%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU224+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 : n015.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 17:43:26 EDT 2023 % Result : Theorem 15.14s 2.83s % Output : Proof 16.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU224+1 : TPTP v8.1.2. Released v3.3.0. % 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n015.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Wed Aug 23 15:40:20 EDT 2023 % 0.14/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 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 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 % 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 % 2.39/1.06 Prover 4: Preprocessing ... % 2.39/1.06 Prover 1: Preprocessing ... % 3.09/1.10 Prover 0: Preprocessing ... % 3.09/1.10 Prover 6: Preprocessing ... % 3.09/1.10 Prover 5: Preprocessing ... % 3.09/1.10 Prover 3: Preprocessing ... % 3.09/1.10 Prover 2: Preprocessing ... % 5.90/1.59 Prover 1: Warning: ignoring some quantifiers % 5.90/1.60 Prover 3: Warning: ignoring some quantifiers % 5.90/1.62 Prover 5: Proving ... % 5.90/1.62 Prover 1: Constructing countermodel ... % 5.90/1.62 Prover 3: Constructing countermodel ... % 5.90/1.63 Prover 6: Proving ... % 5.90/1.68 Prover 2: Proving ... % 8.70/1.91 Prover 4: Warning: ignoring some quantifiers % 8.93/1.96 Prover 4: Constructing countermodel ... % 10.17/2.11 Prover 0: Proving ... % 11.66/2.31 Prover 3: gave up % 11.66/2.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.90/2.37 Prover 7: Preprocessing ... % 11.90/2.50 Prover 7: Warning: ignoring some quantifiers % 11.90/2.51 Prover 7: Constructing countermodel ... % 15.14/2.82 Prover 7: Found proof (size 34) % 15.14/2.82 Prover 7: proved (498ms) % 15.14/2.82 Prover 4: stopped % 15.14/2.82 Prover 1: stopped % 15.14/2.82 Prover 0: stopped % 15.14/2.82 Prover 2: stopped % 15.14/2.82 Prover 6: stopped % 15.14/2.83 Prover 5: stopped % 15.14/2.83 % 15.14/2.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.14/2.83 % 15.14/2.83 % SZS output start Proof for theBenchmark % 15.14/2.84 Assumptions after simplification: % 15.14/2.84 --------------------------------- % 15.14/2.84 % 15.14/2.84 (commutativity_k3_xboole_0) % 15.14/2.86 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, v0) = v2) % 15.14/2.86 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = v2 & $i(v2))) & ! % 15.14/2.86 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | % 15.14/2.86 ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2))) % 15.14/2.86 % 15.14/2.86 (d3_xboole_0) % 15.77/2.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 15.77/2.87 (set_intersection2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 15.77/2.87 $i(v0) | ~ in(v3, v2) | in(v3, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 15.77/2.87 $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ $i(v3) | ~ % 15.77/2.87 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, v2) | in(v3, v0)) & ! [v0: $i] : % 15.77/2.87 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) % 15.77/2.87 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, v1) | ~ in(v3, % 15.77/2.87 v0) | in(v3, v2)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 15.77/2.87 : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 15.77/2.87 $i(v0) | ? [v4: $i] : ($i(v4) & ( ~ in(v4, v2) | ~ in(v4, v1) | ~ in(v4, % 15.77/2.87 v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1))))) % 15.77/2.87 % 15.77/2.87 (dt_k7_relat_1) % 15.77/2.