TSTP Solution File: BOO034-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : BOO034-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 23:46:00 EDT 2022
% Result : Unsatisfiable 0.53s 0.73s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 58
% Number of leaves : 74
% Syntax : Number of clauses : 281 ( 147 unt; 0 nHn; 155 RR)
% Number of literals : 478 ( 477 equ; 201 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 706 ( 50 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(V,W,X),Y,multiply(V,W,Z)) = multiply(V,W,multiply(X,Y,Z)) ).
cnf(ternary_multiply_1,axiom,
multiply(Y,X,X) = X ).
cnf(ternary_multiply_2,axiom,
multiply(X,X,Y) = X ).
cnf(left_inverse,axiom,
multiply(inverse(Y),Y,X) = X ).
cnf(right_inverse,axiom,
multiply(X,Y,inverse(Y)) = X ).
cnf(prove_single_axiom,negated_conjecture,
multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)) != b ).
cnf(refute_0_0,plain,
multiply(multiply(c,d,e),f,multiply(c,d,g)) = multiply(c,d,multiply(e,f,g)),
inference(subst,[],[associativity:[bind(V,$fot(c)),bind(W,$fot(d)),bind(X,$fot(e)),bind(Y,$fot(f)),bind(Z,$fot(g))]]) ).
cnf(refute_0_1,plain,
inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))) = inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),
introduced(tautology,[refl,[$fot(inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))))]]) ).
cnf(refute_0_2,plain,
( inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))) != inverse(multiply(multiply(c,d,e),f,multiply(c,d,g)))
| multiply(multiply(c,d,e),f,multiply(c,d,g)) != multiply(c,d,multiply(e,f,g))
| inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))) = inverse(multiply(c,d,multiply(e,f,g))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g)))) ),[1,0],$fot(multiply(c,d,multiply(e,f,g)))]]) ).
cnf(refute_0_3,plain,
( multiply(multiply(c,d,e),f,multiply(c,d,g)) != multiply(c,d,multiply(e,f,g))
| inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))) = inverse(multiply(c,d,multiply(e,f,g))) ),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g)))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))) = inverse(multiply(c,d,multiply(e,f,g))),
inference(resolve,[$cnf( $equal(multiply(multiply(c,d,e),f,multiply(c,d,g)),multiply(c,d,multiply(e,f,g))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)) = multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)),
introduced(tautology,[refl,[$fot(multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)))]]) ).
cnf(refute_0_6,plain,
( inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))) != inverse(multiply(c,d,multiply(e,f,g)))
| multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)) != multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c))
| multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)) = multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)),multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c))) ),[1,1],$fot(inverse(multiply(c,d,multiply(e,f,g))))]]) ).
cnf(refute_0_7,plain,
( inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))) != inverse(multiply(c,d,multiply(e,f,g)))
| multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)) = multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)),multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)) = multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),inverse(multiply(c,d,multiply(e,f,g)))) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
( multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) != b
| multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)) != multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c))
| multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)) = b ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)),multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c))) ),[1],$fot(b)]]) ).
cnf(refute_0_10,plain,
( multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) != b
| multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)) = b ),
inference(resolve,[$cnf( $equal(multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)),multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) != b,
inference(resolve,[$cnf( $equal(multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)),b) )],[refute_0_10,prove_single_axiom]) ).
cnf(refute_0_12,plain,
multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12),multiply(X_8,X_9,X_12)) = multiply(X_8,X_9,X_12),
inference(subst,[],[ternary_multiply_1:[bind(X,$fot(multiply(X_8,X_9,X_12))),bind(Y,$fot(multiply(X_8,X_9,X_10)))]]) ).
cnf(refute_0_13,plain,
multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12),multiply(X_8,X_9,X_12)) = multiply(X_8,X_9,multiply(X_10,multiply(X_8,X_9,X_12),X_12)),
inference(subst,[],[associativity:[bind(V,$fot(X_8)),bind(W,$fot(X_9)),bind(X,$fot(X_10)),bind(Y,$fot(multiply(X_8,X_9,X_12))),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_14,plain,
( multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12),multiply(X_8,X_9,X_12)) != multiply(X_8,X_9,X_12)
| multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12),multiply(X_8,X_9,X_12)) != multiply(X_8,X_9,multiply(X_10,multiply(X_8,X_9,X_12),X_12))
| multiply(X_8,X_9,multiply(X_10,multiply(X_8,X_9,X_12),X_12)) = multiply(X_8,X_9,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12),multiply(X_8,X_9,X_12)),multiply(X_8,X_9,X_12)) ),[0],$fot(multiply(X_8,X_9,multiply(X_10,multiply(X_8,X_9,X_12),X_12)))]]) ).
