0.07/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.13/0.34	% Computer : n011.cluster.edu
0.13/0.34	% Model    : x86_64 x86_64
0.13/0.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory   : 8042.1875MB
0.13/0.34	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit : 1440
0.13/0.34	% WCLimit  : 180
0.13/0.34	% DateTime : Mon Jul  3 04:15:54 EDT 2023
0.13/0.34	% CPUTime  : 
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(X, Y) = apply(apply(t, 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_q_combinator): apply(apply(apply(X, f(X)), g(X)), h(X)) = apply(g(X), apply(f(X), h(X))).
0.20/0.50	The goal is true when:
0.20/0.50	  X = apply(apply(b, apply(t, b)), apply(apply(b, b), t))
0.20/0.50	
0.20/0.50	Proof:
0.20/0.50	  apply(apply(apply(apply(apply(b, apply(t, b)), apply(apply(b, b), t)), f(apply(apply(b, apply(t, b)), apply(apply(b, b), t)))), g(apply(apply(b, apply(t, b)), apply(apply(b, b), t)))), h(apply(apply(b, apply(t, b)), apply(apply(b, b), t))))
0.20/0.50	= { by axiom 2 (b_definition) }
0.20/0.50	  apply(apply(apply(apply(t, b), apply(apply(apply(b, b), t), f(apply(apply(b, apply(t, b)), apply(apply(b, b), t))))), g(apply(apply(b, apply(t, b)), apply(apply(b, b), t)))), h(apply(apply(b, apply(t, b)), apply(apply(b, b), t))))
0.20/0.50	= { by axiom 1 (t_definition) R->L }
0.20/0.50	  apply(apply(apply(apply(apply(apply(b, b), t), f(apply(apply(b, apply(t, b)), apply(apply(b, b), t)))), b), g(apply(apply(b, apply(t, b)), apply(apply(b, b), t)))), h(apply(apply(b, apply(t, b)), apply(apply(b, b), t))))
0.20/0.50	= { by axiom 2 (b_definition) }
0.20/0.50	  apply(apply(apply(apply(b, apply(t, f(apply(apply(b, apply(t, b)), apply(apply(b, b), t))))), b), g(apply(apply(b, apply(t, b)), apply(apply(b, b), t)))), h(apply(apply(b, apply(t, b)), apply(apply(b, b), t))))
0.20/0.50	= { by axiom 2 (b_definition) }
0.20/0.50	  apply(apply(apply(t, f(apply(apply(b, apply(t, b)), apply(apply(b, b), t)))), apply(b, g(apply(apply(b, apply(t, b)), apply(apply(b, b), t))))), h(apply(apply(b, apply(t, b)), apply(apply(b, b), t))))
0.20/0.50	= { by axiom 1 (t_definition) R->L }
0.20/0.50	  apply(apply(apply(b, g(apply(apply(b, apply(t, b)), apply(apply(b, b), t)))), f(apply(apply(b, apply(t, b)), apply(apply(b, b), t)))), h(apply(apply(b, apply(t, b)), apply(apply(b, b), t))))
0.20/0.50	= { by axiom 2 (b_definition) }
0.20/0.50	  apply(g(apply(apply(b, apply(t, b)), apply(apply(b, b), t))), apply(f(apply(apply(b, apply(t, b)), apply(apply(b, b), t))), h(apply(apply(b, apply(t, b)), apply(apply(b, b), t)))))
0.20/0.50	% SZS output end Proof
0.20/0.50	
0.20/0.50	RESULT: Unsatisfiable (the axioms are contradictory).
0.20/0.50	EOF