%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU165+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 : n024.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 17:42:58 EDT 2023 % Result : Theorem 13.21s 2.57s % Output : Proof 16.59s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SEU165+2 : TPTP v8.1.2. Released v3.3.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n024.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 18:48:39 EDT 2023 % 0.13/0.34 % 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 ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.42/1.19 Prover 1: Preprocessing ... % 3.42/1.20 Prover 4: Preprocessing ... % 3.99/1.23 Prover 3: Preprocessing ... % 3.99/1.23 Prover 6: Preprocessing ... % 3.99/1.23 Prover 0: Preprocessing ... % 3.99/1.23 Prover 2: Preprocessing ... % 3.99/1.25 Prover 5: Preprocessing ... % 10.34/2.18 Prover 5: Proving ... % 10.34/2.19 Prover 1: Warning: ignoring some quantifiers % 10.93/2.27 Prover 1: Constructing countermodel ... % 11.54/2.28 Prover 6: Proving ... % 11.72/2.31 Prover 4: Warning: ignoring some quantifiers % 11.87/2.33 Prover 3: Warning: ignoring some quantifiers % 11.87/2.36 Prover 3: Constructing countermodel ... % 12.61/2.42 Prover 2: Proving ... % 12.61/2.43 Prover 4: Constructing countermodel ... % 12.61/2.46 Prover 0: Proving ... % 13.21/2.57 Prover 3: proved (1920ms) % 13.21/2.57 % 13.21/2.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.21/2.57 % 13.21/2.57 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.21/2.57 Prover 2: stopped % 13.84/2.58 Prover 5: stopped % 13.84/2.60 Prover 6: stopped % 13.84/2.60 Prover 0: stopped % 13.84/2.60 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.84/2.60 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.84/2.60 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.84/2.60 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.59/2.71 Prover 7: Preprocessing ... % 14.72/2.73 Prover 10: Preprocessing ... % 14.72/2.74 Prover 8: Preprocessing ... % 14.72/2.75 Prover 11: Preprocessing ... % 14.72/2.75 Prover 13: Preprocessing ... % 15.47/2.82 Prover 1: Found proof (size 49) % 15.47/2.83 Prover 1: proved (2182ms) % 15.47/2.83 Prover 10: stopped % 15.47/2.83 Prover 4: stopped % 15.47/2.83 Prover 13: stopped % 15.47/2.83 Prover 11: stopped % 15.47/2.87 Prover 7: Warning: ignoring some quantifiers % 15.97/2.90 Prover 7: Constructing countermodel ... % 15.97/2.92 Prover 7: stopped % 15.97/2.95 Prover 8: Warning: ignoring some quantifiers % 15.97/2.97 Prover 8: Constructing countermodel ... % 16.41/2.99 Prover 8: stopped % 16.41/2.99 % 16.41/2.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 16.41/2.99 % 16.41/2.99 % SZS output start Proof for theBenchmark % 16.50/3.00 Assumptions after simplification: % 16.50/3.00 --------------------------------- % 16.50/3.00 % 16.50/3.00 (d2_zfmisc_1) % 16.59/3.03 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 16.59/3.04 (cartesian_product2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 16.59/3.04 [v4: $i] : ? [v5: any] : (in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ! [v6: % 16.59/3.04 $i] : ! [v7: $i] : ( ~ (ordered_pair(v6, v7) = v4) | ~ $i(v7) | ~ % 16.59/3.04 $i(v6) | ? [v8: any] : ? [v9: any] : (in(v7, v2) = v9 & in(v6, v1) = % 16.59/3.04 v8 & ( ~ (v9 = 0) | ~ (v8 = 0))))) & (v5 = 0 | ? [v6: $i] : ? % 16.59/3.04 [v7: $i] : (ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0 % 16.59/3.04 & $i(v7) & $i(v6))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 