%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SYN374+1 : TPTP v8.1.2. Released v2.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n003.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 : Fri Sep 1 03:27:25 EDT 2023 % Result : Theorem 3.77s 1.30s % Output : Proof 4.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SYN374+1 : TPTP v8.1.2. Released v2.0.0. % 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n003.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sat Aug 26 18:02:54 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.98/0.98 Prover 4: Preprocessing ... % 1.98/0.98 Prover 1: Preprocessing ... % 2.20/1.02 Prover 6: Preprocessing ... % 2.20/1.02 Prover 2: Preprocessing ... % 2.20/1.02 Prover 5: Preprocessing ... % 2.20/1.02 Prover 0: Preprocessing ... % 2.20/1.02 Prover 3: Preprocessing ... % 2.37/1.12 Prover 2: Proving ... % 2.89/1.13 Prover 4: Constructing countermodel ... % 2.89/1.13 Prover 5: Proving ... % 2.89/1.13 Prover 6: Proving ... % 2.89/1.13 Prover 3: Constructing countermodel ... % 2.89/1.13 Prover 1: Constructing countermodel ... % 2.89/1.13 Prover 0: Proving ... % 3.77/1.30 Prover 3: proved (664ms) % 3.77/1.30 % 3.77/1.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.77/1.30 % 3.77/1.30 Prover 2: stopped % 3.77/1.31 Prover 5: stopped % 3.77/1.31 Prover 6: stopped % 3.77/1.31 Prover 0: stopped % 3.77/1.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.77/1.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.77/1.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.77/1.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.77/1.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.77/1.32 Prover 7: Preprocessing ... % 3.77/1.32 Prover 8: Preprocessing ... % 3.77/1.32 Prover 11: Preprocessing ... % 3.77/1.33 Prover 10: Preprocessing ... % 3.77/1.34 Prover 13: Preprocessing ... % 3.77/1.35 Prover 4: Found proof (size 37) % 3.77/1.35 Prover 4: proved (709ms) % 3.77/1.35 Prover 1: stopped % 3.77/1.35 Prover 7: Warning: ignoring some quantifiers % 3.77/1.35 Prover 7: Constructing countermodel ... % 3.77/1.35 Prover 7: stopped % 3.77/1.36 Prover 8: Warning: ignoring some quantifiers % 4.06/1.36 Prover 8: Constructing countermodel ... % 4.06/1.36 Prover 10: Warning: ignoring some quantifiers % 4.06/1.36 Prover 13: Warning: ignoring some quantifiers % 4.06/1.36 Prover 8: stopped % 4.06/1.36 Prover 10: Constructing countermodel ... % 4.06/1.36 Prover 13: Constructing countermodel ... % 4.06/1.36 Prover 10: stopped % 4.06/1.36 Prover 13: stopped % 4.06/1.37 Prover 11: Constructing countermodel ... % 4.06/1.37 Prover 11: stopped % 4.06/1.37 % 4.06/1.