TSTP Solution File: COL066-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : COL066-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n028.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 18:31:58 EDT 2023
% Result : Unsatisfiable 123.05s 16.42s
% Output : Proof 123.05s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL066-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n028.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 04:55:23 EDT 2023
% 0.14/0.34 % CPUTime :
% 123.05/16.42 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 123.05/16.42
% 123.05/16.42 % SZS status Unsatisfiable
% 123.05/16.42
% 123.05/16.42 % SZS output start Proof
% 123.05/16.42 Axiom 1 (w_definition): apply(apply(w, X), Y) = apply(apply(X, Y), Y).
% 123.05/16.42 Axiom 2 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
% 123.05/16.42 Axiom 3 (q_definition): apply(apply(apply(q, X), Y), Z) = apply(Y, apply(X, Z)).
% 123.05/16.42
% 123.05/16.42 Goal 1 (prove_p_combinator): apply(apply(apply(apply(X, f(X)), g(X)), g(X)), h(X)) = apply(apply(f(X), g(X)), apply(apply(f(X), g(X)), h(X))).
% 123.05/16.42 The goal is true when:
% 123.05/16.42 X = apply(apply(b, apply(w, apply(q, apply(q, b)))), q)
% 123.05/16.42
% 123.05/16.42 Proof:
% 123.05/16.42 apply(apply(apply(apply(apply(apply(b, apply(w, apply(q, apply(q, b)))), q), f(apply(apply(b, apply(w, apply(q, apply(q, b)))), q))), g(apply(apply(b, apply(w, apply(q, apply(q, b)))), q))), g(apply(apply(b, apply(w, apply(q, apply(q, b)))), q))), h(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)))
% 123.05/16.42 = { by axiom 1 (w_definition) R->L }
% 123.05/16.42 apply(apply(apply(w, apply(apply(apply(b, apply(w, apply(q, apply(q, b)))), q), f(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)))), g(apply(apply(b, apply(w, apply(q, apply(q, b)))), q))), h(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)))
% 123.05/16.42 = { by axiom 2 (b_definition) }
% 123.05/16.42 apply(apply(apply(w, apply(apply(w, apply(q, apply(q, b))), apply(q, f(apply(apply(b, apply(w, apply(q, apply(q, b)))), q))))), g(apply(apply(b, apply(w, apply(q, apply(q, b)))), q))), h(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)))
% 123.05/16.42 = { by axiom 1 (w_definition) }
% 123.05/16.42 apply(apply(apply(w, apply(apply(apply(q, apply(q, b)), apply(q, f(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)))), apply(q, f(apply(apply(b, apply(w, apply(q, apply(q, b)))), q))))), g(apply(apply(b, apply(w, apply(q, apply(q, b)))), q))), h(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)))
% 123.05/16.42 = { by axiom 3 (q_definition) }
% 123.05/16.42 apply(apply(apply(w, apply(apply(q, f(apply(apply(b, apply(w, apply(q, apply(q, b)))), q))), apply(apply(q, b), apply(q, f(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)))))), g(apply(apply(b, apply(w, apply(q, apply(q, b)))), q))), h(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)))
% 123.05/16.42 = { by axiom 1 (w_definition) }
% 123.05/16.42 apply(apply(apply(apply(apply(q, f(apply(apply(b, apply(w, apply(q, apply(q, b)))), q))), apply(apply(q, b), apply(q, f(apply(apply(b, apply(w, apply(q, apply(q, b)))), q))))), g(apply(apply(b, apply(w, apply(q, apply(q, b)))), q))), g(apply(apply(b, apply(w, apply(q, apply(q, b)))), q))), h(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)))
% 123.05/16.42 = { by axiom 3 (q_definition) }
% 123.05/16.42 apply(apply(apply(apply(apply(q, b), apply(q, f(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)))), apply(f(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)), g(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)))), g(apply(apply(b, apply(w, apply(q, apply(q, b)))), q))), h(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)))
% 123.05/16.42 = { by axiom 3 (q_definition) }
% 123.05/16.42 apply(apply(apply(apply(q, f(apply(apply(b, apply(w, apply(q, apply(q, b)))), q))), apply(b, apply(f(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)), g(apply(apply(b, apply(w, apply(q, apply(q, b)))), q))))), g(apply(apply(b, apply(w, apply(q, apply(q, b)))), q))), h(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)))
% 123.05/16.42 = { by axiom 3 (q_definition) }
% 123.05/16.42 apply(apply(apply(b, apply(f(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)), g(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)))), apply(f(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)), g(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)))), h(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)))
% 123.05/16.42 = { by axiom 1 (w_definition) R->L }
% 123.05/16.42 apply(apply(apply(w, b), apply(f(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)), g(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)))), h(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)))
% 123.05/16.42 = { by axiom 1 (w_definition) }
% 123.05/16.42 apply(apply(apply(b, apply(f(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)), g(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)))), apply(f(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)), g(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)))), h(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)))
% 123.05/16.42 = { by axiom 2 (b_definition) }
% 123.05/16.42 apply(apply(f(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)), g(apply(apply(b, apply(w, apply(q, apply(q, b)))), q))), apply(apply(f(apply(apply(b, apply(w, apply(q, apply(q, b)))), q)), g(apply(apply(b, apply(w, apply(q, apply(q, b)))), q))), h(apply(apply(b, apply(w, apply(q, apply(q, b)))), q))))
% 123.05/16.42 % SZS output end Proof
% 123.05/16.42
% 123.05/16.42 RESULT: Unsatisfiable (the axioms are contradictory).
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