%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET979+1 : TPTP v8.1.2. Released v3.2.0. % 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 15:27:16 EDT 2023 % Result : Theorem 5.51s 1.50s % Output : Proof 7.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SET979+1 : TPTP v8.1.2. Released v3.2.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n011.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sat Aug 26 09:15:54 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.65 ________ _____ % 0.20/0.65 ___ __ \_________(_)________________________________ % 0.20/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.65 % 0.20/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.65 (2023-06-19) % 0.20/0.65 % 0.20/0.65 (c) Philipp Rümmer, 2009-2023 % 0.20/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.65 Amanda Stjerna. % 0.20/0.65 Free software under BSD-3-Clause. % 0.20/0.65 % 0.20/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.65 % 0.20/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.66 Running up to 7 provers in parallel. % 0.20/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.98/1.02 Prover 4: Preprocessing ... % 1.98/1.02 Prover 1: Preprocessing ... % 2.52/1.06 Prover 3: Preprocessing ... % 2.52/1.06 Prover 6: Preprocessing ... % 2.52/1.06 Prover 5: Preprocessing ... % 2.52/1.06 Prover 0: Preprocessing ... % 2.52/1.06 Prover 2: Preprocessing ... % 3.11/1.26 Prover 1: Warning: ignoring some quantifiers % 3.11/1.26 Prover 3: Warning: ignoring some quantifiers % 3.11/1.28 Prover 1: Constructing countermodel ... % 3.11/1.28 Prover 3: Constructing countermodel ... % 3.80/1.28 Prover 6: Proving ... % 3.80/1.30 Prover 4: Constructing countermodel ... % 3.80/1.30 Prover 5: Proving ... % 3.80/1.32 Prover 0: Proving ... % 4.50/1.37 Prover 2: Proving ... % 5.51/1.49 Prover 3: proved (827ms) % 5.51/1.49 % 5.51/1.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 5.51/1.50 % 5.51/1.50 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.51/1.50 Prover 5: stopped % 5.51/1.50 Prover 0: stopped % 5.51/1.51 Prover 2: stopped % 5.51/1.52 Prover 6: stopped % 5.51/1.52 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.51/1.52 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.51/1.52 Prover 7: Preprocessing ... % 5.51/1.52 Prover 8: Preprocessing ... % 5.51/1.52 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.51/1.52 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.51/1.54 Prover 13: Preprocessing ... % 5.51/1.54 Prover 10: Preprocessing ... % 5.51/1.54 Prover 11: Preprocessing ... % 6.13/1.57 Prover 8: Warning: ignoring some quantifiers % 6.29/1.58 Prover 8: Constructing countermodel ... % 6.29/1.59 Prover 10: Constructing countermodel ... % 6.29/1.61 Prover 13: Warning: ignoring some quantifiers % 6.29/1.61 Prover 13: Constructing countermodel ... % 6.29/1.62 Prover 11: Constructing countermodel ... % 6.59/1.62 Prover 7: Constructing countermodel ... % 6.59/1.62 Prover 4: Found proof (size 30) % 6.59/1.62 Prover 4: proved (948ms) % 6.59/1.62 Prover 8: stopped % 6.59/1.62 Prover 13: stopped % 6.59/1.62 Prover 1: stopped % 6.59/1.62 Prover 11: stopped % 6.59/1.62 Prover 7: stopped % 6.59/1.63 Prover 10: stopped % 6.59/1.63 % 6.59/1.