0.00/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.33	% Computer   : n012.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 12:49:11 EDT 2019
0.12/0.33	% CPUTime    : 
0.61/0.84	% SZS status Unsatisfiable
0.61/0.84	
0.61/0.84	% SZS output start Proof
0.61/0.84	Take the following subset of the input axioms:
0.70/0.87	  fof(c01, axiom, ![A]: mult(unit, A)=A).
0.70/0.87	  fof(c02, axiom, ![A]: mult(A, unit)=A).
0.70/0.87	  fof(c03, axiom, ![A]: unit=mult(A, i(A))).
0.70/0.87	  fof(c04, axiom, ![A]: mult(i(A), A)=unit).
0.70/0.87	  fof(c05, axiom, ![A, B]: mult(i(A), i(B))=i(mult(A, B))).
0.70/0.87	  fof(c06, axiom, ![A, B]: B=mult(i(A), mult(A, B))).
0.70/0.87	  fof(c07, axiom, ![A, B]: A=rd(mult(A, B), B)).
0.70/0.87	  fof(c08, axiom, ![A, B]: A=mult(rd(A, B), B)).
0.70/0.87	  fof(c09, axiom, ![A, B, C]: mult(mult(A, mult(B, A)), C)=mult(A, mult(B, mult(A, C)))).
0.70/0.87	  fof(c10, axiom, ![A, B, C]: mult(mult(A, B), C)=mult(mult(A, mult(B, C)), asoc(A, B, C))).
0.70/0.87	  fof(c11, axiom, ![A, B]: mult(mult(B, A), op_k(A, B))=mult(A, B)).
0.70/0.87	  fof(c12, axiom, ![A, B, C]: op_l(A, B, C)=mult(i(mult(C, B)), mult(C, mult(B, A)))).
0.70/0.87	  fof(c13, axiom, ![A, B, C]: rd(mult(mult(A, B), C), mult(B, C))=op_r(A, B, C)).
0.70/0.87	  fof(c14, axiom, ![A, B]: op_t(A, B)=mult(i(B), mult(A, B))).
0.70/0.87	  fof(c18, axiom, ![A, B, D, C]: op_t(op_r(A, B, C), D)=op_r(op_t(A, D), B, C)).
0.70/0.87	  fof(c20, axiom, ![A, B, C]: op_t(op_t(A, B), C)=op_t(op_t(A, C), B)).
0.70/0.87	  fof(c21, axiom, ![A, B, D, C, E]: unit=asoc(asoc(A, B, C), D, E)).
0.70/0.87	  fof(c22, axiom, ![A, B, D, C, E]: unit=asoc(A, B, asoc(C, D, E))).
0.70/0.87	  fof(goals, negated_conjecture, op_k(op_k(a, b), c)!=unit).
0.70/0.87	
0.70/0.87	Now clausify the problem and encode Horn clauses using encoding 3 of
0.70/0.87	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.70/0.87	We repeatedly replace C & s=t => u=v by the two clauses:
0.70/0.87	  fresh(y, y, x1...xn) = u
0.70/0.87	  C => fresh(s, t, x1...xn) = v
0.70/0.87	where fresh is a fresh function symbol and x1..xn are the free
0.70/0.87	variables of u and v.
0.70/0.87	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.70/0.87	input problem has no model of domain size 1).
0.70/0.87	
0.70/0.87	The encoding turns the above axioms into the following unit equations and goals:
0.70/0.87	
0.70/0.87	Axiom 1 (c01): mult(unit, X) = X.
0.70/0.87	Axiom 2 (c21): unit = asoc(asoc(X, Y, Z), W, V).
0.70/0.87	Axiom 3 (c07): X = rd(mult(X, Y), Y).
0.70/0.87	Axiom 4 (c20): op_t(op_t(X, Y), Z) = op_t(op_t(X, Z), Y).
0.70/0.87	Axiom 5 (c12): op_l(X, Y, Z) = mult(i(mult(Z, Y)), mult(Z, mult(Y, X))).
0.70/0.87	Axiom 6 (c05): mult(i(X), i(Y)) = i(mult(X, Y)).
0.70/0.87	Axiom 7 (c08): X = mult(rd(X, Y), Y).
0.70/0.87	Axiom 8 (c10): mult(mult(X, Y), Z) = mult(mult(X, mult(Y, Z)), asoc(X, Y, Z)).
0.70/0.87	Axiom 9 (c11): mult(mult(X, Y), op_k(Y, X)) = mult(Y, X).
0.70/0.87	Axiom 10 (c04): mult(i(X), X) = unit.
0.70/0.87	Axiom 11 (c09): mult(mult(X, mult(Y, X)), Z) = mult(X, mult(Y, mult(X, Z))).
