TSTP Solution File: COL042-10 by Twee---2.5.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : COL042-10 : TPTP v8.2.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 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 : Mon Jun 24 04:50:16 EDT 2024
% Result : Unsatisfiable 281.35s 35.79s
% Output : Proof 281.35s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : COL042-10 : TPTP v8.2.0. Released v7.3.0.
% 0.04/0.13 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.13/0.35 % Computer : n023.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Jun 18 16:34:09 EDT 2024
% 0.13/0.35 % CPUTime :
% 281.35/35.79 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 281.35/35.79
% 281.35/35.79 % SZS status Unsatisfiable
% 281.35/35.79
% 281.35/35.80 % SZS output start Proof
% 281.35/35.80 Axiom 1 (w1_definition): apply(apply(w1, X), Y) = apply(apply(Y, X), X).
% 281.35/35.80 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 281.35/35.80 Axiom 3 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
% 281.35/35.80 Axiom 4 (strong_fixed_point): ifeq(apply(X, fixed_pt), apply(fixed_pt, apply(X, fixed_pt)), fixed_point(X), true) = true.
% 281.35/35.80
% 281.35/35.80 Lemma 5: apply(apply(w1, Z), apply(apply(b, X), Y)) = apply(apply(X, apply(Y, Z)), Z).
% 281.35/35.80 Proof:
% 281.35/35.80 apply(apply(w1, Z), apply(apply(b, X), Y))
% 281.35/35.80 = { by axiom 1 (w1_definition) }
% 281.35/35.80 apply(apply(apply(apply(b, X), Y), Z), Z)
% 281.35/35.80 = { by axiom 3 (b_definition) }
% 281.35/35.80 apply(apply(X, apply(Y, Z)), Z)
% 281.35/35.80
% 281.35/35.80 Goal 1 (prove_strong_fixed_point): fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)) = true.
% 281.35/35.80 Proof:
% 281.35/35.80 fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b))
% 281.35/35.80 = { by axiom 2 (ifeq_axiom) R->L }
% 281.35/35.80 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 281.35/35.80 = { by axiom 3 (b_definition) }
% 281.35/35.80 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b)), apply(b, fixed_pt)), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 281.35/35.80 = { by axiom 3 (b_definition) }
% 281.35/35.80 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(apply(w1, w1), apply(apply(apply(b, apply(b, w1)), b), apply(b, fixed_pt))), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 281.35/35.80 = { by axiom 1 (w1_definition) }
% 281.35/35.80 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(apply(apply(apply(apply(b, apply(b, w1)), b), apply(b, fixed_pt)), w1), w1), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 281.35/35.80 = { by axiom 3 (b_definition) }
% 281.35/35.80 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(apply(apply(apply(b, w1), apply(b, apply(b, fixed_pt))), w1), w1), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 281.35/35.80 = { by axiom 3 (b_definition) }
% 281.35/35.80 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(apply(w1, apply(apply(b, apply(b, fixed_pt)), w1)), w1), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 281.35/35.80 = { by axiom 1 (w1_definition) }
% 281.35/35.80 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(apply(w1, apply(apply(b, apply(b, fixed_pt)), w1)), apply(apply(b, apply(b, fixed_pt)), w1)), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 281.35/35.80 = { by lemma 5 }
% 281.35/35.80 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(apply(apply(b, fixed_pt), apply(w1, apply(apply(b, apply(b, fixed_pt)), w1))), apply(apply(b, apply(b, fixed_pt)), w1)), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 281.35/35.80 = { by axiom 3 (b_definition) }
% 281.35/35.80 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(fixed_pt, apply(apply(w1, apply(apply(b, apply(b, fixed_pt)), w1)), apply(apply(b, apply(b, fixed_pt)), w1))), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 281.35/35.80 = { by axiom 1 (w1_definition) R->L }
% 281.35/35.80 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(fixed_pt, apply(apply(w1, apply(apply(b, apply(b, fixed_pt)), w1)), w1)), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 281.35/35.80 = { by lemma 5 R->L }
% 281.35/35.80 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(fixed_pt, apply(apply(w1, w1), apply(apply(b, w1), apply(b, apply(b, fixed_pt))))), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 281.35/35.80 = { by axiom 3 (b_definition) R->L }
% 281.35/35.80 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(fixed_pt, apply(apply(w1, w1), apply(apply(apply(b, apply(b, w1)), b), apply(b, fixed_pt)))), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 281.35/35.80 = { by axiom 3 (b_definition) R->L }
% 281.35/35.80 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(fixed_pt, apply(apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b)), apply(b, fixed_pt))), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 281.35/35.80 = { by axiom 3 (b_definition) R->L }
% 281.35/35.80 ifeq(apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt), apply(fixed_pt, apply(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b), fixed_pt)), fixed_point(apply(apply(b, apply(apply(b, apply(w1, w1)), apply(apply(b, apply(b, w1)), b))), b)), true)
% 281.35/35.80 = { by axiom 4 (strong_fixed_point) }
% 281.35/35.80 true
% 281.35/35.80 % SZS output end Proof
% 281.35/35.80
% 281.35/35.80 RESULT: Unsatisfiable (the axioms are contradictory).
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