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.06/1.37 % 4.06/1.38 % SZS output start Proof for theBenchmark % 4.06/1.38 Assumptions after simplification: % 4.06/1.38 --------------------------------- % 4.06/1.38 % 4.06/1.38 (x2125) % 4.71/1.41 ? [v0: $i] : ? [v1: int] : ? [v2: $i] : ? [v3: int] : ? [v4: $i] : ? % 4.71/1.42 [v5: int] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: any] : ($i(v8) % 4.71/1.42 & $i(v6) & $i(v4) & $i(v2) & $i(v0) & ((big_p(v8) = v9 & ! [v10: $i] : ! % 4.71/1.42 [v11: int] : ( ~ (v9 = 0) | v11 = 0 | ~ (big_p(v10) = v11) | ~ % 4.71/1.42 $i(v10)) & ! [v10: $i] : (v9 = 0 | ~ (big_p(v10) = 0) | ~ $i(v10)) % 4.71/1.42 & ((v7 = 0 & ~ (v5 = 0) & big_p(v6) = 0 & big_p(v4) = v5) | ( ! [v10: % 4.71/1.42 $i] : ! [v11: int] : (v11 = 0 | ~ (big_p(v10) = v11) | ~ % 4.71/1.42 $i(v10)) & ! [v10: $i] : ( ~ (big_p(v10) = 0) | ~ $i(v10))))) | % 4.71/1.42 ( ! [v10: $i] : ! [v11: any] : ( ~ (big_p(v10) = v11) | ~ $i(v10) | ? % 4.71/1.42 [v12: $i] : ? [v13: any] : (big_p(v12) = v13 & $i(v12) & ( ~ (v13 = % 4.71/1.42 0) | ~ (v11 = 0)) & (v13 = 0 | v11 = 0))) & ((v3 = 0 & % 4.71/1.42 big_p(v2) = 0 & ! [v10: $i] : ! [v11: int] : (v11 = 0 | ~ % 4.71/1.42 (big_p(v10) = v11) | ~ $i(v10))) | ( ~ (v1 = 0) & big_p(v0) = v1 % 4.71/1.42 & ! [v10: $i] : ( ~ (big_p(v10) = 0) | ~ $i(v10))))))) % 4.71/1.42 % 4.71/1.42 Those formulas are unsatisfiable: % 4.71/1.42 --------------------------------- % 4.71/1.42 % 4.71/1.42 Begin of proof % 4.71/1.42 | % 4.71/1.42 | DELTA: instantiating (x2125) with fresh symbols all_3_0, all_3_1, all_3_2, % 4.71/1.42 | all_3_3, all_3_4, all_3_5, all_3_6, all_3_7, all_3_8, all_3_9 gives: % 4.71/1.42 | (1) $i(all_3_1) & $i(all_3_3) & $i(all_3_5) & $i(all_3_7) & $i(all_3_9) & % 4.71/1.42 | ((big_p(all_3_1) = all_3_0 & ! [v0: $i] : ! [v1: int] : ( ~ (all_3_0 % 4.71/1.42 | = 0) | v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] % 4.71/1.42 | : (all_3_0 = 0 | ~ (big_p(v0) = 0) | ~ $i(v0)) & ((all_3_2 = 0 & % 4.71/1.42 | ~ (all_3_4 = 0) & big_p(all_3_3) = 0 & big_p(all_3_5) = % 4.71/1.42 | all_3_4) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 4.71/1.42 | (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( ~ (big_p(v0) % 4.71/1.42 | = 0) | ~ $i(v0))))) | ( ! [v0: $i] : ! [v1: any] : ( ~ % 4.71/1.42 | (big_p(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: any] : % 4.71/1.43 | (big_p(v2) = v3 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 % 4.71/1.43 | | v1 = 0))) & ((all_3_6 = 0 & big_p(all_3_7) = 0 & ! [v0: % 4.71/1.43 | $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ % 4.71/1.43 | $i(v0))) | ( ~ (all_3_8 = 0) & big_p(all_3_9) = all_3_8 & ! % 4.71/1.43 | [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)))))) % 4.71/1.43 | % 4.71/1.43 | ALPHA: (1) implies: % 4.71/1.43 | (2) $i(all_3_9) % 4.71/1.43 | (3) $i(all_3_7) % 4.71/1.43 | (4) $i(all_3_5) % 4.71/1.43 | (5) $i(all_3_3) % 4.71/1.43 | (6) $i(all_3_1) % 4.82/1.43 | (7) (big_p(all_3_1) = all_3_0 & ! [v0: $i] : ! [v1: int] : ( ~ (all_3_0 = % 4.82/1.43 | 0) | v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : % 4.82/1.43 | (all_3_0 = 0 | ~ (big_p(v0) = 0) | ~ $i(v0)) & ((all_3_2 = 0 & ~ % 4.82/1.43 | (all_3_4 = 0) & big_p(all_3_3) = 0 & big_p(all_3_5) = all_3_4) | % 4.82/1.43 | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ % 4.82/1.43 | $i(v0)) & ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0))))) | ( % 