cnf(refute_0_15,plain,
( multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12),multiply(X_8,X_9,X_12)) != multiply(X_8,X_9,X_12)
| multiply(X_8,X_9,multiply(X_10,multiply(X_8,X_9,X_12),X_12)) = multiply(X_8,X_9,X_12) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12),multiply(X_8,X_9,X_12)),multiply(X_8,X_9,multiply(X_10,multiply(X_8,X_9,X_12),X_12))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
multiply(X_8,X_9,multiply(X_10,multiply(X_8,X_9,X_12),X_12)) = multiply(X_8,X_9,X_12),
inference(resolve,[$cnf( $equal(multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12),multiply(X_8,X_9,X_12)),multiply(X_8,X_9,X_12)) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
multiply(X_21,X_22,multiply(X_19,multiply(X_21,X_22,inverse(X_22)),inverse(X_22))) = multiply(X_21,X_22,inverse(X_22)),
inference(subst,[],[refute_0_16:[bind(X_10,$fot(X_19)),bind(X_12,$fot(inverse(X_22))),bind(X_8,$fot(X_21)),bind(X_9,$fot(X_22))]]) ).
cnf(refute_0_18,plain,
multiply(X_21,X_22,inverse(X_22)) = X_21,
inference(subst,[],[right_inverse:[bind(X,$fot(X_21)),bind(Y,$fot(X_22))]]) ).
cnf(refute_0_19,plain,
( multiply(X_21,X_22,inverse(X_22)) != X_21
| multiply(X_21,X_22,multiply(X_19,multiply(X_21,X_22,inverse(X_22)),inverse(X_22))) != multiply(X_21,X_22,inverse(X_22))
| multiply(X_21,X_22,multiply(X_19,X_21,inverse(X_22))) = multiply(X_21,X_22,inverse(X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_21,X_22,multiply(X_19,multiply(X_21,X_22,inverse(X_22)),inverse(X_22))),multiply(X_21,X_22,inverse(X_22))) ),[0,2,1],$fot(X_21)]]) ).
cnf(refute_0_20,plain,
( multiply(X_21,X_22,multiply(X_19,multiply(X_21,X_22,inverse(X_22)),inverse(X_22))) != multiply(X_21,X_22,inverse(X_22))
| multiply(X_21,X_22,multiply(X_19,X_21,inverse(X_22))) = multiply(X_21,X_22,inverse(X_22)) ),
inference(resolve,[$cnf( $equal(multiply(X_21,X_22,inverse(X_22)),X_21) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
multiply(X_21,X_22,multiply(X_19,X_21,inverse(X_22))) = multiply(X_21,X_22,inverse(X_22)),
inference(resolve,[$cnf( $equal(multiply(X_21,X_22,multiply(X_19,multiply(X_21,X_22,inverse(X_22)),inverse(X_22))),multiply(X_21,X_22,inverse(X_22))) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
( multiply(X_21,X_22,inverse(X_22)) != X_21
| multiply(X_21,X_22,multiply(X_19,X_21,inverse(X_22))) != multiply(X_21,X_22,inverse(X_22))
| multiply(X_21,X_22,multiply(X_19,X_21,inverse(X_22))) = X_21 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_21,X_22,multiply(X_19,X_21,inverse(X_22))),multiply(X_21,X_22,inverse(X_22))) ),[1],$fot(X_21)]]) ).
cnf(refute_0_23,plain,
( multiply(X_21,X_22,multiply(X_19,X_21,inverse(X_22))) != multiply(X_21,X_22,inverse(X_22))
| multiply(X_21,X_22,multiply(X_19,X_21,inverse(X_22))) = X_21 ),
inference(resolve,[$cnf( $equal(multiply(X_21,X_22,inverse(X_22)),X_21) )],[refute_0_18,refute_0_22]) ).
cnf(refute_0_24,plain,
multiply(X_21,X_22,multiply(X_19,X_21,inverse(X_22))) = X_21,
inference(resolve,[$cnf( $equal(multiply(X_21,X_22,multiply(X_19,X_21,inverse(X_22))),multiply(X_21,X_22,inverse(X_22))) )],[refute_0_21,refute_0_23]) ).
