%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU014+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 : n001.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 17:42:18 EDT 2023 % Result : Theorem 16.04s 2.93s % Output : Proof 16.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU014+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.35 % Computer : n001.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Wed Aug 23 14:02:09 EDT 2023 % 0.17/0.35 % CPUTime : % 0.22/0.59 ________ _____ % 0.22/0.59 ___ __ \_________(_)________________________________ % 0.22/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.59 % 0.22/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.59 (2023-06-19) % 0.22/0.59 % 0.22/0.59 (c) Philipp Rümmer, 2009-2023 % 0.22/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.59 Amanda Stjerna. % 0.22/0.59 Free software under BSD-3-Clause. % 0.22/0.59 % 0.22/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.59 % 0.22/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.22/0.61 Running up to 7 provers in parallel. % 0.22/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.73/1.09 Prover 1: Preprocessing ... % 2.73/1.09 Prover 4: Preprocessing ... % 3.15/1.13 Prover 0: Preprocessing ... % 3.15/1.13 Prover 5: Preprocessing ... % 3.15/1.13 Prover 2: Preprocessing ... % 3.15/1.13 Prover 6: Preprocessing ... % 3.15/1.13 Prover 3: Preprocessing ... % 6.51/1.63 Prover 1: Warning: ignoring some quantifiers % 6.84/1.65 Prover 3: Warning: ignoring some quantifiers % 6.84/1.67 Prover 3: Constructing countermodel ... % 6.84/1.68 Prover 1: Constructing countermodel ... % 6.84/1.69 Prover 2: Proving ... % 6.84/1.69 Prover 5: Proving ... % 6.84/1.70 Prover 6: Proving ... % 7.93/1.84 Prover 4: Warning: ignoring some quantifiers % 8.32/1.88 Prover 4: Constructing countermodel ... % 9.41/2.02 Prover 0: Proving ... % 10.42/2.15 Prover 3: gave up % 10.42/2.16 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.42/2.20 Prover 7: Preprocessing ... % 10.42/2.32 Prover 7: Warning: ignoring some quantifiers % 10.42/2.33 Prover 7: Constructing countermodel ... % 16.04/2.93 Prover 7: Found proof (size 68) % 16.04/2.93 Prover 7: proved (768ms) % 16.04/2.93 Prover 1: stopped % 16.04/2.93 Prover 6: stopped % 16.04/2.93 Prover 2: stopped % 16.04/2.93 Prover 5: stopped % 16.04/2.93 Prover 0: stopped % 16.04/2.93 Prover 4: stopped % 16.04/2.93 % 16.04/2.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 16.04/2.93 % 16.04/2.94 % SZS output start Proof for theBenchmark % 16.04/2.95 Assumptions after simplification: % 16.04/2.95 --------------------------------- % 16.04/2.95 % 16.04/2.95 (d8_funct_1) % 16.04/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v2 % 16.04/2.98 | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v3) = v4) | ~ (apply(v0, v2) = % 16.04/2.98 v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ one_to_one(v0) | ~ % 16.04/2.98 relation(v0) | ~ function(v0) | ~ in(v3, v1) | ~ in(v2, v1)) & ! [v0: % 16.04/2.98 $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~ % 16.04/2.98 relation(v0) | ~ function(v0) | one_to_one(v0) | ? [v2: $i] : ? [v3: $i] % 16.04/2.98 : ? [v4: $i] : ( ~ (v3 = v2) & apply(v0, v3) = v4 & apply(v0, v2) = v4 & % 16.04/2.98 $i(v4) & $i(v3) & $i(v2) & in(v3, v1) & in(v2, v1))) % 16.04/2.98 % 16.04/2.98 (dt_k5_relat_1) % 16.04/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, v1) = % 16.04/2.98 v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ relation(v0) | % 16.04/2.98 relation(v2)) % 16.04/2.98 % 16.04/2.98 (fc1_funct_1) % 16.04/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, v1) = % 16.04/2.98 v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ relation(v0) | ~ % 16.04/2.98 function(v1) | ~ function(v0) | relation(v2)) & ! [v0: $i] : ! [v1: $i] : % 16.04/2.98 ! [v2: $i] : ( ~ (relation_composition(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 16.04/2.98 | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | % 16.04/2.98 function(v2)) % 16.04/2.98 % 16.04/2.98 (t23_funct_1) % 16.54/2.