%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : DAT034_1 : TPTP v8.1.2. Released v5.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n010.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 22:18:57 EDT 2023 % Result : Theorem 5.88s 1.54s % Output : Proof 7.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : DAT034_1 : TPTP v8.1.2. Released v5.0.0. % 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n010.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Thu Aug 24 14:27:35 EDT 2023 % 0.14/0.35 % CPUTime : % 0.19/0.62 ________ _____ % 0.19/0.62 ___ __ \_________(_)________________________________ % 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.62 % 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.62 (2023-06-19) % 0.19/0.62 % 0.19/0.62 (c) Philipp Rümmer, 2009-2023 % 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.62 Amanda Stjerna. % 0.19/0.62 Free software under BSD-3-Clause. % 0.19/0.62 % 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.62 % 0.19/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.63 Running up to 7 provers in parallel. % 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.58/1.08 Prover 1: Preprocessing ... % 2.58/1.08 Prover 4: Preprocessing ... % 2.58/1.12 Prover 5: Preprocessing ... % 2.58/1.12 Prover 0: Preprocessing ... % 2.58/1.12 Prover 2: Preprocessing ... % 2.58/1.12 Prover 6: Preprocessing ... % 2.58/1.12 Prover 3: Preprocessing ... % 4.12/1.40 Prover 5: Proving ... % 4.12/1.41 Prover 1: Constructing countermodel ... % 4.12/1.41 Prover 6: Constructing countermodel ... % 4.12/1.42 Prover 3: Constructing countermodel ... % 4.12/1.42 Prover 4: Constructing countermodel ... % 4.12/1.43 Prover 0: Proving ... % 5.43/1.47 Prover 2: Proving ... % 5.88/1.54 Prover 6: proved (886ms) % 5.88/1.54 % 5.88/1.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.88/1.54 % 5.88/1.54 Prover 5: stopped % 5.88/1.54 Prover 0: stopped % 5.88/1.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.88/1.54 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.88/1.54 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.88/1.54 Prover 2: stopped % 5.88/1.54 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.88/1.55 Prover 3: stopped % 5.88/1.55 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.18/1.58 Prover 11: Preprocessing ... % 6.18/1.58 Prover 13: Preprocessing ... % 6.18/1.59 Prover 8: Preprocessing ... % 6.18/1.59 Prover 7: Preprocessing ... % 6.18/1.60 Prover 10: Preprocessing ... % 6.70/1.66 Prover 8: Warning: ignoring some quantifiers % 6.90/1.67 Prover 8: Constructing countermodel ... % 6.90/1.67 Prover 10: Constructing countermodel ... % 6.90/1.69 Prover 13: Warning: ignoring some quantifiers % 6.90/1.70 Prover 13: Constructing countermodel ... % 7.30/1.75 Prover 11: Constructing countermodel ... % 7.30/1.75 Prover 4: Found proof (size 62) % 7.30/1.75 Prover 4: proved (1107ms) % 7.30/1.75 Prover 13: stopped % 7.30/1.75 Prover 10: stopped % 7.30/1.75 Prover 8: stopped % 7.52/1.76 Prover 7: Constructing countermodel ... % 7.52/1.76 Prover 1: Found proof (size 67) % 7.52/1.76 Prover 1: proved (1117ms) % 7.52/1.76 Prover 7: stopped % 7.52/1.76 Prover 11: stopped % 7.52/1.76 % 7.52/1.