0.03/0.14	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.15	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.15/0.37	% Computer   : n017.cluster.edu
0.15/0.37	% Model      : x86_64 x86_64
0.15/0.37	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.15/0.37	% Memory     : 8042.1875MB
0.15/0.37	% OS         : Linux 3.10.0-693.el7.x86_64
0.15/0.37	% CPULimit   : 180
0.15/0.37	% DateTime   : Thu Aug 29 11:01:34 EDT 2019
0.15/0.37	% CPUTime    : 
0.23/0.41	% SZS status Unsatisfiable
0.23/0.41	
0.23/0.41	% SZS output start Proof
0.23/0.41	Take the following subset of the input axioms:
0.23/0.41	  fof(prove_these_axioms_3, negated_conjecture, multiply(multiply(a3, b3), c3)!=multiply(a3, multiply(b3, c3))).
0.23/0.41	  fof(single_axiom, axiom, ![C, A, B, D]: C=inverse(multiply(multiply(multiply(inverse(multiply(multiply(A, B), C)), A), B), multiply(D, inverse(D))))).
0.23/0.41	
0.23/0.41	Now clausify the problem and encode Horn clauses using encoding 3 of
0.23/0.41	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.23/0.41	We repeatedly replace C & s=t => u=v by the two clauses:
0.23/0.41	  fresh(y, y, x1...xn) = u
0.23/0.41	  C => fresh(s, t, x1...xn) = v
0.23/0.41	where fresh is a fresh function symbol and x1..xn are the free
0.23/0.41	variables of u and v.
0.23/0.41	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.23/0.41	input problem has no model of domain size 1).
0.23/0.41	
0.23/0.41	The encoding turns the above axioms into the following unit equations and goals:
0.23/0.41	
0.23/0.41	Axiom 1 (single_axiom): X = inverse(multiply(multiply(multiply(inverse(multiply(multiply(Y, Z), X)), Y), Z), multiply(W, inverse(W)))).
0.23/0.41	
0.23/0.41	Lemma 2: multiply(X, inverse(X)) = multiply(?, inverse(?)).
0.23/0.41	Proof:
0.23/0.41	  multiply(X, inverse(X))
0.23/0.41	= { by axiom 1 (single_axiom) }
0.23/0.41	  inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(Z, W), Y)), Z), W), multiply(X, inverse(X)))), multiply(inverse(multiply(multiply(Z, W), Y)), Z)), W), multiply(V, inverse(V))))
0.23/0.41	= { by axiom 1 (single_axiom) }
0.23/0.41	  inverse(multiply(multiply(multiply(Y, multiply(inverse(multiply(multiply(Z, W), Y)), Z)), W), multiply(V, inverse(V))))
0.23/0.41	= { by axiom 1 (single_axiom) }
0.23/0.41	  inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(Z, W), Y)), Z), W), multiply(?, inverse(?)))), multiply(inverse(multiply(multiply(Z, W), Y)), Z)), W), multiply(V, inverse(V))))
0.23/0.41	= { by axiom 1 (single_axiom) }
0.23/0.41	  multiply(?, inverse(?))
0.23/0.41	
0.23/0.41	Lemma 3: inverse(multiply(multiply(multiply(inverse(multiply(?, inverse(?))), X), Y), multiply(?, inverse(?)))) = inverse(multiply(X, Y)).
0.23/0.41	Proof:
0.23/0.41	  inverse(multiply(multiply(multiply(inverse(multiply(?, inverse(?))), X), Y), multiply(?, inverse(?))))
0.23/0.41	= { by lemma 2 }
0.23/0.41	  inverse(multiply(multiply(multiply(inverse(multiply(multiply(X, Y), inverse(multiply(X, Y)))), X), Y), multiply(?, inverse(?))))
0.23/0.41	= { by axiom 1 (single_axiom) }
0.23/0.41	  inverse(multiply(X, Y))
0.23/0.41	
0.23/0.41	Lemma 4: inverse(multiply(multiply(multiply(?, inverse(?)), X), multiply(?, inverse(?)))) = inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), X)).
0.23/0.41	Proof:
0.23/0.41	  inverse(multiply(multiply(multiply(?, inverse(?)), X), multiply(?, inverse(?))))
0.23/0.41	= { by lemma 2 }
0.23/0.41	  inverse(multiply(multiply(multiply(inverse(multiply(?, inverse(?))), inverse(inverse(multiply(?, inverse(?))))), X), multiply(?, inverse(?))))
0.23/0.41	= { by lemma 3 }
0.23/0.41	  inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), X))
0.23/0.41	
0.23/0.41	Lemma 5: inverse(multiply(multiply(inverse(multiply(multiply(X, Y), inverse(multiply(?, inverse(?))))), X), Y)) = multiply(?, inverse(?)).
