0.07/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.14	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.13/0.35	% Computer   : n009.cluster.edu
0.13/0.35	% Model      : x86_64 x86_64
0.13/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.35	% Memory     : 8042.1875MB
0.13/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.35	% CPULimit   : 180
0.13/0.35	% DateTime   : Thu Aug 29 10:05:27 EDT 2019
0.13/0.36	% CPUTime    : 
0.13/0.37	% SZS status Unsatisfiable
0.13/0.37	
0.13/0.37	% SZS output start Proof
0.13/0.37	Take the following subset of the input axioms:
0.13/0.37	  fof(multiply, axiom, ![A, B]: multiply(A, B)=divide(A, inverse(B))).
0.13/0.37	  fof(prove_these_axioms_2, negated_conjecture, multiply(multiply(inverse(b2), b2), a2)!=a2).
0.13/0.37	  fof(single_axiom, axiom, ![A, B, C, D]: divide(divide(A, A), divide(B, divide(divide(C, divide(D, B)), inverse(D))))=C).
0.13/0.37	
0.13/0.37	Now clausify the problem and encode Horn clauses using encoding 3 of
0.13/0.37	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.13/0.37	We repeatedly replace C & s=t => u=v by the two clauses:
0.13/0.37	  fresh(y, y, x1...xn) = u
0.13/0.37	  C => fresh(s, t, x1...xn) = v
0.13/0.37	where fresh is a fresh function symbol and x1..xn are the free
0.13/0.37	variables of u and v.
0.13/0.37	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.13/0.37	input problem has no model of domain size 1).
0.13/0.37	
0.13/0.37	The encoding turns the above axioms into the following unit equations and goals:
0.13/0.37	
0.13/0.37	Axiom 1 (single_axiom): divide(divide(X, X), divide(Y, divide(divide(Z, divide(W, Y)), inverse(W)))) = Z.
0.13/0.37	Axiom 2 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
0.13/0.37	
0.13/0.37	Lemma 3: divide(divide(Y, Y), divide(Z, multiply(divide(X, divide(W, Z)), W))) = X.
0.13/0.37	Proof:
0.13/0.37	  divide(divide(Y, Y), divide(Z, multiply(divide(X, divide(W, Z)), W)))
0.13/0.37	= { by axiom 2 (multiply) }
0.13/0.37	  divide(divide(Y, Y), divide(Z, divide(divide(X, divide(W, Z)), inverse(W))))
0.13/0.37	= { by axiom 1 (single_axiom) }
0.13/0.37	  X
0.13/0.37	
0.13/0.37	Lemma 4: divide(X, X) = divide(?, ?).
0.13/0.37	Proof:
0.13/0.37	  divide(X, X)
0.13/0.37	= { by lemma 3 }
0.13/0.37	  divide(divide(Y, Y), divide(divide(divide(Z, divide(W, V)), inverse(W)), multiply(divide(divide(X, X), divide(V, divide(divide(Z, divide(W, V)), inverse(W)))), V)))
0.13/0.37	= { by axiom 1 (single_axiom) }
0.13/0.37	  divide(divide(Y, Y), divide(divide(divide(Z, divide(W, V)), inverse(W)), multiply(Z, V)))
0.13/0.37	= { by axiom 1 (single_axiom) }
0.13/0.37	  divide(divide(Y, Y), divide(divide(divide(Z, divide(W, V)), inverse(W)), multiply(divide(divide(?, ?), divide(V, divide(divide(Z, divide(W, V)), inverse(W)))), V)))
0.13/0.37	= { by lemma 3 }
0.13/0.37	  divide(?, ?)
0.13/0.37	
0.13/0.37	Lemma 5: divide(divide(?, ?), divide(Y, multiply(divide(?, ?), X))) = divide(X, Y).
0.13/0.37	Proof:
0.13/0.37	  divide(divide(?, ?), divide(Y, multiply(divide(?, ?), X)))
0.13/0.37	= { by axiom 2 (multiply) }
0.13/0.37	  divide(divide(?, ?), divide(Y, divide(divide(?, ?), inverse(X))))
0.13/0.37	= { by lemma 4 }
0.13/0.37	  divide(divide(?, ?), divide(Y, divide(divide(divide(X, Y), divide(X, Y)), inverse(X))))
0.13/0.37	= { by axiom 1 (single_axiom) }
0.13/0.37	  divide(X, Y)
0.13/0.37	
0.13/0.37	Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
0.13/0.37	Proof:
0.13/0.37	  multiply(multiply(inverse(b2), b2), a2)
0.13/0.37	= { by axiom 2 (multiply) }
0.13/0.37	  multiply(divide(inverse(b2), inverse(b2)), a2)
0.13/0.37	= { by lemma 4 }
0.13/0.37	  multiply(divide(?, ?), a2)
0.13/0.37	= { by axiom 2 (multiply) }
0.13/0.37	  divide(divide(?, ?), inverse(a2))
0.13/0.37	= { by lemma 5 }
0.13/0.37	  divide(divide(?, ?), divide(inverse(a2), multiply(divide(?, ?), divide(?, ?))))
0.13/0.37	= { by lemma 4 }
0.13/0.37	  divide(divide(?, ?), divide(inverse(a2), multiply(divide(divide(?, ?), divide(?, ?)), divide(?, ?))))
0.13/0.37	= { by lemma 4 }
0.13/0.38	  divide(divide(?, ?), divide(inverse(a2), multiply(divide(divide(?, ?), divide(multiply(divide(?, ?), a2), multiply(divide(?, ?), a2))), divide(?, ?))))
0.13/0.38	= { by lemma 5 }
0.13/0.38	  divide(divide(?, ?), divide(inverse(a2), multiply(divide(a2, multiply(divide(?, ?), a2)), divide(?, ?))))
0.13/0.38	= { by axiom 2 (multiply) }
0.13/0.38	  divide(divide(?, ?), divide(inverse(a2), divide(divide(a2, multiply(divide(?, ?), a2)), inverse(divide(?, ?)))))
0.13/0.38	= { by axiom 2 (multiply) }
0.13/0.38	  divide(divide(?, ?), divide(inverse(a2), divide(divide(a2, divide(divide(?, ?), inverse(a2))), inverse(divide(?, ?)))))
0.13/0.38	= { by axiom 1 (single_axiom) }
0.13/0.38	  a2
0.13/0.38	% SZS output end Proof
0.13/0.38	
0.13/0.38	RESULT: Unsatisfiable (the axioms are contradictory).
0.13/0.38	EOF