TSTP Solution File: LCL897-10 by Twee---2.5.0

View Problem - Process Solution

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% File     : Twee---2.5.0
% Problem  : LCL897-10 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding

% Computer : n020.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 : Mon Jun 24 11:23:25 EDT 2024

% Result   : Unsatisfiable 0.19s 0.43s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : LCL897-10 : TPTP v8.2.0. Released v8.1.0.
% 0.12/0.12  % Command  : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.12/0.33  % Computer : n020.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sat Jun 22 17:38:24 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.19/0.43  Command-line arguments: --random-mode --random-mode-goal-directed --no-flatten-goal --no-connectedness --no-ground-joining
% 0.19/0.43  
% 0.19/0.43  % SZS status Unsatisfiable
% 0.19/0.43  
% 0.19/0.44  % SZS output start Proof
% 0.19/0.44  Axiom 1 (sos_02): X + Y = Y + X.
% 0.19/0.44  Axiom 2 (sos_07): (X + Y)  = => Z = X  = => (Y  = => Z).
% 0.19/0.44  Axiom 3 (sos_08): X + (X  = => Y) = Y + (Y  = => X).
% 0.19/0.44  Axiom 4 (sos_01): (X + Y) + Z = X + (Y + Z).
% 0.19/0.44  
% 0.19/0.44  Lemma 5: Y  = => (X  = => Z) = X  = => (Y  = => Z).
% 0.19/0.44  Proof:
% 0.19/0.44    Y  = => (X  = => Z)
% 0.19/0.44  = { by axiom 2 (sos_07) R->L }
% 0.19/0.44    (Y + X)  = => Z
% 0.19/0.44  = { by axiom 1 (sos_02) R->L }
% 0.19/0.44    (X + Y)  = => Z
% 0.19/0.44  = { by axiom 2 (sos_07) }
% 0.19/0.44    X  = => (Y  = => Z)
% 0.19/0.44  
% 0.19/0.44  Lemma 6: Y  = => ((Y  = => X)  = => Z) = X  = => ((X  = => Y)  = => Z).
% 0.19/0.44  Proof:
% 0.19/0.44    Y  = => ((Y  = => X)  = => Z)
% 0.19/0.44  = { by axiom 2 (sos_07) R->L }
% 0.19/0.44    (Y + (Y  = => X))  = => Z
% 0.19/0.44  = { by axiom 3 (sos_08) R->L }
% 0.19/0.44    (X + (X  = => Y))  = => Z
% 0.19/0.44  = { by axiom 2 (sos_07) }
% 0.19/0.44    X  = => ((X  = => Y)  = => Z)
% 0.19/0.44  
% 0.19/0.44  Lemma 7: (X  = => Z) + (Z  = => ((Z  = => X)  = => Y)) = (X  = => Y) + (X  = => ((X  = => Y)  = => Z)).
% 0.19/0.44  Proof:
% 0.19/0.44    (X  = => Z) + (Z  = => ((Z  = => X)  = => Y))
% 0.19/0.44  = { by lemma 6 }
% 0.19/0.44    (X  = => Z) + (X  = => ((X  = => Z)  = => Y))
% 0.19/0.44  = { by lemma 5 }
% 0.19/0.44    (X  = => Z) + ((X  = => Z)  = => (X  = => Y))
% 0.19/0.44  = { by axiom 3 (sos_08) }
% 0.19/0.44    (X  = => Y) + ((X  = => Y)  = => (X  = => Z))
% 0.19/0.44  = { by lemma 5 R->L }
% 0.19/0.44    (X  = => Y) + (X  = => ((X  = => Y)  = => Z))
% 0.19/0.44  
% 0.19/0.44  Lemma 8: Y + (Z + (Y  = => (Z  = => X))) = X + (X  = => (Y + Z)).