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v0, % 15.77/2.87 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | relation(v2)) % 15.77/2.87 % 15.77/2.87 (fc4_funct_1) % 15.77/2.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v0, % 15.77/2.87 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ function(v0) | % 15.77/2.88 relation(v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 15.77/2.88 (relation_dom_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 15.77/2.88 relation(v0) | ~ function(v0) | function(v2)) % 15.77/2.88 % 15.77/2.88 (l82_funct_1) % 15.77/2.88 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 15.77/2.88 $i] : (relation_dom(v3) = v4 & relation_dom_restriction(v2, v0) = v3 & % 15.77/2.88 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & relation(v2) & function(v2) & % 15.77/2.88 ((relation_dom(v2) = v5 & $i(v5) & in(v1, v5) & in(v1, v0) & ~ in(v1, v4)) % 15.77/2.88 | (in(v1, v4) & ( ~ in(v1, v0) | (relation_dom(v2) = v5 & $i(v5) & ~ % 15.77/2.88 in(v1, v5)))))) % 15.77/2.88 % 15.77/2.88 (t68_funct_1) % 15.77/2.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 15.77/2.89 (relation_dom(v1) = v2) | ~ (relation_dom_restriction(v3, v0) = v4) | ~ % 15.77/2.89 $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ relation(v3) | ~ relation(v1) | ~ % 15.77/2.89 function(v3) | ~ function(v1) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 15.77/2.89 ? [v8: $i] : ? [v9: $i] : ($i(v7) & ( ~ (v4 = v1) | (v6 = v2 & % 15.77/2.89 relation_dom(v3) = v5 & set_intersection2(v5, v0) = v2 & $i(v5) & % 15.77/2.89 $i(v2) & ! [v10: $i] : ! [v11: $i] : ( ~ (apply(v3, v10) = v11) | ~ % 15.77/2.89 $i(v10) | ~ in(v10, v2) | (apply(v1, v10) = v11 & $i(v11))) & ! % 15.77/2.89 [v10: $i] : ! [v11: $i] : ( ~ (apply(v1, v10) = v11) | ~ $i(v10) | % 15.77/2.89 ~ in(v10, v2) | (apply(v3, v10) = v11 & $i(v11))))) & (v4 = v1 | ( ~ % 15.77/2.89 (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & $i(v9) & $i(v8) % 15.77/2.89 & in(v7, v2)) | ( ~ (v6 = v2) & relation_dom(v3) = v5 & % 15.77/2.89 set_intersection2(v5, v0) = v6 & $i(v6) & $i(v5))))) & ? [v0: $i] : % 15.77/2.89 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (relation_dom(v3) = % 15.77/2.89 v4) | ~ (relation_dom(v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 15.77/2.89 relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5: % 15.77/2.89 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & % 15.77/2.89 ((v6 = v2 & set_intersection2(v4, v0) = v2 & $i(v2) & ! [v10: $i] : ! % 15.77/2.89 [v11: $i] : ( ~ (apply(v3, v10) = v11) | ~ $i(v10) | ~ in(v10, v2) | % 15.77/2.89 (apply(v1, v10) = v11 & $i(v11))) & ! [v10: $i] : ! [v11: $i] : ( % 15.77/2.89 ~ (apply(v1, v10) = v11) | ~ $i(v10) | ~ in(v10, v2) | (apply(v3, % 15.77/2.89 v10) = v11 & $i(v11)))) | ( ~ (v5 = v1) & % 15.77/2.89 relation_dom_restriction(v3, v0) = v5 & $i(v5))) & ((v5 = v1 & % 15.77/2.89 relation_dom_restriction(v3, v0) = v1) | ( ~ (v9 = v8) & apply(v3, v7) % 15.77/2.89 = v9 & apply(v1, v7) = v8 & $i(v9) & $i(v8) & in(v7, v2)) | ( ~ (v6 = % 15.77/2.89 v2) & set_intersection2(v4, v0) = v6 & $i(v6))))) % 15.77/2.89 % 15.77/2.89 (function-axioms) % 15.77/2.