0.08/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.08/0.14	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.14/0.35	% Computer   : n014.cluster.edu
0.14/0.35	% Model      : x86_64 x86_64
0.14/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.35	% Memory     : 8042.1875MB
0.14/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.35	% CPULimit   : 180
0.14/0.35	% DateTime   : Thu Aug 29 12:59:54 EDT 2019
0.14/0.35	% CPUTime    : 
0.20/0.55	% SZS status Unsatisfiable
0.20/0.55	
0.20/0.55	% SZS output start Proof
0.20/0.55	Take the following subset of the input axioms:
0.20/0.55	  fof(f01, axiom, ![B, A]: B=mult(A, ld(A, B))).
0.20/0.55	  fof(f02, axiom, ![B, A]: B=ld(A, mult(A, B))).
0.20/0.55	  fof(f03, axiom, ![B, A]: A=mult(rd(A, B), B)).
0.20/0.55	  fof(f04, axiom, ![B, A]: rd(mult(A, B), B)=A).
0.20/0.55	  fof(f05, axiom, ![B, A, C]: mult(mult(A, mult(A, A)), mult(B, C))=mult(mult(A, B), mult(mult(A, A), C))).
0.20/0.55	  fof(f06, axiom, ![B, A, C]: mult(mult(A, B), mult(C, C))=mult(mult(A, C), mult(B, C))).
0.20/0.55	  fof(goals, negated_conjecture, mult(mult(a, b), mult(a, c))!=mult(mult(a, a), mult(b, c))).
0.20/0.55	
0.20/0.55	Now clausify the problem and encode Horn clauses using encoding 3 of
0.20/0.55	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.20/0.55	We repeatedly replace C & s=t => u=v by the two clauses:
0.20/0.55	  fresh(y, y, x1...xn) = u
0.20/0.55	  C => fresh(s, t, x1...xn) = v
0.20/0.55	where fresh is a fresh function symbol and x1..xn are the free
0.20/0.55	variables of u and v.
0.20/0.55	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.20/0.55	input problem has no model of domain size 1).
0.20/0.55	
0.20/0.55	The encoding turns the above axioms into the following unit equations and goals:
0.20/0.55	
0.20/0.55	Axiom 1 (f06): mult(mult(X, Y), mult(Z, Z)) = mult(mult(X, Z), mult(Y, Z)).
0.20/0.55	Axiom 2 (f02): X = ld(Y, mult(Y, X)).
0.20/0.55	Axiom 3 (f05): mult(mult(X, mult(X, X)), mult(Y, Z)) = mult(mult(X, Y), mult(mult(X, X), Z)).
0.20/0.55	Axiom 4 (f03): X = mult(rd(X, Y), Y).
0.20/0.55	Axiom 5 (f04): rd(mult(X, Y), Y) = X.
0.20/0.55	Axiom 6 (f01): X = mult(Y, ld(Y, X)).
0.20/0.55	
0.20/0.55	Goal 1 (goals): mult(mult(a, b), mult(a, c)) = mult(mult(a, a), mult(b, c)).
0.20/0.55	Proof:
0.20/0.55	  mult(mult(a, b), mult(a, c))
0.20/0.55	= { by axiom 2 (f02) }
0.20/0.55	  ld(mult(a, mult(a, c)), mult(mult(a, mult(a, c)), mult(mult(a, b), mult(a, c))))
0.20/0.55	= { by axiom 1 (f06) }
0.20/0.55	  ld(mult(a, mult(a, c)), mult(mult(a, mult(a, b)), mult(mult(a, c), mult(a, c))))
0.20/0.55	= { by axiom 1 (f06) }
0.20/0.55	  ld(mult(a, mult(a, c)), mult(mult(a, mult(a, b)), mult(mult(a, a), mult(c, c))))
0.20/0.55	= { by axiom 3 (f05) }
0.20/0.55	  ld(mult(a, mult(a, c)), mult(mult(a, mult(a, a)), mult(mult(a, b), mult(c, c))))
0.20/0.55	= { by axiom 6 (f01) }
0.20/0.55	  ld(mult(a, mult(a, c)), mult(mult(a, mult(a, a)), mult(mult(a, c), ld(mult(a, c), mult(mult(a, b), mult(c, c))))))
0.20/0.55	= { by axiom 3 (f05) }
0.20/0.55	  ld(mult(a, mult(a, c)), mult(mult(a, mult(a, c)), mult(mult(a, a), ld(mult(a, c), mult(mult(a, b), mult(c, c))))))
0.20/0.55	= { by axiom 2 (f02) }
0.20/0.55	  mult(mult(a, a), ld(mult(a, c), mult(mult(a, b), mult(c, c))))
0.20/0.55	= { by axiom 6 (f01) }
0.20/0.55	  mult(mult(a, a), ld(mult(a, c), mult(mult(rd(mult(a, c), c), ld(rd(mult(a, c), c), mult(a, b))), mult(c, c))))
0.20/0.55	= { by axiom 1 (f06) }
0.20/0.55	  mult(mult(a, a), ld(mult(a, c), mult(mult(rd(mult(a, c), c), c), mult(ld(rd(mult(a, c), c), mult(a, b)), c))))
0.20/0.55	= { by axiom 4 (f03) }
0.20/0.55	  mult(mult(a, a), ld(mult(a, c), mult(mult(a, c), mult(ld(rd(mult(a, c), c), mult(a, b)), c))))
0.20/0.55	= { by axiom 2 (f02) }
0.20/0.55	  mult(mult(a, a), mult(ld(rd(mult(a, c), c), mult(a, b)), c))
0.20/0.55	= { by axiom 5 (f04) }
0.20/0.55	  mult(mult(a, a), mult(ld(a, mult(a, b)), c))
0.20/0.55	= { by axiom 2 (f02) }
0.20/0.55	  mult(mult(a, a), mult(b, c))
0.20/0.55	% SZS output end Proof
0.20/0.55	
0.20/0.55	RESULT: Unsatisfiable (the axioms are contradictory).
0.20/0.55	EOF