cnf(refute_0_25,plain,
multiply(X_21,X_22,multiply(multiply(X_29,inverse(X_22),X_26),X_21,inverse(X_22))) = X_21,
inference(subst,[],[refute_0_24:[bind(X_19,$fot(multiply(X_29,inverse(X_22),X_26)))]]) ).
cnf(refute_0_26,plain,
multiply(multiply(X_8,X_12,X_10),X_11,multiply(X_8,X_12,X_12)) = multiply(X_8,X_12,multiply(X_10,X_11,X_12)),
inference(subst,[],[associativity:[bind(V,$fot(X_8)),bind(W,$fot(X_12)),bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_27,plain,
multiply(X_8,X_12,X_12) = X_12,
inference(subst,[],[ternary_multiply_1:[bind(X,$fot(X_12)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_28,plain,
( multiply(X_8,X_12,X_12) != X_12
| multiply(multiply(X_8,X_12,X_10),X_11,multiply(X_8,X_12,X_12)) != multiply(X_8,X_12,multiply(X_10,X_11,X_12))
| multiply(multiply(X_8,X_12,X_10),X_11,X_12) = multiply(X_8,X_12,multiply(X_10,X_11,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_8,X_12,X_10),X_11,multiply(X_8,X_12,X_12)),multiply(X_8,X_12,multiply(X_10,X_11,X_12))) ),[0,2],$fot(X_12)]]) ).
cnf(refute_0_29,plain,
( multiply(multiply(X_8,X_12,X_10),X_11,multiply(X_8,X_12,X_12)) != multiply(X_8,X_12,multiply(X_10,X_11,X_12))
| multiply(multiply(X_8,X_12,X_10),X_11,X_12) = multiply(X_8,X_12,multiply(X_10,X_11,X_12)) ),
inference(resolve,[$cnf( $equal(multiply(X_8,X_12,X_12),X_12) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
multiply(multiply(X_8,X_12,X_10),X_11,X_12) = multiply(X_8,X_12,multiply(X_10,X_11,X_12)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_8,X_12,X_10),X_11,multiply(X_8,X_12,X_12)),multiply(X_8,X_12,multiply(X_10,X_11,X_12))) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
multiply(multiply(X_29,inverse(X_22),X_26),X_21,inverse(X_22)) = multiply(X_29,inverse(X_22),multiply(X_26,X_21,inverse(X_22))),
inference(subst,[],[refute_0_30:[bind(X_10,$fot(X_26)),bind(X_11,$fot(X_21)),bind(X_12,$fot(inverse(X_22))),bind(X_8,$fot(X_29))]]) ).
cnf(refute_0_32,plain,
( multiply(X_21,X_22,multiply(multiply(X_29,inverse(X_22),X_26),X_21,inverse(X_22))) != X_21
| multiply(multiply(X_29,inverse(X_22),X_26),X_21,inverse(X_22)) != multiply(X_29,inverse(X_22),multiply(X_26,X_21,inverse(X_22)))
| multiply(X_21,X_22,multiply(X_29,inverse(X_22),multiply(X_26,X_21,inverse(X_22)))) = X_21 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_21,X_22,multiply(multiply(X_29,inverse(X_22),X_26),X_21,inverse(X_22))),X_21) ),[0,2],$fot(multiply(X_29,inverse(X_22),multiply(X_26,X_21,inverse(X_22))))]]) ).
cnf(refute_0_33,plain,
( multiply(X_21,X_22,multiply(multiply(X_29,inverse(X_22),X_26),X_21,inverse(X_22))) != X_21
| multiply(X_21,X_22,multiply(X_29,inverse(X_22),multiply(X_26,X_21,inverse(X_22)))) = X_21 ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_29,inverse(X_22),X_26),X_21,inverse(X_22)),multiply(X_29,inverse(X_22),multiply(X_26,X_21,inverse(X_22)))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
multiply(X_21,X_22,multiply(X_29,inverse(X_22),multiply(X_26,X_21,inverse(X_22)))) = X_21,
inference(resolve,[$cnf( $equal(multiply(X_21,X_22,multiply(multiply(X_29,inverse(X_22),X_26),X_21,inverse(X_22))),X_21) )],[refute_0_25,refute_0_33]) ).
