%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET018+4 : TPTP v8.1.2. Released v2.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n006.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 15:23:10 EDT 2023 % Result : Theorem 13.01s 2.84s % Output : Proof 15.04s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SET018+4 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.10/0.33 % Computer : n006.cluster.edu % 0.10/0.33 % Model : x86_64 x86_64 % 0.10/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.33 % Memory : 8042.1875MB % 0.10/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.33 % CPULimit : 300 % 0.10/0.33 % WCLimit : 300 % 0.10/0.33 % DateTime : Sat Aug 26 14:39:07 EDT 2023 % 0.10/0.33 % CPUTime : % 0.16/0.63 ________ _____ % 0.16/0.63 ___ __ \_________(_)________________________________ % 0.16/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.63 % 0.16/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.63 (2023-06-19) % 0.16/0.63 % 0.16/0.63 (c) Philipp Rümmer, 2009-2023 % 0.16/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.63 Amanda Stjerna. % 0.16/0.63 Free software under BSD-3-Clause. % 0.16/0.63 % 0.16/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.63 % 0.16/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.16/0.65 Running up to 7 provers in parallel. % 0.16/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.16/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.16/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.16/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.16/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.16/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.16/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.49/1.12 Prover 1: Preprocessing ... % 2.49/1.12 Prover 4: Preprocessing ... % 2.49/1.16 Prover 0: Preprocessing ... % 2.49/1.16 Prover 6: Preprocessing ... % 2.49/1.16 Prover 5: Preprocessing ... % 2.49/1.16 Prover 2: Preprocessing ... % 2.49/1.16 Prover 3: Preprocessing ... % 6.14/1.65 Prover 6: Proving ... % 6.14/1.67 Prover 5: Proving ... % 6.14/1.67 Prover 3: Constructing countermodel ... % 6.14/1.68 Prover 2: Proving ... % 6.14/1.69 Prover 1: Constructing countermodel ... % 6.14/1.70 Prover 4: Constructing countermodel ... % 6.71/1.77 Prover 0: Proving ... % 7.64/1.88 Prover 3: gave up % 7.64/1.89 Prover 1: gave up % 7.64/1.90 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.64/1.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.06/1.95 Prover 8: Preprocessing ... % 8.06/1.95 Prover 7: Preprocessing ... % 8.06/2.02 Prover 4: gave up % 8.06/2.02 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 8.06/2.06 Prover 7: Warning: ignoring some quantifiers % 8.06/2.07 Prover 9: Preprocessing ... % 8.06/2.07 Prover 7: Constructing countermodel ... % 9.01/2.10 Prover 8: Warning: ignoring some quantifiers % 9.01/2.11 Prover 8: Constructing countermodel ... % 10.36/2.25 Prover 8: gave up % 10.36/2.