%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU034+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 : n027.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 17:42:21 EDT 2023 % Result : Theorem 10.69s 2.31s % Output : Proof 16.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU034+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n027.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Aug 23 20:49:46 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.65 ________ _____ % 0.20/0.65 ___ __ \_________(_)________________________________ % 0.20/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.65 % 0.20/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.65 (2023-06-19) % 0.20/0.65 % 0.20/0.65 (c) Philipp Rümmer, 2009-2023 % 0.20/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.65 Amanda Stjerna. % 0.20/0.65 Free software under BSD-3-Clause. % 0.20/0.65 % 0.20/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.65 % 0.20/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.66 Running up to 7 provers in parallel. % 0.20/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.82/1.14 Prover 1: Preprocessing ... % 2.82/1.14 Prover 4: Preprocessing ... % 2.82/1.17 Prover 5: Preprocessing ... % 2.82/1.17 Prover 2: Preprocessing ... % 2.82/1.17 Prover 0: Preprocessing ... % 2.82/1.18 Prover 6: Preprocessing ... % 2.82/1.18 Prover 3: Preprocessing ... % 6.26/1.66 Prover 1: Warning: ignoring some quantifiers % 6.97/1.69 Prover 3: Warning: ignoring some quantifiers % 7.09/1.70 Prover 1: Constructing countermodel ... % 7.09/1.71 Prover 6: Proving ... % 7.09/1.71 Prover 3: Constructing countermodel ... % 7.09/1.71 Prover 2: Proving ... % 7.21/1.73 Prover 5: Proving ... % 8.53/1.92 Prover 4: Warning: ignoring some quantifiers % 8.53/1.95 Prover 4: Constructing countermodel ... % 9.13/2.06 Prover 0: Proving ... % 10.69/2.30 Prover 3: proved (1633ms) % 10.69/2.31 % 10.69/2.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.69/2.31 % 10.69/2.31 Prover 0: stopped % 10.69/2.31 Prover 6: stopped % 10.69/2.33 Prover 2: stopped % 10.69/2.33 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.69/2.33 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.69/2.33 Prover 5: stopped % 10.69/2.33 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.69/2.33 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.69/2.33 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.61/2.38 Prover 7: Preprocessing ... % 11.61/2.40 Prover 13: Preprocessing ... % 11.61/2.40 Prover 8: Preprocessing ... % 11.61/2.41 Prover 11: Preprocessing ... % 11.61/2.41 Prover 10: Preprocessing ... % 12.24/2.45 Prover 7: Warning: ignoring some quantifiers % 12.24/2.46 Prover 7: Constructing countermodel ... % 12.68/2.51 Prover 10: Warning: ignoring some quantifiers % 12.68/2.53 Prover 13: Warning: ignoring some quantifiers % 12.68/2.54 Prover 10: Constructing countermodel ... % 12.68/2.55 Prover 13: Constructing countermodel ... % 13.40/2.57 Prover 8: Warning: ignoring some quantifiers % 13.40/2.58 Prover 8: Constructing countermodel ... % 13.40/2.60 Prover 11: Warning: ignoring some quantifiers % 13.71/2.62 Prover 11: Constructing countermodel ... % 14.89/2.83 Prover 10: gave up % 14.89/2.84 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 15.47/2.86 Prover 16: Preprocessing ... % 15.47/2.89 Prover 7: Found proof (size 103) % 15.47/2.89 Prover 7: proved (575ms) % 15.47/2.89 Prover 1: stopped % 15.47/2.89 Prover 8: stopped % 15.47/2.89 Prover 13: stopped % 15.47/2.89 Prover 11: stopped % 15.47/2.89 Prover 4: stopped % 15.47/2.91 Prover 16: stopped % 15.47/2.91 % 15.47/2.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.47/2.91 % 15.47/2.94 % SZS output start Proof for theBenchmark % 15.47/2.94 Assumptions after simplification: % 15.47/2.94 --------------------------------- % 15.47/2.95 % 15.47/2.95 (dt_k2_funct_1) % 15.47/2.97 ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~ % 15.47/2.97 relation(v0) | ~ function(v0) | relation(v1)) & ! [v0: $i] : ! [v1: $i] : % 15.47/2.97 ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~ relation(v0) | ~ % 15.47/2.97 function(v0) | function(v1)) % 15.47/2.97 % 15.47/2.97 (fc2_funct_1) % 15.47/2.97 ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~ $i(v0) | % 15.47/2.97 relation(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) % 15.47/2.97 | ~ $i(v0) | function(v1)) % 15.47/2.98 % 15.47/2.98 (t44_funct_1) % 15.47/2.