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.77/2.89 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 15.77/2.89 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) % 15.77/2.89 = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0: $i] : ! % 15.77/2.89 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3, % 15.77/2.89 v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 15.77/2.89 $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ % 15.77/2.89 (relation_dom(v2) = v0)) % 15.77/2.89 % 15.77/2.89 Further assumptions not needed in the proof: % 15.77/2.89 -------------------------------------------- % 15.91/2.89 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1, dt_k1_funct_1, % 15.91/2.89 dt_k1_relat_1, dt_k1_xboole_0, dt_k3_xboole_0, dt_m1_subset_1, % 15.91/2.89 existence_m1_subset_1, fc12_relat_1, fc13_relat_1, fc1_relat_1, fc1_xboole_0, % 15.91/2.89 fc4_relat_1, fc5_relat_1, fc7_relat_1, idempotence_k3_xboole_0, rc1_funct_1, % 15.91/2.89 rc1_relat_1, rc1_xboole_0, rc2_funct_1, rc2_relat_1, rc2_xboole_0, rc3_funct_1, % 15.91/2.89 rc3_relat_1, t1_subset, t2_boole, t2_subset, t6_boole, t7_boole, t8_boole % 15.91/2.89 % 15.91/2.89 Those formulas are unsatisfiable: % 15.91/2.89 --------------------------------- % 15.91/2.89 % 15.91/2.89 Begin of proof % 15.91/2.89 | % 15.91/2.89 | ALPHA: (commutativity_k3_xboole_0) implies: % 15.91/2.90 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, % 15.91/2.90 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = % 15.91/2.90 | v2 & $i(v2))) % 15.91/2.90 | % 15.91/2.90 | ALPHA: (d3_xboole_0) implies: % 15.91/2.90 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 15.91/2.90 | (set_intersection2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 15.91/2.90 | | ~ $i(v0) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) % 15.91/2.90 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 15.91/2.90 | (set_intersection2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 15.91/2.90 | | ~ $i(v0) | ~ in(v3, v2) | in(v3, v0)) % 15.91/2.90 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 15.91/2.90 | (set_intersection2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 15.91/2.90 | | ~ $i(v0) | ~ in(v3, v2) | in(v3, v1)) % 15.91/2.90 | % 15.91/2.90 | ALPHA: (fc4_funct_1) implies: % 15.91/2.90 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 15.91/2.90 | (relation_dom_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 15.91/2.90 | relation(v0) | ~ function(v0) | function(v2)) % 15.91/2.90 | % 15.91/2.90 | ALPHA: (t68_funct_1) implies: % 15.91/2.90 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 15.91/2.90 | ~ (relation_dom(v1) = v2) | ~ (relation_dom_restriction(v3, v0) = % 15.91/2.90 | v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ relation(v3) | ~ % 15.91/2.90 | relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5: $i] : ? % 15.91/2.90 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v7) & ( ~ % 15.91/2.90 | (v4 = v1) | (v6 = v2 & relation_dom(v3) = v5 & % 15.91/2.90 | set_intersection2(v5, v0) = v2 & $i(v5) & $i(v2) & ! [v10: $i] % 15.91/2.90 | : ! [v11: $i] : ( ~ (apply(v3, v10) = v11) | ~ $i(v10) | ~ % 15.91/2.90 | in(v10, v2) | (apply(v1, v10) = v11 & $i(v11))) & ! [v10: % 15.91/2.90 | $i] : ! [v11: $i] : ( ~ (apply(v1, v10) = v11) | ~ $i(v10) % 15.91/2.90 | | ~ in(v10, v2) | (apply(v3, v10) = v11 & $i(v11))))) & (v4 % 15.91/2.90 | = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & % 15.91/2.90 | $i(v9) & $i(v8) & in(v7, v2)) | ( ~ (v6 = v2) & % 15.91/2.90 | relation_dom(v3) = v5 & set_intersection2(v5, v0) = v6 & $i(v6) % 15.91/2.90 | & $i(v5))))) % 15.91/2.90 | % 15.91/2.90 | ALPHA: (function-axioms) implies: % 15.91/2.90 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 15.91/2.90 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 15.91/2.90 | % 15.91/2.90 | DELTA: instantiating (l82_funct_1) with fresh symbols all_43_0, all_43_1, % 15.91/2.90 | all_43_2, all_43_3, all_43_4, all_43_5 gives: % 15.91/2.90 | (8) relation_dom(all_43_2) = all_43_1 & relation_dom_restriction(all_43_3, % 15.91/2.90 | all_43_5) = all_43_2 & $i(all_43_1) & $i(all_43_2) & $i(all_43_3) & % 15.91/2.90 | $i(all_43_4) & $i(all_43_5) & relation(all_43_3) & function(all_43_3) & % 15.91/2.90 | ((relation_dom(all_43_3) = all_43_0 & $i(all_43_0) & in(all_43_4, % 15.91/2.90 | all_43_0) & in(all_43_4, all_43_5) & ~ in(all_43_4, all_43_1)) | % 15.91/2.90 | (in(all_43_4, all_43_1) & ( ~ in(all_43_4, all_43_5) | % 15.91/2.90 | (relation_dom(all_43_3) = all_43_0 & $i(all_43_0) & ~ % 15.91/2.90 | in(all_43_4, all_43_0))))) % 15.91/2.90 | % 15.91/2.90 | ALPHA: (8) implies: % 15.91/2.91 | (9) function(all_43_3) % 15.91/2.91 | (10) relation(all_43_3) % 15.91/2.91 | (11) $i(all_43_5) % 15.91/2.91 | (12) $i(all_43_4) % 15.91/2.91 | (13) $i(all_43_3) % 15.91/2.91 | (14) $i(all_43_2) % 15.91/2.91 | (15) relation_dom_restriction(all_43_3, all_43_5) = all_43_2 % 15.91/2.91 | (16) relation_dom(all_43_2) = all_43_1 % 15.91/2.91 | (17) (relation_dom(all_43_3) = all_43_0 & $i(all_43_0) & in(all_43_4, % 15.91/2.91 | all_43_0) & in(all_43_4, all_43_5) & ~ in(all_43_4, all_43_1)) | % 15.91/2.91 | (in(all_43_4, all_43_1) & ( ~ in(all_43_4, all_43_5) | % 15.91/2.91 | (relation_dom(all_43_3) = all_43_0 & $i(all_43_0) & ~ % 15.91/2.91 | in(all_43_4, all_43_0)))) % 15.91/2.91 | % 15.91/2.91 | GROUND_INST: instantiating (5) with all_43_3, all_43_5, all_43_2, simplifying % 15.91/2.91 | with (9), (10), (11), (13), (15) gives: % 15.91/2.91 | (18) function(all_43_2) % 15.91/2.91 | % 15.91/2.91 | GROUND_INST: instantiating (dt_k7_relat_1) with all_43_3, all_43_5, all_43_2, % 15.91/2.91 | simplifying with (10), (11), (13), (15) gives: % 15.91/2.91 | (19) relation(all_43_2) % 15.91/2.91 | % 15.91/2.91 | GROUND_INST: instantiating (6) with all_43_5, all_43_2, all_43_1, all_43_3, % 15.91/2.91 | all_43_2, simplifying with (9), (10), (11), (13), (14), (15), % 15.91/2.91 | (16), (18), (19) gives: % 15.91/2.91 | (20) ? [v0: $i] : ? [v1: $i] : (relation_dom(all_43_3) = v0 & % 15.91/2.91 | set_intersection2(v0, all_43_5) = all_43_1 & $i(v1) & $i(v0) & % 15.91/2.91 | $i(all_43_1) & ! [v2: $i] : ! [v3: $i] : ( ~ (apply(all_43_2, v2) % 15.91/2.91 | = v3) | ~ $i(v2) | ~ in(v2, all_43_1) | (apply(all_43_3, v2) = % 15.91/2.91 | v3 & $i(v3))) & ! [v2: $i] : ! [v3: $i] : ( ~ (apply(all_43_3, % 15.91/2.91 | v2) = v3) | ~ $i(v2) | ~ in(v2, all_43_1) | (apply(all_43_2, % 15.91/2.91 | v2) = v3 & $i(v3)))) % 15.91/2.91 | % 15.91/2.91 | DELTA: instantiating (20) with fresh symbols all_62_0, all_62_1 gives: % 15.91/2.91 | (21) relation_dom(all_43_3) = all_62_1 & set_intersection2(all_62_1, % 15.91/2.91 | all_43_5) = all_43_1 & $i(all_62_0) & $i(all_62_1) & $i(all_43_1) & % 15.91/2.91 | ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_43_2, v0) = v1) | ~ $i(v0) % 15.91/2.91 | | ~ in(v0, all_43_1) | (apply(all_43_3, v0) = v1 & $i(v1))) & ! % 15.91/2.91 | [v0: $i] : ! [v1: $i] : ( ~ (apply(all_43_3, v0) = v1) | ~ $i(v0) | % 15.91/2.91 | ~ in(v0, all_43_1) | (apply(all_43_2, v0) = v1 & $i(v1))) % 15.91/2.91 | % 15.91/2.91 | ALPHA: (21) implies: % 15.91/2.91 | (22) $i(all_62_1) % 15.91/2.91 | (23) set_intersection2(all_62_1, all_43_5) = all_43_1 % 15.91/2.91 | (24) relation_dom(all_43_3) = all_62_1 % 15.91/2.91 | % 15.91/2.91 | GROUND_INST: instantiating (1) with all_43_5, all_62_1, all_43_1, simplifying % 15.91/2.91 | with (11), (22), (23) gives: % 15.91/2.91 | (25) set_intersection2(all_43_5, all_62_1) = all_43_1 & $i(all_43_1) % 15.91/2.91 | % 15.91/2.91 | ALPHA: (25) implies: % 15.91/2.91 | (26) $i(all_43_1) % 15.91/2.91 | (27) set_intersection2(all_43_5, all_62_1) = all_43_1 % 15.91/2.91 | % 15.91/2.91 | BETA: splitting (17) gives: % 15.91/2.91 | % 15.91/2.91 | Case 1: % 15.91/2.91 | | % 15.91/2.92 | | (28) relation_dom(all_43_3) = all_43_0 & $i(all_43_0) & in(all_43_4, % 15.91/2.92 | | all_43_0) & in(all_43_4, all_43_5) & ~ in(all_43_4, all_43_1) % 15.91/2.92 | | % 15.91/2.92 | | ALPHA: (28) implies: % 15.91/2.92 | | (29) ~ in(all_43_4, all_43_1) % 15.91/2.92 | | (30) in(all_43_4, all_43_5) % 15.91/2.92 | | (31) in(all_43_4, all_43_0) % 15.91/2.92 | | (32) relation_dom(all_43_3) = all_43_0 % 15.91/2.92 | | % 15.91/2.92 | | GROUND_INST: instantiating (7) with all_62_1, all_43_0, all_43_3, % 15.91/2.92 | | simplifying with (24), (32) gives: % 15.91/2.92 | | (33) all_62_1 = all_43_0 % 15.91/2.92 | | % 15.91/2.92 | | REDUCE: (23), (33) imply: % 15.91/2.92 | | (34) set_intersection2(all_43_0, all_43_5) = all_43_1 % 15.91/2.92 | | % 15.91/2.92 | | REDUCE: (22), (33) imply: % 15.91/2.92 | | (35) $i(all_43_0) % 15.91/2.92 | | % 15.91/2.92 | | GROUND_INST: instantiating (2) with all_43_0, all_43_5, all_43_1, all_43_4, % 15.91/2.92 | | simplifying with (11), (12), (26), (29), (30), (31), (34), (35) % 15.91/2.92 | | gives: % 15.91/2.92 | | (36) $false % 15.91/2.92 | | % 15.91/2.92 | | CLOSE: (36) is inconsistent. % 15.91/2.92 | | % 15.91/2.92 | Case 2: % 15.91/2.92 | | % 15.91/2.92 | | (37) in(all_43_4, all_43_1) & ( ~ in(all_43_4, all_43_5) | % 15.91/2.92 | | (relation_dom(all_43_3) = all_43_0 & $i(all_43_0) & ~ % 15.91/2.92 | | in(all_43_4, all_43_0))) % 15.91/2.92 | | % 15.91/2.92 | | ALPHA: (37) implies: % 15.91/2.92 | | (38) in(all_43_4, all_43_1) % 15.91/2.92 | | (39) ~ in(all_43_4, all_43_5) | (relation_dom(all_43_3) = all_43_0 & % 15.91/2.92 | | $i(all_43_0) & ~ in(all_43_4, all_43_0)) % 15.91/2.92 | | % 15.91/2.92 | | GROUND_INST: instantiating (4) with all_43_5, all_62_1, all_43_1, all_43_4, % 15.91/2.92 | | simplifying with (11), (12), (22), (26), (27), (38) gives: % 15.91/2.92 | | (40) in(all_43_4, all_62_1) % 15.91/2.92 | | % 15.91/2.92 | | GROUND_INST: instantiating (3) with all_43_5, all_62_1, all_43_1, all_43_4, % 15.91/2.92 | | simplifying with (11), (12), (22), (26), (27), (38) gives: % 15.91/2.92 | | (41) in(all_43_4, all_43_5) % 15.91/2.92 | | % 15.91/2.92 | | BETA: splitting (39) gives: % 15.91/2.92 | | % 15.91/2.92 | | Case 1: % 15.91/2.92 | | | % 15.91/2.92 | | | (42) ~ in(all_43_4, all_43_5) % 15.91/2.92 | | | % 15.91/2.92 | | | PRED_UNIFY: (41), (42) imply: % 15.91/2.92 | | | (43) $false % 15.91/2.92 | | | % 15.91/2.92 | | | CLOSE: (43) is inconsistent. % 15.91/2.92 | | | % 15.91/2.92 | | Case 2: % 15.91/2.92 | | | % 15.91/2.92 | | | (44) relation_dom(all_43_3) = all_43_0 & $i(all_43_0) & ~ in(all_43_4, % 15.91/2.92 | | | all_43_0) % 15.91/2.92 | | | % 15.91/2.92 | | | ALPHA: (44) implies: % 16.06/2.92 | | | (45) ~ in(all_43_4, all_43_0) % 16.06/2.92 | | | (46) relation_dom(all_43_3) = all_43_0 % 16.06/2.92 | | | % 16.06/2.92 | | | GROUND_INST: instantiating (7) with all_62_1, all_43_0, all_43_3, % 16.06/2.92 | | | simplifying with (24), (46) gives: % 16.06/2.92 | | | (47) all_62_1 = all_43_0 % 16.06/2.92 | | | % 16.06/2.92 | | | PRED_UNIFY: (40), (45) imply: % 16.06/2.92 | | | (48) ~ (all_62_1 = all_43_0) % 16.06/2.92 | | | % 16.06/2.92 | | | REDUCE: (47), (48) imply: % 16.06/2.92 | | | (49) $false % 16.06/2.92 | | | % 16.06/2.92 | | | CLOSE: (49) is inconsistent. % 16.06/2.92 | | | % 16.06/2.92 | | End of split % 16.06/2.92 | | % 16.06/2.92 | End of split % 16.06/2.92 | % 16.06/2.92 End of proof % 16.06/2.93 % SZS output end Proof for theBenchmark % 16.06/2.93 % 16.06/2.93 2303ms %------------------------------------------------------------------------------