%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU125+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n009.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 : Thu Aug 31 17:42:37 EDT 2023 % Result : Theorem 6.17s 1.60s % Output : Proof 8.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU125+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n009.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Aug 23 18:07:06 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.12/1.03 Prover 4: Preprocessing ... % 2.12/1.03 Prover 1: Preprocessing ... % 2.63/1.08 Prover 6: Preprocessing ... % 2.63/1.08 Prover 5: Preprocessing ... % 2.63/1.08 Prover 0: Preprocessing ... % 2.63/1.08 Prover 2: Preprocessing ... % 2.63/1.08 Prover 3: Preprocessing ... % 3.64/1.40 Prover 1: Warning: ignoring some quantifiers % 3.64/1.40 Prover 4: Warning: ignoring some quantifiers % 3.64/1.40 Prover 3: Warning: ignoring some quantifiers % 3.64/1.41 Prover 2: Proving ... % 3.64/1.41 Prover 5: Proving ... % 4.65/1.42 Prover 6: Proving ... % 4.65/1.42 Prover 4: Constructing countermodel ... % 4.65/1.42 Prover 3: Constructing countermodel ... % 4.65/1.42 Prover 1: Constructing countermodel ... % 4.65/1.43 Prover 0: Proving ... % 6.17/1.60 Prover 0: proved (985ms) % 6.17/1.60 % 6.17/1.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.17/1.60 % 6.17/1.60 Prover 6: stopped % 6.28/1.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.28/1.61 Prover 5: stopped % 6.32/1.61 Prover 3: stopped % 6.32/1.61 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.32/1.61 Prover 2: stopped % 6.32/1.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.32/1.62 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.32/1.62 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.32/1.65 Prover 8: Preprocessing ... % 6.32/1.65 Prover 7: Preprocessing ... % 6.32/1.65 Prover 11: Preprocessing ... % 6.32/1.65 Prover 13: Preprocessing ... % 6.32/1.65 Prover 10: Preprocessing ... % 6.32/1.70 Prover 10: Warning: ignoring some quantifiers % 6.95/1.70 Prover 10: Constructing countermodel ... % 6.95/1.71 Prover 7: Warning: ignoring some quantifiers % 6.95/1.71 Prover 7: Constructing countermodel ... % 6.95/1.72 Prover 8: Warning: ignoring some quantifiers % 6.95/1.72 Prover 13: Warning: ignoring some quantifiers % 6.95/1.72 Prover 13: Constructing countermodel ... % 6.95/1.72 Prover 8: Constructing countermodel ... % 6.95/1.72 Prover 1: gave up % 6.95/1.74 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 6.95/1.76 Prover 16: Preprocessing ... % 6.95/1.77 Prover 11: Warning: ignoring some quantifiers % 6.95/1.77 Prover 11: Constructing countermodel ... % 7.56/1.79 Prover 10: gave up % 7.56/1.79 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 7.56/1.80 Prover 13: gave up % 7.56/1.80 Prover 4: Found proof (size 50) % 7.56/1.80 Prover 4: proved (1182ms) % 7.56/1.80 Prover 11: stopped % 7.56/1.80 Prover 8: stopped % 7.56/1.81 Prover 7: stopped % 7.56/1.81 Prover 16: Warning: ignoring some quantifiers % 7.56/1.82 Prover 19: Preprocessing ... % 7.56/1.82 Prover 16: Constructing countermodel ... % 7.56/1.82 Prover 16: stopped % 7.56/1.87 Prover 19: Warning: ignoring some quantifiers % 7.56/1.87 Prover 19: Constructing countermodel ... % 7.56/1.88 Prover 19: stopped % 7.56/1.88 % 7.56/1.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.56/1.88 % 8.11/1.89 % SZS output start Proof for theBenchmark % 8.11/1.89 Assumptions after simplification: % 8.11/1.89 --------------------------------- % 8.11/1.89 % 8.11/1.89 (commutativity_k2_xboole_0) % 8.18/1.