%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU189+1 : TPTP v8.1.2. Released v3.3.0. % 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 17:43:09 EDT 2023 % Result : Theorem 7.03s 1.71s % Output : Proof 9.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU189+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n001.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Thu Aug 24 01:16:10 EDT 2023 % 0.13/0.35 % 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 % 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.64 Running up to 7 provers in parallel. % 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 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 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 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 % 2.33/1.02 Prover 1: Preprocessing ... % 2.33/1.02 Prover 4: Preprocessing ... % 2.80/1.06 Prover 0: Preprocessing ... % 2.80/1.06 Prover 3: Preprocessing ... % 2.80/1.06 Prover 5: Preprocessing ... % 2.80/1.06 Prover 2: Preprocessing ... % 2.80/1.06 Prover 6: Preprocessing ... % 4.35/1.32 Prover 1: Warning: ignoring some quantifiers % 4.76/1.36 Prover 3: Warning: ignoring some quantifiers % 4.76/1.37 Prover 1: Constructing countermodel ... % 4.76/1.37 Prover 3: Constructing countermodel ... % 4.76/1.38 Prover 6: Proving ... % 4.76/1.38 Prover 5: Proving ... % 4.76/1.38 Prover 2: Proving ... % 4.76/1.38 Prover 4: Warning: ignoring some quantifiers % 4.76/1.40 Prover 4: Constructing countermodel ... % 5.17/1.48 Prover 0: Proving ... % 7.03/1.71 Prover 3: proved (1063ms) % 7.03/1.71 % 7.03/1.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.03/1.71 % 7.03/1.71 Prover 2: stopped % 7.03/1.71 Prover 5: stopped % 7.03/1.71 Prover 6: stopped % 7.03/1.71 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.03/1.71 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.03/1.72 Prover 0: stopped % 7.03/1.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.03/1.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.03/1.72 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.62/1.76 Prover 10: Preprocessing ... % 7.62/1.76 Prover 8: Preprocessing ... % 7.62/1.77 Prover 13: Preprocessing ... % 7.62/1.77 Prover 7: Preprocessing ... % 7.62/1.77 Prover 11: Preprocessing ... % 8.10/1.86 Prover 10: Warning: ignoring some quantifiers % 8.41/1.86 Prover 8: Warning: ignoring some quantifiers % 8.41/1.87 Prover 10: Constructing countermodel ... % 8.41/1.87 Prover 8: Constructing countermodel ... % 8.41/1.88 Prover 13: Warning: ignoring some quantifiers % 8.41/1.88 Prover 7: Warning: ignoring some quantifiers % 8.41/1.89 Prover 13: Constructing countermodel ... % 8.41/1.89 Prover 7: Constructing countermodel ... % 8.41/1.91 Prover 1: Found proof (size 51) % 8.41/1.91 Prover 11: Warning: ignoring some quantifiers % 8.41/1.91 Prover 1: proved (1265ms) % 8.41/1.91 Prover 11: Constructing countermodel ... % 8.41/1.91 Prover 10: stopped % 8.41/1.91 Prover 7: stopped % 8.41/1.91 Prover 13: stopped % 8.41/1.91 Prover 8: stopped % 8.41/1.92 Prover 4: stopped % 8.41/1.92 Prover 11: stopped % 8.41/1.92 % 8.41/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.41/1.92 % 8.41/1.93 % SZS output start Proof for theBenchmark % 8.41/1.93 Assumptions after simplification: % 8.41/1.93 --------------------------------- % 