0.00/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.34	% Computer   : n003.cluster.edu
0.12/0.34	% Model      : x86_64 x86_64
0.12/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.34	% Memory     : 8042.1875MB
0.12/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.34	% CPULimit   : 180
0.12/0.34	% DateTime   : Thu Aug 29 13:03:32 EDT 2019
0.19/0.34	% CPUTime    : 
3.32/3.50	% SZS status Unsatisfiable
3.32/3.50	
3.32/3.50	% SZS output start Proof
3.32/3.50	Take the following subset of the input axioms:
3.32/3.50	  fof(f01, axiom, ![A, B]: mult(A, ld(A, B))=B).
3.32/3.50	  fof(f02, axiom, ![A, B]: ld(A, mult(A, B))=B).
3.32/3.50	  fof(f03, axiom, ![A, B]: mult(rd(A, B), B)=A).
3.32/3.50	  fof(f04, axiom, ![A, B]: rd(mult(A, B), B)=A).
3.32/3.50	  fof(f05, axiom, ![A, B, C]: mult(mult(A, B), mult(mult(A, A), C))=mult(mult(A, mult(A, A)), mult(B, C))).
3.32/3.50	  fof(f06, axiom, ![A, B, C]: mult(mult(A, B), mult(A, C))=mult(mult(A, A), mult(B, C))).
3.32/3.50	  fof(f07, axiom, ![A, B, C]: mult(mult(A, C), mult(B, C))=mult(mult(A, B), mult(C, C))).
3.32/3.50	  fof(goals, negated_conjecture, mult(mult(rd(a, a), b), mult(a, c))!=mult(a, mult(b, c))).
3.32/3.50	
3.32/3.50	Now clausify the problem and encode Horn clauses using encoding 3 of
3.32/3.50	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
3.32/3.50	We repeatedly replace C & s=t => u=v by the two clauses:
3.32/3.50	  fresh(y, y, x1...xn) = u
3.32/3.50	  C => fresh(s, t, x1...xn) = v
3.32/3.50	where fresh is a fresh function symbol and x1..xn are the free
3.32/3.50	variables of u and v.
3.32/3.50	A predicate p(X) is encoded as p(X)=true (this is sound, because the
3.32/3.50	input problem has no model of domain size 1).
3.32/3.50	
3.32/3.50	The encoding turns the above axioms into the following unit equations and goals:
3.32/3.50	
3.32/3.50	Axiom 1 (f07): mult(mult(X, Y), mult(Z, Y)) = mult(mult(X, Z), mult(Y, Y)).
3.32/3.50	Axiom 2 (f03): mult(rd(X, Y), Y) = X.
3.32/3.50	Axiom 3 (f02): ld(X, mult(X, Y)) = Y.
3.32/3.50	Axiom 4 (f04): rd(mult(X, Y), Y) = X.
3.32/3.50	Axiom 5 (f01): mult(X, ld(X, Y)) = Y.
3.32/3.50	Axiom 6 (f06): mult(mult(X, Y), mult(X, Z)) = mult(mult(X, X), mult(Y, Z)).
3.32/3.50	Axiom 7 (f05): mult(mult(X, Y), mult(mult(X, X), Z)) = mult(mult(X, mult(X, X)), mult(Y, Z)).
3.32/3.50	
3.32/3.50	Lemma 8: rd(mult(X, mult(Z, Z)), Y) = mult(rd(X, rd(Y, Z)), Z).
