%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU045+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 : n031.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 17:42:23 EDT 2023 % Result : Theorem 15.72s 2.86s % Output : Proof 15.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SEU045+1 : TPTP v8.1.2. Released v3.2.0. % 0.04/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n031.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 : Wed Aug 23 18:57:20 EDT 2023 % 0.13/0.35 % 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 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.63/1.10 Prover 4: Preprocessing ... % 2.63/1.10 Prover 1: Preprocessing ... % 2.99/1.14 Prover 0: Preprocessing ... % 2.99/1.14 Prover 6: Preprocessing ... % 2.99/1.14 Prover 5: Preprocessing ... % 2.99/1.14 Prover 2: Preprocessing ... % 2.99/1.14 Prover 3: Preprocessing ... % 6.27/1.58 Prover 1: Warning: ignoring some quantifiers % 6.27/1.61 Prover 3: Warning: ignoring some quantifiers % 6.27/1.64 Prover 1: Constructing countermodel ... % 6.27/1.64 Prover 3: Constructing countermodel ... % 6.27/1.64 Prover 5: Proving ... % 6.86/1.66 Prover 6: Proving ... % 8.08/1.82 Prover 2: Proving ... % 10.64/2.21 Prover 4: Warning: ignoring some quantifiers % 11.21/2.25 Prover 0: Proving ... % 11.52/2.28 Prover 4: Constructing countermodel ... % 12.18/2.40 Prover 3: gave up % 12.18/2.41 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.73/2.45 Prover 7: Preprocessing ... % 13.51/2.57 Prover 7: Warning: ignoring some quantifiers % 13.51/2.59 Prover 7: Constructing countermodel ... % 14.82/2.72 Prover 1: gave up % 14.82/2.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.07/2.76 Prover 8: Preprocessing ... % 15.72/2.84 Prover 7: Found proof (size 20) % 15.72/2.84 Prover 7: proved (430ms) % 15.72/2.84 Prover 2: stopped % 15.72/2.84 Prover 0: stopped % 15.72/2.84 Prover 6: stopped % 15.72/2.84 Prover 4: stopped % 15.72/2.84 Prover 5: stopped % 15.72/2.85 Prover 8: Warning: ignoring some quantifiers % 15.72/2.85 Prover 8: Constructing countermodel ... % 15.72/2.86 Prover 8: stopped % 15.72/2.86 % 15.72/2.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.72/2.86 % 15.72/2.86 % SZS output start Proof for theBenchmark % 15.72/2.86 Assumptions after simplification: % 15.72/2.86 --------------------------------- % 15.72/2.87 % 15.72/2.87 (dt_k8_relat_1) % 15.96/2.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0, % 15.96/2.89 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | relation(v2)) % 15.96/2.89 % 15.96/2.89 (fc5_funct_1) % 15.96/2.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0, % 15.96/2.89 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ function(v1) | ~ relation(v1) | % 15.96/2.89 function(v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 15.96/2.89 (relation_rng_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 15.96/2.89 function(v1) | ~ relation(v1) | relation(v2)) % 15.96/2.89 % 15.96/2.89 (t85_funct_1) % 15.96/2.