0.06/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.12	% 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 : n028.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 : 1440
0.13/0.33	% WCLimit  : 180
0.13/0.33	% DateTime : Mon Jul  3 04:46:58 EDT 2023
0.13/0.33	% CPUTime  : 
5.09/1.01	% SZS status Unsatisfiable
5.09/1.01	
5.09/1.02	% SZS output start Proof
5.09/1.02	Axiom 1 (t_definition): apply(apply(t, X), Y) = apply(Y, X).
5.09/1.02	Axiom 2 (b_definition): apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)).
5.09/1.02	
5.09/1.02	Goal 1 (prove_c_combinator): apply(apply(apply(X, f(X)), g(X)), h(X)) = apply(apply(f(X), h(X)), g(X)).
5.09/1.02	The goal is true when:
5.09/1.02	  X = apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))
5.09/1.02	
5.09/1.02	Proof:
5.09/1.02	  apply(apply(apply(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)), f(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), g(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), h(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))
5.09/1.02	= { by axiom 2 (b_definition) }
5.09/1.02	  apply(apply(apply(apply(t, apply(apply(b, b), t)), apply(apply(apply(b, b), t), f(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))), g(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), h(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))
5.09/1.02	= { by axiom 1 (t_definition) }
5.09/1.02	  apply(apply(apply(apply(apply(apply(b, b), t), f(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), apply(apply(b, b), t)), g(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), h(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))
5.09/1.02	= { by axiom 2 (b_definition) }
5.09/1.02	  apply(apply(apply(apply(b, apply(t, f(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))), apply(apply(b, b), t)), g(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), h(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))
5.09/1.02	= { by axiom 2 (b_definition) }
5.09/1.02	  apply(apply(apply(t, f(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), apply(apply(apply(b, b), t), g(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))), h(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))
5.09/1.02	= { by axiom 1 (t_definition) }
5.09/1.02	  apply(apply(apply(apply(apply(b, b), t), g(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), f(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), h(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))
5.09/1.02	= { by axiom 2 (b_definition) }
5.09/1.02	  apply(apply(apply(b, apply(t, g(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))), f(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), h(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))
5.09/1.02	= { by axiom 2 (b_definition) }
5.09/1.02	  apply(apply(t, g(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), apply(f(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))), h(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))))
5.09/1.02	= { by axiom 1 (t_definition) }
5.09/1.02	  apply(apply(f(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))), h(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t)))), g(apply(apply(b, apply(t, apply(apply(b, b), t))), apply(apply(b, b), t))))
5.09/1.02	% SZS output end Proof
5.09/1.02	
5.09/1.02	RESULT: Unsatisfiable (the axioms are contradictory).
5.09/1.03	EOF