%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ARI681_1 : TPTP v8.1.2. Released v6.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n011.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 17:48:47 EDT 2023 % Result : Theorem 3.88s 1.37s % Output : Proof 5.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : ARI681_1 : TPTP v8.1.2. Released v6.3.0. % 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n011.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Tue Aug 29 18:50:56 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.09/1.02 Prover 5: Preprocessing ... % 2.09/1.02 Prover 6: Preprocessing ... % 2.09/1.02 Prover 4: Preprocessing ... % 2.09/1.02 Prover 3: Preprocessing ... % 2.09/1.02 Prover 0: Preprocessing ... % 2.09/1.02 Prover 1: Preprocessing ... % 2.09/1.02 Prover 2: Preprocessing ... % 2.57/1.07 Prover 2: Constructing countermodel ... % 2.57/1.07 Prover 0: Constructing countermodel ... % 2.57/1.08 Prover 5: Constructing countermodel ... % 2.57/1.08 Prover 3: Constructing countermodel ... % 2.57/1.08 Prover 4: Constructing countermodel ... % 2.57/1.08 Prover 6: Constructing countermodel ... % 2.57/1.08 Prover 1: Constructing countermodel ... % 3.88/1.37 Prover 6: proved (733ms) % 3.88/1.37 % 3.88/1.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.88/1.37 % 3.88/1.37 Prover 0: stopped % 3.88/1.37 Prover 2: proved (741ms) % 3.88/1.37 % 3.88/1.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.88/1.37 % 3.88/1.38 Prover 5: stopped % 3.88/1.38 Prover 3: stopped % 3.88/1.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.88/1.38 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.88/1.38 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.88/1.38 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.88/1.39 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.88/1.39 Prover 7: Preprocessing ... % 3.88/1.39 Prover 10: Preprocessing ... % 3.88/1.40 Prover 8: Preprocessing ... % 3.88/1.41 Prover 8: Constructing countermodel ... % 3.88/1.41 Prover 13: Preprocessing ... % 3.88/1.41 Prover 10: Constructing countermodel ... % 3.88/1.41 Prover 11: Preprocessing ... % 3.88/1.41 Prover 7: Constructing countermodel ... % 3.88/1.42 Prover 11: Constructing countermodel ... % 3.88/1.42 Prover 13: Constructing countermodel ... % 4.88/1.47 Prover 1: Found proof (size 56) % 4.88/1.47 Prover 1: proved (833ms) % 4.88/1.47 Prover 8: stopped % 4.88/1.47 Prover 13: stopped % 4.88/1.47 Prover 7: stopped % 4.88/1.47 Prover 10: stopped % 4.88/1.47 Prover 11: stopped % 4.88/1.47 Prover 4: Found proof (size 56) % 4.88/1.47 Prover 4: proved (838ms) % 4.88/1.47 % 4.88/1.