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.36/2.29 Prover 10: Preprocessing ... % 10.93/2.34 Prover 9: Constructing countermodel ... % 11.29/2.40 Prover 10: Warning: ignoring some quantifiers % 11.29/2.42 Prover 10: Constructing countermodel ... % 13.01/2.83 Prover 10: Found proof (size 96) % 13.01/2.83 Prover 10: proved (580ms) % 13.01/2.84 Prover 9: stopped % 13.01/2.84 Prover 7: stopped % 13.01/2.84 Prover 5: stopped % 13.01/2.84 Prover 2: stopped % 13.01/2.84 Prover 0: stopped % 13.01/2.84 Prover 6: stopped % 13.01/2.84 % 13.01/2.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.01/2.84 % 14.23/2.87 % SZS output start Proof for theBenchmark % 14.23/2.88 Assumptions after simplification: % 14.23/2.88 --------------------------------- % 14.23/2.88 % 14.23/2.88 (equal_set) % 14.23/2.89 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ equal_set(v0, v1) | % 14.23/2.89 subset(v1, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 14.23/2.89 equal_set(v0, v1) | subset(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) % 14.23/2.89 | ~ $i(v0) | ~ subset(v1, v0) | ~ subset(v0, v1) | equal_set(v0, v1)) % 14.23/2.89 % 14.23/2.89 (singleton) % 14.93/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v1) = v2) | % 14.93/2.93 ~ $i(v1) | ~ $i(v0) | ~ member(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 14.93/2.93 (singleton(v0) = v1) | ~ $i(v0) | member(v0, v1)) % 14.93/2.93 % 14.93/2.93 (subset) % 14.93/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 14.93/2.93 ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1)) & ? [v0: $i] : ? % 14.93/2.93 [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | subset(v0, v1) | ? [v2: $i] : ($i(v2) & % 14.93/2.93 member(v2, v0) & ~ member(v2, v1))) % 14.93/2.93 % 14.93/2.93 (thI50b) % 14.93/2.94 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 14.93/2.94 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ( ~ (v3 = v1) % 14.93/2.94 & unordered_pair(v7, v8) = v9 & unordered_pair(v4, v5) = v6 & % 14.93/2.94 unordered_pair(v2, v3) = v8 & unordered_pair(v0, v1) = v5 & singleton(v2) = % 14.93/2.94 v7 & singleton(v0) = v4 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 14.93/2.94 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & equal_set(v6, v9)) % 14.93/2.94 % 14.93/2.94 (unordered_pair) % 15.04/2.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 = v0 | % 15.04/2.95 ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 15.04/2.95 member(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 15.04/2.95 (unordered_pair(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | member(v0, v2)) & ! % 15.04/2.95 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ % 15.04/2.95 $i(v1) | ~ $i(v0) | member(v0, v2)) % 15.04/2.95 % 15.04/2.95 Further assumptions not needed in the proof: % 15.04/2.95 -------------------------------------------- % 15.04/2.95 difference, empty_set, intersection, power_set, product, sum, union % 15.04/2.95 % 15.04/2.95 Those formulas are unsatisfiable: % 15.04/2.95 --------------------------------- % 15.04/2.95 % 15.04/2.95 Begin of proof % 15.04/2.95 | % 15.04/2.95 | ALPHA: (subset) implies: % 15.04/2.95 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 15.04/2.95 | $i(v0) | ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1)) % 