%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU031+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 : n002.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 17:42:20 EDT 2023 % Result : Theorem 20.00s 3.53s % Output : Proof 21.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU031+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n002.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 18:39:46 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/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 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 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 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 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 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 % 2.87/1.18 Prover 1: Preprocessing ... % 2.87/1.18 Prover 4: Preprocessing ... % 3.65/1.22 Prover 5: Preprocessing ... % 3.65/1.22 Prover 0: Preprocessing ... % 3.65/1.23 Prover 3: Preprocessing ... % 3.65/1.23 Prover 2: Preprocessing ... % 3.65/1.23 Prover 6: Preprocessing ... % 6.49/1.69 Prover 1: Warning: ignoring some quantifiers % 7.20/1.74 Prover 3: Warning: ignoring some quantifiers % 7.20/1.75 Prover 5: Proving ... % 7.20/1.75 Prover 1: Constructing countermodel ... % 7.20/1.77 Prover 3: Constructing countermodel ... % 7.20/1.79 Prover 6: Proving ... % 7.85/1.80 Prover 2: Proving ... % 9.97/2.15 Prover 4: Warning: ignoring some quantifiers % 9.97/2.19 Prover 4: Constructing countermodel ... % 10.67/2.26 Prover 0: Proving ... % 15.53/2.89 Prover 1: gave up % 15.95/2.91 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 16.39/2.99 Prover 7: Preprocessing ... % 16.71/3.03 Prover 7: Warning: ignoring some quantifiers % 16.71/3.04 Prover 7: Constructing countermodel ... % 20.00/3.53 Prover 7: Found proof (size 78) % 20.00/3.53 Prover 7: proved (623ms) % 20.00/3.53 Prover 3: stopped % 20.00/3.53 Prover 0: stopped % 20.00/3.53 Prover 5: stopped % 20.00/3.53 Prover 2: stopped % 20.00/3.53 Prover 6: stopped % 20.00/3.53 Prover 4: stopped % 20.00/3.53 % 20.00/3.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 20.00/3.53 % 20.70/3.55 % SZS output start Proof for theBenchmark % 20.70/3.55 Assumptions after simplification: % 20.70/3.55 --------------------------------- % 20.70/3.55 % 20.70/3.55 (dt_k2_funct_1) % 20.70/3.58 ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~ % 20.70/3.58 relation(v0) | ~ function(v0) | relation(v1)) & ! [v0: $i] : ! [v1: $i] : % 20.70/3.58 ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~ relation(v0) | ~ % 20.70/3.58 function(v0) | function(v1)) % 20.70/3.58 % 20.70/3.58 (l72_funct_1) % 20.70/3.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 20.70/3.58 $i] : ! [v6: $i] : (v5 = v1 | ~ (relation_rng(v1) = v0) | ~ % 20.70/3.58 (relation_dom(v5) = v6) | ~ (identity_relation(v0) = v2) | ~ % 20.70/3.58 (relation_composition(v1, v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~ $i(v1) | ~ % 20.70/3.58 $i(v0) | ~ relation(v5) | ~ relation(v3) | ~ relation(v1) | ~ % 20.70/3.58 function(v5) | ~ function(v3) | ~ function(v1) | ? [v7: $i] : ? [v8: $i] % 20.70/3.58 : (( ~ (v8 = v2) & relation_composition(v3, v5) = v8 & $i(v8)) | ( ~ (v7 = % 20.70/3.58 v4) & identity_relation(v6) = v7 & $i(v7)))) & ! [v0: $i] : ! [v1: % 20.70/3.58 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v1 | ~ % 20.70/3.58 (relation_rng(v1) = v0) | ~ (identity_relation(v0) = v2) | ~ % 20.70/3.58 (relation_composition(v3, v5) = v2) | ~ (relation_composition(v1, v3) = v4) % 20.70/3.58 | ~ $i(v5) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ relation(v5) | ~ % 20.70/3.58 relation(v3) | ~ relation(v1) | ~ function(v5) | ~ function(v3) | ~ % 20.70/3.58 function(v1) | ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v4) & relation_dom(v5) % 20.70/3.58 = v6 & identity_relation(v6) = v7 & $i(v7) & $i(v6))) % 20.70/3.58 % 20.70/3.58 (t55_funct_1) % 20.70/3.59 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 20.70/3.59 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3: % 20.70/3.59 $i] : (relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = % 20.70/3.59 v3 & function_inverse(v0) = v2 & $i(v3) & $i(v2) & $i(v1))) & ! [v0: $i] % 20.70/3.59 : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~ one_to_one(v0) | % 20.70/3.59 ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3: $i] : % 20.70/3.59 (relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2 & % 20.70/3.59 function_inverse(v0) = v3 & $i(v3) & $i(v2) & $i(v1))) & ! [v0: $i] : ! % 20.70/3.59 [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~ one_to_one(v0) | % 20.70/3.59 ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3: $i] : % 20.70/3.59 (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & % 20.70/3.59 relation_dom(v0) = v3 & $i(v3) & $i(v2))) % 20.70/3.59 % 20.70/3.59 (t61_funct_1) % 20.93/3.59 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 20.93/3.59 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3: % 20.93/3.59 $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v4 & % 20.93/3.59 identity_relation(v4) = v3 & identity_relation(v1) = v5 & % 20.93/3.59 relation_composition(v2, v0) = v5 & relation_composition(v0, v2) = v3 & % 20.93/3.59 function_inverse(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2))) & ! [v0: % 20.93/3.59 $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~ % 20.93/3.59 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3: % 20.93/3.59 $i] : ? [v4: $i] : ? [v5: $i] : (relation_rng(v0) = v5 & % 20.93/3.59 identity_relation(v5) = v4 & identity_relation(v1) = v3 & % 20.93/3.59 relation_composition(v2, v0) = v4 & relation_composition(v0, v2) = v3 & % 20.93/3.59 function_inverse(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2))) & ! [v0: % 20.93/3.59 $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~ % 20.93/3.59 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3: % 20.93/3.59 $i] : ? [v4: $i] : ? [v5: $i] : (relation_rng(v0) = v5 & % 20.93/3.59 relation_dom(v0) = v3 & identity_relation(v5) = v4 & identity_relation(v3) % 20.93/3.59 = v2 & relation_composition(v1, v0) = v4 & relation_composition(v0, v1) = % 20.93/3.59 v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2))) % 20.93/3.59 % 20.93/3.59 (t64_funct_1) % 20.93/3.59 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 20.93/3.59 $i] : ( ~ (v5 = v4) & relation_rng(v5) = v1 & relation_rng(v0) = v2 & % 20.93/3.59 relation_dom(v0) = v1 & identity_relation(v2) = v3 & % 20.93/3.59 relation_composition(v5, v0) = v3 & function_inverse(v0) = v4 & $i(v5) & % 20.93/3.59 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & one_to_one(v0) & relation(v5) & % 20.93/3.59 relation(v0) & function(v5) & function(v0)) % 20.93/3.59 % 20.93/3.59 (function-axioms) % 20.93/3.