%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SYN950+1 : TPTP v8.1.2. Released v3.1.0. % 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 03:29:20 EDT 2023 % Result : Theorem 3.19s 1.17s % Output : Proof 4.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SYN950+1 : TPTP v8.1.2. Released v3.1.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n003.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Sat Aug 26 21:41:24 EDT 2023 % 0.13/0.33 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.60 Running up to 7 provers in parallel. % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.69/0.95 Prover 1: Preprocessing ... % 1.69/0.95 Prover 4: Preprocessing ... % 2.06/0.99 Prover 0: Preprocessing ... % 2.06/1.00 Prover 2: Preprocessing ... % 2.06/1.00 Prover 5: Preprocessing ... % 2.06/1.00 Prover 6: Preprocessing ... % 2.06/1.00 Prover 3: Preprocessing ... % 2.59/1.07 Prover 1: Constructing countermodel ... % 2.59/1.07 Prover 3: Constructing countermodel ... % 2.59/1.07 Prover 2: Proving ... % 2.59/1.07 Prover 6: Proving ... % 2.59/1.07 Prover 5: Proving ... % 2.78/1.09 Prover 4: Constructing countermodel ... % 2.78/1.10 Prover 0: Proving ... % 3.19/1.14 Prover 3: gave up % 3.19/1.14 Prover 1: gave up % 3.19/1.16 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.19/1.16 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.19/1.17 Prover 7: Preprocessing ... % 3.19/1.17 Prover 8: Preprocessing ... % 3.19/1.17 Prover 0: proved (559ms) % 3.19/1.17 % 3.19/1.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.19/1.17 % 3.19/1.18 Prover 6: stopped % 3.19/1.19 Prover 2: stopped % 3.19/1.19 Prover 7: Warning: ignoring some quantifiers % 3.19/1.19 Prover 7: Constructing countermodel ... % 3.19/1.19 Prover 5: stopped % 3.19/1.19 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.19/1.19 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.19/1.19 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.19/1.19 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 3.19/1.20 Prover 8: Warning: ignoring some quantifiers % 3.19/1.20 Prover 8: Constructing countermodel ... % 3.19/1.20 Prover 13: Preprocessing ... % 3.19/1.21 Prover 16: Preprocessing ... % 3.19/1.21 Prover 10: Preprocessing ... % 3.19/1.21 Prover 11: Preprocessing ... % 3.70/1.22 Prover 10: Warning: ignoring some quantifiers % 3.70/1.22 Prover 10: Constructing countermodel ... % 3.70/1.23 Prover 16: Warning: ignoring some quantifiers % 3.70/1.23 Prover 16: Constructing countermodel ... % 3.70/1.23 Prover 13: Warning: ignoring some quantifiers % 3.70/1.24 Prover 13: Constructing countermodel ... % 3.70/1.24 Prover 10: gave up % 3.70/1.25 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 3.70/1.25 Prover 8: gave up % 3.70/1.25 Prover 19: Preprocessing ... % 3.70/1.26 Prover 7: gave up % 4.12/1.28 Prover 11: Constructing countermodel ... % 4.12/1.28 Prover 16: gave up % 4.12/1.29 Prover 13: gave up % 4.12/1.29 Prover 19: Warning: ignoring some quantifiers % 4.12/1.30 Prover 19: Constructing countermodel ... % 4.12/1.33 Prover 4: Found proof (size 52) % 4.12/1.33 Prover 4: proved (708ms) % 4.12/1.33 Prover 19: stopped % 4.12/1.33 Prover 11: stopped % 4.12/1.33 % 4.12/1.