TSTP Solution File: COL006-5 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : COL006-5 : TPTP v8.1.2. Released v2.1.0.
% 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 : n022.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 : Wed Aug 30 18:31:36 EDT 2023
% Result : Unsatisfiable 0.19s 0.62s
% 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 : COL006-5 : TPTP v8.1.2. Released v2.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.34 % Computer : n022.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sun Aug 27 04:27:24 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.19/0.62 Command-line arguments: --flatten
% 0.19/0.62
% 0.19/0.62 % SZS status Unsatisfiable
% 0.19/0.62
% 0.19/0.62 % SZS output start Proof
% 0.19/0.62 Axiom 1 (k_definition): apply(apply(k, X), Y) = X.
% 0.19/0.62 Axiom 2 (s_definition): apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z)).
% 0.19/0.62 Axiom 3 (strong_fixed_point): strong_fixed_point = apply(apply(s, apply(k, apply(apply(s, apply(apply(s, k), k)), apply(apply(s, k), k)))), apply(apply(s, apply(k, apply(apply(s, s), apply(s, k)))), apply(apply(s, apply(k, s)), k))).
% 0.19/0.62
% 0.19/0.62 Lemma 4: apply(apply(apply(s, k), X), Y) = Y.
% 0.19/0.62 Proof:
% 0.19/0.62 apply(apply(apply(s, k), X), Y)
% 0.19/0.62 = { by axiom 2 (s_definition) }
% 0.19/0.62 apply(apply(k, Y), apply(X, Y))
% 0.19/0.62 = { by axiom 1 (k_definition) }
% 0.19/0.62 Y
% 0.19/0.62
% 0.19/0.62 Lemma 5: apply(apply(apply(s, apply(k, X)), Y), Z) = apply(X, apply(Y, Z)).
% 0.19/0.62 Proof:
% 0.19/0.62 apply(apply(apply(s, apply(k, X)), Y), Z)
% 0.19/0.62 = { by axiom 2 (s_definition) }
% 0.19/0.62 apply(apply(apply(k, X), Z), apply(Y, Z))
% 0.19/0.62 = { by axiom 1 (k_definition) }
% 0.19/0.62 apply(X, apply(Y, Z))
% 0.19/0.62
% 0.19/0.62 Lemma 6: apply(apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z)), X) = apply(X, X).
% 0.19/0.62 Proof:
% 0.19/0.62 apply(apply(apply(s, apply(apply(s, k), Y)), apply(apply(s, k), Z)), X)
% 0.19/0.62 = { by axiom 2 (s_definition) }
% 0.19/0.62 apply(apply(apply(apply(s, k), Y), X), apply(apply(apply(s, k), Z), X))
% 0.19/0.62 = { by lemma 4 }
% 0.19/0.62 apply(X, apply(apply(apply(s, k), Z), X))
% 0.19/0.62 = { by lemma 4 }
% 0.19/0.63 apply(X, X)
% 0.19/0.63
% 0.19/0.63 Goal 1 (prove_strong_fixed_point): apply(strong_fixed_point, fixed_pt) = apply(fixed_pt, apply(strong_fixed_point, fixed_pt)).
