%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU155+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 : n011.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 17:42:50 EDT 2023 % Result : Theorem 11.68s 2.38s % Output : Proof 14.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU155+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n011.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 : Wed Aug 23 16:30:51 EDT 2023 % 0.14/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.37/1.18 Prover 4: Preprocessing ... % 3.37/1.18 Prover 1: Preprocessing ... % 3.37/1.22 Prover 5: Preprocessing ... % 3.37/1.22 Prover 2: Preprocessing ... % 3.37/1.22 Prover 0: Preprocessing ... % 3.37/1.22 Prover 6: Preprocessing ... % 3.37/1.22 Prover 3: Preprocessing ... % 8.89/1.97 Prover 1: Warning: ignoring some quantifiers % 8.89/1.99 Prover 5: Proving ... % 9.34/2.03 Prover 1: Constructing countermodel ... % 9.34/2.12 Prover 6: Proving ... % 9.34/2.13 Prover 3: Warning: ignoring some quantifiers % 9.34/2.13 Prover 4: Warning: ignoring some quantifiers % 9.34/2.19 Prover 3: Constructing countermodel ... % 9.98/2.23 Prover 2: Proving ... % 9.98/2.26 Prover 4: Constructing countermodel ... % 9.98/2.29 Prover 0: Proving ... % 11.68/2.38 Prover 3: proved (1732ms) % 11.68/2.38 % 11.68/2.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.68/2.38 % 11.68/2.38 Prover 2: stopped % 11.68/2.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.68/2.38 Prover 5: stopped % 11.68/2.38 Prover 0: stopped % 11.68/2.40 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.68/2.40 Prover 6: stopped % 11.68/2.40 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.68/2.40 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.68/2.40 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.68/2.42 Prover 1: Found proof (size 23) % 11.68/2.42 Prover 1: proved (1786ms) % 11.68/2.43 Prover 4: stopped % 12.39/2.47 Prover 7: Preprocessing ... % 12.39/2.49 Prover 8: Preprocessing ... % 12.39/2.49 Prover 13: Preprocessing ... % 12.81/2.50 Prover 11: Preprocessing ... % 12.81/2.50 Prover 10: Preprocessing ... % 12.81/2.53 Prover 7: stopped % 13.27/2.55 Prover 10: stopped % 13.27/2.57 Prover 13: stopped % 13.27/2.58 Prover 11: stopped % 13.78/2.67 Prover 8: Warning: ignoring some quantifiers % 13.78/2.69 Prover 8: Constructing countermodel ... % 13.99/2.71 Prover 8: stopped % 13.99/2.71 % 13.99/2.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.99/2.71 % 13.99/2.71 % SZS output start Proof for theBenchmark % 13.99/2.72 Assumptions after simplification: % 13.99/2.72 --------------------------------- % 13.99/2.72 % 13.99/2.72 (d3_tarski) % 14.20/2.74 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 14.20/2.74 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, % 14.20/2.74 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 14.20/2.74 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) % 14.20/2.74 = 0) | ~ $i(v2) | in(v2, v1) = 0)) % 14.20/2.74 % 14.20/2.74 (d4_tarski) % 14.20/2.75 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (union(v1) = v2) | ~ % 14.20/2.75 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 & $i(v3) % 14.20/2.75 & ( ~ (v4 = 0) | ! [v5: $i] : ( ~ (in(v3, v5) = 0) | ~ $i(v5) | ? [v6: % 14.20/2.75 int] : ( ~ (v6 = 0) & in(v5, v1) = v6))) & (v4 = 0 | ? [v5: $i] : % 14.20/2.75 (in(v5, v1) = 0 & in(v3, v5) = 0 & $i(v5))))) & ! [v0: $i] : ! [v1: % 14.20/2.75 $i] : ( ~ (union(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: % 14.20/2.75 int] : (v3 = 0 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ % 14.20/2.75 (in(v2, v4) = 0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & in(v4, % 14.20/2.75 v0) = v5))) & ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? % 14.20/2.75 [v3: $i] : (in(v3, v0) = 0 & in(v2, v3) = 0 & $i(v3))))) % 14.20/2.75 % 14.20/2.75 (l50_zfmisc_1) % 14.20/2.75 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 14.20/2.75 union(v1) = v2 & subset(v0, v2) = v3 & in(v0, v1) = 0 & $i(v2) & $i(v1) & % 14.20/2.75 $i(v0)) % 14.20/2.75 % 14.20/2.75 (function-axioms) % 14.20/2.76 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 14.20/2.76 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 14.20/2.76 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.20/2.76 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 14.20/2.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.20/2.76 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 14.20/2.76 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.20/2.76 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 14.20/2.76 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.20/2.76 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! % 14.20/2.76 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = % 14.20/2.76 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 14.20/2.76 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.20/2.76 (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0: % 14.20/2.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.20/2.76 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 14.20/2.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 14.20/2.76 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 14.20/2.76 [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0: $i] % 14.20/2.76 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ % 14.20/2.76 (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 14.20/2.76 ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 14.20/2.76 % 14.20/2.76 Further assumptions not needed in the proof: % 14.20/2.76 -------------------------------------------- % 14.20/2.76 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski, % 14.20/2.76 commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_xboole_0, d1_tarski, % 14.20/2.76 d1_xboole_0, d1_zfmisc_1, d2_tarski, d2_xboole_0, d3_xboole_0, d4_xboole_0, % 14.20/2.76 d7_xboole_0, d8_xboole_0, dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, % 14.20/2.76 dt_k2_tarski, dt_k2_xboole_0, dt_k3_tarski, dt_k3_xboole_0, dt_k4_xboole_0, % 14.20/2.76 fc1_xboole_0, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, % 14.20/2.76 idempotence_k3_xboole_0, irreflexivity_r2_xboole_0, l1_zfmisc_1, l23_zfmisc_1, % 14.20/2.76 l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, l3_zfmisc_1, l4_zfmisc_1, % 14.20/2.76 rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski, symmetry_r1_xboole_0, % 14.20/2.76 