0.00/0.08	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.09	% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.08/0.28	% Computer : n003.cluster.edu
0.08/0.28	% Model    : x86_64 x86_64
0.08/0.28	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.08/0.28	% Memory   : 8042.1875MB
0.08/0.28	% OS       : Linux 3.10.0-693.el7.x86_64
0.08/0.28	% CPULimit : 1440
0.08/0.28	% WCLimit  : 180
0.08/0.28	% DateTime : Mon Jul  3 04:13:45 EDT 2023
0.13/0.28	% CPUTime  : 
0.13/0.41	% SZS status Unsatisfiable
0.13/0.41	
0.13/0.42	% SZS output start Proof
0.13/0.42	Axiom 1 (t_definition): apply(apply(t, X), Y) = apply(Y, X).
0.13/0.42	Axiom 2 (b_definition): apply(X, apply(Y, Z)) = apply(apply(apply(b, X), Y), Z).
0.13/0.42	
0.13/0.42	Goal 1 (prove_q1_combinator): apply(apply(apply(X, f(X)), g(X)), h(X)) = apply(f(X), apply(h(X), g(X))).
0.13/0.42	The goal is true when:
0.13/0.42	  X = apply(apply(b, apply(t, t)), apply(apply(b, b), b))
0.13/0.42	
0.13/0.42	Proof:
0.13/0.42	  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))))
0.13/0.42	= { by axiom 2 (b_definition) R->L }
0.13/0.42	  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))))
0.13/0.42	= { by axiom 1 (t_definition) }
0.13/0.42	  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))))
0.13/0.42	= { by axiom 2 (b_definition) R->L }
0.13/0.42	  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))))
0.13/0.42	= { by axiom 2 (b_definition) R->L }
0.13/0.42	  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))))
0.13/0.42	= { by axiom 2 (b_definition) R->L }
0.13/0.42	  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)))))
0.13/0.42	= { by axiom 1 (t_definition) }
0.13/0.42	  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)))))
0.13/0.42	% SZS output end Proof
0.13/0.42	
0.13/0.42	RESULT: Unsatisfiable (the axioms are contradictory).
0.13/0.42	EOF