0.70/0.87	Axiom 12 (c18): op_t(op_r(X, Y, Z), W) = op_r(op_t(X, W), Y, Z).
0.70/0.87	Axiom 13 (c06): X = mult(i(Y), mult(Y, X)).
0.70/0.87	Axiom 14 (c13): rd(mult(mult(X, Y), Z), mult(Y, Z)) = op_r(X, Y, Z).
0.70/0.87	Axiom 15 (c22): unit = asoc(X, Y, asoc(Z, W, V)).
0.70/0.87	Axiom 16 (c03): unit = mult(X, i(X)).
0.70/0.87	Axiom 17 (c14): op_t(X, Y) = mult(i(Y), mult(X, Y)).
0.70/0.87	Axiom 18 (c02): mult(X, unit) = X.
0.70/0.87	
0.70/0.87	Lemma 19: rd(unit, X) = i(X).
0.70/0.87	Proof:
0.70/0.87	  rd(unit, X)
0.70/0.87	= { by axiom 10 (c04) }
0.70/0.87	  rd(mult(i(X), X), X)
0.70/0.87	= { by axiom 3 (c07) }
0.70/0.87	  i(X)
0.70/0.87	
0.70/0.87	Lemma 20: mult(i(mult(Y, X)), Y) = op_l(i(X), X, Y).
0.70/0.87	Proof:
0.70/0.87	  mult(i(mult(Y, X)), Y)
0.70/0.87	= { by axiom 18 (c02) }
0.70/0.87	  mult(i(mult(Y, X)), mult(Y, unit))
0.70/0.87	= { by axiom 16 (c03) }
0.70/0.87	  mult(i(mult(Y, X)), mult(Y, mult(X, i(X))))
0.70/0.87	= { by axiom 5 (c12) }
0.70/0.87	  op_l(i(X), X, Y)
0.70/0.87	
0.70/0.87	Lemma 21: mult(i(mult(Y, X)), mult(X, Y)) = op_k(X, Y).
0.70/0.87	Proof:
0.70/0.87	  mult(i(mult(Y, X)), mult(X, Y))
0.70/0.87	= { by axiom 9 (c11) }
0.70/0.87	  mult(i(mult(Y, X)), mult(mult(Y, X), op_k(X, Y)))
0.70/0.87	= { by axiom 13 (c06) }
0.70/0.87	  op_k(X, Y)
0.70/0.87	
0.70/0.87	Lemma 22: mult(X, op_l(i(Y), Y, X)) = rd(X, Y).
0.70/0.87	Proof:
0.70/0.87	  mult(X, op_l(i(Y), Y, X))
0.70/0.87	= { by lemma 20 }
0.70/0.87	  mult(X, mult(i(mult(X, Y)), X))
0.70/0.87	= { by axiom 3 (c07) }
0.70/0.87	  rd(mult(mult(X, mult(i(mult(X, Y)), X)), Y), Y)
0.70/0.87	= { by axiom 11 (c09) }
0.70/0.87	  rd(mult(X, mult(i(mult(X, Y)), mult(X, Y))), Y)
0.70/0.87	= { by axiom 10 (c04) }
0.70/0.87	  rd(mult(X, unit), Y)
0.70/0.87	= { by axiom 18 (c02) }
0.70/0.87	  rd(X, Y)
0.70/0.87	
0.70/0.87	Lemma 23: i(rd(X, Y)) = rd(Y, X).
0.70/0.87	Proof:
0.70/0.87	  i(rd(X, Y))
0.70/0.87	= { by axiom 3 (c07) }
0.70/0.87	  rd(mult(i(rd(X, Y)), mult(rd(X, Y), Y)), mult(rd(X, Y), Y))
0.70/0.87	= { by axiom 13 (c06) }
0.70/0.87	  rd(Y, mult(rd(X, Y), Y))
0.70/0.87	= { by axiom 7 (c08) }
0.70/0.87	  rd(Y, X)
0.70/0.87	
0.70/0.87	Lemma 24: mult(mult(i(Y), rd(Y, X)), X) = op_k(rd(X, Y), Y).
0.70/0.87	Proof:
0.70/0.87	  mult(mult(i(Y), rd(Y, X)), X)
0.70/0.87	= { by lemma 23 }
0.70/0.87	  mult(mult(i(Y), i(rd(X, Y))), X)
0.70/0.87	= { by axiom 6 (c05) }
0.70/0.87	  mult(i(mult(Y, rd(X, Y))), X)
0.70/0.87	= { by axiom 7 (c08) }
0.70/0.87	  mult(i(mult(Y, rd(X, Y))), mult(rd(X, Y), Y))
0.70/0.87	= { by lemma 21 }
0.70/0.87	  op_k(rd(X, Y), Y)
0.70/0.87	
0.70/0.87	Lemma 25: i(i(X)) = X.
