TSTP Solution File: ARI681_1 by Princess---230619
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%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------