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~ % 8.18/1.92 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 8.18/1.92 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 8.18/1.92 | (set_union2(v1, v0) = v2 & $i(v2))) % 8.18/1.92 % 8.18/1.92 (d2_xboole_0) % 8.18/1.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 8.18/1.94 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | ~ % 8.18/1.94 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) % 8.18/1.94 & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v0: $i] : ! % 8.18/1.94 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 8.18/1.94 (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) | % 8.18/1.94 ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & % 8.18/1.94 in(v3, v0) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : % 8.18/1.94 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (set_union2(v0, v1) = % 8.18/1.94 v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 8.18/1.94 | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 % 8.18/1.94 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 8.18/1.94 $i] : ! [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | % 8.18/1.94 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 8.18/1.94 (in(v3, v2) = v6 & in(v3, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = % 8.18/1.94 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 8.18/1.94 [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | % 8.18/1.94 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, % 8.18/1.94 v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) & % 8.18/1.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1) % 8.18/1.94 = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 8.18/1.94 $i(v0) | ? [v4: any] : ? [v5: any] : (in(v3, v1) = v5 & in(v3, v0) = v4 & % 8.18/1.94 (v5 = 0 | v4 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 8.18/1.94 $i] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 8.18/1.94 $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4, % 8.18/1.94 v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( % 8.18/1.94 ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) % 8.18/1.94 % 8.18/1.94 (d3_tarski) % 8.18/1.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 8.18/1.94 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 8.18/1.95 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : ! % 8.18/1.95 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ % 8.18/1.95 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 & % 8.18/1.95 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 8.18/1.95 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 8.18/1.95 $i(v0) | in(v2, v1) = 0) % 8.18/1.95 % 8.18/1.95 (t8_xboole_1) % 8.18/1.95 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 8.18/1.95 = 0) & subset(v3, v1) = v4 & subset(v2, v1) = 0 & subset(v0, v1) = 0 & % 8.18/1.95 set_union2(v0, v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 8.18/1.95 % 8.18/1.95 (function-axioms) % 8.18/1.95 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 8.18/1.95 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 8.18/1.