% 0.19/0.63 Proof:
% 0.19/0.63 apply(strong_fixed_point, fixed_pt)
% 0.19/0.63 = { by axiom 3 (strong_fixed_point) }
% 0.19/0.63 apply(apply(apply(s, apply(k, apply(apply(s, apply(apply(s, k), k)), apply(apply(s, k), k)))), apply(apply(s, apply(k, apply(apply(s, s), apply(s, k)))), apply(apply(s, apply(k, s)), k))), fixed_pt)
% 0.19/0.63 = { by lemma 5 }
% 0.19/0.63 apply(apply(apply(s, apply(apply(s, k), k)), apply(apply(s, k), k)), apply(apply(apply(s, apply(k, apply(apply(s, s), apply(s, k)))), apply(apply(s, apply(k, s)), k)), fixed_pt))
% 0.19/0.63 = { by lemma 6 }
% 0.19/0.63 apply(apply(apply(apply(s, apply(k, apply(apply(s, s), apply(s, k)))), apply(apply(s, apply(k, s)), k)), fixed_pt), apply(apply(apply(s, apply(k, apply(apply(s, s), apply(s, k)))), apply(apply(s, apply(k, s)), k)), fixed_pt))
% 0.19/0.63 = { by lemma 5 }
% 0.19/0.63 apply(apply(apply(apply(s, s), apply(s, k)), apply(apply(apply(s, apply(k, s)), k), fixed_pt)), apply(apply(apply(s, apply(k, apply(apply(s, s), apply(s, k)))), apply(apply(s, apply(k, s)), k)), fixed_pt))
% 0.19/0.63 = { by axiom 2 (s_definition) }
% 0.19/0.63 apply(apply(apply(s, apply(apply(apply(s, apply(k, s)), k), fixed_pt)), apply(apply(s, k), apply(apply(apply(s, apply(k, s)), k), fixed_pt))), apply(apply(apply(s, apply(k, apply(apply(s, s), apply(s, k)))), apply(apply(s, apply(k, s)), k)), fixed_pt))
% 0.19/0.63 = { by axiom 2 (s_definition) }
% 0.19/0.63 apply(apply(apply(apply(apply(s, apply(k, s)), k), fixed_pt), apply(apply(apply(s, apply(k, apply(apply(s, s), apply(s, k)))), apply(apply(s, apply(k, s)), k)), fixed_pt)), apply(apply(apply(s, k), apply(apply(apply(s, apply(k, s)), k), fixed_pt)), apply(apply(apply(s, apply(k, apply(apply(s, s), apply(s, k)))), apply(apply(s, apply(k, s)), k)), fixed_pt)))
% 0.19/0.63 = { by lemma 4 }
% 0.19/0.63 apply(apply(apply(apply(apply(s, apply(k, s)), k), fixed_pt), apply(apply(apply(s, apply(k, apply(apply(s, s), apply(s, k)))), apply(apply(s, apply(k, s)), k)), fixed_pt)), apply(apply(apply(s, apply(k, apply(apply(s, s), apply(s, k)))), apply(apply(s, apply(k, s)), k)), fixed_pt))
% 0.19/0.63 = { by lemma 5 }
% 0.19/0.63 apply(apply(apply(s, apply(k, fixed_pt)), apply(apply(apply(s, apply(k, apply(apply(s, s), apply(s, k)))), apply(apply(s, apply(k, s)), k)), fixed_pt)), apply(apply(apply(s, apply(k, apply(apply(s, s), apply(s, k)))), apply(apply(s, apply(k, s)), k)), fixed_pt))
% 0.19/0.63 = { by axiom 2 (s_definition) }
% 0.19/0.63 apply(apply(apply(k, fixed_pt), apply(apply(apply(s, apply(k, apply(apply(s, s), apply(s, k)))), apply(apply(s, apply(k, s)), k)), fixed_pt)), apply(apply(apply(apply(s, apply(k, apply(apply(s, s), apply(s, k)))), apply(apply(s, apply(k, s)), k)), fixed_pt), apply(apply(apply(s, apply(k, apply(apply(s, s), apply(s, k)))), apply(apply(s, apply(k, s)), k)), fixed_pt)))
% 0.19/0.63 = { by axiom 1 (k_definition) }
% 0.19/0.63 apply(fixed_pt, apply(apply(apply(apply(s, apply(k, apply(apply(s, s), apply(s, k)))), apply(apply(s, apply(k, s)), k)), fixed_pt), apply(apply(apply(s, apply(k, apply(apply(s, s), apply(s, k)))), apply(apply(s, apply(k, s)), k)), fixed_pt)))
% 0.19/0.63 = { by lemma 6 R->L }
% 0.19/0.63 apply(fixed_pt, apply(apply(apply(s, apply(apply(s, k), k)), apply(apply(s, k), k)), apply(apply(apply(s, apply(k, apply(apply(s, s), apply(s, k)))), apply(apply(s, apply(k, s)), k)), fixed_pt)))
% 0.19/0.63 = { by lemma 5 R->L }
% 0.19/0.63 apply(fixed_pt, apply(apply(apply(s, apply(k, apply(apply(s, apply(apply(s, k), k)), apply(apply(s, k), k)))), apply(apply(s, apply(k, apply(apply(s, s), apply(s, k)))), apply(apply(s, apply(k, s)), k))), fixed_pt))
% 0.19/0.63 = { by axiom 3 (strong_fixed_point) R->L }
% 0.19/0.63 apply(fixed_pt, apply(strong_fixed_point, fixed_pt))
% 0.19/0.63 % SZS output end Proof
% 0.19/0.63
% 0.19/0.63 RESULT: Unsatisfiable (the axioms are contradictory).
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