16.59/3.04 (cartesian_product2(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! % 16.59/3.04 [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | ! % 16.59/3.04 [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v6) = v3) | ~ $i(v6) | % 16.59/3.04 ~ $i(v5) | ? [v7: any] : ? [v8: any] : (in(v6, v1) = v8 & in(v5, v0) % 16.59/3.04 = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))) & ! [v3: $i] : ( ~ (in(v3, % 16.59/3.04 v2) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: $i] : (ordered_pair(v4, % 16.59/3.04 v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0 & $i(v5) & $i(v4))))) % 16.59/3.04 % 16.59/3.04 (l55_zfmisc_1) % 16.59/3.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 16.59/3.04 $i] : ! [v6: int] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = v5) | ~ % 16.59/3.04 (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ~ $i(v3) | ~ $i(v2) | % 16.59/3.04 ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : (in(v1, v3) = v8 & % 16.59/3.04 in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0: $i] : ! [v1: % 16.59/3.04 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 16.59/3.04 (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ % 16.59/3.04 (in(v4, v5) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v1, % 16.59/3.04 v3) = 0 & in(v0, v2) = 0)) % 16.59/3.04 % 16.59/3.04 (t106_zfmisc_1) % 16.59/3.04 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 16.59/3.04 $i] : ? [v6: any] : ? [v7: any] : ? [v8: any] : (cartesian_product2(v2, % 16.59/3.04 v3) = v5 & ordered_pair(v0, v1) = v4 & in(v4, v5) = v6 & in(v1, v3) = v8 & % 16.59/3.04 in(v0, v2) = v7 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v8 % 16.59/3.04 = 0 & v7 = 0 & ~ (v6 = 0)) | (v6 = 0 & ( ~ (v8 = 0) | ~ (v7 = 0))))) % 16.59/3.04 % 16.59/3.04 (function-axioms) % 16.59/3.05 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 16.59/3.05 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 16.59/3.05 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.59/3.05 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 16.59/3.05 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.59/3.05 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & % 16.59/3.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.59/3.05 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: % 16.59/3.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 16.59/3.05 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 16.59/3.05 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.59/3.05 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 16.59/3.05 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.59/3.05 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! % 16.59/3.05 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = % 16.59/3.05 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 16.59/3.05 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.59/3.05 (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0: % 16.59/3.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 16.59/3.05 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 16.59/3.05 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 16.59/3.05 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 16.59/3.05 [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0: $i] % 16.59/3.05 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ % 16.59/3.05 (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | % 16.59/3.05 ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 16.59/3.05 % 