cnf(refute_0_35,plain,
multiply(multiply(V,W,X),Y,multiply(V,W,multiply(X_23,V,inverse(W)))) = multiply(V,W,multiply(X,Y,multiply(X_23,V,inverse(W)))),
inference(subst,[],[associativity:[bind(Z,$fot(multiply(X_23,V,inverse(W))))]]) ).
cnf(refute_0_36,plain,
multiply(V,W,multiply(X_23,V,inverse(W))) = V,
inference(subst,[],[refute_0_24:[bind(X_19,$fot(X_23)),bind(X_21,$fot(V)),bind(X_22,$fot(W))]]) ).
cnf(refute_0_37,plain,
( multiply(V,W,multiply(X_23,V,inverse(W))) != V
| multiply(multiply(V,W,X),Y,multiply(V,W,multiply(X_23,V,inverse(W)))) != multiply(V,W,multiply(X,Y,multiply(X_23,V,inverse(W))))
| multiply(multiply(V,W,X),Y,V) = multiply(V,W,multiply(X,Y,multiply(X_23,V,inverse(W)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(V,W,X),Y,multiply(V,W,multiply(X_23,V,inverse(W)))),multiply(V,W,multiply(X,Y,multiply(X_23,V,inverse(W))))) ),[0,2],$fot(V)]]) ).
cnf(refute_0_38,plain,
( multiply(multiply(V,W,X),Y,multiply(V,W,multiply(X_23,V,inverse(W)))) != multiply(V,W,multiply(X,Y,multiply(X_23,V,inverse(W))))
| multiply(multiply(V,W,X),Y,V) = multiply(V,W,multiply(X,Y,multiply(X_23,V,inverse(W)))) ),
inference(resolve,[$cnf( $equal(multiply(V,W,multiply(X_23,V,inverse(W))),V) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
multiply(multiply(V,W,X),Y,V) = multiply(V,W,multiply(X,Y,multiply(X_23,V,inverse(W)))),
inference(resolve,[$cnf( $equal(multiply(multiply(V,W,X),Y,multiply(V,W,multiply(X_23,V,inverse(W)))),multiply(V,W,multiply(X,Y,multiply(X_23,V,inverse(W))))) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
multiply(multiply(Z,W,X),Y,multiply(Z,W,Z)) = multiply(Z,W,multiply(X,Y,Z)),
inference(subst,[],[associativity:[bind(V,$fot(Z))]]) ).
cnf(refute_0_41,plain,
multiply(multiply(X_9,X_9,X_10),X_11,multiply(X_9,X_9,X_12)) = multiply(X_9,X_9,multiply(X_10,X_11,X_12)),
inference(subst,[],[associativity:[bind(V,$fot(X_9)),bind(W,$fot(X_9)),bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_42,plain,
multiply(X_9,X_9,X_12) = X_9,
inference(subst,[],[ternary_multiply_2:[bind(X,$fot(X_9)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_43,plain,
( multiply(X_9,X_9,X_12) != X_9
| multiply(multiply(X_9,X_9,X_10),X_11,multiply(X_9,X_9,X_12)) != multiply(X_9,X_9,multiply(X_10,X_11,X_12))
| multiply(multiply(X_9,X_9,X_10),X_11,X_9) = multiply(X_9,X_9,multiply(X_10,X_11,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_9,X_9,X_10),X_11,multiply(X_9,X_9,X_12)),multiply(X_9,X_9,multiply(X_10,X_11,X_12))) ),[0,2],$fot(X_9)]]) ).
cnf(refute_0_44,plain,
( multiply(multiply(X_9,X_9,X_10),X_11,multiply(X_9,X_9,X_12)) != multiply(X_9,X_9,multiply(X_10,X_11,X_12))
| multiply(multiply(X_9,X_9,X_10),X_11,X_9) = multiply(X_9,X_9,multiply(X_10,X_11,X_12)) ),
inference(resolve,[$cnf( $equal(multiply(X_9,X_9,X_12),X_9) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
multiply(multiply(X_9,X_9,X_10),X_11,X_9) = multiply(X_9,X_9,multiply(X_10,X_11,X_12)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_9,X_9,X_10),X_11,multiply(X_9,X_9,X_12)),multiply(X_9,X_9,multiply(X_10,X_11,X_12))) )],[refute_0_41,refute_0_44]) ).
cnf(refute_0_46,plain,
multiply(X_9,X_9,X_10) = X_9,
inference(subst,[],[ternary_multiply_2:[bind(X,$fot(X_9)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_47,plain,
multiply(multiply(X_9,X_9,X_10),X_11,X_9) = multiply(multiply(X_9,X_9,X_10),X_11,X_9),
introduced(tautology,[refl,[$fot(multiply(multiply(X_9,X_9,X_10),X_11,X_9))]]) ).