0.70/0.87	Proof:
0.70/0.87	  i(i(X))
0.70/0.87	= { by lemma 19 }
0.70/0.87	  rd(unit, i(X))
0.70/0.87	= { by axiom 16 (c03) }
0.70/0.87	  rd(mult(X, i(X)), i(X))
0.70/0.87	= { by axiom 3 (c07) }
0.70/0.87	  X
0.70/0.87	
0.70/0.87	Lemma 26: i(mult(X, i(Y))) = mult(i(X), Y).
0.70/0.87	Proof:
0.70/0.87	  i(mult(X, i(Y)))
0.70/0.87	= { by axiom 6 (c05) }
0.70/0.87	  mult(i(X), i(i(Y)))
0.70/0.87	= { by lemma 25 }
0.70/0.87	  mult(i(X), Y)
0.70/0.87	
0.70/0.87	Lemma 27: mult(mult(Y, X), i(mult(X, Y))) = op_k(i(X), i(Y)).
0.70/0.87	Proof:
0.70/0.87	  mult(mult(Y, X), i(mult(X, Y)))
0.70/0.87	= { by lemma 25 }
0.70/0.87	  mult(i(i(mult(Y, X))), i(mult(X, Y)))
0.70/0.87	= { by axiom 6 (c05) }
0.70/0.87	  mult(i(mult(i(Y), i(X))), i(mult(X, Y)))
0.70/0.87	= { by axiom 6 (c05) }
0.70/0.87	  mult(i(mult(i(Y), i(X))), mult(i(X), i(Y)))
0.70/0.87	= { by lemma 21 }
0.70/0.87	  op_k(i(X), i(Y))
0.70/0.87	
0.70/0.87	Lemma 28: i(op_k(i(X), i(Y))) = op_k(X, Y).
0.70/0.87	Proof:
0.70/0.87	  i(op_k(i(X), i(Y)))
0.70/0.87	= { by lemma 27 }
0.70/0.87	  i(mult(mult(Y, X), i(mult(X, Y))))
0.70/0.87	= { by lemma 26 }
0.70/0.87	  mult(i(mult(Y, X)), mult(X, Y))
0.70/0.87	= { by lemma 21 }
0.70/0.87	  op_k(X, Y)
0.70/0.87	
0.70/0.87	Lemma 29: op_k(i(X), i(Y)) = i(op_k(X, Y)).
0.70/0.87	Proof:
0.70/0.87	  op_k(i(X), i(Y))
0.70/0.87	= { by lemma 25 }
0.70/0.87	  i(i(op_k(i(X), i(Y))))
0.70/0.87	= { by lemma 28 }
0.70/0.87	  i(op_k(X, Y))
0.70/0.87	
0.70/0.87	Lemma 30: mult(op_l(i(Y), Y, X), Y) = op_k(i(X), mult(X, Y)).
0.70/0.87	Proof:
0.70/0.87	  mult(op_l(i(Y), Y, X), Y)
0.70/0.87	= { by lemma 20 }
0.70/0.87	  mult(mult(i(mult(X, Y)), X), Y)
0.70/0.87	= { by axiom 13 (c06) }
0.70/0.87	  mult(mult(i(mult(X, Y)), X), mult(i(X), mult(X, Y)))
0.70/0.87	= { by lemma 26 }
0.70/0.87	  mult(mult(i(mult(X, Y)), X), i(mult(X, i(mult(X, Y)))))
0.70/0.87	= { by lemma 27 }
0.70/0.87	  op_k(i(X), i(i(mult(X, Y))))
0.70/0.87	= { by lemma 29 }
0.70/0.87	  i(op_k(X, i(mult(X, Y))))
0.70/0.87	= { by lemma 25 }
0.70/0.87	  i(op_k(i(i(X)), i(mult(X, Y))))
0.70/0.87	= { by lemma 28 }
0.70/0.87	  op_k(i(X), mult(X, Y))
0.70/0.87	
0.70/0.87	Lemma 31: op_k(i(X), mult(X, Y)) = op_k(rd(Y, X), X).
0.70/0.87	Proof:
0.70/0.87	  op_k(i(X), mult(X, Y))
0.70/0.87	= { by lemma 30 }
0.70/0.87	  mult(op_l(i(Y), Y, X), Y)
0.70/0.87	= { by axiom 13 (c06) }
0.70/0.87	  mult(mult(i(X), mult(X, op_l(i(Y), Y, X))), Y)
0.70/0.87	= { by lemma 22 }
0.70/0.87	  mult(mult(i(X), rd(X, Y)), Y)
0.70/0.87	= { by lemma 24 }
0.70/0.87	  op_k(rd(Y, X), X)
0.70/0.87	
0.70/0.87	Lemma 32: asoc(X, Y, op_k(Z, W)) = unit.