16.59/3.05 Further assumptions not needed in the proof: % 16.59/3.05 -------------------------------------------- % 16.59/3.05 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski, % 16.59/3.05 commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_xboole_0, d1_tarski, % 16.59/3.05 d1_xboole_0, d1_zfmisc_1, d2_tarski, d2_xboole_0, d3_tarski, d3_xboole_0, % 16.59/3.05 d4_tarski, d4_xboole_0, d5_tarski, d7_xboole_0, d8_xboole_0, dt_k1_tarski, % 16.59/3.05 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski, dt_k2_xboole_0, dt_k2_zfmisc_1, % 16.59/3.05 dt_k3_tarski, dt_k3_xboole_0, dt_k4_tarski, dt_k4_xboole_0, fc1_xboole_0, % 16.59/3.05 fc1_zfmisc_1, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, % 16.59/3.05 idempotence_k3_xboole_0, irreflexivity_r2_xboole_0, l1_zfmisc_1, l23_zfmisc_1, % 16.59/3.05 l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, l3_zfmisc_1, l4_zfmisc_1, % 16.59/3.05 l50_zfmisc_1, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski, % 16.59/3.05 symmetry_r1_xboole_0, t10_zfmisc_1, t12_xboole_1, t17_xboole_1, t19_xboole_1, % 16.59/3.05 t1_boole, t1_xboole_1, t1_zfmisc_1, t26_xboole_1, t28_xboole_1, t2_boole, % 16.59/3.05 t2_tarski, t2_xboole_1, t33_xboole_1, t33_zfmisc_1, t36_xboole_1, t37_xboole_1, % 16.59/3.05 t37_zfmisc_1, t38_zfmisc_1, t39_xboole_1, t39_zfmisc_1, t3_boole, t3_xboole_0, % 16.59/3.05 t3_xboole_1, t40_xboole_1, t45_xboole_1, t46_zfmisc_1, t48_xboole_1, t4_boole, % 16.59/3.05 t4_xboole_0, t60_xboole_1, t63_xboole_1, t65_zfmisc_1, t69_enumset1, t6_boole, % 16.59/3.05 t6_zfmisc_1, t7_boole, t7_xboole_1, t83_xboole_1, t8_boole, t8_xboole_1, % 16.59/3.05 t8_zfmisc_1, t92_zfmisc_1, t99_zfmisc_1, t9_zfmisc_1 % 16.59/3.05 % 16.59/3.05 Those formulas are unsatisfiable: % 16.59/3.05 --------------------------------- % 16.59/3.05 % 16.59/3.05 Begin of proof % 16.59/3.05 | % 16.59/3.05 | ALPHA: (d2_zfmisc_1) implies: % 16.59/3.05 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cartesian_product2(v0, % 16.59/3.05 | v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! % 16.59/3.05 | [v4: int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | ! [v5: % 16.59/3.05 | $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v6) = v3) | ~ $i(v6) % 16.59/3.05 | | ~ $i(v5) | ? [v7: any] : ? [v8: any] : (in(v6, v1) = v8 & % 16.59/3.05 | in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))) & ! [v3: % 16.59/3.05 | $i] : ( ~ (in(v3, v2) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: % 16.59/3.05 | $i] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) % 16.59/3.05 | = 0 & $i(v5) & $i(v4))))) % 16.59/3.05 | % 16.59/3.05 | ALPHA: (l55_zfmisc_1) implies: % 16.59/3.05 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 16.59/3.05 | ! [v5: $i] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ % 16.59/3.05 | (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = 0) | ~ $i(v3) | ~ % 16.59/3.05 | $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v1, v3) = 0 & in(v0, v2) = 0)) % 16.59/3.05 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 16.59/3.05 | ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = % 16.59/3.05 | v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ~ % 16.59/3.05 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: % 16.59/3.05 | any] : (in(v1, v3) = v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = % 16.59/3.05 | 0)))) % 16.59/3.05 | % 16.59/3.05 | ALPHA: (function-axioms) implies: % 16.59/3.05 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 16.59/3.05 