0.10/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.12	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.13/0.33	% Computer   : n021.cluster.edu
0.13/0.33	% Model      : x86_64 x86_64
0.13/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.33	% Memory     : 8042.1875MB
0.13/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.33	% CPULimit   : 1200
0.13/0.33	% WCLimit    : 120
0.13/0.33	% DateTime   : Tue Jul 13 11:44:55 EDT 2021
0.13/0.33	% CPUTime    : 
5.32/1.06	% SZS status Unsatisfiable
5.32/1.06	
5.32/1.07	% SZS output start Proof
5.32/1.07	Axiom 1 (t_definition): apply(X, Y) = apply(apply(t, Y), X).
5.32/1.07	Axiom 2 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
5.32/1.07	
5.32/1.07	Goal 1 (prove_f_combinator): apply(apply(h(X), g(X)), f(X)) = apply(apply(apply(X, f(X)), g(X)), h(X)).
5.32/1.07	The goal is true when:
5.32/1.07	  X = apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t)))
5.32/1.07	
5.32/1.07	Proof:
5.32/1.07	  apply(apply(h(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t)))), g(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t))))), f(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t)))))
5.32/1.07	= { by axiom 1 (t_definition) }
5.32/1.07	  apply(apply(t, f(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t))))), apply(h(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t)))), g(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t))))))
5.32/1.07	= { by axiom 1 (t_definition) }
5.32/1.07	  apply(apply(t, f(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t))))), apply(apply(t, g(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t))))), h(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t))))))
5.32/1.07	= { by axiom 2 (b_definition) R->L }
5.32/1.07	  apply(apply(apply(b, apply(t, f(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t)))))), apply(t, g(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t)))))), h(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t)))))
5.32/1.07	= { by axiom 2 (b_definition) R->L }
5.32/1.07	  apply(apply(apply(apply(apply(b, b), t), f(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t))))), apply(t, g(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t)))))), h(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t)))))
5.32/1.07	= { by axiom 2 (b_definition) R->L }
5.32/1.07	  apply(apply(apply(apply(b, apply(apply(apply(b, b), t), f(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t)))))), t), g(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t))))), h(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t)))))
5.32/1.07	= { by axiom 2 (b_definition) R->L }
5.32/1.07	  apply(apply(apply(apply(apply(apply(b, b), apply(apply(b, b), t)), f(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t))))), t), g(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t))))), h(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t)))))
5.32/1.07	= { by axiom 1 (t_definition) }
5.32/1.07	  apply(apply(apply(apply(t, t), apply(apply(apply(b, b), apply(apply(b, b), t)), f(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t)))))), g(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t))))), h(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t)))))
5.32/1.07	= { by axiom 2 (b_definition) R->L }
5.32/1.07	  apply(apply(apply(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t))), f(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t))))), g(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t))))), h(apply(apply(b, apply(t, t)), apply(apply(b, b), apply(apply(b, b), t)))))
5.32/1.07	% SZS output end Proof
5.32/1.07	
5.32/1.07	RESULT: Unsatisfiable (the axioms are contradictory).
5.32/1.08	EOF