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v0) = v1) | ~ % 15.47/2.98 (relation_dom(v2) = v1) | ~ $i(v2) | ~ $i(v0) | ~ relation(v2) | ~ % 15.47/2.98 relation(v0) | ~ function(v2) | ~ function(v0) | ? [v3: $i] : ? [v4: $i] % 15.47/2.98 : ((v4 = v2 & identity_relation(v1) = v2) | ( ~ (v3 = v0) & % 15.47/2.98 relation_composition(v0, v2) = v3 & $i(v3)))) & ! [v0: $i] : ! [v1: % 15.47/2.98 $i] : ! [v2: $i] : ( ~ (relation_rng(v0) = v1) | ~ % 15.47/2.98 (relation_composition(v0, v2) = v0) | ~ $i(v2) | ~ $i(v0) | ~ % 15.47/2.98 relation(v2) | ~ relation(v0) | ~ function(v2) | ~ function(v0) | ? [v3: % 15.47/2.98 $i] : ? [v4: $i] : (relation_dom(v2) = v3 & $i(v3) & ( ~ (v3 = v1) | (v4 % 15.47/2.98 = v2 & identity_relation(v1) = v2)))) % 15.47/2.98 % 15.47/2.98 (t52_funct_1) % 15.47/2.98 ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~ $i(v0) | % 15.47/2.98 one_to_one(v1)) % 15.47/2.98 % 15.47/2.98 (t55_funct_1) % 15.47/2.99 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 15.47/2.99 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3: % 15.47/2.99 $i] : (relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = % 15.47/2.99 v3 & function_inverse(v0) = v2 & $i(v3) & $i(v2) & $i(v1))) & ! [v0: $i] % 15.47/2.99 : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~ one_to_one(v0) | % 15.47/2.99 ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3: $i] : % 15.47/2.99 (relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2 & % 15.47/2.99 function_inverse(v0) = v3 & $i(v3) & $i(v2) & $i(v1))) & ! [v0: $i] : ! % 15.47/2.99 [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~ one_to_one(v0) | % 15.47/2.99 ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3: $i] : % 15.47/2.99 (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & % 15.47/2.99 relation_dom(v0) = v3 & $i(v3) & $i(v2))) % 15.47/2.99 % 15.47/2.99 (t61_funct_1) % 15.47/2.99 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~ % 15.47/2.99 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3: % 15.47/2.99 $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v4 & % 15.47/2.99 identity_relation(v4) = v3 & identity_relation(v1) = v5 & % 15.47/2.99 relation_composition(v2, v0) = v5 & relation_composition(v0, v2) = v3 & % 15.47/2.99 function_inverse(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2))) & ! [v0: % 15.47/2.99 $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~ % 15.47/2.99 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3: % 15.47/2.99 $i] : ? [v4: $i] : ? [v5: $i] : (relation_rng(v0) = v5 & % 15.47/2.99 identity_relation(v5) = v4 & identity_relation(v1) = v3 & % 15.47/2.99 relation_composition(v2, v0) = v4 & relation_composition(v0, v2) = v3 & % 15.47/2.99 function_inverse(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2))) & ! [v0: % 15.47/2.99 $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~ % 15.47/2.99 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3: % 15.47/2.99 $i] : ? [v4: $i] : ? [v5: $i] : (relation_rng(v0) = v5 & % 15.47/2.99 relation_dom(v0) = v3 & identity_relation(v5) = v4 & identity_relation(v3) % 15.47/2.99 = v2 & relation_composition(v1, v0) = v4 & relation_composition(v0, v1) = % 15.47/2.99 v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2))) % 15.47/2.99 % 15.47/2.99 (t67_funct_1) % 15.47/2.99 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) & % 15.47/2.99 identity_relation(v0) = v1 & function_inverse(v1) = v2 & $i(v2) & $i(v1) & % 15.47/2.99 $i(v0)) % 15.47/2.99 % 15.47/2.99 (t71_relat_1) % 15.47/2.99 ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~ $i(v0) | % 15.47/2.99 relation_rng(v1) = v0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 15.47/2.99 (identity_relation(v0) = v1) | ~ $i(v0) | relation_dom(v1) = v0) % 15.47/2.99 % 15.47/2.99 (function-axioms) % 15.47/2.