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 16.59/3.05 | % 16.59/3.05 | DELTA: instantiating (t106_zfmisc_1) with fresh symbols all_109_0, all_109_1, % 16.59/3.05 | all_109_2, all_109_3, all_109_4, all_109_5, all_109_6, all_109_7, % 16.59/3.05 | all_109_8 gives: % 16.59/3.06 | (5) cartesian_product2(all_109_6, all_109_5) = all_109_3 & % 16.59/3.06 | ordered_pair(all_109_8, all_109_7) = all_109_4 & in(all_109_4, % 16.59/3.06 | all_109_3) = all_109_2 & in(all_109_7, all_109_5) = all_109_0 & % 16.59/3.06 | in(all_109_8, all_109_6) = all_109_1 & $i(all_109_3) & $i(all_109_4) & % 16.59/3.06 | $i(all_109_5) & $i(all_109_6) & $i(all_109_7) & $i(all_109_8) & % 16.59/3.06 | ((all_109_0 = 0 & all_109_1 = 0 & ~ (all_109_2 = 0)) | (all_109_2 = 0 % 16.59/3.06 | & ( ~ (all_109_0 = 0) | ~ (all_109_1 = 0)))) % 16.59/3.06 | % 16.59/3.06 | ALPHA: (5) implies: % 16.59/3.06 | (6) $i(all_109_8) % 16.59/3.06 | (7) $i(all_109_7) % 16.59/3.06 | (8) $i(all_109_6) % 16.59/3.06 | (9) $i(all_109_5) % 16.59/3.06 | (10) $i(all_109_4) % 16.59/3.06 | (11) $i(all_109_3) % 16.59/3.06 | (12) in(all_109_8, all_109_6) = all_109_1 % 16.59/3.06 | (13) in(all_109_7, all_109_5) = all_109_0 % 16.59/3.06 | (14) in(all_109_4, all_109_3) = all_109_2 % 16.59/3.06 | (15) ordered_pair(all_109_8, all_109_7) = all_109_4 % 16.59/3.06 | (16) cartesian_product2(all_109_6, all_109_5) = all_109_3 % 16.59/3.06 | (17) (all_109_0 = 0 & all_109_1 = 0 & ~ (all_109_2 = 0)) | (all_109_2 = 0 % 16.59/3.06 | & ( ~ (all_109_0 = 0) | ~ (all_109_1 = 0))) % 16.59/3.06 | % 16.59/3.06 | GROUND_INST: instantiating (3) with all_109_8, all_109_7, all_109_6, % 16.59/3.06 | all_109_5, all_109_4, all_109_3, all_109_2, simplifying with (6), % 16.59/3.06 | (7), (8), (9), (14), (15), (16) gives: % 16.59/3.06 | (18) all_109_2 = 0 | ? [v0: any] : ? [v1: any] : (in(all_109_7, % 16.59/3.06 | all_109_5) = v1 & in(all_109_8, all_109_6) = v0 & ( ~ (v1 = 0) | % 16.59/3.06 | ~ (v0 = 0))) % 16.59/3.06 | % 16.59/3.06 | GROUND_INST: instantiating (1) with all_109_6, all_109_5, all_109_3, % 16.59/3.06 | simplifying with (8), (9), (11), (16) gives: % 16.59/3.06 | (19) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_109_3) = v1) | % 16.59/3.06 | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v3) = % 16.59/3.06 | v0) | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : % 16.59/3.06 | (in(v3, all_109_5) = v5 & in(v2, all_109_6) = v4 & ( ~ (v5 = 0) | % 16.59/3.06 | ~ (v4 = 0))))) & ! [v0: $i] : ( ~ (in(v0, all_109_3) = 0) | % 16.59/3.06 | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v2) = v0 & % 16.59/3.06 | in(v2, all_109_5) = 0 & in(v1, all_109_6) = 0 & $i(v2) & $i(v1))) % 16.59/3.06 | % 16.59/3.06 | ALPHA: (19) implies: % 16.59/3.06 | (20) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_109_3) = v1) | % 16.59/3.06 | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v3) = % 16.59/3.06 | v0) | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : % 16.59/3.06 | (in(v3, all_109_5) = v5 & in(v2, all_109_6) = v4 & ( ~ (v5 = 0) | % 16.59/3.06 | ~ (v4 = 0))))) % 16.59/3.06 | % 16.59/3.06 | GROUND_INST: instantiating (20) with all_109_4, all_109_2, simplifying with % 16.59/3.06 | (10), (14) gives: % 16.59/3.06 | (21) all_109_2 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v1) % 16.59/3.06 | = all_109_4) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] % 16.59/3.06 | : (in(v1, all_109_5) = v3 & in(v0, all_109_6) = v2 & ( ~ (v3 = 0) | % 16.59/3.06 | ~ (v2 = 0)))) % 16.59/3.06 | % 16.59/3.06 | BETA: splitting (17) gives: % 16.59/3.06 | % 16.59/3.06 | Case 1: % 16.59/3.06 | | % 16.59/3.06 | | (22) all_109_0 = 0 & all_109_1 = 0 & ~ (all_109_2 = 0) % 16.59/3.06 | | % 16.59/3.06 | | ALPHA: (22) implies: % 16.59/3.07 | | (23) all_109_1 = 0 % 16.59/3.07 | | (24) all_109_0 = 0 % 16.59/3.07 | | (25) ~ (all_109_2 = 0) % 16.59/3.07 | | % 16.59/3.07 | | REDUCE: (13), (24) imply: % 16.59/3.07 | | (26) in(all_109_7, all_109_5) = 0 % 16.59/3.07 | | % 16.59/3.07 | | REDUCE: (12), (23) imply: % 16.59/3.07 | | (27) in(all_109_8, all_109_6) = 0 % 16.59/3.07 | | % 16.59/3.07 | | BETA: splitting (18) gives: % 16.59/3.07 | | % 16.59/3.07 | | Case 1: % 16.59/3.07 | | | % 16.59/3.07 | | | (28) all_109_2 = 0 % 16.59/3.07 | | | % 16.59/3.07 | | | REDUCE: (25), (28) imply: % 16.59/3.07 | | | (29) $false % 16.59/3.07 | | | % 16.59/3.07 | | | CLOSE: (29) is inconsistent. % 16.59/3.07 | | | % 16.59/3.07 | | Case 2: % 16.59/3.07 | | | % 16.59/3.07 | | | (30) ? [v0: any] : ? [v1: any] : (in(all_109_7, all_109_5) = v1 & % 16.59/3.07 | | | in(all_109_8, all_109_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 16.59/3.07 | | | % 16.59/3.07 | | | DELTA: instantiating (30) with fresh symbols all_152_0, all_152_1 gives: % 16.59/3.07 | | | (31) in(all_109_7, all_109_5) = all_152_0 & in(all_109_8, all_109_6) = % 16.59/3.07 | | | all_152_1 & ( ~ (all_152_0 = 0) | ~ (all_152_1 = 0)) % 16.59/3.07 | | | % 16.59/3.07 | | | ALPHA: (31) implies: % 16.59/3.07 | | | (32) in(all_109_8, all_109_6) = all_152_1 % 16.59/3.07 | | | (33) in(all_109_7, all_109_5) = all_152_0 % 16.59/3.07 | | | (34) ~ (all_152_0 = 0) | ~ (all_152_1 = 0) % 16.59/3.07 | | | % 16.59/3.07 | | | BETA: splitting (21) gives: % 16.59/3.07 | | | % 16.59/3.07 | | | Case 1: % 16.59/3.07 | | | | % 16.59/3.07 | | | | (35) all_109_2 = 0 % 16.59/3.07 | | | | % 16.59/3.07 | | | | REDUCE: (25), (35) imply: % 16.59/3.07 | | | | (36) $false % 16.59/3.07 | | | | % 16.59/3.07 | | | | CLOSE: (36) is inconsistent. % 16.59/3.07 | | | | % 16.59/3.07 | | | Case 2: % 16.59/3.07 | | | | % 16.59/3.07 | | | | (37) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0, v1) = % 16.59/3.07 | | | | all_109_4) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 16.59/3.07 | | | | any] : (in(v1, all_109_5) = v3 & in(v0, all_109_6) = v2 & ( % 16.59/3.07 | | | | ~ (v3 = 0) | ~ (v2 = 0)))) % 16.59/3.07 | | | | % 16.59/3.07 | | | | DELTA: instantiating (30) with fresh symbols all_159_0, all_159_1 gives: % 16.59/3.07 | | | | (38) in(all_109_7, all_109_5) = all_159_0 & in(all_109_8, all_109_6) % 16.59/3.07 | | | | = all_159_1 & ( ~ (all_159_0 = 0) | ~ (all_159_1 = 0)) % 16.59/3.07 | | | | % 16.59/3.07 | | | | ALPHA: (38) implies: % 16.59/3.07 | | | | (39) in(all_109_8, all_109_6) = all_159_1 % 16.59/3.07 | | | | (40) in(all_109_7, all_109_5) = all_159_0 % 16.59/3.07 | | | | % 16.59/3.07 | | | | GROUND_INST: instantiating (4) with all_152_1, all_159_1, all_109_6, % 16.59/3.07 | | | | all_109_8, simplifying with (32), (39) gives: % 16.59/3.07 | | | | (41) all_159_1 = all_152_1 % 16.59/3.07 | | | | % 16.59/3.07 | | | | GROUND_INST: instantiating (4) with 0, all_159_1, all_109_6, all_109_8, % 16.59/3.07 | | | | simplifying with (27), (39) gives: % 16.59/3.07 | | | | (42) all_159_1 = 0 % 16.59/3.07 | | | | % 16.59/3.07 | | | | GROUND_INST: instantiating (4) with all_152_0, all_159_0, all_109_5, % 16.59/3.07 | | | | all_109_7, simplifying with (33), (40) gives: % 16.59/3.07 | | | | (43) all_159_0 = all_152_0 % 16.59/3.07 | | | | % 16.59/3.07 | | | | GROUND_INST: instantiating (4) with 