TSTP Solution File: COL044-10 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : COL044-10 : TPTP v8.1.2. Released v7.5.0.
% 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 70.68s 9.26s
% Output : Proof 71.40s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : COL044-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.09/0.30 % Computer : n009.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Sun Aug 27 04:39:05 EDT 2023
% 0.09/0.30 % CPUTime :
% 70.68/9.26 Command-line arguments: --flatten
% 70.68/9.26
% 70.68/9.26 % SZS status Unsatisfiable
% 70.68/9.26
% 70.68/9.26 % SZS output start Proof
% 70.68/9.26 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 70.68/9.26 Axiom 2 (n_definition): apply(apply(apply(n, X), Y), Z) = apply(apply(apply(X, Z), Y), Z).
% 70.68/9.27 Axiom 3 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
% 70.68/9.27 Axiom 4 (strong_fixed_point): ifeq(apply(X, fixed_pt), apply(fixed_pt, apply(X, fixed_pt)), fixed_point(X), true) = true.
% 70.68/9.27
% 70.68/9.27 Lemma 5: apply(apply(apply(n, apply(b, X)), Z), Y) = apply(apply(X, apply(Y, Z)), Y).
% 70.68/9.27 Proof:
% 70.68/9.27 apply(apply(apply(n, apply(b, X)), Z), Y)
% 70.68/9.27 = { by axiom 2 (n_definition) }
% 70.68/9.27 apply(apply(apply(apply(b, X), Y), Z), Y)
% 70.68/9.27 = { by axiom 3 (b_definition) }
% 70.68/9.27 apply(apply(X, apply(Y, Z)), Y)
% 70.68/9.27
% 70.68/9.27 Lemma 6: apply(apply(apply(n, apply(n, apply(b, b))), X), Y) = apply(apply(X, Y), apply(X, Y)).
% 70.68/9.27 Proof:
% 70.68/9.27 apply(apply(apply(n, apply(n, apply(b, b))), X), Y)
% 70.68/9.27 = { by axiom 2 (n_definition) }
% 70.68/9.27 apply(apply(apply(apply(n, apply(b, b)), Y), X), Y)
% 70.68/9.27 = { by lemma 5 }
% 70.68/9.27 apply(apply(apply(b, apply(X, Y)), X), Y)
% 70.68/9.27 = { by axiom 3 (b_definition) }
% 70.68/9.27 apply(apply(X, Y), apply(X, Y))
% 70.68/9.27
% 70.68/9.27 Lemma 7: apply(apply(apply(n, apply(apply(b, b), X)), Z), Y) = apply(apply(X, Y), apply(Z, Y)).
% 70.68/9.27 Proof:
% 70.68/9.27 apply(apply(apply(n, apply(apply(b, b), X)), Z), Y)
% 70.68/9.27 = { by axiom 2 (n_definition) }
% 70.68/9.27 apply(apply(apply(apply(apply(b, b), X), Y), Z), Y)
% 70.68/9.27 = { by axiom 3 (b_definition) }
% 70.68/9.27 apply(apply(apply(b, apply(X, Y)), Z), Y)
% 70.68/9.27 = { by axiom 3 (b_definition) }
% 70.68/9.27 apply(apply(X, Y), apply(Z, Y))
% 70.68/9.27
% 70.68/9.27 Goal 1 (prove_strong_fixed_point): fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)) = true.
% 70.68/9.27 Proof:
% 70.68/9.27 fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b))
% 70.68/9.27 = { by axiom 1 (ifeq_axiom) R->L }
% 70.68/9.27 ifeq(apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)), true)
% 70.68/9.27 = { by axiom 3 (b_definition) }
% 70.68/9.27 ifeq(apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), apply(apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b), apply(b, fixed_pt)), fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)), true)
% 70.68/9.27 = { by axiom 3 (b_definition) }
% 70.68/9.27 ifeq(apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), apply(apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n), apply(b, apply(b, fixed_pt))), fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)), true)
% 70.68/9.27 = { by lemma 7 }
% 70.68/9.27 ifeq(apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), apply(apply(apply(apply(n, apply(n, apply(b, b))), n), apply(b, apply(b, fixed_pt))), apply(n, apply(b, apply(b, fixed_pt)))), fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)), true)
% 70.68/9.27 = { by lemma 6 }
% 70.68/9.27 ifeq(apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), 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)))), fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)), true)
% 70.68/9.27 = { by lemma 5 }
% 70.68/9.27 ifeq(apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), 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)))), fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)), true)
% 71.40/9.27 = { by lemma 6 R->L }
% 71.40/9.27 ifeq(apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), apply(apply(apply(b, fixed_pt), apply(apply(apply(n, apply(n, apply(b, b))), n), apply(b, apply(b, fixed_pt)))), apply(n, apply(b, apply(b, fixed_pt)))), fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)), true)
% 71.40/9.27 = { by axiom 3 (b_definition) }
% 71.40/9.27 ifeq(apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), apply(fixed_pt, apply(apply(apply(apply(n, apply(n, apply(b, b))), n), apply(b, apply(b, fixed_pt))), apply(n, apply(b, apply(b, fixed_pt))))), fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)), true)
% 71.40/9.27 = { by lemma 7 R->L }
% 71.40/9.27 ifeq(apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), apply(fixed_pt, apply(apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n), apply(b, apply(b, fixed_pt)))), fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)), true)
% 71.40/9.27 = { by axiom 3 (b_definition) R->L }
% 71.40/9.27 ifeq(apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), apply(fixed_pt, apply(apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b), apply(b, fixed_pt))), fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)), true)
% 71.40/9.27 = { by axiom 3 (b_definition) R->L }
% 71.40/9.27 ifeq(apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt), apply(fixed_pt, apply(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b), fixed_pt)), fixed_point(apply(apply(b, apply(apply(b, apply(apply(n, apply(apply(b, b), apply(apply(n, apply(n, apply(b, b))), n))), n)), b)), b)), true)
% 71.40/9.27 = { by axiom 4 (strong_fixed_point) }
% 71.40/9.27 true
% 71.40/9.27 % SZS output end Proof
% 71.40/9.27
% 71.40/9.27 RESULT: Unsatisfiable (the axioms are contradictory).
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