%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : DAT021_1 : TPTP v8.1.2. Released v5.0.0. % 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 : Wed Aug 30 22:18:54 EDT 2023 % Result : Theorem 6.30s 1.64s % Output : Proof 7.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : DAT021_1 : TPTP v8.1.2. Released v5.0.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.36 % Computer : n001.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Thu Aug 24 15:15:41 EDT 2023 % 0.14/0.36 % CPUTime : % 0.21/0.63 ________ _____ % 0.21/0.63 ___ __ \_________(_)________________________________ % 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.63 % 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.63 (2023-06-19) % 0.21/0.63 % 0.21/0.63 (c) Philipp Rümmer, 2009-2023 % 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.63 Amanda Stjerna. % 0.21/0.63 Free software under BSD-3-Clause. % 0.21/0.63 % 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.63 % 0.21/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.65 Running up to 7 provers in parallel. % 0.21/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.41/1.09 Prover 1: Preprocessing ... % 2.41/1.09 Prover 4: Preprocessing ... % 2.63/1.12 Prover 5: Preprocessing ... % 2.63/1.12 Prover 3: Preprocessing ... % 2.63/1.12 Prover 2: Preprocessing ... % 2.63/1.12 Prover 6: Preprocessing ... % 2.63/1.12 Prover 0: Preprocessing ... % 3.96/1.31 Prover 4: Constructing countermodel ... % 3.96/1.31 Prover 1: Constructing countermodel ... % 3.96/1.31 Prover 5: Proving ... % 3.96/1.31 Prover 2: Proving ... % 3.96/1.31 Prover 6: Constructing countermodel ... % 3.96/1.32 Prover 3: Constructing countermodel ... % 3.96/1.33 Prover 0: Proving ... % 6.30/1.63 Prover 3: proved (973ms) % 6.30/1.63 % 6.30/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.30/1.64 % 6.30/1.64 Prover 6: stopped % 6.30/1.64 Prover 2: stopped % 6.30/1.64 Prover 5: stopped % 6.30/1.64 Prover 0: stopped % 6.30/1.65 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.30/1.65 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.30/1.65 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.30/1.65 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.30/1.65 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.30/1.66 Prover 1: Found proof (size 71) % 6.30/1.66 Prover 1: proved (1002ms) % 6.30/1.67 Prover 4: Found proof (size 69) % 6.30/1.67 Prover 4: proved (999ms) % 6.30/1.68 Prover 13: Preprocessing ... % 6.30/1.68 Prover 8: Preprocessing ... % 6.64/1.68 Prover 10: Preprocessing ... % 6.64/1.69 Prover 11: Preprocessing ... % 6.64/1.69 Prover 7: Preprocessing ... % 6.64/1.70 Prover 7: stopped % 6.64/1.70 Prover 10: stopped % 6.64/1.71 Prover 13: stopped % 6.64/1.71 Prover 11: stopped % 6.64/1.73 Prover 8: Warning: ignoring some quantifiers % 6.64/1.73 Prover 8: Constructing countermodel ... % 6.64/1.73 Prover 8: stopped % 6.64/1.73 % 6.64/1.