%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU145+2 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n005.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 17:42:45 EDT 2023 % Result : Theorem 10.14s 2.19s % Output : Proof 13.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU145+2 : 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 : n005.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 18:06:09 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.93/1.11 Prover 1: Preprocessing ... % 2.93/1.11 Prover 4: Preprocessing ... % 2.93/1.14 Prover 2: Preprocessing ... % 2.93/1.14 Prover 3: Preprocessing ... % 2.93/1.14 Prover 6: Preprocessing ... % 2.93/1.14 Prover 5: Preprocessing ... % 2.93/1.14 Prover 0: Preprocessing ... % 7.57/1.74 Prover 1: Warning: ignoring some quantifiers % 7.57/1.75 Prover 5: Proving ... % 8.05/1.80 Prover 6: Proving ... % 8.05/1.84 Prover 1: Constructing countermodel ... % 8.05/1.85 Prover 3: Warning: ignoring some quantifiers % 8.57/1.89 Prover 3: Constructing countermodel ... % 8.57/1.90 Prover 4: Warning: ignoring some quantifiers % 8.81/1.92 Prover 2: Proving ... % 8.99/2.02 Prover 4: Constructing countermodel ... % 9.66/2.07 Prover 0: Proving ... % 10.14/2.17 Prover 3: proved (1534ms) % 10.14/2.17 % 10.14/2.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.14/2.19 % 10.14/2.19 Prover 5: stopped % 10.14/2.19 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.14/2.19 Prover 0: stopped % 10.14/2.19 Prover 2: stopped % 10.14/2.21 Prover 6: stopped % 10.14/2.21 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.14/2.21 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.14/2.21 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.14/2.21 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.14/2.27 Prover 13: Preprocessing ... % 10.14/2.29 Prover 7: Preprocessing ... % 11.61/2.32 Prover 10: Preprocessing ... % 11.61/2.32 Prover 8: Preprocessing ... % 11.87/2.34 Prover 11: Preprocessing ... % 11.87/2.43 Prover 7: Warning: ignoring some quantifiers % 12.60/2.43 Prover 1: Found proof (size 46) % 12.60/2.43 Prover 1: proved (1803ms) % 12.60/2.45 Prover 13: Warning: ignoring some quantifiers % 12.60/2.45 Prover 11: stopped % 12.60/2.45 Prover 4: stopped % 12.60/2.45 Prover 7: Constructing countermodel ... % 12.60/2.46 Prover 10: Warning: ignoring some quantifiers % 12.60/2.47 Prover 13: Constructing countermodel ... % 12.60/2.47 Prover 7: stopped % 12.60/2.48 Prover 10: Constructing countermodel ... % 12.60/2.48 Prover 8: Warning: ignoring some quantifiers % 12.60/2.49 Prover 13: stopped % 12.60/2.49 Prover 10: stopped % 13.03/2.50 Prover 8: Constructing countermodel ... % 13.03/2.51 Prover 8: stopped % 13.03/2.51 % 13.03/2.