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.88/1.47 % 4.88/1.48 % SZS output start Proof for theBenchmark % 4.88/1.48 Assumptions after simplification: % 4.88/1.48 --------------------------------- % 4.88/1.48 % 4.88/1.48 (conj) % 5.17/1.49 ? [v0: int] : ($lesseq(1, v0) & $product(a, c) = v0) % 5.17/1.49 % 5.17/1.49 (conj_001) % 5.17/1.49 ? [v0: int] : ($lesseq(1, v0) & $product(c, d) = v0) % 5.17/1.49 % 5.17/1.49 (conj_002) % 5.17/1.49 ? [v0: int] : ($lesseq(1, v0) & $product(a, b) = v0) % 5.17/1.49 % 5.17/1.49 (conj_003) % 5.17/1.49 ? [v0: int] : ($lesseq(v0, 0)$product(b, d) = v0) % 5.17/1.49 % 5.17/1.49 Those formulas are unsatisfiable: % 5.17/1.49 --------------------------------- % 5.17/1.49 % 5.17/1.49 Begin of proof % 5.17/1.49 | % 5.17/1.50 | DELTA: instantiating (conj_003) with fresh symbol all_2_0 gives: % 5.17/1.50 | (1) $lesseq(all_2_0, 0)$product(b, d) = all_2_0 % 5.17/1.50 | % 5.17/1.50 | ALPHA: (1) implies: % 5.17/1.50 | (2) $lesseq(all_2_0, 0) % 5.17/1.50 | (3) $product(b, d) = all_2_0 % 5.17/1.50 | % 5.17/1.50 | DELTA: instantiating (conj) with fresh symbol all_5_0 gives: % 5.17/1.50 | (4) $lesseq(1, all_5_0) & $product(a, c) = all_5_0 % 5.17/1.50 | % 5.17/1.50 | ALPHA: (4) implies: % 5.17/1.50 | (5) $lesseq(1, all_5_0) % 5.17/1.50 | (6) $product(a, c) = all_5_0 % 5.17/1.50 | % 5.17/1.50 | DELTA: instantiating (conj_002) with fresh symbol all_8_0 gives: % 5.17/1.50 | (7) $lesseq(1, all_8_0) & $product(a, b) = all_8_0 % 5.17/1.50 | % 5.17/1.50 | ALPHA: (7) implies: % 5.17/1.50 | (8) $lesseq(1, all_8_0) % 5.17/1.50 | (9) $product(a, b) = all_8_0 % 5.17/1.50 | % 5.17/1.50 | DELTA: instantiating (conj_001) with fresh symbol all_11_0 gives: % 5.17/1.50 | (10) $lesseq(1, all_11_0) & $product(c, d) = all_11_0 % 5.17/1.50 | % 5.17/1.50 | ALPHA: (10) implies: % 5.17/1.50 | (11) $lesseq(1, all_11_0) % 5.17/1.50 | (12) $product(c, d) = all_11_0 % 5.17/1.50 | % 5.17/1.50 | CUT: with $lesseq(b, 0): % 5.17/1.50 | % 5.17/1.50 | Case 1: % 5.17/1.50 | | % 5.17/1.50 | | (13) $lesseq(b, 0) % 5.17/1.50 | | % 5.17/1.50 | | THEORY_AXIOM GroebnerMultiplication: % 5.17/1.51 | | (14) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4: % 5.17/1.51 | | int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : (v4 = 0 | ~ % 5.17/1.51 | | ($lesseq(1, v7)) | ~ ($lesseq(1, v6)) | ~ ($lesseq(1, v5)) | ~ % 5.17/1.51 | | ($lesseq(v4, 0) | ~ ($lesseq(v3, 0) | ~ ($product(v3, v2) = v4) % 5.17/1.51 | | | ~ ($product(v1, v2) = v7) | ~ ($product(v0, v3) = v6) | ~ % 5.17/1.51 | | ($product(v0, v1) = v5)) % 5.17/1.51 | | % 5.17/1.51 | | GROUND_INST: instantiating (14) with a, c, d, b, all_2_0, all_5_0, all_8_0, % 5.17/1.51 | | all_11_0, simplifying with (3), (6), (9), (12) gives: % 5.17/1.51 | | (15) all_2_0 = 0 | ~ ($lesseq(1, all_11_0)) | ~ ($lesseq(1, all_8_0)) | % 5.17/1.51 | | ~ ($lesseq(1, all_5_0)) | ~ ($lesseq(all_2_0, 0) | ~ ($lesseq(b, % 5.17/1.51 | | 0) % 5.17/1.51 | | % 5.17/1.51 | | BETA: splitting (15) gives: % 5.17/1.51 | | % 5.17/1.51 | | Case 1: % 5.17/1.51 | | | % 5.17/1.51 | | | (16) ~ ($lesseq(1, all_11_0)) | ~ ($lesseq(1, all_8_0)) | ~ % 5.17/1.51 | | | ($lesseq(1, all_5_0)) % 5.17/1.51 | | | % 5.17/1.51 | | | BETA: splitting (16) gives: % 5.17/1.51 | | | % 5.17/1.51 | | | Case 1: % 5.17/1.51 | | | | % 5.17/1.51 | | | | (17) $lesseq(all_11_0, 0) % 5.17/1.51 | | | | % 5.17/1.51 | | | | COMBINE_INEQS: (11), (17) imply: % 5.17/1.51 | | | | (18) $false % 5.17/1.51 | | | | % 5.17/1.51 | | | | CLOSE: (18) is inconsistent. % 5.17/1.51 | | | | % 5.17/1.51 | | | Case 2: % 5.17/1.51 | | | | % 5.17/1.51 | | | | (19) ~ ($lesseq(1, all_8_0)) | ~ ($lesseq(1, all_5_0)) % 5.17/1.51 | | | | % 5.17/1.51 | | | | BETA: splitting (19) gives: % 5.17/1.51 | | | | % 5.17/1.51 | | | | Case 1: % 5.17/1.51 | | | | | % 5.17/1.51 | | | | | (20) $lesseq(all_8_0, 0) % 5.17/1.51 | | | | | % 5.17/1.51 | | | | | COMBINE_INEQS: (8), (20) imply: % 5.17/1.51 | | | | | (21) $false % 5.17/1.51 | | | | | % 5.17/1.51 | | | | | CLOSE: (21) is inconsistent. % 5.17/1.51 | | | | | % 5.17/1.51 | | | | Case 2: % 5.17/1.51 | | | | | % 5.17/1.51 | | | | | (22) $lesseq(all_5_0, 0) % 5.17/1.51 | | | | | % 5.17/1.51 | | | | | COMBINE_INEQS: (5), (22) imply: % 5.17/1.51 | | | | | (23) $false % 5.17/1.51 | | | | | % 5.17/1.51 | | | | | CLOSE: (23) is inconsistent. % 5.17/1.51 | | | | | % 5.17/1.51 | | | | End of split % 5.17/1.51 | | | | % 5.17/1.51 | | | End of split % 5.17/1.51 | | | % 5.17/1.51 | | Case 2: % 5.17/1.51 | | | % 5.17/1.51 | | | (24) all_2_0 = 0 | ~ ($lesseq(all_2_0, 0) | ~ ($lesseq(b, 0) % 5.17/1.51 | | | % 5.17/1.51 | | | BETA: splitting (24) gives: % 5.17/1.51 | | | % 5.17/1.51 | | | Case 1: % 5.17/1.51 | | | | % 5.17/1.51 | | | | (25) $lesseq(1, all_2_0) % 5.17/1.51 | | | | % 5.17/1.51 | | | | COMBINE_INEQS: (2), (25) imply: % 5.17/1.51 | | | | (26) $false % 5.17/1.51 | | | | % 5.17/1.51 | | | | CLOSE: (26) is inconsistent. % 5.17/1.51 | | | | % 5.17/1.51 | | | Case 2: % 5.17/1.51 | | | | % 5.17/1.51 | | | | (27) all_2_0 = 0 | ~ ($lesseq(b, 0) % 5.17/1.51 | | | | % 5.17/1.51 | | | | BETA: splitting (27) gives: % 5.17/1.51 | | | | % 5.17/1.51 | | | | Case 1: % 5.17/1.51 | | | | | % 5.17/1.51 | | | | | (28) $lesseq(1, b) % 5.17/1.51 | | | | | % 5.17/1.51 | | | | | COMBINE_INEQS: (13), (28) imply: % 5.17/1.51 | | | | | (29) $false % 5.17/1.51 | | | | | % 5.17/1.51 | | | | | CLOSE: (29) is inconsistent. % 5.17/1.51 | | | | | % 5.17/1.51 | | | | Case 2: % 5.17/1.51 | | | | | % 5.17/1.51 | | | | | (30) all_2_0 = 0 % 5.17/1.51 | | | | | % 5.17/1.51 | | | | | REDUCE: (3), (30) imply: % 5.17/1.52 | | | | | (31) $product(b, d) = 0 % 5.17/1.52 | | | | | % 5.17/1.52 | | | | | THEORY_AXIOM GroebnerMultiplication: % 5.17/1.52 | | | | | (32) ! [v0: int] : ! [v1: int] : (v1 = 0 | v0 = 0 | ~ % 5.17/1.52 | | | | | ($product(v1, v0) = 