8.41/1.93 % 8.41/1.93 (fc5_relat_1) % 8.93/1.96 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2: % 8.93/1.96 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & empty(v1) = v4 & % 8.93/1.96 empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) % 8.93/1.96 % 8.93/1.96 (fc6_relat_1) % 8.93/1.97 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: % 8.93/1.97 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & empty(v1) = v4 & % 8.93/1.97 empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) % 8.93/1.97 % 8.93/1.97 (t60_relat_1) % 8.93/1.97 relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set & % 8.93/1.97 $i(empty_set) % 8.93/1.97 % 8.93/1.97 (t64_relat_1) % 8.93/1.97 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : (v0 = empty_set | ~ % 8.93/1.97 (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : % 8.93/1.97 (relation_dom(v0) = v3 & relation(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | ( ~ (v3 % 8.93/1.97 = empty_set) & ~ (v1 = empty_set))))) % 8.93/1.97 % 8.93/1.97 (t65_relat_1) % 8.93/1.97 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_rng(v0) = % 8.93/1.97 v2 & relation_dom(v0) = v1 & relation(v0) = 0 & $i(v2) & $i(v1) & $i(v0) & % 8.93/1.97 ((v2 = empty_set & ~ (v1 = empty_set)) | (v1 = empty_set & ~ (v2 = % 8.93/1.97 empty_set)))) % 8.93/1.97 % 8.93/1.97 (function-axioms) % 9.09/1.98 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 9.09/1.98 [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 9.09/1.98 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 9.09/1.98 : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: % 9.09/1.98 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ % 9.09/1.98 (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 9.09/1.98 v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: % 9.09/1.98 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 9.09/1.98 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool] % 9.09/1.98 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | % 9.09/1.98 ~ (empty(v2) = v0)) % 9.09/1.98 % 9.09/1.98 Further assumptions not needed in the proof: % 9.09/1.98 -------------------------------------------- % 9.09/1.98 antisymmetry_r2_hidden, cc1_relat_1, dt_k1_relat_1, dt_k1_xboole_0, % 9.09/1.98 dt_k2_relat_1, dt_m1_subset_1, existence_m1_subset_1, fc1_xboole_0, fc4_relat_1, % 9.09/1.98 fc7_relat_1, fc8_relat_1, rc1_relat_1, rc1_xboole_0, rc2_relat_1, rc2_xboole_0, % 9.09/1.98 t1_subset, t2_subset, t6_boole, t7_boole, t8_boole % 9.09/1.98 % 9.09/1.98 Those formulas are unsatisfiable: % 9.09/1.98 --------------------------------- % 9.09/1.98 % 9.09/1.98 Begin of proof % 9.09/1.98 | % 9.09/1.98 | ALPHA: (t60_relat_1) implies: % 9.09/1.98 | (1) relation_dom(empty_set) = empty_set % 9.09/1.98 | (2) relation_rng(empty_set) = empty_set % 9.09/1.98 | % 9.09/1.98 | ALPHA: (t64_relat_1) implies: % 9.09/1.98 | (3) ! [v0: $i] : ! [v1: $i] : (v0 = empty_set | ~ (relation_rng(v0) = % 9.09/1.98 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : (relation_dom(v0) = % 9.09/1.98 | v3 & relation(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | ( ~ (v3 = % 9.09/1.98 | empty_set) & ~ (v1 = empty_set))))) % 9.09/1.98 | % 9.09/1.98 | ALPHA: (t65_relat_1) implies: % 9.09/1.99 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_rng(v0) = v2 & % 