0.70/0.87	Proof:
0.70/0.87	  asoc(X, Y, op_k(Z, W))
0.70/0.87	= { by axiom 3 (c07) }
0.70/0.87	  asoc(X, Y, op_k(rd(mult(Z, W), W), W))
0.70/0.87	= { by lemma 31 }
0.70/0.87	  asoc(X, Y, op_k(i(W), mult(W, mult(Z, W))))
0.70/0.87	= { by lemma 30 }
0.70/0.87	  asoc(X, Y, mult(op_l(i(mult(Z, W)), mult(Z, W), W), mult(Z, W)))
0.70/0.87	= { by lemma 20 }
0.70/0.87	  asoc(X, Y, mult(mult(i(mult(W, mult(Z, W))), W), mult(Z, W)))
0.70/0.87	= { by axiom 8 (c10) }
0.70/0.87	  asoc(X, Y, mult(mult(i(mult(W, mult(Z, W))), mult(W, mult(Z, W))), asoc(i(mult(W, mult(Z, W))), W, mult(Z, W))))
0.70/0.87	= { by axiom 10 (c04) }
0.70/0.87	  asoc(X, Y, mult(unit, asoc(i(mult(W, mult(Z, W))), W, mult(Z, W))))
0.70/0.87	= { by axiom 1 (c01) }
0.70/0.87	  asoc(X, Y, asoc(i(mult(W, mult(Z, W))), W, mult(Z, W)))
0.70/0.87	= { by axiom 15 (c22) }
0.70/0.87	  unit
0.70/0.87	
0.70/0.87	Lemma 33: i(op_k(Y, X)) = op_k(X, Y).
0.70/0.87	Proof:
0.70/0.87	  i(op_k(Y, X))
0.70/0.87	= { by lemma 19 }
0.70/0.87	  rd(unit, op_k(Y, X))
0.70/0.87	= { by lemma 32 }
0.70/0.87	  rd(asoc(i(mult(mult(X, Y), op_k(Y, X))), mult(X, Y), op_k(Y, X)), op_k(Y, X))
0.70/0.87	= { by axiom 1 (c01) }
0.70/0.87	  rd(mult(unit, asoc(i(mult(mult(X, Y), op_k(Y, X))), mult(X, Y), op_k(Y, X))), op_k(Y, X))
0.70/0.87	= { by axiom 10 (c04) }
0.70/0.87	  rd(mult(mult(i(mult(mult(X, Y), op_k(Y, X))), mult(mult(X, Y), op_k(Y, X))), asoc(i(mult(mult(X, Y), op_k(Y, X))), mult(X, Y), op_k(Y, X))), op_k(Y, X))
0.70/0.87	= { by axiom 8 (c10) }
0.70/0.87	  rd(mult(mult(i(mult(mult(X, Y), op_k(Y, X))), mult(X, Y)), op_k(Y, X)), op_k(Y, X))
0.70/0.87	= { by axiom 9 (c11) }
0.70/0.87	  rd(mult(mult(i(mult(Y, X)), mult(X, Y)), op_k(Y, X)), op_k(Y, X))
0.70/0.87	= { by lemma 21 }
0.70/0.87	  rd(mult(op_k(X, Y), op_k(Y, X)), op_k(Y, X))
0.70/0.87	= { by axiom 3 (c07) }
0.70/0.87	  op_k(X, Y)
0.70/0.87	
0.70/0.87	Lemma 34: mult(Y, mult(i(Y), X)) = X.
0.70/0.87	Proof:
0.70/0.87	  mult(Y, mult(i(Y), X))
0.70/0.87	= { by lemma 25 }
0.70/0.87	  mult(i(i(Y)), mult(i(Y), X))
0.70/0.87	= { by axiom 13 (c06) }
0.70/0.87	  X
0.70/0.87	
0.70/0.87	Lemma 35: mult(op_t(X, Y), i(X)) = mult(i(X), op_t(X, Y)).
