TSTP Solution File: ARI681_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------