%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ITP209_1 : TPTP v8.1.2. Released v8.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n012.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 04:10:03 EDT 2023 % Result : Theorem 8.11s 1.83s % Output : Proof 11.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : ITP209_1 : TPTP v8.1.2. Released v8.0.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n012.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 : Sun Aug 27 13:33:10 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.63 ________ _____ % 0.20/0.63 ___ __ \_________(_)________________________________ % 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.63 % 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.63 (2023-06-19) % 0.20/0.63 % 0.20/0.63 (c) Philipp Rümmer, 2009-2023 % 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.63 Amanda Stjerna. % 0.20/0.63 Free software under BSD-3-Clause. % 0.20/0.63 % 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.63 % 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.55/1.10 Prover 4: Preprocessing ... % 2.55/1.12 Prover 1: Preprocessing ... % 3.10/1.16 Prover 6: Preprocessing ... % 3.10/1.16 Prover 2: Preprocessing ... % 3.10/1.16 Prover 0: Preprocessing ... % 3.10/1.16 Prover 3: Preprocessing ... % 3.10/1.18 Prover 5: Preprocessing ... % 4.72/1.46 Prover 6: Proving ... % 4.72/1.48 Prover 3: Constructing countermodel ... % 4.72/1.48 Prover 1: Constructing countermodel ... % 4.72/1.54 Prover 0: Proving ... % 4.72/1.54 Prover 4: Constructing countermodel ... % 4.72/1.54 Prover 5: Proving ... % 4.72/1.55 Prover 2: Proving ... % 8.11/1.82 Prover 3: proved (1158ms) % 8.11/1.82 % 8.11/1.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.11/1.83 % 8.11/1.83 Prover 0: stopped % 8.11/1.83 Prover 5: stopped % 8.11/1.83 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.11/1.83 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.11/1.83 Prover 6: stopped % 8.11/1.84 Prover 2: stopped % 8.30/1.85 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.30/1.85 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.30/1.85 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.30/1.86 Prover 7: Preprocessing ... % 8.30/1.87 Prover 10: Preprocessing ... % 8.30/1.88 Prover 11: Preprocessing ... % 8.30/1.88 Prover 8: Preprocessing ... % 8.30/1.90 Prover 13: Preprocessing ... % 8.89/1.95 Prover 10: Warning: ignoring some quantifiers % 8.89/1.96 Prover 10: Constructing countermodel ... % 9.28/2.01 Prover 8: Warning: ignoring some quantifiers % 9.28/2.01 Prover 8: Constructing countermodel ... % 9.28/2.02 Prover 7: Warning: ignoring some quantifiers % 9.28/2.03 Prover 11: Constructing countermodel ... % 9.28/2.03 Prover 13: Warning: ignoring some quantifiers % 9.28/2.03 Prover 7: Constructing countermodel ... % 9.28/2.05 Prover 13: Constructing countermodel ... % 11.27/2.28 Prover 10: Found proof (size 43) % 11.27/2.28 Prover 10: proved (440ms) % 11.27/2.28 Prover 7: stopped % 11.27/2.28 Prover 8: stopped % 11.27/2.28 Prover 1: stopped % 11.27/2.28 Prover 4: stopped % 11.27/2.28 Prover 11: stopped % 11.27/2.28 Prover 13: stopped % 11.27/2.28 % 11.27/2.