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.47/2.99 (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = % 15.47/2.99 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 15.47/2.99 (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: $i] : ! % 15.47/2.99 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ % 15.47/2.99 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 15.47/2.99 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] : ! % 15.47/2.99 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ % 15.47/2.99 (identity_relation(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.47/2.99 (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) % 15.47/3.00 % 15.47/3.00 Further assumptions not needed in the proof: % 15.47/3.00 -------------------------------------------- % 15.47/3.00 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1, dt_k5_relat_1, % 15.47/3.00 dt_k6_relat_1, existence_m1_subset_1, fc10_relat_1, fc12_relat_1, fc1_funct_1, % 15.47/3.00 fc1_subset_1, fc1_xboole_0, fc4_relat_1, fc5_relat_1, fc6_relat_1, fc7_relat_1, % 15.47/3.00 fc8_relat_1, fc9_relat_1, rc1_funct_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0, % 15.47/3.00 rc2_funct_1, rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1, % 15.47/3.00 reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, % 15.47/3.00 t6_boole, t7_boole, t8_boole % 15.47/3.00 % 15.47/3.00 Those formulas are unsatisfiable: % 15.47/3.00 --------------------------------- % 15.47/3.00 % 15.47/3.00 Begin of proof % 15.47/3.00 | % 15.47/3.00 | ALPHA: (dt_k2_funct_1) implies: % 15.47/3.00 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) % 15.47/3.00 | | ~ relation(v0) | ~ function(v0) | function(v1)) % 15.47/3.00 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) % 15.47/3.00 | | ~ relation(v0) | ~ function(v0) | relation(v1)) % 15.47/3.00 | % 15.47/3.00 | ALPHA: (fc2_funct_1) implies: % 15.47/3.00 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~ % 15.47/3.00 | $i(v0) | function(v1)) % 15.47/3.00 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~ % 15.47/3.00 | $i(v0) | relation(v1)) % 15.47/3.00 | % 15.47/3.00 | ALPHA: (t44_funct_1) implies: % 15.47/3.00 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v0) = v1) | % 15.47/3.00 | ~ (relation_dom(v2) = v1) | ~ $i(v2) | ~ $i(v0) | ~ relation(v2) % 15.47/3.00 | | ~ relation(v0) | ~ function(v2) | ~ function(v0) | ? [v3: $i] : % 15.47/3.00 | ? [v4: $i] : ((v4 = v2 & identity_relation(v1) = v2) | ( ~ (v3 = v0) % 15.47/3.00 | & relation_composition(v0, v2) = v3 & $i(v3)))) % 15.47/3.00 | % 15.47/3.00 | ALPHA: (t55_funct_1) implies: % 15.47/3.00 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) % 15.47/3.00 | | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] % 15.47/3.00 | : ? [v3: $i] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & % 15.47/3.00 | relation_dom(v1) = v2 & relation_dom(v0) = v3 & $i(v3) & $i(v2))) % 15.47/3.00 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | % 15.47/3.00 | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : % 15.47/3.00 | ? [v3: $i] : (relation_rng(v3) = v1 & relation_rng(v0) = v2 & % 15.47/3.00 | relation_dom(v3) = v2 & function_inverse(v0) = v3 & $i(v3) & $i(v2) % 15.47/3.00 | & $i(v1))) % 15.47/3.01 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | % 15.47/3.01 | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : % 15.47/3.01 | ? [v3: $i] : (relation_rng(v2) = v3 & relation_dom(v2) = v1 & % 15.47/3.01 | relation_dom(v0) = v3 & function_inverse(v0) = v2 & $i(v3) & $i(v2) % 15.47/3.01 | & $i(v1))) % 15.47/3.01 | % 15.47/3.01 | ALPHA: (t61_funct_1) implies: % 15.47/3.01 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) % 15.47/3.01 | | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] % 15.47/3.01 | : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (relation_rng(v0) = v5 & % 15.47/3.01 | relation_dom(v0) = v3 & identity_relation(v5) = v4 & % 15.47/3.01 | identity_relation(v3) = v2 & relation_composition(v1, v0) = v4 & % 15.47/3.01 | relation_composition(v0, v1) = v2 & $i(v5) & $i(v4) & $i(v3) & % 15.47/3.01 | $i(v2))) % 15.47/3.01 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | % 15.47/3.01 | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : % 15.47/3.01 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (relation_rng(v0) = v5 & % 15.47/3.01 | identity_relation(v5) = v4 & identity_relation(v1) = v3 & % 15.47/3.01 | relation_composition(v2, v0) = v4 & relation_composition(v0, v2) = % 15.47/3.01 | v3 & function_inverse(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & % 15.47/3.01 | $i(v2))) % 15.47/3.01 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | % 15.47/3.01 | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : % 15.47/3.01 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v4 & % 15.47/3.01 | identity_relation(v4) = v3 & identity_relation(v1) = v5 & % 15.47/3.01 | relation_composition(v2, v0) = v5 & relation_composition(v0, v2) = % 15.47/3.01 | v3 & function_inverse(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & % 15.47/3.01 | $i(v2))) % 15.47/3.01 | % 15.47/3.01 | ALPHA: (t71_relat_1) implies: % 15.47/3.01 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~ % 15.47/3.01 | $i(v0) | relation_dom(v1) = v0) % 15.47/3.01 | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~ % 15.47/3.01 | $i(v0) | relation_rng(v1) = v0) % 15.47/3.01 | % 15.47/3.01 | ALPHA: (function-axioms) implies: % 15.47/3.01 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 15.47/3.01 | (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) % 15.47/3.01 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 15.47/3.01 | (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) % 15.47/3.01 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 15.47/3.01 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 15.47/3.01 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 15.47/3.01 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 15.47/3.02 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.47/3.02 | (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, % 15.47/3.02 | v2) = v0)) % 15.47/3.02 | % 15.47/3.02 | DELTA: instantiating (t67_funct_1) with fresh symbols all_53_0, all_53_1, % 15.47/3.02 | all_53_2 gives: % 15.47/3.02 | (19) ~ (all_53_0 = all_53_1) & identity_relation(all_53_2) = all_53_1 & % 15.47/3.02 | function_inverse(all_53_1) = all_53_0 & $i(all_53_0) & $i(all_53_1) & % 15.47/3.02 | $i(all_53_2) % 15.47/3.02 | % 15.47/3.02 | ALPHA: (19) implies: % 15.47/3.02 | (20) ~ (all_53_0 = all_53_1) % 15.47/3.02 | (21) $i(all_53_2) % 15.47/3.02 | (22) $i(all_53_1) % 15.47/3.02 | (23) function_inverse(all_53_1) = all_53_0 % 15.47/3.02 | (24) identity_relation(all_53_2) = all_53_1 % 15.47/3.02 | % 15.47/3.02 | GROUND_INST: instantiating (13) with all_53_2, all_53_1, simplifying with % 15.47/3.02 | (21), (24) gives: % 15.47/3.02 | (25) relation_rng(all_53_1) = all_53_2 % 15.47/3.02 | % 15.47/3.02 | GROUND_INST: instantiating (12) with all_53_2, all_53_1, simplifying with % 15.47/3.02 | (21), (24) gives: % 15.47/3.02 | (26) relation_dom(all_53_1) = all_53_2 % 15.47/3.02 | % 15.47/3.02 | GROUND_INST: instantiating (t52_funct_1) with all_53_2, all_53_1, simplifying % 15.47/3.02 | with (21), (24) gives: % 15.47/3.02 | (27) one_to_one(all_53_1) % 15.47/3.02 | % 15.47/3.02 | GROUND_INST: instantiating (4) with all_53_2, all_53_1, simplifying with (21), % 15.47/3.02 | (24) gives: % 15.47/3.02 | (28) relation(all_53_1) % 15.47/3.02 | % 15.47/3.02 | GROUND_INST: instantiating (3) with all_53_2, all_53_1, simplifying with (21), % 15.47/3.02 | (24) gives: % 15.47/3.02 | (29) function(all_53_1) % 15.47/3.02 | % 15.47/3.02 | GROUND_INST: instantiating (2) with all_53_1, all_53_0, simplifying with (22), % 15.47/3.02 | (23), (28), (29) gives: % 15.47/3.02 | (30) relation(all_53_0) % 15.47/3.02 | % 15.47/3.02 | GROUND_INST: instantiating (1) with all_53_1, all_53_0, simplifying