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