3.32/3.50	Proof:
3.32/3.50	  rd(mult(X, mult(Z, Z)), Y)
3.32/3.50	= { by axiom 2 (f03) }
3.32/3.50	  rd(mult(mult(rd(X, rd(Y, Z)), rd(Y, Z)), mult(Z, Z)), Y)
3.32/3.50	= { by axiom 1 (f07) }
3.32/3.50	  rd(mult(mult(rd(X, rd(Y, Z)), Z), mult(rd(Y, Z), Z)), Y)
3.32/3.50	= { by axiom 2 (f03) }
3.32/3.50	  rd(mult(mult(rd(X, rd(Y, Z)), Z), Y), Y)
3.32/3.50	= { by axiom 4 (f04) }
3.32/3.50	  mult(rd(X, rd(Y, Z)), Z)
3.32/3.50	
3.32/3.50	Goal 1 (goals): mult(mult(rd(a, a), b), mult(a, c)) = mult(a, mult(b, c)).
3.32/3.50	Proof:
3.32/3.50	  mult(mult(rd(a, a), b), mult(a, c))
3.32/3.50	= { by axiom 4 (f04) }
3.32/3.50	  mult(mult(rd(a, rd(mult(a, b), b)), b), mult(a, c))
3.32/3.50	= { by axiom 4 (f04) }
3.32/3.50	  mult(mult(rd(a, rd(mult(a, rd(mult(b, c), c)), b)), b), mult(a, c))
3.32/3.50	= { by axiom 3 (f02) }
3.32/3.50	  mult(mult(rd(a, rd(mult(a, rd(mult(b, c), ld(a, mult(a, c)))), b)), b), mult(a, c))
3.32/3.50	= { by axiom 4 (f04) }
3.32/3.50	  mult(mult(rd(a, rd(rd(mult(mult(a, rd(mult(b, c), ld(a, mult(a, c)))), mult(a, c)), mult(a, c)), b)), b), mult(a, c))
3.32/3.50	= { by axiom 5 (f01) }
3.32/3.50	  mult(mult(rd(a, rd(rd(mult(mult(a, rd(mult(b, c), ld(a, mult(a, c)))), mult(a, ld(a, mult(a, c)))), mult(a, c)), b)), b), mult(a, c))
3.32/3.50	= { by axiom 6 (f06) }
3.32/3.50	  mult(mult(rd(a, rd(rd(mult(mult(a, a), mult(rd(mult(b, c), ld(a, mult(a, c))), ld(a, mult(a, c)))), mult(a, c)), b)), b), mult(a, c))
3.32/3.50	= { by axiom 2 (f03) }
3.32/3.50	  mult(mult(rd(a, rd(rd(mult(mult(a, a), mult(b, c)), mult(a, c)), b)), b), mult(a, c))
3.32/3.50	= { by lemma 8 }
3.32/3.50	  mult(rd(mult(a, mult(b, b)), rd(mult(mult(a, a), mult(b, c)), mult(a, c))), mult(a, c))
3.32/3.50	= { by lemma 8 }
3.32/3.50	  rd(mult(mult(a, mult(b, b)), mult(mult(a, c), mult(a, c))), mult(mult(a, a), mult(b, c)))
3.32/3.50	= { by axiom 6 (f06) }
3.32/3.50	  rd(mult(mult(a, mult(b, b)), mult(mult(a, a), mult(c, c))), mult(mult(a, a), mult(b, c)))
3.32/3.50	= { by axiom 7 (f05) }
3.32/3.50	  rd(mult(mult(a, mult(a, a)), mult(mult(b, b), mult(c, c))), mult(mult(a, a), mult(b, c)))
3.32/3.50	= { by axiom 1 (f07) }
3.32/3.50	  rd(mult(mult(a, mult(a, a)), mult(mult(b, c), mult(b, c))), mult(mult(a, a), mult(b, c)))
3.32/3.50	= { by axiom 1 (f07) }
3.32/3.50	  rd(mult(mult(a, mult(b, c)), mult(mult(a, a), mult(b, c))), mult(mult(a, a), mult(b, c)))
3.32/3.50	= { by axiom 4 (f04) }
3.32/3.50	  mult(a, mult(b, c))
3.32/3.50	% SZS output end Proof
3.32/3.50	
3.32/3.50	RESULT: Unsatisfiable (the axioms are contradictory).
3.34/3.51	EOF