % 29.56/4.66 | | ALPHA: (33) implies: % 29.56/4.66 | | (34) leq(all_25_3, v50) = 0 % 29.56/4.66 | | % 29.56/4.66 | | GROUND_INST: instantiating (less_leq_trans) with v50, all_25_3, v50, % 29.56/4.66 | | simplifying with (8), (17), (25), (34) gives: % 29.56/4.66 | | (35) less(v50, v50) = 0 % 29.56/4.66 | | % 29.56/4.66 | | GROUND_INST: instantiating (irreflexive) with v50, simplifying with (8), % 29.56/4.66 | | (35) gives: % 29.56/4.66 | | (36) $false % 29.56/4.66 | | % 29.56/4.66 | | CLOSE: (36) is inconsistent. % 29.56/4.67 | | % 29.56/4.67 | Case 2: % 29.56/4.67 | | % 29.56/4.67 | | (37) ~ (all_25_0 = 0) % 29.56/4.67 | | % 29.56/4.67 | | BETA: splitting (29) gives: % 29.56/4.67 | | % 29.56/4.67 | | Case 1: % 29.56/4.67 | | | % 29.56/4.67 | | | (38) all_25_2 = 0 % 29.56/4.67 | | | % 29.56/4.67 | | | REDUCE: (21), (38) imply: % 29.56/4.67 | | | (39) in_lopen(all_25_5, v0, v200) = 0 % 29.56/4.67 | | | % 29.56/4.67 | | | GROUND_INST: instantiating (1) with all_25_5, v0, v200, simplifying with % 29.56/4.67 | | | (7), (10), (15), (39) gives: % 29.56/4.67 | | | (40) leq(all_25_5, v200) = 0 & less(v0, all_25_5) = 0 % 29.56/4.67 | | | % 29.56/4.67 | | | ALPHA: (40) implies: % 29.56/4.67 | | | (41) leq(all_25_5, v200) = 0 % 29.56/4.67 | | | % 29.56/4.67 | | | GROUND_INST: instantiating (less_leq_trans) with v200, all_25_5, v200, % 29.56/4.67 | | | simplifying with (10), (15), (27), (41) gives: % 29.56/4.67 | | | (42) less(v200, v200) = 0 % 29.56/4.67 | | | % 29.56/4.67 | | | GROUND_INST: instantiating (irreflexive) with v200, simplifying with (10), % 29.56/4.67 | | | (42) gives: % 29.56/4.67 | | | (43) $false % 29.56/4.67 | | | % 29.56/4.67 | | | CLOSE: (43) is inconsistent. % 29.56/4.67 | | | % 29.56/4.67 | | Case 2: % 29.56/4.67 | | | % 29.56/4.67 | | | (44) ~ (all_25_2 = 0) % 29.56/4.67 | | | (45) ? [v0: any] : ? [v1: any] : (leq(all_25_5, v200) = v1 & less(v0, % 29.56/4.67 | | | all_25_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 29.56/4.67 | | | % 29.56/4.67 | | | DELTA: instantiating (45) with fresh symbols all_78_0, all_78_1 gives: % 29.56/4.67 | | | (46) leq(all_25_5, v200) = all_78_0 & less(v0, all_25_5) = all_78_1 & ( % 29.56/4.67 | | | ~ (all_78_0 = 0) | ~ (all_78_1 = 0)) % 29.56/4.67 | | | % 29.56/4.67 | | | ALPHA: (46) implies: % 29.56/4.67 | | | (47) less(v0, all_25_5) = all_78_1 % 29.56/4.67 | | | (48) ~ (all_78_0 = 0) | ~ (all_78_1 = 0) % 29.56/4.67 | | | % 29.56/4.67 | | | BETA: splitting (24) gives: % 29.56/4.67 | | | % 29.56/4.67 | | | Case 1: % 29.56/4.67 | | | | % 29.56/4.67 | | | | (49) all_25_0 = 0 % 29.56/4.67 | | | | % 29.56/4.67 | | | | REDUCE: (37), (49) imply: % 29.56/4.67 | | | | (50) $false % 29.56/4.67 | | | | % 29.56/4.67 | | | | CLOSE: (50) is inconsistent. % 29.56/4.67 | | | | % 