TSTP Solution File: COL003-13 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : COL003-13 : 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 : n018.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 18:31:31 EDT 2023
% Result : Unsatisfiable 0.22s 0.43s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : COL003-13 : TPTP v8.1.2. Released v2.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35 % Computer : n018.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun Aug 27 05:19:45 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.22/0.43 Command-line arguments: --flatten
% 0.22/0.43
% 0.22/0.43 % SZS status Unsatisfiable
% 0.22/0.43
% 0.22/0.43 % SZS output start Proof
% 0.22/0.43 Axiom 1 (w_definition): apply(apply(w, X), Y) = apply(apply(X, Y), Y).
% 0.22/0.43 Axiom 2 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
% 0.22/0.43 Axiom 3 (strong_fixed_point): strong_fixed_point = apply(apply(b, apply(w, w)), apply(apply(b, apply(apply(b, w), b)), b)).
% 0.22/0.43
% 0.22/0.43 Lemma 4: apply(apply(w, w), X) = apply(apply(X, X), X).
% 0.22/0.43 Proof:
% 0.22/0.43 apply(apply(w, w), X)
% 0.22/0.43 = { by axiom 1 (w_definition) }
% 0.22/0.43 apply(apply(w, X), X)
% 0.22/0.43 = { by axiom 1 (w_definition) }
% 0.22/0.43 apply(apply(X, X), X)
% 0.22/0.43
% 0.22/0.43 Goal 1 (prove_strong_fixed_point): apply(strong_fixed_point, fixed_pt) = apply(fixed_pt, apply(strong_fixed_point, fixed_pt)).
% 0.22/0.43 Proof:
% 0.22/0.43 apply(strong_fixed_point, fixed_pt)
% 0.22/0.43 = { by axiom 3 (strong_fixed_point) }
% 0.22/0.43 apply(apply(apply(b, apply(w, w)), apply(apply(b, apply(apply(b, w), b)), b)), fixed_pt)
% 0.22/0.43 = { by axiom 2 (b_definition) }
% 0.22/0.43 apply(apply(w, w), apply(apply(apply(b, apply(apply(b, w), b)), b), fixed_pt))
% 0.22/0.43 = { by lemma 4 }
% 0.22/0.43 apply(apply(apply(apply(apply(b, apply(apply(b, w), b)), b), fixed_pt), apply(apply(apply(b, apply(apply(b, w), b)), b), fixed_pt)), apply(apply(apply(b, apply(apply(b, w), b)), b), fixed_pt))
% 0.22/0.43 = { by axiom 2 (b_definition) }
% 0.22/0.43 apply(apply(apply(apply(apply(b, w), b), apply(b, fixed_pt)), apply(apply(apply(b, apply(apply(b, w), b)), b), fixed_pt)), apply(apply(apply(b, apply(apply(b, w), b)), b), fixed_pt))
% 0.22/0.43 = { by axiom 2 (b_definition) }
% 0.22/0.43 apply(apply(apply(w, apply(b, apply(b, fixed_pt))), apply(apply(apply(b, apply(apply(b, w), b)), b), fixed_pt)), apply(apply(apply(b, apply(apply(b, w), b)), b), fixed_pt))
% 0.22/0.43 = { by axiom 1 (w_definition) }
% 0.22/0.43 apply(apply(apply(apply(b, apply(b, fixed_pt)), apply(apply(apply(b, apply(apply(b, w), b)), b), fixed_pt)), apply(apply(apply(b, apply(apply(b, w), b)), b), fixed_pt)), apply(apply(apply(b, apply(apply(b, w), b)), b), fixed_pt))
% 0.22/0.43 = { by axiom 2 (b_definition) }
% 0.22/0.43 apply(apply(apply(b, fixed_pt), apply(apply(apply(apply(b, apply(apply(b, w), b)), b), fixed_pt), apply(apply(apply(b, apply(apply(b, w), b)), b), fixed_pt))), apply(apply(apply(b, apply(apply(b, w), b)), b), fixed_pt))
% 0.22/0.43 = { by axiom 2 (b_definition) }
% 0.22/0.43 apply(fixed_pt, apply(apply(apply(apply(apply(b, apply(apply(b, w), b)), b), fixed_pt), apply(apply(apply(b, apply(apply(b, w), b)), b), fixed_pt)), apply(apply(apply(b, apply(apply(b, w), b)), b), fixed_pt)))
% 0.22/0.43 = { by lemma 4 R->L }
% 0.22/0.43 apply(fixed_pt, apply(apply(w, w), apply(apply(apply(b, apply(apply(b, w), b)), b), fixed_pt)))
% 0.22/0.43 = { by axiom 2 (b_definition) R->L }
% 0.22/0.43 apply(fixed_pt, apply(apply(apply(b, apply(w, w)), apply(apply(b, apply(apply(b, w), b)), b)), fixed_pt))
% 0.22/0.43 = { by axiom 3 (strong_fixed_point) R->L }
% 0.22/0.43 apply(fixed_pt, apply(strong_fixed_point, fixed_pt))
% 0.22/0.43 % SZS output end Proof
% 0.22/0.43
% 0.22/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
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