%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : MGT070+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n006.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 06:17:28 AM UTC 2026 % Result : Theorem 15.45s 2.68s % Output : Proof 20.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : MGT070+1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.37 % Computer : n006.cluster.edu % 0.10/0.37 % Model : x86_64 x86_64 % 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.37 % Memory : 8046.5625MB % 0.10/0.37 % OS : Linux 6.8.0-71-generic % 0.10/0.37 % CPULimit : 300 % 0.10/0.37 % WCLimit : 300 % 0.10/0.37 % DateTime : Mon Sep 7 13:53:46 UTC 2026 % 0.10/0.37 % CPUTime : % 0.10/0.38 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. % 0.52/0.56 ________ _____ % 0.52/0.56 ___ __ \_________(_)________________________________ % 0.52/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.52/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.52/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.52/0.56 % 0.52/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.52/0.56 (2023-06-19) % 0.52/0.56 % 0.52/0.56 (c) Philipp Rümmer, 2009-2023 % 0.52/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.52/0.56 Amanda Stjerna. % 0.52/0.56 Free software under BSD-3-Clause. % 0.52/0.56 % 0.52/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.52/0.56 % 0.52/0.56 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.52/0.57 Running up to 7 provers in parallel. % 0.52/0.58 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.52/0.58 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.52/0.58 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.52/0.58 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.52/0.58 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.52/0.58 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.52/0.58 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.26/1.18 Prover 4: Preprocessing ... % 4.43/1.21 Prover 1: Preprocessing ... % 4.43/1.26 Prover 6: Preprocessing ... % 4.43/1.26 Prover 0: Preprocessing ... % 4.43/1.26 Prover 2: Preprocessing ... % 4.43/1.26 Prover 3: Preprocessing ... % 4.43/1.26 Prover 5: Preprocessing ... % 9.95/2.02 Prover 5: Proving ... % 9.95/2.03 Prover 2: Proving ... % 10.99/2.09 Prover 3: Constructing countermodel ... % 10.99/2.10 Prover 6: Proving ... % 12.27/2.24 Prover 1: Constructing countermodel ... % 12.27/2.29 Prover 4: Constructing countermodel ... % 13.88/2.40 Prover 0: Proving ... % 15.45/2.67 Prover 0: proved (2092ms) % 15.45/2.68 % 15.45/2.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.45/2.68 % 15.45/2.68 Prover 3: stopped % 15.45/2.68 Prover 2: stopped % 15.45/2.68 Prover 5: stopped % 15.45/2.69 Prover 6: stopped % 15.45/2.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.45/2.69 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.45/2.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.45/2.69 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.45/2.69 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.24/2.76 Prover 7: Preprocessing ... % 17.04/2.82 Prover 11: Preprocessing ... % 17.04/2.82 Prover 13: Preprocessing ... % 17.04/2.87 Prover 8: Preprocessing ... % 17.04/2.87 Prover 10: Preprocessing ... % 17.83/2.92 Prover 7: Warning: ignoring some quantifiers % 17.83/2.94 Prover 7: Constructing countermodel ... % 17.83/2.96 Prover 4: Found proof (size 50) % 17.83/2.96 Prover 4: proved (2384ms) % 