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.93/3.60 (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = % 20.93/3.60 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 20.93/3.60 (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: $i] : ! % 20.93/3.60 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ % 20.93/3.60 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 20.93/3.60 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] : ! % 20.93/3.60 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ % 20.93/3.60 (identity_relation(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 20.93/3.60 (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) % 20.93/3.60 % 20.93/3.60 Further assumptions not needed in the proof: % 20.93/3.60 -------------------------------------------- % 20.93/3.60 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1, dt_k5_relat_1, % 20.93/3.60 dt_k6_relat_1, existence_m1_subset_1, fc10_relat_1, fc12_relat_1, fc1_funct_1, % 20.93/3.60 fc1_subset_1, fc1_xboole_0, fc2_funct_1, fc4_relat_1, fc5_relat_1, fc6_relat_1, % 20.93/3.60 fc7_relat_1, fc8_relat_1, fc9_relat_1, rc1_funct_1, rc1_relat_1, rc1_subset_1, % 20.93/3.60 rc1_xboole_0, rc2_funct_1, rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_funct_1, % 20.93/3.60 rc3_relat_1, reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, % 20.93/3.60 t5_subset, t6_boole, t7_boole, t8_boole % 20.93/3.60 % 20.93/3.60 Those formulas are unsatisfiable: % 20.93/3.60 --------------------------------- % 20.93/3.60 % 20.93/3.60 Begin of proof % 20.93/3.60 | % 20.93/3.60 | ALPHA: (dt_k2_funct_1) implies: % 20.93/3.60 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) % 20.93/3.60 | | ~ relation(v0) | ~ function(v0) | function(v1)) % 20.93/3.60 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) % 20.93/3.60 | | ~ relation(v0) | ~ function(v0) | relation(v1)) % 20.93/3.60 | % 20.93/3.60 | ALPHA: (l72_funct_1) implies: % 20.93/3.60 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 20.93/3.60 | ! [v5: $i] : ! [v6: $i] : (v5 = v1 | ~ (relation_rng(v1) = v0) | ~ % 20.93/3.60 | (relation_dom(v5) = v6) | ~ (identity_relation(v0) = v2) | ~ % 20.93/3.60 | (relation_composition(v1, v3) = v4) | ~ $i(v5) | ~ $i(v3) | ~ % 20.93/3.60 | $i(v1) | ~ $i(v0) | ~ relation(v5) | ~ relation(v3) | ~ % 20.93/3.60 | relation(v1) | ~ function(v5) | ~ function(v3) | ~ function(v1) | % 20.93/3.60 | ? [v7: $i] : ? [v8: $i] : (( ~ (v8 = v2) & relation_composition(v3, % 20.93/3.60 | v5) = v8 & $i(v8)) | ( ~ (v7 = v4) & identity_relation(v6) = v7 % 20.93/3.60 | & $i(v7)))) % 20.93/3.60 | % 20.93/3.60 | ALPHA: (t55_funct_1) implies: % 20.93/3.60 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) % 20.93/3.60 | | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] % 20.93/3.60 | : ? [v3: $i] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & % 20.93/3.60 | relation_dom(v1) = v2 & relation_dom(v0) = v3 & $i(v3) & $i(v2))) % 20.93/3.60 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | % 20.93/3.60 | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : % 20.93/3.60 | ? [v3: $i] : (relation_rng(v3) = v1 & relation_rng(v0) = v2 & % 20.93/3.60 | relation_dom(v3) = v2 & function_inverse(v0) = v3 & $i(v3) & $i(v2) % 20.93/3.60 | & $i(v1))) % 20.93/3.60 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | % 20.93/3.60 | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : % 20.93/3.60 | ? [v3: $i] : (relation_rng(v2) = v3 & relation_dom(v2) = v1 & % 20.93/3.60 | relation_dom(v0) = v3 & function_inverse(v0) = v2 & $i(v3) & $i(v2) % 20.93/3.60 | & $i(v1))) % 20.93/3.60 | % 20.93/3.60 | ALPHA: (t61_funct_1) implies: % 20.93/3.61 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) % 20.93/3.61 | | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] % 20.93/3.61 | : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (relation_rng(v0) = v5 & % 20.93/3.61 | relation_dom(v0) = v3 & identity_relation(v5) = v4 & % 20.93/3.61 | identity_relation(v3) = v2 & relation_composition(v1, v0) = v4 & % 20.93/3.61 | relation_composition(v0, v1) = v2 & $i(v5) & $i(v4) & $i(v3) & % 20.93/3.61 | $i(v2))) % 20.93/3.61 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | % 20.93/3.61 | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : % 20.93/3.61 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (relation_rng(v0) = v5 & % 20.93/3.61 | identity_relation(v5) = v4 & identity_relation(v1) = v3 & % 20.93/3.61 | relation_composition(v2, v0) = v4 & relation_composition(v0, v2) = % 20.93/3.61 | v3 & function_inverse(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & % 20.93/3.61 | $i(v2))) % 20.93/3.61 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | % 20.93/3.61 | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : % 20.93/3.61 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v4 & % 20.93/3.61 | identity_relation(v4) = v3 & identity_relation(v1) = v5 & % 20.93/3.61 | relation_composition(v2, v0) = v5 & relation_composition(v0, v2) = % 20.93/3.61 | v3 & function_inverse(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & % 20.93/3.61 | $i(v2))) % 20.93/3.61 | % 20.93/3.61 | ALPHA: (function-axioms) implies: % 20.93/3.61 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 20.93/3.61 | (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) % 20.93/3.61 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 20.93/3.61 | (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) % 20.93/3.61 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 20.93/3.61 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 20.93/3.61 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 20.93/3.61 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 20.93/3.61 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 20.93/3.61 | (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, % 20.93/3.61 | v2) = v0)) % 20.93/3.61 | % 20.93/3.61 | DELTA: instantiating (t64_funct_1) with fresh symbols all_51_0, all_51_1, % 20.93/3.61 | all_51_2, all_51_3, all_51_4, all_51_5 gives: % 20.93/3.61 | (15) ~ (all_51_0 = all_51_1) & relation_rng(all_51_0) = all_51_4 & % 20.93/3.61 | relation_rng(all_51_5) = all_51_3 & relation_dom(all_51_5) = all_51_4 % 20.93/3.61 | & identity_relation(all_51_3) = all_51_2 & % 20.93/3.61 | relation_composition(all_51_0, all_51_5) = all_51_2 & % 20.93/3.61 | function_inverse(all_51_5) = all_51_1 & $i(all_51_0) & $i(all_51_1) & % 20.93/3.61 | $i(all_51_2) & $i(all_51_3) & $i(all_51_4) & $i(all_51_5) & % 20.93/3.61 | one_to_one(all_51_5) & relation(all_51_0) & relation(all_51_5) & % 20.93/3.61 | function(all_51_0) & function(all_51_5) % 20.93/3.61 | % 20.93/3.61 | ALPHA: (15) implies: % 20.93/3.61 | (16) ~ (all_51_0 = all_51_1) % 20.93/3.61 | (17) function(all_51_5) % 20.93/3.61 | (18) function(all_51_0) % 20.93/3.61 | (19) relation(all_51_5) % 20.93/3.61 | (20) relation(all_51_0) % 20.93/3.61 | (21) one_to_one(all_51_5) % 20.93/3.61 | (22) $i(all_51_5) % 20.93/3.61 | (23) $i(all_51_0) % 20.93/3.61 | (24) function_inverse(all_51_5) = all_51_1 % 20.93/3.61 | (25) relation_composition(all_51_0, all_51_5) = all_51_2 % 20.93/3.61 | (26) identity_relation(all_51_3) = all_51_2 % 20.93/3.61 | (27) relation_dom(all_51_5) = all_51_4 % 20.93/3.61 | (28) relation_rng(all_51_5) = all_51_3 % 20.93/3.61 | (29) relation_rng(all_51_0) = all_51_4 % 20.93/3.61 | % 20.93/3.61 | GROUND_INST: instantiating (7) with all_51_5, all_51_1, simplifying with (17), % 20.93/3.61 | (19), (21), (22), (24) gives: % 20.93/3.62 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 20.93/3.62 | (relation_rng(all_51_5) = v3 & relation_dom(all_51_5) = v1 & % 20.93/3.62 | identity_relation(v3) = v2 & identity_relation(v1) = v0 & % 20.93/3.62 | relation_composition(all_51_1, all_51_5) = v2 & % 20.93/3.62 | relation_composition(all_51_5, all_51_1) = v0 & $i(v3) & $i(v2) & % 20.93/3.62 | $i(v1) & $i(v0)) % 20.93/3.62 | % 20.93/3.62 | GROUND_INST: instantiating (4) with all_51_5, all_51_1, simplifying with (17), % 20.93/3.62 | (19), (21), (22), (24) gives: % 20.93/3.62 | (31) ? [v0: $i] : ? [v1: $i] : (relation_rng(all_51_1) = v1 & % 20.93/3.62 | relation_rng(all_51_5) = v0 & relation_dom(all_51_1) = v0 & % 20.93/3.62 | relation_dom(all_51_5) = v1 & $i(v1) & $i(v0)) % 20.93/3.62 | % 20.93/3.62 | GROUND_INST: instantiating (2) with all_51_5, all_51_1, simplifying with (17), % 20.93/3.62 | (19), (22), (24) gives: % 20.93/3.62 | (32) relation(all_51_1) % 20.93/3.62 | % 20.93/3.62 | GROUND_INST: instantiating (1) with all_51_5, all_51_1, simplifying with (17), % 20.93/3.62 | (19), (22), (24) gives: % 20.93/3.62 | (33) function(all_51_1) % 20.93/3.62 | % 20.93/3.62 | GROUND_INST: instantiating (8) with all_51_5, all_51_4, simplifying with (17), % 20.93/3.62 | (19), (21), (22), (27) gives: % 20.93/3.62 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 20.93/3.62 | (relation_rng(all_51_5) = v3 & identity_relation(v3) = v2 & % 20.93/3.62 | identity_relation(all_51_4) = v1 & relation_composition(v0, % 20.93/3.62 | all_51_5) = v2 & relation_composition(all_51_5, v0) = v1 & % 20.93/3.62 | function_inverse(all_51_5) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 20.93/3.62 | % 20.93/3.62 | GROUND_INST: instantiating (5) with all_51_5, all_51_4, simplifying with (17), % 20.93/3.62 | (19), (21), (22), (27) gives: % 20.93/3.62 | (35) ? [v0: $i] : ? [v1: $i] : (relation_rng(v1) = all_51_4 & % 20.93/3.62 | relation_rng(all_51_5) = v0 & relation_dom(v1) = v0 & % 20.93/3.62 | function_inverse(all_51_5) = v1 & $i(v1) & $i(v0) & $i(all_51_4)) % 20.93/3.62 | % 20.93/3.62 | GROUND_INST: instantiating (9) with all_51_5, all_51_3, simplifying with (17), % 20.93/3.62 | (19), (21), (22), (28) gives: % 20.93/3.62 | (36) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 20.93/3.62 | (relation_dom(all_51_5) = v2 & identity_relation(v2) = v1 & % 20.93/3.62 | identity_relation(all_51_3) = v3 & relation_composition(v0, % 20.93/3.62 | all_51_5) = v3 & relation_composition(all_51_5, v0) = v1 & % 20.93/3.62 | function_inverse(all_51_5) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 20.93/3.62 | % 20.93/3.62 | GROUND_INST: instantiating (6) with all_51_5, all_51_3, simplifying with (17), % 20.93/3.62 | (19), (21), (22), (28) gives: % 20.93/3.62 | (37) ? [v0: $i] : ? [v1: $i] : (relation_rng(v0) = v1 & relation_dom(v0) % 20.93/3.62 | = all_51_3 & relation_dom(all_51_5) = v1 & % 20.93/3.62 | function_inverse(all_51_5) = v0 & $i(v1) & $i(v0) & $i(all_51_3)) % 20.93/3.62 | % 20.93/3.62 | DELTA: instantiating (31) with fresh symbols all_63_0, all_63_1 gives: % 20.93/3.62 | (38) relation_rng(all_51_1) = all_63_0 & relation_rng(all_51_5) = all_63_1 % 20.93/3.62 | & relation_dom(all_51_1) = all_63_1 & relation_dom(all_51_5) = % 20.93/3.62 | all_63_0 & $i(all_63_0) & $i(all_63_1) % 20.93/3.62 | % 20.93/3.62 | ALPHA: (38) implies: % 20.93/3.62 | (39) $i(all_63_0) % 20.93/3.62 | (40) relation_dom(all_51_5) = all_63_0 % 20.93/3.62 | (41) relation_dom(all_51_1) = all_63_1 % 20.93/3.62 | (42) relation_rng(all_51_5) = all_63_1 % 20.93/3.62 | % 20.93/3.62 | DELTA: instantiating (37) with fresh symbols all_65_0, all_65_1 gives: % 20.93/3.62 | (43) relation_rng(all_65_1) = all_65_0 & relation_dom(all_65_1) = all_51_3 % 20.93/3.62 | & relation_dom(all_51_5) = all_65_0 & function_inverse(all_51_5) = % 20.93/3.62 | all_65_1 & $i(all_65_0) & $i(all_65_1) & $i(all_51_3) % 