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.27/2.28 % 11.27/2.29 % SZS output start Proof for theBenchmark % 11.27/2.29 Assumptions after simplification: % 11.27/2.29 --------------------------------- % 11.27/2.29 % 11.27/2.29 (conj_0) % 11.27/2.32 a(c) & a(b) & a(a2) & fun_a_fun_a_a(f) & ? [v0: fun_a_a] : ? [v1: a] : ? % 11.27/2.32 [v2: fun_a_a] : ? [v3: a] : ? [v4: a] : ? [v5: fun_a_a] : ? [v6: a] : ( ~ % 11.27/2.32 (v6 = v3) & aa_a_fun_a_a(f, v4) = v5 & aa_a_fun_a_a(f, v1) = v2 & % 11.27/2.32 aa_a_fun_a_a(f, a2) = v0 & aa_a_a(v5, b) = v6 & aa_a_a(v2, c) = v3 & % 11.27/2.32 aa_a_a(v0, c) = v4 & aa_a_a(v0, b) = v1 & a(v6) & a(v4) & a(v3) & a(v1) & % 11.27/2.32 fun_a_a(v5) & fun_a_a(v2) & fun_a_a(v0)) % 11.27/2.32 % 11.27/2.32 (fact_1_commute) % 11.27/2.32 fun_a_fun_a_a(f) & ! [v0: a] : ! [v1: a] : ! [v2: fun_a_a] : ! [v3: a] : ( % 11.27/2.32 ~ (aa_a_fun_a_a(f, v0) = v2) | ~ (aa_a_a(v2, v1) = v3) | ~ a(v1) | ~ % 11.27/2.32 a(v0) | ? [v4: fun_a_a] : (aa_a_fun_a_a(f, v1) = v4 & aa_a_a(v4, v0) = v3 & % 11.27/2.32 a(v3) & fun_a_a(v4))) % 11.27/2.32 % 11.27/2.32 (fact_2_left__commute) % 11.27/2.32 fun_a_fun_a_a(f) & ! [v0: a] : ! [v1: a] : ! [v2: a] : ! [v3: fun_a_a] : % 11.27/2.32 ! [v4: fun_a_a] : ! [v5: a] : ! [v6: a] : ( ~ (aa_a_fun_a_a(f, v1) = v4) | % 11.27/2.33 ~ (aa_a_fun_a_a(f, v0) = v3) | ~ (aa_a_a(v4, v2) = v5) | ~ (aa_a_a(v3, v5) % 11.27/2.33 = v6) | ~ a(v2) | ~ a(v1) | ~ a(v0) | ? [v7: a] : (aa_a_a(v4, v7) = v6 % 11.27/2.33 & aa_a_a(v3, v2) = v7 & a(v7) & a(v6))) % 11.27/2.33 % 11.27/2.33 (fact_3_right__assoc) % 11.27/2.33 fun_a_fun_a_a(f) & ! [v0: a] : ! [v1: a] : ! [v2: a] : ! [v3: fun_a_a] : % 11.27/2.33 ! [v4: a] : ! [v5: fun_a_a] : ! [v6: a] : ( ~ (aa_a_fun_a_a(f, v4) = v5) | % 11.27/2.33 ~ (aa_a_fun_a_a(f, v0) = v3) | ~ (aa_a_a(v5, v2) = v6) | ~ (aa_a_a(v3, v1) % 11.27/2.33 = v4) | ~ a(v2) | ~ a(v1) | ~ a(v0) | ? [v7: fun_a_a] : ? [v8: a] : % 11.27/2.33 (aa_a_fun_a_a(f, v1) = v7 & aa_a_a(v7, v2) = v8 & aa_a_a(v3, v8) = v6 & % 11.27/2.33 a(v8) & a(v6) & fun_a_a(v7))) % 11.27/2.33 % 11.27/2.33 (function-axioms) % 11.74/2.33 ! [v0: fun_a_a] : ! [v1: fun_a_a] : ! [v2: a] : ! [v3: fun_a_fun_a_a] : % 11.74/2.33 (v1 = v0 | ~ (aa_a_fun_a_a(v3, v2) = v1) | ~ (aa_a_fun_a_a(v3, v2) = v0)) & % 11.74/2.33 ! [v0: a] : ! [v1: a] : ! [v2: a] : ! [v3: fun_a_a] : (v1 = v0 | ~ % 11.74/2.33 (aa_a_a(v3, v2) = v1) | ~ (aa_a_a(v3, v2) = v0)) % 