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.59/1.63 % 6.69/1.64 % SZS output start Proof for theBenchmark % 6.69/1.64 Assumptions after simplification: % 6.69/1.64 --------------------------------- % 6.69/1.64 % 6.69/1.64 (t120_zfmisc_1) % 6.69/1.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 6.69/1.68 $i] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) % 6.69/1.68 = v3) | ~ (set_union2(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 6.69/1.68 ? [v6: $i] : (cartesian_product2(v2, v6) = v5 & set_union2(v0, v1) = v6 & % 6.69/1.68 $i(v6) & $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 6.69/1.68 : ! [v4: $i] : ! [v5: $i] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ % 6.69/1.68 (cartesian_product2(v0, v2) = v3) | ~ (set_union2(v3, v4) = v5) | ~ $i(v2) % 6.69/1.68 | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : (cartesian_product2(v6, v2) = v5 & % 6.69/1.68 set_union2(v0, v1) = v6 & $i(v6) & $i(v5))) & ! [v0: $i] : ! [v1: $i] : % 6.69/1.68 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (cartesian_product2(v3, v2) = v4) % 6.69/1.68 | ~ (set_union2(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 6.69/1.68 $i] : ? [v6: $i] : (cartesian_product2(v1, v2) = v6 & % 6.69/1.68 cartesian_product2(v0, v2) = v5 & set_union2(v5, v6) = v4 & $i(v6) & % 6.69/1.68 $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 6.69/1.68 : ! [v4: $i] : ( ~ (cartesian_product2(v2, v3) = v4) | ~ (set_union2(v0, v1) % 6.69/1.68 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : % 6.69/1.68 (cartesian_product2(v2, v1) = v6 & cartesian_product2(v2, v0) = v5 & % 6.69/1.68 set_union2(v5, v6) = v4 & $i(v6) & $i(v5) & $i(v4))) % 6.69/1.68 % 6.69/1.68 (t132_zfmisc_1) % 6.69/1.68 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 6.69/1.68 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 6.69/1.68 ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : (singleton(v1) = v7 & % 6.69/1.68 singleton(v0) = v5 & cartesian_product2(v7, v2) = v8 & % 6.69/1.68 cartesian_product2(v5, v2) = v6 & cartesian_product2(v3, v2) = v4 & % 6.69/1.69 cartesian_product2(v2, v7) = v12 & cartesian_product2(v2, v5) = v11 & % 6.69/1.69 cartesian_product2(v2, v3) = v10 & set_union2(v11, v12) = v13 & % 6.69/1.69 set_union2(v6, v8) = v9 & unordered_pair(v0, v1) = v3 & $i(v13) & $i(v12) & % 6.69/1.69 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 6.69/1.69 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v13 = v10) | ~ (v9 = v4))) % 6.69/1.69 % 6.69/1.69 (t41_enumset1) % 6.69/1.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 6.69/1.69 (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v3) = % 6.69/1.69 v4) | ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v4 & $i(v4))) & ! % 6.69/1.69 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ % 6.69/1.69 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (singleton(v1) = v4 & % 6.69/1.69 singleton(v0) = v3 & set_union2(v3, v4) = v2 & $i(v4) & $i(v3) & $i(v2))) % 6.69/1.69 % 6.69/1.69 (function-axioms) % 6.69/1.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 6.69/1.69 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & % 6.69/1.