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (apply(v1, v0) = v2) | ~ $i(v1) % 16.54/2.99 | ~ $i(v0) | ~ relation(v1) | ~ function(v1) | ? [v3: $i] : % 16.54/2.99 (relation_dom(v1) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ( ~ % 16.54/2.99 (relation_composition(v1, v4) = v5) | ~ $i(v4) | ~ relation(v4) | ~ % 16.54/2.99 function(v4) | ~ in(v0, v3) | ? [v6: $i] : (apply(v5, v0) = v6 & % 16.54/2.99 apply(v4, v2) = v6 & $i(v6))) & ! [v4: $i] : ! [v5: $i] : ( ~ % 16.54/2.99 (apply(v4, v2) = v5) | ~ $i(v4) | ~ relation(v4) | ~ function(v4) | % 16.54/2.99 ~ in(v0, v3) | ? [v6: $i] : (relation_composition(v1, v4) = v6 & % 16.54/2.99 apply(v6, v0) = v5 & $i(v6) & $i(v5))))) % 16.54/2.99 % 16.54/2.99 (t46_relat_1) % 16.54/2.99 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 16.54/2.99 relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! [v3: $i] : % 16.54/2.99 ! [v4: $i] : ( ~ (relation_composition(v0, v3) = v4) | ~ $i(v3) | ~ % 16.54/2.99 relation(v3) | ? [v5: $i] : ? [v6: $i] : ((v6 = v2 & relation_dom(v4) % 16.54/2.99 = v2) | (relation_dom(v3) = v5 & $i(v5) & ~ subset(v1, v5)))) & ! % 16.54/2.99 [v3: $i] : ! [v4: $i] : ( ~ (relation_dom(v3) = v4) | ~ $i(v3) | ~ % 16.54/2.99 subset(v1, v4) | ~ relation(v3) | ? [v5: $i] : % 16.54/2.99 (relation_composition(v0, v3) = v5 & relation_dom(v5) = v2 & $i(v5))))) % 16.54/2.99 & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~ % 16.54/2.99 relation(v0) | ? [v2: $i] : (relation_rng(v0) = v2 & $i(v2) & ! [v3: $i] : % 16.54/2.99 ! [v4: $i] : ( ~ (relation_composition(v0, v3) = v4) | ~ $i(v3) | ~ % 16.54/2.99 relation(v3) | ? [v5: $i] : ? [v6: $i] : ((v6 = v1 & relation_dom(v4) % 16.54/2.99 = v1 & $i(v1)) | (relation_dom(v3) = v5 & $i(v5) & ~ subset(v2, % 16.54/2.99 v5)))) & ! [v3: $i] : ! [v4: $i] : ( ~ (relation_dom(v3) = v4) | % 16.54/2.99 ~ $i(v3) | ~ subset(v2, v4) | ~ relation(v3) | ? [v5: $i] : % 16.54/2.99 (relation_composition(v0, v3) = v5 & relation_dom(v5) = v1 & $i(v5) & % 16.54/2.99 $i(v1))))) % 16.54/2.99 % 16.54/2.99 (t47_funct_1) % 16.54/2.99 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 16.54/2.99 (relation_rng(v2) = v4 & relation_composition(v2, v0) = v3 & relation_dom(v0) % 16.54/2.99 = v1 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & subset(v4, v1) & % 16.54/2.99 one_to_one(v3) & relation(v2) & relation(v0) & function(v2) & function(v0) & % 16.54/2.99 ~ one_to_one(v2)) % 16.54/2.99 % 16.54/2.99 (function-axioms) % 16.54/2.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.54/2.99 (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = % 16.54/2.99 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 16.54/2.99 ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 16.54/2.99 $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ % 16.54/2.99 (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 16.54/2.99 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] : ! % 16.54/2.99 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ % 16.54/2.99 (relation_dom(v2) = v0)) % 16.54/2.99 % 16.54/2.99 Further assumptions not needed in the proof: % 16.54/2.99 -------------------------------------------- % 