0.07/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.35	% Computer   : n012.cluster.edu
0.12/0.35	% Model      : x86_64 x86_64
0.12/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.35	% Memory     : 8042.1875MB
0.12/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.35	% CPULimit   : 180
0.12/0.35	% DateTime   : Thu Aug 29 10:15:27 EDT 2019
0.12/0.35	% CPUTime    : 
0.12/0.38	% SZS status Unsatisfiable
0.12/0.38	
0.12/0.38	% SZS output start Proof
0.12/0.38	Take the following subset of the input axioms:
0.12/0.39	  fof(multiply, axiom, ![A, B]: multiply(A, B)=divide(A, inverse(B))).
0.12/0.39	  fof(prove_these_axioms_3, negated_conjecture, multiply(multiply(a3, b3), c3)!=multiply(a3, multiply(b3, c3))).
0.12/0.39	  fof(single_axiom, axiom, ![A, B, C, D]: divide(divide(A, A), divide(B, divide(divide(C, divide(D, B)), inverse(D))))=C).
0.12/0.39	
0.12/0.39	Now clausify the problem and encode Horn clauses using encoding 3 of
0.12/0.39	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.12/0.39	We repeatedly replace C & s=t => u=v by the two clauses:
0.12/0.39	  fresh(y, y, x1...xn) = u
0.12/0.39	  C => fresh(s, t, x1...xn) = v
0.12/0.39	where fresh is a fresh function symbol and x1..xn are the free
0.12/0.39	variables of u and v.
0.12/0.39	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.12/0.39	input problem has no model of domain size 1).
0.12/0.39	
0.12/0.39	The encoding turns the above axioms into the following unit equations and goals:
0.12/0.39	
0.12/0.39	Axiom 1 (single_axiom): divide(divide(X, X), divide(Y, divide(divide(Z, divide(W, Y)), inverse(W)))) = Z.
0.12/0.39	Axiom 2 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
0.12/0.39	
0.12/0.39	Lemma 3: divide(divide(Y, Y), divide(Z, multiply(divide(X, divide(W, Z)), W))) = X.
0.12/0.39	Proof:
0.12/0.39	  divide(divide(Y, Y), divide(Z, multiply(divide(X, divide(W, Z)), W)))
0.12/0.39	= { by axiom 2 (multiply) }
0.12/0.39	  divide(divide(Y, Y), divide(Z, divide(divide(X, divide(W, Z)), inverse(W))))
0.12/0.39	= { by axiom 1 (single_axiom) }
0.12/0.39	  X
0.12/0.39	
0.12/0.39	Lemma 4: divide(X, X) = divide(?, ?).
0.12/0.39	Proof:
0.12/0.39	  divide(X, X)
0.12/0.39	= { by lemma 3 }
0.12/0.39	  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)))
0.12/0.39	= { by axiom 1 (single_axiom) }
0.12/0.39	  divide(divide(Y, Y), divide(divide(divide(Z, divide(W, V)), inverse(W)), multiply(Z, V)))
0.12/0.39	= { by axiom 1 (single_axiom) }
0.12/0.39	  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)))
0.12/0.39	= { by lemma 3 }
0.12/0.39	  divide(?, ?)
0.12/0.39	
0.12/0.39	Lemma 5: divide(divide(?, ?), divide(Y, multiply(divide(?, ?), X))) = divide(X, Y).
0.12/0.39	Proof:
0.12/0.39	  divide(divide(?, ?), divide(Y, multiply(divide(?, ?), X)))
0.12/0.39	= { by axiom 2 (multiply) }
0.12/0.39	  divide(divide(?, ?), divide(Y, divide(divide(?, ?), inverse(X))))
0.12/0.39	= { by lemma 4 }
0.12/0.39	  divide(divide(?, ?), divide(Y, divide(divide(divide(X, Y), divide(X, Y)), inverse(X))))
0.12/0.39	= { by axiom 1 (single_axiom) }
0.12/0.39	  divide(X, Y)
0.12/0.39	
0.12/0.39	Lemma 6: divide(divide(Y, Y), divide(inverse(Z), multiply(divide(X, multiply(W, Z)), W))) = X.
