0.07/0.12	% 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
0.13/0.34	% Computer   : n024.cluster.edu
0.13/0.34	% Model      : x86_64 x86_64
0.13/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory     : 8042.1875MB
0.13/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 180
0.13/0.34	% DateTime   : Thu Aug 29 10:40:20 EDT 2019
0.13/0.34	% 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(prove_these_axioms_3, negated_conjecture, multiply(multiply(a3, b3), c3)!=multiply(a3, multiply(b3, c3))).
0.13/0.37	  fof(single_axiom, axiom, ![A, B, C]: multiply(multiply(multiply(A, B), C), inverse(multiply(A, C)))=B).
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): multiply(multiply(multiply(X, Y), Z), inverse(multiply(X, Z))) = Y.
0.13/0.37	
0.13/0.37	Lemma 2: multiply(Y, inverse(multiply(multiply(Z, Y), inverse(multiply(Z, X))))) = X.
0.13/0.37	Proof:
0.13/0.37	  multiply(Y, inverse(multiply(multiply(Z, Y), inverse(multiply(Z, X)))))
0.13/0.37	= { by axiom 1 (single_axiom) }
0.13/0.37	  multiply(multiply(multiply(multiply(Z, Y), X), inverse(multiply(Z, X))), inverse(multiply(multiply(Z, Y), inverse(multiply(Z, X)))))
0.13/0.37	= { by axiom 1 (single_axiom) }
0.13/0.37	  X
0.13/0.37	
0.13/0.37	Lemma 3: inverse(multiply(multiply(X, Y), inverse(multiply(X, Z)))) = multiply(multiply(Z, ?), inverse(multiply(Y, ?))).
0.13/0.37	Proof:
0.13/0.37	  inverse(multiply(multiply(X, Y), inverse(multiply(X, Z))))
0.13/0.37	= { by axiom 1 (single_axiom) }
0.13/0.37	  multiply(multiply(multiply(Y, inverse(multiply(multiply(X, Y), inverse(multiply(X, Z))))), ?), inverse(multiply(Y, ?)))
0.13/0.37	= { by lemma 2 }
0.13/0.37	  multiply(multiply(Z, ?), inverse(multiply(Y, ?)))
0.13/0.37	
0.13/0.37	Lemma 4: multiply(X, multiply(multiply(?, ?), inverse(multiply(?, ?)))) = X.
0.13/0.37	Proof:
0.13/0.37	  multiply(X, multiply(multiply(?, ?), inverse(multiply(?, ?))))
0.13/0.37	= { by lemma 3 }
0.13/0.37	  multiply(X, inverse(multiply(multiply(?, ?), inverse(multiply(?, ?)))))
0.13/0.37	= { by lemma 2 }
0.13/0.37	  multiply(X, inverse(multiply(multiply(multiply(?, inverse(multiply(multiply(?, ?), inverse(multiply(?, ?))))), ?), inverse(multiply(?, ?)))))
0.13/0.37	= { by axiom 1 (single_axiom) }
0.13/0.37	  multiply(X, inverse(inverse(multiply(multiply(?, ?), inverse(multiply(?, ?))))))
0.13/0.37	= { by axiom 1 (single_axiom) }
0.13/0.37	  multiply(X, inverse(multiply(multiply(multiply(?, inverse(multiply(multiply(?, ?), inverse(multiply(?, ?))))), X), inverse(multiply(?, X)))))
0.13/0.37	= { by lemma 2 }
0.13/0.37	  multiply(X, inverse(multiply(multiply(?, X), inverse(multiply(?, X)))))
0.13/0.37	= { by lemma 2 }
0.13/0.38	  X
0.13/0.38	
0.13/0.38	Lemma 5: multiply(multiply(Y, X), inverse(Y)) = X.