with (22), % 15.47/3.02 | (23), (28), (29) gives: % 15.47/3.02 | (31) function(all_53_0) % 15.47/3.02 | % 15.47/3.02 | GROUND_INST: instantiating (9) with all_53_1, all_53_0, simplifying with (22), % 15.47/3.02 | (23), (27), (28), (29) gives: % 15.47/3.02 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 15.47/3.02 | (relation_rng(all_53_1) = v3 & relation_dom(all_53_1) = v1 & % 15.47/3.02 | identity_relation(v3) = v2 & identity_relation(v1) = v0 & % 15.47/3.02 | relation_composition(all_53_0, all_53_1) = v2 & % 15.47/3.02 | relation_composition(all_53_1, all_53_0) = v0 & $i(v3) & $i(v2) & % 15.47/3.02 | $i(v1) & $i(v0)) % 15.47/3.02 | % 15.47/3.02 | GROUND_INST: instantiating (6) with all_53_1, all_53_0, simplifying with (22), % 15.47/3.02 | (23), (27), (28), (29) gives: % 15.47/3.02 | (33) ? [v0: $i] : ? [v1: $i] : (relation_rng(all_53_0) = v1 & % 15.47/3.02 | relation_rng(all_53_1) = v0 & relation_dom(all_53_0) = v0 & % 15.47/3.02 | relation_dom(all_53_1) = v1 & $i(v1) & $i(v0)) % 15.47/3.02 | % 15.47/3.02 | GROUND_INST: instantiating (10) with all_53_1, all_53_2, simplifying with % 15.47/3.02 | (22), (26), (27), (28), (29) gives: % 15.47/3.03 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 15.47/3.03 | (relation_rng(all_53_1) = v3 & identity_relation(v3) = v2 & % 15.47/3.03 | identity_relation(all_53_2) = v1 & relation_composition(v0, % 15.47/3.03 | all_53_1) = v2 & relation_composition(all_53_1, v0) = v1 & % 15.47/3.03 | function_inverse(all_53_1) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 15.47/3.03 | % 15.47/3.03 | GROUND_INST: instantiating (7) with all_53_1, all_53_2, simplifying with (22), % 15.47/3.03 | (26), (27), (28), (29) gives: % 15.47/3.03 | (35) ? [v0: $i] : ? [v1: $i] : (relation_rng(v1) = all_53_2 & % 15.47/3.03 | relation_rng(all_53_1) = v0 & relation_dom(v1) = v0 & % 15.47/3.03 | function_inverse(all_53_1) = v1 & $i(v1) & $i(v0) & $i(all_53_2)) % 15.47/3.03 | % 15.47/3.03 | GROUND_INST: instantiating (11) with all_53_1, all_53_2, simplifying with % 15.47/3.03 | (22), (25), (27), (28), (29) gives: % 15.47/3.03 | (36) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 15.47/3.03 | (relation_dom(all_53_1) = v2 & identity_relation(v2) = v1 & % 15.47/3.03 | identity_relation(all_53_2) = v3 & relation_composition(v0, % 15.47/3.03 | all_53_1) = v3 & relation_composition(all_53_1, v0) = v1 & % 15.47/3.03 | function_inverse(all_53_1) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 15.47/3.03 | % 15.47/3.03 | GROUND_INST: instantiating (8) with all_53_1, all_53_2, simplifying with (22), % 15.47/3.03 | (25), (27), (28), (29) gives: % 15.47/3.03 | (37) ? [v0: $i] : ? [v1: $i] : (relation_rng(v0) = v1 & relation_dom(v0) % 15.47/3.03 | = all_53_2 & relation_dom(all_53_1) = v1 & % 15.47/3.03 | function_inverse(all_53_1) = v0 & $i(v1) & $i(v0) & $i(all_53_2)) % 15.47/3.03 | % 15.47/3.03 | DELTA: instantiating (33) with fresh symbols all_72_0, all_72_1 gives: % 15.47/3.03 | (38) relation_rng(all_53_0) = all_72_0 & relation_rng(all_53_1) = all_72_1 % 15.47/3.03 | & relation_dom(all_53_0) = all_72_1 & relation_dom(all_53_1) = % 15.47/3.03 | all_72_0 & $i(all_72_0) & $i(all_72_1) % 15.47/3.03 | % 15.47/3.03 | ALPHA: (38) implies: % 15.47/3.03 | (39) relation_dom(all_53_1) = all_72_0 % 15.47/3.03 | (40) relation_dom(all_53_0) = all_72_1 % 15.47/3.03 | (41) relation_rng(all_53_1) = all_72_1 % 15.47/3.03 | % 15.47/3.03 | DELTA: instantiating (37) with fresh symbols all_74_0, all_74_1 gives: % 15.47/3.03 | (42) relation_rng(all_74_1) = all_74_0 & relation_dom(all_74_1) = all_53_2 % 15.47/3.03 | & relation_dom(all_53_1) = all_74_0 & function_inverse(all_53_1) = % 15.47/3.03 | all_74_1 & $i(all_74_0) & $i(all_74_1) & $i(all_53_2) % 15.47/3.03 | % 15.47/3.03 | ALPHA: (42) implies: % 15.47/3.03 | (43) $i(all_74_1) % 15.47/3.03 | (44) function_inverse(all_53_1) = all_74_1 % 15.47/3.03 | (45) relation_dom(all_53_1) = all_74_0 % 15.47/3.03 | % 15.47/3.03 | DELTA: instantiating (35) with fresh symbols all_76_0, all_76_1 gives: % 15.47/3.03 | (46) relation_rng(all_76_0) = all_53_2 & relation_rng(all_53_1) = all_76_1 % 15.47/3.03 | & relation_dom(all_76_0) = all_76_1 & function_inverse(all_53_1) = % 15.47/3.03 | all_76_0 & $i(all_76_0) & $i(all_76_1) & $i(all_53_2) % 15.47/3.03 | % 15.47/3.03 | ALPHA: (46) implies: % 15.47/3.03 | (47) function_inverse(all_53_1) = all_76_0 % 15.47/3.03 | (48) relation_rng(all_53_1) = all_76_1 % 15.47/3.03 | % 15.47/3.03 | DELTA: instantiating (36) with fresh symbols all_78_0, all_78_1, all_78_2, % 15.47/3.03 | all_78_3 gives: % 15.47/3.03 | (49) relation_dom(all_53_1) = all_78_1 & identity_relation(all_78_1) = % 15.47/3.03 | all_78_2 & identity_relation(all_53_2) = all_78_0 & % 15.47/3.03 | relation_composition(all_78_3, all_53_1) = all_78_0 & % 15.47/3.03 | relation_composition(all_53_1, all_78_3) = all_78_2 & % 15.47/3.03 | function_inverse(all_53_1) = all_78_3 & $i(all_78_0) & $i(all_78_1) & % 15.47/3.03 | $i(all_78_2) & $i(all_78_3) % 15.47/3.03 | % 15.47/3.03 | ALPHA: (49) implies: % 15.47/3.04 | (50) $i(all_78_2) % 15.47/3.04 | (51) function_inverse(all_53_1) = all_78_3 % 15.47/3.04 | (52) relation_composition(all_53_1, all_78_3) = all_78_2 % 15.47/3.04 | (53) identity_relation(all_78_1) = all_78_2 % 15.47/3.04 | (54) relation_dom(all_53_1) = all_78_1 % 15.47/3.04 | % 15.47/3.04 | DELTA: instantiating (34) with fresh symbols all_80_0, all_80_1, all_80_2, % 15.47/3.04 | all_80_3 gives: % 15.47/3.04 | (55) relation_rng(all_53_1) = all_80_0 & identity_relation(all_80_0) = % 15.47/3.04 | all_80_1 & identity_relation(all_53_2) = all_80_2 & % 15.47/3.04 | relation_composition(all_80_3, all_53_1) = all_80_1 & % 15.47/3.04 | relation_composition(all_53_1, all_80_3) = all_80_2 & % 15.47/3.04 | function_inverse(all_53_1) = all_80_3 & $i(all_80_0) & $i(all_80_1) & % 15.47/3.04 | $i(all_80_2) & $i(all_80_3) % 15.47/3.04 | % 15.47/3.04 | ALPHA: (55) implies: % 15.47/3.04 | (56) function_inverse(all_53_1) = all_80_3 % 15.47/3.04 | (57) identity_relation(all_53_2) = all_80_2 % 15.47/3.04 | (58) relation_rng(all_53_1) = all_80_0 % 15.47/3.04 | % 15.47/3.04 | DELTA: instantiating (32) with fresh symbols all_82_0, all_82_1, all_82_2, % 15.47/3.04 | all_82_3 gives: % 15.47/3.04 | (59) relation_rng(all_53_1) = all_82_0 & relation_dom(all_53_1) = all_82_2 % 15.47/3.04 | & identity_relation(all_82_0) = all_82_1 & identity_relation(all_82_2) % 15.47/3.04 | = all_82_3 & relation_composition(all_53_0, all_53_1) = all_82_1 & % 15.47/3.04 | relation_composition(all_53_1, all_53_0) = all_82_3 & $i(all_82_0) & % 15.47/3.04 | $i(all_82_1) & $i(all_82_2) & $i(all_82_3) % 15.47/3.04 | % 15.47/3.04 | ALPHA: (59) implies: % 15.47/3.04 | (60) identity_relation(all_82_2) = all_82_3 % 15.47/3.04 | (61) relation_dom(all_53_1) = all_82_2 % 15.47/3.04 | (62) relation_rng(all_53_1) = all_82_0 % 15.47/3.04 | % 15.47/3.04 | GROUND_INST: instantiating (14) with all_76_0, all_78_3, all_53_1, simplifying % 15.47/3.04 | with (47), (51) gives: % 15.47/3.04 | (63) all_78_3 = all_76_0 % 15.47/3.04 | % 15.47/3.04 | GROUND_INST: instantiating (14) with all_74_1, all_78_3, all_53_1, simplifying % 15.47/3.04 | with (44), (51) gives: % 15.47/3.04 | (64) all_78_3 = all_74_1 % 15.47/3.04 | % 15.47/3.04 | GROUND_INST: instantiating (14) with all_53_0, all_80_3, all_53_1, simplifying % 15.47/3.04 | with (23), (56) gives: % 15.47/3.04 | (65) all_80_3 = all_53_0 % 15.47/3.04 | % 15.47/3.04 | GROUND_INST: instantiating (14) with all_76_0, all_80_3, all_53_1, simplifying % 15.47/3.04 | with (47), (56) gives: % 15.47/3.04 | (66) all_80_3 = all_76_0 % 15.47/3.04 | % 15.47/3.04 | GROUND_INST: instantiating (15) with all_53_1, all_80_2, all_53_2, simplifying % 15.47/3.04 | with (24), (57) gives: % 15.47/3.04 | (67) all_80_2 = all_53_1 % 15.47/3.04 | % 15.47/3.04 | GROUND_INST: instantiating (15) with all_78_2, all_82_3, all_78_1, simplifying % 15.47/3.04 | with (53) gives: % 15.47/3.04 | (68) all_82_3 = all_78_2 | ~ (identity_relation(all_78_1) = all_82_3) % 15.47/3.04 | % 15.47/3.04 | GROUND_INST: instantiating (15) with all_80_2, all_82_3, all_53_2, simplifying % 