16.54/3.00 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, existence_m1_subset_1, % 16.54/3.00 fc10_relat_1, fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc4_relat_1, % 16.54/3.00 fc5_relat_1, fc6_relat_1, fc7_relat_1, fc8_relat_1, fc9_relat_1, rc1_funct_1, % 16.54/3.00 rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_relat_1, rc2_subset_1, % 16.54/3.00 rc2_xboole_0, rc3_relat_1, reflexivity_r1_tarski, t1_subset, t2_subset, % 16.54/3.00 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole % 16.54/3.00 % 16.54/3.00 Those formulas are unsatisfiable: % 16.54/3.00 --------------------------------- % 16.54/3.00 % 16.54/3.00 Begin of proof % 16.54/3.00 | % 16.54/3.00 | ALPHA: (d8_funct_1) implies: % 16.54/3.00 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | % 16.54/3.00 | ~ relation(v0) | ~ function(v0) | one_to_one(v0) | ? [v2: $i] : ? % 16.54/3.00 | [v3: $i] : ? [v4: $i] : ( ~ (v3 = v2) & apply(v0, v3) = v4 & % 16.54/3.00 | apply(v0, v2) = v4 & $i(v4) & $i(v3) & $i(v2) & in(v3, v1) & in(v2, % 16.54/3.00 | v1))) % 16.54/3.00 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 16.54/3.00 | (v3 = v2 | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v3) = v4) | ~ % 16.54/3.00 | (apply(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ % 16.54/3.00 | one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ~ in(v3, v1) | % 16.54/3.00 | ~ in(v2, v1)) % 16.54/3.00 | % 16.54/3.00 | ALPHA: (fc1_funct_1) implies: % 16.54/3.00 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, % 16.54/3.00 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ % 16.54/3.00 | relation(v0) | ~ function(v1) | ~ function(v0) | function(v2)) % 16.54/3.00 | % 16.54/3.00 | ALPHA: (t46_relat_1) implies: % 16.54/3.00 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | % 16.54/3.00 | ~ relation(v0) | ? [v2: $i] : (relation_rng(v0) = v2 & $i(v2) & ! % 16.54/3.00 | [v3: $i] : ! [v4: $i] : ( ~ (relation_composition(v0, v3) = v4) | % 16.54/3.00 | ~ $i(v3) | ~ relation(v3) | ? [v5: $i] : ? [v6: $i] : ((v6 = % 16.54/3.00 | v1 & relation_dom(v4) = v1 & $i(v1)) | (relation_dom(v3) = v5 % 16.54/3.00 | & $i(v5) & ~ subset(v2, v5)))) & ! [v3: $i] : ! [v4: $i] : % 16.54/3.00 | ( ~ (relation_dom(v3) = v4) | ~ $i(v3) | ~ subset(v2, v4) | ~ % 16.54/3.00 | relation(v3) | ? [v5: $i] : (relation_composition(v0, v3) = v5 & % 16.54/3.00 | relation_dom(v5) = v1 & $i(v5) & $i(v1))))) % 16.54/3.00 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | % 16.54/3.00 | ~ relation(v0) | ? [v2: $i] : (relation_dom(v0) = v2 & $i(v2) & ! % 16.54/3.00 | [v3: $i] : ! [v4: $i] : ( ~ (relation_composition(v0, v3) = v4) | % 16.54/3.00 | ~ $i(v3) | ~ relation(v3) | ? [v5: $i] : ? [v6: $i] : ((v6 = % 16.54/3.00 | v2 & relation_dom(v4) = v2) | (relation_dom(v3) = v5 & $i(v5) % 16.54/3.00 | & ~ subset(v1, v5)))) & ! [v3: $i] : ! [v4: $i] : ( ~ % 16.54/3.00 | (relation_dom(v3) = v4) | ~ $i(v3) | ~ subset(v1, v4) | ~ % 16.54/3.00 | relation(v3) | ? [v5: $i] : (relation_composition(v0, v3) = v5 & % 16.54/3.00 | relation_dom(v5) = v2 & $i(v5))))) % 16.54/3.00 | % 16.54/3.00 | ALPHA: (function-axioms) implies: % 16.54/3.00 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 16.54/3.01 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 16.54/3.01 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.54/3.01 | (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 16.54/3.01 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 16.54/3.01 | (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, % 16.54/3.01 | v2) = v0)) % 16.54/3.01 | % 16.54/3.01 | DELTA: instantiating (t47_funct_1) with fresh symbols all_43_0, all_43_1, % 16.54/3.01 | all_43_2, all_43_3, all_43_4 gives: % 16.54/3.01 | (9) relation_rng(all_43_2) = all_43_0 & relation_composition(all_43_2, % 16.54/3.01 | all_43_4) = all_43_1 & relation_dom(all_43_4) = all_43_3 & % 16.54/3.01 | $i(all_43_0) & $i(all_43_1) & $i(all_43_2) & $i(all_43_3) & % 16.54/3.01 | $i(all_43_4) & subset(all_43_0, all_43_3) & one_to_one(all_43_1) & % 16.54/3.01 | relation(all_43_2) & relation(all_43_4) & function(all_43_2) & % 16.54/3.01 | function(all_43_4) & ~ one_to_one(all_43_2) % 16.54/3.01 | % 16.54/3.01 | ALPHA: (9) implies: % 16.54/3.01 | (10) ~ one_to_one(all_43_2) % 16.54/3.01 | (11) function(all_43_4) % 16.54/3.01 | (12) function(all_43_2) % 16.54/3.01 | (13) relation(all_43_4) % 16.54/3.01 | (14) relation(all_43_2) % 16.54/3.01 | (15) one_to_one(all_43_1) % 16.54/3.01 | (16) subset(all_43_0, all_43_3) % 16.54/3.01 | (17) $i(all_43_4) % 16.54/3.01 | (18) $i(all_43_2) % 16.54/3.01 | (19) relation_dom(all_43_4) = all_43_3 % 16.54/3.01 | (20) relation_composition(all_43_2, all_43_4) = all_43_1 % 16.54/3.01 | (21) relation_rng(all_43_2) = all_43_0 % 16.54/3.01 | % 16.54/3.01 | GROUND_INST: instantiating (3) with all_43_2, all_43_4, all_43_1, simplifying % 16.54/3.01 | with (11), (12), (13), (14), (17), (18), (20) gives: % 16.54/3.01 | (22) function(all_43_1) % 16.54/3.01 | % 16.54/3.01 | GROUND_INST: instantiating (dt_k5_relat_1) with all_43_2, all_43_4, all_43_1, % 16.54/3.01 | simplifying with (13), (14), (17), (18), (20) gives: % 16.54/3.01 | (23) relation(all_43_1) % 16.54/3.01 | % 16.54/3.01 | GROUND_INST: instantiating (5) with all_43_2, all_43_0, simplifying with (14), % 16.54/3.01 | (18), (21) gives: % 16.54/3.01 | (24) ? [v0: $i] : (relation_dom(all_43_2) = v0 & $i(v0) & ! [v1: $i] : ! % 16.54/3.01 | [v2: $i] : ( ~ (relation_composition(all_43_2, v1) = v2) | ~ $i(v1) % 16.54/3.01 | | ~ relation(v1) | ? [v3: $i] : ? [v4: $i] : ((v4 = v0 & % 16.54/3.01 | relation_dom(v2) = v0) | (relation_dom(v1) = v3 & $i(v3) & ~ % 16.54/3.01 | subset(all_43_0, v3)))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 16.54/3.01 | (relation_dom(v1) = v2) | ~ $i(v1) | ~ subset(all_43_0, v2) | ~ % 16.54/3.01 | relation(v1) | ? [v3: $i] : (relation_composition(all_43_2, v1) = % 16.54/3.01 | v3 & relation_dom(v3) = v0 & $i(v3)))) % 16.54/3.01 | % 16.54/3.01 | DELTA: instantiating (24) with fresh symbol all_55_0 gives: % 16.54/3.01 | (25) relation_dom(all_43_2) = all_55_0 & $i(all_55_0) & ! [v0: $i] : ! % 16.54/3.01 | [v1: $i] : ( ~ (relation_composition(all_43_2, v0) = v1) | ~ $i(v0) | % 16.54/3.01 | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 = all_55_0 & % 16.54/3.01 | relation_dom(v1) = all_55_0) | (relation_dom(v0) = v2 & $i(v2) & % 16.54/3.01 | ~ subset(all_43_0, v2)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 16.54/3.01 | (relation_dom(v0) = v1) | ~ $i(v0) | ~ subset(all_43_0, v1) | ~ % 16.54/3.01 | relation(v0) | ? [v2: $i] : (relation_composition(all_43_2, v0) = % 16.54/3.01 | v2 & relation_dom(v2) = all_55_0 & $i(v2))) % 16.54/3.01 | % 16.54/3.01 | ALPHA: (25) implies: % 16.54/3.02 | (26) relation_dom(all_43_2) = all_55_0 % 16.54/3.02 | (27) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | % 16.54/3.02 | ~ subset(all_43_0, v1) | ~ relation(v0) | ? [v2: $i] : % 16.54/3.02 | (relation_composition(all_43_2, v0) = v2 & relation_dom(v2) = % 16.54/3.02 | all_55_0 & $i(v2))) % 16.54/3.02 | % 16.54/3.02 | GROUND_INST: instantiating (27) with all_43_4, all_43_3, simplifying with % 16.54/3.02 | (13), (16), (17), (19) gives: % 16.54/3.02 | (28) ? [v0: $i] : (relation_composition(all_43_2, all_43_4) = v0 & % 16.54/3.02 | relation_dom(v0) = all_55_0 & $i(v0)) % 16.54/3.02 | % 16.54/3.02 | DELTA: instantiating (28) with fresh symbol all_58_0 gives: % 16.54/3.02 | (29) relation_composition(all_43_2, all_43_4) = all_58_0 & % 16.54/3.02 | relation_dom(all_58_0) = all_55_0 & $i(all_58_0) % 16.54/3.02 | % 16.54/3.02 | ALPHA: (29) implies: % 16.54/3.02 | (30) $i(all_58_0) % 16.54/3.02 | (31) relation_dom(all_58_0) = all_55_0 % 16.54/3.02 | (32) relation_composition(all_43_2, all_43_4) = all_58_0 % 16.54/3.02 | % 16.54/3.02 | GROUND_INST: instantiating (8) with all_43_1, all_58_0, all_43_4, all_43_2, % 16.54/3.02 | simplifying with (20), (32) gives: % 16.54/3.02 | (33) all_58_0 = all_43_1 % 16.54/3.02 | % 16.54/3.02 | REDUCE: (31), (33) imply: % 16.54/3.02 | (34) relation_dom(all_43_1) = all_55_0 % 16.54/3.02 | % 16.54/3.02 | REDUCE: (30), (33) imply: % 16.54/3.02 | (35) $i(all_43_1) % 16.54/3.02 | % 16.54/3.02 | GROUND_INST: instantiating (1) with all_43_2, all_55_0, simplifying with (10), % 16.54/3.02 | (12), (14), (18), (26) gives: % 16.54/3.02 | (36) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) & % 16.54/3.02 | apply(all_43_2, v1) = v2 & apply(all_43_2, v0) = v2 & $i(v2) & % 16.54/3.02 | $i(v1) & $i(v0) & in(v1, all_55_0) & in(v0, all_55_0)) % 16.54/3.02 | % 16.54/3.02 | GROUND_INST: instantiating (4) with all_43_1, all_55_0, simplifying with (23), % 16.54/3.02 | (34), (35) gives: % 16.54/3.02 | (37) ? [v0: $i] : (relation_rng(all_43_1) = v0 & $i(v0) & ! [v1: $i] : ! % 16.54/3.02 | [v2: $i] : ( ~ (relation_composition(all_43_1, v1) = v2) | ~ $i(v1) % 16.54/3.02 | | ~ relation(v1) | ? [v3: $i] : ? [v4: int] : ((v4 = all_55_0 & % 16.54/3.02 | relation_dom(v2) = all_55_0 & $i(all_55_0)) | % 16.54/3.02 | (relation_dom(v1) = v3 & $i(v3) & ~ subset(v0, v3)))) & ! [v1: % 16.54/3.02 | $i] : ! [v2: $i] : ( ~ (relation_dom(v1) = v2) | ~ $i(v1) | ~ % 16.54/3.02 | subset(v0, v2) | ~ relation(v1) | ? [v3: $i] : % 16.54/3.02 | (relation_composition(all_43_1, v1) = v3 & relation_dom(v3) = % 16.54/3.02 | all_55_0 & $i(v3) & $i(all_55_0)))) % 16.54/3.02 | % 16.54/3.02 | DELTA: instantiating (28) with fresh symbol all_77_0 gives: % 16.54/3.02 | (38) relation_composition(all_43_2, all_43_4) = all_77_0 & % 16.54/3.02 | relation_dom(all_77_0) = all_55_0 & $i(all_77_0) % 16.54/3.02 | % 16.54/3.02 | ALPHA: (38) implies: % 16.54/3.02 | (39) $i(all_77_0) % 16.54/3.02 | (40) relation_dom(all_77_0) = all_55_0 % 16.54/3.02 | (41) relation_composition(all_43_2, all_43_4) = all_77_0 % 16.54/3.02 | % 16.54/3.02 | DELTA: instantiating (36) with fresh symbols all_79_0, all_79_1, all_79_2 % 16.54/3.02 | gives: % 16.54/3.02 | (42) ~ (all_79_1 = all_79_2) & apply(all_43_2, all_79_1) = all_79_0 & % 16.54/3.02 | apply(all_43_2, all_79_2) = all_79_0 & $i(all_79_0) & $i(all_79_1) & % 16.54/3.02 | $i(all_79_2) & in(all_79_1, all_55_0) & in(all_79_2, all_55_0) % 16.54/3.02 | % 16.54/3.02 | ALPHA: (42) implies: % 16.54/3.02 | (43) ~ (all_79_1 = all_79_2) % 16.54/3.02 | (44) in(all_79_2, all_55_0) % 16.54/3.02 | (45) in(all_79_1, all_55_0) % 16.54/3.02 | (46) $i(all_79_2) % 16.54/3.02 | (47) $i(all_79_1) % 16.54/3.02 | (48) apply(all_43_2, all_79_2) = all_79_0 % 16.54/3.02 | (49) apply(all_43_2, all_79_1) = all_79_0 % 16.54/3.02 | % 16.54/3.02 | DELTA: instantiating (37) with fresh symbol all_84_0 gives: % 16.54/3.03 | (50) relation_rng(all_43_1) = all_84_0 & $i(all_84_0) & ! [v0: $i] : ! % 16.54/3.03 | [v1: $i] : ( ~ (relation_composition(all_43_1, v0) = v1) | ~ $i(v0) | % 16.54/3.03 | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 = all_55_0 & % 16.54/3.03 | relation_dom(v1) = all_55_0 & $i(all_55_0)) | (relation_dom(v0) % 16.54/3.03 | = v2 & $i(v2) & ~ subset(all_84_0, v2)))) & ! [v0: $i] : ! % 16.54/3.03 | [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~ % 16.54/3.03 | subset(all_84_0, v1) | ~ relation(v0) | ? [v2: $i] : % 16.54/3.03 | (relation_composition(all_43_1, v0) = v2 & relation_dom(v2) = % 16.54/3.03 | all_55_0 & $i(v2) & $i(all_55_0))) % 16.54/3.03 | % 16.54/3.03 | ALPHA: (50) implies: % 16.54/3.03 | (51) relation_rng(all_43_1) = all_84_0 % 16.54/3.03 | % 16.54/3.03 | GROUND_INST: instantiating (8) with all_43_1, all_77_0, all_43_4, all_43_2, % 16.54/3.03 | simplifying with (20), (41) gives: % 16.54/3.03 | (52) all_77_0 = all_43_1 % 16.54/3.03 | % 16.54/3.03 | GROUND_INST: instantiating (t23_funct_1) with all_79_2, all_43_2, all_79_0, % 16.54/3.03 | simplifying with (12), (14), (18), (46), (48) gives: % 16.54/3.03 | (53) ? [v0: $i] : (relation_dom(all_43_2) = v0 & $i(v0) & ! [v1: $i] : ! % 16.54/3.03 | [v2: $i] : ( ~ (relation_composition(all_43_2, v1) = v2) | ~ $i(v1) % 16.54/3.03 | | ~ relation(v1) | ~ function(v1) | ~ in(all_79_2, v0) | ? % 16.54/3.03 | [v3: $i] : (apply(v2, all_79_2) = v3 & apply(v1, all_79_0) = v3 & % 16.54/3.03 | $i(v3))) & ! [v1: $i] : ! [v2: $i] : ( ~ (apply(v1, all_79_0) % 16.54/3.03 | = v2) | ~ $i(v1) | ~ relation(v1) | ~ function(v1) | ~ % 16.54/3.03 | in(all_79_2, v0) | ? [v3: $i] : (relation_composition(all_43_2, % 16.54/3.03 | v1) = v3 & apply(v3, all_79_2) = v2 & $i(v3) & $i(v2)))) % 16.54/3.03 | % 16.54/3.03 | GROUND_INST: instantiating (t23_funct_1) with all_79_1, all_43_2, all_79_0, % 16.54/3.03 | simplifying with (12), (14), (18), (47), (49) gives: % 16.54/3.03 | (54) ? [v0: $i] : (relation_dom(all_43_2) = v0 & $i(v0) & ! [v1: $i] : ! % 16.54/3.03 | [v2: $i] : ( ~ (relation_composition(all_43_2, v1) = v2) | ~ $i(v1) % 16.54/3.03 | | ~ relation(v1) | ~ function(v1) | ~ in(all_79_1, v0) | ? % 16.54/3.03 | [v3: $i] : (apply(v2, all_79_1) = v3 & apply(v1, all_79_0) = v3 & % 16.54/3.03 | $i(v3))) & ! [v1: $i] : ! [v2: $i] : ( ~ (apply(v1, all_79_0) % 16.54/3.03 | = v2) | ~ $i(v1) | ~ relation(v1) | ~ function(v1) | ~ % 16.54/3.03 | in(all_79_1, v0) | ? [v3: $i] : (relation_composition(all_43_2, % 16.54/3.03 | v1) = v3 & apply(v3, all_79_1) = v2 & $i(v3) & $i(v2)))) % 16.54/3.03 | % 16.54/3.03 | GROUND_INST: instantiating (5) with all_43_1, all_84_0, simplifying with (23), % 16.54/3.03 | (35), (51) gives: % 16.54/3.03 | (55) ? [v0: $i] : (relation_dom(all_43_1) = v0 & $i(v0) & ! [v1: $i] : ! % 16.54/3.03 | [v2: $i] : ( ~ (relation_composition(all_43_1, v1) = v2) | ~ $i(v1) % 16.54/3.03 | | ~ relation(v1) | ? [v3: $i] : ? [v4: $i] : ((v4 = v0 & % 16.54/3.03 | relation_dom(v2) = v0) | (relation_dom(v1) = v3 & $i(v3) & ~ % 16.54/3.03 | subset(all_84_0, v3)))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 16.54/3.03 | (relation_dom(v1) = v2) | ~ $i(v1) | ~ subset(all_84_0, v2) | ~ % 16.54/3.03 | relation(v1) | ? [v3: $i] : (relation_composition(all_43_1, v1) = % 16.54/3.03 | v3 & relation_dom(v3) = v0 & $i(v3)))) % 16.54/3.03 | % 16.54/3.03 | DELTA: instantiating (55) with fresh symbol all_105_0 gives: % 16.54/3.03 | (56) relation_dom(all_43_1) = all_105_0 & $i(all_105_0) & ! [v0: $i] : ! % 16.54/3.03 | [v1: $i] : ( ~ (relation_composition(all_43_1, v0) = v1) | ~ $i(v0) | % 16.54/3.03 | ~ relation(v0) | ? [v2: $i] : ? [v3: int] : ((v3 = all_105_0 & % 16.54/3.03 | relation_dom(v1) = all_105_0) | (relation_dom(v0) = v2 & $i(v2) % 16.54/3.03 | & ~ subset(all_84_0, v2)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 