0.13/0.38	Proof:
0.13/0.38	  multiply(multiply(Y, X), inverse(Y))
0.13/0.38	= { by lemma 4 }
0.13/0.38	  multiply(multiply(multiply(Y, X), multiply(multiply(?, ?), inverse(multiply(?, ?)))), inverse(Y))
0.13/0.38	= { by lemma 4 }
0.13/0.38	  multiply(multiply(multiply(Y, X), multiply(multiply(?, ?), inverse(multiply(?, ?)))), inverse(multiply(Y, multiply(multiply(?, ?), inverse(multiply(?, ?))))))
0.13/0.38	= { by axiom 1 (single_axiom) }
0.13/0.38	  X
0.13/0.38	
0.13/0.38	Lemma 6: multiply(Y, inverse(multiply(X, Y))) = inverse(X).
0.13/0.38	Proof:
0.13/0.38	  multiply(Y, inverse(multiply(X, Y)))
0.13/0.38	= { by lemma 5 }
0.13/0.38	  multiply(multiply(multiply(X, Y), inverse(X)), inverse(multiply(X, Y)))
0.13/0.38	= { by lemma 5 }
0.13/0.38	  inverse(X)
0.13/0.38	
0.13/0.38	Lemma 7: multiply(Y, inverse(inverse(X))) = multiply(X, Y).
0.13/0.38	Proof:
0.13/0.38	  multiply(Y, inverse(inverse(X)))
0.13/0.38	= { by lemma 6 }
0.13/0.38	  multiply(Y, inverse(multiply(multiply(X, Y), inverse(multiply(X, multiply(X, Y))))))
0.13/0.38	= { by lemma 2 }
0.13/0.38	  multiply(X, Y)
0.13/0.38	
0.13/0.38	Lemma 8: multiply(multiply(X, inverse(X)), Y) = Y.
0.13/0.38	Proof:
0.13/0.38	  multiply(multiply(X, inverse(X)), Y)
0.13/0.38	= { by axiom 1 (single_axiom) }
0.13/0.38	  multiply(multiply(multiply(X, multiply(multiply(X, inverse(X)), Y)), inverse(X)), inverse(multiply(X, inverse(X))))
0.13/0.38	= { by lemma 5 }
0.13/0.38	  multiply(multiply(multiply(X, inverse(X)), Y), inverse(multiply(X, inverse(X))))
0.13/0.38	= { by lemma 5 }
0.13/0.38	  Y
0.13/0.38	
0.13/0.38	Lemma 9: multiply(X, Y) = multiply(Y, X).
0.13/0.38	Proof:
0.13/0.38	  multiply(X, Y)
0.13/0.38	= { by lemma 5 }
0.13/0.38	  multiply(multiply(inverse(Y), multiply(X, Y)), inverse(inverse(Y)))
0.13/0.38	= { by lemma 5 }
0.13/0.38	  multiply(multiply(multiply(Y, multiply(inverse(Y), multiply(X, Y))), inverse(Y)), inverse(inverse(Y)))
0.13/0.38	= { by lemma 7 }
0.13/0.38	  multiply(multiply(multiply(multiply(inverse(Y), multiply(X, Y)), inverse(inverse(Y))), inverse(Y)), inverse(inverse(Y)))
0.13/0.38	= { by lemma 5 }
0.13/0.38	  multiply(multiply(multiply(X, Y), inverse(Y)), inverse(inverse(Y)))
0.13/0.38	= { by lemma 8 }
0.13/0.38	  multiply(multiply(multiply(multiply(multiply(?, inverse(?)), X), Y), inverse(Y)), inverse(inverse(Y)))
0.13/0.38	= { by lemma 8 }
0.13/0.38	  multiply(multiply(multiply(multiply(multiply(?, inverse(?)), X), Y), inverse(multiply(multiply(?, inverse(?)), Y))), inverse(inverse(Y)))
0.13/0.38	= { by axiom 1 (single_axiom) }
0.13/0.38	  multiply(X, inverse(inverse(Y)))
0.13/0.38	= { by lemma 7 }
0.13/0.38	  multiply(Y, X)
0.13/0.38	
0.13/0.38	Lemma 10: inverse(multiply(X, inverse(Y))) = multiply(Y, inverse(X)).
