TSTP Solution File: COL061-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : COL061-1 : 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 : n020.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 18:31:52 EDT 2023
% Result : Unsatisfiable 0.20s 0.49s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL061-1 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n020.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 : Sun Aug 27 04:22:29 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.49 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.20/0.49
% 0.20/0.49 % SZS status Unsatisfiable
% 0.20/0.49
% 0.20/0.50 % SZS output start Proof
% 0.20/0.50 Axiom 1 (t_definition): apply(apply(t, X), Y) = apply(Y, X).
% 0.20/0.50 Axiom 2 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
% 0.20/0.50
% 0.20/0.50 Goal 1 (prove_q1_combinator): apply(apply(apply(X, f(X)), g(X)), h(X)) = apply(f(X), apply(h(X), g(X))).
% 0.20/0.50 The goal is true when:
% 0.20/0.50 X = apply(apply(b, apply(t, t)), apply(apply(b, b), b))
% 0.20/0.50
% 0.20/0.50 Proof:
% 0.20/0.50 apply(apply(apply(apply(apply(b, apply(t, t)), apply(apply(b, b), b)), f(apply(apply(b, apply(t, t)), apply(apply(b, b), b)))), g(apply(apply(b, apply(t, t)), apply(apply(b, b), b)))), h(apply(apply(b, apply(t, t)), apply(apply(b, b), b))))
% 0.20/0.50 = { by axiom 2 (b_definition) }
% 0.20/0.50 apply(apply(apply(apply(t, t), apply(apply(apply(b, b), b), f(apply(apply(b, apply(t, t)), apply(apply(b, b), b))))), g(apply(apply(b, apply(t, t)), apply(apply(b, b), b)))), h(apply(apply(b, apply(t, t)), apply(apply(b, b), b))))
% 0.20/0.50 = { by axiom 1 (t_definition) }
% 0.20/0.50 apply(apply(apply(apply(apply(apply(b, b), b), f(apply(apply(b, apply(t, t)), apply(apply(b, b), b)))), t), g(apply(apply(b, apply(t, t)), apply(apply(b, b), b)))), h(apply(apply(b, apply(t, t)), apply(apply(b, b), b))))
% 0.20/0.50 = { by axiom 2 (b_definition) }
% 0.20/0.50 apply(apply(apply(apply(b, apply(b, f(apply(apply(b, apply(t, t)), apply(apply(b, b), b))))), t), g(apply(apply(b, apply(t, t)), apply(apply(b, b), b)))), h(apply(apply(b, apply(t, t)), apply(apply(b, b), b))))
% 0.20/0.50 = { by axiom 2 (b_definition) }
% 0.20/0.50 apply(apply(apply(b, f(apply(apply(b, apply(t, t)), apply(apply(b, b), b)))), apply(t, g(apply(apply(b, apply(t, t)), apply(apply(b, b), b))))), h(apply(apply(b, apply(t, t)), apply(apply(b, b), b))))
% 0.20/0.50 = { by axiom 2 (b_definition) }
% 0.20/0.50 apply(f(apply(apply(b, apply(t, t)), apply(apply(b, b), b))), apply(apply(t, g(apply(apply(b, apply(t, t)), apply(apply(b, b), b)))), h(apply(apply(b, apply(t, t)), apply(apply(b, b), b)))))
% 0.20/0.50 = { by axiom 1 (t_definition) }
% 0.20/0.50 apply(f(apply(apply(b, apply(t, t)), apply(apply(b, b), b))), apply(h(apply(apply(b, apply(t, t)), apply(apply(b, b), b))), g(apply(apply(b, apply(t, t)), apply(apply(b, b), b)))))
% 0.20/0.50 % SZS output end Proof
% 0.20/0.50
% 0.20/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------