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.52/1.76 % 7.52/1.78 % SZS output start Proof for theBenchmark % 7.52/1.78 Assumptions after simplification: % 7.52/1.78 --------------------------------- % 7.52/1.78 % 7.52/1.78 (ax3) % 7.52/1.81 ! [v0: int] : ! [v1: collection] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = % 7.52/1.81 v2) | ~ collection(v1) | ? [v3: collection] : ? [v4: int] : (add(v0, % 7.52/1.81 v1) = v3 & count(v3) = v4 & count(v1) = $sum(v4, -1) & collection(v3))) % 7.52/1.81 & ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, % 7.52/1.81 v1) = v2) | ~ collection(v1) | ? [v3: int] : ( ~ (v3 = 0) & in(v0, v2) % 7.52/1.81 = v3)) & ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ % 7.52/1.81 (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: any] : ? [v4: int] : ? % 7.52/1.81 [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1) = v3 & % 7.52/1.81 ($difference(v5, v4) = -1 | v3 = 0))) & ! [v0: int] : ! [v1: collection] % 7.52/1.81 : ! [v2: collection] : ( ~ (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: % 7.52/1.81 int] : ? [v4: int] : ? [v5: any] : (count(v2) = v3 & count(v1) = v4 & % 7.52/1.81 in(v0, v1) = v5 & ( ~ (v5 = 0) | ~ ($difference(v4, v3) = -1)))) & ! % 7.52/1.81 [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1) = 0) | ~ collection(v1) | % 7.52/1.81 ? [v2: collection] : ? [v3: int] : ? [v4: int] : ( ~ ($difference(v4, v3) % 7.52/1.81 = -1) & add(v0, v1) = v2 & count(v2) = v3 & count(v1) = v4 & % 7.52/1.81 collection(v2))) % 7.52/1.81 % 7.52/1.81 (ax4) % 7.52/1.82 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : ! % 7.52/1.82 [v4: int] : (v4 = 0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ~ % 7.52/1.82 collection(v1) | ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0: % 7.52/1.82 int] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] : (v3 = 0 | % 7.52/1.82 ~ (add(v0, v1) = v2) | ~ (in(v0, v2) = v3) | ~ collection(v1)) & ! [v0: % 7.52/1.82 int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : (v2 = v0 | % 7.52/1.82 ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ collection(v1) | in(v0, v1) % 7.52/1.82 = 0) & ! [v0: int] : ! [v1: collection] : ! [v2: int] : (v2 = 0 | ~ % 7.52/1.82 (in(v0, v1) = v2) | ~ collection(v1) | ? [v3: collection] : ? [v4: int] : % 7.52/1.82 ? [v5: int] : ( ~ (v5 = v4) & add(v0, v1) = v3 & count(v3) = v4 & count(v1) % 7.52/1.82 = v5 & collection(v3))) & ! [v0: int] : ! [v1: collection] : ! [v2: % 7.52/1.82 collection] : ( ~ (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: any] : ? % 7.52/1.82 [v4: int] : ? [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1) = % 7.52/1.82 v3 & ( ~ (v3 = 0) | v5 = v4))) & ! [v0: int] : ! [v1: collection] : ! % 7.52/1.82 [v2: collection] : ( ~ (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: int] : % 7.52/1.82 ? [v4: int] : ? [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1) % 7.52/1.82 = v5 & ( ~ (v4 = v3) | v5 = 0))) & ! [v0: int] : ! [v1: collection] : ( % 7.52/1.82 ~ (in(v0, v1) = 0) | ~ collection(v1) | ? [v2: collection] : ? [v3: int] % 7.52/1.82 : (add(v0, v1) = v2 & count(v2) = v3 & count(v1) = v3 & collection(v2))) % 7.52/1.82 % 7.52/1.82 (co1) % 7.52/1.82 ? [v0: collection] : ? [v1: int] : ? [v2: int] : ? [v3: collection] : ? % 7.52/1.82 [v4: int] : ($lesseq(2, $difference(v4, v2)) & add(v1, v0) = v3 & count(v3) = % 7.52/1.82 v4 & count(v0) = v2 & collection(v3) & collection(v0)) % 7.52/1.82 % 7.52/1.82 (function-axioms) % 7.52/1.82 ! [v0: collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] % 7.52/1.82 : (v1 = v0 | ~ (remove(v3, v2) = v1) | ~ (remove(v3, v2) = v0)) & ! [v0: % 7.52/1.82 collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] : (v1 % 7.52/1.82 = v0 | ~ (add(v3, v2) = v1) | ~ (add(v3, v2) = v0)) & ! [v0: % 7.52/1.82 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: collection] : ! % 7.52/1.82 [v3: int] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 7.52/1.82 int] : ! [v1: int] : ! [v2: collection] : (v1 = v0 | ~ (count(v2) = v1) | % 7.52/1.82 ~ (count(v2) = v0)) % 7.52/1.82 % 7.52/1.82 Further assumptions not needed in the proof: % 7.52/1.82 -------------------------------------------- % 7.52/1.83 ax1, ax2, ax5, ax6, ax7 % 7.52/1.83 % 7.52/1.83 Those formulas are unsatisfiable: % 7.52/1.83 --------------------------------- % 7.52/1.83 % 7.52/1.83 Begin of proof % 7.52/1.83 | % 7.52/1.83 | ALPHA: (ax3) implies: % 7.87/1.83 | (1) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0, % 7.87/1.83 | v1) = v2) | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ? % 7.87/1.83 | [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~ % 7.87/1.83 | (v5 = 0) | ~ ($difference(v4, v3) = -1)))) % 7.87/1.83 | (2) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0, % 7.87/1.83 | v1) = v2) | ~ collection(v1) | ? [v3: any] : ? [v4: int] : ? % 7.87/1.83 | [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1) = v3 & % 7.87/1.83 | ($difference(v5, v4) = -1 | v3 = 0))) % 7.87/1.83 | % 7.87/1.83 | ALPHA: (ax4) implies: % 7.87/1.83 | (3) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0, % 7.87/1.83 | v1) = v2) | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ? % 7.87/1.83 | [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~ % 7.87/1.83 | (v4 = v3) | v5 = 0))) % 7.87/1.83 | (4) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0, % 7.87/1.83 | v1) = v2) | ~ collection(v1) | ? [v3: any] : ? [v4: int] : ? % 7.87/1.83 | [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1) = v3 & ( ~ % 7.87/1.83 | (v3 = 0) | v5 = v4))) % 7.87/1.83 | % 7.87/1.83 | ALPHA: (function-axioms) implies: % 7.87/1.84 | (5) ! [v0: int] : ! [v1: int] : ! [v2: collection] : (v1 = v0 | ~ % 7.87/1.84 | (count(v2) = v1) | ~ (count(v2) = v0)) % 7.87/1.84 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 7.87/1.84 | collection] : ! [v3: int] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ % 7.87/1.84 | (in(v3, v2) = v0)) % 7.87/1.84 | % 7.87/1.84 | DELTA: instantiating (co1) with fresh symbols all_13_0, all_13_1, all_13_2, % 7.87/1.84 | all_13_3, all_13_4 gives: % 7.87/1.84 | (7) $lesseq(2, $difference(all_13_0, all_13_2)) & add(all_13_3, all_13_4) = % 7.87/1.84 | all_13_1 & count(all_13_1) = all_13_0 & count(all_13_4) = all_13_2 & % 7.87/1.84 | collection(all_13_1) & collection(all_13_4) % 7.87/1.84 | % 7.87/1.84 | ALPHA: (7) implies: % 7.87/1.84 | (8) $lesseq(2, $difference(all_13_0, all_13_2)) % 7.87/1.84 | (9) collection(all_13_4) % 7.87/1.84 | (10) count(all_13_4) = all_13_2 % 7.87/1.84 | (11) count(all_13_1) = all_13_0 % 7.87/1.84 | (12) add(all_13_3, all_13_4) = all_13_1 % 7.87/1.84 | % 7.87/1.84 | GROUND_INST: instantiating (4) with all_13_3, all_13_4, all_13_1, simplifying % 7.87/1.84 | with (9), (12) gives: % 7.87/1.84 | (13) ? [v0: any] : ? [v1: int] : ? [v2: int] : (count(all_13_1) = v1 & % 7.87/1.84 | count(all_13_4) = v2 & in(all_13_3, all_13_4) = v0 & ( ~ (v0 = 0) | % 7.87/1.84 | v2 = v1)) % 7.87/1.84 | % 7.87/1.84 | GROUND_INST: instantiating (2) with all_13_3, all_13_4, all_13_1, simplifying % 7.87/1.84 | with (9), (12) gives: % 7.87/1.84 | (14) ? [v0: any] : ? [v1: int] : ? [v2: int] : (count(all_13_1) = v1 & % 7.87/1.84 | count(all_13_4) = v2 & in(all_13_3, all_13_4) = v0 & % 7.87/1.84 | ($difference(v2, v1) = -1 | v0 = 0)) % 7.87/1.84 | % 7.87/1.84 | GROUND_INST: instantiating (1) with all_13_3, all_13_4, all_13_1, simplifying % 7.87/1.84 | with (9), (12) gives: % 7.87/1.84 | (15) ? [v0: int] : ? [v1: int] : ? [v2: any] : (count(all_13_1) = v0 & % 7.87/1.84 | count(all_13_4) = v1 & in(all_13_3, all_13_4) = v2 & ( ~ (v2 = 0) | % 7.87/1.84 | ~ ($difference(v1, v0) = -1))) % 7.87/1.84 | % 7.87/1.84 | GROUND_INST: instantiating (3) with all_13_3, all_13_4, all_13_1, simplifying % 7.87/1.84 | with (9), (12) gives: % 7.87/1.84 | (16) ? [v0: int] : ? [v1: int] : ? [v2: any] : (count(all_13_1) = v0 & % 7.87/1.84 | count(all_13_4) = v1 & in(all_13_3, all_13_4) = v2 & ( ~ (v1 = v0) | % 7.87/1.84 | v2 = 0)) % 7.87/1.84 | % 7.87/1.84 | DELTA: instantiating (13) with fresh symbols all_25_0, all_25_1, all_25_2 % 7.87/1.84 | gives: % 7.87/1.85 | (17) count(all_13_1) = all_25_1 & count(all_13_4) = all_25_0 & in(all_13_3, % 7.87/1.85 | all_13_4) = all_25_2 & ( ~ (all_25_2 = 0) | all_25_0 = all_25_1) % 7.87/1.85 | % 7.87/1.85 | ALPHA: (17) implies: % 7.87/1.85 | (18) in(all_13_3, all_13_4) = all_25_2 % 7.87/1.85 | (19) count(all_13_4) = all_25_0 % 7.87/1.85 | (20) count(all_13_1) = all_25_1 % 7.87/1.85 | (21) ~ (all_25_2 = 0) | all_25_0 = all_25_1 % 7.87/1.85 | % 7.87/1.85 | DELTA: instantiating (16) with fresh symbols all_27_0, all_27_1, all_27_2 % 7.87/1.85 | gives: % 7.87/1.85 | (22) count(all_13_1) = all_27_2 & count(all_13_4) = all_27_1 & in(all_13_3, % 7.87/1.85 | all_13_4) = all_27_0 & ( ~ (all_27_1 = all_27_2) | all_27_0 = 0) % 7.87/1.85 | % 7.87/1.85 | ALPHA: (22) implies: % 7.87/1.85 | (23) in(all_13_3, all_13_4) = all_27_0 % 7.87/1.85 | (24) count(all_13_4) = all_27_1 % 7.87/1.85 | (25) count(all_13_1) = all_27_2 % 7.87/1.85 | % 7.87/1.85 | DELTA: instantiating (15) with fresh symbols all_29_0, all_29_1, all_29_2 % 7.87/1.85 | gives: % 7.87/1.85 | (26) count(all_13_1) = all_29_2 & count(all_13_4) = all_29_1 & in(all_13_3, % 7.87/1.85 | all_13_4) = all_29_0 & ( ~ (all_29_0 = 0) | ~ % 7.87/1.85 | ($difference(all_29_1, all_29_2) = -1)) % 7.87/1.85 | % 7.87/1.85 | ALPHA: (26) implies: % 7.87/1.85 | (27) in(all_13_3, all_13_4) = all_29_0 % 7.87/1.85 | (28) count(all_13_4) = all_29_1 % 7.87/1.85 | (29) count(all_13_1) = all_29_2 % 7.87/1.85 | % 7.87/1.85 | DELTA: instantiating (14) with fresh symbols all_31_0, all_31_1, all_31_2 % 7.87/1.85 | gives: % 7.87/1.85 | (30) count(all_13_1) = all_31_1 & count(all_13_4) = all_31_0 & in(all_13_3, % 7.87/1.85 | all_13_4) = all_31_2 & ($difference(all_31_0, all_31_1) = -1 | % 7.87/1.85 | all_31_2 = 0) % 7.87/1.85 | % 7.87/1.85 | ALPHA: (30) implies: % 7.87/1.85 | (31) in(all_13_3, all_13_4) = all_31_2 % 7.87/1.85 | (32) count(all_13_4) = all_31_0 % 7.87/1.85 | (33) count(all_13_1) = all_31_1 % 7.87/1.85 | (34) $difference(all_31_0, all_31_1) = -1 | all_31_2 = 0 % 7.87/1.85 | % 7.87/1.85 | GROUND_INST: instantiating (6) with all_25_2, all_29_0, all_13_4, all_13_3, % 7.87/1.85 | simplifying with (18), (27) gives: % 7.87/1.85 | (35) all_29_0 = all_25_2 % 7.87/1.85 | % 7.87/1.85 | GROUND_INST: instantiating (6) with all_29_0, all_31_2, all_13_4, all_13_3, % 7.87/1.85 | simplifying with (27), (31) gives: % 7.87/1.85 | (36) all_31_2 = all_29_0 % 7.87/1.85 | % 7.87/1.85 | GROUND_INST: instantiating (6) with all_27_0, all_31_2, all_13_4, all_13_3, % 7.87/1.85 | simplifying with (23), (31) gives: % 7.87/1.85 | (37) all_31_2 = all_27_0 % 7.87/1.85 | % 7.87/1.85 | GROUND_INST: instantiating (5) with all_13_2, all_29_1, all_13_4, simplifying % 7.87/1.85 | with (10), (28) gives: % 7.87/1.85 | (38) all_29_1 = all_13_2 % 7.87/1.85 | % 7.87/1.85 | GROUND_INST: instantiating (5) with all_27_1, all_29_1, all_13_4, simplifying % 7.87/1.85 | with (24), (28) gives: % 7.87/1.85 | (39) all_29_1 = all_27_1 % 7.87/1.85 | % 7.87/1.85 | GROUND_INST: instantiating (5) with all_29_1, all_31_0, all_13_4, simplifying % 7.87/1.85 | with (28), (32) gives: % 7.87/1.85 | (40) all_31_0 = all_29_1 % 7.87/1.85 | % 7.87/1.85 | GROUND_INST: instantiating (5) with all_25_0, all_31_0, all_13_4, simplifying % 7.87/1.85 | with (19), (32) gives: % 7.87/1.85 | (41) all_31_0 = all_25_0 % 7.87/1.85 | % 7.87/1.85 | GROUND_INST: instantiating (5) with all_25_1, all_29_2, all_13_1, simplifying % 7.87/1.85 | with (20), (29) gives: % 7.87/1.85 | (42) all_29_2 = all_25_1 % 7.87/1.85 | % 7.87/1.86 | GROUND_INST: instantiating (5) with all_13_0, all_31_1, all_13_1, simplifying % 7.87/1.86 | with (11), (33) gives: % 7.87/1.86 | (43) all_31_1 = all_13_0 % 7.87/1.86 | % 7.87/1.86 | GROUND_INST: instantiating (5) with all_29_2, all_31_1, all_13_1, simplifying % 7.87/1.86 | with (29), (33) gives: % 7.87/1.86 | (44) all_31_1 = all_29_2 % 7.87/1.86 | % 7.87/1.86 | GROUND_INST: instantiating (5) with all_27_2, all_31_1, all_13_1, simplifying % 7.87/1.86 | with (25), (33) gives: % 7.87/1.86 | (45) all_31_1 = all_27_2 % 7.87/1.86 | % 7.87/1.86 | COMBINE_EQS: (40), (41) imply: % 7.87/1.86 | (46) all_29_1 = all_25_0 % 7.87/1.86 | % 7.87/1.86 | SIMP: (46) implies: % 7.87/1.86 | (47) all_29_1 = all_25_0 % 7.87/1.86 | % 7.87/1.86 | COMBINE_EQS: (44), (45) imply: % 7.87/1.86 | (48) all_29_2 = all_27_2 % 7.87/1.86 | % 7.87/1.86 | SIMP: (48) implies: % 7.87/1.86 | (49) all_29_2 = all_27_2 % 7.87/1.86 | % 7.87/1.86 | COMBINE_EQS: (43), (45) imply: % 7.87/1.86 | (50) all_27_2 = all_13_0 % 7.87/1.86 | % 7.87/1.86 | COMBINE_EQS: (36), (37) imply: % 7.87/1.86 | (51) all_29_0 = all_27_0 % 7.87/1.86 | % 7.87/1.86 | SIMP: (51) implies: % 7.87/1.86 | (52) all_29_0 = all_27_0 % 7.87/1.86 | % 7.87/1.86 | COMBINE_EQS: (35), (52) imply: % 7.87/1.86 | (53) all_27_0 = all_25_2 % 7.87/1.86 | % 7.87/1.86 | SIMP: (53) implies: % 7.87/1.86 | (54) all_27_0 = all_25_2 % 7.87/1.86 | % 7.87/1.86 | COMBINE_EQS: (39), (47) imply: % 7.87/1.86 | (55) all_27_1 = all_25_0 % 7.87/1.86 | % 7.87/1.86 | COMBINE_EQS: (38), (39) imply: % 7.87/1.86 | (56) all_27_1 = all_13_2 % 7.87/1.86 | % 7.87/1.86 | COMBINE_EQS: (42), (49) imply: % 7.87/1.86 | (57) all_27_2 = all_25_1 % 7.87/1.86 | % 7.87/1.86 | SIMP: (57) implies: % 7.87/1.86 | (58) all_27_2 = all_25_1 % 7.87/1.86 | % 7.87/1.86 | COMBINE_EQS: (55), (56) imply: % 7.87/1.86 | (59) all_25_0 = all_13_2 % 7.87/1.86 | % 7.87/1.86 | COMBINE_EQS: (50), (58) imply: % 7.87/1.86 | (60) all_25_1 = all_13_0 % 7.87/1.86 | % 7.87/1.86 | COMBINE_EQS: (37), (54) imply: % 7.87/1.86 | (61) all_31_2 = all_25_2 % 7.87/1.86 | % 7.87/1.86 | COMBINE_EQS: (41), (59) imply: % 7.87/1.86 | (62) all_31_0 = all_13_2 % 7.87/1.86 | % 7.87/1.86 | BETA: splitting (21) gives: % 7.87/1.86 | % 7.87/1.86 | Case 1: % 7.87/1.86 | | % 7.87/1.86 | | (63) ~ (all_25_2 = 0) % 7.87/1.86 | | % 7.87/1.86 | | BETA: splitting (34) gives: % 7.87/1.86 | | % 7.87/1.86 | | Case 1: % 7.87/1.86 | | | % 7.87/1.86 | | | (64) all_31_2 = 0 % 7.87/1.86 | | | % 7.87/1.86 | | | COMBINE_EQS: (61), (64) imply: % 7.87/1.86 | | | (65) all_25_2 = 0 % 7.87/1.86 | | | % 7.87/1.86 | | | REDUCE: (63), (65) imply: % 7.87/1.86 | | | (66) $false % 7.87/1.86 | | | % 7.87/1.86 | | | CLOSE: (66) is inconsistent. % 7.87/1.86 | | | % 7.87/1.86 | | Case 2: % 7.87/1.86 | | | % 7.87/1.86 | | | (67) $difference(all_31_0, all_31_1) = -1 % 7.87/1.86 | | | % 7.87/1.86 | | | COMBINE_EQS: (62), (67) imply: % 7.87/1.86 | | | (68) $difference(all_31_1, all_13_2) = 1 % 7.87/1.86 | | | % 7.87/1.86 | | | SIMP: (68) implies: % 7.87/1.86 | | | (69) $difference(all_31_1, all_13_2) = 1 % 7.87/1.86 | | | % 7.87/1.86 | | | COMBINE_EQS: (43), (69) imply: % 7.87/1.86 | | | (70) $difference(all_13_0, all_13_2) = 1 % 7.87/1.86 | | | % 7.87/1.86 | | | REDUCE: (8), (70) imply: % 7.87/1.86 | | | (71) $false % 7.87/1.86 | | | % 7.87/1.86 | | | CLOSE: (71) is inconsistent. % 7.87/1.86 | | | % 7.87/1.86 | | End of split % 7.87/1.86 | | % 7.87/1.86 | Case 2: % 7.87/1.86 | | % 7.87/1.86 | | (72) all_25_0 = all_25_1 % 7.87/1.86 | | % 7.87/1.86 | | COMBINE_EQS: (59), (72) imply: % 7.87/1.86 | | (73) all_25_1 = all_13_2 % 7.87/1.86 | | % 7.87/1.86 | | SIMP: (73) implies: % 7.87/1.86 | | (74) all_25_1 = all_13_2 % 7.87/1.86 | | % 7.87/1.86 | | COMBINE_EQS: (60), (74) imply: % 7.87/1.86 | | (75) all_13_0 = all_13_2 % 7.87/1.86 | | % 7.87/1.86 | | REDUCE: (8), (75) imply: % 7.87/1.87 | | (76) $false % 7.87/1.87 | | % 7.87/1.87 | | CLOSE: (76) is inconsistent. % 7.87/1.87 | | % 7.87/1.87 | End of split % 7.87/1.87 | % 7.87/1.87 End of proof % 7.87/1.87 % SZS output end Proof for theBenchmark % 7.87/1.87 % 7.87/1.87 1243ms %------------------------------------------------------------------------------