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 15.96/2.90 (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom(v1) = v2) | ~ % 15.96/2.90 $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ function(v3) | ~ function(v1) | ~ % 15.96/2.90 relation(v3) | ~ relation(v1) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 15.96/2.90 ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ($i(v9) & $i(v6) & ( ~ (v4 = v1) | % 15.96/2.90 (relation_dom(v3) = v5 & $i(v5) & ! [v11: $i] : ! [v12: $i] : ( ~ % 15.96/2.90 (apply(v3, v11) = v12) | ~ $i(v11) | ~ in(v12, v0) | ~ in(v11, % 15.96/2.90 v5) | in(v11, v2)) & ! [v11: $i] : ! [v12: $i] : ( ~ (apply(v3, % 15.96/2.90 v11) = v12) | ~ $i(v11) | ~ in(v11, v2) | in(v12, v0)) & ! % 15.96/2.90 [v11: $i] : ! [v12: $i] : ( ~ (apply(v3, v11) = v12) | ~ $i(v11) | % 15.96/2.90 ~ in(v11, v2) | in(v11, v5)) & ! [v11: $i] : ! [v12: $i] : ( ~ % 15.96/2.90 (apply(v3, v11) = v12) | ~ $i(v11) | ~ in(v11, v2) | (apply(v1, % 15.96/2.90 v11) = v12 & $i(v12))) & ! [v11: $i] : ! [v12: $i] : ( ~ % 15.96/2.90 (apply(v1, v11) = v12) | ~ $i(v11) | ~ in(v11, v2) | (apply(v3, % 15.96/2.90 v11) = v12 & $i(v12))))) & (v4 = v1 | ( ~ (v8 = v7) & apply(v3, % 15.96/2.90 v6) = v8 & apply(v1, v6) = v7 & $i(v8) & $i(v7) & in(v6, v2)) | % 15.96/2.90 (relation_dom(v3) = v5 & $i(v5) & ( ~ in(v9, v5) | ~ in(v9, v2) | % 15.96/2.90 (apply(v3, v9) = v10 & $i(v10) & ~ in(v10, v0))) & (in(v9, v2) | % 15.96/2.90 (apply(v3, v9) = v10 & $i(v10) & in(v10, v0) & in(v9, v5))))))) & ? % 15.96/2.90 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 15.96/2.90 (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ $i(v3) | ~ $i(v1) % 15.96/2.90 | ~ $i(v0) | ~ function(v3) | ~ function(v1) | ~ relation(v3) | ~ % 15.96/2.90 relation(v1) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 15.96/2.90 [v9: $i] : ? [v10: $i] : ($i(v9) & $i(v6) & ((v5 = v1 & % 15.96/2.90 relation_rng_restriction(v0, v3) = v1) | ( ~ (v8 = v7) & apply(v3, v6) % 15.96/2.90 = v8 & apply(v1, v6) = v7 & $i(v8) & $i(v7) & in(v6, v2)) | (( ~ % 15.96/2.90 in(v9, v4) | ~ in(v9, v2) | (apply(v3, v9) = v10 & $i(v10) & ~ % 15.96/2.90 in(v10, v0))) & (in(v9, v2) | (apply(v3, v9) = v10 & $i(v10) & % 15.96/2.90 in(v10, v0) & in(v9, v4))))) & (( ~ (v5 = v1) & % 15.96/2.90 relation_rng_restriction(v0, v3) = v5 & $i(v5)) | ( ! [v11: $i] : ! % 15.96/2.90 [v12: $i] : ( ~ (apply(v3, v11) = v12) | ~ $i(v11) | ~ in(v12, v0) | % 15.96/2.90 ~ in(v11, v4) | in(v11, v2)) & ! [v11: $i] : ! [v12: $i] : ( ~ % 15.96/2.90 (apply(v3, v11) = v12) | ~ $i(v11) | ~ in(v11, v2) | in(v12, v0)) % 15.96/2.90 & ! [v11: $i] : ! [v12: $i] : ( ~ (apply(v3, v11) = v12) | ~ % 15.96/2.90 $i(v11) | ~ in(v11, v2) | in(v11, v4)) & ! [v11: $i] : ! [v12: % 15.96/2.90 $i] : ( ~ (apply(v3, v11) = v12) | ~ $i(v11) | ~ in(v11, v2) | % 15.96/2.90 (apply(v1, v11) = v12 & $i(v12))) & ! [v11: $i] : ! [v12: $i] : ( % 15.96/2.91 ~ (apply(v1, v11) = v12) | ~ $i(v11) | ~ in(v11, v2) | (apply(v3, % 15.96/2.91 v11) = v12 & $i(v12))))))) % 15.96/2.91 % 15.96/2.91 (t87_funct_1) % 15.96/2.91 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 15.96/2.91 $i] : ? [v6: $i] : ( ~ (v6 = v5) & apply(v3, v1) = v5 & apply(v2, v1) = v6 % 15.96/2.91 & relation_rng_restriction(v0, v2) = v3 & relation_dom(v3) = v4 & $i(v6) & % 15.96/2.91 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & in(v1, v4) & % 15.96/2.91 function(v2) & relation(v2)) % 15.96/2.91 % 15.96/2.91 (function-axioms) % 15.96/2.