0)) % 5.17/1.52 | | | | | % 5.17/1.52 | | | | | GROUND_INST: instantiating (32) with d, b, simplifying with (31) % 5.17/1.52 | | | | | gives: % 5.17/1.52 | | | | | (33) b = 0 | d = 0 % 5.17/1.52 | | | | | % 5.17/1.52 | | | | | BETA: splitting (33) gives: % 5.17/1.52 | | | | | % 5.17/1.52 | | | | | Case 1: % 5.17/1.52 | | | | | | % 5.17/1.52 | | | | | | (34) b = 0 % 5.17/1.52 | | | | | | % 5.17/1.52 | | | | | | REDUCE: (9), (34) imply: % 5.17/1.52 | | | | | | (35) $product(a, 0) = all_8_0 % 5.17/1.52 | | | | | | % 5.17/1.52 | | | | | | THEORY_AXIOM GroebnerMultiplication: % 5.17/1.52 | | | | | | (36) ! [v0: int] : ! [v1: int] : (v1 = 0 | ~ ($product(v0, 0) % 5.17/1.52 | | | | | | = v1)) % 5.17/1.52 | | | | | | % 5.17/1.52 | | | | | | GROUND_INST: instantiating (36) with a, all_8_0, simplifying with % 5.17/1.52 | | | | | | (35) gives: % 5.17/1.52 | | | | | | (37) all_8_0 = 0 % 5.17/1.52 | | | | | | % 5.17/1.52 | | | | | | REDUCE: (8), (37) imply: % 5.17/1.52 | | | | | | (38) $false % 5.17/1.52 | | | | | | % 5.17/1.52 | | | | | | CLOSE: (38) is inconsistent. % 5.17/1.52 | | | | | | % 5.17/1.52 | | | | | Case 2: % 5.17/1.52 | | | | | | % 5.17/1.52 | | | | | | (39) d = 0 % 5.17/1.52 | | | | | | % 5.17/1.52 | | | | | | REDUCE: (12), (39) imply: % 5.17/1.52 | | | | | | (40) $product(c, 0) = all_11_0 % 5.17/1.52 | | | | | | % 5.17/1.52 | | | | | | THEORY_AXIOM GroebnerMultiplication: % 5.17/1.52 | | | | | | (41) ! [v0: int] : ! [v1: int] : (v1 = 0 | ~ ($product(v0, 0) % 5.17/1.52 | | | | | | = v1)) % 5.17/1.52 | | | | | | % 5.17/1.52 | | | | | | GROUND_INST: instantiating (41) with c, all_11_0, simplifying with % 5.17/1.52 | | | | | | (40) gives: % 5.17/1.52 | | | | | | (42) all_11_0 = 0 % 5.17/1.52 | | | | | | % 5.17/1.52 | | | | | | REDUCE: (11), (42) imply: % 5.17/1.52 | | | | | | (43) $false % 5.17/1.52 | | | | | | % 5.17/1.52 | | | | | | CLOSE: (43) is inconsistent. % 5.17/1.52 | | | | | | % 5.17/1.52 | | | | | End of split % 5.17/1.52 | | | | | % 5.17/1.52 | | | | End of split % 5.17/1.52 | | | | % 5.17/1.52 | | | End of split % 5.17/1.52 | | | % 5.17/1.52 | | End of split % 5.17/1.52 | | % 5.17/1.52 | Case 2: % 5.17/1.52 | | % 5.17/1.52 | | (44) $lesseq(1, b) % 5.17/1.52 | | % 5.17/1.52 | | THEORY_AXIOM GroebnerMultiplication: % 5.17/1.52 | | (45) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4: % 5.17/1.52 | | int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : ( ~ % 5.17/1.52 | | ($lesseq(1, v7)) | ~ ($lesseq(1, v6)) | ~ ($lesseq(1, v5)) | ~ % 5.17/1.52 | | ($lesseq(v4, 0) | ~ ($lesseq(1, v3)) | ~ ($product(v3, v2) = v4) % 5.17/1.52 | | | ~ ($product(v1, v2) = v7) | ~ ($product(v0, v3) = v6) | ~ % 5.17/1.52 | | ($product(v0, v1) = v5)) % 5.17/1.52 | | % 5.17/1.52 | | GROUND_INST: instantiating (45) with a, c, d, b, all_2_0, all_5_0, all_8_0, % 