0.23/0.41	Proof:
0.23/0.41	  inverse(multiply(multiply(inverse(multiply(multiply(X, Y), inverse(multiply(?, inverse(?))))), X), Y))
0.23/0.41	= { by lemma 3 }
0.23/0.41	  inverse(multiply(multiply(multiply(inverse(multiply(?, inverse(?))), multiply(inverse(multiply(multiply(X, Y), inverse(multiply(?, inverse(?))))), X)), Y), multiply(?, inverse(?))))
0.23/0.41	= { by axiom 1 (single_axiom) }
0.23/0.41	  inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(X, Y), inverse(multiply(?, inverse(?))))), X), Y), multiply(?, inverse(?)))), multiply(inverse(multiply(multiply(X, Y), inverse(multiply(?, inverse(?))))), X)), Y), multiply(?, inverse(?))))
0.23/0.41	= { by axiom 1 (single_axiom) }
0.23/0.41	  multiply(?, inverse(?))
0.23/0.41	
0.23/0.41	Lemma 6: inverse(multiply(multiply(inverse(multiply(?, inverse(?))), X), inverse(X))) = multiply(?, inverse(?)).
0.23/0.41	Proof:
0.23/0.41	  inverse(multiply(multiply(inverse(multiply(?, inverse(?))), X), inverse(X)))
0.23/0.41	= { by lemma 2 }
0.23/0.41	  inverse(multiply(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(?, inverse(?))))), X), inverse(X)))
0.23/0.41	= { by lemma 2 }
0.23/0.41	  inverse(multiply(multiply(inverse(multiply(multiply(X, inverse(X)), inverse(multiply(?, inverse(?))))), X), inverse(X)))
0.23/0.41	= { by lemma 5 }
0.23/0.41	  multiply(?, inverse(?))
0.23/0.41	
0.23/0.41	Lemma 7: inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), X)) = inverse(X).
0.23/0.41	Proof:
0.23/0.41	  inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), X))
0.23/0.41	= { by lemma 4 }
0.23/0.41	  inverse(multiply(multiply(multiply(?, inverse(?)), X), multiply(?, inverse(?))))
0.23/0.41	= { by lemma 2 }
0.23/0.41	  inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(?, inverse(?)))), X), multiply(?, inverse(?))))
0.23/0.41	= { by lemma 6 }
0.23/0.41	  inverse(multiply(multiply(multiply(inverse(multiply(multiply(inverse(multiply(?, inverse(?))), X), inverse(X))), inverse(multiply(?, inverse(?)))), X), multiply(?, inverse(?))))
0.23/0.41	= { by axiom 1 (single_axiom) }
0.23/0.41	  inverse(X)
0.23/0.41	
0.23/0.41	Lemma 8: inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), inverse(multiply(?, inverse(?))))) = inverse(multiply(multiply(?, inverse(?)), multiply(?, inverse(?)))).
0.23/0.41	Proof:
0.23/0.41	  inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), inverse(multiply(?, inverse(?)))))
0.23/0.41	= { by lemma 4 }
0.23/0.41	  inverse(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(?, inverse(?)))), multiply(?, inverse(?))))
0.23/0.41	= { by lemma 2 }
0.23/0.41	  inverse(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))))
0.23/0.41	
0.23/0.41	Lemma 9: inverse(inverse(multiply(?, inverse(?)))) = multiply(?, inverse(?)).
0.23/0.41	Proof:
0.23/0.41	  inverse(inverse(multiply(?, inverse(?))))
0.23/0.41	= { by lemma 7 }
0.23/0.41	  inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), inverse(multiply(?, inverse(?)))))
0.23/0.41	= { by lemma 4 }
0.23/0.41	  inverse(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(?, inverse(?)))), multiply(?, inverse(?))))
0.23/0.41	= { by lemma 6 }
0.23/0.41	  inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(?, inverse(?))), multiply(?, inverse(?))), inverse(multiply(?, inverse(?))))), inverse(multiply(?, inverse(?)))), multiply(?, inverse(?))))
0.23/0.41	= { by lemma 5 }
0.23/0.42	  multiply(?, inverse(?))
0.23/0.42	
0.23/0.42	Lemma 10: inverse(inverse(inverse(inverse(X)))) = X.
0.23/0.42	Proof:
0.23/0.42	  inverse(inverse(inverse(inverse(X))))
0.23/0.42	= { by lemma 7 }
0.23/0.42	  inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), inverse(inverse(inverse(X)))))
0.23/0.42	= { by lemma 7 }
0.23/0.42	  inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), inverse(inverse(inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), X))))))
0.23/0.42	= { by lemma 9 }
0.23/0.42	  inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), inverse(inverse(inverse(multiply(multiply(?, inverse(?)), X))))))
0.23/0.42	= { by lemma 4 }
0.23/0.42	  inverse(multiply(multiply(multiply(?, inverse(?)), inverse(inverse(inverse(multiply(multiply(?, inverse(?)), X))))), multiply(?, inverse(?))))
0.23/0.42	= { by lemma 2 }
0.23/0.42	  inverse(multiply(multiply(multiply(inverse(multiply(multiply(?, inverse(?)), X)), inverse(inverse(multiply(multiply(?, inverse(?)), X)))), inverse(inverse(inverse(multiply(multiply(?, inverse(?)), X))))), multiply(?, inverse(?))))