0, all_159_0, all_109_5, all_109_7, % 16.59/3.07 | | | | simplifying with (26), (40) gives: % 16.59/3.07 | | | | (44) all_159_0 = 0 % 16.59/3.07 | | | | % 16.59/3.07 | | | | COMBINE_EQS: (43), (44) imply: % 16.59/3.07 | | | | (45) all_152_0 = 0 % 16.59/3.07 | | | | % 16.59/3.07 | | | | SIMP: (45) implies: % 16.59/3.07 | | | | (46) all_152_0 = 0 % 16.59/3.07 | | | | % 16.59/3.07 | | | | COMBINE_EQS: (41), (42) imply: % 16.59/3.07 | | | | (47) all_152_1 = 0 % 16.59/3.07 | | | | % 16.59/3.07 | | | | SIMP: (47) implies: % 16.59/3.07 | | | | (48) all_152_1 = 0 % 16.59/3.07 | | | | % 16.59/3.07 | | | | BETA: splitting (34) gives: % 16.59/3.07 | | | | % 16.59/3.07 | | | | Case 1: % 16.59/3.07 | | | | | % 16.59/3.07 | | | | | (49) ~ (all_152_0 = 0) % 16.59/3.07 | | | | | % 16.59/3.07 | | | | | REDUCE: (46), (49) imply: % 16.59/3.07 | | | | | (50) $false % 16.59/3.07 | | | | | % 16.59/3.07 | | | | | CLOSE: (50) is inconsistent. % 16.59/3.07 | | | | | % 16.59/3.07 | | | | Case 2: % 16.59/3.07 | | | | | % 16.59/3.07 | | | | | (51) ~ (all_152_1 = 0) % 16.59/3.07 | | | | | % 16.59/3.07 | | | | | REDUCE: (48), (51) imply: % 16.59/3.07 | | | | | (52) $false % 16.59/3.07 | | | | | % 16.59/3.07 | | | | | CLOSE: (52) is inconsistent. % 16.59/3.07 | | | | | % 16.59/3.08 | | | | End of split % 16.59/3.08 | | | | % 16.59/3.08 | | | End of split % 16.59/3.08 | | | % 16.59/3.08 | | End of split % 16.59/3.08 | | % 16.59/3.08 | Case 2: % 16.59/3.08 | | % 16.59/3.08 | | (53) all_109_2 = 0 & ( ~ (all_109_0 = 0) | ~ (all_109_1 = 0)) % 16.59/3.08 | | % 16.59/3.08 | | ALPHA: (53) implies: % 16.59/3.08 | | (54) all_109_2 = 0 % 16.59/3.08 | | (55) ~ (all_109_0 = 0) | ~ (all_109_1 = 0) % 16.59/3.08 | | % 16.59/3.08 | | REDUCE: (14), (54) imply: % 16.59/3.08 | | (56) in(all_109_4, all_109_3) = 0 % 16.59/3.08 | | % 16.59/3.08 | | GROUND_INST: instantiating (2) with all_109_8, all_109_7, all_109_6, % 16.59/3.08 | | all_109_5, all_109_4, all_109_3, simplifying with (6), (7), % 16.59/3.08 | | (8), (9), (15), (16), (56) gives: % 16.59/3.08 | | (57) in(all_109_7, all_109_5) = 0 & in(all_109_8, all_109_6) = 0 % 16.59/3.08 | | % 16.59/3.08 | | ALPHA: (57) implies: % 16.59/3.08 | | (58) in(all_109_8, all_109_6) = 0 % 16.59/3.08 | | (59) in(all_109_7, all_109_5) = 0 % 16.59/3.08 | | % 16.59/3.08 | | GROUND_INST: instantiating (4) with all_109_1, 0, all_109_6, all_109_8, % 16.59/3.08 | | simplifying with (12), (58) gives: % 16.59/3.08 | | (60) all_109_1 = 0 % 16.59/3.08 | | % 16.59/3.08 | | GROUND_INST: instantiating (4) with all_109_0, 0, all_109_5, all_109_7, % 16.59/3.08 | | simplifying with (13), (59) gives: % 16.59/3.08 | | (61) all_109_0 = 0 % 16.59/3.08 | | % 16.59/3.08 | | BETA: splitting (55) gives: % 16.59/3.08 | | % 16.59/3.08 | | Case 1: % 16.59/3.08 | | | % 16.59/3.08 | | | (62) ~ (all_109_0 = 0) % 16.59/3.08 | | | % 16.59/3.08 | | | REDUCE: (61), (62) imply: % 16.59/3.08 | | | (63) $false % 16.59/3.08 | | | % 16.59/3.08 | | | CLOSE: (63) is inconsistent. % 16.59/3.08 | | | % 16.59/3.08 | | Case 2: % 16.59/3.08 | | | % 16.59/3.08 | | | (64) ~ (all_109_1 = 0) % 16.59/3.08 | | | % 16.59/3.08 | | | REDUCE: (60), (64) imply: % 16.59/3.08 | | | (65) $false % 16.59/3.08 | | | % 16.59/3.08 | | | CLOSE: (65) is inconsistent. % 16.59/3.08 | | | % 16.59/3.08 | | End of split % 16.59/3.08 | | % 16.59/3.08 | End of split % 16.59/3.08 | % 16.59/3.08 End of proof % 16.59/3.08 % SZS output end Proof for theBenchmark % 16.59/3.08 % 16.59/3.08 2466ms %------------------------------------------------------------------------------