0.70/0.87	Proof:
0.70/0.87	  mult(op_t(X, Y), i(X))
0.70/0.87	= { by lemma 34 }
0.70/0.87	  mult(i(X), mult(i(i(X)), mult(op_t(X, Y), i(X))))
0.70/0.87	= { by axiom 17 (c14) }
0.70/0.87	  mult(i(X), op_t(op_t(X, Y), i(X)))
0.70/0.87	= { by axiom 4 (c20) }
0.70/0.87	  mult(i(X), op_t(op_t(X, i(X)), Y))
0.70/0.87	= { by lemma 25 }
0.70/0.87	  mult(i(X), op_t(op_t(i(i(X)), i(X)), Y))
0.70/0.87	= { by axiom 17 (c14) }
0.70/0.87	  mult(i(X), op_t(mult(i(i(X)), mult(i(i(X)), i(X))), Y))
0.70/0.87	= { by axiom 10 (c04) }
0.70/0.87	  mult(i(X), op_t(mult(i(i(X)), unit), Y))
0.70/0.87	= { by axiom 18 (c02) }
0.70/0.87	  mult(i(X), op_t(i(i(X)), Y))
0.70/0.87	= { by lemma 25 }
0.70/0.87	  mult(i(X), op_t(X, Y))
0.70/0.87	
0.70/0.87	Lemma 36: mult(Y, i(mult(Y, X))) = i(X).
0.70/0.87	Proof:
0.70/0.87	  mult(Y, i(mult(Y, X)))
0.70/0.87	= { by axiom 6 (c05) }
0.70/0.87	  mult(Y, mult(i(Y), i(X)))
0.70/0.87	= { by lemma 34 }
0.70/0.87	  i(X)
0.70/0.87	
0.70/0.87	Lemma 37: op_t(op_r(rd(X, Y), Z, W), Y) = op_r(mult(i(Y), X), Z, W).
0.70/0.87	Proof:
0.70/0.87	  op_t(op_r(rd(X, Y), Z, W), Y)
0.70/0.87	= { by axiom 12 (c18) }
0.70/0.87	  op_r(op_t(rd(X, Y), Y), Z, W)
0.70/0.87	= { by axiom 17 (c14) }
0.70/0.87	  op_r(mult(i(Y), mult(rd(X, Y), Y)), Z, W)
0.70/0.87	= { by axiom 7 (c08) }
0.70/0.87	  op_r(mult(i(Y), X), Z, W)
0.70/0.87	
0.70/0.87	Lemma 38: rd(mult(X, Z), mult(Y, Z)) = op_r(rd(X, Y), Y, Z).
0.70/0.87	Proof:
0.70/0.87	  rd(mult(X, Z), mult(Y, Z))
0.70/0.87	= { by axiom 7 (c08) }
0.70/0.88	  rd(mult(mult(rd(X, Y), Y), Z), mult(Y, Z))
0.70/0.88	= { by axiom 14 (c13) }
0.70/0.88	  op_r(rd(X, Y), Y, Z)
0.70/0.88	
0.70/0.88	Lemma 39: mult(op_r(X, Y, Z), mult(Y, Z)) = mult(mult(X, Y), Z).
0.70/0.88	Proof:
0.70/0.88	  mult(op_r(X, Y, Z), mult(Y, Z))
0.70/0.88	= { by axiom 14 (c13) }
0.70/0.88	  mult(rd(mult(mult(X, Y), Z), mult(Y, Z)), mult(Y, Z))
0.70/0.88	= { by axiom 7 (c08) }
0.70/0.88	  mult(mult(X, Y), Z)
0.70/0.88	
0.70/0.88	Lemma 40: mult(i(Y), op_t(Y, X)) = i(op_k(X, Y)).
0.70/0.88	Proof:
0.70/0.88	  mult(i(Y), op_t(Y, X))
0.70/0.88	= { by lemma 35 }
0.70/0.88	  mult(op_t(Y, X), i(Y))
0.70/0.88	= { by axiom 13 (c06) }
0.70/0.88	  mult(op_t(mult(i(X), mult(X, Y)), X), i(Y))
0.70/0.88	= { by lemma 26 }
0.70/0.88	  mult(op_t(i(mult(X, i(mult(X, Y)))), X), i(Y))
0.70/0.88	= { by lemma 19 }
0.70/0.88	  mult(op_t(rd(unit, mult(X, i(mult(X, Y)))), X), i(Y))
0.70/0.88	= { by axiom 10 (c04) }
0.70/0.88	  mult(op_t(rd(mult(i(i(mult(X, Y))), i(mult(X, Y))), mult(X, i(mult(X, Y)))), X), i(Y))
0.70/0.88	= { by lemma 38 }
0.70/0.88	  mult(op_t(op_r(rd(i(i(mult(X, Y))), X), X, i(mult(X, Y))), X), i(Y))
0.70/0.88	= { by lemma 37 }
0.70/0.88	  mult(op_r(mult(i(X), i(i(mult(X, Y)))), X, i(mult(X, Y))), i(Y))
0.70/0.88	= { by axiom 6 (c05) }
0.70/0.88	  mult(op_r(i(mult(X, i(mult(X, Y)))), X, i(mult(X, Y))), i(Y))
0.70/0.88	= { by lemma 36 }
0.70/0.88	  mult(op_r(i(i(Y)), X, i(mult(X, Y))), i(Y))
0.70/0.88	= { by lemma 25 }
0.70/0.88	  mult(op_r(Y, X, i(mult(X, Y))), i(Y))
0.70/0.88	= { by lemma 36 }
0.70/0.88	  mult(op_r(Y, X, i(mult(X, Y))), mult(X, i(mult(X, Y))))
0.70/0.88	= { by lemma 39 }
0.70/0.88	  mult(mult(Y, X), i(mult(X, Y)))
0.70/0.88	= { by lemma 27 }
0.70/0.88	  op_k(i(X), i(Y))
0.70/0.88	= { by lemma 29 }
0.70/0.88	  i(op_k(X, Y))
0.70/0.88	
0.70/0.88	Lemma 41: rd(X, unit) = X.