15.04/2.95 | % 15.04/2.95 | ALPHA: (equal_set) implies: % 15.04/2.95 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ equal_set(v0, % 15.04/2.95 | v1) | subset(v0, v1)) % 15.04/2.95 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ equal_set(v0, % 15.04/2.95 | v1) | subset(v1, v0)) % 15.04/2.96 | % 15.04/2.96 | ALPHA: (singleton) implies: % 15.04/2.96 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | % 15.04/2.96 | member(v0, v1)) % 15.04/2.96 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v1) % 15.04/2.96 | = v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v0, v2)) % 15.04/2.96 | % 15.04/2.96 | ALPHA: (unordered_pair) implies: % 15.04/2.96 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = % 15.04/2.96 | v2) | ~ $i(v1) | ~ $i(v0) | member(v0, v2)) % 15.04/2.96 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = % 15.04/2.96 | v2) | ~ $i(v1) | ~ $i(v0) | member(v0, v2)) % 15.04/2.96 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 = % 15.04/2.96 | v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 15.04/2.96 | $i(v0) | ~ member(v0, v3)) % 15.04/2.96 | % 15.04/2.97 | DELTA: instantiating (thI50b) with fresh symbols all_18_0, all_18_1, all_18_2, % 15.04/2.97 | all_18_3, all_18_4, all_18_5, all_18_6, all_18_7, all_18_8, all_18_9 % 15.04/2.97 | gives: % 15.04/2.97 | (9) ~ (all_18_6 = all_18_8) & unordered_pair(all_18_2, all_18_1) = % 15.04/2.97 | all_18_0 & unordered_pair(all_18_5, all_18_4) = all_18_3 & % 15.04/2.97 | unordered_pair(all_18_7, all_18_6) = all_18_1 & % 15.04/2.97 | unordered_pair(all_18_9, all_18_8) = all_18_4 & singleton(all_18_7) = % 15.04/2.97 | all_18_2 & singleton(all_18_9) = all_18_5 & $i(all_18_0) & $i(all_18_1) % 15.04/2.97 | & $i(all_18_2) & $i(all_18_3) & $i(all_18_4) & $i(all_18_5) & % 15.04/2.97 | $i(all_18_6) & $i(all_18_7) & $i(all_18_8) & $i(all_18_9) & % 15.04/2.97 | equal_set(all_18_3, all_18_0) % 15.04/2.97 | % 15.04/2.97 | ALPHA: (9) implies: % 15.04/2.97 | (10) ~ (all_18_6 = all_18_8) % 15.04/2.97 | (11) equal_set(all_18_3, all_18_0) % 15.04/2.97 | (12) $i(all_18_9) % 15.04/2.97 | (13) $i(all_18_8) % 15.04/2.97 | (14) $i(all_18_7) % 15.04/2.97 | (15) $i(all_18_6) % 15.04/2.97 | (16) $i(all_18_5) % 15.04/2.97 | (17) $i(all_18_4) % 15.04/2.97 | (18) $i(all_18_3) % 15.04/2.97 | (19) $i(all_18_2) % 15.04/2.97 | (20) $i(all_18_1) % 15.04/2.97 | (21) $i(all_18_0) % 15.04/2.97 | (22) singleton(all_18_9) = all_18_5 % 15.04/2.97 | (23) singleton(all_18_7) = all_18_2 % 15.04/2.97 | (24) unordered_pair(all_18_9, all_18_8) = all_18_4 % 15.04/2.97 | (25) unordered_pair(all_18_7, all_18_6) = all_18_1 % 15.04/2.97 | (26) unordered_pair(all_18_5, all_18_4) = all_18_3 % 15.04/2.97 | (27) unordered_pair(all_18_2, all_18_1) = all_18_0 % 15.04/2.97 | % 15.04/2.98 | GROUND_INST: instantiating (3) with all_18_3, all_18_0, simplifying with (11), % 15.04/2.98 | (18), (21) gives: % 15.04/2.98 | (28) subset(all_18_0, all_18_3) % 15.04/2.98 | % 15.04/2.98 | GROUND_INST: instantiating (2) with all_18_3, all_18_0, simplifying with (11), % 15.04/2.98 | (18), (21) gives: % 15.04/2.98 | (29) subset(all_18_3, all_18_0) % 15.04/2.98 | % 