17.83/2.97 Prover 1: stopped % 17.83/2.98 Prover 11: stopped % 17.83/2.98 Prover 10: Warning: ignoring some quantifiers % 17.83/2.98 Prover 7: stopped % 17.83/3.01 Prover 10: Constructing countermodel ... % 17.83/3.02 Prover 13: Warning: ignoring some quantifiers % 17.83/3.02 Prover 10: stopped % 18.81/3.04 Prover 13: Constructing countermodel ... % 18.81/3.06 Prover 13: stopped % 19.32/3.14 Prover 8: Warning: ignoring some quantifiers % 19.32/3.16 Prover 8: Constructing countermodel ... % 19.32/3.18 Prover 8: stopped % 19.32/3.18 % 19.32/3.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 19.32/3.18 % 19.67/3.21 % SZS output start Proof for theBenchmark % 19.67/3.22 Assumptions after simplification: % 19.67/3.22 --------------------------------- % 19.67/3.22 % 19.67/3.22 (dense) % 19.67/3.27 ! [v0: $i] : ! [v1: $i] : ( ~ (less(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 19.67/3.27 ? [v2: $i] : (less(v2, v1) = 0 & less(v0, v2) = 0 & $i(v2))) % 19.67/3.27 % 19.67/3.27 (h_0_sup) % 19.67/3.27 less(n0, nsup) = 0 & $i(nsup) & $i(n0) % 19.67/3.27 % 19.67/3.27 (h_inf_0) % 19.67/3.27 less(ninf, n0) = 0 & $i(n0) & $i(ninf) % 19.67/3.27 % 19.67/3.27 (less_implies_leq) % 19.67/3.28 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0, v1) = v2) | % 19.67/3.28 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & less(v0, v1) = v3)) & % 19.67/3.28 ! [v0: $i] : ! [v1: $i] : ( ~ (less(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 19.67/3.28 leq(v0, v1) = 0) % 19.67/3.28 % 19.67/3.28 (sharpness_compat) % 19.67/3.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 19.67/3.29 | ~ (completion_compatible(v0, v2, v3) = v4) | ~ (leq(v1, v3) = 0) | ~ % 19.67/3.29 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 19.67/3.29 ? [v7: any] : (leq(v2, v0) = v5 & leq(v0, v3) = v6 & less(v0, v1) = v7 & ( ~ % 19.67/3.29 (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 19.67/3.30 [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 19.67/3.30 (completion_compatible(v0, v2, v3) = v4) | ~ (less(v0, v1) = 0) | ~ $i(v3) % 19.67/3.30 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: % 19.67/3.30 any] : (leq(v2, v0) = v5 & leq(v1, v3) = v7 & leq(v0, v3) = v6 & ( ~ (v7 = % 19.67/3.30 0) | ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 19.67/3.30 [v2: $i] : ! [v3: $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, v3) = 0) | ~ % 19.67/3.30 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 19.67/3.30 ? [v6: any] : (completion_compatible(v0, v2, v3) = v6 & leq(v0, v3) = v4 & % 19.67/3.30 less(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) & ! [v0: $i] : % 19.67/3.30 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v0, % 19.67/3.30 v3) = 0) | ~ (less(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 19.67/3.30 ~ $i(v0) | ? [v4: any] : ? [v5: any] : (completion_compatible(v0, v2, v3) % 19.67/3.30 = v5 & leq(v1, v3) = v4 & ( ~ (v4 = 0) | v5 = 0))) % 19.67/3.30 % 20.13/3.30 (unknown_sound_compatible) % 20.13/3.30 $i(nsup) & $i(ninf) & ! [v0: $i] : ( ~ (completion_compatible(v0, ninf, nsup) % 20.13/3.30 = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (leq(v0, nsup) = v2 & % 20.13/3.30 leq(ninf, v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) & ! [v0: $i] : ( ~ % 20.13/3.30 (leq(v0, nsup) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : % 20.13/3.30 (completion_compatible(v0, ninf, nsup) = v2 & leq(ninf, v0) = v1 & ( ~ (v2 = % 20.13/3.30 0) | ~ (v1 = 