0.70/0.88	Proof:
0.70/0.88	  rd(X, unit)
0.70/0.88	= { by axiom 18 (c02) }
0.70/0.88	  rd(mult(X, unit), unit)
0.70/0.88	= { by axiom 3 (c07) }
0.70/0.88	  X
0.70/0.88	
0.70/0.88	Lemma 42: op_r(rd(X, Y), Y, i(Y)) = mult(X, i(Y)).
0.70/0.88	Proof:
0.70/0.88	  op_r(rd(X, Y), Y, i(Y))
0.70/0.88	= { by lemma 38 }
0.70/0.88	  rd(mult(X, i(Y)), mult(Y, i(Y)))
0.70/0.88	= { by axiom 16 (c03) }
0.70/0.88	  rd(mult(X, i(Y)), unit)
0.70/0.88	= { by lemma 41 }
0.70/0.88	  mult(X, i(Y))
0.70/0.88	
0.70/0.88	Lemma 43: mult(mult(X, i(Y)), Y) = op_r(X, i(Y), Y).
0.70/0.88	Proof:
0.70/0.88	  mult(mult(X, i(Y)), Y)
0.70/0.88	= { by lemma 39 }
0.70/0.88	  mult(op_r(X, i(Y), Y), mult(i(Y), Y))
0.70/0.88	= { by axiom 10 (c04) }
0.70/0.88	  mult(op_r(X, i(Y), Y), unit)
0.70/0.88	= { by axiom 18 (c02) }
0.70/0.88	  op_r(X, i(Y), Y)
0.70/0.88	
0.70/0.88	Lemma 44: op_r(X, i(Y), Y) = op_t(X, rd(Y, X)).
0.70/0.88	Proof:
0.70/0.88	  op_r(X, i(Y), Y)
0.70/0.88	= { by lemma 43 }
0.70/0.88	  mult(mult(X, i(Y)), Y)
0.70/0.88	= { by lemma 42 }
0.70/0.88	  mult(op_r(rd(X, Y), Y, i(Y)), Y)
0.70/0.88	= { by lemma 25 }
0.70/0.88	  mult(op_r(i(i(rd(X, Y))), Y, i(Y)), Y)
0.70/0.88	= { by lemma 25 }
0.70/0.88	  mult(op_r(i(i(rd(X, Y))), i(i(Y)), i(Y)), Y)
0.70/0.88	= { by lemma 43 }
0.70/0.88	  mult(mult(mult(i(i(rd(X, Y))), i(i(Y))), i(Y)), Y)
0.70/0.88	= { by lemma 43 }
0.70/0.88	  op_r(mult(i(i(rd(X, Y))), i(i(Y))), i(Y), Y)
0.70/0.88	= { by lemma 25 }
0.70/0.88	  op_r(mult(i(i(rd(X, Y))), Y), i(Y), Y)
0.70/0.88	= { by lemma 37 }
0.70/0.88	  op_t(op_r(rd(Y, i(rd(X, Y))), i(Y), Y), i(rd(X, Y)))
0.70/0.88	= { by lemma 25 }
0.70/0.88	  op_t(op_r(rd(i(i(Y)), i(rd(X, Y))), i(Y), Y), i(rd(X, Y)))
0.70/0.88	= { by axiom 7 (c08) }
0.70/0.88	  op_t(op_r(rd(i(mult(rd(i(Y), rd(X, Y)), rd(X, Y))), i(rd(X, Y))), i(Y), Y), i(rd(X, Y)))
0.70/0.88	= { by axiom 6 (c05) }
0.70/0.88	  op_t(op_r(rd(mult(i(rd(i(Y), rd(X, Y))), i(rd(X, Y))), i(rd(X, Y))), i(Y), Y), i(rd(X, Y)))
0.70/0.88	= { by axiom 3 (c07) }
0.70/0.88	  op_t(op_r(i(rd(i(Y), rd(X, Y))), i(Y), Y), i(rd(X, Y)))
0.70/0.88	= { by lemma 23 }
0.70/0.88	  op_t(op_r(rd(rd(X, Y), i(Y)), i(Y), Y), i(rd(X, Y)))
0.70/0.88	= { by lemma 38 }
0.70/0.88	  op_t(rd(mult(rd(X, Y), Y), mult(i(Y), Y)), i(rd(X, Y)))
0.70/0.88	= { by axiom 10 (c04) }
0.70/0.88	  op_t(rd(mult(rd(X, Y), Y), unit), i(rd(X, Y)))
0.70/0.88	= { by lemma 41 }
0.70/0.88	  op_t(mult(rd(X, Y), Y), i(rd(X, Y)))
0.70/0.88	= { by axiom 7 (c08) }
0.70/0.88	  op_t(X, i(rd(X, Y)))
0.70/0.88	= { by lemma 23 }
0.70/0.88	  op_t(X, rd(Y, X))
0.70/0.88	
0.70/0.88	Lemma 45: mult(X, asoc(X, i(Y), Y)) = op_t(X, rd(Y, X)).
