TSTP Solution File: SYN392+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SYN392+1 : TPTP v8.1.2. Released v2.0.0.
% 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 : Fri Sep  1 03:27:30 EDT 2023

% Result   : Theorem 2.74s 1.12s
% Output   : Proof 3.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SYN392+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34  % Computer : n001.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sat Aug 26 18:40:16 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  
% 0.21/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63  Running up to 7 provers in parallel.
% 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 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 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
% 1.91/1.00  Prover 1: Preprocessing ...
% 1.91/1.00  Prover 4: Preprocessing ...
% 2.19/1.04  Prover 0: Preprocessing ...
% 2.19/1.04  Prover 3: Preprocessing ...
% 2.19/1.04  Prover 5: Preprocessing ...
% 2.19/1.04  Prover 6: Preprocessing ...
% 2.19/1.04  Prover 2: Preprocessing ...
% 2.19/1.04  Prover 1: Constructing countermodel ...
% 2.19/1.05  Prover 4: Constructing countermodel ...
% 2.19/1.06  Prover 0: Constructing countermodel ...
% 2.19/1.06  Prover 3: Constructing countermodel ...
% 2.19/1.06  Prover 6: Constructing countermodel ...
% 2.19/1.06  Prover 2: Constructing countermodel ...
% 2.19/1.07  Prover 5: Constructing countermodel ...
% 2.74/1.12  Prover 5: proved (479ms)
% 2.74/1.12  
% 2.74/1.12  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.74/1.12  
% 2.74/1.12  Prover 2: stopped
% 2.74/1.12  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 2.74/1.13  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 2.74/1.13  Prover 0: stopped
% 2.74/1.13  Prover 3: stopped
% 2.74/1.13  Prover 6: stopped
% 2.74/1.14  Prover 8: Preprocessing ...
% 2.74/1.14  Prover 7: Preprocessing ...
% 2.74/1.14  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 2.74/1.14  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 2.74/1.14  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 2.74/1.14  Prover 10: Preprocessing ...
% 2.74/1.15  Prover 11: Preprocessing ...
% 2.74/1.15  Prover 8: Constructing countermodel ...
% 2.74/1.15  Prover 7: Constructing countermodel ...
% 2.74/1.15  Prover 10: Constructing countermodel ...
% 2.74/1.15  Prover 13: Preprocessing ...
% 2.74/1.16  Prover 11: Constructing countermodel ...
% 2.74/1.17  Prover 13: Constructing countermodel ...
% 2.74/1.17  Prover 4: Found proof (size 45)
% 2.74/1.17  Prover 4: proved (532ms)
% 2.74/1.17  Prover 13: stopped
% 2.74/1.17  Prover 1: Found proof (size 45)
% 2.74/1.17  Prover 8: stopped
% 2.74/1.17  Prover 1: proved (539ms)
% 2.74/1.17  Prover 7: stopped
% 2.74/1.17  Prover 10: stopped
% 2.74/1.17  Prover 11: stopped
% 2.74/1.17  
% 2.74/1.17  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.74/1.17  
% 2.74/1.18  % SZS output start Proof for theBenchmark
% 3.21/1.18  Assumptions after simplification:
% 3.21/1.18  ---------------------------------
% 3.21/1.18  
% 3.21/1.19    (pel14)
% 3.21/1.19    (( ~ p2 | p1) & ( ~ p1 | p2) & ((p2 &  ~ p1) | (p1 &  ~ p2))) | (((p2 & p1) |
% 3.21/1.19        ( ~ p2 &  ~ p1)) & ((p2 &  ~ p1) | (p1 &  ~ p2)))
% 3.21/1.19  
% 3.21/1.19  Those formulas are unsatisfiable:
% 3.21/1.19  ---------------------------------
% 3.21/1.19  
% 3.21/1.19  Begin of proof
% 3.21/1.19  | 
% 3.21/1.19  | BETA: splitting (pel14) gives:
% 3.21/1.19  | 
% 3.21/1.19  | Case 1:
% 3.21/1.19  | | 
% 3.21/1.19  | |   (1)  ( ~ p2 | p1) & ( ~ p1 | p2) & ((p2 &  ~ p1) | (p1 &  ~ p2))
% 3.21/1.20  | | 
% 3.21/1.20  | | ALPHA: (1) implies:
% 3.21/1.20  | |   (2)  (p2 &  ~ p1) | (p1 &  ~ p2)
% 3.21/1.20  | |   (3)   ~ p1 | p2
% 3.21/1.20  | |   (4)   ~ p2 | p1
% 3.21/1.20  | | 
% 3.21/1.20  | | BETA: splitting (3) gives:
% 3.21/1.20  | | 
% 3.21/1.20  | | Case 1:
% 3.21/1.20  | | | 
% 3.21/1.20  | | |   (5)   ~ p1
% 3.21/1.20  | | | 
% 3.21/1.20  | | | BETA: splitting (4) gives:
% 3.21/1.20  | | | 
% 3.21/1.20  | | | Case 1:
% 3.21/1.20  | | | | 
% 3.21/1.20  | | | |   (6)   ~ p2
% 3.21/1.20  | | | | 
% 3.21/1.20  | | | | BETA: splitting (2) gives:
% 3.21/1.20  | | | | 
% 3.21/1.20  | | | | Case 1:
% 3.21/1.20  | | | | | 
% 3.21/1.20  | | | | |   (7)  p2 &  ~ p1
% 3.21/1.20  | | | | | 
% 3.21/1.20  | | | | | ALPHA: (7) implies:
% 3.21/1.20  | | | | |   (8)  p2
% 3.21/1.20  | | | | | 
% 3.21/1.20  | | | | | PRED_UNIFY: (6), (8) imply:
% 3.21/1.20  | | | | |   (9)  $false
% 3.21/1.20  | | | | | 
% 3.21/1.20  | | | | | CLOSE: (9) is inconsistent.