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 6.64/1.73 % 6.64/1.74 % SZS output start Proof for theBenchmark % 6.64/1.75 Assumptions after simplification: % 6.64/1.75 --------------------------------- % 6.64/1.75 % 6.64/1.75 (ax1) % 7.11/1.77 collection(empty) & ! [v0: int] : ~ (in(v0, empty) = 0) % 7.11/1.77 % 7.11/1.77 (ax4) % 7.11/1.77 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : ! % 7.11/1.77 [v4: int] : (v4 = 0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ~ % 7.11/1.77 collection(v1) | ( ~ (v2 = v0) & ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) = % 7.11/1.77 v5))) & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: % 7.11/1.77 collection] : (v2 = v0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ % 7.11/1.77 collection(v1) | in(v0, v1) = 0) % 7.11/1.77 % 7.11/1.77 (co1) % 7.11/1.77 collection(empty) & ? [v0: collection] : ? [v1: collection] : ? [v2: % 7.11/1.77 collection] : (add(5, v1) = v2 & add(3, v0) = v1 & add(1, empty) = v0 & % 7.11/1.78 collection(v2) & collection(v1) & collection(v0) & ? [v3: int] : ? [v4: % 7.11/1.78 int] : ( ~ (v4 = v3) & $lesseq(9, $sum(v4, v3)) & in(v4, v2) = 0 & in(v3, % 7.11/1.78 v2) = 0)) % 7.11/1.78 % 7.11/1.78 Further assumptions not needed in the proof: % 7.11/1.78 -------------------------------------------- % 7.11/1.78 ax2, ax3, ax5 % 7.11/1.78 % 7.11/1.78 Those formulas are unsatisfiable: % 7.11/1.78 --------------------------------- % 7.11/1.78 % 7.11/1.78 Begin of proof % 7.11/1.78 | % 7.11/1.78 | ALPHA: (ax1) implies: % 7.11/1.78 | (1) ! [v0: int] : ~ (in(v0, empty) = 0) % 7.11/1.78 | % 7.11/1.78 | ALPHA: (ax4) implies: % 7.11/1.78 | (2) ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] % 7.11/1.78 | : (v2 = v0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ % 7.11/1.78 | collection(v1) | in(v0, v1) = 0) % 7.11/1.78 | % 7.11/1.78 | ALPHA: (co1) implies: % 7.11/1.78 | (3) collection(empty) % 7.11/1.78 | (4) ? [v0: collection] : ? [v1: collection] : ? [v2: collection] : % 7.11/1.78 | (add(5, v1) = v2 & add(3, v0) = v1 & add(1, empty) = v0 & % 7.11/1.78 | collection(v2) & collection(v1) & collection(v0) & ? [v3: int] : ? % 7.11/1.78 | [v4: int] : ( ~ (v4 = v3) & $lesseq(9, $sum(v4, v3)) & in(v4, v2) = 0 % 7.11/1.78 | & in(v3, v2) = 0)) % 7.11/1.78 | % 7.11/1.78 | DELTA: instantiating (4) with fresh symbols all_11_0, all_11_1, all_11_2 % 7.11/1.78 | gives: % 7.11/1.79 | (5) add(5, all_11_1) = all_11_0 & add(3, all_11_2) = all_11_1 & add(1, % 7.11/1.79 | empty) = all_11_2 & collection(all_11_0) & collection(all_11_1) & % 7.11/1.79 | collection(all_11_2) & ? [v0: int] : ? [v1: int] : ( ~ (v1 = v0) & % 7.11/1.79 | $lesseq(9, $sum(v1, v0)) & in(v1, all_11_0) = 0 & in(v0, all_11_0) = % 7.11/1.79 | 0) % 7.11/1.79 | % 7.11/1.79 | ALPHA: (5) implies: % 7.11/1.79 | (6) collection(all_11_2) % 7.11/1.79 | (7) collection(all_11_1) % 7.11/1.79 | (8) add(1, empty) = all_11_2 % 7.11/1.79 | (9) add(3, all_11_2) = all_11_1 % 7.11/1.79 | (10) add(5, all_11_1) = all_11_0 % 7.11/1.79 | (11) ? [v0: int] : ? [v1: int] : ( ~ (v1 = v0) & $lesseq(9, $sum(v1, v0)) % 7.11/1.79 | & in(v1, all_11_0) = 0 & in(v0, all_11_0) = 0) % 7.11/1.79 | % 7.11/1.79 | DELTA: instantiating (11) with fresh symbols all_13_0, all_13_1 gives: % 7.11/1.79 | (12) ~ (all_13_0 = all_13_1) & $lesseq(9, $sum(all_13_0, all_13_1)) & % 7.11/1.79 | in(all_13_0, all_11_0) = 0 & in(all_13_1, all_11_0) = 0 % 7.11/1.79 | % 7.11/1.79 | ALPHA: (12) implies: % 7.11/1.79 | (13) ~ (all_13_0 = all_13_1) % 7.11/1.79 | (14) $lesseq(9, $sum(all_13_0, all_13_1)) % 7.11/1.79 | (15) in(all_13_1, all_11_0) = 0 % 7.11/1.79 | (16) in(all_13_0, all_11_0) = 0 % 7.11/1.79 | % 7.11/1.79 | GROUND_INST: instantiating (2) with all_13_0, all_11_1, 5, all_11_0, % 7.11/1.79 | simplifying with (7), (10), (16) gives: % 7.11/1.80 | (17) all_13_0 = 5 | in(all_13_0, all_11_1) = 0 % 7.11/1.80 | % 7.11/1.80 | GROUND_INST: instantiating (2) with all_13_1, all_11_1, 5, all_11_0, % 7.11/1.80 | simplifying with (7), (10), (15) gives: % 7.11/1.80 | (18) all_13_1 = 5 | in(all_13_1, all_11_1) = 0 % 7.11/1.80 | % 7.11/1.80 | BETA: splitting (18) gives: % 7.11/1.80 | % 7.11/1.80 | Case 1: % 7.11/1.80 | | % 7.11/1.80 | | (19) in(all_13_1, all_11_1) = 0 % 7.11/1.80 | | % 7.11/1.80 | | GROUND_INST: instantiating (2) with all_13_1, all_11_2, 3, all_11_1, % 7.11/1.80 | | simplifying with (6), (9), (19) gives: % 7.11/1.80 | | (20) all_13_1 = 3 | in(all_13_1, all_11_2) = 0 % 7.11/1.80 | | % 7.11/1.80 | | BETA: splitting (17) gives: % 7.11/1.80 | | % 7.11/1.80 | | Case 1: % 7.11/1.80 | | | % 7.11/1.80 | | | (21) in(all_13_0, all_11_1) = 0 % 7.11/1.80 | | | % 7.11/1.80 | | | GROUND_INST: instantiating (2) with all_13_0, all_11_2, 3, all_11_1, % 7.11/1.80 | | | simplifying with (6), (9), (21) gives: % 7.11/1.80 | | | (22) all_13_0 = 3 | in(all_13_0, all_11_2) = 0 % 7.11/1.80 | | | % 7.11/1.80 | | | BETA: splitting (20) gives: % 7.11/1.80 | | | % 7.11/1.80 | | | Case 1: % 7.11/1.80 | | | | % 7.11/1.80 | | | | (23) in(all_13_1, all_11_2) = 0 % 7.11/1.80 | | | | % 7.11/1.80 | | | | GROUND_INST: instantiating (2) with all_13_1, empty, 1, all_11_2, % 7.11/1.80 | | | | simplifying with (3), (8), (23) gives: % 7.11/1.80 | | | | (24) all_13_1 = 1 | in(all_13_1, empty) = 0 % 7.11/1.80 | | | | % 7.11/1.80 | | | | BETA: splitting (22) gives: % 7.11/1.80 | | | | % 7.11/1.80 | | | | Case 1: % 7.11/1.80 | | | | | % 7.11/1.80 | | | | | (25) in(all_13_0, all_11_2) = 0 % 7.11/1.80 | | | | | % 7.11/1.80 | | | | | GROUND_INST: instantiating (2) with all_13_0, empty, 1, all_11_2, % 7.11/1.80 | | | | | simplifying with (3), (8), (25) gives: % 7.11/1.80 | | | | | (26) all_13_0 = 1 | in(all_13_0, empty) = 0 % 7.11/1.80 | | | | | % 7.11/1.80 | | | | | BETA: splitting (24) gives: % 7.11/1.80 | | | | | % 7.11/1.80 | | | | | Case 1: % 7.11/1.80 | | | | | | % 7.11/1.80 | | | | | | (27) in(all_13_1, empty) = 0 % 7.11/1.80 | | | | | | % 7.11/1.80 | | | | | | GROUND_INST: instantiating (1) with all_13_1, simplifying with (27) % 7.11/1.80 | | | | | | gives: % 7.11/1.80 | | | | | | (28) $false % 7.11/1.80 | | | | | | % 7.11/1.80 | | | | | | CLOSE: (28) is inconsistent. % 7.11/1.80 | | | | | | % 7.11/1.80 | | | | | Case 2: % 7.11/1.80 | | | | | | % 7.11/1.80 | | | | | | (29) all_13_1 = 1 % 7.11/1.80 | | | | | | % 7.11/1.80 | | | | | | REDUCE: (14), (29) imply: % 7.11/1.80 | | | | | | (30) $lesseq(8, all_13_0) % 7.11/1.80 | | | | | | % 7.11/1.80 | | | | | | BETA: splitting (26) gives: % 7.11/1.80 | | | | | | % 7.11/1.80 | | | | | | Case 1: % 7.11/1.80 | | | | | | | % 7.11/1.81 | | | | | | | (31) in(all_13_0, empty) = 0 % 7.11/1.81 | | | | | | | % 7.11/1.81 | | | | | | | GROUND_INST: instantiating (1) with all_13_0, simplifying with % 7.11/1.81 | | | | | | | (31) gives: % 7.11/1.81 | | | | | | | (32) $false % 7.11/1.81 | | | | | | | % 7.11/1.81 | | | | | | | CLOSE: (32) is inconsistent. % 7.11/1.81 | | | | | | | % 7.11/1.81 | | | | | | Case 2: % 7.11/1.81 | | | | | | | % 7.11/1.81 | | | | | | | (33) all_13_0 = 1 % 7.11/1.81 | | | | | | | % 7.11/1.81 | | | | | | | REDUCE: (30), (33) imply: % 7.11/1.81 | | | | | | | (34) $false % 7.11/1.81 | | | | | | | % 7.11/1.81 | | | | | | | CLOSE: (34) is inconsistent. % 7.11/1.81 | | | | | | | % 7.11/1.81 | | | | | | End of split % 7.11/1.81 | | | | | | % 7.11/1.81 | | | | | End of split % 7.11/1.81 | | | | | % 7.11/1.81 | | | | Case 2: % 7.11/1.81 | | | | | % 7.11/1.81 | | | | | (35) all_13_0 = 3 % 7.11/1.81 | | | | | % 7.11/1.81 | | | | | REDUCE: (14), (35) imply: % 7.11/1.81 | | | | | (36) $lesseq(6, all_13_1) % 7.11/1.81 | | | | | % 7.11/1.81 | | | | | BETA: splitting (24) gives: % 7.11/1.81 | | | | | % 7.11/1.81 | | | | | Case 1: % 7.11/1.81 | | | | | | % 7.11/1.81 | | | | | | (37) in(all_13_1, empty) = 0 % 7.11/1.81 | | | | | | % 7.11/1.81 | | | | | | GROUND_INST: instantiating (1) with all_13_1, simplifying with (37) % 7.11/1.81 | | | | | | gives: % 7.11/1.81 | | | | | | (38) $false % 7.11/1.81 | | | | | | % 7.11/1.81 | | | | | | CLOSE: (38) is inconsistent. % 7.11/1.81 | | | | | | % 7.11/1.81 | | | | | Case 2: % 7.11/1.81 | | | | | | % 7.11/1.81 | | | | | | (39) all_13_1 = 1 % 7.11/1.81 | | | | | | % 7.11/1.81 | | | | | | REDUCE: (36), (39) imply: % 7.11/1.81 | | | | | | (40) $false % 7.11/1.81 | | | | | | % 7.11/1.81 | | | | | | CLOSE: (40) is inconsistent. % 7.11/1.81 | | | | | | % 7.11/1.81 | | | | | End of split % 7.11/1.81 | | | | | % 7.11/1.81 | | | | End of split % 7.11/1.81 | | | | % 7.11/1.81 | | | Case 2: % 7.11/1.81 | | | | % 7.11/1.81 | | | | (41) all_13_1 = 3 % 7.11/1.81 | | | | % 7.11/1.81 | | | | REDUCE: (14), (41) imply: % 7.11/1.81 | | | | (42) $lesseq(6, all_13_0) % 7.11/1.81 | | | | % 7.11/1.81 | | | | BETA: splitting (22) gives: % 7.11/1.81 | | | | % 7.11/1.81 | | | | Case 1: % 7.11/1.81 | | | | | % 7.11/1.81 | | | | | (43) in(all_13_0, all_11_2) = 0 % 7.11/1.81 | | | | | % 7.11/1.81 | | | | | GROUND_INST: instantiating (2) with all_13_0, empty, 1, all_11_2, % 7.11/1.81 | | | | | simplifying with (3), (8), (43) gives: % 7.11/1.81 | | | | | (44) all_13_0 = 1 | in(all_13_0, empty) = 0 % 7.11/1.81 | | | | | % 7.11/1.81 | | | | | BETA: splitting (44) gives: % 7.11/1.81 | | | | | % 7.11/1.81 | | | | | Case 1: % 7.11/1.81 | | | | | | % 7.11/1.81 | | | | | | (45) in(all_13_0, empty) = 0 % 7.11/1.81 | | | | | | % 7.11/1.81 | | | | | | GROUND_INST: instantiating (1) with all_13_0, simplifying with (45) % 7.11/1.81 | | | | | | gives: % 7.11/1.81 | | | | | | (46) $false % 7.11/1.81 | | | | | | % 7.11/1.81 | | | | | | CLOSE: (46) is inconsistent. % 7.11/1.81 | | | | | | % 7.11/1.81 | | | | | Case 2: % 7.11/1.81 | | | | | | % 7.11/1.81 | | | | | | (47) all_13_0 = 1 % 7.11/1.81 | | | | | | % 7.11/1.81 | | | | | | REDUCE: (42), (47) imply: % 7.11/1.81 | | | | | | (48) $false % 7.11/1.81 | | | | | | % 7.11/1.81 | | | | | | CLOSE: (48) is inconsistent. % 7.11/1.81 | | | | | | % 7.11/1.81 | | | | | End of split % 7.11/1.81 | | | | | % 7.11/1.81 | | | | Case 2: % 7.11/1.81 | | | | | % 7.34/1.81 | | | | | (49) all_13_0 = 3 % 7.34/1.81 | | | | | % 7.34/1.81 | | | | | REDUCE: (42), (49) imply: % 7.34/1.81 | | | | | (50) $false % 7.34/1.81 | | | | | % 7.34/1.81 | | | | | CLOSE: (50) is inconsistent. % 7.34/1.81 | | | | | % 7.34/1.81 | | | | End of split % 7.34/1.81 | | | | % 7.34/1.81 | | | End of split % 7.34/1.81 | | | % 7.34/1.81 | | Case 2: % 7.34/1.81 | | | % 7.34/1.81 | | | (51) all_13_0 = 5 % 7.34/1.81 | | | % 7.34/1.81 | | | REDUCE: (14), (51) imply: % 7.34/1.81 | | | (52) $lesseq(4, all_13_1) % 7.34/1.81 | | | % 7.34/1.81 | | | BETA: splitting (20) gives: % 7.34/1.81 | | | % 7.34/1.81 | | | Case 1: % 7.34/1.81 | | | | % 7.34/1.81 | | | | (53) in(all_13_1, all_11_2) = 0 % 7.34/1.81 | | | | % 7.34/1.81 | | | | GROUND_INST: instantiating (2) with all_13_1, empty, 1, all_11_2, % 7.34/1.81 | | | | simplifying with (3), (8), (53) gives: % 7.34/1.82 | | | | (54) all_13_1 = 1 | in(all_13_1, empty) = 0 % 7.34/1.82 | | | | % 7.34/1.82 | | | | BETA: splitting (54) gives: % 7.34/1.82 | | | | % 7.34/1.82 | | | | Case 1: % 7.34/1.82 | | | | | % 7.34/1.82 | | | | | (55) in(all_13_1, empty) = 0 % 7.34/1.82 | | | | | % 7.34/1.82 | | | | | GROUND_INST: instantiating (1) with all_13_1, simplifying with (55) % 7.34/1.82 | | | | | gives: % 7.34/1.82 | | | | | (56) $false % 7.34/1.82 | | | | | % 7.34/1.82 | | | | | CLOSE: (56) is inconsistent. % 7.34/1.82 | | | | | % 7.34/1.82 | | | | Case 2: % 7.34/1.82 | | | | | % 7.34/1.82 | | | | | (57) all_13_1 = 1 % 7.34/1.82 | | | | | % 7.34/1.82 | | | | | REDUCE: (52), (57) imply: % 7.34/1.82 | | | | | (58) $false % 7.34/1.82 | | | | | % 7.34/1.82 | | | | | CLOSE: (58) is inconsistent. % 7.34/1.82 | | | | | % 7.34/1.82 | | | | End of split % 7.34/1.82 | | | | % 7.34/1.82 | | | Case 2: % 7.34/1.82 | | | | % 7.34/1.82 | | | | (59) all_13_1 = 3 % 7.34/1.82 | | | | % 7.34/1.82 | | | | REDUCE: (52), (59) imply: % 7.34/1.82 | | | | (60) $false % 7.34/1.82 | | | | % 7.34/1.82 | | | | CLOSE: (60) is inconsistent. % 7.34/1.82 | | | | % 7.34/1.82 | | | End of split % 7.34/1.82 | | | % 7.34/1.82 | | End of split % 7.34/1.82 | | % 7.34/1.82 | Case 2: % 7.34/1.82 | | % 7.34/1.82 | | (61) all_13_1 = 5 % 7.34/1.82 | | % 7.34/1.82 | | REDUCE: (14), (61) imply: % 7.34/1.82 | | (62) $lesseq(4, all_13_0) % 7.34/1.82 | | % 7.34/1.82 | | REDUCE: (13), (61) imply: % 7.34/1.82 | | (63) ~ (all_13_0 = 5) % 7.34/1.82 | | % 7.34/1.82 | | BETA: splitting (17) gives: % 7.34/1.82 | | % 7.34/1.82 | | Case 1: % 7.34/1.82 | | | % 7.34/1.82 | | | (64) in(all_13_0, all_11_1) = 0 % 7.34/1.82 | | | % 7.34/1.82 | | | GROUND_INST: instantiating (2) with all_13_0, all_11_2, 3, all_11_1, % 7.34/1.82 | | | simplifying with (6), (9), (64) gives: % 7.34/1.82 | | | (65) all_13_0 = 3 | in(all_13_0, all_11_2) = 0 % 7.34/1.82 | | | % 7.34/1.82 | | | BETA: splitting (65) gives: % 7.34/1.82 | | | % 7.34/1.82 | | | Case 1: % 7.34/1.82 | | | | % 7.34/1.82 | | | | (66) in(all_13_0, all_11_2) = 0 % 7.34/1.82 | | | | % 7.34/1.82 | | | | GROUND_INST: instantiating (2) with all_13_0, empty, 1, all_11_2, % 7.34/1.82 | | | | simplifying with (3), (8), (66) gives: % 7.34/1.82 | | | | (67) all_13_0 = 1 | in(all_13_0, empty) = 0 % 7.34/1.82 | | | | % 7.34/1.82 | | | | BETA: splitting (67) gives: % 7.34/1.82 | | | | % 7.34/1.82 | | | | Case 1: % 7.34/1.82 | | | | | % 7.34/1.82 | | | | | (68) in(all_13_0, empty) = 0 % 7.34/1.82 | | | | | % 7.34/1.82 | | | | | GROUND_INST: instantiating (1) with all_13_0, simplifying with (68) % 7.34/1.82 | | | | | gives: % 7.34/1.82 | | | | | (69) $false % 7.34/1.82 | | | | | % 7.34/1.82 | | | | | CLOSE: (69) is inconsistent. % 7.34/1.82 | | | | | % 7.34/1.82 | | | | Case 2: % 7.34/1.82 | | | | | % 7.34/1.82 | | | | | (70) all_13_0 = 1 % 7.34/1.82 | | | | | % 7.34/1.82 | | | | | REDUCE: (62), (70) imply: % 7.34/1.82 | | | | | (71) $false % 7.34/1.82 | | | | | % 7.34/1.82 | | | | | CLOSE: (71) is inconsistent. % 7.34/1.82 | | | | | % 7.34/1.82 | | | | End of split % 7.34/1.82 | | | | % 7.34/1.82 | | | Case 2: % 7.34/1.82 | | | | % 7.34/1.82 | | | | (72) all_13_0 = 3 % 7.34/1.82 | | | | % 7.34/1.82 | | | | REDUCE: (62), (72) imply: % 7.34/1.82 | | | | (73) $false % 7.34/1.82 | | | | % 7.34/1.82 | | | | CLOSE: (73) is inconsistent. % 7.34/1.82 | | | | % 7.34/1.82 | | | End of split % 7.34/1.82 | | | % 7.34/1.82 | | Case 2: % 7.34/1.82 | | | % 7.34/1.82 | | | (74) all_13_0 = 5 % 7.34/1.82 | | | % 7.34/1.82 | | | REDUCE: (63), (74) imply: % 7.34/1.82 | | | (75) $false % 7.34/1.82 | | | % 7.34/1.82 | | | CLOSE: (75) is inconsistent. % 7.34/1.82 | | | % 7.34/1.82 | | End of split % 7.34/1.82 | | % 7.34/1.82 | End of split % 7.34/1.82 | % 7.34/1.82 End of proof % 7.34/1.82 % SZS output end Proof for theBenchmark % 7.34/1.82 % 7.34/1.82 1188ms %------------------------------------------------------------------------------