15.47/3.04 | with (57) gives: % 15.47/3.04 | (69) all_82_3 = all_80_2 | ~ (identity_relation(all_53_2) = all_82_3) % 15.47/3.04 | % 15.47/3.04 | GROUND_INST: instantiating (16) with all_53_2, all_78_1, all_53_1, simplifying % 15.47/3.04 | with (26), (54) gives: % 15.47/3.04 | (70) all_78_1 = all_53_2 % 15.47/3.04 | % 15.47/3.04 | GROUND_INST: instantiating (16) with all_74_0, all_78_1, all_53_1, simplifying % 15.47/3.04 | with (45), (54) gives: % 15.47/3.04 | (71) all_78_1 = all_74_0 % 15.47/3.04 | % 15.47/3.04 | GROUND_INST: instantiating (16) with all_74_0, all_82_2, all_53_1, simplifying % 15.47/3.04 | with (45), (61) gives: % 15.47/3.04 | (72) all_82_2 = all_74_0 % 15.47/3.04 | % 15.47/3.04 | GROUND_INST: instantiating (16) with all_72_0, all_82_2, all_53_1, simplifying % 15.47/3.04 | with (39), (61) gives: % 15.47/3.04 | (73) all_82_2 = all_72_0 % 15.47/3.04 | % 15.47/3.04 | GROUND_INST: instantiating (17) with all_53_2, all_76_1, all_53_1, simplifying % 15.47/3.04 | with (25), (48) gives: % 15.47/3.04 | (74) all_76_1 = all_53_2 % 15.47/3.04 | % 15.47/3.04 | GROUND_INST: instantiating (17) with all_76_1, all_80_0, all_53_1, simplifying % 15.47/3.04 | with (48), (58) gives: % 15.47/3.04 | (75) all_80_0 = all_76_1 % 15.47/3.04 | % 15.47/3.04 | GROUND_INST: instantiating (17) with all_80_0, all_82_0, all_53_1, simplifying % 15.47/3.04 | with (58), (62) gives: % 15.47/3.04 | (76) all_82_0 = all_80_0 % 15.47/3.04 | % 15.47/3.04 | GROUND_INST: instantiating (17) with all_72_1, all_82_0, all_53_1, simplifying % 15.47/3.04 | with (41), (62) gives: % 15.47/3.04 | (77) all_82_0 = all_72_1 % 15.47/3.04 | % 15.47/3.05 | COMBINE_EQS: (76), (77) imply: % 15.47/3.05 | (78) all_80_0 = all_72_1 % 15.47/3.05 | % 15.47/3.05 | SIMP: (78) implies: % 15.47/3.05 | (79) all_80_0 = all_72_1 % 15.47/3.05 | % 15.47/3.05 | COMBINE_EQS: (72), (73) imply: % 15.47/3.05 | (80) all_74_0 = all_72_0 % 15.47/3.05 | % 15.47/3.05 | SIMP: (80) implies: % 15.47/3.05 | (81) all_74_0 = all_72_0 % 15.47/3.05 | % 15.47/3.05 | COMBINE_EQS: (75), (79) imply: % 15.47/3.05 | (82) all_76_1 = all_72_1 % 15.47/3.05 | % 15.47/3.05 | SIMP: (82) implies: % 15.47/3.05 | (83) all_76_1 = all_72_1 % 15.47/3.05 | % 15.47/3.05 | COMBINE_EQS: (65), (66) imply: % 15.47/3.05 | (84) all_76_0 = all_53_0 % 15.47/3.05 | % 15.47/3.05 | SIMP: (84) implies: % 15.47/3.05 | (85) all_76_0 = all_53_0 % 15.47/3.05 | % 15.47/3.05 | COMBINE_EQS: (70), (71) imply: % 15.47/3.05 | (86) all_74_0 = all_53_2 % 15.47/3.05 | % 15.47/3.05 | SIMP: (86) implies: % 15.47/3.05 | (87) all_74_0 = all_53_2 % 15.47/3.05 | % 15.47/3.05 | COMBINE_EQS: (63), (64) imply: % 15.47/3.05 | (88) all_76_0 = all_74_1 % 15.47/3.05 | % 15.47/3.05 | SIMP: (88) implies: % 15.47/3.05 | (89) all_76_0 = all_74_1 % 15.47/3.05 | % 15.47/3.05 | COMBINE_EQS: (85), (89) imply: % 15.47/3.05 | (90) all_74_1 = all_53_0 % 15.47/3.05 | % 15.47/3.05 | COMBINE_EQS: (74), (83) imply: % 15.47/3.05 | (91) all_72_1 = all_53_2 % 15.47/3.05 | % 15.47/3.05 | SIMP: (91) implies: % 15.47/3.05 | (92) all_72_1 = all_53_2 % 15.47/3.05 | % 15.47/3.05 | COMBINE_EQS: (81), (87) imply: % 15.47/3.05 | (93) all_72_0 = all_53_2 % 15.47/3.05 | % 15.47/3.05 | COMBINE_EQS: (64), (90) imply: % 15.47/3.05 | (94) all_78_3 = all_53_0 % 15.47/3.05 | % 15.47/3.05 | COMBINE_EQS: (73), (93) imply: % 15.47/3.05 | (95) all_82_2 = all_53_2 % 15.47/3.05 | % 15.47/3.05 | REDUCE: (40), (92) imply: % 15.47/3.05 | (96) relation_dom(all_53_0) = all_53_2 % 15.47/3.05 | % 15.47/3.05 | REDUCE: (60), (95) imply: % 15.47/3.05 | (97) identity_relation(all_53_2) = all_82_3 % 15.47/3.05 | % 15.47/3.05 | REDUCE: (53), (70) imply: % 15.47/3.05 | (98) identity_relation(all_53_2) = all_78_2 % 15.47/3.05 | % 15.47/3.05 | REDUCE: (52), (94) imply: % 15.47/3.05 | (99) relation_composition(all_53_1, all_53_0) = all_78_2 % 15.47/3.05 | % 15.47/3.05 | REDUCE: (43), (90) imply: % 15.47/3.05 | (100) $i(all_53_0) % 15.47/3.05 | % 15.47/3.05 | BETA: splitting (69) gives: % 15.47/3.05 | % 15.47/3.05 | Case 1: % 15.47/3.05 | | % 15.47/3.05 | | (101) ~ (identity_relation(all_53_2) = all_82_3) % 15.47/3.05 | | % 15.47/3.05 | | PRED_UNIFY: (97), (101) imply: % 15.47/3.05 | | (102) $false % 15.47/3.05 | | % 15.47/3.05 | | CLOSE: (102) is inconsistent. % 15.47/3.05 | | % 15.47/3.05 | Case 2: % 15.47/3.05 | | % 15.47/3.05 | | (103) all_82_3 = all_80_2 % 15.47/3.05 | | % 15.47/3.05 | | COMBINE_EQS: (67), (103) imply: % 15.47/3.05 | | (104) all_82_3 = all_53_1 % 15.47/3.05 | | % 15.47/3.05 | | BETA: splitting (68) gives: % 15.47/3.05 | | % 16.33/3.05 | | Case 1: % 16.33/3.05 | | | % 16.33/3.05 | | | (105) ~ (identity_relation(all_78_1) = all_82_3) % 16.33/3.05 | | | % 16.33/3.05 | | | REDUCE: (70), (104), (105) imply: % 16.33/3.05 | | | (106) ~ (identity_relation(all_53_2) = all_53_1) % 16.33/3.05 | | | % 16.33/3.05 | | | PRED_UNIFY: (24), (106) imply: % 16.33/3.05 | | | (107) $false % 16.33/3.05 | | | % 16.33/3.05 | | | CLOSE: (107) is inconsistent. % 16.33/3.05 | | | % 16.33/3.05 | | Case 2: % 16.33/3.05 | | | % 16.33/3.05 | | | (108) all_82_3 = all_78_2 % 16.33/3.05 | | | % 16.33/3.05 | | | COMBINE_EQS: (104), (108) imply: % 16.33/3.05 | | | (109) all_78_2 = all_53_1 % 16.33/3.05 | | | % 16.33/3.05 | | | SIMP: (109) implies: % 16.33/3.05 | | | (110) all_78_2 = all_53_1 % 16.33/3.05 | | | % 16.33/3.05 | | | REDUCE: (99), (110) imply: % 16.33/3.05 | | | (111) relation_composition(all_53_1, all_53_0) = all_53_1 % 16.33/3.05 | | | % 16.33/3.05 | | | GROUND_INST: instantiating (5) with all_53_1, all_53_2, all_53_0, % 16.33/3.05 | | | simplifying with (22), (25), (28), (29), (30), (31), (96), % 16.33/3.05 | | | (100) gives: % 16.33/3.06 | | | (112) ? [v0: any] : ? [v1: int] : ((v1 = all_53_0 & % 16.33/3.06 | | | identity_relation(all_53_2) = all_53_0) | ( ~ (v0 = all_53_1) % 16.33/3.06 | | | & relation_composition(all_53_1, all_53_0) = v0 & $i(v0))) % 16.33/3.06 | | | % 16.33/3.06 | | | DELTA: instantiating (112) with fresh symbols all_111_0, all_111_1 gives: % 16.33/3.06 | | | (113) (all_111_0 = all_53_0 & identity_relation(all_53_2) = all_53_0) | % 16.33/3.06 | | | ( ~ (all_111_1 = all_53_1) & relation_composition(all_53_1, % 16.33/3.06 | | | all_53_0) = all_111_1 & $i(all_111_1)) % 16.33/3.06 | | | % 16.33/3.06 | | | BETA: splitting (113) gives: % 16.33/3.06 | | | % 16.33/3.06 | | | Case 1: % 16.33/3.06 | | | | % 16.33/3.06 | | | | (114) all_111_0 = all_53_0 & identity_relation(all_53_2) = all_53_0 % 16.33/3.06 | | | | % 16.33/3.06 | | | | ALPHA: (114) implies: % 16.33/3.06 | | | | (115) identity_relation(all_53_2) = all_53_0 % 16.33/3.06 | | | | % 16.33/3.06 | | | | GROUND_INST: instantiating (15) with all_53_1, all_53_0, all_53_2, % 16.33/3.06 | | | | simplifying with (24), (115) gives: % 16.33/3.06 | | | | (116) all_53_0 = all_53_1 % 16.33/3.06 | | | | % 16.33/3.06 | | | | REDUCE: (20), (116) imply: % 16.33/3.06 | | | | (117) $false % 16.33/3.06 | | | | % 16.33/3.06 | | | | CLOSE: (117) is inconsistent. % 16.33/3.06 | | | | % 16.33/3.06 | | | Case 2: % 16.33/3.06 | | | | % 16.33/3.06 | | | | (118) ~ (all_111_1 = all_53_1) & relation_composition(all_53_1, % 16.33/3.06 | | | | all_53_0) = all_111_1 & $i(all_111_1) % 16.33/3.06 | | | | % 16.33/3.06 | | | | ALPHA: (118) implies: % 16.33/3.06 | | | | (119) ~ (all_111_1 = all_53_1) % 16.33/3.06 | | | | (120) relation_composition(all_53_1, all_53_0) = all_111_1 % 16.33/3.06 | | | | % 16.33/3.06 | | | | GROUND_INST: instantiating (18) with all_53_1, all_111_1, all_53_0, % 16.33/3.06 | | | | all_53_1, simplifying with (111), (120) gives: % 16.33/3.06 | | | | (121) all_111_1 = all_53_1 % 16.33/3.06 | | | | % 16.33/3.06 | | | | REDUCE: (119), (121) imply: % 16.33/3.06 | | | | (122) $false % 16.33/3.06 | | | | % 16.33/3.06 | | | | CLOSE: (122) is inconsistent. % 16.33/3.06 | | | | % 16.33/3.06 | | | End of split % 16.33/3.06 | | | % 16.33/3.06 | | End of split % 16.33/3.06 | | % 16.33/3.06 | End of split % 16.33/3.06 | % 16.33/3.06 End of proof % 16.33/3.06 % SZS output end Proof for theBenchmark % 16.33/3.06 % 16.33/3.06 2410ms %------------------------------------------------------------------------------