TSTP Solution File: COL042-8 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : COL042-8 : 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 : n024.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 18:31:45 EDT 2023
% Result : Unsatisfiable 0.21s 0.60s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL042-8 : TPTP v8.1.2. Released v2.1.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 03:57:23 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.60 Command-line arguments: --no-flatten-goal
% 0.21/0.60
% 0.21/0.60 % SZS status Unsatisfiable
% 0.21/0.60
% 0.21/0.60 % SZS output start Proof
% 0.21/0.60 Axiom 1 (w1_definition): apply(apply(w1, X), Y) = apply(apply(Y, X), X).
% 0.21/0.60 Axiom 2 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
% 0.21/0.60 Axiom 3 (strong_fixed_point): strong_fixed_point = apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b).
% 0.21/0.60
% 0.21/0.60 Lemma 4: apply(apply(w1, X), apply(apply(b, Y), Z)) = apply(apply(Y, apply(Z, X)), X).
% 0.21/0.60 Proof:
% 0.21/0.60 apply(apply(w1, X), apply(apply(b, Y), Z))
% 0.21/0.60 = { by axiom 1 (w1_definition) }
% 0.21/0.60 apply(apply(apply(apply(b, Y), Z), X), X)
% 0.21/0.60 = { by axiom 2 (b_definition) }
% 0.21/0.60 apply(apply(Y, apply(Z, X)), X)
% 0.21/0.60
% 0.21/0.60 Lemma 5: apply(apply(w1, apply(apply(b, apply(b, X)), w1)), w1) = apply(strong_fixed_point, X).
% 0.21/0.60 Proof:
% 0.21/0.60 apply(apply(w1, apply(apply(b, apply(b, X)), w1)), w1)
% 0.21/0.60 = { by lemma 4 R->L }
% 0.21/0.60 apply(apply(w1, w1), apply(apply(b, w1), apply(b, apply(b, X))))
% 0.21/0.60 = { by axiom 2 (b_definition) R->L }
% 0.21/0.60 apply(apply(w1, w1), apply(apply(apply(b, apply(b, w1)), b), apply(b, X)))
% 0.21/0.60 = { by axiom 2 (b_definition) R->L }
% 0.21/0.60 apply(apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b)), apply(b, X))
% 0.21/0.60 = { by axiom 2 (b_definition) R->L }
% 0.21/0.60 apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), X)
% 0.21/0.60 = { by axiom 3 (strong_fixed_point) R->L }
% 0.21/0.60 apply(strong_fixed_point, X)
% 0.21/0.60
% 0.21/0.60 Goal 1 (prove_strong_fixed_point): apply(strong_fixed_point, fixed_pt) = apply(fixed_pt, apply(strong_fixed_point, fixed_pt)).
% 0.21/0.60 Proof:
% 0.21/0.60 apply(strong_fixed_point, fixed_pt)
% 0.21/0.60 = { by lemma 5 R->L }
% 0.21/0.60 apply(apply(w1, apply(apply(b, apply(b, fixed_pt)), w1)), w1)
% 0.21/0.60 = { by axiom 1 (w1_definition) }
% 0.21/0.60 apply(apply(w1, apply(apply(b, apply(b, fixed_pt)), w1)), apply(apply(b, apply(b, fixed_pt)), w1))
% 0.21/0.60 = { by lemma 4 }
% 0.21/0.60 apply(apply(apply(b, fixed_pt), apply(w1, apply(apply(b, apply(b, fixed_pt)), w1))), apply(apply(b, apply(b, fixed_pt)), w1))
% 0.21/0.60 = { by axiom 2 (b_definition) }
% 0.21/0.60 apply(fixed_pt, apply(apply(w1, apply(apply(b, apply(b, fixed_pt)), w1)), apply(apply(b, apply(b, fixed_pt)), w1)))
% 0.21/0.60 = { by axiom 1 (w1_definition) R->L }
% 0.21/0.60 apply(fixed_pt, apply(apply(w1, apply(apply(b, apply(b, fixed_pt)), w1)), w1))
% 0.21/0.60 = { by lemma 5 }
% 0.21/0.60 apply(fixed_pt, apply(strong_fixed_point, fixed_pt))
% 0.21/0.60 % SZS output end Proof
% 0.21/0.60
% 0.21/0.60 RESULT: Unsatisfiable (the axioms are contradictory).
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