5.17/1.52 | | all_11_0, simplifying with (3), (6), (9), (12) gives: % 5.17/1.52 | | (46) ~ ($lesseq(1, all_11_0)) | ~ ($lesseq(1, all_8_0)) | ~ % 5.17/1.52 | | ($lesseq(1, all_5_0)) | ~ ($lesseq(all_2_0, 0) | ~ ($lesseq(1, b)) % 5.17/1.52 | | % 5.17/1.52 | | BETA: splitting (46) gives: % 5.17/1.52 | | % 5.17/1.52 | | Case 1: % 5.17/1.52 | | | % 5.17/1.52 | | | (47) ~ ($lesseq(1, all_11_0)) | ~ ($lesseq(1, all_8_0)) % 5.17/1.52 | | | % 5.17/1.52 | | | BETA: splitting (47) gives: % 5.17/1.52 | | | % 5.17/1.52 | | | Case 1: % 5.17/1.52 | | | | % 5.17/1.52 | | | | (48) $lesseq(all_11_0, 0) % 5.17/1.52 | | | | % 5.17/1.52 | | | | COMBINE_INEQS: (11), (48) imply: % 5.17/1.52 | | | | (49) $false % 5.17/1.52 | | | | % 5.17/1.52 | | | | CLOSE: (49) is inconsistent. % 5.17/1.52 | | | | % 5.17/1.52 | | | Case 2: % 5.17/1.52 | | | | % 5.17/1.53 | | | | (50) $lesseq(all_8_0, 0) % 5.17/1.53 | | | | % 5.17/1.53 | | | | COMBINE_INEQS: (8), (50) imply: % 5.17/1.53 | | | | (51) $false % 5.17/1.53 | | | | % 5.17/1.53 | | | | CLOSE: (51) is inconsistent. % 5.17/1.53 | | | | % 5.17/1.53 | | | End of split % 5.17/1.53 | | | % 5.17/1.53 | | Case 2: % 5.17/1.53 | | | % 5.17/1.53 | | | (52) ~ ($lesseq(1, all_5_0)) | ~ ($lesseq(all_2_0, 0) | ~ % 5.17/1.53 | | | ($lesseq(1, b)) % 5.17/1.53 | | | % 5.17/1.53 | | | BETA: splitting (52) gives: % 5.17/1.53 | | | % 5.17/1.53 | | | Case 1: % 5.17/1.53 | | | | % 5.17/1.53 | | | | (53) $lesseq(1, all_2_0) % 5.17/1.53 | | | | % 5.17/1.53 | | | | COMBINE_INEQS: (2), (53) imply: % 5.17/1.53 | | | | (54) $false % 5.17/1.53 | | | | % 5.17/1.53 | | | | CLOSE: (54) is inconsistent. % 5.17/1.53 | | | | % 5.17/1.53 | | | Case 2: % 5.17/1.53 | | | | % 5.17/1.53 | | | | (55) ~ ($lesseq(1, all_5_0)) | ~ ($lesseq(1, b)) % 5.17/1.53 | | | | % 5.17/1.53 | | | | BETA: splitting (55) gives: % 5.17/1.53 | | | | % 5.17/1.53 | | | | Case 1: % 5.17/1.53 | | | | | % 5.17/1.53 | | | | | (56) $lesseq(b, 0) % 5.17/1.53 | | | | | % 5.17/1.53 | | | | | COMBINE_INEQS: (44), (56) imply: % 5.17/1.53 | | | | | (57) $false % 5.17/1.53 | | | | | % 5.17/1.53 | | | | | CLOSE: (57) is inconsistent. % 5.17/1.53 | | | | | % 5.17/1.53 | | | | Case 2: % 5.17/1.53 | | | | | % 5.17/1.53 | | | | | (58) $lesseq(all_5_0, 0) % 5.17/1.53 | | | | | % 5.17/1.53 | | | | | COMBINE_INEQS: (5), (58) imply: % 5.17/1.53 | | | | | (59) $false % 5.17/1.53 | | | | | % 5.17/1.53 | | | | | CLOSE: (59) is inconsistent. % 5.17/1.53 | | | | | % 5.17/1.53 | | | | End of split % 5.17/1.53 | | | | % 5.17/1.53 | | | End of split % 5.17/1.53 | | | % 5.17/1.53 | | End of split % 5.17/1.53 | | % 5.17/1.53 | End of split % 5.17/1.53 | % 5.17/1.53 End of proof % 5.17/1.53 % SZS output end Proof for theBenchmark % 5.17/1.53 % 5.17/1.53 913ms %------------------------------------------------------------------------------