4.82/1.43 | ! [v0: $i] : ! [v1: any] : ( ~ (big_p(v0) = v1) | ~ $i(v0) | ? % 4.82/1.43 | [v2: $i] : ? [v3: any] : (big_p(v2) = v3 & $i(v2) & ( ~ (v3 = 0) | % 4.82/1.43 | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & ((all_3_6 = 0 & % 4.82/1.43 | big_p(all_3_7) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 4.82/1.43 | (big_p(v0) = v1) | ~ $i(v0))) | ( ~ (all_3_8 = 0) & % 4.82/1.43 | big_p(all_3_9) = all_3_8 & ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ % 4.82/1.43 | $i(v0))))) % 4.82/1.43 | % 4.82/1.43 | BETA: splitting (7) gives: % 4.82/1.43 | % 4.82/1.43 | Case 1: % 4.82/1.43 | | % 4.82/1.44 | | (8) big_p(all_3_1) = all_3_0 & ! [v0: $i] : ! [v1: int] : ( ~ (all_3_0 % 4.82/1.44 | | = 0) | v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : % 4.82/1.44 | | (all_3_0 = 0 | ~ (big_p(v0) = 0) | ~ $i(v0)) & ((all_3_2 = 0 & ~ % 4.82/1.44 | | (all_3_4 = 0) & big_p(all_3_3) = 0 & big_p(all_3_5) = all_3_4) | % 4.82/1.44 | | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ % 4.82/1.44 | | $i(v0)) & ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)))) % 4.82/1.44 | | % 4.82/1.44 | | ALPHA: (8) implies: % 4.82/1.44 | | (9) big_p(all_3_1) = all_3_0 % 4.82/1.44 | | (10) (all_3_2 = 0 & ~ (all_3_4 = 0) & big_p(all_3_3) = 0 & % 4.82/1.44 | | big_p(all_3_5) = all_3_4) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 % 4.82/1.44 | | | ~ (big_p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ( ~ % 4.82/1.44 | | (big_p(v0) = 0) | ~ $i(v0))) % 4.82/1.44 | | (11) ! [v0: $i] : (all_3_0 = 0 | ~ (big_p(v0) = 0) | ~ $i(v0)) % 4.82/1.44 | | (12) ! [v0: $i] : ! [v1: int] : ( ~ (all_3_0 = 0) | v1 = 0 | ~ % 4.82/1.44 | | (big_p(v0) = v1) | ~ $i(v0)) % 4.82/1.44 | | % 4.82/1.44 | | BETA: splitting (10) gives: % 4.82/1.44 | | % 4.82/1.44 | | Case 1: % 4.82/1.44 | | | % 4.82/1.44 | | | (13) all_3_2 = 0 & ~ (all_3_4 = 0) & big_p(all_3_3) = 0 & % 4.82/1.44 | | | big_p(all_3_5) = all_3_4 % 4.82/1.44 | | | % 4.82/1.44 | | | ALPHA: (13) implies: % 4.82/1.44 | | | (14) ~ (all_3_4 = 0) % 4.82/1.44 | | | (15) big_p(all_3_5) = all_3_4 % 4.82/1.44 | | | (16) big_p(all_3_3) = 0 % 4.82/1.44 | | | % 4.82/1.44 | | | GROUND_INST: instantiating (12) with all_3_5, all_3_4, simplifying with % 4.82/1.44 | | | (4), (15) gives: % 4.82/1.44 | | | (17) ~ (all_3_0 = 0) | all_3_4 = 0 % 4.82/1.44 | | | % 4.82/1.44 | | | GROUND_INST: instantiating (11) with all_3_3, simplifying with (5), (16) % 4.82/1.44 | | | gives: % 4.82/1.44 | | | (18) all_3_0 = 0 % 4.82/1.44 | | | % 4.82/1.44 | | | BETA: splitting (17) gives: % 4.82/1.44 | | | % 4.82/1.44 | | | Case 1: % 4.82/1.44 | | | | % 4.82/1.44 | | | | (19) ~ (all_3_0 = 0) % 4.82/1.44 | | | | % 4.82/1.44 | | | | REDUCE: (18), (19) imply: % 4.82/1.44 | | | | (20) $false % 4.82/1.44 | | | | % 4.82/1.44 | | | | CLOSE: (20) is inconsistent. % 4.82/1.44 | | | | % 4.82/1.44 | | | Case 2: % 4.82/1.44 | | | | % 4.82/1.44 | | | | (21) all_3_4 = 0 % 4.82/1.44 | | | | % 4.82/1.44 | | | | REDUCE: (14), (21) imply: % 4.82/1.44 | | | | (22) $false % 4.82/1.44 | | | | % 4.82/1.44 | | | | CLOSE: (22) is inconsistent. % 4.82/1.44 | | | | % 4.82/1.44 | | | End of split % 4.82/1.44 | | | % 4.82/1.44 | | Case 2: % 4.82/1.44 | | | % 4.82/1.44 | | | (23) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ % 4.82/1.44 | | | $i(v0)) & ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) % 4.82/1.44 | | | % 4.82/1.44 | | | ALPHA: (23) implies: % 4.82/1.44 | | | (24) ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) % 4.82/1.45 | | | (25) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ % 4.82/1.45 | | | $i(v0)) % 4.82/1.45 | | | % 4.82/1.45 | | | GROUND_INST: instantiating (25) with all_3_1, all_3_0, simplifying with % 4.82/1.45 | | | (6), (9) gives: % 4.82/1.45 | | | (26) all_3_0 = 0 % 4.82/1.45 | | | % 4.82/1.45 | | | REDUCE: (9), (26) imply: % 4.82/1.45 | | | (27) big_p(all_3_1) = 0 % 4.82/1.45 | | | % 4.82/1.45 | | | GROUND_INST: instantiating (24) with all_3_1, simplifying with (6), (27) % 4.82/1.45 | | | gives: % 4.82/1.45 | | | (28) $false % 4.82/1.45 | | | % 4.82/1.45 | | | CLOSE: (28) is inconsistent. % 4.82/1.45 | | | % 4.82/1.45 | | End of split % 4.82/1.45 | | % 4.82/1.45 | Case 2: % 4.82/1.45 | | % 4.82/1.45 | | (29) ! [v0: $i] : ! [v1: any] : ( ~ (big_p(v0) = v1) | ~ $i(v0) | ? % 4.82/1.45 | | [v2: $i] : ? [v3: any] : (big_p(v2) = v3 & $i(v2) & ( ~ (v3 = 0) % 4.82/1.45 | | | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) & ((all_3_6 = 0 & % 4.82/1.45 | | big_p(all_3_7) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 4.82/1.45 | | (big_p(v0) = v1) | ~ $i(v0))) | ( ~ (all_3_8 = 0) & % 4.82/1.45 | | big_p(all_3_9) = all_3_8 & ! [v0: $i] : ( ~ (big_p(v0) = 0) | % 4.82/1.45 | | ~ $i(v0)))) % 4.82/1.45 | | % 4.82/1.45 | | ALPHA: (29) implies: % 4.82/1.45 | | (30) (all_3_6 = 0 & big_p(all_3_7) = 0 & ! [v0: $i] : ! [v1: int] : (v1 % 4.82/1.45 | | = 0 | ~ (big_p(v0) = v1) | ~ $i(v0))) | ( ~ (all_3_8 = 0) & % 4.82/1.45 | | big_p(all_3_9) = all_3_8 & ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ % 4.82/1.45 | | $i(v0))) % 4.82/1.45 | | (31) ! [v0: $i] : ! [v1: any] : ( ~ (big_p(v0) = v1) | ~ $i(v0) | ? % 4.82/1.45 | | [v2: $i] : ? [v3: any] : (big_p(v2) = v3 & $i(v2) & ( ~ (v3 = 0) % 4.82/1.45 | | | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))) % 4.82/1.45 | | % 4.82/1.45 | | BETA: splitting (30) gives: % 4.82/1.45 | | % 4.82/1.45 | | Case 1: % 4.82/1.45 | | | % 4.82/1.45 | | | (32) all_3_6 = 0 & big_p(all_3_7) = 0 & ! [v0: $i] : ! [v1: int] : % 4.82/1.45 | | | (v1 = 0 | ~ (big_p(v0) = v1) | ~ $i(v0)) % 4.82/1.45 | | | % 4.82/1.45 | | | ALPHA: (32) implies: % 4.82/1.45 | | | (33) big_p(all_3_7) = 0 % 4.82/1.45 | | | (34) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (big_p(v0) = v1) | ~ % 4.82/1.45 | | | $i(v0)) % 4.82/1.45 | | | % 4.82/1.45 | | | GROUND_INST: instantiating (31) with all_3_7, 0, simplifying with (3), % 4.82/1.45 | | | (33) gives: % 4.82/1.45 | | | (35) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & big_p(v0) = v1 & % 