0)))) & ! [v0: $i] : ( ~ (leq(ninf, v0) = 0) | ~ % 20.13/3.30 $i(v0) | ? [v1: any] : ? [v2: any] : (completion_compatible(v0, ninf, % 20.13/3.30 nsup) = v2 & leq(v0, nsup) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) % 20.13/3.30 % 20.13/3.30 (function-axioms) % 20.13/3.32 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 20.13/3.32 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (completion_conflict(v5, % 20.13/3.32 v4, v3, v2) = v1) | ~ (completion_conflict(v5, v4, v3, v2) = v0)) & ! % 20.13/3.32 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 20.13/3.32 $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (axis_subsumes(v5, v4, v3, % 20.13/3.32 v2) = v1) | ~ (axis_subsumes(v5, v4, v3, v2) = v0)) & ! [v0: % 20.13/3.32 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.13/3.32 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (axis_compatible(v5, v4, v3, v2) = % 20.13/3.32 v1) | ~ (axis_compatible(v5, v4, v3, v2) = v0)) & ! [v0: % 20.13/3.32 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.13/3.32 : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~ (axis_conflict(v5, v4, v3, v2) = % 20.13/3.32 v1) | ~ (axis_conflict(v5, v4, v3, v2) = v0)) & ! [v0: % 20.13/3.32 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.13/3.32 : ! [v4: $i] : (v1 = v0 | ~ (completion_compatible(v4, v3, v2) = v1) | ~ % 20.13/3.32 (completion_compatible(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 20.13/3.32 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 20.13/3.32 ~ (in_open(v4, v3, v2) = v1) | ~ (in_open(v4, v3, v2) = v0)) & ! [v0: % 20.13/3.32 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.13/3.32 : ! [v4: $i] : (v1 = v0 | ~ (in_ropen(v4, v3, v2) = v1) | ~ (in_ropen(v4, % 20.13/3.32 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 20.13/3.32 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (in_lopen(v4, v3, % 20.13/3.32 v2) = v1) | ~ (in_lopen(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] % 20.13/3.32 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = % 20.13/3.32 v0 | ~ (in_closed(v4, v3, v2) = v1) | ~ (in_closed(v4, v3, v2) = v0)) & ! % 20.13/3.32 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.13/3.32 (box_verdict(v3, v2) = v1) | ~ (box_verdict(v3, v2) = v0)) & ! [v0: % 20.13/3.32 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.13/3.32 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: % 20.13/3.32 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 20.13/3.32 : (v1 = v0 | ~ (less(v3, v2) = v1) | ~ (less(v3, v2) = v0)) & ! [v0: % 20.13/3.32 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 20.13/3.32 ~ (is_verdict(v2) = v1) | ~ (is_verdict(v2) = v0)) % 20.13/3.32 % 20.13/3.32 Further assumptions not needed in the proof: % 20.13/3.32 -------------------------------------------- % 20.13/3.32 axis_compatible_def, axis_conflict_def, axis_subsumes_def, box_compatible, % 20.13/3.32 box_conflict, box_unknown, box_verdict_total, compatible_is_verdict, % 20.13/3.32 completion_compat, completion_conflict, conflict_is_verdict, h_inf_lb, h_sup_ub, % 20.13/3.32 h_unknown, in_closed, in_lopen, in_open, in_ropen, irreflexive, leq_antisym, % 20.13/3.32 leq_def, leq_less_trans, leq_trans, less_leq_trans, monotone_conflict, % 20.13/3.32 redundancy, sharpness_conflict, transitive, trichotomy, unknown_is_verdict, % 20.13/3.32 verdict_enum, verdicts_distinct_cf_cp, verdicts_distinct_cf_un, % 20.13/3.32 verdicts_distinct_cp_un % 