t10_zfmisc_1, t12_xboole_1, t17_xboole_1, t19_xboole_1, t1_boole, t1_xboole_1, % 14.20/2.76 t1_zfmisc_1, t26_xboole_1, t28_xboole_1, t2_boole, t2_tarski, t2_xboole_1, % 14.20/2.76 t33_xboole_1, t36_xboole_1, t37_xboole_1, t39_xboole_1, t3_boole, t3_xboole_0, % 14.20/2.76 t3_xboole_1, t40_xboole_1, t45_xboole_1, t48_xboole_1, t4_boole, t4_xboole_0, % 14.20/2.76 t60_xboole_1, t63_xboole_1, t69_enumset1, t6_boole, t6_zfmisc_1, t7_boole, % 14.20/2.76 t7_xboole_1, t83_xboole_1, t8_boole, t8_xboole_1, t8_zfmisc_1, t9_zfmisc_1 % 14.20/2.76 % 14.20/2.76 Those formulas are unsatisfiable: % 14.20/2.76 --------------------------------- % 14.20/2.76 % 14.20/2.76 Begin of proof % 14.20/2.76 | % 14.20/2.76 | ALPHA: (d3_tarski) implies: % 14.20/2.76 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 14.20/2.76 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 14.20/2.76 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 14.20/2.76 | % 14.20/2.76 | ALPHA: (d4_tarski) implies: % 14.20/2.76 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (union(v0) = v1) | ~ $i(v1) | ~ % 14.20/2.76 | $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2, v1) = v3) % 14.20/2.76 | | ~ $i(v2) | ! [v4: $i] : ( ~ (in(v2, v4) = 0) | ~ $i(v4) | ? % 14.20/2.76 | [v5: int] : ( ~ (v5 = 0) & in(v4, v0) = v5))) & ! [v2: $i] : ( % 14.20/2.76 | ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : (in(v3, v0) = 0 & % 14.20/2.76 | in(v2, v3) = 0 & $i(v3))))) % 14.20/2.77 | % 14.20/2.77 | ALPHA: (function-axioms) implies: % 14.20/2.77 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 14.20/2.77 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 14.20/2.77 | % 14.20/2.77 | DELTA: instantiating (l50_zfmisc_1) with fresh symbols all_81_0, all_81_1, % 14.20/2.77 | all_81_2, all_81_3 gives: % 14.20/2.77 | (4) ~ (all_81_0 = 0) & union(all_81_2) = all_81_1 & subset(all_81_3, % 14.20/2.77 | all_81_1) = all_81_0 & in(all_81_3, all_81_2) = 0 & $i(all_81_1) & % 14.20/2.77 | $i(all_81_2) & $i(all_81_3) % 14.20/2.77 | % 14.20/2.77 | ALPHA: (4) implies: % 14.20/2.77 | (5) ~ (all_81_0 = 0) % 14.20/2.77 | (6) $i(all_81_3) % 14.20/2.77 | (7) $i(all_81_2) % 14.20/2.77 | (8) $i(all_81_1) % 14.20/2.77 | (9) in(all_81_3, all_81_2) = 0 % 14.20/2.77 | (10) subset(all_81_3, all_81_1) = all_81_0 % 14.20/2.77 | (11) union(all_81_2) = all_81_1 % 14.20/2.77 | % 14.20/2.77 | GROUND_INST: instantiating (1) with all_81_3, all_81_1, all_81_0, simplifying % 14.20/2.77 | with (6), (8), (10) gives: % 14.20/2.77 | (12) all_81_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 14.20/2.77 | all_81_1) = v1 & in(v0, all_81_3) = 0 & $i(v0)) % 14.20/2.77 | % 14.20/2.77 | GROUND_INST: instantiating (2) with all_81_2, all_81_1, simplifying with (7), % 14.20/2.77 | (8), (11) gives: % 14.20/2.77 | (13) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_81_1) = v1) | ~ % 14.20/2.77 | $i(v0) | ! [v2: $i] : ( ~ (in(v0, v2) = 0) | ~ $i(v2) | ? [v3: % 14.20/2.77 | int] : ( ~ (v3 = 0) & in(v2, all_81_2) = v3))) & ! [v0: $i] : ( % 14.20/2.77 | ~ (in(v0, all_81_1) = 0) | ~ $i(v0) | ? [v1: $i] : (in(v1, % 14.20/2.77 | all_81_2) = 0 & in(v0, v1) = 0 & $i(v1))) % 14.20/2.77 | % 14.20/2.77 | ALPHA: (13) implies: % 14.20/2.77 | (14) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_81_1) = v1) | ~ % 14.20/2.77 | $i(v0) | ! [v2: $i] : ( ~ (in(v0, v2) = 0) | ~ $i(v2) | ? [v3: % 14.20/2.77 | int] : ( ~ (v3 = 0) & in(v2, all_81_2) = v3))) % 14.20/2.77 | % 14.20/2.77 | BETA: splitting (12) gives: % 14.20/2.77 | % 14.20/2.77 | Case 1: % 14.20/2.77 | | % 14.20/2.77 | | (15) all_81_0 = 0 % 14.20/2.77 | | % 14.20/2.77 | | REDUCE: (5), (15) imply: % 14.20/2.77 | | (16) $false % 14.20/2.77 | | % 14.20/2.77 | | CLOSE: (16) is inconsistent. % 14.20/2.77 | | % 14.20/2.78 | Case 2: % 14.20/2.78 | | % 14.20/2.78 | | (17) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_81_1) = v1 & % 14.20/2.78 | | in(v0, all_81_3) = 0 & $i(v0)) % 14.20/2.78 | | % 14.20/2.78 | | DELTA: instantiating (17) with fresh symbols all_115_0, all_115_1 gives: % 14.20/2.78 | | (18) ~ (all_115_0 = 0) & in(all_115_1, all_81_1) = all_115_0 & % 14.20/2.78 | | in(all_115_1, all_81_3) = 0 & $i(all_115_1) % 14.20/2.78 | | % 14.20/2.78 | | ALPHA: (18) implies: % 14.20/2.78 | | (19) ~ (all_115_0 = 0) % 14.20/2.78 | | (20) $i(all_115_1) % 14.20/2.78 | | (21) in(all_115_1, all_81_3) = 0 % 14.20/2.78 | | (22) in(all_115_1, all_81_1) = all_115_0 % 14.20/2.78 | | % 14.20/2.78 | | GROUND_INST: instantiating (14) with all_115_1, all_115_0, simplifying with % 14.20/2.78 | | (20), (22) gives: % 14.20/2.78 | | (23) all_115_0 = 0 | ! [v0: $i] : ( ~ (in(all_115_1, v0) = 0) | ~ % 14.20/2.78 | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_81_2) = v1)) % 14.20/2.78 | | % 14.20/2.78 | | BETA: splitting (23) gives: % 14.20/2.78 | | % 14.20/2.78 | | Case 1: % 14.20/2.78 | | | % 14.20/2.78 | | | (24) all_115_0 = 0 % 14.20/2.78 | | | % 14.20/2.78 | | | REDUCE: (19), (24) imply: % 14.20/2.78 | | | (25) $false % 14.20/2.78 | | | % 14.20/2.78 | | | CLOSE: (25) is inconsistent. % 14.20/2.78 | | | % 14.20/2.78 | | Case 2: % 14.20/2.78 | | | % 14.20/2.78 | | | (26) ! [v0: $i] : ( ~ (in(all_115_1, v0) = 0) | ~ $i(v0) | ? [v1: % 14.20/2.78 | | | int] : ( ~ (v1 = 0) & in(v0, all_81_2) = v1)) % 14.20/2.78 | | | % 14.20/2.78 | | | GROUND_INST: instantiating (26) with all_81_3, simplifying with (6), (21) % 14.20/2.78 | | | gives: % 14.20/2.78 | | | (27) ? [v0: int] : ( ~ (v0 = 0) & in(all_81_3, all_81_2) = v0) % 14.20/2.78 | | | % 14.20/2.78 | | | DELTA: instantiating (27) with fresh symbol all_131_0 gives: % 14.20/2.78 | | | (28) ~ (all_131_0 = 0) & in(all_81_3, all_81_2) = all_131_0 % 14.20/2.78 | | | % 14.20/2.78 | | | ALPHA: (28) implies: % 14.20/2.78 | | | (29) ~ (all_131_0 = 0) % 14.20/2.78 | | | (30) in(all_81_3, all_81_2) = all_131_0 % 14.20/2.78 | | | % 14.20/2.78 | | | GROUND_INST: instantiating (3) with 0, all_131_0, all_81_2, all_81_3, % 14.20/2.78 | | | simplifying with (9), (30) gives: % 14.20/2.78 | | | (31) all_131_0 = 0 % 14.20/2.78 | | | % 14.20/2.78 | | | REDUCE: (29), (31) imply: % 14.20/2.78 | | | (32) $false % 14.20/2.78 | | | % 14.20/2.78 | | | CLOSE: (32) is inconsistent. % 14.20/2.78 | | | % 14.20/2.78 | | End of split % 14.20/2.78 | | % 14.20/2.78 | End of split % 14.20/2.78 | % 14.20/2.78 End of proof % 14.20/2.78 % SZS output end Proof for theBenchmark % 14.20/2.78 % 14.20/2.78 2166ms %------------------------------------------------------------------------------