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.12/1.33 % 4.12/1.34 % SZS output start Proof for theBenchmark % 4.12/1.34 Assumptions after simplification: % 4.12/1.34 --------------------------------- % 4.12/1.34 % 4.12/1.34 (prove_this) % 4.12/1.40 ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : (p(v1) = v3 & p(v0) % 4.12/1.40 = v2 & $i(v1) & $i(v0) & ! [v4: $i] : ! [v5: MultipleValueBool] : ( ~ (v3 % 4.12/1.40 = 0) | ~ (v2 = 0) | ~ (p(v4) = v5) | ~ $i(v4)) & ! [v4: $i] : ! % 4.12/1.40 [v5: MultipleValueBool] : ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (q(v4) = v5) | ~ % 4.12/1.40 $i(v4)) & ! [v4: $i] : ! [v5: int] : ( ~ (v3 = 0) | v5 = 0 | ~ (p(v4) = % 4.12/1.40 v5) | ~ $i(v4)) & ! [v4: $i] : ! [v5: MultipleValueBool] : ( ~ (v3 = % 4.12/1.40 0) | ~ (q(v4) = v5) | ~ $i(v4) | p(v4) = 0) & ! [v4: $i] : ! [v5: % 4.12/1.40 int] : ( ~ (v2 = 0) | v5 = 0 | ~ (q(v4) = v5) | ~ $i(v4)) & ! [v4: $i] % 4.12/1.40 : ! [v5: MultipleValueBool] : ( ~ (v2 = 0) | ~ (p(v4) = v5) | ~ $i(v4) | % 4.12/1.40 q(v4) = 0) & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (p(v4) = v5) | ~ % 4.12/1.40 $i(v4) | q(v4) = 0) & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (p(v4) = % 4.12/1.40 v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & q(v4) = v6)) & ! [v4: % 4.12/1.40 $i] : ! [v5: int] : (v5 = 0 | ~ (q(v4) = v5) | ~ $i(v4) | p(v4) = 0) & % 4.12/1.40 ! [v4: $i] : ( ~ (q(v4) = 0) | ~ $i(v4) | p(v4) = 0)) % 4.12/1.40 % 4.12/1.40 (function-axioms) % 4.12/1.40 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = % 4.12/1.40 v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 4.12/1.40 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2) % 4.12/1.40 = v0)) % 4.12/1.40 % 4.12/1.40 Those formulas are unsatisfiable: % 4.12/1.40 --------------------------------- % 4.12/1.40 % 4.12/1.40 Begin of proof % 4.12/1.40 | % 4.12/1.40 | ALPHA: (function-axioms) implies: % 4.12/1.40 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.12/1.40 | (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2) = v0)) % 4.12/1.40 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.12/1.40 | (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) % 4.12/1.40 | % 4.12/1.41 | DELTA: instantiating (prove_this) with fresh symbols all_3_0, all_3_1, % 4.12/1.41 | all_3_2, all_3_3 gives: % 4.12/1.41 | (3) p(all_3_2) = all_3_0 & p(all_3_3) = all_3_1 & $i(all_3_2) & $i(all_3_3) % 4.12/1.41 | & ! [v0: $i] : ! [v1: MultipleValueBool] : ( ~ (all_3_0 = 0) | ~ % 4.12/1.41 | (all_3_1 = 0) | ~ (p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: % 4.12/1.41 | MultipleValueBool] : ( ~ (all_3_0 = 0) | ~ (all_3_1 = 0) | ~ (q(v0) % 4.12/1.41 | = v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: int] : ( ~ (all_3_0 = 0) % 4.12/1.41 | | v1 = 0 | ~ (p(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: % 4.12/1.41 | MultipleValueBool] : ( ~ (all_3_0 = 0) | ~ (q(v0) = v1) | ~ $i(v0) % 4.12/1.41 | | p(v0) = 0) & ! [v0: $i] : ! [v1: int] : ( ~ (all_3_1 = 0) | v1 = % 4.12/1.41 | 0 | ~ (q(v0) = v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: % 4.12/1.41 | MultipleValueBool] : ( ~ (all_3_1 = 0) | ~ (p(v0) = v1) | ~ $i(v0) % 4.12/1.41 | | q(v0) = 0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p(v0) = v1) % 4.12/1.41 | | ~ $i(v0) | q(v0) = 0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ % 4.12/1.41 | (p(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & q(v0) = v2)) % 4.12/1.41 | & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (q(v0) = v1) | ~ $i(v0) | % 4.12/1.41 | p(v0) = 0) & ! [v0: $i] : ( ~ (q(v0) = 0) | ~ $i(v0) | p(v0) = 0) % 4.12/1.41 | % 4.12/1.41 | ALPHA: (3) implies: % 4.12/1.41 | (4) $i(all_3_3) % 4.12/1.42 | (5) $i(all_3_2) % 4.12/1.42 | (6) p(all_3_3) = all_3_1 % 4.12/1.42 | (7) p(all_3_2) = all_3_0 % 4.12/1.42 | (8) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p(v0) = v1) | ~ $i(v0) | ? % 4.12/1.42 | [v2: int] : ( ~ (v2 = 0) & q(v0) = v2)) % 4.12/1.42 | (9) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (p(v0) = v1) | ~ $i(v0) | % 4.12/1.42 | q(v0) = 0) % 4.12/1.42 | (10) ! [v0: $i] : ! [v1: MultipleValueBool] : ( ~ (all_3_1 = 0) | ~ % 4.12/1.42 | (p(v0) = v1) | ~ $i(v0) | q(v0) = 0) % 4.12/1.42 | (11) ! [v0: $i] : ! [v1: int] : ( ~ (all_3_0 = 0) | v1 = 0 | ~ (p(v0) = % 4.12/1.42 | v1) | ~ $i(v0)) % 4.12/1.42 | (12) ! [v0: $i] : ! [v1: MultipleValueBool] : ( ~ (all_3_0 = 0) | ~ % 4.12/1.42 | (all_3_1 = 0) | ~ (p(v0) = v1) | ~ $i(v0)) % 4.12/1.42 | % 4.12/1.42 | GROUND_INST: instantiating (11) with all_3_3, all_3_1, simplifying with (4), % 4.12/1.42 | (6) gives: % 4.12/1.42 | (13) ~ (all_3_0 = 0) | all_3_1 = 0 % 4.12/1.42 | % 4.12/1.42 | GROUND_INST: instantiating (12) with all_3_2, 0, simplifying with (5) gives: % 4.12/1.42 | (14) ~ (all_3_0 = 0) | ~ (all_3_1 = 0) | ~ (p(all_3_2) = 0) % 4.12/1.42 | % 4.12/1.42 | GROUND_INST: instantiating (10) with all_3_2, all_3_0, simplifying with (5), % 4.12/1.42 | (7) gives: % 4.12/1.42 | (15) ~ (all_3_1 = 0) | q(all_3_2) = 0 % 4.12/1.42 | % 4.12/1.42 | GROUND_INST: instantiating (9) with all_3_2, all_3_0, simplifying with (5), % 4.12/1.42 | (7) gives: % 4.12/1.42 | (16) all_3_0 = 0 | q(all_3_2) = 0 % 4.12/1.42 | % 4.12/1.42 | GROUND_INST: instantiating (8) with all_3_2, all_3_0, simplifying with (5), % 4.12/1.42 | (7) gives: % 4.12/1.42 | (17) all_3_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & q(all_3_2) = v0) % 4.12/1.42 | % 4.12/1.42 | BETA: splitting (16) gives: % 4.12/1.42 | % 4.12/1.42 | Case 1: % 4.12/1.42 | | % 4.12/1.42 | | (18) q(all_3_2) = 0 % 4.12/1.42 | | % 4.12/1.42 | | BETA: splitting (17) gives: % 4.12/1.42 | | % 4.12/1.42 | | Case 1: % 4.12/1.42 | | | % 4.12/1.42 | | | (19) all_3_0 = 0 % 4.12/1.42 | | | % 4.12/1.42 | | | REDUCE: (7), (19) imply: % 4.12/1.42 | | | (20) p(all_3_2) = 0 % 4.12/1.42 | | | % 4.12/1.42 | | | BETA: splitting (13) gives: % 4.12/1.42 | | | % 4.12/1.42 | | | Case 1: % 4.12/1.42 | | | | % 4.12/1.43 | | | | (21) ~ (all_3_0 = 0) % 4.12/1.43 | | | | % 4.12/1.43 | | | | REF_CLOSE: (2), (7), (20), (21) are inconsistent by sub-proof #2. % 4.12/1.43 | | | | % 4.12/1.43 | | | Case 2: % 4.12/1.43 | | | | % 4.12/1.43 | | | | (22) all_3_1 = 0 % 4.12/1.43 | | | | % 4.12/1.43 | | | | BETA: splitting (14) gives: % 4.12/1.43 | | | | % 4.12/1.43 | | | | Case 1: % 4.12/1.43 | | | | | % 4.12/1.43 | | | | | (23) ~ (p(all_3_2) = 0) % 4.12/1.43 | | | | | % 4.12/1.43 | | | | | BETA: splitting (17) gives: % 4.12/1.43 | | | | | % 4.12/1.43 | | | | | Case 1: % 4.12/1.43 | | | | | | % 4.12/1.43 | | | | | | % 4.12/1.43 | | | | | | PRED_UNIFY: (20), (23) imply: % 4.12/1.43 | | | | | | (24) $false % 4.12/1.43 | | | | | | % 4.12/1.43 | | | | | | CLOSE: (24) is inconsistent. % 4.12/1.43 | | | | | | % 4.12/1.43 | | | | | Case 2: % 4.12/1.43 | | | | | | % 4.12/1.43 | | | | | | (25) ? [v0: int] : ( ~ (v0 = 0) & q(all_3_2) = v0) % 4.12/1.43 | | | | | | % 4.12/1.43 | | | | | | DELTA: instantiating (25) with fresh symbol all_37_0 gives: % 4.12/1.43 | | | | | | (26) ~ (all_37_0 = 0) & q(all_3_2) = all_37_0 % 4.12/1.43 | | | | | | % 4.12/1.43 | | | | | | REF_CLOSE: (1), (18), (26) are inconsistent by sub-proof #1. % 4.12/1.43 | | | | | | % 4.12/1.43 | | | | | End of split % 4.12/1.43 | | | | | % 4.12/1.43 | | | | Case 2: % 4.12/1.43 | | | | | % 4.12/1.43 | | | | | (27) ~ (all_3_0 = 0) | ~ (all_3_1 = 0) % 4.12/1.43 | | | | | % 4.12/1.43 | | | | | BETA: splitting (27) gives: % 4.12/1.43 | | | | | % 4.12/1.43 | | | | | Case 1: % 4.12/1.43 | | | | | | % 4.12/1.43 | | | | | | (28) ~ (all_3_0 = 0) % 4.12/1.43 | | | | | | % 4.12/1.43 | | | | | | REF_CLOSE: (2), (7), (20), (28) are inconsistent by sub-proof #2. % 4.12/1.43 | | | | | | % 4.12/1.43 | | | | | Case 2: % 4.12/1.43 | | | | | | % 4.12/1.43 | | | | | | (29) ~ (all_3_1 = 0) % 4.12/1.43 | | | | | | % 4.12/1.43 | | | | | | REDUCE: (22), (29) imply: % 4.12/1.43 | | | | | | (30) $false % 4.12/1.43 | | | | | | % 4.12/1.43 | | | | | | CLOSE: (30) is inconsistent. % 4.12/1.43 | | | | | | % 4.12/1.43 | | | | | End of split % 4.12/1.43 | | | | | % 4.12/1.43 | | | | End of split % 4.12/1.43 | | | | % 4.12/1.43 | | | End of split % 4.12/1.43 | | | % 4.12/1.43 | | Case 2: % 4.12/1.43 | | | % 4.12/1.43 | | | (31) ? [v0: int] : ( ~ (v0 = 0) & q(all_3_2) = v0) % 4.12/1.43 | | | % 4.12/1.43 | | | DELTA: instantiating (31) with fresh symbol all_37_0 gives: % 4.12/1.43 | | | (32) ~ (all_37_0 = 0) & q(all_3_2) = all_37_0 % 4.12/1.43 | | | % 4.12/1.43 | | | REF_CLOSE: (1), (18), (32) are inconsistent by sub-proof #1. % 4.12/1.43 | | | % 4.12/1.43 | | End of split % 4.12/1.43 | | % 4.12/1.43 | Case 2: % 4.12/1.43 | | % 4.12/1.43 | | (33) all_3_0 = 0 % 4.12/1.43 | | (34) ~ (q(all_3_2) = 0) % 4.12/1.43 | | % 4.12/1.43 | | REDUCE: (7), (33) imply: % 4.12/1.43 | | (35) p(all_3_2) = 0 % 4.12/1.43 | | % 4.12/1.43 | | BETA: splitting (15) gives: % 4.12/1.43 | | % 4.12/1.43 | | Case 1: % 4.12/1.43 | | | % 4.12/1.43 | | | (36) q(all_3_2) = 0 % 4.12/1.43 | | | % 4.12/1.43 | | | PRED_UNIFY: (34), (36) imply: % 4.12/1.43 | | | (37) $false % 4.12/1.43 | | | % 4.12/1.43 | | | CLOSE: (37) is inconsistent. % 4.12/1.43 | | | % 4.12/1.43 | | Case 2: % 4.12/1.43 | | | % 4.12/1.43 | | | (38) ~ (all_3_1 = 0) % 4.12/1.43 | | | % 4.12/1.43 | | | BETA: splitting (13) gives: % 4.12/1.43 | | | % 4.12/1.43 | | | Case 1: % 4.12/1.43 | | | | % 4.12/1.43 | | | | (39) ~ (all_3_0 = 0) % 4.12/1.43 | | | | % 4.12/1.43 | | | | REF_CLOSE: (2), (7), (35), (39) are inconsistent by sub-proof #2. % 4.12/1.43 | | | | % 4.12/1.43 | | | Case 2: % 4.12/1.43 | | | | % 4.12/1.43 | | | | (40) all_3_1 = 0 % 4.12/1.43 | | | | % 4.12/1.43 | | | | REDUCE: (38), (40) imply: % 4.12/1.43 | | | | (41) $false % 4.12/1.43 | | | | % 4.12/1.43 | | | | CLOSE: (41) is inconsistent. % 4.12/1.43 | | | | % 4.12/1.43 | | | End of split % 4.12/1.43 | | | % 4.12/1.43 | | End of split % 4.12/1.43 | | % 4.12/1.43 | End of split % 4.12/1.43 | % 4.12/1.43 End of proof % 4.12/1.43 % 4.12/1.43 Sub-proof #1 shows that the following formulas are inconsistent: % 4.12/1.43 ---------------------------------------------------------------- % 4.12/1.44 (1) ~ (all_37_0 = 0) & q(all_3_2) = all_37_0 % 4.12/1.44 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.12/1.44 (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2) = v0)) % 4.12/1.44 (3) q(all_3_2) = 0 % 4.12/1.44 % 4.12/1.44 Begin of proof % 4.12/1.44 | % 4.12/1.44 | ALPHA: (1) implies: % 4.12/1.44 | (4) ~ (all_37_0 = 0) % 4.12/1.44 | (5) q(all_3_2) = all_37_0 % 4.12/1.44 | % 4.12/1.44 | GROUND_INST: instantiating (2) with 0, all_37_0, all_3_2, simplifying with % 4.12/1.44 | (3), (5) gives: % 4.12/1.44 | (6) all_37_0 = 0 % 4.12/1.44 | % 4.12/1.44 | REDUCE: (4), (6) imply: % 4.12/1.44 | (7) $false % 4.12/1.44 | % 4.12/1.44 | CLOSE: (7) is inconsistent. % 4.12/1.44 | % 4.12/1.44 End of proof % 4.12/1.44 % 4.12/1.44 Sub-proof #2 shows that the following formulas are inconsistent: % 4.12/1.44 ---------------------------------------------------------------- % 4.12/1.44 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.12/1.44 (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0)) % 4.12/1.44 (2) p(all_3_2) = all_3_0 % 4.12/1.44 (3) p(all_3_2) = 0 % 4.12/1.44 (4) ~ (all_3_0 = 0) % 4.12/1.44 % 4.12/1.44 Begin of proof % 4.12/1.44 | % 4.12/1.44 | GROUND_INST: instantiating (1) with all_3_0, 0, all_3_2, simplifying with (2), % 4.12/1.44 | (3) gives: % 4.12/1.44 | (5) all_3_0 = 0 % 4.12/1.44 | % 4.12/1.44 | REDUCE: (4), (5) imply: % 4.12/1.44 | (6) $false % 4.12/1.44 | % 4.12/1.44 | CLOSE: (6) is inconsistent. % 4.12/1.44 | % 4.12/1.44 End of proof % 4.12/1.44 % SZS output end Proof for theBenchmark % 4.12/1.44 % 4.12/1.44 847ms %------------------------------------------------------------------------------