16.54/3.03 | (relation_dom(v0) = v1) | ~ $i(v0) | ~ subset(all_84_0, v1) | ~ % 16.54/3.03 | relation(v0) | ? [v2: $i] : (relation_composition(all_43_1, v0) = % 16.54/3.03 | v2 & relation_dom(v2) = all_105_0 & $i(v2))) % 16.54/3.03 | % 16.54/3.03 | ALPHA: (56) implies: % 16.54/3.04 | (57) relation_dom(all_43_1) = all_105_0 % 16.54/3.04 | % 16.54/3.04 | DELTA: instantiating (54) with fresh symbol all_108_0 gives: % 16.54/3.04 | (58) relation_dom(all_43_2) = all_108_0 & $i(all_108_0) & ! [v0: $i] : ! % 16.54/3.04 | [v1: $i] : ( ~ (relation_composition(all_43_2, v0) = v1) | ~ $i(v0) | % 16.54/3.04 | ~ relation(v0) | ~ function(v0) | ~ in(all_79_1, all_108_0) | ? % 16.54/3.04 | [v2: $i] : (apply(v1, all_79_1) = v2 & apply(v0, all_79_0) = v2 & % 16.54/3.04 | $i(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (apply(v0, all_79_0) = % 16.54/3.04 | v1) | ~ $i(v0) | ~ relation(v0) | ~ function(v0) | ~ % 16.54/3.04 | in(all_79_1, all_108_0) | ? [v2: $i] : % 16.54/3.04 | (relation_composition(all_43_2, v0) = v2 & apply(v2, all_79_1) = v1 % 16.54/3.04 | & $i(v2) & $i(v1))) % 16.54/3.04 | % 16.54/3.04 | ALPHA: (58) implies: % 16.54/3.04 | (59) relation_dom(all_43_2) = all_108_0 % 16.54/3.04 | (60) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_composition(all_43_2, v0) = % 16.54/3.04 | v1) | ~ $i(v0) | ~ relation(v0) | ~ function(v0) | ~ % 16.54/3.04 | in(all_79_1, all_108_0) | ? [v2: $i] : (apply(v1, all_79_1) = v2 & % 16.54/3.04 | apply(v0, all_79_0) = v2 & $i(v2))) % 16.54/3.04 | % 16.54/3.04 | GROUND_INST: instantiating (60) with all_43_4, all_43_1, simplifying with % 16.54/3.04 | (11), (13), (17), (20) gives: % 16.54/3.04 | (61) ~ in(all_79_1, all_108_0) | ? [v0: $i] : (apply(all_43_1, all_79_1) % 16.54/3.04 | = v0 & apply(all_43_4, all_79_0) = v0 & $i(v0)) % 16.54/3.04 | % 16.54/3.04 | DELTA: instantiating (53) with fresh symbol all_111_0 gives: % 16.54/3.04 | (62) relation_dom(all_43_2) = all_111_0 & $i(all_111_0) & ! [v0: $i] : ! % 16.54/3.04 | [v1: $i] : ( ~ (relation_composition(all_43_2, v0) = v1) | ~ $i(v0) | % 16.54/3.04 | ~ relation(v0) | ~ function(v0) | ~ in(all_79_2, all_111_0) | ? % 16.54/3.04 | [v2: $i] : (apply(v1, all_79_2) = v2 & apply(v0, all_79_0) = v2 & % 16.54/3.04 | $i(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (apply(v0, all_79_0) = % 16.54/3.04 | v1) | ~ $i(v0) | ~ relation(v0) | ~ function(v0) | ~ % 16.54/3.04 | in(all_79_2, all_111_0) | ? [v2: $i] : % 16.54/3.04 | (relation_composition(all_43_2, v0) = v2 & apply(v2, all_79_2) = v1 % 16.54/3.04 | & $i(v2) & $i(v1))) % 16.54/3.04 | % 16.54/3.04 | ALPHA: (62) implies: % 16.54/3.04 | (63) relation_dom(all_43_2) = all_111_0 % 16.54/3.04 | (64) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_composition(all_43_2, v0) = % 16.54/3.04 | v1) | ~ $i(v0) | ~ relation(v0) | ~ function(v0) | ~ % 16.54/3.04 | in(all_79_2, all_111_0) | ? [v2: $i] : (apply(v1, all_79_2) = v2 & % 16.54/3.04 | apply(v0, all_79_0) = v2 & $i(v2))) % 16.54/3.04 | % 16.54/3.04 | GROUND_INST: instantiating (64) with all_43_4, all_43_1, simplifying with % 16.54/3.04 | (11), (13), (17), (20) gives: % 16.54/3.04 | (65) ~ in(all_79_2, all_111_0) | ? [v0: $i] : (apply(all_43_1, all_79_2) % 16.54/3.04 | = v0 & apply(all_43_4, all_79_0) = v0 & $i(v0)) % 16.54/3.04 | % 16.54/3.04 | GROUND_INST: instantiating (6) with all_55_0, all_111_0, all_43_2, simplifying % 16.54/3.04 | with (26), (63) gives: % 16.54/3.04 | (66) all_111_0 = all_55_0 % 16.54/3.04 | % 16.54/3.04 | GROUND_INST: instantiating (6) with all_108_0, all_111_0, all_43_2, % 16.54/3.04 | simplifying with (59), (63) gives: % 16.54/3.04 | (67) all_111_0 = all_108_0 % 16.54/3.04 | % 16.54/3.04 | GROUND_INST: instantiating (6) with all_55_0, all_105_0, all_43_1, simplifying % 16.54/3.04 | with (34), (57) gives: % 16.54/3.04 | (68) all_105_0 = all_55_0 % 16.54/3.04 | % 16.54/3.04 | COMBINE_EQS: (66), (67) imply: % 16.54/3.04 | (69) all_108_0 = all_55_0 % 16.54/3.04 | % 16.54/3.04 | BETA: splitting (61) gives: % 16.54/3.04 | % 16.54/3.05 | Case 1: % 16.54/3.05 | | % 16.54/3.05 | | (70) ~ in(all_79_1, all_108_0) % 16.54/3.05 | | % 16.54/3.05 | | REDUCE: (69), (70) imply: % 16.54/3.05 | | (71) ~ in(all_79_1, all_55_0) % 16.54/3.05 | | % 16.54/3.05 | | PRED_UNIFY: (45), (71) imply: % 16.54/3.05 | | (72) $false % 16.54/3.05 | | % 16.54/3.05 | | CLOSE: (72) is inconsistent. % 16.54/3.05 | | % 16.54/3.05 | Case 2: % 16.54/3.05 | | % 16.54/3.05 | | (73) in(all_79_1, all_108_0) % 16.54/3.05 | | (74) ? [v0: $i] : (apply(all_43_1, all_79_1) = v0 & apply(all_43_4, % 16.54/3.05 | | all_79_0) = v0 & $i(v0)) % 16.54/3.05 | | % 16.54/3.05 | | DELTA: instantiating (74) with fresh symbol all_122_0 gives: % 16.54/3.05 | | (75) apply(all_43_1, all_79_1) = all_122_0 & apply(all_43_4, all_79_0) = % 16.54/3.05 | | all_122_0 & $i(all_122_0) % 16.54/3.05 | | % 16.54/3.05 | | ALPHA: (75) implies: % 16.54/3.05 | | (76) apply(all_43_4, all_79_0) = all_122_0 % 16.54/3.05 | | (77) apply(all_43_1, all_79_1) = all_122_0 % 16.54/3.05 | | % 16.54/3.05 | | BETA: splitting (65) gives: % 16.54/3.05 | | % 16.54/3.05 | | Case 1: % 16.54/3.05 | | | % 16.54/3.05 | | | (78) ~ in(all_79_2, all_111_0) % 16.54/3.05 | | | % 16.54/3.05 | | | REDUCE: (66), (78) imply: % 16.54/3.05 | | | (79) ~ in(all_79_2, all_55_0) % 16.54/3.05 | | | % 16.54/3.05 | | | PRED_UNIFY: (44), (79) imply: % 16.54/3.05 | | | (80) $false % 16.54/3.05 | | | % 16.54/3.05 | | | CLOSE: (80) is inconsistent. % 16.54/3.05 | | | % 16.54/3.05 | | Case 2: % 16.54/3.05 | | | % 16.54/3.05 | | | (81) in(all_79_2, all_111_0) % 16.54/3.05 | | | (82) ? [v0: $i] : (apply(all_43_1, all_79_2) = v0 & apply(all_43_4, % 16.54/3.05 | | | all_79_0) = v0 & $i(v0)) % 16.54/3.05 | | | % 16.54/3.05 | | | DELTA: instantiating (82) with fresh symbol all_127_0 gives: % 16.54/3.05 | | | (83) apply(all_43_1, all_79_2) = all_127_0 & apply(all_43_4, all_79_0) % 16.54/3.05 | | | = all_127_0 & $i(all_127_0) % 16.54/3.05 | | | % 16.54/3.05 | | | ALPHA: (83) implies: % 16.54/3.05 | | | (84) apply(all_43_4, all_79_0) = all_127_0 % 16.54/3.05 | | | (85) apply(all_43_1, all_79_2) = all_127_0 % 16.54/3.05 | | | % 16.54/3.05 | | | GROUND_INST: instantiating (7) with all_122_0, all_127_0, all_79_0, % 16.54/3.05 | | | all_43_4, simplifying with (76), (84) gives: % 16.54/3.05 | | | (86) all_127_0 = all_122_0 % 16.54/3.05 | | | % 16.54/3.05 | | | REDUCE: (85), (86) imply: % 16.54/3.05 | | | (87) apply(all_43_1, all_79_2) = all_122_0 % 16.54/3.05 | | | % 16.54/3.05 | | | GROUND_INST: instantiating (2) with all_43_1, all_55_0, all_79_2, % 16.54/3.05 | | | all_79_1, all_122_0, simplifying with (15), (22), (23), (34), % 16.54/3.05 | | | (35), (44), (45), (46), (47), (77), (87) gives: % 16.54/3.05 | | | (88) all_79_1 = all_79_2 % 16.54/3.05 | | | % 16.54/3.05 | | | REDUCE: (43), (88) imply: % 16.54/3.05 | | | (89) $false % 16.54/3.05 | | | % 16.54/3.05 | | | CLOSE: (89) is inconsistent. % 16.54/3.05 | | | % 16.54/3.05 | | End of split % 16.54/3.05 | | % 16.54/3.05 | End of split % 16.54/3.05 | % 16.54/3.05 End of proof % 16.54/3.05 % SZS output end Proof for theBenchmark % 16.54/3.05 % 16.54/3.05 2459ms %------------------------------------------------------------------------------