cnf(refute_0_48,plain,
( multiply(X_9,X_9,X_10) != X_9
| multiply(multiply(X_9,X_9,X_10),X_11,X_9) != multiply(multiply(X_9,X_9,X_10),X_11,X_9)
| multiply(multiply(X_9,X_9,X_10),X_11,X_9) = multiply(X_9,X_11,X_9) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_9,X_9,X_10),X_11,X_9),multiply(multiply(X_9,X_9,X_10),X_11,X_9)) ),[1,0],$fot(X_9)]]) ).
cnf(refute_0_49,plain,
( multiply(X_9,X_9,X_10) != X_9
| multiply(multiply(X_9,X_9,X_10),X_11,X_9) = multiply(X_9,X_11,X_9) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_9,X_9,X_10),X_11,X_9),multiply(multiply(X_9,X_9,X_10),X_11,X_9)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
multiply(multiply(X_9,X_9,X_10),X_11,X_9) = multiply(X_9,X_11,X_9),
inference(resolve,[$cnf( $equal(multiply(X_9,X_9,X_10),X_9) )],[refute_0_46,refute_0_49]) ).
cnf(refute_0_51,plain,
( multiply(multiply(X_9,X_9,X_10),X_11,X_9) != multiply(X_9,X_11,X_9)
| multiply(multiply(X_9,X_9,X_10),X_11,X_9) != multiply(X_9,X_9,multiply(X_10,X_11,X_12))
| multiply(X_9,X_11,X_9) = multiply(X_9,X_9,multiply(X_10,X_11,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_9,X_9,X_10),X_11,X_9),multiply(X_9,X_9,multiply(X_10,X_11,X_12))) ),[0],$fot(multiply(X_9,X_11,X_9))]]) ).
cnf(refute_0_52,plain,
( multiply(multiply(X_9,X_9,X_10),X_11,X_9) != multiply(X_9,X_9,multiply(X_10,X_11,X_12))
| multiply(X_9,X_11,X_9) = multiply(X_9,X_9,multiply(X_10,X_11,X_12)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_9,X_9,X_10),X_11,X_9),multiply(X_9,X_11,X_9)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
multiply(X_9,X_9,multiply(X_10,X_11,X_12)) = X_9,
inference(subst,[],[ternary_multiply_2:[bind(X,$fot(X_9)),bind(Y,$fot(multiply(X_10,X_11,X_12)))]]) ).
cnf(refute_0_54,plain,
( multiply(X_9,X_11,X_9) != multiply(X_9,X_9,multiply(X_10,X_11,X_12))
| multiply(X_9,X_9,multiply(X_10,X_11,X_12)) != X_9
| multiply(X_9,X_11,X_9) = X_9 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_9,X_11,X_9),X_9) ),[0],$fot(multiply(X_9,X_9,multiply(X_10,X_11,X_12)))]]) ).
cnf(refute_0_55,plain,
( multiply(X_9,X_11,X_9) != multiply(X_9,X_9,multiply(X_10,X_11,X_12))
| multiply(X_9,X_11,X_9) = X_9 ),
inference(resolve,[$cnf( $equal(multiply(X_9,X_9,multiply(X_10,X_11,X_12)),X_9) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( multiply(multiply(X_9,X_9,X_10),X_11,X_9) != multiply(X_9,X_9,multiply(X_10,X_11,X_12))
| multiply(X_9,X_11,X_9) = X_9 ),
inference(resolve,[$cnf( $equal(multiply(X_9,X_11,X_9),multiply(X_9,X_9,multiply(X_10,X_11,X_12))) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
multiply(X_9,X_11,X_9) = X_9,
inference(resolve,[$cnf( $equal(multiply(multiply(X_9,X_9,X_10),X_11,X_9),multiply(X_9,X_9,multiply(X_10,X_11,X_12))) )],[refute_0_45,refute_0_56]) ).
cnf(refute_0_58,plain,
multiply(Z,W,Z) = Z,
inference(subst,[],[refute_0_57:[bind(X_11,$fot(W)),bind(X_9,$fot(Z))]]) ).