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 8.18/1.95 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: % 8.18/1.95 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 8.18/1.95 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 8.18/1.95 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 8.18/1.95 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 8.18/1.95 % 8.18/1.95 Further assumptions not needed in the proof: % 8.18/1.95 -------------------------------------------- % 8.18/1.95 antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k2_xboole_0, fc1_xboole_0, % 8.18/1.95 fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, rc1_xboole_0, rc2_xboole_0, % 8.18/1.95 reflexivity_r1_tarski, t1_boole, t6_boole, t7_boole, t8_boole % 8.18/1.95 % 8.18/1.95 Those formulas are unsatisfiable: % 8.18/1.95 --------------------------------- % 8.18/1.95 % 8.18/1.95 Begin of proof % 8.18/1.95 | % 8.18/1.95 | ALPHA: (commutativity_k2_xboole_0) implies: % 8.18/1.95 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) % 8.18/1.95 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) % 8.18/1.95 | % 8.18/1.95 | ALPHA: (d2_xboole_0) implies: % 8.18/1.95 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 8.18/1.95 | (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ % 8.18/1.95 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 8.18/1.95 | (in(v3, v1) = v5 & in(v3, v0) = v4 & (v5 = 0 | v4 = 0))) % 8.18/1.95 | % 8.18/1.95 | ALPHA: (d3_tarski) implies: % 8.18/1.96 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 8.18/1.96 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 8.18/1.96 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 8.18/1.96 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 8.18/1.96 | (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | % 8.18/1.96 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) % 8.18/1.96 | % 8.18/1.96 | ALPHA: (function-axioms) implies: % 8.18/1.96 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.18/1.96 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 8.18/1.96 | % 8.18/1.96 | DELTA: instantiating (t8_xboole_1) with fresh symbols all_20_0, all_20_1, % 8.18/1.96 | all_20_2, all_20_3, all_20_4 gives: % 8.18/1.96 | (6) ~ (all_20_0 = 0) & subset(all_20_1, all_20_3) = all_20_0 & % 8.18/1.96 | subset(all_20_2, all_20_3) = 0 & subset(all_20_4, all_20_3) = 0 & % 8.18/1.96 | set_union2(all_20_4, all_20_2) = all_20_1 & $i(all_20_1) & $i(all_20_2) % 8.18/1.96 | & $i(all_20_3) & $i(all_20_4) % 8.18/1.96 | % 8.18/1.96 | ALPHA: (6) implies: % 8.18/1.96 | (7) ~ (all_20_0 = 0) % 8.18/1.96 | (8) $i(all_20_4) % 8.18/1.96 | (9) $i(all_20_3) % 8.18/1.96 | (10) $i(all_20_2) % 8.18/1.96 | (11) set_union2(all_20_4, all_20_2) = all_20_1 % 8.18/1.96 | (12) subset(all_20_4, all_20_3) = 0 % 8.18/1.96 | (13) subset(all_20_2, all_20_3) = 0 % 8.18/1.96 | (14) subset(all_20_1, all_20_3) = all_20_0 % 8.18/1.96 | % 8.18/1.96 | GROUND_INST: instantiating (1) with all_20_2, all_20_4, all_20_1, simplifying % 8.18/1.96 | with (8), (10), (11) gives: % 8.18/1.96 | (15) set_union2(all_20_2, all_20_4) = all_20_1 & $i(all_20_1) % 8.18/1.96 | % 8.18/1.96 | ALPHA: (15) implies: % 8.18/1.96 | (16) $i(all_20_1) % 8.18/1.96 | (17) set_union2(all_20_2, all_20_4) = all_20_1 % 8.18/1.96 | % 8.18/1.96 | GROUND_INST: instantiating (3) with all_20_1, all_20_3, all_20_0, simplifying % 8.18/1.96 | with (9), (14), (16) gives: % 8.18/1.96 | (18) all_20_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 8.18/1.96 | all_20_1) = 0 & in(v0, all_20_3) = v1 & $i(v0)) % 8.18/1.96 | % 8.18/1.96 | BETA: splitting (18) gives: % 8.18/1.96 | % 8.18/1.97 | Case 1: % 8.18/1.97 | | % 8.18/1.97 | | (19) all_20_0 = 0 % 8.18/1.97 | | % 8.18/1.97 | | REDUCE: (7), (19) imply: % 8.18/1.97 | | (20) $false % 8.18/1.97 | | % 8.18/1.97 | | CLOSE: (20) is inconsistent. % 8.18/1.97 | | % 8.18/1.97 | Case 2: % 8.18/1.97 | | % 