TSTP Solution File: COL043-3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : COL043-3 : TPTP v8.1.2. Bugfixed v2.3.0.
% 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 : n009.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 18:31:46 EDT 2023
% Result : Unsatisfiable 8.21s 1.45s
% Output : Proof 8.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COL043-3 : TPTP v8.1.2. Bugfixed v2.3.0.
% 0.06/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 04:36:50 EDT 2023
% 0.12/0.34 % CPUTime :
% 8.21/1.45 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 8.21/1.45
% 8.21/1.45 % SZS status Unsatisfiable
% 8.21/1.45
% 8.21/1.45 % SZS output start Proof
% 8.21/1.45 Axiom 1 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
% 8.21/1.45 Axiom 2 (h_definition): apply(apply(apply(h, X), Y), Z) = apply(apply(apply(X, Y), Z), Y).
% 8.21/1.45 Axiom 3 (strong_fixed_point): strong_fixed_point = apply(apply(b, apply(apply(b, apply(apply(h, apply(apply(b, apply(apply(b, h), apply(b, b))), apply(h, apply(apply(b, h), apply(b, b))))), h)), b)), b).
% 8.21/1.45
% 8.21/1.46 Lemma 4: apply(apply(apply(h, apply(apply(b, X), Y)), Z), W) = apply(apply(apply(X, apply(Y, Z)), W), Z).
% 8.21/1.46 Proof:
% 8.21/1.46 apply(apply(apply(h, apply(apply(b, X), Y)), Z), W)
% 8.21/1.46 = { by axiom 2 (h_definition) }
% 8.21/1.46 apply(apply(apply(apply(apply(b, X), Y), Z), W), Z)
% 8.21/1.46 = { by axiom 1 (b_definition) }
% 8.21/1.46 apply(apply(apply(X, apply(Y, Z)), W), Z)
% 8.21/1.46
% 8.21/1.46 Lemma 5: apply(apply(apply(h, apply(b, apply(b, X))), apply(h, apply(b, apply(b, X)))), apply(h, apply(b, apply(b, X)))) = apply(strong_fixed_point, X).
% 8.21/1.46 Proof:
% 8.21/1.46 apply(apply(apply(h, apply(b, apply(b, X))), apply(h, apply(b, apply(b, X)))), apply(h, apply(b, apply(b, X))))
% 8.21/1.46 = { by axiom 1 (b_definition) R->L }
% 8.21/1.46 apply(apply(apply(apply(b, apply(h, apply(b, apply(b, X)))), h), apply(b, apply(b, X))), apply(h, apply(b, apply(b, X))))
% 8.21/1.46 = { by axiom 1 (b_definition) R->L }
% 8.21/1.46 apply(apply(apply(apply(apply(apply(b, b), h), apply(b, apply(b, X))), h), apply(b, apply(b, X))), apply(h, apply(b, apply(b, X))))
% 8.21/1.46 = { by axiom 2 (h_definition) R->L }
% 8.21/1.46 apply(apply(apply(apply(h, apply(apply(b, b), h)), apply(b, apply(b, X))), h), apply(h, apply(b, apply(b, X))))
% 8.21/1.46 = { by lemma 4 R->L }
% 8.21/1.46 apply(apply(apply(apply(h, apply(apply(b, h), apply(b, b))), h), apply(b, apply(b, X))), apply(h, apply(b, apply(b, X))))
% 8.21/1.46 = { by axiom 1 (b_definition) R->L }
% 8.21/1.46 apply(apply(apply(b, apply(apply(apply(h, apply(apply(b, h), apply(b, b))), h), apply(b, apply(b, X)))), h), apply(b, apply(b, X)))
% 8.21/1.46 = { by axiom 1 (b_definition) R->L }
% 8.21/1.46 apply(apply(apply(apply(apply(b, b), apply(apply(h, apply(apply(b, h), apply(b, b))), h)), apply(b, apply(b, X))), h), apply(b, apply(b, X)))
% 8.21/1.46 = { by axiom 2 (h_definition) R->L }
% 8.21/1.46 apply(apply(apply(h, apply(apply(b, b), apply(apply(h, apply(apply(b, h), apply(b, b))), h))), apply(b, apply(b, X))), h)
% 8.21/1.46 = { by axiom 1 (b_definition) R->L }
% 8.21/1.46 apply(apply(apply(apply(apply(b, h), apply(b, b)), apply(apply(h, apply(apply(b, h), apply(b, b))), h)), apply(b, apply(b, X))), h)
% 8.21/1.46 = { by lemma 4 R->L }
% 8.21/1.46 apply(apply(apply(h, apply(apply(b, apply(apply(b, h), apply(b, b))), apply(h, apply(apply(b, h), apply(b, b))))), h), apply(b, apply(b, X)))
% 8.21/1.46 = { by axiom 1 (b_definition) R->L }
% 8.21/1.46 apply(apply(apply(b, apply(apply(h, apply(apply(b, apply(apply(b, h), apply(b, b))), apply(h, apply(apply(b, h), apply(b, b))))), h)), b), apply(b, X))
% 8.21/1.46 = { by axiom 1 (b_definition) R->L }
% 8.21/1.46 apply(apply(apply(b, apply(apply(b, apply(apply(h, apply(apply(b, apply(apply(b, h), apply(b, b))), apply(h, apply(apply(b, h), apply(b, b))))), h)), b)), b), X)
% 8.21/1.46 = { by axiom 3 (strong_fixed_point) R->L }
% 8.21/1.46 apply(strong_fixed_point, X)
% 8.21/1.46
% 8.21/1.46 Goal 1 (prove_strong_fixed_point): apply(strong_fixed_point, fixed_pt) = apply(fixed_pt, apply(strong_fixed_point, fixed_pt)).
% 8.21/1.46 Proof:
% 8.21/1.46 apply(strong_fixed_point, fixed_pt)
% 8.21/1.46 = { by lemma 5 R->L }
% 8.21/1.46 apply(apply(apply(h, apply(b, apply(b, fixed_pt))), apply(h, apply(b, apply(b, fixed_pt)))), apply(h, apply(b, apply(b, fixed_pt))))
% 8.21/1.46 = { by axiom 2 (h_definition) }
% 8.21/1.46 apply(apply(apply(apply(b, apply(b, fixed_pt)), apply(h, apply(b, apply(b, fixed_pt)))), apply(h, apply(b, apply(b, fixed_pt)))), apply(h, apply(b, apply(b, fixed_pt))))
% 8.21/1.46 = { by axiom 1 (b_definition) }
% 8.21/1.46 apply(apply(apply(b, fixed_pt), apply(apply(h, apply(b, apply(b, fixed_pt))), apply(h, apply(b, apply(b, fixed_pt))))), apply(h, apply(b, apply(b, fixed_pt))))
% 8.21/1.46 = { by axiom 1 (b_definition) }
% 8.21/1.46 apply(fixed_pt, apply(apply(apply(h, apply(b, apply(b, fixed_pt))), apply(h, apply(b, apply(b, fixed_pt)))), apply(h, apply(b, apply(b, fixed_pt)))))
% 8.21/1.46 = { by lemma 5 }
% 8.21/1.46 apply(fixed_pt, apply(strong_fixed_point, fixed_pt))
% 8.21/1.46 % SZS output end Proof
% 8.21/1.46
% 8.21/1.46 RESULT: Unsatisfiable (the axioms are contradictory).
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