0.12/0.39	Proof:
0.12/0.39	  divide(divide(Y, Y), divide(inverse(Z), multiply(divide(X, multiply(W, Z)), W)))
0.12/0.39	= { by axiom 2 (multiply) }
0.12/0.39	  divide(divide(Y, Y), divide(inverse(Z), divide(divide(X, multiply(W, Z)), inverse(W))))
0.12/0.39	= { by axiom 2 (multiply) }
0.12/0.39	  divide(divide(Y, Y), divide(inverse(Z), divide(divide(X, divide(W, inverse(Z))), inverse(W))))
0.12/0.39	= { by axiom 1 (single_axiom) }
0.12/0.39	  X
0.12/0.39	
0.12/0.39	Lemma 7: multiply(divide(?, ?), X) = X.
0.12/0.39	Proof:
0.12/0.39	  multiply(divide(?, ?), X)
0.12/0.39	= { by axiom 2 (multiply) }
0.12/0.39	  divide(divide(?, ?), inverse(X))
0.12/0.39	= { by lemma 5 }
0.12/0.39	  divide(divide(?, ?), divide(inverse(X), multiply(divide(?, ?), divide(?, ?))))
0.12/0.39	= { by lemma 4 }
0.12/0.39	  divide(divide(?, ?), divide(inverse(X), multiply(divide(divide(?, ?), divide(?, ?)), divide(?, ?))))
0.12/0.39	= { by lemma 4 }
0.12/0.39	  divide(divide(?, ?), divide(inverse(X), multiply(divide(divide(?, ?), divide(multiply(divide(?, ?), X), multiply(divide(?, ?), X))), divide(?, ?))))
0.12/0.39	= { by lemma 5 }
0.12/0.39	  divide(divide(?, ?), divide(inverse(X), multiply(divide(X, multiply(divide(?, ?), X)), divide(?, ?))))
0.12/0.39	= { by lemma 6 }
0.12/0.39	  X
0.12/0.39	
0.12/0.39	Lemma 8: divide(divide(?, ?), divide(Y, X)) = divide(X, Y).
0.12/0.39	Proof:
0.12/0.39	  divide(divide(?, ?), divide(Y, X))
0.12/0.39	= { by lemma 7 }
0.12/0.39	  divide(divide(?, ?), divide(Y, multiply(divide(?, ?), X)))
0.12/0.39	= { by lemma 4 }
0.12/0.39	  divide(divide(?, ?), divide(Y, multiply(divide(divide(X, Y), divide(X, Y)), X)))
0.12/0.39	= { by lemma 3 }
0.12/0.39	  divide(X, Y)
0.12/0.39	
0.12/0.39	Lemma 9: divide(multiply(divide(X, divide(Y, Z)), Y), Z) = X.
0.12/0.39	Proof:
0.12/0.39	  divide(multiply(divide(X, divide(Y, Z)), Y), Z)
0.12/0.39	= { by axiom 2 (multiply) }
0.12/0.39	  divide(divide(divide(X, divide(Y, Z)), inverse(Y)), Z)
0.12/0.39	= { by lemma 8 }
0.12/0.39	  divide(divide(?, ?), divide(Z, divide(divide(X, divide(Y, Z)), inverse(Y))))
0.12/0.39	= { by axiom 1 (single_axiom) }
0.12/0.40	  X
0.12/0.40	
0.12/0.40	Lemma 10: multiply(divide(X, divide(Y, Z)), Y) = multiply(X, Z).