8.18/1.97 | | (21) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_20_1) = 0 & % 8.18/1.97 | | in(v0, all_20_3) = v1 & $i(v0)) % 8.18/1.97 | | % 8.18/1.97 | | DELTA: instantiating (21) with fresh symbols all_38_0, all_38_1 gives: % 8.18/1.97 | | (22) ~ (all_38_0 = 0) & in(all_38_1, all_20_1) = 0 & in(all_38_1, % 8.18/1.97 | | all_20_3) = all_38_0 & $i(all_38_1) % 8.18/1.97 | | % 8.18/1.97 | | ALPHA: (22) implies: % 8.18/1.97 | | (23) ~ (all_38_0 = 0) % 8.18/1.97 | | (24) $i(all_38_1) % 8.18/1.97 | | (25) in(all_38_1, all_20_3) = all_38_0 % 8.18/1.97 | | (26) in(all_38_1, all_20_1) = 0 % 8.18/1.97 | | % 8.18/1.97 | | GROUND_INST: instantiating (4) with all_20_2, all_20_3, all_38_1, all_38_0, % 8.18/1.97 | | simplifying with (9), (10), (13), (24), (25) gives: % 8.18/1.97 | | (27) all_38_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_38_1, all_20_2) % 8.18/1.97 | | = v0) % 8.18/1.97 | | % 8.18/1.97 | | GROUND_INST: instantiating (4) with all_20_4, all_20_3, all_38_1, all_38_0, % 8.18/1.97 | | simplifying with (8), (9), (12), (24), (25) gives: % 8.18/1.97 | | (28) all_38_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_38_1, all_20_4) % 8.18/1.97 | | = v0) % 8.18/1.97 | | % 8.18/1.97 | | GROUND_INST: instantiating (2) with all_20_4, all_20_2, all_20_1, all_38_1, % 8.18/1.97 | | simplifying with (8), (10), (11), (16), (24), (26) gives: % 8.18/1.97 | | (29) ? [v0: any] : ? [v1: any] : (in(all_38_1, all_20_2) = v1 & % 8.18/1.97 | | in(all_38_1, all_20_4) = v0 & (v1 = 0 | v0 = 0)) % 8.18/1.97 | | % 8.18/1.97 | | GROUND_INST: instantiating (2) with all_20_2, all_20_4, all_20_1, all_38_1, % 8.18/1.97 | | simplifying with (8), (10), (16), (17), (24), (26) gives: % 8.18/1.98 | | (30) ? [v0: any] : ? [v1: any] : (in(all_38_1, all_20_2) = v0 & % 8.18/1.98 | | in(all_38_1, all_20_4) = v1 & (v1 = 0 | v0 = 0)) % 8.18/1.98 | | % 8.18/1.98 | | DELTA: instantiating (29) with fresh symbols all_55_0, all_55_1 gives: % 8.18/1.98 | | (31) in(all_38_1, all_20_2) = all_55_0 & in(all_38_1, all_20_4) = % 8.18/1.98 | | all_55_1 & (all_55_0 = 0 | all_55_1 = 0) % 8.18/1.98 | | % 8.18/1.98 | | ALPHA: (31) implies: % 8.18/1.98 | | (32) in(all_38_1, all_20_4) = all_55_1 % 8.18/1.98 | | (33) in(all_38_1, all_20_2) = all_55_0 % 8.18/1.98 | | % 8.18/1.98 | | DELTA: instantiating (30) with fresh symbols all_59_0, all_59_1 gives: % 8.18/1.98 | | (34) in(all_38_1, all_20_2) = all_59_1 & in(all_38_1, all_20_4) = % 8.18/1.98 | | all_59_0 & (all_59_0 = 0 | all_59_1 = 0) % 8.18/1.98 | | % 8.18/1.98 | | ALPHA: (34) implies: % 8.18/1.98 | | (35) in(all_38_1, all_20_4) = all_59_0 % 8.18/1.98 | | (36) in(all_38_1, all_20_2) = all_59_1 % 8.18/1.98 | | (37) all_59_0 = 0 | all_59_1 = 0 % 8.18/1.98 | | % 8.18/1.98 | | BETA: splitting (28) gives: % 8.18/1.98 | | % 8.18/1.98 | | Case 1: % 8.18/1.98 | | | % 8.18/1.98 | | | (38) all_38_0 = 0 % 8.18/1.98 | | | % 8.18/1.98 | | | REDUCE: (23), (38) imply: % 8.18/1.98 | | | (39) $false % 8.18/1.98 | | | % 8.18/1.98 | | | CLOSE: (39) is inconsistent. % 8.18/1.98 | | | % 8.18/1.98 | | Case 2: % 8.18/1.98 | | | % 8.18/1.98 | | | (40) ? [v0: int] : ( ~ (v0 = 0) & in(all_38_1, all_20_4) = v0) % 8.18/1.98 | | | % 8.18/1.98 | | | DELTA: instantiating (40) with fresh symbol all_65_0 gives: % 8.18/1.98 | | | (41) ~ (all_65_0 = 0) & in(all_38_1, all_20_4) = all_65_0 % 8.18/1.98 | | | % 8.18/1.98 | | | ALPHA: (41) implies: % 8.18/1.98 | | | (42) ~ (all_65_0 = 0) % 8.18/1.98 | | | (43) in(all_38_1, all_20_4) = all_65_0 % 8.18/1.98 | | | % 8.18/1.98 | | | BETA: splitting (27) gives: % 