20.13/3.32 % 20.13/3.32 Those formulas are unsatisfiable: % 20.13/3.32 --------------------------------- % 20.13/3.32 % 20.13/3.32 Begin of proof % 20.13/3.32 | % 20.13/3.32 | ALPHA: (less_implies_leq) implies: % 20.13/3.32 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (less(v0, v1) = 0) | ~ $i(v1) | ~ % 20.13/3.33 | $i(v0) | leq(v0, v1) = 0) % 20.13/3.33 | % 20.13/3.33 | ALPHA: (sharpness_compat) implies: % 20.13/3.33 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (leq(v2, % 20.13/3.33 | v0) = 0) | ~ (leq(v0, v3) = 0) | ~ (less(v0, v1) = 0) | ~ % 20.13/3.33 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: % 20.13/3.33 | any] : (completion_compatible(v0, v2, v3) = v5 & leq(v1, v3) = v4 & % 20.13/3.33 | ( ~ (v4 = 0) | v5 = 0))) % 20.13/3.33 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (leq(v2, % 20.13/3.33 | v0) = 0) | ~ (leq(v1, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~ % 20.13/3.33 | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : % 20.13/3.33 | (completion_compatible(v0, v2, v3) = v6 & leq(v0, v3) = v4 & less(v0, % 20.13/3.33 | v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0))) % 20.13/3.33 | % 20.13/3.33 | ALPHA: (h_inf_0) implies: % 20.13/3.33 | (4) less(ninf, n0) = 0 % 20.13/3.33 | % 20.13/3.33 | ALPHA: (h_0_sup) implies: % 20.13/3.33 | (5) $i(n0) % 20.13/3.33 | (6) less(n0, nsup) = 0 % 20.13/3.33 | % 20.13/3.34 | ALPHA: (unknown_sound_compatible) implies: % 20.13/3.34 | (7) $i(ninf) % 20.13/3.34 | (8) $i(nsup) % 20.13/3.34 | (9) ! [v0: $i] : ( ~ (leq(ninf, v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 20.13/3.34 | [v2: any] : (completion_compatible(v0, ninf, nsup) = v2 & leq(v0, % 20.13/3.34 | nsup) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) % 20.13/3.34 | (10) ! [v0: $i] : ( ~ (leq(v0, nsup) = 0) | ~ $i(v0) | ? [v1: any] : ? % 20.13/3.34 | [v2: any] : (completion_compatible(v0, ninf, nsup) = v2 & leq(ninf, % 20.13/3.34 | v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) % 20.13/3.34 | % 20.13/3.34 | ALPHA: (function-axioms) implies: % 20.13/3.34 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 20.13/3.34 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = % 20.13/3.34 | v0)) % 20.13/3.34 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 20.13/3.34 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (completion_compatible(v4, % 20.13/3.34 | v3, v2) = v1) | ~ (completion_compatible(v4, v3, v2) = v0)) % 20.13/3.34 | % 20.13/3.35 | GROUND_INST: instantiating (1) with ninf, n0, simplifying with (4), (5), (7) % 20.13/3.35 | gives: % 20.13/3.35 | (13) leq(ninf, n0) = 0 % 20.13/3.35 | % 20.13/3.35 | GROUND_INST: instantiating (1) with n0, nsup, simplifying with (5), (6), (8) % 20.13/3.35 | gives: % 20.13/3.35 | (14) leq(n0, nsup) = 0 % 20.13/3.35 | % 20.13/3.35 | GROUND_INST: instantiating (dense) with n0, nsup, simplifying with (5), (6), % 20.13/3.35 | (8) gives: % 20.13/3.35 | (15) ? [v0: $i] : (less(v0, nsup) = 0 & less(n0, v0) = 0 & $i(v0)) % 20.13/3.35 | % 20.13/3.35 | DELTA: instantiating (15) with fresh symbol all_41_0 gives: % 20.13/3.35 | (16) less(all_41_0, nsup) = 0 & less(n0, all_41_0) = 0 & $i(all_41_0) % 20.13/3.35 | % 20.13/3.35 | ALPHA: (16) implies: % 20.13/3.35 | (17) $i(all_41_0) % 20.13/3.35 | (18) less(n0, all_41_0) = 0 % 20.13/3.35 | (19) less(all_41_0, nsup) = 0 % 20.13/3.35 | % 20.13/3.35 | GROUND_INST: instantiating (1) with all_41_0, nsup, simplifying with (8), % 20.13/3.35 | (17), (19) gives: % 20.13/3.35 | (20) leq(all_41_0, nsup) = 0 % 20.13/3.35 | % 20.13/3.35 | GROUND_INST: instantiating (9) with n0, simplifying with (5), (13) gives: % 20.13/3.36 | (21) ? [v0: any] : ? [v1: any] : (completion_compatible(n0, ninf, nsup) = % 20.13/3.36 | v1 & leq(n0, nsup) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 20.13/3.36 | % 20.13/3.36 | GROUND_INST: instantiating (2) with n0, nsup, ninf, nsup, simplifying with % 20.13/3.36 | (5), (6), (7), (8), (13), (14) gives: % 20.13/3.36 | (22) ? [v0: any] : ? [v1: any] : (completion_compatible(n0, ninf, nsup) = % 20.13/3.36 | v1 & leq(nsup, nsup) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 20.13/3.36 | % 20.13/3.36 | GROUND_INST: instantiating (2) with n0, all_41_0, ninf, nsup, simplifying with % 20.13/3.36 | (5), (7), (8), (13), (14), (17), (18) gives: % 20.13/3.36 | (23) ? [v0: any] : ? [v1: any] : (completion_compatible(n0, ninf, nsup) = % 20.13/3.36 | v1 & leq(all_41_0, nsup) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 20.13/3.36 | % 20.13/3.36 | GROUND_INST: instantiating (3) with n0, n0, ninf, nsup, simplifying with (5), % 20.13/3.36 | (7), (8), (13), (14) gives: % 20.13/3.36 | (24) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 20.13/3.36 | (completion_compatible(n0, ninf, nsup) = v2 & leq(n0, nsup) = v0 & % 20.13/3.36 | less(n0, n0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 20.13/3.36 | % 20.13/3.36 | GROUND_INST: instantiating (10) with n0, simplifying with (5), (14) gives: % 20.13/3.36 | (25) ? [v0: any] : ? [v1: any] : (completion_compatible(n0, ninf, nsup) = % 20.13/3.37 | v1 & leq(ninf, n0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 20.13/3.37 | % 20.13/3.37 | DELTA: instantiating (25) with fresh symbols all_61_0, all_61_1 gives: % 20.13/3.37 | (26) completion_compatible(n0, ninf, nsup) = all_61_0 & leq(ninf, n0) = % 20.13/3.37 | all_61_1 & ( ~ (all_61_0 = 0) | ~ (all_61_1 = 0)) % 20.13/3.37 | % 20.13/3.37 | ALPHA: (26) implies: % 20.13/3.37 | (27) leq(ninf, n0) = all_61_1 % 20.13/3.37 | (28) completion_compatible(n0, ninf, nsup) = all_61_0 % 20.13/3.37 | (29) ~ (all_61_0 = 0) | ~ (all_61_1 = 0) % 20.13/3.37 | % 20.13/3.37 | DELTA: instantiating (21) with fresh symbols all_63_0, all_63_1 gives: % 20.13/3.37 | (30) completion_compatible(n0, ninf, nsup) = all_63_0 & leq(n0, nsup) = % 20.13/3.37 | all_63_1 & ( ~ (all_63_0 = 0) | ~ (all_63_1 = 0)) % 20.13/3.37 | % 20.13/3.37 | ALPHA: (30) implies: % 20.13/3.37 | (31) completion_compatible(n0, ninf, nsup) = all_63_0 % 20.13/3.37 | % 20.13/3.37 | DELTA: instantiating (23) with fresh symbols all_65_0, all_65_1 gives: % 20.13/3.37 | (32) completion_compatible(n0, ninf, nsup) = all_65_0 & leq(all_41_0, nsup) % 20.13/3.37 | = all_65_1 & ( ~ (all_65_1 = 0) | all_65_0 = 0) % 20.13/3.37 | % 20.13/3.37 | ALPHA: (32) implies: % 20.13/3.37 | (33) leq(all_41_0, nsup) = all_65_1 % 20.13/3.37 | (34) completion_compatible(n0, ninf, nsup) = all_65_0 % 20.13/3.37 | (35) ~ (all_65_1 = 0) | all_65_0 = 0 % 20.13/3.37 | % 20.13/3.37 | DELTA: instantiating (22) with fresh symbols all_67_0, all_67_1 gives: % 20.13/3.37 | (36) completion_compatible(n0, ninf, nsup) = all_67_0 & leq(nsup, nsup) = % 20.13/3.37 | all_67_1 & ( ~ (all_67_1 = 0) | all_67_0 = 0) % 20.13/3.37 | % 20.13/3.37 | ALPHA: (36) implies: % 20.13/3.37 | (37) completion_compatible(n0, ninf, nsup) = all_67_0 % 20.13/3.37 | % 20.13/3.37 | DELTA: instantiating (24) with fresh symbols all_73_0, all_73_1, all_73_2 % 20.13/3.37 | gives: % 20.13/3.37 | (38) completion_compatible(n0, ninf, nsup) = all_73_0 & leq(n0, nsup) = % 20.13/3.37 | all_73_2 & less(n0, n0) = all_73_1 & ( ~ (all_73_1 = 0) | ~ (all_73_2 % 20.13/3.37 | = 0) | all_73_0 = 0) % 20.13/3.37 | % 20.13/3.37 | ALPHA: (38) implies: % 20.13/3.38 | (39) completion_compatible(n0, ninf, nsup) = all_73_0 % 20.13/3.38 | % 20.13/3.38 | GROUND_INST: instantiating (11) with 0, all_61_1, n0, ninf, simplifying with % 20.13/3.38 | (13), (27) gives: % 20.13/3.38 | (40) all_61_1 = 0 % 20.13/3.38 | % 20.13/3.38 | GROUND_INST: instantiating (11) with 0, all_65_1, nsup, all_41_0, simplifying % 20.13/3.38 | with (20), (33) gives: % 20.13/3.38 | (41) all_65_1 = 0 % 20.13/3.38 | % 20.13/3.38 | GROUND_INST: instantiating (12) with all_63_0, all_65_0, nsup, ninf, n0, % 20.13/3.38 | simplifying with (31), (34) gives: % 20.13/3.38 | (42) all_65_0 = all_63_0 % 20.13/3.38 | % 20.13/3.38 | GROUND_INST: instantiating (12) with all_65_0, all_67_0, nsup, ninf, n0, % 20.13/3.38 | simplifying with (34), (37) gives: % 20.13/3.38 | (43) all_67_0 = all_65_0 % 20.13/3.38 | % 20.13/3.38 | GROUND_INST: instantiating (12) with all_67_0, all_73_0, nsup, ninf, n0, % 20.13/3.38 | simplifying with (37), (39) gives: % 20.13/3.38 | (44) all_73_0 = all_67_0 % 20.13/3.38 | % 20.13/3.38 | GROUND_INST: instantiating (12) with all_61_0, all_73_0, nsup, ninf, n0, % 20.13/3.38 | simplifying with (28), (39) gives: % 20.13/3.38 | (45) all_73_0 = all_61_0 % 20.13/3.38 | % 20.13/3.38 | COMBINE_EQS: (44), (45) imply: % 20.13/3.38 | (46) all_67_0 = all_61_0 % 20.13/3.38 | % 20.13/3.38 | SIMP: (46) implies: % 20.13/3.38 | (47) all_67_0 = all_61_0 % 20.13/3.38 | % 20.13/3.38 | COMBINE_EQS: (43), (47) imply: % 20.13/3.38 | (48) all_65_0 = all_61_0 % 20.13/3.38 | % 20.13/3.38 | SIMP: (48) implies: % 20.13/3.38 | (49) all_65_0 = all_61_0 % 20.13/3.38 | % 20.13/3.38 | COMBINE_EQS: (42), (49) imply: % 20.13/3.38 | (50) all_63_0 = all_61_0 % 20.13/3.38 | % 20.13/3.38 | BETA: splitting (29) gives: % 20.13/3.38 | % 20.13/3.38 | Case 1: % 20.13/3.38 | | % 20.13/3.39 | | (51) ~ (all_61_0 = 0) % 20.13/3.39 | | % 20.13/3.39 | | BETA: splitting (35) gives: % 20.13/3.39 | | % 20.13/3.39 | | Case 1: % 20.13/3.39 | | | % 20.13/3.39 | | | (52) ~ (all_65_1 = 0) % 20.13/3.39 | | | % 20.13/3.39 | | | REDUCE: (41), (52) imply: % 20.13/3.39 | | | (53) $false % 20.13/3.39 | | | % 20.13/3.39 | | | CLOSE: (53) is inconsistent. % 20.13/3.39 | | | % 20.13/3.39 | | Case 2: % 20.13/3.39 | | | % 20.13/3.39 | | | (54) all_65_0 = 0 % 20.13/3.39 | | | % 20.13/3.39 | | | COMBINE_EQS: (49), (54) imply: % 20.13/3.39 | | | (55) all_61_0 = 0 % 20.13/3.39 | | | % 20.13/3.39 | | | SIMP: (55) implies: % 20.13/3.39 | | | (56) all_61_0 = 0 % 20.13/3.39 | | | % 20.13/3.39 | | | REDUCE: (51), (56) imply: % 20.13/3.39 | | | (57) $false % 20.13/3.39 | | | % 20.13/3.39 | | | CLOSE: (57) is inconsistent. % 20.13/3.39 | | | % 20.13/3.39 | | End of split % 20.13/3.39 | | % 20.13/3.39 | Case 2: % 20.13/3.39 | | % 20.13/3.39 | | (58) ~ (all_61_1 = 0) % 20.13/3.39 | | % 20.13/3.39 | | REDUCE: (40), (58) imply: % 20.13/3.39 | | (59) $false % 20.13/3.39 | | % 20.13/3.39 | | CLOSE: (59) is inconsistent. % 20.13/3.39 | | % 20.13/3.39 | End of split % 20.13/3.39 | % 20.13/3.39 End of proof % 20.13/3.39 % SZS output end Proof for theBenchmark % 20.13/3.39 % 20.13/3.39 2828ms %------------------------------------------------------------------------------