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.03/2.51 % 13.03/2.51 % SZS output start Proof for theBenchmark % 13.03/2.52 Assumptions after simplification: % 13.03/2.52 --------------------------------- % 13.03/2.52 % 13.03/2.52 (d1_tarski) % 13.03/2.55 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | % 13.03/2.55 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 & % 13.03/2.55 $i(v3) & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) & ! [v0: $i] % 13.03/2.55 : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: % 13.03/2.55 $i] : (v2 = v0 | ~ (in(v2, v1) = 0) | ~ $i(v2)) & ! [v2: int] : (v2 = % 13.03/2.55 0 | ~ (in(v0, v1) = v2)))) % 13.03/2.55 % 13.03/2.55 (d3_tarski) % 13.03/2.55 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 13.03/2.55 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, % 13.03/2.55 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 13.03/2.55 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) % 13.03/2.55 = 0) | ~ $i(v2) | in(v2, v1) = 0)) % 13.03/2.55 % 13.03/2.55 (d4_xboole_0) % 13.34/2.55 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 13.34/2.55 (set_difference(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 13.34/2.55 $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4, v2) = v7 & % 13.34/2.55 in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v6 = 0) | ~ (v5 = 0) | % 13.34/2.55 v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0))))) & ! [v0: $i] : ! [v1: % 13.34/2.55 $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) = v2) | ~ $i(v2) | ~ % 13.34/2.55 $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: any] : ( ~ (in(v3, v0) = v4) | % 13.34/2.55 ~ $i(v3) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = % 13.34/2.55 v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 = 0))))) & ! [v3: $i] : ( ~ % 13.34/2.55 (in(v3, v0) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) % 13.34/2.55 = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))))) % 13.34/2.55 % 13.34/2.55 (l3_zfmisc_1) % 13.34/2.56 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: $i] : ? [v5: % 13.34/2.56 $i] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v3 = 0) & set_difference(v1, v4) = % 13.34/2.56 v5 & singleton(v2) = v4 & subset(v0, v5) = v6 & subset(v0, v1) = 0 & in(v2, % 13.34/2.56 v0) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v1) & $i(v0)) % 13.34/2.56 % 13.34/2.56 (t1_xboole_1) % 13.34/2.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 13.34/2.56 (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 13.34/2.56 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) % 13.34/2.56 % 13.34/2.56 (function-axioms) % 13.37/2.56 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 13.37/2.56 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 13.37/2.56 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.37/2.56 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 13.37/2.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.37/2.56 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 13.37/2.56 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.37/2.56 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 13.37/2.56 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.37/2.56 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! % 13.37/2.56 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = % 13.37/2.56 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 13.37/2.56 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 13.37/2.56 (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0: % 13.37/2.