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 6.69/1.69 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! % 6.69/1.69 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = % 6.69/1.69 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 6.69/1.69 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! % 6.69/1.69 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 % 6.69/1.69 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 6.69/1.69 % 6.69/1.69 Further assumptions not needed in the proof: % 6.69/1.69 -------------------------------------------- % 6.69/1.69 commutativity_k2_tarski, commutativity_k2_xboole_0, fc2_xboole_0, fc3_xboole_0, % 6.69/1.69 idempotence_k2_xboole_0, rc1_xboole_0, rc2_xboole_0 % 6.69/1.69 % 6.69/1.69 Those formulas are unsatisfiable: % 6.69/1.69 --------------------------------- % 6.69/1.69 % 6.69/1.69 Begin of proof % 6.69/1.69 | % 6.69/1.69 | ALPHA: (t120_zfmisc_1) implies: % 6.69/1.70 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 6.69/1.70 | ! [v5: $i] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ % 6.69/1.70 | (cartesian_product2(v0, v2) = v3) | ~ (set_union2(v3, v4) = v5) | ~ % 6.69/1.70 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : % 6.69/1.70 | (cartesian_product2(v6, v2) = v5 & set_union2(v0, v1) = v6 & $i(v6) & % 6.69/1.70 | $i(v5))) % 6.69/1.70 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 6.69/1.70 | ! [v5: $i] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ % 6.69/1.70 | (cartesian_product2(v2, v0) = v3) | ~ (set_union2(v3, v4) = v5) | ~ % 6.69/1.70 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : % 6.69/1.70 | (cartesian_product2(v2, v6) = v5 & set_union2(v0, v1) = v6 & $i(v6) & % 6.69/1.70 | $i(v5))) % 6.69/1.70 | % 6.69/1.70 | ALPHA: (t41_enumset1) implies: % 6.69/1.70 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = % 6.69/1.70 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 6.69/1.70 | (singleton(v1) = v4 & singleton(v0) = v3 & set_union2(v3, v4) = v2 & % 6.69/1.70 | $i(v4) & $i(v3) & $i(v2))) % 6.69/1.70 | % 6.69/1.70 | ALPHA: (function-axioms) implies: % 6.69/1.70 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) % 6.69/1.70 | = v1) | ~ (singleton(v2) = v0)) % 6.69/1.70 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 6.69/1.70 | (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 6.69/1.70 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 6.69/1.70 | (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = % 6.69/1.70 | v0)) % 6.69/1.70 | % 6.69/1.70 | DELTA: instantiating (t132_zfmisc_1) with fresh symbols all_14_0, all_14_1, % 6.69/1.70 | all_14_2, all_14_3, all_14_4, all_14_5, all_14_6, all_14_7, all_14_8, % 6.69/1.70 | all_14_9, all_14_10, all_14_11, all_14_12, all_14_13 gives: % 6.69/1.70 | (7) singleton(all_14_12) = all_14_6 & singleton(all_14_13) = all_14_8 & % 6.69/1.70 | cartesian_product2(all_14_6, all_14_11) = all_14_5 & % 6.69/1.70 | cartesian_product2(all_14_8, all_14_11) = all_14_7 & % 6.69/1.70 | cartesian_product2(all_14_10, all_14_11) = all_14_9 & % 6.69/1.70 | cartesian_product2(all_14_11, all_14_6) = all_14_1 & % 6.69/1.70 | cartesian_product2(all_14_11, all_14_8) = all_14_2 & % 6.69/1.70 | cartesian_product2(all_14_11, all_14_10) = all_14_3 & % 6.69/1.70 | set_union2(all_14_2, all_14_1) = all_14_0 & set_union2(all_14_7, % 6.69/1.70 | all_14_5) = all_14_4 & unordered_pair(all_14_13, all_14_12) = % 6.69/1.71 | all_14_10 & $i(all_14_0) & $i(all_14_1) & $i(all_14_2) & $i(all_14_3) & % 6.69/1.71 | $i(all_14_4) & $i(all_14_5) & $i(all_14_6) & $i(all_14_7) & % 6.69/1.71 | $i(all_14_8) & $i(all_14_9) & $i(all_14_10) & $i(all_14_11) & % 6.69/1.71 | $i(all_14_12) & $i(all_14_13) & ( ~ (all_14_0 = all_14_3) | ~ % 6.69/1.71 | (all_14_4 = all_14_9)) % 6.69/1.71 | % 6.69/1.71 | ALPHA: (7) implies: % 6.69/1.71 | (8) $i(all_14_13) % 6.69/1.71 | (9) $i(all_14_12) % 6.69/1.71 | (10) $i(all_14_11) % 6.69/1.71 | (11) $i(all_14_8) % 6.69/1.71 | (12) $i(all_14_6) % 6.69/1.71 | (13) unordered_pair(all_14_13, all_14_12) = all_14_10 % 6.69/1.71 | (14) set_union2(all_14_7, all_14_5) = all_14_4 % 6.69/1.71 | (15) set_union2(all_14_2, all_14_1) = all_14_0 % 6.69/1.71 | (16) cartesian_product2(all_14_11, all_14_10) = all_14_3 % 6.69/1.71 | (17) cartesian_product2(all_14_11, all_14_8) = all_14_2 % 6.69/1.71 | (18) cartesian_product2(all_14_11, all_14_6) = all_14_1 % 6.69/1.71 | (19) cartesian_product2(all_14_10, all_14_11) = all_14_9 % 6.69/1.71 | (20) cartesian_product2(all_14_8, all_14_11) = all_14_7 % 6.69/1.71 | (21) cartesian_product2(all_14_6, all_14_11) = all_14_5 % 6.69/1.71 | (22) singleton(all_14_13) = all_14_8 % 6.69/1.71 | (23) singleton(all_14_12) = all_14_6 % 6.69/1.71 | (24) ~ (all_14_0 = all_14_3) | ~ (all_14_4 = all_14_9) % 6.69/1.71 | % 6.69/1.71 | GROUND_INST: instantiating (3) with all_14_13, all_14_12, all_14_10, % 6.69/1.71 | simplifying with (8), (9), (13) gives: % 6.69/1.71 | (25) ? [v0: $i] : ? [v1: $i] : (singleton(all_14_12) = v1 & % 6.69/1.71 | singleton(all_14_13) = v0 & set_union2(v0, v1) = all_14_10 & $i(v1) % 6.69/1.71 | & $i(v0) & $i(all_14_10)) % 6.69/1.71 | % 6.69/1.71 | GROUND_INST: instantiating (2) with all_14_8, all_14_6, all_14_11, all_14_2, % 6.69/1.71 | all_14_1, all_14_0, simplifying with (10), (11), (12), (15), % 6.69/1.71 | (17), (18) gives: % 6.69/1.71 | (26) ? [v0: $i] : (cartesian_product2(all_14_11, v0) = all_14_0 & % 6.69/1.71 | set_union2(all_14_8, all_14_6) = v0 & $i(v0) & $i(all_14_0)) % 6.69/1.71 | % 6.69/1.71 | GROUND_INST: instantiating (1) with all_14_8, all_14_6, all_14_11, all_14_7, % 6.69/1.71 | all_14_5, all_14_4, simplifying with (10), (11), (12), (14), % 6.69/1.71 | (20), (21) gives: % 6.69/1.71 | (27) ? [v0: $i] : (cartesian_product2(v0, all_14_11) = all_14_4 & % 6.69/1.71 | set_union2(all_14_8, all_14_6) = v0 & $i(v0) & $i(all_14_4)) % 6.69/1.71 | % 6.69/1.71 | DELTA: instantiating (27) with fresh symbol all_24_0 gives: % 6.69/1.71 | (28) cartesian_product2(all_24_0, all_14_11) = all_14_4 & % 6.69/1.71 | set_union2(all_14_8, all_14_6) = all_24_0 & $i(all_24_0) & % 6.69/1.71 | $i(all_14_4) % 6.69/1.71 | % 6.69/1.71 | ALPHA: (28) implies: % 6.69/1.71 | (29) set_union2(all_14_8, all_14_6) = all_24_0 % 6.69/1.71 | (30) cartesian_product2(all_24_0, all_14_11) = all_14_4 % 6.69/1.71 | % 6.69/1.71 | DELTA: instantiating (26) with fresh symbol all_26_0 gives: % 6.69/1.71 | (31) cartesian_product2(all_14_11, all_26_0) = all_14_0 & % 6.69/1.71 | set_union2(all_14_8, all_14_6) = all_26_0 & $i(all_26_0) & % 6.69/1.71 | $i(all_14_0) % 6.69/1.71 | % 6.69/1.71 | ALPHA: (31) implies: % 6.69/1.71 | (32) set_union2(all_14_8, all_14_6) = all_26_0 % 6.69/1.71 | (33) cartesian_product2(all_14_11, all_26_0) = all_14_0 % 6.69/1.71 | % 6.69/1.71 | DELTA: instantiating (25) with fresh symbols all_34_0, all_34_1 gives: % 7.08/1.71 | (34) singleton(all_14_12) = all_34_0 & singleton(all_14_13) = all_34_1 & % 7.08/1.71 | set_union2(all_34_1, all_34_0) = all_14_10 & $i(all_34_0) & % 7.08/1.72 | $i(all_34_1) & $i(all_14_10) % 7.08/1.72 | % 7.08/1.72 | ALPHA: (34) implies: % 7.08/1.72 | (35) set_union2(all_34_1, all_34_0) = all_14_10 % 7.08/1.72 | (36) singleton(all_14_13) = all_34_1 % 7.08/1.72 | (37) singleton(all_14_12) = all_34_0 % 7.08/1.72 | % 7.08/1.72 | GROUND_INST: instantiating (5) with all_24_0, all_26_0, all_14_6, all_14_8, % 7.08/1.72 | simplifying with (29), (32) gives: % 7.08/1.72 | (38) all_26_0 = all_24_0 % 7.08/1.72 | % 7.08/1.72 | GROUND_INST: instantiating (4) with all_14_8, all_34_1, all_14_13, simplifying % 7.08/1.72 | with (22), (36) gives: % 7.08/1.72 | (39) all_34_1 = all_14_8 % 7.08/1.72 | % 7.08/1.72 | GROUND_INST: instantiating (4) with all_14_6, all_34_0, all_14_12, simplifying % 7.08/1.72 | with (23), (37) gives: % 7.08/1.72 | (40) all_34_0 = all_14_6 % 7.08/1.72 | % 7.08/1.72 | REDUCE: (33), (38) imply: % 7.08/1.72 | (41) cartesian_product2(all_14_11, all_24_0) = all_14_0 % 7.08/1.72 | % 7.08/1.72 | REDUCE: (35), (39), (40) imply: % 7.08/1.72 | (42) set_union2(all_14_8, all_14_6) = all_14_10 % 7.08/1.72 | % 7.08/1.72 | GROUND_INST: instantiating (5) with all_24_0, all_14_10, all_14_6, all_14_8, % 7.08/1.72 | simplifying with (29), (42) gives: % 7.08/1.72 | (43) all_24_0 = all_14_10 % 7.08/1.72 | % 7.08/1.72 | REDUCE: (30), (43) imply: % 7.08/1.72 | (44) cartesian_product2(all_14_10, all_14_11) = all_14_4 % 7.08/1.72 | % 7.08/1.72 | REDUCE: (41), (43) imply: % 7.08/1.72 | (45) cartesian_product2(all_14_11, all_14_10) = all_14_0 % 7.08/1.72 | % 7.08/1.72 | GROUND_INST: instantiating (6) with all_14_3, all_14_0, all_14_10, all_14_11, % 7.08/1.72 | simplifying with (16), (45) gives: % 7.08/1.72 | (46) all_14_0 = all_14_3 % 7.08/1.72 | % 7.08/1.72 | GROUND_INST: instantiating (6) with all_14_9, all_14_4, all_14_11, all_14_10, % 7.08/1.72 | simplifying with (19), (44) gives: % 7.08/1.72 | (47) all_14_4 = all_14_9 % 7.08/1.72 | % 7.08/1.72 | BETA: splitting (24) gives: % 7.08/1.72 | % 7.08/1.72 | Case 1: % 7.08/1.72 | | % 7.08/1.72 | | (48) ~ (all_14_0 = all_14_3) % 7.08/1.72 | | % 7.08/1.72 | | REDUCE: (46), (48) imply: % 7.08/1.72 | | (49) $false % 7.08/1.72 | | % 7.08/1.72 | | CLOSE: (49) is inconsistent. % 7.08/1.72 | | % 7.08/1.72 | Case 2: % 7.08/1.72 | | % 7.08/1.72 | | (50) ~ (all_14_4 = all_14_9) % 7.08/1.72 | | % 7.08/1.72 | | REDUCE: (47), (50) imply: % 7.08/1.72 | | (51) $false % 7.08/1.72 | | % 7.08/1.72 | | CLOSE: (51) is inconsistent. % 7.08/1.72 | | % 7.08/1.72 | End of split % 7.08/1.72 | % 7.08/1.72 End of proof % 7.08/1.72 % SZS output end Proof for theBenchmark % 7.08/1.72 % 7.08/1.72 1076ms %------------------------------------------------------------------------------