0.70/0.88	Proof:
0.70/0.88	  mult(X, asoc(X, i(Y), Y))
0.70/0.88	= { by axiom 18 (c02) }
0.70/0.88	  mult(mult(X, unit), asoc(X, i(Y), Y))
0.70/0.88	= { by axiom 10 (c04) }
0.70/0.88	  mult(mult(X, mult(i(Y), Y)), asoc(X, i(Y), Y))
0.70/0.88	= { by axiom 8 (c10) }
0.70/0.88	  mult(mult(X, i(Y)), Y)
0.70/0.88	= { by lemma 43 }
0.70/0.88	  op_r(X, i(Y), Y)
0.70/0.88	= { by lemma 44 }
0.73/0.90	  op_t(X, rd(Y, X))
0.73/0.90	
0.73/0.90	Goal 1 (goals): op_k(op_k(a, b), c) = unit.
0.73/0.90	Proof:
0.73/0.90	  op_k(op_k(a, b), c)
0.73/0.90	= { by lemma 33 }
0.73/0.90	  i(op_k(c, op_k(a, b)))
0.73/0.90	= { by lemma 40 }
0.73/0.90	  mult(i(op_k(a, b)), op_t(op_k(a, b), c))
0.73/0.90	= { by lemma 35 }
0.73/0.90	  mult(op_t(op_k(a, b), c), i(op_k(a, b)))
0.73/0.90	= { by axiom 7 (c08) }
0.73/0.90	  mult(op_t(mult(rd(op_k(a, b), i(c)), i(c)), c), i(op_k(a, b)))
0.73/0.90	= { by lemma 42 }
0.73/0.90	  mult(op_t(op_r(rd(rd(op_k(a, b), i(c)), c), c, i(c)), c), i(op_k(a, b)))
0.73/0.90	= { by lemma 37 }
0.73/0.90	  mult(op_r(mult(i(c), rd(op_k(a, b), i(c))), c, i(c)), i(op_k(a, b)))
0.73/0.90	= { by lemma 33 }
0.73/0.90	  mult(op_r(mult(i(c), rd(i(op_k(b, a)), i(c))), c, i(c)), i(op_k(a, b)))
0.73/0.90	= { by lemma 29 }
0.73/0.90	  mult(op_r(mult(i(c), rd(op_k(i(b), i(a)), i(c))), c, i(c)), i(op_k(a, b)))
0.73/0.90	= { by axiom 9 (c11) }
0.73/0.90	  mult(op_r(mult(mult(rd(op_k(i(b), i(a)), i(c)), i(c)), op_k(i(c), rd(op_k(i(b), i(a)), i(c)))), c, i(c)), i(op_k(a, b)))
0.73/0.90	= { by axiom 7 (c08) }
0.73/0.90	  mult(op_r(mult(op_k(i(b), i(a)), op_k(i(c), rd(op_k(i(b), i(a)), i(c)))), c, i(c)), i(op_k(a, b)))
0.73/0.90	= { by lemma 29 }
0.73/0.90	  mult(op_r(mult(i(op_k(b, a)), op_k(i(c), rd(op_k(i(b), i(a)), i(c)))), c, i(c)), i(op_k(a, b)))
0.73/0.90	= { by lemma 33 }
0.73/0.90	  mult(op_r(mult(i(op_k(b, a)), i(op_k(rd(op_k(i(b), i(a)), i(c)), i(c)))), c, i(c)), i(op_k(a, b)))
0.73/0.90	= { by lemma 40 }
0.73/0.90	  mult(op_r(mult(i(op_k(b, a)), mult(i(i(c)), op_t(i(c), rd(op_k(i(b), i(a)), i(c))))), c, i(c)), i(op_k(a, b)))
0.73/0.90	= { by lemma 45 }
0.73/0.90	  mult(op_r(mult(i(op_k(b, a)), mult(i(i(c)), mult(i(c), asoc(i(c), i(op_k(i(b), i(a))), op_k(i(b), i(a)))))), c, i(c)), i(op_k(a, b)))
0.73/0.90	= { by axiom 13 (c06) }
0.73/0.90	  mult(op_r(mult(i(op_k(b, a)), asoc(i(c), i(op_k(i(b), i(a))), op_k(i(b), i(a)))), c, i(c)), i(op_k(a, b)))