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.96/2.91 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 15.96/2.91 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) % 15.96/2.91 = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) & ! [v0: $i] : ! % 15.96/2.91 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ % 15.96/2.91 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 15.96/2.91 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 15.96/2.91 % 15.96/2.91 Further assumptions not needed in the proof: % 15.96/2.91 -------------------------------------------- % 15.96/2.91 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1, % 15.96/2.91 existence_m1_subset_1, fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc4_relat_1, % 15.96/2.91 fc5_relat_1, fc7_relat_1, rc1_funct_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0, % 15.96/2.91 rc2_funct_1, rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1, % 15.96/2.91 reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, % 15.96/2.91 t6_boole, t7_boole, t8_boole % 15.96/2.91 % 15.96/2.91 Those formulas are unsatisfiable: % 15.96/2.91 --------------------------------- % 15.96/2.91 % 15.96/2.91 Begin of proof % 15.96/2.91 | % 15.96/2.91 | ALPHA: (fc5_funct_1) implies: % 15.96/2.91 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 15.96/2.91 | (relation_rng_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 15.96/2.91 | function(v1) | ~ relation(v1) | function(v2)) % 15.96/2.91 | % 15.96/2.91 | ALPHA: (t85_funct_1) implies: % 15.96/2.91 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 15.96/2.91 | ~ (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom(v1) = % 15.96/2.91 | v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ function(v3) | ~ % 15.96/2.91 | function(v1) | ~ relation(v3) | ~ relation(v1) | ? [v5: $i] : ? % 15.96/2.91 | [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : % 15.96/2.91 | ($i(v9) & $i(v6) & ( ~ (v4 = v1) | (relation_dom(v3) = v5 & $i(v5) & % 15.96/2.91 | ! [v11: $i] : ! [v12: $i] : ( ~ (apply(v3, v11) = v12) | ~ % 15.96/2.91 | $i(v11) | ~ in(v12, v0) | ~ in(v11, v5) | in(v11, v2)) & ! % 15.96/2.91 | [v11: $i] : ! [v12: $i] : ( ~ (apply(v3, v11) = v12) | ~ % 15.96/2.91 | $i(v11) | ~ in(v11, v2) | in(v12, v0)) & ! [v11: $i] : ! % 15.96/2.91 | [v12: $i] : ( ~ (apply(v3, v11) = v12) | ~ $i(v11) | ~ % 15.96/2.91 | in(v11, v2) | in(v11, v5)) & ! [v11: $i] : ! [v12: $i] : ( % 15.96/2.91 | ~ (apply(v3, v11) = v12) | ~ $i(v11) | ~ in(v11, v2) | % 15.96/2.91 | (apply(v1, v11) = v12 & $i(v12))) & ! [v11: $i] : ! [v12: % 15.96/2.91 | $i] : ( ~ (apply(v1, v11) = v12) | ~ $i(v11) | ~ in(v11, % 15.96/2.91 | v2) | (apply(v3, v11) = v12 & $i(v12))))) & (v4 = v1 | ( ~ % 15.96/2.91 | (v8 = v7) & apply(v3, v6) = v8 & apply(v1, v6) = v7 & $i(v8) & % 15.96/2.91 | $i(v7) & in(v6, v2)) | (relation_dom(v3) = v5 & $i(v5) & ( ~ % 15.96/2.91 | in(v9, v5) | ~ in(v9, v2) | (apply(v3, v9) = v10 & $i(v10) & % 15.96/2.91 | ~ in(v10, v0))) & (in(v9, v2) | (apply(v3, v9) = v10 & % 15.96/2.91 | $i(v10) & in(v10, v0) & in(v9, v5))))))) % 15.96/2.91 | % 15.96/2.91 | ALPHA: (function-axioms) implies: % 15.96/2.92 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.96/2.92 | (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 15.96/2.92 | % 15.96/2.92 | DELTA: instantiating (t87_funct_1) with fresh symbols all_42_0, all_42_1, % 15.96/2.92 | all_42_2, all_42_3, all_42_4, all_42_5, all_42_6 gives: % 15.96/2.92 | (4) ~ (all_42_0 = all_42_1) & apply(all_42_3, all_42_5) = all_42_1 & % 15.96/2.92 | apply(all_42_4, all_42_5) = all_42_0 & % 15.96/2.92 | relation_rng_restriction(all_42_6, all_42_4) = all_42_3 & % 15.96/2.92 | relation_dom(all_42_3) = all_42_2 & $i(all_42_0) & $i(all_42_1) & % 15.96/2.92 | $i(all_42_2) & $i(all_42_3) & $i(all_42_4) & $i(all_42_5) & % 15.96/2.92 | $i(all_42_6) & in(all_42_5, all_42_2) & function(all_42_4) & % 15.96/2.92 | relation(all_42_4) % 15.96/2.92 | % 15.96/2.92 | ALPHA: (4) implies: % 15.96/2.92 | (5) ~ (all_42_0 = all_42_1) % 15.96/2.92 | (6) relation(all_42_4) % 15.96/2.92 | (7) function(all_42_4) % 15.96/2.92 | (8) in(all_42_5, all_42_2) % 15.96/2.92 | (9) $i(all_42_6) % 15.96/2.92 | (10) $i(all_42_5) % 15.96/2.92 | (11) $i(all_42_4) % 15.96/2.92 | (12) $i(all_42_3) % 15.96/2.92 | (13) relation_dom(all_42_3) = all_42_2 % 15.96/2.92 | (14) relation_rng_restriction(all_42_6, all_42_4) = all_42_3 % 15.96/2.92 | (15) apply(all_42_4, all_42_5) = all_42_0 % 15.96/2.92 | (16) apply(all_42_3, all_42_5) = all_42_1 % 15.96/2.92 | % 15.96/2.92 | GROUND_INST: instantiating (3) with all_42_0, all_42_1, all_42_5, all_42_4, % 15.96/2.92 | simplifying with (15) gives: % 15.96/2.92 | (17) all_42_0 = all_42_1 | ~ (apply(all_42_4, all_42_5) = all_42_1) % 15.96/2.92 | % 15.96/2.92 | GROUND_INST: instantiating (1) with all_42_6, all_42_4, all_42_3, simplifying % 15.96/2.92 | with (6), (7), (9), (11), (14) gives: % 15.96/2.92 | (18) function(all_42_3) % 15.96/2.92 | % 15.96/2.92 | GROUND_INST: instantiating (dt_k8_relat_1) with all_42_6, all_42_4, all_42_3, % 15.96/2.92 | simplifying with (6), (9), (11), (14) gives: % 15.96/2.92 | (19) relation(all_42_3) % 15.96/2.92 | % 15.96/2.92 | GROUND_INST: instantiating (2) with all_42_6, all_42_3, all_42_2, all_42_4, % 15.96/2.92 | all_42_3, simplifying with (6), (7), (9), (11), (12), (13), (14), % 15.96/2.92 | (18), (19) gives: % 15.96/2.92 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_dom(all_42_4) = v0 % 15.96/2.92 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ % 15.96/2.92 | (apply(all_42_3, v3) = v4) | ~ $i(v3) | ~ in(v3, all_42_2) | % 15.96/2.92 | (apply(all_42_4, v3) = v4 & $i(v4))) & ! [v3: $i] : ! [v4: $i] : % 15.96/2.92 | ( ~ (apply(all_42_4, v3) = v4) | ~ $i(v3) | ~ in(v4, all_42_6) | % 15.96/2.92 | ~ in(v3, v0) | in(v3, all_42_2)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 15.96/2.92 | (apply(all_42_4, v3) = v4) | ~ $i(v3) | ~ in(v3, all_42_2) | % 15.96/2.92 | in(v4, all_42_6)) & ! [v3: $i] : ! [v4: $i] : ( ~ % 15.96/2.92 | (apply(all_42_4, v3) = v4) | ~ $i(v3) | ~ in(v3, all_42_2) | % 15.96/2.92 | in(v3, v0)) & ! [v3: $i] : ! [v4: $i] : ( ~ (apply(all_42_4, v3) % 15.96/2.92 | = v4) | ~ $i(v3) | ~ in(v3, all_42_2) | (apply(all_42_3, v3) = % 15.96/2.92 | v4 & $i(v4)))) % 15.96/2.92 | % 15.96/2.92 | DELTA: instantiating (20) with fresh symbols all_65_0, all_65_1, all_65_2 % 15.96/2.92 | gives: % 15.96/2.93 | (21) relation_dom(all_42_4) = all_65_2 & $i(all_65_0) & $i(all_65_1) & % 15.96/2.93 | $i(all_65_2) & ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_3, v0) = % 15.96/2.93 | v1) | ~ $i(v0) | ~ in(v0, all_42_2) | (apply(all_42_4, v0) = v1 % 15.96/2.93 | & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_4, v0) % 15.96/2.93 | = v1) | ~ $i(v0) | ~ in(v1, all_42_6) | ~ in(v0, all_65_2) | % 15.96/2.93 | in(v0, all_42_2)) & ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_4, % 15.96/2.93 | v0) = v1) | ~ $i(v0) | ~ in(v0, all_42_2) | in(v1, all_42_6)) % 15.96/2.93 | & ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_4, v0) = v1) | ~ % 15.96/2.93 | $i(v0) | ~ in(v0, all_42_2) | in(v0, all_65_2)) & ! [v0: $i] : ! % 15.96/2.93 | [v1: $i] : ( ~ (apply(all_42_4, v0) = v1) | ~ $i(v0) | ~ in(v0, % 15.96/2.93 | all_42_2) | (apply(all_42_3, v0) = v1 & $i(v1))) % 15.96/2.93 | % 15.96/2.93 | ALPHA: (21) implies: % 15.96/2.93 | (22) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_42_3, v0) = v1) | ~ $i(v0) % 15.96/2.93 | | ~ in(v0, all_42_2) | (apply(all_42_4, v0) = v1 & $i(v1))) % 15.96/2.93 | % 15.96/2.93 | GROUND_INST: instantiating (22) with all_42_5, all_42_1, simplifying with (8), % 15.96/2.93 | (10), (16) gives: % 15.96/2.93 | (23) apply(all_42_4, all_42_5) = all_42_1 & $i(all_42_1) % 15.96/2.93 | % 15.96/2.93 | ALPHA: (23) implies: % 15.96/2.93 | (24) apply(all_42_4, all_42_5) = all_42_1 % 15.96/2.93 | % 15.96/2.93 | BETA: splitting (17) gives: % 15.96/2.93 | % 15.96/2.93 | Case 1: % 15.96/2.93 | | % 15.96/2.93 | | (25) ~ (apply(all_42_4, all_42_5) = all_42_1) % 15.96/2.93 | | % 15.96/2.93 | | PRED_UNIFY: (24), (25) imply: % 15.96/2.93 | | (26) $false % 15.96/2.93 | | % 15.96/2.93 | | CLOSE: (26) is inconsistent. % 15.96/2.93 | | % 15.96/2.93 | Case 2: % 15.96/2.93 | | % 15.96/2.93 | | (27) all_42_0 = all_42_1 % 15.96/2.93 | | % 15.96/2.93 | | REDUCE: (5), (27) imply: % 15.96/2.93 | | (28) $false % 15.96/2.93 | | % 15.96/2.93 | | CLOSE: (28) is inconsistent. % 15.96/2.93 | | % 15.96/2.93 | End of split % 15.96/2.93 | % 15.96/2.93 End of proof % 15.96/2.93 % SZS output end Proof for theBenchmark % 15.96/2.93 % 15.96/2.93 2317ms %------------------------------------------------------------------------------