TSTP Solution File: COL003-10 by Twee---2.4.2
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- Process Solution
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% File : Twee---2.4.2
% Problem : COL003-10 : TPTP v8.1.2. Released v7.3.0.
% 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 : n017.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 18:31:31 EDT 2023
% Result : Unsatisfiable 0.19s 0.57s
% Output : Proof 0.19s
% 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 : COL003-10 : TPTP v8.1.2. Released v7.3.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n017.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 04:47:11 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.57
% 0.19/0.57 % SZS status Unsatisfiable
% 0.19/0.57
% 0.19/0.57 % SZS output start Proof
% 0.19/0.57 Axiom 1 (w_definition): apply(apply(w, X), Y) = apply(apply(X, Y), Y).
% 0.19/0.57 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.19/0.57 Axiom 3 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
% 0.19/0.57 Axiom 4 (strong_fixed_point): ifeq(apply(X, fixed_pt), apply(fixed_pt, apply(X, fixed_pt)), fixed_point(X), true) = true.
% 0.19/0.57
% 0.19/0.57 Lemma 5: apply(apply(w, apply(apply(b, X), Y)), Z) = apply(apply(X, apply(Y, Z)), Z).
% 0.19/0.57 Proof:
% 0.19/0.57 apply(apply(w, apply(apply(b, X), Y)), Z)
% 0.19/0.57 = { by axiom 1 (w_definition) }
% 0.19/0.57 apply(apply(apply(apply(b, X), Y), Z), Z)
% 0.19/0.57 = { by axiom 3 (b_definition) }
% 0.19/0.57 apply(apply(X, apply(Y, Z)), Z)
% 0.19/0.57
% 0.19/0.57 Goal 1 (prove_strong_fixed_point): fixed_point(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b)) = true.
% 0.19/0.57 Proof:
% 0.19/0.57 fixed_point(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b))
% 0.19/0.57 = { by axiom 2 (ifeq_axiom) R->L }
% 0.19/0.57 ifeq(apply(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b), fixed_pt), apply(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b), fixed_pt), fixed_point(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b)), true)
% 0.19/0.57 = { by axiom 3 (b_definition) }
% 0.19/0.57 ifeq(apply(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b), fixed_pt), apply(apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b)), apply(b, fixed_pt)), fixed_point(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b)), true)
% 0.19/0.57 = { by axiom 3 (b_definition) }
% 0.19/0.57 ifeq(apply(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b), fixed_pt), apply(apply(w, w), apply(apply(apply(b, apply(b, w)), b), apply(b, fixed_pt))), fixed_point(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b)), true)
% 0.19/0.57 = { by axiom 1 (w_definition) }
% 0.19/0.57 ifeq(apply(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b), fixed_pt), apply(apply(w, apply(apply(apply(b, apply(b, w)), b), apply(b, fixed_pt))), apply(apply(apply(b, apply(b, w)), b), apply(b, fixed_pt))), fixed_point(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b)), true)
% 0.19/0.57 = { by axiom 3 (b_definition) }
% 0.19/0.57 ifeq(apply(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b), fixed_pt), apply(apply(w, apply(apply(b, w), apply(b, apply(b, fixed_pt)))), apply(apply(apply(b, apply(b, w)), b), apply(b, fixed_pt))), fixed_point(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b)), true)
% 0.19/0.57 = { by lemma 5 }
% 0.19/0.57 ifeq(apply(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b), fixed_pt), apply(apply(w, apply(apply(b, apply(b, fixed_pt)), apply(apply(apply(b, apply(b, w)), b), apply(b, fixed_pt)))), apply(apply(apply(b, apply(b, w)), b), apply(b, fixed_pt))), fixed_point(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b)), true)
% 0.19/0.57 = { by lemma 5 }
% 0.19/0.57 ifeq(apply(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b), fixed_pt), apply(apply(apply(b, fixed_pt), apply(apply(apply(apply(b, apply(b, w)), b), apply(b, fixed_pt)), apply(apply(apply(b, apply(b, w)), b), apply(b, fixed_pt)))), apply(apply(apply(b, apply(b, w)), b), apply(b, fixed_pt))), fixed_point(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b)), true)
% 0.19/0.57 = { by axiom 3 (b_definition) }
% 0.19/0.57 ifeq(apply(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b), fixed_pt), apply(fixed_pt, apply(apply(apply(apply(apply(b, apply(b, w)), b), apply(b, fixed_pt)), apply(apply(apply(b, apply(b, w)), b), apply(b, fixed_pt))), apply(apply(apply(b, apply(b, w)), b), apply(b, fixed_pt)))), fixed_point(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b)), true)
% 0.19/0.57 = { by axiom 1 (w_definition) R->L }
% 0.19/0.57 ifeq(apply(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b), fixed_pt), apply(fixed_pt, apply(apply(w, apply(apply(apply(b, apply(b, w)), b), apply(b, fixed_pt))), apply(apply(apply(b, apply(b, w)), b), apply(b, fixed_pt)))), fixed_point(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b)), true)
% 0.19/0.57 = { by axiom 1 (w_definition) R->L }
% 0.19/0.57 ifeq(apply(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b), fixed_pt), apply(fixed_pt, apply(apply(w, w), apply(apply(apply(b, apply(b, w)), b), apply(b, fixed_pt)))), fixed_point(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b)), true)
% 0.19/0.57 = { by axiom 3 (b_definition) R->L }
% 0.19/0.57 ifeq(apply(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b), fixed_pt), apply(fixed_pt, apply(apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b)), apply(b, fixed_pt))), fixed_point(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b)), true)
% 0.19/0.57 = { by axiom 3 (b_definition) R->L }
% 0.19/0.57 ifeq(apply(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b), fixed_pt), apply(fixed_pt, apply(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b), fixed_pt)), fixed_point(apply(apply(b, apply(apply(b, apply(w, w)), apply(apply(b, apply(b, w)), b))), b)), true)
% 0.19/0.57 = { by axiom 4 (strong_fixed_point) }
% 0.19/0.57 true
% 0.19/0.57 % SZS output end Proof
% 0.19/0.57
% 0.19/0.57 RESULT: Unsatisfiable (the axioms are contradictory).
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