0.11/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.13	% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.12/0.34	% Computer : n024.cluster.edu
0.12/0.34	% Model    : x86_64 x86_64
0.12/0.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.34	% Memory   : 8042.1875MB
0.12/0.34	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.34	% CPULimit : 960
0.12/0.34	% WCLimit  : 120
0.12/0.34	% DateTime : Tue Aug  9 02:11:52 EDT 2022
0.12/0.34	% CPUTime  : 
0.12/0.39	% SZS status Unsatisfiable
0.12/0.39	
0.12/0.40	% SZS output start Proof
0.12/0.40	Axiom 1 (k_definition): X = apply(apply(k, X), Y).
0.12/0.40	Axiom 2 (abstraction): apply(apply(X, apply(k, Y)), apply(Z, Y)) = apply(apply(apply(abstraction, X), Z), Y).
0.12/0.40	
0.12/0.40	Goal 1 (prove_diagonal_combinator): apply(apply(X, b(X)), c(X)) = apply(b(X), b(X)).
0.12/0.40	The goal is true when:
0.12/0.40	  X = apply(apply(abstraction, abstraction), k)
0.12/0.40	
0.12/0.40	Proof:
0.12/0.40	  apply(apply(apply(apply(abstraction, abstraction), k), b(apply(apply(abstraction, abstraction), k))), c(apply(apply(abstraction, abstraction), k)))
0.12/0.40	= { by axiom 2 (abstraction) R->L }
0.12/0.40	  apply(apply(apply(abstraction, apply(k, b(apply(apply(abstraction, abstraction), k)))), apply(k, b(apply(apply(abstraction, abstraction), k)))), c(apply(apply(abstraction, abstraction), k)))
0.12/0.40	= { by axiom 2 (abstraction) R->L }
0.12/0.40	  apply(apply(apply(k, b(apply(apply(abstraction, abstraction), k))), apply(k, c(apply(apply(abstraction, abstraction), k)))), apply(apply(k, b(apply(apply(abstraction, abstraction), k))), c(apply(apply(abstraction, abstraction), k))))
0.12/0.40	= { by axiom 1 (k_definition) R->L }
0.12/0.40	  apply(apply(apply(k, b(apply(apply(abstraction, abstraction), k))), apply(k, c(apply(apply(abstraction, abstraction), k)))), b(apply(apply(abstraction, abstraction), k)))
0.12/0.40	= { by axiom 1 (k_definition) R->L }
0.12/0.40	  apply(b(apply(apply(abstraction, abstraction), k)), b(apply(apply(abstraction, abstraction), k)))
0.12/0.40	% SZS output end Proof
0.12/0.40	
0.12/0.40	RESULT: Unsatisfiable (the axioms are contradictory).
0.12/0.40	EOF