11.74/2.33 % 11.74/2.33 Further assumptions not needed in the proof: % 11.74/2.33 -------------------------------------------- % 11.74/2.33 fact_0_ac__operator__axioms, fact_4_ac__operator_Ointro, % 11.74/2.33 fact_5_ac__operator_Ocommute, fact_6_ac__operator_Oleft__assoc, % 11.74/2.33 fact_7_ac__operator_Oright__assoc, fact_8_ac__operator_Oleft__commute, % 11.74/2.33 fact_9_ac__operator__def, help_pp_1_1_U, help_pp_2_1_U % 11.74/2.33 % 11.74/2.33 Those formulas are unsatisfiable: % 11.74/2.33 --------------------------------- % 11.74/2.33 % 11.74/2.33 Begin of proof % 11.74/2.33 | % 11.74/2.33 | ALPHA: (fact_1_commute) implies: % 11.74/2.33 | (1) ! [v0: a] : ! [v1: a] : ! [v2: fun_a_a] : ! [v3: a] : ( ~ % 11.74/2.33 | (aa_a_fun_a_a(f, v0) = v2) | ~ (aa_a_a(v2, v1) = v3) | ~ a(v1) | ~ % 11.74/2.33 | a(v0) | ? [v4: fun_a_a] : (aa_a_fun_a_a(f, v1) = v4 & aa_a_a(v4, v0) % 11.74/2.33 | = v3 & a(v3) & fun_a_a(v4))) % 11.74/2.33 | % 11.74/2.33 | ALPHA: (fact_2_left__commute) implies: % 11.74/2.33 | (2) ! [v0: a] : ! [v1: a] : ! [v2: a] : ! [v3: fun_a_a] : ! [v4: % 11.74/2.33 | fun_a_a] : ! [v5: a] : ! [v6: a] : ( ~ (aa_a_fun_a_a(f, v1) = v4) | % 11.74/2.33 | ~ (aa_a_fun_a_a(f, v0) = v3) | ~ (aa_a_a(v4, v2) = v5) | ~ % 11.74/2.33 | (aa_a_a(v3, v5) = v6) | ~ a(v2) | ~ a(v1) | ~ a(v0) | ? [v7: a] : % 11.74/2.33 | (aa_a_a(v4, v7) = v6 & aa_a_a(v3, v2) = v7 & a(v7) & a(v6))) % 11.74/2.33 | % 11.74/2.33 | ALPHA: (fact_3_right__assoc) implies: % 11.74/2.34 | (3) ! [v0: a] : ! [v1: a] : ! [v2: a] : ! [v3: fun_a_a] : ! [v4: a] : % 11.74/2.34 | ! [v5: fun_a_a] : ! [v6: a] : ( ~ (aa_a_fun_a_a(f, v4) = v5) | ~ % 11.74/2.34 | (aa_a_fun_a_a(f, v0) = v3) | ~ (aa_a_a(v5, v2) = v6) | ~ % 11.74/2.34 | (aa_a_a(v3, v1) = v4) | ~ a(v2) | ~ a(v1) | ~ a(v0) | ? [v7: % 11.74/2.34 | fun_a_a] : ? [v8: a] : (aa_a_fun_a_a(f, v1) = v7 & aa_a_a(v7, v2) % 11.74/2.34 | = v8 & aa_a_a(v3, v8) = v6 & a(v8) & a(v6) & fun_a_a(v7))) % 11.74/2.34 | % 11.74/2.34 | ALPHA: (conj_0) implies: % 11.74/2.34 | (4) a(a2) % 11.74/2.34 | (5) a(b) % 11.74/2.34 | (6) a(c) % 11.74/2.34 | (7) ? [v0: fun_a_a] : ? [v1: a] : ? [v2: fun_a_a] : ? [v3: a] : ? [v4: % 11.74/2.34 | a] : ? [v5: fun_a_a] : ? [v6: a] : ( ~ (v6 = v3) & aa_a_fun_a_a(f, % 11.74/2.34 | v4) = v5 & aa_a_fun_a_a(f, v1) = v2 & aa_a_fun_a_a(f, a2) = v0 & % 11.74/2.34 | aa_a_a(v5, b) = v6 & aa_a_a(v2, c) = v3 & aa_a_a(v0, c) = v4 & % 11.74/2.34 | aa_a_a(v0, b) = v1 & a(v6) & a(v4) & a(v3) & a(v1) & fun_a_a(v5) & % 11.74/2.34 | fun_a_a(v2) & fun_a_a(v0)) % 11.74/2.34 | % 11.74/2.34 | ALPHA: (function-axioms) implies: % 11.74/2.34 | (8) ! [v0: a] : ! [v1: a] : ! [v2: a] : ! [v3: fun_a_a] : (v1 = v0 | ~ % 11.74/2.34 | (aa_a_a(v3, v2) = v1) | ~ (aa_a_a(v3, v2) = v0)) % 11.74/2.34 | (9) ! [v0: fun_a_a] : ! [v1: fun_a_a] : ! [v2: a] : ! [v3: % 11.74/2.34 | fun_a_fun_a_a] : (v1 = v0 | ~ (aa_a_fun_a_a(v3, v2) = v1) | ~ % 11.74/2.34 | (aa_a_fun_a_a(v3, v2) = v0)) % 11.74/2.34 | % 11.74/2.34 | DELTA: instantiating (7) with fresh symbols all_20_0, all_20_1, all_20_2, % 11.74/2.34 | all_20_3, all_20_4, all_20_5, all_20_6 gives: % 11.74/2.34 | (10) ~ (all_20_0 = all_20_3) & aa_a_fun_a_a(f, all_20_2) = all_20_1 & % 11.74/2.34 | aa_a_fun_a_a(f, all_20_5) = all_20_4 & aa_a_fun_a_a(f, a2) = all_20_6 % 11.74/2.34 | & aa_a_a(all_20_1, b) = all_20_0 & aa_a_a(all_20_4, c) = all_20_3 & % 11.74/2.34 | aa_a_a(all_20_6, c) = all_20_2 & aa_a_a(all_20_6, b) = all_20_5 & % 11.74/2.34 | a(all_20_0) & a(all_20_2) & a(all_20_3) & a(all_20_5) & % 11.74/2.34 | fun_a_a(all_20_1) & fun_a_a(all_20_4) & fun_a_a(all_20_6) % 11.74/2.34 | % 11.74/2.34 | ALPHA: (10) implies: % 11.74/2.34 | (11) ~ (all_20_0 = all_20_3) % 11.74/2.34 | (12) a(all_20_5) % 11.74/2.34 | (13) a(all_20_2) % 11.74/2.34 | (14) aa_a_a(all_20_6, b) = all_20_5 % 11.74/2.34 | (15) aa_a_a(all_20_6, c) = all_20_2 % 11.74/2.34 | (16) aa_a_a(all_20_4, c) = all_20_3 % 11.74/2.34 | (17) aa_a_a(all_20_1, b) = all_20_0 % 11.74/2.34 | (18) aa_a_fun_a_a(f, a2) = all_20_6 % 11.74/2.34 | (19) aa_a_fun_a_a(f, all_20_5) = all_20_4 % 11.74/2.34 | (20) aa_a_fun_a_a(f, all_20_2) = all_20_1 % 11.74/2.34 | % 11.74/2.34 | GROUND_INST: instantiating (1) with a2, c, all_20_6, all_20_2, simplifying % 11.74/2.34 | with (4), (6), (15), (18) gives: % 11.74/2.35 | (21) ? [v0: fun_a_a] : (aa_a_fun_a_a(f, c) = v0 & aa_a_a(v0, a2) = % 11.74/2.35 | all_20_2 & a(all_20_2) & fun_a_a(v0)) % 11.74/2.35 | % 11.74/2.35 | GROUND_INST: instantiating (1) with a2, b, all_20_6, all_20_5, simplifying % 11.74/2.35 | with (4), (5), (14), (18) gives: % 11.74/2.35 | (22) ? [v0: fun_a_a] : (aa_a_fun_a_a(f, b) = v0 & aa_a_a(v0, a2) = % 11.74/2.35 | all_20_5 & a(all_20_5) & fun_a_a(v0)) % 11.74/2.35 | % 11.74/2.35 | GROUND_INST: instantiating (3) with a2, b, c, all_20_6, all_20_5, all_20_4, % 11.74/2.35 | all_20_3, simplifying with (4), (5), (6), (14), (16), (18), (19) % 11.74/2.35 | gives: % 11.74/2.35 | (23) ? [v0: fun_a_a] : ? [v1: a] : (aa_a_fun_a_a(f, b) = v0 & aa_a_a(v0, % 11.74/2.35 | c) = v1 & aa_a_a(all_20_6, v1) = all_20_3 & a(v1) & a(all_20_3) & % 11.74/2.35 | fun_a_a(v0)) % 11.74/2.35 | % 11.74/2.35 | GROUND_INST: instantiating (1) with all_20_5, c, all_20_4, all_20_3, % 11.74/2.35 | simplifying with (6), (12), (16), (19) gives: % 11.74/2.35 | (24) ? [v0: fun_a_a] : (aa_a_fun_a_a(f, c) = v0 & aa_a_a(v0, all_20_5) = % 11.74/2.35 | all_20_3 & a(all_20_3) & fun_a_a(v0)) % 11.74/2.35 | % 11.74/2.35 | GROUND_INST: instantiating (3) with a2, c, b, all_20_6, all_20_2, all_20_1, % 11.74/2.35 | all_20_0, simplifying with (4), (5), (6), (15), (17), (18), (20) % 11.74/2.35 | gives: % 11.74/2.35 | (25) ? [v0: fun_a_a] : ? [v1: a] : (aa_a_fun_a_a(f, c) = v0 & aa_a_a(v0, % 11.74/2.35 | b) = v1 & aa_a_a(all_20_6, v1) = all_20_0 & a(v1) & a(all_20_0) & % 11.74/2.35 | fun_a_a(v0)) % 11.74/2.35 | % 11.74/2.35 | GROUND_INST: instantiating (1) with all_20_2, b, all_20_1, all_20_0, % 11.74/2.35 | simplifying with (5), (13), (17), (20) gives: % 11.74/2.35 | (26) ? [v0: fun_a_a] : (aa_a_fun_a_a(f, b) = v0 & aa_a_a(v0, all_20_2) = % 11.74/2.35 | all_20_0 & a(all_20_0) & fun_a_a(v0)) % 11.74/2.35 | % 11.74/2.35 | DELTA: instantiating (26) with fresh symbol all_29_0 gives: % 11.74/2.35 | (27) aa_a_fun_a_a(f, b) = all_29_0 & aa_a_a(all_29_0, all_20_2) = all_20_0 % 11.74/2.35 | & a(all_20_0) & fun_a_a(all_29_0) % 11.74/2.35 | % 11.74/2.35 | ALPHA: (27) implies: % 11.74/2.35 | (28) aa_a_a(all_29_0, all_20_2) = all_20_0 % 11.74/2.35 | (29) aa_a_fun_a_a(f, b) = all_29_0 % 11.74/2.35 | % 11.74/2.35 | DELTA: instantiating (22) with fresh symbol all_31_0 gives: % 11.74/2.35 | (30) aa_a_fun_a_a(f, b) = all_31_0 & aa_a_a(all_31_0, a2) = all_20_5 & % 11.74/2.35 | a(all_20_5) & fun_a_a(all_31_0) % 11.74/2.35 | % 11.74/2.35 | ALPHA: (30) implies: % 11.74/2.35 | (31) aa_a_a(all_31_0, a2) = all_20_5 % 11.74/2.35 | (32) aa_a_fun_a_a(f, b) = all_31_0 % 11.74/2.35 | % 11.74/2.35 | DELTA: instantiating (21) with fresh symbol all_33_0 gives: % 11.74/2.35 | (33) aa_a_fun_a_a(f, c) = all_33_0 & aa_a_a(all_33_0, a2) = all_20_2 & % 11.74/2.35 | a(all_20_2) & fun_a_a(all_33_0) % 11.74/2.35 | % 11.74/2.35 | ALPHA: (33) implies: % 11.74/2.35 | (34) aa_a_a(all_33_0, a2) = all_20_2 % 11.74/2.35 | (35) aa_a_fun_a_a(f, c) = all_33_0 % 11.74/2.35 | % 11.74/2.35 | DELTA: instantiating (24) with fresh symbol all_35_0 gives: % 11.74/2.35 | (36) aa_a_fun_a_a(f, c) = all_35_0 & aa_a_a(all_35_0, all_20_5) = all_20_3 % 11.74/2.35 | & a(all_20_3) & fun_a_a(all_35_0) % 11.74/2.35 | % 11.74/2.35 | ALPHA: (36) implies: % 11.74/2.35 | (37) aa_a_a(all_35_0, all_20_5) = all_20_3 % 11.74/2.35 | (38) aa_a_fun_a_a(f, c) = all_35_0 % 11.74/2.35 | % 11.74/2.35 | DELTA: instantiating (25) with fresh symbols all_37_0, all_37_1 gives: % 11.74/2.35 | (39) aa_a_fun_a_a(f, c) = all_37_1 & aa_a_a(all_37_1, b) = all_37_0 & % 11.74/2.35 | aa_a_a(all_20_6, all_37_0) = all_20_0 & a(all_37_0) & a(all_20_0) & % 11.74/2.35 | fun_a_a(all_37_1) % 11.74/2.35 | % 11.74/2.35 | ALPHA: (39) implies: % 11.74/2.35 | (40) aa_a_fun_a_a(f, c) = all_37_1 % 11.74/2.35 | % 11.74/2.35 | DELTA: instantiating (23) with fresh symbols all_39_0, all_39_1 gives: % 11.74/2.36 | (41) aa_a_fun_a_a(f, b) = all_39_1 & aa_a_a(all_39_1, c) = all_39_0 & % 11.74/2.36 | aa_a_a(all_20_6, all_39_0) = all_20_3 & a(all_39_0) & a(all_20_3) & % 11.74/2.36 | fun_a_a(all_39_1) % 11.74/2.36 | % 11.74/2.36 | ALPHA: (41) implies: % 11.74/2.36 | (42) aa_a_fun_a_a(f, b) = all_39_1 % 11.74/2.36 | % 11.74/2.36 | GROUND_INST: instantiating (9) with all_31_0, all_39_1, b, f, simplifying with % 11.74/2.36 | (32), (42) gives: % 11.74/2.36 | (43) all_39_1 = all_31_0 % 11.74/2.36 | % 11.74/2.36 | GROUND_INST: instantiating (9) with all_29_0, all_39_1, b, f, simplifying with % 11.74/2.36 | (29), (42) gives: % 11.74/2.36 | (44) all_39_1 = all_29_0 % 11.74/2.36 | % 11.74/2.36 | GROUND_INST: instantiating (9) with all_35_0, all_37_1, c, f, simplifying with % 11.74/2.36 | (38), (40) gives: % 11.74/2.36 | (45) all_37_1 = all_35_0 % 11.74/2.36 | % 11.74/2.36 | GROUND_INST: instantiating (9) with all_33_0, all_37_1, c, f, simplifying with % 11.74/2.36 | (35), (40) gives: % 11.74/2.36 | (46) all_37_1 = all_33_0 % 11.74/2.36 | % 11.74/2.36 | COMBINE_EQS: (43), (44) imply: % 11.74/2.36 | (47) all_31_0 = all_29_0 % 11.74/2.36 | % 11.74/2.36 | COMBINE_EQS: (45), (46) imply: % 11.74/2.36 | (48) all_35_0 = all_33_0 % 11.74/2.36 | % 11.74/2.36 | REDUCE: (37), (48) imply: % 11.74/2.36 | (49) aa_a_a(all_33_0, all_20_5) = all_20_3 % 11.74/2.36 | % 11.74/2.36 | REDUCE: (31), (47) imply: % 11.74/2.36 | (50) aa_a_a(all_29_0, a2) = all_20_5 % 11.74/2.36 | % 11.74/2.36 | GROUND_INST: instantiating (2) with b, c, a2, all_29_0, all_33_0, all_20_2, % 11.74/2.36 | all_20_0, simplifying with (4), (5), (6), (28), (29), (34), (35) % 11.74/2.36 | gives: % 11.74/2.36 | (51) ? [v0: a] : (aa_a_a(all_33_0, v0) = all_20_0 & aa_a_a(all_29_0, a2) = % 11.74/2.36 | v0 & a(v0) & a(all_20_0)) % 11.74/2.36 | % 11.74/2.36 | DELTA: instantiating (51) with fresh symbol all_52_0 gives: % 11.74/2.36 | (52) aa_a_a(all_33_0, all_52_0) = all_20_0 & aa_a_a(all_29_0, a2) = % 11.74/2.36 | all_52_0 & a(all_52_0) & a(all_20_0) % 11.74/2.36 | % 11.74/2.36 | ALPHA: (52) implies: % 11.74/2.36 | (53) aa_a_a(all_29_0, a2) = all_52_0 % 11.74/2.36 | (54) aa_a_a(all_33_0, all_52_0) = all_20_0 % 11.74/2.36 | % 11.74/2.36 | GROUND_INST: instantiating (8) with all_20_5, all_52_0, a2, all_29_0, % 11.74/2.36 | simplifying with (50), (53) gives: % 11.74/2.36 | (55) all_52_0 = all_20_5 % 11.74/2.36 | % 11.74/2.36 | REDUCE: (54), (55) imply: % 11.74/2.36 | (56) aa_a_a(all_33_0, all_20_5) = all_20_0 % 11.74/2.36 | % 11.74/2.36 | GROUND_INST: instantiating (8) with all_20_3, all_20_0, all_20_5, all_33_0, % 11.74/2.36 | simplifying with (49), (56) gives: % 11.74/2.36 | (57) all_20_0 = all_20_3 % 11.74/2.36 | % 11.74/2.36 | REDUCE: (11), (57) imply: % 11.74/2.36 | (58) $false % 11.74/2.36 | % 11.74/2.36 | CLOSE: (58) is inconsistent. % 11.74/2.36 | % 11.74/2.36 End of proof % 11.74/2.36 % SZS output end Proof for theBenchmark % 11.74/2.36 % 11.74/2.36 1730ms %------------------------------------------------------------------------------