0.12/0.40	Proof:
0.12/0.40	  multiply(divide(X, divide(Y, Z)), Y)
0.12/0.40	= { by lemma 6 }
0.12/0.40	  divide(divide(?, ?), divide(inverse(Z), multiply(divide(multiply(divide(X, divide(Y, Z)), Y), multiply(divide(multiply(divide(X, divide(Y, Z)), Y), Z), Z)), divide(multiply(divide(X, divide(Y, Z)), Y), Z))))
0.12/0.40	= { by lemma 8 }
0.12/0.40	  divide(divide(?, ?), divide(inverse(Z), multiply(divide(divide(?, ?), divide(multiply(divide(multiply(divide(X, divide(Y, Z)), Y), Z), Z), multiply(divide(X, divide(Y, Z)), Y))), divide(multiply(divide(X, divide(Y, Z)), Y), Z))))
0.12/0.40	= { by lemma 8 }
0.12/0.40	  divide(divide(?, ?), divide(inverse(Z), multiply(divide(divide(?, ?), divide(multiply(divide(divide(?, ?), divide(Z, multiply(divide(X, divide(Y, Z)), Y))), Z), multiply(divide(X, divide(Y, Z)), Y))), divide(multiply(divide(X, divide(Y, Z)), Y), Z))))
0.12/0.40	= { by axiom 2 (multiply) }
0.12/0.40	  divide(divide(?, ?), divide(inverse(Z), multiply(divide(divide(?, ?), divide(divide(divide(divide(?, ?), divide(Z, multiply(divide(X, divide(Y, Z)), Y))), inverse(Z)), multiply(divide(X, divide(Y, Z)), Y))), divide(multiply(divide(X, divide(Y, Z)), Y), Z))))
0.12/0.40	= { by lemma 7 }
0.12/0.40	  divide(divide(?, ?), divide(inverse(Z), multiply(divide(divide(?, ?), divide(divide(divide(divide(?, ?), divide(Z, multiply(divide(X, divide(Y, Z)), Y))), inverse(Z)), multiply(divide(?, ?), multiply(divide(X, divide(Y, Z)), Y)))), divide(multiply(divide(X, divide(Y, Z)), Y), Z))))
0.12/0.40	= { by axiom 1 (single_axiom) }
0.12/0.40	  divide(divide(?, ?), divide(inverse(Z), multiply(divide(divide(?, ?), divide(divide(divide(divide(?, ?), divide(Z, multiply(divide(X, divide(Y, Z)), Y))), inverse(Z)), multiply(divide(divide(?, ?), divide(multiply(divide(X, divide(Y, Z)), Y), divide(divide(divide(?, ?), divide(Z, multiply(divide(X, divide(Y, Z)), Y))), inverse(Z)))), multiply(divide(X, divide(Y, Z)), Y)))), divide(multiply(divide(X, divide(Y, Z)), Y), Z))))
0.12/0.40	= { by lemma 3 }
0.12/0.40	  divide(divide(?, ?), divide(inverse(Z), multiply(divide(?, ?), divide(multiply(divide(X, divide(Y, Z)), Y), Z))))
0.12/0.40	= { by lemma 7 }
0.12/0.40	  divide(divide(?, ?), divide(inverse(Z), divide(multiply(divide(X, divide(Y, Z)), Y), Z)))
0.12/0.40	= { by lemma 8 }
0.12/0.40	  divide(divide(multiply(divide(X, divide(Y, Z)), Y), Z), inverse(Z))
0.12/0.40	= { by axiom 2 (multiply) }
0.12/0.40	  multiply(divide(multiply(divide(X, divide(Y, Z)), Y), Z), Z)
0.12/0.40	= { by lemma 9 }
0.12/0.40	  multiply(X, Z)
0.12/0.40	
0.12/0.40	Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
0.12/0.40	Proof:
0.12/0.40	  multiply(multiply(a3, b3), c3)
0.12/0.40	= { by lemma 10 }
0.12/0.40	  multiply(multiply(divide(a3, divide(?, b3)), ?), c3)
0.12/0.40	= { by lemma 10 }
0.12/0.40	  multiply(divide(multiply(divide(a3, divide(?, b3)), ?), divide(multiply(divide(b3, divide(?, c3)), ?), c3)), multiply(divide(b3, divide(?, c3)), ?))
0.12/0.40	= { by lemma 9 }
0.12/0.40	  multiply(divide(multiply(divide(a3, divide(?, b3)), ?), b3), multiply(divide(b3, divide(?, c3)), ?))
0.12/0.40	= { by lemma 9 }
0.12/0.40	  multiply(a3, multiply(divide(b3, divide(?, c3)), ?))
0.12/0.40	= { by lemma 10 }
0.12/0.40	  multiply(a3, multiply(b3, c3))
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