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 13.37/2.56 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 13.37/2.56 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 13.37/2.56 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 13.37/2.56 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 13.37/2.56 % 13.37/2.56 Further assumptions not needed in the proof: % 13.37/2.56 -------------------------------------------- % 13.37/2.56 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski, % 13.37/2.56 commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_xboole_0, d1_xboole_0, % 13.37/2.56 d2_tarski, d2_xboole_0, d3_xboole_0, d7_xboole_0, d8_xboole_0, dt_k1_tarski, % 13.37/2.56 dt_k1_xboole_0, dt_k2_tarski, dt_k2_xboole_0, dt_k3_xboole_0, dt_k4_xboole_0, % 13.37/2.56 fc1_xboole_0, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, % 13.37/2.56 idempotence_k3_xboole_0, irreflexivity_r2_xboole_0, l1_zfmisc_1, l2_zfmisc_1, % 13.37/2.56 l32_xboole_1, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski, % 13.37/2.56 symmetry_r1_xboole_0, t12_xboole_1, t17_xboole_1, t19_xboole_1, t1_boole, % 13.37/2.56 t26_xboole_1, t28_xboole_1, t2_boole, t2_tarski, t2_xboole_1, t33_xboole_1, % 13.37/2.56 t36_xboole_1, t37_xboole_1, t39_xboole_1, t3_boole, t3_xboole_0, t3_xboole_1, % 13.37/2.56 t40_xboole_1, t45_xboole_1, t48_xboole_1, t4_boole, t4_xboole_0, t60_xboole_1, % 13.37/2.56 t63_xboole_1, t69_enumset1, t6_boole, t7_boole, t7_xboole_1, t83_xboole_1, % 13.37/2.56 t8_boole, t8_xboole_1 % 13.37/2.56 % 13.37/2.56 Those formulas are unsatisfiable: % 13.37/2.56 --------------------------------- % 13.37/2.56 % 13.37/2.56 Begin of proof % 13.37/2.56 | % 13.37/2.56 | ALPHA: (d1_tarski) implies: % 13.37/2.56 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~ % 13.37/2.56 | $i(v0) | ( ! [v2: $i] : (v2 = v0 | ~ (in(v2, v1) = 0) | ~ $i(v2)) & % 13.37/2.56 | ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2)))) % 13.37/2.56 | % 13.37/2.56 | ALPHA: (d3_tarski) implies: % 13.37/2.57 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 13.37/2.57 | $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) = 0) | ~ $i(v2) | in(v2, v1) % 13.37/2.57 | = 0)) % 13.37/2.57 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 13.37/2.57 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 13.37/2.57 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 13.37/2.57 | % 13.37/2.57 | ALPHA: (d4_xboole_0) implies: % 13.37/2.57 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) = % 13.37/2.57 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: % 13.37/2.57 | any] : ( ~ (in(v3, v0) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: % 13.37/2.57 | any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 % 13.37/2.57 | = 0 & ~ (v6 = 0))))) & ! [v3: $i] : ( ~ (in(v3, v0) = 0) % 13.37/2.57 | | ~ $i(v3) | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & % 13.37/2.57 | in(v3, v1) = v4 & (v5 = 0 | v4 = 0))))) % 13.37/2.57 | % 13.37/2.57 | ALPHA: (function-axioms) implies: % 13.37/2.57 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 13.37/2.57 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 13.37/2.57 | % 13.37/2.57 | DELTA: instantiating (l3_zfmisc_1) with fresh symbols all_71_0, all_71_1, % 13.37/2.57 | all_71_2, all_71_3, all_71_4, all_71_5, all_71_6 gives: % 13.37/2.57 | (6) ~ (all_71_0 = 0) & ~ (all_71_3 = 0) & set_difference(all_71_5, % 13.37/2.57 | all_71_2) = all_71_1 & singleton(all_71_4) = all_71_2 & % 13.37/2.57 | subset(all_71_6, all_71_1) = all_71_0 & subset(all_71_6, all_71_5) = 0 % 13.37/2.57 | & in(all_71_4, all_71_6) = all_71_3 & $i(all_71_1) & $i(all_71_2) & % 13.37/2.57 | $i(all_71_4) & $i(all_71_5) & $i(all_71_6) % 13.37/2.57 | % 13.37/2.57 | ALPHA: (6) implies: % 13.37/2.57 | (7) ~ (all_71_3 = 0) % 13.37/2.57 | (8) ~ (all_71_0 = 0) % 13.37/2.57 | (9) $i(all_71_6) % 13.37/2.57 | (10) $i(all_71_5) % 13.37/2.57 | (11) $i(all_71_4) % 13.37/2.57 | (12) $i(all_71_2) % 13.37/2.57 | (13) $i(all_71_1) % 13.37/2.57 | (14) in(all_71_4, all_71_6) = all_71_3 % 13.37/2.57 | (15) subset(all_71_6, all_71_5) = 0 % 13.37/2.57 | (16) subset(all_71_6, all_71_1) = all_71_0 % 13.37/2.57 | (17) singleton(all_71_4) = all_71_2 % 13.37/2.57 | (18) set_difference(all_71_5, all_71_2) = all_71_1 % 13.37/2.57 | % 13.37/2.57 | GROUND_INST: instantiating (2) with all_71_6, all_71_5, simplifying with (9), % 13.37/2.57 | (10), (15) gives: % 13.37/2.57 | (19) ! [v0: $i] : ( ~ (in(v0, all_71_6) = 0) | ~ $i(v0) | in(v0, % 13.37/2.57 | all_71_5) = 0) % 13.37/2.57 | % 13.37/2.57 | GROUND_INST: instantiating (t1_xboole_1) with all_71_6, all_71_5, all_71_1, % 13.37/2.57 | all_71_0, simplifying with (9), (10), (13), (15), (16) gives: % 13.37/2.57 | (20) all_71_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_71_5, % 13.37/2.57 | all_71_1) = v0) % 13.37/2.57 | % 13.37/2.57 | GROUND_INST: instantiating (3) with all_71_6, all_71_1, all_71_0, simplifying % 13.37/2.57 | with (9), (13), (16) gives: % 13.37/2.58 | (21) all_71_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 13.37/2.58 | all_71_1) = v1 & in(v0, all_71_6) = 0 & $i(v0)) % 13.37/2.58 | % 13.37/2.58 | GROUND_INST: instantiating (1) with all_71_4, all_71_2, simplifying with (11), % 13.37/2.58 | (12), (17) gives: % 13.37/2.58 | (22) ! [v0: any] : (v0 = all_71_4 | ~ (in(v0, all_71_2) = 0) | ~ $i(v0)) % 13.37/2.58 | & ! [v0: int] : (v0 = 0 | ~ (in(all_71_4, all_71_2) = v0)) % 13.37/2.58 | % 13.37/2.58 | ALPHA: (22) implies: % 13.37/2.58 | (23) ! [v0: any] : (v0 = all_71_4 | ~ (in(v0, all_71_2) = 0) | ~ $i(v0)) % 13.37/2.58 | % 13.37/2.58 | GROUND_INST: instantiating (4) with all_71_5, all_71_2, all_71_1, simplifying % 13.37/2.58 | with (10), (12), (13), (18) gives: % 13.37/2.58 | (24) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_71_5) = v1) | ~ $i(v0) | % 13.37/2.58 | ? [v2: any] : ? [v3: any] : (in(v0, all_71_1) = v2 & in(v0, % 13.37/2.58 | all_71_2) = v3 & ( ~ (v2 = 0) | (v1 = 0 & ~ (v3 = 0))))) & ! % 13.37/2.58 | [v0: $i] : ( ~ (in(v0, all_71_5) = 0) | ~ $i(v0) | ? [v1: any] : ? % 13.37/2.58 | [v2: any] : (in(v0, all_71_1) = v2 & in(v0, all_71_2) = v1 & (v2 = 0 % 13.37/2.58 | | v1 = 0))) % 13.37/2.58 | % 13.37/2.58 | ALPHA: (24) implies: % 13.37/2.58 | (25) ! [v0: $i] : ( ~ (in(v0, all_71_5) = 0) | ~ $i(v0) | ? [v1: any] : % 13.37/2.58 | ? [v2: any] : (in(v0, all_71_1) = v2 & in(v0, all_71_2) = v1 & (v2 = % 13.37/2.58 | 0 | v1 = 0))) % 13.37/2.58 | (26) ! [v0: $i] : ! [v1: any] : ( ~ (in(v0, all_71_5) = v1) | ~ $i(v0) | % 13.37/2.58 | ? [v2: any] : ? [v3: any] : (in(v0, all_71_1) = v2 & in(v0, % 13.37/2.58 | all_71_2) = v3 & ( ~ (v2 = 0) | (v1 = 0 & ~ (v3 = 0))))) % 13.37/2.58 | % 13.37/2.58 | BETA: splitting (21) gives: % 13.37/2.58 | % 13.37/2.58 | Case 1: % 13.37/2.58 | | % 13.37/2.58 | | (27) all_71_0 = 0 % 13.37/2.58 | | % 13.37/2.58 | | REDUCE: (8), (27) imply: % 13.37/2.58 | | (28) $false % 13.37/2.58 | | % 13.37/2.58 | | CLOSE: (28) is inconsistent. % 13.37/2.58 | | % 13.37/2.58 | Case 2: % 13.37/2.58 | | % 13.37/2.58 | | (29) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_71_1) = v1 & % 13.37/2.58 | | in(v0, all_71_6) = 0 & $i(v0)) % 13.37/2.58 | | % 13.37/2.58 | | DELTA: instantiating (29) with fresh symbols all_94_0, all_94_1 gives: % 13.37/2.58 | | (30) ~ (all_94_0 = 0) & in(all_94_1, all_71_1) = all_94_0 & in(all_94_1, % 13.37/2.58 | | all_71_6) = 0 & $i(all_94_1) % 13.37/2.58 | | % 13.37/2.58 | | ALPHA: (30) implies: % 13.37/2.58 | | (31) ~ (all_94_0 = 0) % 13.37/2.58 | | (32) $i(all_94_1) % 13.37/2.58 | | (33) in(all_94_1, all_71_6) = 0 % 13.37/2.58 | | (34) in(all_94_1, all_71_1) = all_94_0 % 13.37/2.58 | | % 13.37/2.58 | | BETA: splitting (20) gives: % 13.37/2.58 | | % 13.37/2.58 | | Case 1: % 13.37/2.58 | | | % 13.37/2.58 | | | (35) all_71_0 = 0 % 13.37/2.58 | | | % 13.37/2.58 | | | REDUCE: (8), (35) imply: % 13.37/2.58 | | | (36) $false % 13.37/2.58 | | | % 13.37/2.58 | | | CLOSE: (36) is inconsistent. % 13.37/2.58 | | | % 13.37/2.58 | | Case 2: % 13.37/2.58 | | | % 13.37/2.58 | | | % 13.37/2.58 | | | GROUND_INST: instantiating (19) with all_94_1, simplifying with (32), (33) % 13.37/2.58 | | | gives: % 13.37/2.58 | | | (37) in(all_94_1, all_71_5) = 0 % 13.37/2.58 | | | % 13.37/2.59 | | | GROUND_INST: instantiating (25) with all_94_1, simplifying with (32), (37) % 13.37/2.59 | | | gives: % 13.37/2.59 | | | (38) ? [v0: any] : ? [v1: any] : (in(all_94_1, all_71_1) = v1 & % 13.37/2.59 | | | in(all_94_1, all_71_2) = v0 & (v1 = 0 | v0 = 0)) % 13.37/2.59 | | | % 13.37/2.59 | | | GROUND_INST: instantiating (26) with all_94_1, 0, simplifying with (32), % 13.37/2.59 | | | (37) gives: % 13.37/2.59 | | | (39) ? [v0: any] : ? [v1: any] : (in(all_94_1, all_71_1) = v0 & % 13.37/2.59 | | | in(all_94_1, all_71_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 13.37/2.59 | | | % 13.37/2.59 | | | DELTA: instantiating (39) with fresh symbols all_132_0, all_132_1 gives: % 13.37/2.59 | | | (40) in(all_94_1, all_71_1) = all_132_1 & in(all_94_1, all_71_2) = % 13.37/2.59 | | | all_132_0 & ( ~ (all_132_0 = 0) | ~ (all_132_1 = 0)) % 13.37/2.59 | | | % 13.37/2.59 | | | ALPHA: (40) implies: % 13.37/2.59 | | | (41) in(all_94_1, all_71_2) = all_132_0 % 13.37/2.59 | | | (42) in(all_94_1, all_71_1) = all_132_1 % 13.37/2.59 | | | % 13.37/2.59 | | | DELTA: instantiating (38) with fresh symbols all_134_0, all_134_1 gives: % 13.37/2.59 | | | (43) in(all_94_1, all_71_1) = all_134_0 & in(all_94_1, all_71_2) = % 13.37/2.59 | | | all_134_1 & (all_134_0 = 0 | all_134_1 = 0) % 13.37/2.59 | | | % 13.37/2.59 | | | ALPHA: (43) implies: % 13.37/2.59 | | | (44) in(all_94_1, all_71_2) = all_134_1 % 13.37/2.59 | | | (45) in(all_94_1, all_71_1) = all_134_0 % 13.37/2.59 | | | (46) all_134_0 = 0 | all_134_1 = 0 % 13.37/2.59 | | | % 13.37/2.59 | | | GROUND_INST: instantiating (5) with all_132_0, all_134_1, all_71_2, % 13.37/2.59 | | | all_94_1, simplifying with (41), (44) gives: % 13.37/2.59 | | | (47) all_134_1 = all_132_0 % 13.37/2.59 | | | % 13.37/2.59 | | | GROUND_INST: instantiating (5) with all_94_0, all_134_0, all_71_1, % 13.37/2.59 | | | all_94_1, simplifying with (34), (45) gives: % 13.37/2.59 | | | (48) all_134_0 = all_94_0 % 13.37/2.59 | | | % 13.37/2.59 | | | GROUND_INST: instantiating (5) with all_132_1, all_134_0, all_71_1, % 13.37/2.59 | | | all_94_1, simplifying with (42), (45) gives: % 13.37/2.59 | | | (49) all_134_0 = all_132_1 % 13.37/2.59 | | | % 13.37/2.59 | | | COMBINE_EQS: (48), (49) imply: % 13.37/2.59 | | | (50) all_132_1 = all_94_0 % 13.37/2.59 | | | % 13.37/2.59 | | | BETA: splitting (46) gives: % 13.37/2.59 | | | % 13.37/2.59 | | | Case 1: % 13.37/2.59 | | | | % 13.37/2.59 | | | | (51) all_134_0 = 0 % 13.37/2.59 | | | | % 13.37/2.59 | | | | COMBINE_EQS: (48), (51) imply: % 13.37/2.59 | | | | (52) all_94_0 = 0 % 13.37/2.59 | | | | % 13.37/2.59 | | | | REDUCE: (31), (52) imply: % 13.37/2.59 | | | | (53) $false % 13.37/2.59 | | | | % 13.37/2.59 | | | | CLOSE: (53) is inconsistent. % 13.37/2.59 | | | | % 13.37/2.59 | | | Case 2: % 13.37/2.59 | | | | % 13.37/2.59 | | | | (54) all_134_1 = 0 % 13.37/2.59 | | | | % 13.37/2.59 | | | | COMBINE_EQS: (47), (54) imply: % 13.37/2.59 | | | | (55) all_132_0 = 0 % 13.37/2.59 | | | | % 13.37/2.59 | | | | REDUCE: (41), (55) imply: % 13.37/2.59 | | | | (56) in(all_94_1, all_71_2) = 0 % 13.37/2.59 | | | | % 13.37/2.59 | | | | GROUND_INST: instantiating (23) with all_94_1, simplifying with (32), % 13.37/2.59 | | | | (56) gives: % 13.37/2.59 | | | | (57) all_94_1 = all_71_4 % 13.37/2.59 | | | | % 13.37/2.59 | | | | REDUCE: (33), (57) imply: % 13.37/2.59 | | | | (58) in(all_71_4, all_71_6) = 0 % 13.37/2.59 | | | | % 13.37/2.59 | | | | GROUND_INST: instantiating (5) with all_71_3, 0, all_71_6, all_71_4, % 13.37/2.59 | | | | simplifying with (14), (58) gives: % 13.37/2.59 | | | | (59) all_71_3 = 0 % 13.37/2.59 | | | | % 13.37/2.59 | | | | REDUCE: (7), (59) imply: % 13.37/2.59 | | | | (60) $false % 13.37/2.59 | | | | % 13.37/2.59 | | | | CLOSE: (60) is inconsistent. % 13.37/2.59 | | | | % 13.37/2.59 | | | End of split % 13.37/2.59 | | | % 13.37/2.59 | | End of split % 13.37/2.59 | | % 13.37/2.59 | End of split % 13.37/2.59 | % 13.37/2.59 End of proof % 13.37/2.59 % SZS output end Proof for theBenchmark % 13.37/2.59 % 13.37/2.59 1981ms %------------------------------------------------------------------------------