% 3.21/1.20  | | | | | 
% 3.21/1.20  | | | | Case 2:
% 3.21/1.20  | | | | | 
% 3.21/1.20  | | | | |   (10)  p1 &  ~ p2
% 3.21/1.20  | | | | | 
% 3.21/1.20  | | | | | ALPHA: (10) implies:
% 3.21/1.20  | | | | |   (11)  p1
% 3.21/1.20  | | | | | 
% 3.21/1.20  | | | | | PRED_UNIFY: (5), (11) imply:
% 3.21/1.20  | | | | |   (12)  $false
% 3.21/1.20  | | | | | 
% 3.21/1.20  | | | | | CLOSE: (12) is inconsistent.
% 3.21/1.20  | | | | | 
% 3.21/1.20  | | | | End of split
% 3.21/1.20  | | | | 
% 3.21/1.20  | | | Case 2:
% 3.21/1.20  | | | | 
% 3.21/1.20  | | | |   (13)  p1
% 3.21/1.20  | | | | 
% 3.21/1.20  | | | | PRED_UNIFY: (5), (13) imply:
% 3.21/1.20  | | | |   (14)  $false
% 3.21/1.20  | | | | 
% 3.21/1.20  | | | | CLOSE: (14) is inconsistent.
% 3.21/1.20  | | | | 
% 3.21/1.20  | | | End of split
% 3.21/1.20  | | | 
% 3.21/1.20  | | Case 2:
% 3.21/1.20  | | | 
% 3.21/1.20  | | |   (15)  p1
% 3.21/1.21  | | |   (16)  p2
% 3.21/1.21  | | | 
% 3.21/1.21  | | | BETA: splitting (2) gives:
% 3.21/1.21  | | | 
% 3.21/1.21  | | | Case 1:
% 3.21/1.21  | | | | 
% 3.21/1.21  | | | |   (17)  p2 &  ~ p1
% 3.21/1.21  | | | | 
% 3.21/1.21  | | | | ALPHA: (17) implies:
% 3.21/1.21  | | | |   (18)   ~ p1
% 3.21/1.21  | | | | 
% 3.21/1.21  | | | | PRED_UNIFY: (15), (18) imply:
% 3.21/1.21  | | | |   (19)  $false
% 3.21/1.21  | | | | 
% 3.21/1.21  | | | | CLOSE: (19) is inconsistent.
% 3.21/1.21  | | | | 
% 3.21/1.21  | | | Case 2:
% 3.21/1.21  | | | | 
% 3.21/1.21  | | | |   (20)  p1 &  ~ p2
% 3.21/1.21  | | | | 
% 3.21/1.21  | | | | ALPHA: (20) implies:
% 3.21/1.21  | | | |   (21)   ~ p2
% 3.21/1.21  | | | | 
% 3.21/1.21  | | | | PRED_UNIFY: (16), (21) imply:
% 3.21/1.21  | | | |   (22)  $false
% 3.21/1.21  | | | | 
% 3.21/1.21  | | | | CLOSE: (22) is inconsistent.
