0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.33	% Computer   : n013.cluster.edu
0.12/0.33	% Model      : x86_64 x86_64
0.12/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory     : 8042.1875MB
0.12/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 180
0.12/0.33	% DateTime   : Thu Aug 29 09:27:31 EDT 2019
0.12/0.34	% CPUTime    : 
0.12/0.35	% SZS status Unsatisfiable
0.12/0.35	
0.12/0.35	% SZS output start Proof
0.12/0.35	Take the following subset of the input axioms:
0.12/0.35	  fof(prove_these_axioms_1, negated_conjecture, multiply(inverse(a1), a1)!=multiply(inverse(b1), b1)).
0.12/0.35	  fof(single_axiom, axiom, ![A, B, C]: multiply(multiply(multiply(A, B), C), inverse(multiply(A, C)))=B).
0.12/0.35	
0.12/0.35	Now clausify the problem and encode Horn clauses using encoding 3 of
0.12/0.35	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.12/0.35	We repeatedly replace C & s=t => u=v by the two clauses:
0.12/0.35	  fresh(y, y, x1...xn) = u
0.12/0.35	  C => fresh(s, t, x1...xn) = v
0.12/0.35	where fresh is a fresh function symbol and x1..xn are the free
0.12/0.35	variables of u and v.
0.12/0.35	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.12/0.35	input problem has no model of domain size 1).
0.12/0.35	
0.12/0.35	The encoding turns the above axioms into the following unit equations and goals:
0.12/0.35	
0.12/0.35	Axiom 1 (single_axiom): multiply(multiply(multiply(X, Y), Z), inverse(multiply(X, Z))) = Y.
0.12/0.35	
0.12/0.35	Lemma 2: multiply(Y, inverse(multiply(multiply(Z, Y), inverse(multiply(Z, X))))) = X.
0.12/0.35	Proof:
0.12/0.35	  multiply(Y, inverse(multiply(multiply(Z, Y), inverse(multiply(Z, X)))))
0.12/0.35	= { by axiom 1 (single_axiom) }
0.12/0.35	  multiply(multiply(multiply(multiply(Z, Y), X), inverse(multiply(Z, X))), inverse(multiply(multiply(Z, Y), inverse(multiply(Z, X)))))
0.12/0.35	= { by axiom 1 (single_axiom) }
0.12/0.35	  X
0.12/0.35	
0.12/0.35	Lemma 3: multiply(X, multiply(multiply(?, ?), inverse(multiply(?, ?)))) = X.
0.12/0.35	Proof:
0.12/0.35	  multiply(X, multiply(multiply(?, ?), inverse(multiply(?, ?))))
0.12/0.35	= { by lemma 2 }
0.12/0.35	  multiply(X, multiply(multiply(multiply(?, inverse(multiply(multiply(?, ?), inverse(multiply(?, ?))))), ?), inverse(multiply(?, ?))))
0.12/0.35	= { by axiom 1 (single_axiom) }
0.12/0.35	  multiply(X, inverse(multiply(multiply(?, ?), inverse(multiply(?, ?)))))
0.12/0.35	= { by lemma 2 }
0.12/0.35	  multiply(X, inverse(multiply(multiply(multiply(?, inverse(multiply(multiply(?, ?), inverse(multiply(?, ?))))), ?), inverse(multiply(?, ?)))))
0.12/0.35	= { by axiom 1 (single_axiom) }
0.12/0.35	  multiply(X, inverse(inverse(multiply(multiply(?, ?), inverse(multiply(?, ?))))))
0.12/0.35	= { by axiom 1 (single_axiom) }
0.12/0.35	  multiply(X, inverse(multiply(multiply(multiply(?, inverse(multiply(multiply(?, ?), inverse(multiply(?, ?))))), X), inverse(multiply(?, X)))))
0.12/0.35	= { by lemma 2 }
0.12/0.35	  multiply(X, inverse(multiply(multiply(?, X), inverse(multiply(?, X)))))
0.12/0.35	= { by lemma 2 }
0.12/0.35	  X
0.12/0.35	
0.12/0.35	Lemma 4: multiply(multiply(Y, X), inverse(Y)) = X.