9.09/1.99 | relation_dom(v0) = v1 & relation(v0) = 0 & $i(v2) & $i(v1) & $i(v0) & % 9.09/1.99 | ((v2 = empty_set & ~ (v1 = empty_set)) | (v1 = empty_set & ~ (v2 = % 9.09/1.99 | empty_set)))) % 9.09/1.99 | % 9.09/1.99 | ALPHA: (function-axioms) implies: % 9.09/1.99 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.09/1.99 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 9.09/1.99 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 9.09/1.99 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 9.09/1.99 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 9.09/1.99 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 9.09/1.99 | % 9.09/1.99 | DELTA: instantiating (4) with fresh symbols all_25_0, all_25_1, all_25_2 % 9.09/1.99 | gives: % 9.09/1.99 | (8) relation_rng(all_25_2) = all_25_0 & relation_dom(all_25_2) = all_25_1 & % 9.09/1.99 | relation(all_25_2) = 0 & $i(all_25_0) & $i(all_25_1) & $i(all_25_2) & % 9.09/1.99 | ((all_25_0 = empty_set & ~ (all_25_1 = empty_set)) | (all_25_1 = % 9.09/1.99 | empty_set & ~ (all_25_0 = empty_set))) % 9.09/1.99 | % 9.09/1.99 | ALPHA: (8) implies: % 9.09/1.99 | (9) $i(all_25_2) % 9.09/1.99 | (10) relation(all_25_2) = 0 % 9.09/1.99 | (11) relation_dom(all_25_2) = all_25_1 % 9.09/1.99 | (12) relation_rng(all_25_2) = all_25_0 % 9.09/1.99 | (13) (all_25_0 = empty_set & ~ (all_25_1 = empty_set)) | (all_25_1 = % 9.09/1.99 | empty_set & ~ (all_25_0 = empty_set)) % 9.09/1.99 | % 9.09/1.99 | GROUND_INST: instantiating (fc5_relat_1) with all_25_2, all_25_1, simplifying % 9.09/1.99 | with (9), (11) gives: % 9.09/1.99 | (14) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_25_2) = v1 % 9.09/2.00 | & empty(all_25_1) = v2 & empty(all_25_2) = v0 & ( ~ (v2 = 0) | ~ % 9.09/2.00 | (v1 = 0) | v0 = 0)) % 9.09/2.00 | % 9.09/2.00 | GROUND_INST: instantiating (3) with all_25_2, all_25_0, simplifying with (9), % 9.09/2.00 | (12) gives: % 9.09/2.00 | (15) all_25_2 = empty_set | ? [v0: any] : ? [v1: $i] : % 9.09/2.00 | (relation_dom(all_25_2) = v1 & relation(all_25_2) = v0 & $i(v1) & ( ~ % 9.09/2.00 | (v0 = 0) | ( ~ (v1 = empty_set) & ~ (all_25_0 = empty_set)))) % 9.09/2.00 | % 9.09/2.00 | GROUND_INST: instantiating (fc6_relat_1) with all_25_2, all_25_0, simplifying % 9.09/2.00 | with (9), (12) gives: % 9.09/2.00 | (16) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_25_2) = v1 % 9.09/2.00 | & empty(all_25_0) = v2 & empty(all_25_2) = v0 & ( ~ (v2 = 0) | ~ % 9.09/2.00 | (v1 = 0) | v0 = 0)) % 9.09/2.00 | % 9.09/2.00 | DELTA: instantiating (16) with fresh symbols all_33_0, all_33_1, all_33_2 % 9.09/2.00 | gives: % 9.09/2.00 | (17) relation(all_25_2) = all_33_1 & empty(all_25_0) = all_33_0 & % 9.09/2.00 | empty(all_25_2) = all_33_2 & ( ~ (all_33_0 = 0) | ~ (all_33_1 = 0) | % 9.09/2.00 | all_33_2 = 0) % 9.09/2.00 | % 9.09/2.00 | ALPHA: (17) implies: % 9.09/2.00 | (18) relation(all_25_2) = all_33_1 % 9.09/2.00 | % 9.09/2.00 | DELTA: instantiating (14) with fresh symbols all_37_0, all_37_1, all_37_2 % 9.09/2.00 | gives: % 9.09/2.00 | (19) relation(all_25_2) = all_37_1 & empty(all_25_1) = all_37_0 & % 9.09/2.00 | empty(all_25_2) = all_37_2 & ( ~ (all_37_0 = 0) | ~ (all_37_1 = 0) | % 9.09/2.00 | all_37_2 = 0) % 9.09/2.00 | % 9.09/2.00 | ALPHA: (19) implies: % 9.09/2.00 | (20) relation(all_25_2) = all_37_1 % 9.09/2.00 | % 9.09/2.00 | GROUND_INST: instantiating (5) with 0, all_37_1, all_25_2, simplifying with % 9.09/2.00 | (10), (20) gives: % 9.09/2.00 | (21) all_37_1 = 0 % 9.09/2.00 | % 9.09/2.00 | GROUND_INST: instantiating (5) with all_33_1, all_37_1, all_25_2, simplifying % 9.09/2.00 | with (18), (20) gives: % 9.09/2.00 | (22) all_37_1 = all_33_1 % 9.09/2.00 | % 9.09/2.00 | COMBINE_EQS: (21), (22) imply: % 9.09/2.00 | (23) all_33_1 = 0 % 9.09/2.00 | % 9.09/2.00 | BETA: splitting (13) gives: % 9.09/2.00 | % 9.09/2.00 | Case 1: % 9.09/2.00 | | % 9.09/2.00 | | (24) all_25_0 = empty_set & ~ (all_25_1 = empty_set) % 9.09/2.00 | | % 9.09/2.00 | | ALPHA: (24) implies: % 9.09/2.00 | | (25) all_25_0 = empty_set % 9.09/2.00 | | (26) ~ (all_25_1 = empty_set) % 9.09/2.00 | | % 9.09/2.00 | | BETA: splitting (15) gives: % 9.09/2.00 | | % 9.09/2.00 | | Case 1: % 9.09/2.00 | | | % 9.09/2.00 | | | (27) all_25_2 = empty_set % 9.09/2.00 | | | % 9.09/2.00 | | | REDUCE: (11), (27) imply: % 9.09/2.00 | | | (28) relation_dom(empty_set) = all_25_1 % 9.09/2.00 | | | % 9.09/2.01 | | | GROUND_INST: instantiating (6) with empty_set, all_25_1, empty_set, % 9.09/2.01 | | | simplifying with (1), (28) gives: % 9.09/2.01 | | | (29) all_25_1 = empty_set % 9.09/2.01 | | | % 9.09/2.01 | | | REDUCE: (26), (29) imply: % 9.09/2.01 | | | (30) $false % 9.09/2.01 | | | % 9.09/2.01 | | | CLOSE: (30) is inconsistent. % 9.09/2.01 | | | % 9.09/2.01 | | Case 2: % 9.09/2.01 | | | % 9.09/2.01 | | | (31) ? [v0: any] : ? [v1: $i] : (relation_dom(all_25_2) = v1 & % 9.09/2.01 | | | relation(all_25_2) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ~ (v1 = % 9.09/2.01 | | | empty_set) & ~ (all_25_0 = empty_set)))) % 9.09/2.01 | | | % 9.09/2.01 | | | DELTA: instantiating (31) with fresh symbols all_72_0, all_72_1 gives: % 9.09/2.01 | | | (32) relation_dom(all_25_2) = all_72_0 & relation(all_25_2) = all_72_1 % 9.09/2.01 | | | & $i(all_72_0) & ( ~ (all_72_1 = 0) | ( ~ (all_72_0 = empty_set) & % 9.09/2.01 | | | ~ (all_25_0 = empty_set))) % 9.09/2.01 | | | % 9.09/2.01 | | | ALPHA: (32) implies: % 9.09/2.01 | | | (33) relation(all_25_2) = all_72_1 % 9.09/2.01 | | | (34) ~ (all_72_1 = 0) | ( ~ (all_72_0 = empty_set) & ~ (all_25_0 = % 9.09/2.01 | | | empty_set)) % 9.09/2.01 | | | % 9.09/2.01 | | | BETA: splitting (34) gives: % 9.09/2.01 | | | % 9.09/2.01 | | | Case 1: % 9.09/2.01 | | | | % 9.09/2.01 | | | | (35) ~ (all_72_1 = 0) % 9.09/2.01 | | | | % 9.09/2.01 | | | | GROUND_INST: instantiating (5) with 0, all_72_1, all_25_2, simplifying % 9.09/2.01 | | | | with (10), (33) gives: % 9.09/2.01 | | | | (36) all_72_1 = 0 % 9.09/2.01 | | | | % 9.09/2.01 | | | | REDUCE: (35), (36) imply: % 9.09/2.01 | | | | (37) $false % 9.09/2.01 | | | | % 9.09/2.01 | | | | CLOSE: (37) is inconsistent. % 9.09/2.01 | | | | % 9.09/2.01 | | | Case 2: % 9.09/2.01 | | | | % 9.09/2.01 | | | | (38) ~ (all_72_0 = empty_set) & ~ (all_25_0 = empty_set) % 9.09/2.01 | | | | % 9.09/2.01 | | | | ALPHA: (38) implies: % 9.09/2.01 | | | | (39) ~ (all_25_0 = empty_set) % 9.09/2.01 | | | | % 9.09/2.01 | | | | REDUCE: (25), (39) imply: % 9.09/2.01 | | | | (40) $false % 9.09/2.01 | | | | % 9.09/2.01 | | | | CLOSE: (40) is inconsistent. % 9.09/2.01 | | | | % 9.09/2.01 | | | End of split % 9.09/2.01 | | | % 9.09/2.01 | | End of split % 9.09/2.01 | | % 9.09/2.01 | Case 2: % 9.09/2.01 | | % 9.09/2.01 | | (41) all_25_1 = empty_set & ~ (all_25_0 = empty_set) % 9.09/2.01 | | % 9.09/2.01 | | ALPHA: (41) implies: % 9.09/2.01 | | (42) all_25_1 = empty_set % 9.09/2.01 | | (43) ~ (all_25_0 = empty_set) % 9.09/2.01 | | % 9.09/2.01 | | REDUCE: (11), (42) imply: % 9.09/2.01 | | (44) relation_dom(all_25_2) = empty_set % 9.09/2.01 | | % 9.09/2.01 | | BETA: splitting (15) gives: % 9.09/2.01 | | % 9.09/2.01 | | Case 1: % 9.09/2.01 | | | % 9.09/2.01 | | | (45) all_25_2 = empty_set % 9.09/2.01 | | | % 9.09/2.01 | | | REDUCE: (12), (45) imply: % 9.09/2.01 | | | (46) relation_rng(empty_set) = all_25_0 % 9.09/2.01 | | | % 9.09/2.01 | | | GROUND_INST: instantiating (7) with empty_set, all_25_0, empty_set, % 9.09/2.01 | | | simplifying with (2), (46) gives: % 9.09/2.01 | | | (47) all_25_0 = empty_set % 9.09/2.01 | | | % 9.09/2.02 | | | REDUCE: (43), (47) imply: % 9.09/2.02 | | | (48) $false % 9.09/2.02 | | | % 9.09/2.02 | | | CLOSE: (48) is inconsistent. % 9.09/2.02 | | | % 9.09/2.02 | | Case 2: % 9.09/2.02 | | | % 9.09/2.02 | | | (49) ? [v0: any] : ? [v1: $i] : (relation_dom(all_25_2) = v1 & % 9.09/2.02 | | | relation(all_25_2) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ~ (v1 = % 9.09/2.02 | | | empty_set) & ~ (all_25_0 = empty_set)))) % 9.09/2.02 | | | % 9.09/2.02 | | | DELTA: instantiating (49) with fresh symbols all_72_0, all_72_1 gives: % 9.09/2.02 | | | (50) relation_dom(all_25_2) = all_72_0 & relation(all_25_2) = all_72_1 % 9.09/2.02 | | | & $i(all_72_0) & ( ~ (all_72_1 = 0) | ( ~ (all_72_0 = empty_set) & % 9.09/2.02 | | | ~ (all_25_0 = empty_set))) % 9.09/2.02 | | | % 9.09/2.02 | | | ALPHA: (50) implies: % 9.09/2.02 | | | (51) relation(all_25_2) = all_72_1 % 9.09/2.02 | | | (52) relation_dom(all_25_2) = all_72_0 % 9.09/2.02 | | | (53) ~ (all_72_1 = 0) | ( ~ (all_72_0 = empty_set) & ~ (all_25_0 = % 9.09/2.02 | | | empty_set)) % 9.09/2.02 | | | % 9.09/2.02 | | | GROUND_INST: instantiating (5) with 0, all_72_1, all_25_2, simplifying % 9.09/2.02 | | | with (10), (51) gives: % 9.09/2.02 | | | (54) all_72_1 = 0 % 9.09/2.02 | | | % 9.09/2.02 | | | GROUND_INST: instantiating (6) with empty_set, all_72_0, all_25_2, % 9.09/2.02 | | | simplifying with (44), (52) gives: % 9.09/2.02 | | | (55) all_72_0 = empty_set % 9.09/2.02 | | | % 9.09/2.02 | | | BETA: splitting (53) gives: % 9.09/2.02 | | | % 9.09/2.02 | | | Case 1: % 9.09/2.02 | | | | % 9.09/2.02 | | | | (56) ~ (all_72_1 = 0) % 9.09/2.02 | | | | % 9.09/2.02 | | | | REDUCE: (54), (56) imply: % 9.09/2.02 | | | | (57) $false % 9.09/2.02 | | | | % 9.09/2.02 | | | | CLOSE: (57) is inconsistent. % 9.09/2.02 | | | | % 9.09/2.02 | | | Case 2: % 9.09/2.02 | | | | % 9.09/2.02 | | | | (58) ~ (all_72_0 = empty_set) & ~ (all_25_0 = empty_set) % 9.09/2.02 | | | | % 9.09/2.02 | | | | ALPHA: (58) implies: % 9.09/2.02 | | | | (59) ~ (all_72_0 = empty_set) % 9.09/2.02 | | | | % 9.09/2.02 | | | | REDUCE: (55), (59) imply: % 9.09/2.02 | | | | (60) $false % 9.09/2.02 | | | | % 9.09/2.02 | | | | CLOSE: (60) is inconsistent. % 9.09/2.02 | | | | % 9.09/2.02 | | | End of split % 9.09/2.02 | | | % 9.09/2.02 | | End of split % 9.09/2.02 | | % 9.09/2.02 | End of split % 9.09/2.02 | % 9.09/2.02 End of proof % 9.09/2.02 % SZS output end Proof for theBenchmark % 9.09/2.02 % 9.09/2.02 1396ms %------------------------------------------------------------------------------