0.06/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.11	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.10/0.32	% Computer   : n006.cluster.edu
0.10/0.32	% Model      : x86_64 x86_64
0.10/0.32	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.32	% Memory     : 8042.1875MB
0.10/0.32	% OS         : Linux 3.10.0-693.el7.x86_64
0.10/0.32	% CPULimit   : 180
0.10/0.32	% DateTime   : Thu Aug 29 09:51:24 EDT 2019
0.10/0.32	% CPUTime    : 
0.10/0.33	% SZS status Unsatisfiable
0.10/0.33	
0.10/0.33	% SZS output start Proof
0.10/0.33	Take the following subset of the input axioms:
0.10/0.33	  fof(multiply, axiom, ![B, A]: divide(A, inverse(B))=multiply(A, B)).
0.10/0.33	  fof(prove_these_axioms_4, negated_conjecture, multiply(b, a)!=multiply(a, b)).
0.10/0.33	  fof(single_axiom, axiom, ![B, A, C]: B=divide(A, inverse(divide(divide(B, C), divide(A, C))))).
0.10/0.33	
0.10/0.33	Now clausify the problem and encode Horn clauses using encoding 3 of
0.10/0.33	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.10/0.33	We repeatedly replace C & s=t => u=v by the two clauses:
0.10/0.33	  fresh(y, y, x1...xn) = u
0.10/0.33	  C => fresh(s, t, x1...xn) = v
0.10/0.33	where fresh is a fresh function symbol and x1..xn are the free
0.10/0.33	variables of u and v.
0.10/0.33	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.10/0.33	input problem has no model of domain size 1).
0.10/0.33	
0.10/0.33	The encoding turns the above axioms into the following unit equations and goals:
0.10/0.33	
0.10/0.33	Axiom 1 (multiply): divide(X, inverse(Y)) = multiply(X, Y).
0.10/0.33	Axiom 2 (single_axiom): X = divide(Y, inverse(divide(divide(X, Z), divide(Y, Z)))).
0.10/0.33	
0.10/0.33	Lemma 3: multiply(Y, divide(divide(X, Z), divide(Y, Z))) = X.
0.10/0.33	Proof:
0.10/0.33	  multiply(Y, divide(divide(X, Z), divide(Y, Z)))
0.10/0.33	= { by axiom 1 (multiply) }
0.10/0.33	  divide(Y, inverse(divide(divide(X, Z), divide(Y, Z))))
0.10/0.33	= { by axiom 2 (single_axiom) }
0.10/0.33	  X
0.10/0.33	
0.10/0.33	Lemma 4: multiply(Y, divide(multiply(X, Z), multiply(Y, Z))) = X.
0.10/0.33	Proof:
0.10/0.33	  multiply(Y, divide(multiply(X, Z), multiply(Y, Z)))
0.10/0.33	= { by axiom 1 (multiply) }
0.10/0.33	  multiply(Y, divide(divide(X, inverse(Z)), multiply(Y, Z)))
0.10/0.33	= { by axiom 1 (multiply) }
0.10/0.33	  multiply(Y, divide(divide(X, inverse(Z)), divide(Y, inverse(Z))))
0.10/0.33	= { by lemma 3 }
0.10/0.33	  X
0.10/0.33	
0.10/0.33	Lemma 5: multiply(X, divide(Y, Y)) = X.
0.10/0.33	Proof:
0.10/0.33	  multiply(X, divide(Y, Y))
0.10/0.33	= { by lemma 3 }
0.10/0.33	  multiply(X, divide(multiply(X, divide(divide(Y, ?), divide(X, ?))), Y))
0.10/0.33	= { by lemma 3 }
0.10/0.33	  multiply(X, divide(multiply(X, divide(divide(Y, ?), divide(X, ?))), multiply(X, divide(divide(Y, ?), divide(X, ?)))))
0.10/0.33	= { by lemma 4 }
0.10/0.33	  X
0.10/0.33	
0.10/0.33	Lemma 6: multiply(Y, divide(X, Y)) = X.
0.10/0.33	Proof:
0.10/0.33	  multiply(Y, divide(X, Y))
0.10/0.33	= { by lemma 5 }
0.10/0.33	  multiply(Y, divide(multiply(X, divide(?, ?)), Y))
0.10/0.33	= { by lemma 5 }
0.10/0.33	  multiply(Y, divide(multiply(X, divide(?, ?)), multiply(Y, divide(?, ?))))
0.10/0.33	= { by lemma 4 }
0.10/0.33	  X
0.10/0.33	
0.10/0.33	Lemma 7: multiply(inverse(divide(Y, Y)), X) = X.
0.10/0.33	Proof:
0.10/0.33	  multiply(inverse(divide(Y, Y)), X)
0.10/0.33	= { by lemma 5 }
0.10/0.33	  multiply(inverse(divide(Y, Y)), multiply(X, divide(Y, Y)))
0.10/0.33	= { by axiom 1 (multiply) }
0.10/0.33	  multiply(inverse(divide(Y, Y)), divide(X, inverse(divide(Y, Y))))
0.10/0.33	= { by lemma 6 }
0.10/0.33	  X
0.10/0.33	
0.10/0.33	Goal 1 (prove_these_axioms_4): multiply(b, a) = multiply(a, b).
0.10/0.33	Proof:
0.10/0.33	  multiply(b, a)
0.10/0.33	= { by lemma 4 }
0.10/0.33	  multiply(b, multiply(inverse(divide(?, ?)), divide(multiply(a, b), multiply(inverse(divide(?, ?)), b))))
0.10/0.33	= { by lemma 7 }
0.10/0.33	  multiply(b, divide(multiply(a, b), multiply(inverse(divide(?, ?)), b)))
0.10/0.33	= { by lemma 7 }
0.10/0.33	  multiply(b, divide(multiply(a, b), b))
0.10/0.33	= { by lemma 6 }
0.10/0.33	  multiply(a, b)
0.10/0.33	% SZS output end Proof
0.10/0.33	
0.10/0.33	RESULT: Unsatisfiable (the axioms are contradictory).
0.10/0.34	EOF