TSTP Solution File: LCL897-10 by Twee---2.4.2
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- Process Solution
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% File : Twee---2.4.2
% Problem : LCL897-10 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n015.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 : Thu Aug 31 08:21:06 EDT 2023
% Result : Unsatisfiable 0.19s 0.44s
% 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
% 0.00/0.12 % Problem : LCL897-10 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 06:24:21 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.44 Command-line arguments: --no-flatten-goal
% 0.19/0.44
% 0.19/0.44 % SZS status Unsatisfiable
% 0.19/0.44
% 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 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 5 }
% 0.19/0.44 b + ((b = => a) + ((b = => a) = => (b = => c)))
% 0.19/0.44 = { by axiom 3 (sos_08) }
% 0.19/0.44 b + ((b = => c) + ((b = => c) = => (b = => a)))
% 0.19/0.44 = { by lemma 5 R->L }
% 0.19/0.44 b + ((b = => c) + (b = => ((b = => c) = => a)))
% 0.19/0.44 = { by axiom 4 (sos_01) R->L }
% 0.19/0.44 (b + (b = => c)) + (b = => ((b = => c) = => a))
% 0.19/0.44 = { by axiom 3 (sos_08) R->L }
% 0.19/0.44 (c + (c = => b)) + (b = => ((b = => c) = => a))
% 0.19/0.44 = { by axiom 4 (sos_01) }
% 0.19/0.44 c + ((c = => b) + (b = => ((b = => c) = => a)))
% 0.19/0.44 = { by lemma 6 R->L }
% 0.19/0.44 c + ((c = => b) + (c = => ((c = => b) = => a)))
% 0.19/0.44 = { by lemma 5 }
% 0.19/0.44 c + ((c = => b) + ((c = => b) = => (c = => a)))
% 0.19/0.44 = { by axiom 1 (sos_02) R->L }
% 0.19/0.44 c + (((c = => b) = => (c = => a)) + (c = => b))
% 0.19/0.44 = { by axiom 4 (sos_01) R->L }
% 0.19/0.44 (c + ((c = => b) = => (c = => a))) + (c = => b)
% 0.19/0.44 = { by axiom 1 (sos_02) }
% 0.19/0.44 (c = => b) + (c + ((c = => b) = => (c = => a)))
% 0.19/0.44 = { by axiom 4 (sos_01) R->L }
% 0.19/0.44 ((c = => b) + c) + ((c = => b) = => (c = => a))
% 0.19/0.44 = { by axiom 2 (sos_07) R->L }
% 0.19/0.44 ((c = => b) + c) + (((c = => b) + c) = => a)
% 0.19/0.44 = { by axiom 3 (sos_08) }
% 0.19/0.44 a + (a = => ((c = => b) + c))
% 0.19/0.44 = { by axiom 1 (sos_02) }
% 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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