20.93/3.62 | % 20.93/3.62 | ALPHA: (43) implies: % 20.93/3.62 | (44) $i(all_65_1) % 20.93/3.62 | (45) function_inverse(all_51_5) = all_65_1 % 20.93/3.62 | (46) relation_dom(all_51_5) = all_65_0 % 20.93/3.62 | % 20.93/3.62 | DELTA: instantiating (35) with fresh symbols all_67_0, all_67_1 gives: % 20.93/3.62 | (47) relation_rng(all_67_0) = all_51_4 & relation_rng(all_51_5) = all_67_1 % 20.93/3.62 | & relation_dom(all_67_0) = all_67_1 & function_inverse(all_51_5) = % 20.93/3.62 | all_67_0 & $i(all_67_0) & $i(all_67_1) & $i(all_51_4) % 20.93/3.63 | % 20.93/3.63 | ALPHA: (47) implies: % 20.93/3.63 | (48) function_inverse(all_51_5) = all_67_0 % 20.93/3.63 | (49) relation_rng(all_51_5) = all_67_1 % 20.93/3.63 | % 20.93/3.63 | DELTA: instantiating (30) with fresh symbols all_69_0, all_69_1, all_69_2, % 20.93/3.63 | all_69_3 gives: % 20.93/3.63 | (50) relation_rng(all_51_5) = all_69_0 & relation_dom(all_51_5) = all_69_2 % 20.93/3.63 | & identity_relation(all_69_0) = all_69_1 & identity_relation(all_69_2) % 20.93/3.63 | = all_69_3 & relation_composition(all_51_1, all_51_5) = all_69_1 & % 20.93/3.63 | relation_composition(all_51_5, all_51_1) = all_69_3 & $i(all_69_0) & % 20.93/3.63 | $i(all_69_1) & $i(all_69_2) & $i(all_69_3) % 20.93/3.63 | % 20.93/3.63 | ALPHA: (50) implies: % 20.93/3.63 | (51) relation_composition(all_51_5, all_51_1) = all_69_3 % 20.93/3.63 | (52) identity_relation(all_69_2) = all_69_3 % 20.93/3.63 | (53) relation_dom(all_51_5) = all_69_2 % 20.93/3.63 | (54) relation_rng(all_51_5) = all_69_0 % 20.93/3.63 | % 20.93/3.63 | DELTA: instantiating (36) with fresh symbols all_71_0, all_71_1, all_71_2, % 20.93/3.63 | all_71_3 gives: % 20.93/3.63 | (55) relation_dom(all_51_5) = all_71_1 & identity_relation(all_71_1) = % 20.93/3.63 | all_71_2 & identity_relation(all_51_3) = all_71_0 & % 20.93/3.63 | relation_composition(all_71_3, all_51_5) = all_71_0 & % 20.93/3.63 | relation_composition(all_51_5, all_71_3) = all_71_2 & % 20.93/3.63 | function_inverse(all_51_5) = all_71_3 & $i(all_71_0) & $i(all_71_1) & % 20.93/3.63 | $i(all_71_2) & $i(all_71_3) % 20.93/3.63 | % 20.93/3.63 | ALPHA: (55) implies: % 20.93/3.63 | (56) function_inverse(all_51_5) = all_71_3 % 20.93/3.63 | (57) identity_relation(all_51_3) = all_71_0 % 20.93/3.63 | (58) relation_dom(all_51_5) = all_71_1 % 20.93/3.63 | % 20.93/3.63 | DELTA: instantiating (34) with fresh symbols all_73_0, all_73_1, all_73_2, % 20.93/3.63 | all_73_3 gives: % 20.93/3.63 | (59) relation_rng(all_51_5) = all_73_0 & identity_relation(all_73_0) = % 20.93/3.63 | all_73_1 & identity_relation(all_51_4) = all_73_2 & % 20.93/3.63 | relation_composition(all_73_3, all_51_5) = all_73_1 & % 20.93/3.63 | relation_composition(all_51_5, all_73_3) = all_73_2 & % 20.93/3.63 | function_inverse(all_51_5) = all_73_3 & $i(all_73_0) & $i(all_73_1) & % 20.93/3.63 | $i(all_73_2) & $i(all_73_3) % 20.93/3.63 | % 20.93/3.63 | ALPHA: (59) implies: % 20.93/3.63 | (60) function_inverse(all_51_5) = all_73_3 % 20.93/3.63 | (61) relation_rng(all_51_5) = all_73_0 % 20.93/3.63 | % 20.93/3.63 | GROUND_INST: instantiating (10) with all_51_1, all_71_3, all_51_5, simplifying % 20.93/3.63 | with (24), (56) gives: % 20.93/3.63 | (62) all_71_3 = all_51_1 % 20.93/3.63 | % 20.93/3.63 | GROUND_INST: instantiating (10) with all_67_0, all_71_3, all_51_5, simplifying % 20.93/3.63 | with (48), (56) gives: % 20.93/3.63 | (63) all_71_3 = all_67_0 % 20.93/3.63 | % 20.93/3.63 | GROUND_INST: instantiating (10) with all_67_0, all_73_3, all_51_5, simplifying % 20.93/3.63 | with (48), (60) gives: % 20.93/3.63 | (64) all_73_3 = all_67_0 % 20.93/3.63 | % 20.93/3.63 | GROUND_INST: instantiating (10) with all_65_1, all_73_3, all_51_5, simplifying % 20.93/3.63 | with (45), (60) gives: % 20.93/3.63 | (65) all_73_3 = all_65_1 % 20.93/3.63 | % 20.93/3.63 | GROUND_INST: instantiating (11) with all_51_2, all_71_0, all_51_3, simplifying % 20.93/3.63 | with (26), (57) gives: % 20.93/3.63 | (66) all_71_0 = all_51_2 % 20.93/3.63 | % 20.93/3.63 | GROUND_INST: instantiating (12) with all_65_0, all_69_2, all_51_5, simplifying % 20.93/3.63 | with (46), (53) gives: % 20.93/3.63 | (67) all_69_2 = all_65_0 % 20.93/3.63 | % 20.93/3.63 | GROUND_INST: instantiating (12) with all_63_0, all_69_2, all_51_5, simplifying % 20.93/3.63 | with (40), (53) gives: % 20.93/3.63 | (68) all_69_2 = all_63_0 % 20.93/3.63 | % 20.93/3.63 | GROUND_INST: instantiating (12) with all_51_4, all_71_1, all_51_5, simplifying % 20.93/3.63 | with (27), (58) gives: % 20.93/3.63 | (69) all_71_1 = all_51_4 % 20.93/3.63 | % 20.93/3.63 | GROUND_INST: instantiating (12) with all_65_0, all_71_1, all_51_5, simplifying % 20.93/3.63 | with (46), (58) gives: % 20.93/3.63 | (70) all_71_1 = all_65_0 % 20.93/3.63 | % 20.93/3.63 | GROUND_INST: instantiating (13) with all_51_3, all_67_1, all_51_5, simplifying % 20.93/3.63 | with (28), (49) gives: % 20.93/3.63 | (71) all_67_1 = all_51_3 % 20.93/3.63 | % 20.93/3.63 | GROUND_INST: instantiating (13) with all_67_1, all_69_0, all_51_5, simplifying % 20.93/3.63 | with (49), (54) gives: % 20.93/3.63 | (72) all_69_0 = all_67_1 % 20.93/3.63 | % 20.93/3.63 | GROUND_INST: instantiating (13) with all_69_0, all_73_0, all_51_5, simplifying % 20.93/3.63 | with (54), (61) gives: % 20.93/3.63 | (73) all_73_0 = all_69_0 % 20.93/3.63 | % 20.93/3.63 | GROUND_INST: instantiating (13) with all_63_1, all_73_0, all_51_5, simplifying % 20.93/3.63 | with (42), (61) gives: % 20.93/3.63 | (74) all_73_0 = all_63_1 % 20.93/3.63 | % 20.93/3.63 | COMBINE_EQS: (73), (74) imply: % 20.93/3.63 | (75) all_69_0 = all_63_1 % 20.93/3.63 | % 20.93/3.63 | SIMP: (75) implies: % 20.93/3.63 | (76) all_69_0 = all_63_1 % 20.93/3.63 | % 20.93/3.63 | COMBINE_EQS: (64), (65) imply: % 20.93/3.63 | (77) all_67_0 = all_65_1 % 20.93/3.63 | % 20.93/3.63 | SIMP: (77) implies: % 20.93/3.64 | (78) all_67_0 = all_65_1 % 20.93/3.64 | % 20.93/3.64 | COMBINE_EQS: (69), (70) imply: % 20.93/3.64 | (79) all_65_0 = all_51_4 % 20.93/3.64 | % 20.93/3.64 | SIMP: (79) implies: % 20.93/3.64 | (80) all_65_0 = all_51_4 % 20.93/3.64 | % 20.93/3.64 | COMBINE_EQS: (62), (63) imply: % 20.93/3.64 | (81) all_67_0 = all_51_1 % 20.93/3.64 | % 20.93/3.64 | SIMP: (81) implies: % 20.93/3.64 | (82) all_67_0 = all_51_1 % 20.93/3.64 | % 20.93/3.64 | COMBINE_EQS: (72), (76) imply: % 20.93/3.64 | (83) all_67_1 = all_63_1 % 20.93/3.64 | % 20.93/3.64 | SIMP: (83) implies: % 20.93/3.64 | (84) all_67_1 = all_63_1 % 20.93/3.64 | % 20.93/3.64 | COMBINE_EQS: (67), (68) imply: % 20.93/3.64 | (85) all_65_0 = all_63_0 % 20.93/3.64 | % 20.93/3.64 | SIMP: (85) implies: % 20.93/3.64 | (86) all_65_0 = all_63_0 % 20.93/3.64 | % 20.93/3.64 | COMBINE_EQS: (78), (82) imply: % 20.93/3.64 | (87) all_65_1 = all_51_1 % 20.93/3.64 | % 20.93/3.64 | COMBINE_EQS: (71), (84) imply: % 20.93/3.64 | (88) all_63_1 = all_51_3 % 20.93/3.64 | % 20.93/3.64 | COMBINE_EQS: (80), (86) imply: % 20.93/3.64 | (89) all_63_0 = all_51_4 % 20.93/3.64 | % 20.93/3.64 | SIMP: (89) implies: % 20.93/3.64 | (90) all_63_0 = all_51_4 % 20.93/3.64 | % 20.93/3.64 | COMBINE_EQS: (68), (90) imply: % 20.93/3.64 | (91) all_69_2 = all_51_4 % 20.93/3.64 | % 20.93/3.64 | REDUCE: (41), (88) imply: % 20.93/3.64 | (92) relation_dom(all_51_1) = all_51_3 % 20.93/3.64 | % 20.93/3.64 | REDUCE: (52), (91) imply: % 20.93/3.64 | (93) identity_relation(all_51_4) = all_69_3 % 20.93/3.64 | % 20.93/3.64 | REDUCE: (44), (87) imply: % 20.93/3.64 | (94) $i(all_51_1) % 20.93/3.64 | % 20.93/3.64 | REDUCE: (39), (90) imply: % 20.93/3.64 | (95) $i(all_51_4) % 20.93/3.64 | % 20.93/3.64 | GROUND_INST: instantiating (3) with all_51_4, all_51_0, all_69_3, all_51_5, % 20.93/3.64 | all_51_2, all_51_1, all_51_3, simplifying with (17), (18), (19), % 20.93/3.64 | (20), (22), (23), (25), (29), (32), (33), (92), (93), (94), (95) % 20.93/3.64 | gives: % 20.93/3.64 | (96) all_51_0 = all_51_1 | ? [v0: any] : ? [v1: any] : (( ~ (v1 = % 20.93/3.64 | all_69_3) & relation_composition(all_51_5, all_51_1) = v1 & % 20.93/3.64 | $i(v1)) | ( ~ (v0 = all_51_2) & identity_relation(all_51_3) = v0 & % 20.93/3.64 | $i(v0))) % 20.93/3.64 | % 20.93/3.64 | BETA: splitting (96) gives: % 20.93/3.64 | % 20.93/3.64 | Case 1: % 20.93/3.64 | | % 20.93/3.64 | | (97) all_51_0 = all_51_1 % 20.93/3.64 | | % 20.93/3.64 | | REDUCE: (16), (97) imply: % 20.93/3.64 | | (98) $false % 20.93/3.64 | | % 20.93/3.64 | | CLOSE: (98) is inconsistent. % 20.93/3.64 | | % 20.93/3.64 | Case 2: % 20.93/3.64 | | % 20.93/3.64 | | (99) ? [v0: any] : ? [v1: any] : (( ~ (v1 = all_69_3) & % 20.93/3.64 | | relation_composition(all_51_5, all_51_1) = v1 & $i(v1)) | ( ~ % 20.93/3.64 | | (v0 = all_51_2) & identity_relation(all_51_3) = v0 & $i(v0))) % 20.93/3.64 | | % 20.93/3.64 | | DELTA: instantiating (99) with fresh symbols all_105_0, all_105_1 gives: % 20.93/3.64 | | (100) ( ~ (all_105_0 = all_69_3) & relation_composition(all_51_5, % 20.93/3.64 | | all_51_1) = all_105_0 & $i(all_105_0)) | ( ~ (all_105_1 = % 20.93/3.64 | | all_51_2) & identity_relation(all_51_3) = all_105_1 & % 20.93/3.64 | | $i(all_105_1)) % 20.93/3.64 | | % 20.93/3.64 | | BETA: splitting (100) gives: % 20.93/3.64 | | % 20.93/3.64 | | Case 1: % 20.93/3.64 | | | % 20.93/3.64 | | | (101) ~ (all_105_0 = all_69_3) & relation_composition(all_51_5, % 20.93/3.64 | | | all_51_1) = all_105_0 & $i(all_105_0) % 20.93/3.64 | | | % 20.93/3.64 | | | ALPHA: (101) implies: % 21.20/3.64 | | | (102) ~ (all_105_0 = all_69_3) % 21.20/3.65 | | | (103) relation_composition(all_51_5, all_51_1) = all_105_0 % 21.20/3.65 | | | % 21.20/3.65 | | | GROUND_INST: instantiating (14) with all_69_3, all_105_0, all_51_1, % 21.20/3.65 | | | all_51_5, simplifying with (51), (103) gives: % 21.20/3.65 | | | (104) all_105_0 = all_69_3 % 21.20/3.65 | | | % 21.20/3.65 | | | REDUCE: (102), (104) imply: % 21.20/3.65 | | | (105) $false % 21.20/3.65 | | | % 21.20/3.65 | | | CLOSE: (105) is inconsistent. % 21.20/3.65 | | | % 21.20/3.65 | | Case 2: % 21.20/3.65 | | | % 21.20/3.65 | | | (106) ~ (all_105_1 = all_51_2) & identity_relation(all_51_3) = % 21.20/3.65 | | | all_105_1 & $i(all_105_1) % 21.20/3.65 | | | % 21.20/3.65 | | | ALPHA: (106) implies: % 21.20/3.65 | | | (107) ~ (all_105_1 = all_51_2) % 21.20/3.65 | | | (108) identity_relation(all_51_3) = all_105_1 % 21.20/3.65 | | | % 21.20/3.65 | | | GROUND_INST: instantiating (11) with all_51_2, all_105_1, all_51_3, % 21.20/3.65 | | | simplifying with (26), (108) gives: % 21.20/3.65 | | | (109) all_105_1 = all_51_2 % 21.20/3.65 | | | % 21.20/3.65 | | | REDUCE: (107), (109) imply: % 21.20/3.65 | | | (110) $false % 21.20/3.65 | | | % 21.20/3.65 | | | CLOSE: (110) is inconsistent. % 21.20/3.65 | | | % 21.20/3.65 | | End of split % 21.20/3.65 | | % 21.20/3.65 | End of split % 21.20/3.65 | % 21.20/3.65 End of proof % 21.20/3.65 % SZS output end Proof for theBenchmark % 21.20/3.65 % 21.20/3.65 3024ms %------------------------------------------------------------------------------