0.23/0.42	= { by lemma 2 }
0.23/0.42	  inverse(multiply(multiply(multiply(inverse(multiply(multiply(inverse(inverse(multiply(multiply(?, inverse(?)), X))), inverse(inverse(inverse(multiply(multiply(?, inverse(?)), X))))), X)), inverse(inverse(multiply(multiply(?, inverse(?)), X)))), inverse(inverse(inverse(multiply(multiply(?, inverse(?)), X))))), multiply(?, inverse(?))))
0.23/0.42	= { by axiom 1 (single_axiom) }
0.23/0.42	  X
0.23/0.42	
0.23/0.42	Lemma 11: inverse(multiply(X, multiply(?, inverse(?)))) = inverse(X).
0.23/0.42	Proof:
0.23/0.42	  inverse(multiply(X, multiply(?, inverse(?))))
0.23/0.42	= { by lemma 10 }
0.23/0.42	  inverse(multiply(inverse(inverse(inverse(inverse(X)))), multiply(?, inverse(?))))
0.23/0.42	= { by lemma 7 }
0.23/0.42	  inverse(multiply(inverse(inverse(inverse(inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), X))))), multiply(?, inverse(?))))
0.23/0.42	= { by lemma 10 }
0.23/0.42	  inverse(multiply(multiply(inverse(inverse(multiply(?, inverse(?)))), X), multiply(?, inverse(?))))
0.23/0.42	= { by lemma 9 }
0.23/0.42	  inverse(multiply(multiply(multiply(?, inverse(?)), X), multiply(?, inverse(?))))
0.23/0.42	= { by lemma 4 }
0.23/0.42	  inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), X))
0.23/0.42	= { by lemma 7 }
0.23/0.42	  inverse(X)
0.23/0.42	
0.23/0.42	Lemma 12: multiply(X, multiply(?, inverse(?))) = X.
0.23/0.42	Proof:
0.23/0.42	  multiply(X, multiply(?, inverse(?)))
0.23/0.42	= { by lemma 10 }
0.23/0.42	  inverse(inverse(inverse(inverse(multiply(X, multiply(?, inverse(?)))))))
0.23/0.42	= { by lemma 11 }
0.23/0.42	  inverse(inverse(inverse(inverse(X))))
0.23/0.42	= { by lemma 10 }
0.23/0.42	  X
0.23/0.42	
0.23/0.42	Lemma 13: inverse(multiply(inverse(multiply(Y, X)), Y)) = X.
0.23/0.42	Proof:
0.23/0.42	  inverse(multiply(inverse(multiply(Y, X)), Y))
0.23/0.42	= { by lemma 11 }
0.23/0.42	  inverse(multiply(multiply(inverse(multiply(Y, X)), Y), multiply(?, inverse(?))))
0.23/0.42	= { by lemma 12 }
0.23/0.42	  inverse(multiply(multiply(inverse(multiply(multiply(Y, multiply(?, inverse(?))), X)), Y), multiply(?, inverse(?))))
0.23/0.42	= { by lemma 12 }
0.23/0.42	  inverse(multiply(multiply(multiply(inverse(multiply(multiply(Y, multiply(?, inverse(?))), X)), Y), multiply(?, inverse(?))), multiply(?, inverse(?))))
0.23/0.42	= { by axiom 1 (single_axiom) }
0.23/0.42	  X
0.23/0.42	
0.23/0.42	Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
0.23/0.42	Proof:
0.23/0.42	  multiply(multiply(a3, b3), c3)
0.23/0.42	= { by lemma 10 }
0.23/0.42	  inverse(inverse(inverse(inverse(multiply(multiply(a3, b3), c3)))))
0.23/0.42	= { by lemma 11 }
0.23/0.42	  inverse(inverse(inverse(inverse(multiply(multiply(multiply(a3, b3), c3), multiply(?, inverse(?)))))))
0.23/0.42	= { by lemma 13 }
0.23/0.42	  inverse(inverse(inverse(inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a3, multiply(b3, c3))), a3)), inverse(multiply(a3, multiply(b3, c3))))), b3), c3), multiply(?, inverse(?)))))))
0.23/0.42	= { by lemma 13 }
0.23/0.42	  inverse(inverse(inverse(inverse(multiply(multiply(multiply(inverse(multiply(multiply(b3, c3), inverse(multiply(a3, multiply(b3, c3))))), b3), c3), multiply(?, inverse(?)))))))
0.23/0.42	= { by axiom 1 (single_axiom) }
0.23/0.42	  inverse(inverse(inverse(inverse(multiply(a3, multiply(b3, c3))))))
0.23/0.42	= { by lemma 10 }
0.23/0.42	  multiply(a3, multiply(b3, c3))
0.23/0.42	% SZS output end Proof
0.23/0.42	
0.23/0.42	RESULT: Unsatisfiable (the axioms are contradictory).
0.23/0.42	EOF