cnf(refute_0_59,plain,
( multiply(Z,W,Z) != Z
| multiply(multiply(Z,W,X),Y,multiply(Z,W,Z)) != multiply(Z,W,multiply(X,Y,Z))
| multiply(multiply(Z,W,X),Y,Z) = multiply(Z,W,multiply(X,Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(Z,W,X),Y,multiply(Z,W,Z)),multiply(Z,W,multiply(X,Y,Z))) ),[0,2],$fot(Z)]]) ).
cnf(refute_0_60,plain,
( multiply(multiply(Z,W,X),Y,multiply(Z,W,Z)) != multiply(Z,W,multiply(X,Y,Z))
| multiply(multiply(Z,W,X),Y,Z) = multiply(Z,W,multiply(X,Y,Z)) ),
inference(resolve,[$cnf( $equal(multiply(Z,W,Z),Z) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
multiply(multiply(Z,W,X),Y,Z) = multiply(Z,W,multiply(X,Y,Z)),
inference(resolve,[$cnf( $equal(multiply(multiply(Z,W,X),Y,multiply(Z,W,Z)),multiply(Z,W,multiply(X,Y,Z))) )],[refute_0_40,refute_0_60]) ).
cnf(refute_0_62,plain,
multiply(multiply(V,W,X),Y,V) = multiply(V,W,multiply(X,Y,V)),
inference(subst,[],[refute_0_61:[bind(Z,$fot(V))]]) ).
cnf(refute_0_63,plain,
( multiply(multiply(V,W,X),Y,V) != multiply(V,W,multiply(X,Y,V))
| multiply(multiply(V,W,X),Y,V) != multiply(V,W,multiply(X,Y,multiply(X_23,V,inverse(W))))
| multiply(V,W,multiply(X,Y,V)) = multiply(V,W,multiply(X,Y,multiply(X_23,V,inverse(W)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(V,W,X),Y,V),multiply(V,W,multiply(X,Y,multiply(X_23,V,inverse(W))))) ),[0],$fot(multiply(V,W,multiply(X,Y,V)))]]) ).
cnf(refute_0_64,plain,
( multiply(multiply(V,W,X),Y,V) != multiply(V,W,multiply(X,Y,multiply(X_23,V,inverse(W))))
| multiply(V,W,multiply(X,Y,V)) = multiply(V,W,multiply(X,Y,multiply(X_23,V,inverse(W)))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(V,W,X),Y,V),multiply(V,W,multiply(X,Y,V))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
multiply(V,W,multiply(X,Y,V)) = multiply(V,W,multiply(X,Y,multiply(X_23,V,inverse(W)))),
inference(resolve,[$cnf( $equal(multiply(multiply(V,W,X),Y,V),multiply(V,W,multiply(X,Y,multiply(X_23,V,inverse(W))))) )],[refute_0_39,refute_0_64]) ).
cnf(refute_0_66,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_67,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_68,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
( multiply(V,W,multiply(X,Y,V)) != multiply(V,W,multiply(X,Y,multiply(X_23,V,inverse(W))))
| multiply(V,W,multiply(X,Y,multiply(X_23,V,inverse(W)))) = multiply(V,W,multiply(X,Y,V)) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(multiply(V,W,multiply(X,Y,V)))),bind(Y0,$fot(multiply(V,W,multiply(X,Y,multiply(X_23,V,inverse(W))))))]]) ).
cnf(refute_0_70,plain,
multiply(V,W,multiply(X,Y,multiply(X_23,V,inverse(W)))) = multiply(V,W,multiply(X,Y,V)),
inference(resolve,[$cnf( $equal(multiply(V,W,multiply(X,Y,V)),multiply(V,W,multiply(X,Y,multiply(X_23,V,inverse(W))))) )],[refute_0_65,refute_0_69]) ).
cnf(refute_0_71,plain,
multiply(X_21,X_22,multiply(X_29,inverse(X_22),multiply(X_26,X_21,inverse(X_22)))) = multiply(X_21,X_22,multiply(X_29,inverse(X_22),X_21)),
inference(subst,[],[refute_0_70:[bind(V,$fot(X_21)),bind(W,$fot(X_22)),bind(X,$fot(X_29)),bind(Y,$fot(inverse(X_22))),bind(X_23,$fot(X_26))]]) ).
