TSTP Solution File: COL044-8 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : COL044-8 : 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 : n023.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 18:31:48 EDT 2023
% Result : Unsatisfiable 5.01s 1.06s
% Output : Proof 5.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : COL044-8 : TPTP v8.1.2. Released v2.1.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 04:48:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 5.01/1.06 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 5.01/1.06
% 5.01/1.06 % SZS status Unsatisfiable
% 5.01/1.06
% 5.01/1.06 % SZS output start Proof
% 5.01/1.06 Axiom 1 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
% 5.01/1.06 Axiom 2 (n_definition): apply(apply(apply(n, X), Y), Z) = apply(apply(apply(X, Z), Y), Z).
% 5.01/1.06 Axiom 3 (strong_fixed_point): strong_fixed_point = apply(apply(b, apply(apply(b, apply(apply(n, apply(n, apply(apply(b, apply(b, b)), apply(n, apply(apply(b, b), n))))), n)), b)), b).
% 5.01/1.06
% 5.01/1.06 Lemma 4: apply(apply(apply(n, apply(b, apply(b, X))), apply(n, apply(b, apply(b, X)))), apply(n, apply(b, apply(b, X)))) = apply(strong_fixed_point, X).
% 5.01/1.06 Proof:
% 5.01/1.06 apply(apply(apply(n, apply(b, apply(b, X))), apply(n, apply(b, apply(b, X)))), apply(n, apply(b, apply(b, X))))
% 5.01/1.06 = { by axiom 1 (b_definition) R->L }
% 5.01/1.06 apply(apply(apply(apply(b, apply(n, apply(b, apply(b, X)))), n), apply(b, apply(b, X))), apply(n, apply(b, apply(b, X))))
% 5.01/1.06 = { by axiom 1 (b_definition) R->L }
% 5.01/1.06 apply(apply(apply(apply(apply(apply(b, b), n), apply(b, apply(b, X))), n), apply(b, apply(b, X))), apply(n, apply(b, apply(b, X))))
% 5.01/1.06 = { by axiom 2 (n_definition) R->L }
% 5.01/1.06 apply(apply(apply(apply(n, apply(apply(b, b), n)), n), apply(b, apply(b, X))), apply(n, apply(b, apply(b, X))))
% 5.01/1.06 = { by axiom 1 (b_definition) R->L }
% 5.01/1.06 apply(apply(apply(b, apply(apply(apply(n, apply(apply(b, b), n)), n), apply(b, apply(b, X)))), n), apply(b, apply(b, X)))
% 5.01/1.06 = { by axiom 1 (b_definition) R->L }
% 5.01/1.06 apply(apply(apply(apply(apply(b, b), apply(apply(n, apply(apply(b, b), n)), n)), apply(b, apply(b, X))), n), apply(b, apply(b, X)))
% 5.01/1.06 = { by axiom 1 (b_definition) R->L }
% 5.01/1.06 apply(apply(apply(apply(apply(apply(b, apply(b, b)), apply(n, apply(apply(b, b), n))), n), apply(b, apply(b, X))), n), apply(b, apply(b, X)))
% 5.01/1.06 = { by axiom 2 (n_definition) R->L }
% 5.01/1.06 apply(apply(apply(apply(n, apply(apply(b, apply(b, b)), apply(n, apply(apply(b, b), n)))), apply(b, apply(b, X))), n), apply(b, apply(b, X)))
% 5.01/1.07 = { by axiom 2 (n_definition) R->L }
% 5.01/1.07 apply(apply(apply(n, apply(n, apply(apply(b, apply(b, b)), apply(n, apply(apply(b, b), n))))), n), apply(b, apply(b, X)))
% 5.01/1.07 = { by axiom 1 (b_definition) R->L }
% 5.01/1.07 apply(apply(apply(b, apply(apply(n, apply(n, apply(apply(b, apply(b, b)), apply(n, apply(apply(b, b), n))))), n)), b), apply(b, X))
% 5.01/1.07 = { by axiom 1 (b_definition) R->L }
% 5.01/1.07 apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(n, apply(apply(b, apply(b, b)), apply(n, apply(apply(b, b), n))))), n)), b)), b), X)
% 5.01/1.07 = { by axiom 3 (strong_fixed_point) R->L }
% 5.01/1.07 apply(strong_fixed_point, X)
% 5.01/1.07
% 5.01/1.07 Goal 1 (prove_strong_fixed_point): apply(strong_fixed_point, fixed_pt) = apply(fixed_pt, apply(strong_fixed_point, fixed_pt)).
% 5.01/1.07 Proof:
% 5.01/1.07 apply(strong_fixed_point, fixed_pt)
% 5.01/1.07 = { by lemma 4 R->L }
% 5.01/1.07 apply(apply(apply(n, apply(b, apply(b, fixed_pt))), apply(n, apply(b, apply(b, fixed_pt)))), apply(n, apply(b, apply(b, fixed_pt))))
% 5.01/1.07 = { by axiom 2 (n_definition) }
% 5.01/1.07 apply(apply(apply(apply(b, apply(b, fixed_pt)), apply(n, apply(b, apply(b, fixed_pt)))), apply(n, apply(b, apply(b, fixed_pt)))), apply(n, apply(b, apply(b, fixed_pt))))
% 5.01/1.07 = { by axiom 1 (b_definition) }
% 5.01/1.07 apply(apply(apply(b, fixed_pt), apply(apply(n, apply(b, apply(b, fixed_pt))), apply(n, apply(b, apply(b, fixed_pt))))), apply(n, apply(b, apply(b, fixed_pt))))
% 5.01/1.07 = { by axiom 1 (b_definition) }
% 5.01/1.07 apply(fixed_pt, apply(apply(apply(n, apply(b, apply(b, fixed_pt))), apply(n, apply(b, apply(b, fixed_pt)))), apply(n, apply(b, apply(b, fixed_pt)))))
% 5.01/1.07 = { by lemma 4 }
% 5.01/1.07 apply(fixed_pt, apply(strong_fixed_point, fixed_pt))
% 5.01/1.07 % SZS output end Proof
% 5.01/1.07
% 5.01/1.07 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------