% 3.21/1.21  | | | | 
% 3.21/1.21  | | | End of split
% 3.21/1.21  | | | 
% 3.21/1.21  | | End of split
% 3.21/1.21  | | 
% 3.21/1.21  | Case 2:
% 3.21/1.21  | | 
% 3.21/1.21  | |   (23)  ((p2 & p1) | ( ~ p2 &  ~ p1)) & ((p2 &  ~ p1) | (p1 &  ~ p2))
% 3.21/1.21  | | 
% 3.21/1.21  | | ALPHA: (23) implies:
% 3.21/1.21  | |   (24)  (p2 &  ~ p1) | (p1 &  ~ p2)
% 3.21/1.21  | |   (25)  (p2 & p1) | ( ~ p2 &  ~ p1)
% 3.21/1.21  | | 
% 3.21/1.21  | | BETA: splitting (24) gives:
% 3.21/1.21  | | 
% 3.21/1.21  | | Case 1:
% 3.21/1.21  | | | 
% 3.21/1.21  | | |   (26)  p2 &  ~ p1
% 3.21/1.21  | | | 
% 3.21/1.21  | | | ALPHA: (26) implies:
% 3.21/1.21  | | |   (27)   ~ p1
% 3.21/1.21  | | |   (28)  p2
% 3.21/1.21  | | | 
% 3.21/1.21  | | | BETA: splitting (25) gives:
% 3.21/1.21  | | | 
% 3.21/1.21  | | | Case 1:
% 3.21/1.21  | | | | 
% 3.21/1.21  | | | |   (29)  p2 & p1
% 3.21/1.21  | | | | 
% 3.21/1.21  | | | | ALPHA: (29) implies:
% 3.21/1.21  | | | |   (30)  p1
% 3.21/1.21  | | | | 
% 3.21/1.21  | | | | PRED_UNIFY: (27), (30) imply:
% 3.21/1.21  | | | |   (31)  $false
% 3.21/1.21  | | | | 
% 3.21/1.21  | | | | CLOSE: (31) is inconsistent.
% 3.21/1.21  | | | | 
% 3.21/1.21  | | | Case 2:
% 3.21/1.21  | | | | 
% 3.21/1.21  | | | |   (32)   ~ p2 &  ~ p1
% 3.21/1.21  | | | | 
% 3.21/1.21  | | | | ALPHA: (32) implies:
% 3.21/1.21  | | | |   (33)   ~ p2
% 3.21/1.21  | | | | 
% 3.21/1.21  | | | | PRED_UNIFY: (28), (33) imply:
% 3.21/1.21  | | | |   (34)  $false
% 3.21/1.21  | | | | 
% 3.21/1.21  | | | | CLOSE: (34) is inconsistent.
% 3.21/1.21  | | | | 
% 3.21/1.21  | | | End of split
% 3.21/1.21  | | | 
% 3.21/1.21  | | Case 2:
% 3.21/1.21  | | | 
% 3.21/1.21  | | |   (35)  p1 &  ~ p2
% 3.21/1.21  | | | 
% 3.21/1.21  | | | ALPHA: (35) implies:
% 3.21/1.22  | | |   (36)   ~ p2
% 3.21/1.22  | | |   (37)  p1
% 3.21/1.22  | | | 
% 3.21/1.22  | | | BETA: splitting (25) gives:
% 3.21/1.22  | | | 
% 3.21/1.22  | | | Case 1:
% 3.21/1.22  | | | | 
% 3.21/1.22  | | | |   (38)  p2 & p1
% 3.21/1.22  | | | | 
% 3.21/1.22  | | | | ALPHA: (38) implies:
% 3.21/1.22  | | | |   (39)  p2
% 3.21/1.22  | | | | 
% 3.21/1.22  | | | | PRED_UNIFY: (36), (39) imply:
% 3.21/1.22  | | | |   (40)  $false
% 3.21/1.22  | | | | 
% 3.21/1.22  | | | | CLOSE: (40) is inconsistent.
% 3.21/1.22  | | | | 
% 3.21/1.22  | | | Case 2:
% 3.21/1.22  | | | | 
% 3.21/1.22  | | | |   (41)   ~ p2 &  ~ p1
% 3.21/1.22  | | | | 
% 3.21/1.22  | | | | ALPHA: (41) implies:
% 3.21/1.22  | | | |   (42)   ~ p1
% 3.21/1.22  | | | | 
% 3.21/1.22  | | | | PRED_UNIFY: (37), (42) imply:
% 3.21/1.22  | | | |   (43)  $false
% 3.21/1.22  | | | | 
% 3.21/1.22  | | | | CLOSE: (43) is inconsistent.
% 3.21/1.22  | | | | 
% 3.21/1.22  | | | End of split
% 3.21/1.22  | | | 
% 3.21/1.22  | | End of split
% 3.21/1.22  | | 
% 3.21/1.22  | End of split
% 3.21/1.22  | 
% 3.21/1.22  End of proof
% 3.21/1.22  % SZS output end Proof for theBenchmark
% 3.21/1.22  
% 3.21/1.22  602ms
%------------------------------------------------------------------------------