% 0.19/0.44  Proof:
% 0.19/0.44    Y + (Z + (Y  = => (Z  = => X)))
% 0.19/0.44  = { by axiom 4 (sos_01) R->L }
% 0.19/0.44    (Y + Z) + (Y  = => (Z  = => X))
% 0.19/0.44  = { by axiom 2 (sos_07) R->L }
% 0.19/0.44    (Y + Z) + ((Y + Z)  = => X)
% 0.19/0.44  = { by axiom 3 (sos_08) }
% 0.19/0.44    X + (X  = => (Y + Z))
% 0.19/0.44  
% 0.19/0.44  Lemma 9: X + ((X  = => Y) + (Y  = => ((Y  = => X)  = => Z))) = Y + (Y  = => (X + (X  = => Z))).
% 0.19/0.44  Proof:
% 0.19/0.44    X + ((X  = => Y) + (Y  = => ((Y  = => X)  = => Z)))
% 0.19/0.44  = { by lemma 7 }
% 0.19/0.44    X + ((X  = => Z) + (X  = => ((X  = => Z)  = => Y)))
% 0.19/0.44  = { by lemma 8 }
% 0.19/0.44    Y + (Y  = => (X + (X  = => Z)))
% 0.19/0.44  
% 0.19/0.44  Lemma 10: X + (X  = => (Y + (Y  = => Z))) = Z + (Z  = => (Y + (Y  = => X))).
% 0.19/0.44  Proof:
% 0.19/0.44    X + (X  = => (Y + (Y  = => Z)))
% 0.19/0.44  = { by lemma 9 R->L }
% 0.19/0.44    Y + ((Y  = => X) + (X  = => ((X  = => Y)  = => Z)))
% 0.19/0.44  = { by lemma 6 R->L }
% 0.19/0.44    Y + ((Y  = => X) + (Y  = => ((Y  = => X)  = => Z)))
% 0.19/0.44  = { by lemma 7 R->L }
% 0.19/0.44    Y + ((Y  = => Z) + (Z  = => ((Z  = => Y)  = => X)))
% 0.19/0.44  = { by lemma 9 }
% 0.19/0.44    Z + (Z  = => (Y + (Y  = => X)))
% 0.19/0.44  
% 0.19/0.44  Goal 1 (goals_09): (a + (a  = => b)) + ((a + (a  = => b))  = => c) = a + (a  = => (b + (b  = => c))).
% 0.19/0.44  Proof:
% 0.19/0.44    (a + (a  = => b)) + ((a + (a  = => b))  = => c)
% 0.19/0.44  = { by axiom 2 (sos_07) }
% 0.19/0.44    (a + (a  = => b)) + (a  = => ((a  = => b)  = => c))
% 0.19/0.44  = { by axiom 3 (sos_08) }
% 0.19/0.44    (b + (b  = => a)) + (a  = => ((a  = => b)  = => c))
% 0.19/0.44  = { by axiom 4 (sos_01) }
% 0.19/0.44    b + ((b  = => a) + (a  = => ((a  = => b)  = => c)))
% 0.19/0.44  = { by lemma 6 R->L }
% 0.19/0.44    b + ((b  = => a) + (b  = => ((b  = => a)  = => c)))
% 0.19/0.44  = { by lemma 8 }
% 0.19/0.44    c + (c  = => (b + (b  = => a)))
% 0.19/0.44  = { by axiom 3 (sos_08) R->L }
% 0.19/0.44    c + (c  = => (a + (a  = => b)))
% 0.19/0.44  = { by lemma 10 R->L }
% 0.19/0.44    b + (b  = => (a + (a  = => c)))
% 0.19/0.44  = { by axiom 3 (sos_08) }
% 0.19/0.44    b + (b  = => (c + (c  = => a)))
% 0.19/0.44  = { by lemma 10 R->L }
% 0.19/0.44    a + (a  = => (c + (c  = => b)))
% 0.19/0.44  = { by axiom 3 (sos_08) R->L }
% 0.19/0.44    a + (a  = => (b + (b  = => c)))
% 0.19/0.44  % SZS output end Proof
% 0.19/0.44  
% 0.19/0.44  RESULT: Unsatisfiable (the axioms are contradictory).
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