0.12/0.35	Proof:
0.12/0.35	  multiply(multiply(Y, X), inverse(Y))
0.12/0.35	= { by lemma 3 }
0.12/0.35	  multiply(multiply(multiply(Y, X), multiply(multiply(?, ?), inverse(multiply(?, ?)))), inverse(Y))
0.12/0.35	= { by lemma 3 }
0.12/0.35	  multiply(multiply(multiply(Y, X), multiply(multiply(?, ?), inverse(multiply(?, ?)))), inverse(multiply(Y, multiply(multiply(?, ?), inverse(multiply(?, ?))))))
0.12/0.35	= { by axiom 1 (single_axiom) }
0.12/0.36	  X
0.12/0.36	
0.12/0.36	Lemma 5: multiply(inverse(X), Y) = multiply(Y, inverse(X)).
0.12/0.36	Proof:
0.12/0.36	  multiply(inverse(X), Y)
0.12/0.36	= { by lemma 4 }
0.12/0.36	  multiply(multiply(X, multiply(inverse(X), Y)), inverse(X))
0.12/0.36	= { by lemma 2 }
0.12/0.36	  multiply(multiply(multiply(inverse(X), Y), inverse(multiply(multiply(X, multiply(inverse(X), Y)), inverse(multiply(X, multiply(X, multiply(inverse(X), Y))))))), inverse(X))
0.12/0.36	= { by lemma 4 }
0.12/0.36	  multiply(multiply(multiply(inverse(X), Y), inverse(multiply(multiply(multiply(X, multiply(X, multiply(inverse(X), Y))), inverse(X)), inverse(multiply(X, multiply(X, multiply(inverse(X), Y))))))), inverse(X))
0.12/0.36	= { by lemma 4 }
0.12/0.36	  multiply(multiply(multiply(inverse(X), Y), inverse(inverse(X))), inverse(X))
0.12/0.36	= { by lemma 4 }
0.12/0.36	  multiply(Y, inverse(X))
0.12/0.36	
0.12/0.36	Lemma 6: multiply(X, inverse(multiply(Y, inverse(Y)))) = X.
0.12/0.36	Proof:
0.12/0.36	  multiply(X, inverse(multiply(Y, inverse(Y))))
0.12/0.36	= { by lemma 4 }
0.12/0.36	  multiply(multiply(multiply(Y, X), inverse(Y)), inverse(multiply(Y, inverse(Y))))
0.12/0.36	= { by axiom 1 (single_axiom) }
0.12/0.36	  X
0.12/0.36	
0.12/0.36	Lemma 7: multiply(Y, inverse(Y)) = multiply(?, inverse(?)).
0.12/0.36	Proof:
0.12/0.36	  multiply(Y, inverse(Y))
0.12/0.36	= { by lemma 4 }
0.12/0.36	  multiply(Y, inverse(multiply(multiply(Z, Y), inverse(Z))))
0.12/0.36	= { by lemma 6 }
0.12/0.36	  multiply(Y, inverse(multiply(multiply(Z, Y), inverse(multiply(Z, inverse(multiply(X, inverse(X))))))))
0.12/0.36	= { by lemma 2 }
0.12/0.36	  inverse(multiply(X, inverse(X)))
0.12/0.36	= { by lemma 2 }
0.12/0.36	  multiply(?, inverse(multiply(multiply(Z, ?), inverse(multiply(Z, inverse(multiply(X, inverse(X))))))))
0.12/0.36	= { by lemma 6 }
0.12/0.36	  multiply(?, inverse(multiply(multiply(Z, ?), inverse(Z))))
0.12/0.36	= { by lemma 4 }
0.12/0.36	  multiply(?, inverse(?))
0.12/0.36	
0.12/0.36	Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
0.12/0.36	Proof:
0.12/0.36	  multiply(inverse(a1), a1)
0.12/0.36	= { by lemma 5 }
0.12/0.36	  multiply(a1, inverse(a1))
0.12/0.36	= { by lemma 7 }
0.12/0.36	  multiply(?, inverse(?))
0.12/0.36	= { by lemma 7 }
0.12/0.36	  multiply(b1, inverse(b1))
0.12/0.36	= { by lemma 5 }
0.12/0.36	  multiply(inverse(b1), b1)
0.12/0.36	% SZS output end Proof
0.12/0.36	
0.12/0.36	RESULT: Unsatisfiable (the axioms are contradictory).
0.12/0.36	EOF