TSTP Solution File: COL003-19 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : COL003-19 : 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 : n032.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 18:31:33 EDT 2023
% Result : Unsatisfiable 0.12s 0.59s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : COL003-19 : TPTP v8.1.2. Released v2.1.0.
% 0.00/0.08 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.09/0.27 % Computer : n032.cluster.edu
% 0.09/0.27 % Model : x86_64 x86_64
% 0.09/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.27 % Memory : 8042.1875MB
% 0.09/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.27 % CPULimit : 300
% 0.09/0.27 % WCLimit : 300
% 0.09/0.27 % DateTime : Sun Aug 27 05:21:14 EDT 2023
% 0.09/0.27 % CPUTime :
% 0.12/0.59 Command-line arguments: --no-flatten-goal
% 0.12/0.59
% 0.12/0.59 % SZS status Unsatisfiable
% 0.12/0.59
% 0.12/0.59 % SZS output start Proof
% 0.12/0.59 Axiom 1 (w_definition): apply(apply(w, X), Y) = apply(apply(X, Y), Y).
% 0.12/0.59 Axiom 2 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
% 0.12/0.59 Axiom 3 (strong_fixed_point): strong_fixed_point = apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b).
% 0.12/0.59
% 0.12/0.59 Lemma 4: apply(apply(w, apply(apply(b, w), X)), Y) = apply(apply(w, apply(w, X)), Y).
% 0.12/0.59 Proof:
% 0.12/0.59 apply(apply(w, apply(apply(b, w), X)), Y)
% 0.12/0.59 = { by axiom 1 (w_definition) }
% 0.12/0.59 apply(apply(apply(apply(b, w), X), Y), Y)
% 0.12/0.59 = { by axiom 2 (b_definition) }
% 0.12/0.59 apply(apply(w, apply(X, Y)), Y)
% 0.12/0.59 = { by axiom 1 (w_definition) }
% 0.12/0.59 apply(apply(apply(X, Y), Y), Y)
% 0.12/0.59 = { by axiom 1 (w_definition) R->L }
% 0.12/0.59 apply(apply(apply(w, X), Y), Y)
% 0.12/0.59 = { by axiom 1 (w_definition) R->L }
% 0.12/0.59 apply(apply(w, apply(w, X)), Y)
% 0.12/0.59
% 0.12/0.59 Lemma 5: apply(apply(w, apply(w, X)), apply(apply(b, w), X)) = apply(apply(w, w), apply(apply(b, w), X)).
% 0.12/0.59 Proof:
% 0.12/0.59 apply(apply(w, apply(w, X)), apply(apply(b, w), X))
% 0.12/0.59 = { by lemma 4 R->L }
% 0.12/0.59 apply(apply(w, apply(apply(b, w), X)), apply(apply(b, w), X))
% 0.12/0.59 = { by axiom 1 (w_definition) R->L }
% 0.12/0.59 apply(apply(w, w), apply(apply(b, w), X))
% 0.12/0.59
% 0.12/0.59 Lemma 6: apply(apply(w, w), apply(apply(b, w), apply(b, apply(b, X)))) = apply(strong_fixed_point, X).
% 0.12/0.59 Proof:
% 0.12/0.59 apply(apply(w, w), apply(apply(b, w), apply(b, apply(b, X))))
% 0.12/0.59 = { by axiom 2 (b_definition) R->L }
% 0.12/0.59 apply(apply(w, w), apply(apply(apply(b, apply(b, w)), b), apply(b, X)))
% 0.12/0.59 = { by axiom 2 (b_definition) R->L }
% 0.12/0.59 apply(apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b)), apply(b, X))
% 0.12/0.59 = { by axiom 2 (b_definition) R->L }
% 0.12/0.59 apply(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b), X)
% 0.12/0.59 = { by axiom 3 (strong_fixed_point) R->L }
% 0.12/0.59 apply(strong_fixed_point, X)
% 0.12/0.59
% 0.12/0.59 Goal 1 (prove_strong_fixed_point): apply(strong_fixed_point, fixed_pt) = apply(fixed_pt, apply(strong_fixed_point, fixed_pt)).
% 0.12/0.59 Proof:
% 0.12/0.59 apply(strong_fixed_point, fixed_pt)
% 0.12/0.59 = { by lemma 6 R->L }
% 0.12/0.59 apply(apply(w, w), apply(apply(b, w), apply(b, apply(b, fixed_pt))))
% 0.12/0.59 = { by lemma 5 R->L }
% 0.12/0.59 apply(apply(w, apply(w, apply(b, apply(b, fixed_pt)))), apply(apply(b, w), apply(b, apply(b, fixed_pt))))
% 0.12/0.59 = { by axiom 1 (w_definition) }
% 0.12/0.59 apply(apply(apply(w, apply(b, apply(b, fixed_pt))), apply(apply(b, w), apply(b, apply(b, fixed_pt)))), apply(apply(b, w), apply(b, apply(b, fixed_pt))))
% 0.12/0.59 = { by axiom 1 (w_definition) }
% 0.12/0.59 apply(apply(apply(apply(b, apply(b, fixed_pt)), apply(apply(b, w), apply(b, apply(b, fixed_pt)))), apply(apply(b, w), apply(b, apply(b, fixed_pt)))), apply(apply(b, w), apply(b, apply(b, fixed_pt))))
% 0.12/0.59 = { by axiom 2 (b_definition) }
% 0.12/0.59 apply(apply(apply(b, fixed_pt), apply(apply(apply(b, w), apply(b, apply(b, fixed_pt))), apply(apply(b, w), apply(b, apply(b, fixed_pt))))), apply(apply(b, w), apply(b, apply(b, fixed_pt))))
% 0.12/0.59 = { by axiom 2 (b_definition) }
% 0.12/0.59 apply(fixed_pt, apply(apply(apply(apply(b, w), apply(b, apply(b, fixed_pt))), apply(apply(b, w), apply(b, apply(b, fixed_pt)))), apply(apply(b, w), apply(b, apply(b, fixed_pt)))))
% 0.12/0.59 = { by axiom 1 (w_definition) R->L }
% 0.12/0.59 apply(fixed_pt, apply(apply(w, apply(apply(b, w), apply(b, apply(b, fixed_pt)))), apply(apply(b, w), apply(b, apply(b, fixed_pt)))))
% 0.12/0.59 = { by lemma 4 }
% 0.12/0.59 apply(fixed_pt, apply(apply(w, apply(w, apply(b, apply(b, fixed_pt)))), apply(apply(b, w), apply(b, apply(b, fixed_pt)))))
% 0.12/0.59 = { by lemma 5 }
% 0.12/0.59 apply(fixed_pt, apply(apply(w, w), apply(apply(b, w), apply(b, apply(b, fixed_pt)))))
% 0.12/0.59 = { by lemma 6 }
% 0.12/0.59 apply(fixed_pt, apply(strong_fixed_point, fixed_pt))
% 0.12/0.59 % SZS output end Proof
% 0.12/0.59
% 0.12/0.59 RESULT: Unsatisfiable (the axioms are contradictory).
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