cnf(refute_0_72,plain,
( multiply(X_21,X_22,multiply(X_29,inverse(X_22),multiply(X_26,X_21,inverse(X_22)))) != X_21
| multiply(X_21,X_22,multiply(X_29,inverse(X_22),multiply(X_26,X_21,inverse(X_22)))) != multiply(X_21,X_22,multiply(X_29,inverse(X_22),X_21))
| multiply(X_21,X_22,multiply(X_29,inverse(X_22),X_21)) = X_21 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_21,X_22,multiply(X_29,inverse(X_22),multiply(X_26,X_21,inverse(X_22)))),X_21) ),[0],$fot(multiply(X_21,X_22,multiply(X_29,inverse(X_22),X_21)))]]) ).
cnf(refute_0_73,plain,
( multiply(X_21,X_22,multiply(X_29,inverse(X_22),multiply(X_26,X_21,inverse(X_22)))) != X_21
| multiply(X_21,X_22,multiply(X_29,inverse(X_22),X_21)) = X_21 ),
inference(resolve,[$cnf( $equal(multiply(X_21,X_22,multiply(X_29,inverse(X_22),multiply(X_26,X_21,inverse(X_22)))),multiply(X_21,X_22,multiply(X_29,inverse(X_22),X_21))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
multiply(X_21,X_22,multiply(X_29,inverse(X_22),X_21)) = X_21,
inference(resolve,[$cnf( $equal(multiply(X_21,X_22,multiply(X_29,inverse(X_22),multiply(X_26,X_21,inverse(X_22)))),X_21) )],[refute_0_34,refute_0_73]) ).
cnf(refute_0_75,plain,
multiply(X_21,X_29,multiply(X_29,inverse(X_29),X_21)) = X_21,
inference(subst,[],[refute_0_74:[bind(X_22,$fot(X_29))]]) ).
cnf(refute_0_76,plain,
multiply(multiply(X_8,X_10,X_10),X_11,multiply(X_8,X_10,X_12)) = multiply(X_8,X_10,multiply(X_10,X_11,X_12)),
inference(subst,[],[associativity:[bind(V,$fot(X_8)),bind(W,$fot(X_10)),bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_77,plain,
multiply(X_8,X_10,X_10) = X_10,
inference(subst,[],[ternary_multiply_1:[bind(X,$fot(X_10)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_78,plain,
( multiply(X_8,X_10,X_10) != X_10
| multiply(multiply(X_8,X_10,X_10),X_11,multiply(X_8,X_10,X_12)) != multiply(X_8,X_10,multiply(X_10,X_11,X_12))
| multiply(X_10,X_11,multiply(X_8,X_10,X_12)) = multiply(X_8,X_10,multiply(X_10,X_11,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_8,X_10,X_10),X_11,multiply(X_8,X_10,X_12)),multiply(X_8,X_10,multiply(X_10,X_11,X_12))) ),[0,0],$fot(X_10)]]) ).
cnf(refute_0_79,plain,
( multiply(multiply(X_8,X_10,X_10),X_11,multiply(X_8,X_10,X_12)) != multiply(X_8,X_10,multiply(X_10,X_11,X_12))
| multiply(X_10,X_11,multiply(X_8,X_10,X_12)) = multiply(X_8,X_10,multiply(X_10,X_11,X_12)) ),
inference(resolve,[$cnf( $equal(multiply(X_8,X_10,X_10),X_10) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
multiply(X_10,X_11,multiply(X_8,X_10,X_12)) = multiply(X_8,X_10,multiply(X_10,X_11,X_12)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_8,X_10,X_10),X_11,multiply(X_8,X_10,X_12)),multiply(X_8,X_10,multiply(X_10,X_11,X_12))) )],[refute_0_76,refute_0_79]) ).
cnf(refute_0_81,plain,
multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)) = multiply(X_21,X_29,multiply(X_29,inverse(X_29),X_21)),
inference(subst,[],[refute_0_80:[bind(X_10,$fot(X_29)),bind(X_11,$fot(inverse(X_29))),bind(X_12,$fot(X_21)),bind(X_8,$fot(X_21))]]) ).
cnf(refute_0_82,plain,
( multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)) != multiply(X_21,X_29,multiply(X_29,inverse(X_29),X_21))
| multiply(X_21,X_29,multiply(X_29,inverse(X_29),X_21)) = multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)))),bind(Y0,$fot(multiply(X_21,X_29,multiply(X_29,inverse(X_29),X_21))))]]) ).
