TSTP Solution File: NUN134-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : NUN134-1 : 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 : n019.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 12:52:03 EDT 2023
% 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
% 0.00/0.12 % Problem : NUN134-1 : 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
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 09:15:28 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.43 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.43
% 0.19/0.43 % SZS status Unsatisfiable
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% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 Axiom 1 (times_comm): times(X, Y) = times(Y, X).
% 0.19/0.43 Axiom 2 (plus_comm): X + Y = Y + X.
% 0.19/0.43 Axiom 3 (plus_s): s(X) + Y = s(X + Y).
% 0.19/0.43 Axiom 4 (times_s): times(s(X), Y) = Y + times(X, Y).
% 0.19/0.43 Axiom 5 (sum_s): sum(s(X)) = s(X) + sum(X).
% 0.19/0.43 Axiom 6 (induction_hypothesis): sum(a) + sum(a) = times(a, s(a)).
% 0.19/0.43 Axiom 7 (plus_assoc): X + (Y + Z) = (X + Y) + Z.
% 0.19/0.43
% 0.19/0.43 Lemma 8: Y + s(X) = s(X + Y).
% 0.19/0.43 Proof:
% 0.19/0.43 Y + s(X)
% 0.19/0.43 = { by axiom 2 (plus_comm) R->L }
% 0.19/0.43 s(X) + Y
% 0.19/0.43 = { by axiom 3 (plus_s) }
% 0.19/0.43 s(X + Y)
% 0.19/0.43
% 0.19/0.43 Lemma 9: s(X + (Y + sum(X))) = Y + sum(s(X)).
% 0.19/0.43 Proof:
% 0.19/0.43 s(X + (Y + sum(X)))
% 0.19/0.43 = { by axiom 2 (plus_comm) R->L }
% 0.19/0.43 s(X + (sum(X) + Y))
% 0.19/0.43 = { by axiom 7 (plus_assoc) }
% 0.19/0.43 s((X + sum(X)) + Y)
% 0.19/0.43 = { by axiom 3 (plus_s) R->L }
% 0.19/0.43 s(X + sum(X)) + Y
% 0.19/0.43 = { by axiom 3 (plus_s) R->L }
% 0.19/0.43 (s(X) + sum(X)) + Y
% 0.19/0.43 = { by axiom 5 (sum_s) R->L }
% 0.19/0.43 sum(s(X)) + Y
% 0.19/0.43 = { by axiom 2 (plus_comm) }
% 0.19/0.43 Y + sum(s(X))
% 0.19/0.43
% 0.19/0.43 Goal 1 (goal): sum(s(a)) + sum(s(a)) = times(s(a), s(s(a))).
% 0.19/0.43 Proof:
% 0.19/0.44 sum(s(a)) + sum(s(a))
% 0.19/0.44 = { by lemma 9 R->L }
% 0.19/0.44 s(a + (sum(s(a)) + sum(a)))
% 0.19/0.44 = { by axiom 2 (plus_comm) R->L }
% 0.19/0.44 s(a + (sum(a) + sum(s(a))))
% 0.19/0.44 = { by lemma 9 R->L }
% 0.19/0.44 s(a + s(a + (sum(a) + sum(a))))
% 0.19/0.44 = { by axiom 6 (induction_hypothesis) }
% 0.19/0.44 s(a + s(a + times(a, s(a))))
% 0.19/0.44 = { by lemma 8 R->L }
% 0.19/0.44 s(a + (times(a, s(a)) + s(a)))
% 0.19/0.44 = { by axiom 2 (plus_comm) }
% 0.19/0.44 s(a + (s(a) + times(a, s(a))))
% 0.19/0.44 = { by axiom 4 (times_s) R->L }
% 0.19/0.44 s(a + times(s(a), s(a)))
% 0.19/0.44 = { by lemma 8 R->L }
% 0.19/0.44 times(s(a), s(a)) + s(a)
% 0.19/0.44 = { by axiom 2 (plus_comm) }
% 0.19/0.44 s(a) + times(s(a), s(a))
% 0.19/0.44 = { by axiom 4 (times_s) R->L }
% 0.19/0.44 times(s(s(a)), s(a))
% 0.19/0.44 = { by axiom 1 (times_comm) }
% 0.19/0.44 times(s(a), s(s(a)))
% 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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