29.56/4.67 | | | Case 2: % 29.56/4.67 | | | | % 29.56/4.68 | | | | (51) all_25_1 = 0 | all_25_2 = 0 % 29.56/4.68 | | | | % 29.56/4.68 | | | | BETA: splitting (51) gives: % 29.56/4.68 | | | | % 29.56/4.68 | | | | Case 1: % 29.56/4.68 | | | | | % 29.56/4.68 | | | | | (52) all_25_1 = 0 % 29.56/4.68 | | | | | % 29.56/4.68 | | | | | REDUCE: (22), (52) imply: % 29.56/4.68 | | | | | (53) in_lopen(all_25_4, v0, v100) = 0 % 29.56/4.68 | | | | | % 29.56/4.68 | | | | | GROUND_INST: instantiating (13) with 0, all_78_1, all_25_5, v0, % 29.56/4.68 | | | | | simplifying with (28), (47) gives: % 29.56/4.68 | | | | | (54) all_78_1 = 0 % 29.56/4.68 | | | | | % 29.56/4.68 | | | | | BETA: splitting (48) gives: % 29.56/4.68 | | | | | % 29.56/4.68 | | | | | Case 1: % 29.56/4.68 | | | | | | % 29.56/4.68 | | | | | | % 29.56/4.68 | | | | | | GROUND_INST: instantiating (1) with all_25_4, v0, v100, simplifying % 29.56/4.68 | | | | | | with (7), (9), (16), (53) gives: % 29.56/4.68 | | | | | | (55) leq(all_25_4, v100) = 0 & less(v0, all_25_4) = 0 % 29.56/4.68 | | | | | | % 29.56/4.68 | | | | | | ALPHA: (55) implies: % 29.56/4.68 | | | | | | (56) leq(all_25_4, v100) = 0 % 29.56/4.68 | | | | | | % 29.56/4.68 | | | | | | GROUND_INST: instantiating (less_leq_trans) with v100, all_25_4, % 29.56/4.68 | | | | | | v100, simplifying with (9), (16), (26), (56) gives: % 29.56/4.68 | | | | | | (57) less(v100, v100) = 0 % 29.56/4.68 | | | | | | % 29.56/4.68 | | | | | | GROUND_INST: instantiating (irreflexive) with v100, simplifying with % 29.56/4.68 | | | | | | (9), (57) gives: % 29.56/4.68 | | | | | | (58) $false % 29.56/4.68 | | | | | | % 29.56/4.68 | | | | | | CLOSE: (58) is inconsistent. % 29.56/4.68 | | | | | | % 29.56/4.68 | | | | | Case 2: % 29.56/4.68 | | | | | | % 29.56/4.68 | | | | | | (59) ~ (all_78_1 = 0) % 29.56/4.68 | | | | | | % 29.56/4.68 | | | | | | REDUCE: (54), (59) imply: % 29.56/4.68 | | | | | | (60) $false % 29.56/4.68 | | | | | | % 29.56/4.68 | | | | | | CLOSE: (60) is inconsistent. % 29.56/4.68 | | | | | | % 29.56/4.68 | | | | | End of split % 29.56/4.68 | | | | | % 29.56/4.68 | | | | Case 2: % 29.56/4.68 | | | | | % 29.56/4.68 | | | | | (61) all_25_2 = 0 % 29.56/4.68 | | | | | % 29.56/4.68 | | | | | REDUCE: (44), (61) imply: % 29.56/4.68 | | | | | (62) $false % 29.56/4.68 | | | | | % 29.56/4.68 | | | | | CLOSE: (62) is inconsistent. % 29.56/4.68 | | | | | % 29.56/4.68 | | | | End of split % 29.56/4.68 | | | | % 29.56/4.68 | | | End of split % 29.56/4.68 | | | % 29.56/4.68 | | End of split % 29.56/4.68 | | % 29.56/4.68 | End of split % 29.56/4.68 | % 29.56/4.68 End of proof % 29.56/4.68 % SZS output end Proof for theBenchmark % 29.56/4.68 % 29.56/4.68 3976ms %------------------------------------------------------------------------------