15.04/2.98 | GROUND_INST: instantiating (4) with all_18_9, all_18_5, simplifying with (12), % 15.04/2.98 | (22) gives: % 15.04/2.98 | (30) member(all_18_9, all_18_5) % 15.04/2.98 | % 15.04/2.98 | GROUND_INST: instantiating (7) with all_18_8, all_18_9, all_18_4, simplifying % 15.04/2.98 | with (12), (13), (24) gives: % 15.04/2.98 | (31) member(all_18_8, all_18_4) % 15.04/2.98 | % 15.04/2.98 | GROUND_INST: instantiating (6) with all_18_9, all_18_8, all_18_4, simplifying % 15.04/2.98 | with (12), (13), (24) gives: % 15.04/2.98 | (32) member(all_18_9, all_18_4) % 15.04/2.98 | % 15.04/2.98 | GROUND_INST: instantiating (7) with all_18_6, all_18_7, all_18_1, simplifying % 15.04/2.98 | with (14), (15), (25) gives: % 15.04/2.98 | (33) member(all_18_6, all_18_1) % 15.04/2.98 | % 15.04/2.98 | GROUND_INST: instantiating (7) with all_18_4, all_18_5, all_18_3, simplifying % 15.04/2.98 | with (16), (17), (26) gives: % 15.04/2.98 | (34) member(all_18_4, all_18_3) % 15.04/2.98 | % 15.04/2.98 | GROUND_INST: instantiating (6) with all_18_5, all_18_4, all_18_3, simplifying % 15.04/2.98 | with (16), (17), (26) gives: % 15.04/2.98 | (35) member(all_18_5, all_18_3) % 15.04/2.98 | % 15.04/2.98 | GROUND_INST: instantiating (7) with all_18_1, all_18_2, all_18_0, simplifying % 15.04/2.98 | with (19), (20), (27) gives: % 15.04/2.98 | (36) member(all_18_1, all_18_0) % 15.04/2.98 | % 15.04/2.98 | GROUND_INST: instantiating (6) with all_18_2, all_18_1, all_18_0, simplifying % 15.04/2.98 | with (19), (20), (27) gives: % 15.04/2.98 | (37) member(all_18_2, all_18_0) % 15.04/2.98 | % 15.04/2.98 | GROUND_INST: instantiating (1) with all_18_3, all_18_0, all_18_5, simplifying % 15.04/2.98 | with (16), (18), (21), (29), (35) gives: % 15.04/2.98 | (38) member(all_18_5, all_18_0) % 15.04/2.98 | % 15.04/2.98 | GROUND_INST: instantiating (1) with all_18_3, all_18_0, all_18_4, simplifying % 15.04/2.98 | with (17), (18), (21), (29), (34) gives: % 15.04/2.98 | (39) member(all_18_4, all_18_0) % 15.04/2.98 | % 15.04/2.98 | GROUND_INST: instantiating (1) with all_18_0, all_18_3, all_18_2, simplifying % 15.04/2.98 | with (18), (19), (21), (28), (37) gives: % 15.04/2.98 | (40) member(all_18_2, all_18_3) % 15.04/2.98 | % 15.04/2.99 | GROUND_INST: instantiating (1) with all_18_0, all_18_3, all_18_1, simplifying % 15.04/2.99 | with (18), (20), (21), (28), (36) gives: % 15.04/2.99 | (41) member(all_18_1, all_18_3) % 15.04/2.99 | % 15.04/2.99 | GROUND_INST: instantiating (8) with all_18_5, all_18_2, all_18_1, all_18_0, % 15.04/2.99 | simplifying with (16), (19), (20), (27), (38) gives: % 15.04/2.99 | (42) all_18_1 = all_18_5 | all_18_2 = all_18_5 % 15.04/2.99 | % 15.04/2.99 | GROUND_INST: instantiating (8) with all_18_4, all_18_2, all_18_1, all_18_0, % 15.04/2.99 | simplifying with (17), (19), (20), (27), (39) gives: % 15.04/2.99 | (43) all_18_1 = all_18_4 | all_18_2 = all_18_4 % 15.04/2.99 | % 15.04/2.99 | GROUND_INST: instantiating (8) with all_18_2, all_18_5, all_18_4, all_18_3, % 15.04/2.99 | simplifying with (16), (17), (19), (26), (40) gives: % 15.04/2.99 | (44) all_18_2 = all_18_4 | all_18_2 = all_18_5 % 15.04/2.99 | % 15.04/2.99 | GROUND_INST: instantiating (8) with all_18_1, all_18_5, all_18_4, all_18_3, % 15.04/2.99 | simplifying with (16), (17), (20), (26), (41) gives: % 15.04/2.99 | (45) all_18_1 = all_18_4 | all_18_1 = all_18_5 % 15.04/2.99 | % 15.04/2.99 | BETA: splitting (45) gives: % 15.04/2.99 | % 15.04/2.99 | Case 1: % 15.04/2.99 | | % 15.04/2.99 | | (46) all_18_1 = all_18_4 % 15.04/2.99 | | % 15.04/2.99 | | REDUCE: (25), (46) imply: % 15.04/2.99 | | (47) unordered_pair(all_18_7, all_18_6) = all_18_4 % 15.04/2.99 | | % 15.04/2.99 | | REDUCE: (33), (46) imply: % 15.04/2.99 | | (48) member(all_18_6, all_18_4) % 15.04/2.99 | | % 15.04/2.99 | | GROUND_INST: instantiating (8) with all_18_6, all_18_9, all_18_8, all_18_4, % 15.04/2.99 | | simplifying with (12), (13), (15), (24), (48) gives: % 15.04/2.99 | | (49) all_18_6 = all_18_8 | all_18_6 = all_18_9 % 15.04/2.99 | | % 15.04/2.99 | | GROUND_INST: instantiating (8) with all_18_8, all_18_7, all_18_6, all_18_4, % 15.04/2.99 | | simplifying with (13), (14), (15), (31), (47) gives: % 15.04/2.99 | | (50) all_18_6 = all_18_8 | all_18_7 = all_18_8 % 15.04/2.99 | | % 15.04/2.99 | | BETA: splitting (44) gives: % 15.04/2.99 | | % 15.04/2.99 | | Case 1: % 15.04/2.99 | | | % 15.04/2.99 | | | (51) all_18_2 = all_18_4 % 15.04/2.99 | | | % 15.04/2.99 | | | REDUCE: (23), (51) imply: % 15.04/2.99 | | | (52) singleton(all_18_7) = all_18_4 % 15.04/2.99 | | | % 15.04/2.99 | | | BETA: splitting (42) gives: % 15.04/2.99 | | | % 15.04/2.99 | | | Case 1: % 15.04/2.99 | | | | % 15.04/2.99 | | | | (53) all_18_1 = all_18_5 % 15.04/2.99 | | | | % 15.04/2.99 | | | | COMBINE_EQS: (46), (53) imply: % 15.04/2.99 | | | | (54) all_18_4 = all_18_5 % 15.04/2.99 | | | | % 15.04/2.99 | | | | REDUCE: (52), (54) imply: % 15.04/3.00 | | | | (55) singleton(all_18_7) = all_18_5 % 15.04/3.00 | | | | % 15.04/3.00 | | | | REDUCE: (48), (54) imply: % 15.04/3.00 | | | | (56) member(all_18_6, all_18_5) % 15.04/3.00 | | | | % 15.04/3.00 | | | | BETA: splitting (49) gives: % 15.04/3.00 | | | | % 15.04/3.00 | | | | Case 1: % 15.04/3.00 | | | | | % 15.04/3.00 | | | | | (57) all_18_6 = all_18_8 % 15.04/3.00 | | | | | % 15.04/3.00 | | | | | REDUCE: (10), (57) imply: % 15.04/3.00 | | | | | (58) $false % 15.04/3.00 | | | | | % 15.04/3.00 | | | | | CLOSE: (58) is inconsistent. % 15.04/3.00 | | | | | % 15.04/3.00 | | | | Case 2: % 15.04/3.00 | | | | | % 15.04/3.00 | | | | | (59) all_18_6 = all_18_9 % 15.04/3.00 | | | | | % 15.04/3.00 | | | | | REDUCE: (10), (59) imply: % 15.04/3.00 | | | | | (60) ~ (all_18_8 = all_18_9) % 15.04/3.00 | | | | | % 15.04/3.00 | | | | | SIMP: (60) implies: % 15.04/3.00 | | | | | (61) ~ (all_18_8 = all_18_9) % 15.04/3.00 | | | | | % 15.04/3.00 | | | | | REF_CLOSE: (5), (12), (14), (30), (50), (55), (59), (61) are % 15.04/3.00 | | | | | inconsistent by sub-proof #1. % 15.04/3.00 | | | | | % 15.04/3.00 | | | | End of split % 15.04/3.00 | | | | % 15.04/3.00 | | | Case 2: % 15.04/3.00 | | | | % 15.04/3.00 | | | | (62) all_18_2 = all_18_5 % 15.04/3.00 | | | | (63) ~ (all_18_1 = all_18_5) % 15.04/3.00 | | | | % 15.04/3.00 | | | | COMBINE_EQS: (51), (62) imply: % 15.04/3.00 | | | | (64) all_18_4 = all_18_5 % 15.04/3.00 | | | | % 15.04/3.00 | | | | SIMP: (64) implies: % 15.04/3.00 | | | | (65) all_18_4 = all_18_5 % 15.04/3.00 | | | | % 15.04/3.00 | | | | COMBINE_EQS: (46), (65) imply: % 15.04/3.00 | | | | (66) all_18_1 = all_18_5 % 15.04/3.00 | | | | % 15.04/3.00 | | | | REDUCE: (63), (66) imply: % 15.04/3.00 | | | | (67) $false % 15.04/3.00 | | | | % 15.04/3.00 | | | | CLOSE: (67) is inconsistent. % 15.04/3.00 | | | | % 15.04/3.00 | | | End of split % 15.04/3.00 | | | % 15.04/3.00 | | Case 2: % 15.04/3.00 | | | % 15.04/3.00 | | | (68) all_18_2 = all_18_5 % 15.04/3.00 | | | % 15.04/3.00 | | | REDUCE: (23), (68) imply: % 15.04/3.00 | | | (69) singleton(all_18_7) = all_18_5 % 15.04/3.00 | | | % 15.04/3.00 | | | BETA: splitting (49) gives: % 15.04/3.00 | | | % 15.04/3.00 | | | Case 1: % 15.04/3.00 | | | | % 15.04/3.00 | | | | (70) all_18_6 = all_18_8 % 15.04/3.00 | | | | % 15.04/3.00 | | | | REDUCE: (10), (70) imply: % 15.04/3.00 | | | | (71) $false % 15.04/3.00 | | | | % 15.04/3.00 | | | | CLOSE: (71) is inconsistent. % 15.04/3.00 | | | | % 15.04/3.00 | | | Case 2: % 15.04/3.00 | | | | % 15.04/3.00 | | | | (72) all_18_6 = all_18_9 % 15.04/3.00 | | | | % 15.04/3.00 | | | | REDUCE: (10), (72) imply: % 15.04/3.00 | | | | (73) ~ (all_18_8 = all_18_9) % 15.04/3.00 | | | | % 15.04/3.00 | | | | SIMP: (73) implies: % 15.04/3.00 | | | | (74) ~ (all_18_8 = all_18_9) % 15.04/3.00 | | | | % 15.04/3.00 | | | | REF_CLOSE: (5), (12), (14), (30), (50), (69), (72), (74) are % 15.04/3.00 | | | | inconsistent by sub-proof #1. % 15.04/3.00 | | | | % 15.04/3.00 | | | End of split % 15.04/3.00 | | | % 15.04/3.00 | | End of split % 15.04/3.00 | | % 15.04/3.00 | Case 2: % 15.04/3.00 | | % 15.04/3.00 | | (75) all_18_1 = all_18_5 % 15.04/3.00 | | (76) ~ (all_18_1 = all_18_4) % 15.04/3.00 | | % 15.04/3.00 | | REDUCE: (75), (76) imply: % 15.04/3.00 | | (77) ~ (all_18_4 = all_18_5) % 15.04/3.00 | | % 15.04/3.00 | | SIMP: (77) implies: % 15.04/3.00 | | (78) ~ (all_18_4 = all_18_5) % 15.04/3.00 | | % 15.04/3.00 | | REDUCE: (33), (75) imply: % 15.04/3.00 | | (79) member(all_18_6, all_18_5) % 15.04/3.00 | | % 15.04/3.00 | | BETA: splitting (43) gives: % 15.04/3.00 | | % 15.04/3.00 | | Case 1: % 15.04/3.01 | | | % 15.04/3.01 | | | (80) all_18_1 = all_18_4 % 15.04/3.01 | | | % 15.04/3.01 | | | COMBINE_EQS: (75), (80) imply: % 15.04/3.01 | | | (81) all_18_4 = all_18_5 % 15.04/3.01 | | | % 15.04/3.01 | | | SIMP: (81) implies: % 15.04/3.01 | | | (82) all_18_4 = all_18_5 % 15.04/3.01 | | | % 15.04/3.01 | | | REDUCE: (78), (82) imply: % 15.04/3.01 | | | (83) $false % 15.04/3.01 | | | % 15.04/3.01 | | | CLOSE: (83) is inconsistent. % 15.04/3.01 | | | % 15.04/3.01 | | Case 2: % 15.04/3.01 | | | % 15.04/3.01 | | | (84) all_18_2 = all_18_4 % 15.04/3.01 | | | % 15.04/3.01 | | | REDUCE: (23), (84) imply: % 15.04/3.01 | | | (85) singleton(all_18_7) = all_18_4 % 15.04/3.01 | | | % 15.04/3.01 | | | GROUND_INST: instantiating (5) with all_18_6, all_18_9, all_18_5, % 15.04/3.01 | | | simplifying with (12), (15), (22), (79) gives: % 15.04/3.01 | | | (86) all_18_6 = all_18_9 % 15.04/3.01 | | | % 15.04/3.01 | | | GROUND_INST: instantiating (5) with all_18_8, all_18_7, all_18_4, % 15.04/3.01 | | | simplifying with (13), (14), (31), (85) gives: % 15.04/3.01 | | | (87) all_18_7 = all_18_8 % 15.04/3.01 | | | % 15.04/3.01 | | | GROUND_INST: instantiating (5) with all_18_9, all_18_7, all_18_4, % 15.04/3.01 | | | simplifying with (12), (14), (32), (85) gives: % 15.04/3.01 | | | (88) all_18_7 = all_18_9 % 15.04/3.01 | | | % 15.04/3.01 | | | COMBINE_EQS: (87), (88) imply: % 15.04/3.01 | | | (89) all_18_8 = all_18_9 % 15.04/3.01 | | | % 15.04/3.01 | | | SIMP: (89) implies: % 15.04/3.01 | | | (90) all_18_8 = all_18_9 % 15.04/3.01 | | | % 15.04/3.01 | | | REDUCE: (10), (86), (90) imply: % 15.04/3.01 | | | (91) $false % 15.04/3.01 | | | % 15.04/3.01 | | | CLOSE: (91) is inconsistent. % 15.04/3.01 | | | % 15.04/3.01 | | End of split % 15.04/3.01 | | % 15.04/3.01 | End of split % 15.04/3.01 | % 15.04/3.01 End of proof % 15.04/3.01 % 15.04/3.01 Sub-proof #1 shows that the following formulas are inconsistent: % 15.04/3.01 ---------------------------------------------------------------- % 15.04/3.01 (1) $i(all_18_9) % 15.04/3.01 (2) member(all_18_9, all_18_5) % 15.04/3.01 (3) singleton(all_18_7) = all_18_5 % 15.04/3.01 (4) ~ (all_18_8 = all_18_9) % 15.04/3.01 (5) all_18_6 = all_18_8 | all_18_7 = all_18_8 % 15.04/3.01 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v1) = % 15.04/3.01 v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v0, v2)) % 15.04/3.01 (7) $i(all_18_7) % 15.04/3.01 (8) all_18_6 = all_18_9 % 15.04/3.01 % 15.04/3.01 Begin of proof % 15.04/3.01 | % 15.04/3.01 | BETA: splitting (5) gives: % 15.04/3.01 | % 15.04/3.01 | Case 1: % 15.04/3.01 | | % 15.04/3.01 | | (9) all_18_6 = all_18_8 % 15.04/3.01 | | % 15.04/3.01 | | COMBINE_EQS: (8), (9) imply: % 15.04/3.01 | | (10) all_18_8 = all_18_9 % 15.04/3.01 | | % 15.04/3.01 | | SIMP: (10) implies: % 15.04/3.01 | | (11) all_18_8 = all_18_9 % 15.04/3.01 | | % 15.04/3.01 | | REDUCE: (4), (11) imply: % 15.04/3.01 | | (12) $false % 15.04/3.01 | | % 15.04/3.01 | | CLOSE: (12) is inconsistent. % 15.04/3.01 | | % 15.04/3.01 | Case 2: % 15.04/3.01 | | % 15.04/3.01 | | (13) all_18_7 = all_18_8 % 15.04/3.01 | | (14) ~ (all_18_6 = all_18_8) % 15.04/3.01 | | % 15.04/3.01 | | REDUCE: (8), (14) imply: % 15.04/3.01 | | (15) ~ (all_18_8 = all_18_9) % 15.04/3.01 | | % 15.04/3.01 | | REDUCE: (3), (13) imply: % 15.04/3.01 | | (16) singleton(all_18_8) = all_18_5 % 15.04/3.01 | | % 15.04/3.01 | | REDUCE: (7), (13) imply: % 15.04/3.01 | | (17) $i(all_18_8) % 15.04/3.01 | | % 15.04/3.02 | | GROUND_INST: instantiating (6) with all_18_9, all_18_8, all_18_5, % 15.04/3.02 | | simplifying with (1), (2), (16), (17) gives: % 15.04/3.02 | | (18) all_18_8 = all_18_9 % 15.04/3.02 | | % 15.04/3.02 | | REDUCE: (4), (18) imply: % 15.04/3.02 | | (19) $false % 15.04/3.02 | | % 15.04/3.02 | | CLOSE: (19) is inconsistent. % 15.04/3.02 | | % 15.04/3.02 | End of split % 15.04/3.02 | % 15.04/3.02 End of proof % 15.04/3.02 % SZS output end Proof for theBenchmark % 15.04/3.02 % 15.04/3.02 2385ms %------------------------------------------------------------------------------