0.07/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.12	% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.12/0.33	% Computer : n002.cluster.edu
0.12/0.33	% Model    : x86_64 x86_64
0.12/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory   : 8042.1875MB
0.12/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit : 1440
0.12/0.33	% WCLimit  : 180
0.12/0.33	% DateTime : Mon Jul  3 06:40:22 EDT 2023
0.12/0.33	% CPUTime  : 
83.41/10.93	% SZS status Unsatisfiable
83.41/10.93	
83.41/10.96	% SZS output start Proof
83.41/10.96	Axiom 1 (t_definition): apply(X, Y) = apply(apply(t, Y), X).
83.41/10.96	Axiom 2 (b_definition): apply(X, apply(Y, Z)) = apply(apply(apply(b, X), Y), Z).
83.41/10.96	
83.41/10.96	Goal 1 (prove_g_combinator): apply(apply(f(X), i(X)), apply(g(X), h(X))) = apply(apply(apply(apply(X, f(X)), g(X)), h(X)), i(X)).
83.41/10.96	The goal is true when:
83.41/10.96	  X = apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))
83.41/10.96	
83.41/10.96	Proof:
83.41/10.96	  apply(apply(f(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), i(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))), apply(g(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), h(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))))
83.41/10.96	= { by axiom 1 (t_definition) }
83.41/10.96	  apply(apply(t, apply(g(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), h(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))))), apply(f(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), i(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))))
83.41/10.96	= { by axiom 2 (b_definition) }
83.41/10.96	  apply(apply(apply(b, apply(t, apply(g(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), h(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))))), f(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))), i(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))))
83.41/10.96	= { by axiom 2 (b_definition) }
83.41/10.96	  apply(apply(apply(apply(apply(b, b), t), apply(g(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), h(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))))), f(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))), i(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))))
83.41/10.96	= { by axiom 1 (t_definition) }
83.41/10.96	  apply(apply(apply(t, f(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))), apply(apply(apply(b, b), t), apply(g(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), h(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))))), i(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))))
83.41/10.96	= { by axiom 2 (b_definition) }
83.41/10.96	  apply(apply(apply(apply(b, apply(t, f(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))))), apply(apply(b, b), t)), apply(g(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), h(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))))), i(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))))
83.41/10.96	= { by axiom 2 (b_definition) }
83.41/10.96	  apply(apply(apply(apply(apply(apply(b, b), t), f(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))), apply(apply(b, b), t)), apply(g(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), h(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))))), i(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))))
83.41/10.96	= { by axiom 1 (t_definition) }
83.41/10.96	  apply(apply(apply(apply(t, apply(apply(b, b), t)), apply(apply(apply(b, b), t), f(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))))), apply(g(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), h(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))))), i(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))))
83.41/10.96	= { by axiom 2 (b_definition) }
83.41/10.96	  apply(apply(apply(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)), f(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))), apply(g(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), h(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))))), i(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))))
83.41/10.96	= { by axiom 2 (b_definition) }
83.41/10.96	  apply(apply(apply(apply(b, apply(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)), f(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))))), g(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))), h(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))), i(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))))
83.41/10.96	= { by axiom 2 (b_definition) }
83.41/10.96	  apply(apply(apply(apply(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))), f(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))), g(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))), h(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))), i(apply(apply(b, b), apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))))
83.41/10.96	% SZS output end Proof
83.41/10.96	
83.41/10.96	RESULT: Unsatisfiable (the axioms are contradictory).
83.41/10.99	EOF