0.73/0.90	= { by lemma 28 }
0.73/0.90	  mult(op_r(mult(i(op_k(b, a)), asoc(i(c), op_k(b, a), op_k(i(b), i(a)))), c, i(c)), i(op_k(a, b)))
0.73/0.90	= { by lemma 32 }
0.73/0.90	  mult(op_r(mult(i(op_k(b, a)), unit), c, i(c)), i(op_k(a, b)))
0.73/0.90	= { by axiom 18 (c02) }
0.73/0.90	  mult(op_r(i(op_k(b, a)), c, i(c)), i(op_k(a, b)))
0.73/0.90	= { by lemma 33 }
0.73/0.90	  mult(op_r(op_k(a, b), c, i(c)), i(op_k(a, b)))
0.73/0.90	= { by lemma 25 }
0.73/0.90	  mult(op_r(op_k(a, b), i(i(c)), i(c)), i(op_k(a, b)))
0.73/0.90	= { by lemma 44 }
0.73/0.90	  mult(op_t(op_k(a, b), rd(i(c), op_k(a, b))), i(op_k(a, b)))
0.73/0.90	= { by lemma 45 }
0.73/0.90	  mult(mult(op_k(a, b), asoc(op_k(a, b), i(i(c)), i(c))), i(op_k(a, b)))
0.73/0.90	= { by axiom 3 (c07) }
0.73/0.90	  mult(mult(op_k(a, b), asoc(op_k(rd(mult(a, b), b), b), i(i(c)), i(c))), i(op_k(a, b)))
0.73/0.90	= { by lemma 31 }
0.73/0.90	  mult(mult(op_k(a, b), asoc(op_k(i(b), mult(b, mult(a, b))), i(i(c)), i(c))), i(op_k(a, b)))
0.73/0.90	= { by lemma 30 }
0.73/0.90	  mult(mult(op_k(a, b), asoc(mult(op_l(i(mult(a, b)), mult(a, b), b), mult(a, b)), i(i(c)), i(c))), i(op_k(a, b)))
0.73/0.90	= { by lemma 20 }
0.73/0.90	  mult(mult(op_k(a, b), asoc(mult(mult(i(mult(b, mult(a, b))), b), mult(a, b)), i(i(c)), i(c))), i(op_k(a, b)))
0.73/0.90	= { by axiom 8 (c10) }
0.73/0.90	  mult(mult(op_k(a, b), asoc(mult(mult(i(mult(b, mult(a, b))), mult(b, mult(a, b))), asoc(i(mult(b, mult(a, b))), b, mult(a, b))), i(i(c)), i(c))), i(op_k(a, b)))
0.73/0.90	= { by axiom 10 (c04) }
0.73/0.90	  mult(mult(op_k(a, b), asoc(mult(unit, asoc(i(mult(b, mult(a, b))), b, mult(a, b))), i(i(c)), i(c))), i(op_k(a, b)))
0.73/0.90	= { by axiom 1 (c01) }
0.73/0.90	  mult(mult(op_k(a, b), asoc(asoc(i(mult(b, mult(a, b))), b, mult(a, b)), i(i(c)), i(c))), i(op_k(a, b)))
0.73/0.90	= { by lemma 25 }
0.73/0.90	  mult(mult(op_k(a, b), asoc(asoc(i(mult(b, mult(a, b))), b, mult(a, b)), c, i(c))), i(op_k(a, b)))
0.73/0.90	= { by axiom 2 (c21) }
0.73/0.90	  mult(mult(op_k(a, b), unit), i(op_k(a, b)))
0.73/0.90	= { by axiom 18 (c02) }
0.73/0.90	  mult(op_k(a, b), i(op_k(a, b)))
0.73/0.90	= { by axiom 16 (c03) }
0.73/0.90	  unit
0.73/0.90	% SZS output end Proof
0.73/0.90	
0.73/0.90	RESULT: Unsatisfiable (the axioms are contradictory).
0.73/0.91	EOF