0.13/0.38	Proof:
0.13/0.38	  inverse(multiply(X, inverse(Y)))
0.13/0.38	= { by lemma 5 }
0.13/0.38	  multiply(multiply(inverse(Y), inverse(multiply(X, inverse(Y)))), inverse(inverse(Y)))
0.13/0.38	= { by lemma 6 }
0.13/0.38	  multiply(inverse(X), inverse(inverse(Y)))
0.13/0.38	= { by lemma 7 }
0.13/0.38	  multiply(Y, inverse(X))
0.13/0.38	
0.13/0.38	Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
0.13/0.38	Proof:
0.13/0.38	  multiply(multiply(a3, b3), c3)
0.13/0.38	= { by lemma 9 }
0.13/0.38	  multiply(c3, multiply(a3, b3))
0.13/0.38	= { by lemma 9 }
0.13/0.38	  multiply(c3, multiply(b3, a3))
0.13/0.38	= { by lemma 9 }
0.13/0.38	  multiply(multiply(b3, a3), c3)
0.13/0.38	= { by lemma 5 }
0.13/0.38	  multiply(multiply(?, multiply(multiply(b3, a3), c3)), inverse(?))
0.13/0.38	= { by lemma 9 }
0.13/0.38	  multiply(multiply(multiply(multiply(b3, a3), c3), ?), inverse(?))
0.13/0.38	= { by lemma 4 }
0.13/0.38	  multiply(multiply(multiply(multiply(b3, a3), c3), ?), inverse(multiply(?, multiply(multiply(?, ?), inverse(multiply(?, ?))))))
0.13/0.38	= { by lemma 9 }
0.13/0.38	  multiply(multiply(multiply(multiply(b3, a3), c3), ?), inverse(multiply(multiply(multiply(?, ?), inverse(multiply(?, ?))), ?)))
0.13/0.38	= { by lemma 3 }
0.13/0.38	  inverse(multiply(multiply(?, multiply(multiply(?, ?), inverse(multiply(?, ?)))), inverse(multiply(?, multiply(multiply(b3, a3), c3)))))
0.13/0.38	= { by lemma 2 }
0.13/0.38	  multiply(multiply(b3, c3), inverse(multiply(multiply(multiply(multiply(?, ?), inverse(multiply(?, ?))), multiply(b3, c3)), inverse(multiply(multiply(multiply(?, ?), inverse(multiply(?, ?))), inverse(multiply(multiply(?, multiply(multiply(?, ?), inverse(multiply(?, ?)))), inverse(multiply(?, multiply(multiply(b3, a3), c3))))))))))
0.13/0.38	= { by lemma 2 }
0.13/0.38	  multiply(multiply(b3, c3), inverse(multiply(multiply(multiply(multiply(?, ?), inverse(multiply(?, ?))), multiply(b3, c3)), inverse(multiply(multiply(b3, a3), c3)))))
0.13/0.38	= { by lemma 10 }
0.13/0.38	  multiply(multiply(b3, c3), multiply(multiply(multiply(b3, a3), c3), inverse(multiply(multiply(multiply(?, ?), inverse(multiply(?, ?))), multiply(b3, c3)))))
0.13/0.38	= { by lemma 9 }
0.13/0.38	  multiply(multiply(b3, c3), multiply(multiply(multiply(b3, a3), c3), inverse(multiply(multiply(b3, c3), multiply(multiply(?, ?), inverse(multiply(?, ?)))))))
0.13/0.38	= { by lemma 4 }
0.13/0.38	  multiply(multiply(b3, c3), multiply(multiply(multiply(b3, a3), c3), inverse(multiply(b3, c3))))
0.13/0.38	= { by axiom 1 (single_axiom) }
0.13/0.38	  multiply(multiply(b3, c3), a3)
0.13/0.38	= { by lemma 9 }
0.13/0.38	  multiply(a3, multiply(b3, c3))
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