8.18/1.98 | | | % 8.18/1.98 | | | Case 1: % 8.18/1.98 | | | | % 8.18/1.98 | | | | (44) all_38_0 = 0 % 8.18/1.98 | | | | % 8.18/1.98 | | | | REDUCE: (23), (44) imply: % 8.18/1.98 | | | | (45) $false % 8.18/1.98 | | | | % 8.18/1.98 | | | | CLOSE: (45) is inconsistent. % 8.18/1.98 | | | | % 8.18/1.98 | | | Case 2: % 8.18/1.98 | | | | % 8.18/1.98 | | | | (46) ? [v0: int] : ( ~ (v0 = 0) & in(all_38_1, all_20_2) = v0) % 8.18/1.98 | | | | % 8.18/1.98 | | | | DELTA: instantiating (46) with fresh symbol all_71_0 gives: % 8.18/1.98 | | | | (47) ~ (all_71_0 = 0) & in(all_38_1, all_20_2) = all_71_0 % 8.18/1.98 | | | | % 8.18/1.98 | | | | ALPHA: (47) implies: % 8.18/1.98 | | | | (48) ~ (all_71_0 = 0) % 8.18/1.98 | | | | (49) in(all_38_1, all_20_2) = all_71_0 % 8.18/1.98 | | | | % 8.18/1.98 | | | | GROUND_INST: instantiating (5) with all_59_0, all_65_0, all_20_4, % 8.18/1.98 | | | | all_38_1, simplifying with (35), (43) gives: % 8.18/1.98 | | | | (50) all_65_0 = all_59_0 % 8.18/1.98 | | | | % 8.18/1.98 | | | | GROUND_INST: instantiating (5) with all_55_1, all_65_0, all_20_4, % 8.18/1.98 | | | | all_38_1, simplifying with (32), (43) gives: % 8.18/1.98 | | | | (51) all_65_0 = all_55_1 % 8.18/1.98 | | | | % 8.18/1.98 | | | | GROUND_INST: instantiating (5) with all_59_1, all_71_0, all_20_2, % 8.18/1.98 | | | | all_38_1, simplifying with (36), (49) gives: % 8.18/1.98 | | | | (52) all_71_0 = all_59_1 % 8.18/1.98 | | | | % 8.18/1.98 | | | | GROUND_INST: instantiating (5) with all_55_0, all_71_0, all_20_2, % 8.18/1.98 | | | | all_38_1, simplifying with (33), (49) gives: % 8.18/1.98 | | | | (53) all_71_0 = all_55_0 % 8.18/1.98 | | | | % 8.18/1.98 | | | | COMBINE_EQS: (52), (53) imply: % 8.18/1.98 | | | | (54) all_59_1 = all_55_0 % 8.18/1.98 | | | | % 8.18/1.98 | | | | SIMP: (54) implies: % 8.18/1.99 | | | | (55) all_59_1 = all_55_0 % 8.18/1.99 | | | | % 8.18/1.99 | | | | COMBINE_EQS: (50), (51) imply: % 8.18/1.99 | | | | (56) all_59_0 = all_55_1 % 8.18/1.99 | | | | % 8.18/1.99 | | | | REDUCE: (48), (53) imply: % 8.18/1.99 | | | | (57) ~ (all_55_0 = 0) % 8.18/1.99 | | | | % 8.18/1.99 | | | | REDUCE: (42), (51) imply: % 8.18/1.99 | | | | (58) ~ (all_55_1 = 0) % 8.18/1.99 | | | | % 8.18/1.99 | | | | BETA: splitting (37) gives: % 8.18/1.99 | | | | % 8.18/1.99 | | | | Case 1: % 8.18/1.99 | | | | | % 8.18/1.99 | | | | | (59) all_59_0 = 0 % 8.18/1.99 | | | | | % 8.18/1.99 | | | | | COMBINE_EQS: (56), (59) imply: % 8.18/1.99 | | | | | (60) all_55_1 = 0 % 8.18/1.99 | | | | | % 8.18/1.99 | | | | | SIMP: (60) implies: % 8.18/1.99 | | | | | (61) all_55_1 = 0 % 8.18/1.99 | | | | | % 8.18/1.99 | | | | | REDUCE: (58), (61) imply: % 8.18/1.99 | | | | | (62) $false % 8.18/1.99 | | | | | % 8.18/1.99 | | | | | CLOSE: (62) is inconsistent. % 8.18/1.99 | | | | | % 8.18/1.99 | | | | Case 2: % 8.18/1.99 | | | | | % 8.18/1.99 | | | | | (63) all_59_1 = 0 % 8.18/1.99 | | | | | % 8.18/1.99 | | | | | COMBINE_EQS: (55), (63) imply: % 8.18/1.99 | | | | | (64) all_55_0 = 0 % 8.18/1.99 | | | | | % 8.18/1.99 | | | | | REDUCE: (57), (64) imply: % 8.18/1.99 | | | | | (65) $false % 8.18/1.99 | | | | | % 8.18/1.99 | | | | | CLOSE: (65) is inconsistent. % 8.18/1.99 | | | | | % 8.18/1.99 | | | | End of split % 8.18/1.99 | | | | % 8.18/1.99 | | | End of split % 8.18/1.99 | | | % 8.18/1.99 | | End of split % 8.18/1.99 | | % 8.18/1.99 | End of split % 8.18/1.99 | % 8.18/1.99 End of proof % 8.18/1.99 % SZS output end Proof for theBenchmark % 8.18/1.99 % 8.18/1.99 1389ms %------------------------------------------------------------------------------