4.82/1.45 | | | $i(v0)) % 4.82/1.45 | | | % 4.82/1.45 | | | DELTA: instantiating (35) with fresh symbols all_22_0, all_22_1 gives: % 4.82/1.45 | | | (36) ~ (all_22_0 = 0) & big_p(all_22_1) = all_22_0 & $i(all_22_1) % 4.82/1.45 | | | % 4.82/1.45 | | | ALPHA: (36) implies: % 4.82/1.45 | | | (37) ~ (all_22_0 = 0) % 4.82/1.45 | | | (38) $i(all_22_1) % 4.82/1.45 | | | (39) big_p(all_22_1) = all_22_0 % 4.82/1.45 | | | % 4.82/1.45 | | | GROUND_INST: instantiating (34) with all_22_1, all_22_0, simplifying with % 4.82/1.45 | | | (38), (39) gives: % 4.82/1.45 | | | (40) all_22_0 = 0 % 4.82/1.45 | | | % 4.82/1.46 | | | REDUCE: (37), (40) imply: % 4.82/1.46 | | | (41) $false % 4.82/1.46 | | | % 4.82/1.46 | | | CLOSE: (41) is inconsistent. % 4.82/1.46 | | | % 4.82/1.46 | | Case 2: % 4.82/1.46 | | | % 4.82/1.46 | | | (42) ~ (all_3_8 = 0) & big_p(all_3_9) = all_3_8 & ! [v0: $i] : ( ~ % 4.82/1.46 | | | (big_p(v0) = 0) | ~ $i(v0)) % 4.82/1.46 | | | % 4.82/1.46 | | | ALPHA: (42) implies: % 4.82/1.46 | | | (43) ~ (all_3_8 = 0) % 4.82/1.46 | | | (44) big_p(all_3_9) = all_3_8 % 4.82/1.46 | | | (45) ! [v0: $i] : ( ~ (big_p(v0) = 0) | ~ $i(v0)) % 4.82/1.46 | | | % 4.82/1.46 | | | GROUND_INST: instantiating (31) with all_3_9, all_3_8, simplifying with % 4.82/1.46 | | | (2), (44) gives: % 4.82/1.46 | | | (46) ? [v0: $i] : ? [v1: any] : (big_p(v0) = v1 & $i(v0) & ( ~ (v1 = % 4.82/1.46 | | | 0) | ~ (all_3_8 = 0)) & (v1 = 0 | all_3_8 = 0)) % 4.82/1.46 | | | % 4.82/1.46 | | | DELTA: instantiating (46) with fresh symbols all_22_0, all_22_1 gives: % 4.82/1.46 | | | (47) big_p(all_22_1) = all_22_0 & $i(all_22_1) & ( ~ (all_22_0 = 0) | % 4.82/1.46 | | | ~ (all_3_8 = 0)) & (all_22_0 = 0 | all_3_8 = 0) % 4.82/1.46 | | | % 4.82/1.46 | | | ALPHA: (47) implies: % 4.82/1.46 | | | (48) $i(all_22_1) % 4.82/1.46 | | | (49) big_p(all_22_1) = all_22_0 % 4.82/1.46 | | | (50) all_22_0 = 0 | all_3_8 = 0 % 4.82/1.46 | | | % 4.82/1.46 | | | BETA: splitting (50) gives: % 4.82/1.46 | | | % 4.82/1.46 | | | Case 1: % 4.82/1.46 | | | | % 4.82/1.46 | | | | (51) all_22_0 = 0 % 4.82/1.46 | | | | % 4.82/1.46 | | | | REDUCE: (49), (51) imply: % 4.82/1.46 | | | | (52) big_p(all_22_1) = 0 % 4.82/1.46 | | | | % 4.82/1.46 | | | | GROUND_INST: instantiating (45) with all_22_1, simplifying with (48), % 4.82/1.46 | | | | (52) gives: % 4.82/1.46 | | | | (53) $false % 4.82/1.46 | | | | % 4.82/1.46 | | | | CLOSE: (53) is inconsistent. % 4.82/1.46 | | | | % 4.82/1.46 | | | Case 2: % 4.82/1.46 | | | | % 4.82/1.46 | | | | (54) all_3_8 = 0 % 4.82/1.46 | | | | % 4.82/1.46 | | | | REDUCE: (43), (54) imply: % 4.82/1.46 | | | | (55) $false % 4.82/1.46 | | | | % 4.82/1.46 | | | | CLOSE: (55) is inconsistent. % 4.82/1.46 | | | | % 4.82/1.46 | | | End of split % 4.82/1.46 | | | % 4.82/1.46 | | End of split % 4.82/1.46 | | % 4.82/1.46 | End of split % 4.82/1.46 | % 4.82/1.46 End of proof % 4.82/1.46 % SZS output end Proof for theBenchmark % 4.82/1.46 % 4.82/1.46 852ms %------------------------------------------------------------------------------