0.04/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.04/0.14	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.13/0.35	% Computer   : n006.cluster.edu
0.13/0.35	% Model      : x86_64 x86_64
0.13/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.35	% Memory     : 8042.1875MB
0.13/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.35	% CPULimit   : 180
0.13/0.35	% DateTime   : Thu Aug 29 10:34:54 EDT 2019
0.13/0.35	% CPUTime    : 
0.20/0.37	% SZS status Unsatisfiable
0.20/0.37	
0.20/0.37	% SZS output start Proof
0.20/0.37	Take the following subset of the input axioms:
0.20/0.37	  fof(prove_these_axioms_4, negated_conjecture, multiply(b, a)!=multiply(a, b)).
0.20/0.37	  fof(single_axiom, axiom, ![A, B, C]: multiply(A, multiply(multiply(inverse(multiply(A, B)), C), B))=C).
0.20/0.37	
0.20/0.37	Now clausify the problem and encode Horn clauses using encoding 3 of
0.20/0.37	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.20/0.37	We repeatedly replace C & s=t => u=v by the two clauses:
0.20/0.37	  fresh(y, y, x1...xn) = u
0.20/0.37	  C => fresh(s, t, x1...xn) = v
0.20/0.37	where fresh is a fresh function symbol and x1..xn are the free
0.20/0.37	variables of u and v.
0.20/0.37	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.20/0.37	input problem has no model of domain size 1).
0.20/0.37	
0.20/0.37	The encoding turns the above axioms into the following unit equations and goals:
0.20/0.37	
0.20/0.37	Axiom 1 (single_axiom): multiply(X, multiply(multiply(inverse(multiply(X, Y)), Z), Y)) = Z.
0.20/0.37	
0.20/0.37	Lemma 2: multiply(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W), Z) = multiply(X, multiply(W, Y)).
0.20/0.37	Proof:
0.20/0.37	  multiply(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W), Z)
0.20/0.37	= { by axiom 1 (single_axiom) }
0.20/0.37	  multiply(X, multiply(multiply(inverse(multiply(X, Y)), multiply(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W), Z)), Y))
0.20/0.37	= { by axiom 1 (single_axiom) }
0.20/0.37	  multiply(X, multiply(W, Y))
0.20/0.37	
0.20/0.37	Lemma 3: multiply(multiply(inverse(W), Y), multiply(X, multiply(W, Z))) = multiply(X, multiply(Y, Z)).
0.20/0.37	Proof:
0.20/0.37	  multiply(multiply(inverse(W), Y), multiply(X, multiply(W, Z)))
0.20/0.37	= { by axiom 1 (single_axiom) }
0.20/0.37	  multiply(multiply(inverse(multiply(inverse(multiply(X, Z)), multiply(multiply(inverse(multiply(inverse(multiply(X, Z)), ?)), W), ?))), Y), multiply(X, multiply(W, Z)))
0.20/0.37	= { by lemma 2 }
0.20/0.37	  multiply(multiply(inverse(multiply(inverse(multiply(X, Z)), multiply(multiply(inverse(multiply(inverse(multiply(X, Z)), ?)), W), ?))), Y), multiply(multiply(inverse(multiply(inverse(multiply(X, Z)), ?)), W), ?))
0.20/0.37	= { by lemma 2 }
0.20/0.37	  multiply(X, multiply(Y, Z))
0.20/0.37	
0.20/0.37	Lemma 4: multiply(X, multiply(Y, Z)) = multiply(Y, multiply(X, Z)).
0.20/0.37	Proof:
0.20/0.37	  multiply(X, multiply(Y, Z))
0.20/0.37	= { by lemma 3 }
0.20/0.37	  multiply(multiply(inverse(?), Y), multiply(X, multiply(?, Z)))
0.20/0.37	= { by lemma 3 }
0.20/0.37	  multiply(multiply(inverse(Y), X), multiply(multiply(inverse(?), Y), multiply(Y, multiply(?, Z))))
0.20/0.37	= { by lemma 3 }
0.20/0.37	  multiply(multiply(inverse(Y), X), multiply(Y, multiply(Y, Z)))
0.20/0.37	= { by lemma 3 }
0.20/0.37	  multiply(Y, multiply(X, Z))
0.20/0.37	
0.20/0.37	Lemma 5: multiply(X, multiply(inverse(Y), Y)) = X.
0.20/0.37	Proof:
0.20/0.37	  multiply(X, multiply(inverse(Y), Y))
0.20/0.37	= { by lemma 4 }
0.20/0.37	  multiply(inverse(Y), multiply(X, Y))
0.20/0.37	= { by axiom 1 (single_axiom) }
0.20/0.37	  multiply(inverse(multiply(?, multiply(multiply(inverse(multiply(?, ?)), Y), ?))), multiply(X, Y))
0.20/0.37	= { by axiom 1 (single_axiom) }
0.20/0.37	  multiply(inverse(multiply(?, multiply(multiply(inverse(multiply(?, ?)), Y), ?))), multiply(X, multiply(?, multiply(multiply(inverse(multiply(?, ?)), Y), ?))))
0.20/0.37	= { by lemma 4 }
0.20/0.37	  multiply(inverse(multiply(?, multiply(multiply(inverse(multiply(?, ?)), Y), ?))), multiply(?, multiply(X, multiply(multiply(inverse(multiply(?, ?)), Y), ?))))
0.20/0.37	= { by lemma 2 }
0.20/0.37	  multiply(inverse(multiply(?, multiply(multiply(inverse(multiply(?, ?)), Y), ?))), multiply(multiply(inverse(multiply(inverse(multiply(?, multiply(multiply(inverse(multiply(?, ?)), Y), ?))), ?)), X), ?))
0.20/0.37	= { by axiom 1 (single_axiom) }
0.20/0.37	  X
0.20/0.37	
0.20/0.37	Goal 1 (prove_these_axioms_4): multiply(b, a) = multiply(a, b).
0.20/0.37	Proof:
0.20/0.37	  multiply(b, a)
0.20/0.37	= { by lemma 5 }
0.20/0.37	  multiply(b, multiply(a, multiply(inverse(?), ?)))
0.20/0.37	= { by lemma 4 }
0.20/0.37	  multiply(a, multiply(b, multiply(inverse(?), ?)))
0.20/0.37	= { by lemma 5 }
0.20/0.37	  multiply(a, b)
0.20/0.37	% SZS output end Proof
0.20/0.37	
0.20/0.37	RESULT: Unsatisfiable (the axioms are contradictory).
0.20/0.38	EOF