cnf(refute_0_83,plain,
multiply(X_21,X_29,multiply(X_29,inverse(X_29),X_21)) = multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)),
inference(resolve,[$cnf( $equal(multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)),multiply(X_21,X_29,multiply(X_29,inverse(X_29),X_21))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
( multiply(X_21,X_29,multiply(X_29,inverse(X_29),X_21)) != X_21
| multiply(X_21,X_29,multiply(X_29,inverse(X_29),X_21)) != multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21))
| multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)) = X_21 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_21,X_29,multiply(X_29,inverse(X_29),X_21)),X_21) ),[0],$fot(multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)))]]) ).
cnf(refute_0_85,plain,
( multiply(X_21,X_29,multiply(X_29,inverse(X_29),X_21)) != X_21
| multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)) = X_21 ),
inference(resolve,[$cnf( $equal(multiply(X_21,X_29,multiply(X_29,inverse(X_29),X_21)),multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)) = X_21,
inference(resolve,[$cnf( $equal(multiply(X_21,X_29,multiply(X_29,inverse(X_29),X_21)),X_21) )],[refute_0_75,refute_0_85]) ).
cnf(refute_0_87,plain,
multiply(X_21,X_29,X_21) = X_21,
inference(subst,[],[refute_0_57:[bind(X_11,$fot(X_29)),bind(X_9,$fot(X_21))]]) ).
cnf(refute_0_88,plain,
multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)) = multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)),
introduced(tautology,[refl,[$fot(multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)))]]) ).
cnf(refute_0_89,plain,
( multiply(X_21,X_29,X_21) != X_21
| multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)) != multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21))
| multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)) = multiply(X_29,inverse(X_29),X_21) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)),multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21))) ),[1,2],$fot(X_21)]]) ).
cnf(refute_0_90,plain,
( multiply(X_21,X_29,X_21) != X_21
| multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)) = multiply(X_29,inverse(X_29),X_21) ),
inference(resolve,[$cnf( $equal(multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)),multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)) = multiply(X_29,inverse(X_29),X_21),
inference(resolve,[$cnf( $equal(multiply(X_21,X_29,X_21),X_21) )],[refute_0_87,refute_0_90]) ).
cnf(refute_0_92,plain,
( multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)) != X_21
| multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)) != multiply(X_29,inverse(X_29),X_21)
| multiply(X_29,inverse(X_29),X_21) = X_21 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)),X_21) ),[0],$fot(multiply(X_29,inverse(X_29),X_21))]]) ).
cnf(refute_0_93,plain,
( multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)) != X_21
| multiply(X_29,inverse(X_29),X_21) = X_21 ),
inference(resolve,[$cnf( $equal(multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)),multiply(X_29,inverse(X_29),X_21)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
multiply(X_29,inverse(X_29),X_21) = X_21,
inference(resolve,[$cnf( $equal(multiply(X_29,inverse(X_29),multiply(X_21,X_29,X_21)),X_21) )],[refute_0_86,refute_0_93]) ).
cnf(refute_0_95,plain,
multiply(a,inverse(a),b) = b,
inference(subst,[],[refute_0_94:[bind(X_21,$fot(b)),bind(X_29,$fot(a))]]) ).
cnf(refute_0_96,plain,
multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) = multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)),
introduced(tautology,[refl,[$fot(multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)))]]) ).
cnf(refute_0_97,plain,
( multiply(a,inverse(a),b) != b
| multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) != multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c))
| multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) = multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)),multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c))) ),[1,0],$fot(b)]]) ).
cnf(refute_0_98,plain,
( multiply(a,inverse(a),b) != b
| multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) = multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)),multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) = multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)),
inference(resolve,[$cnf( $equal(multiply(a,inverse(a),b),b) )],[refute_0_95,refute_0_98]) ).
cnf(refute_0_100,plain,
( multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) != b
| multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) != multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c))
| multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) = b ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)),multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c))) ),[1],$fot(b)]]) ).
cnf(refute_0_101,plain,
( multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) != b
| multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) = b ),
inference(resolve,[$cnf( $equal(multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)),multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) != b,
inference(resolve,[$cnf( $equal(multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)),b) )],[refute_0_101,refute_0_11]) ).
cnf(refute_0_103,plain,
multiply(b,multiply(c,d,multiply(e,f,g)),inverse(multiply(c,d,multiply(e,f,g)))) = b,
inference(subst,[],[right_inverse:[bind(X,$fot(b)),bind(Y,$fot(multiply(c,d,multiply(e,f,g))))]]) ).
cnf(refute_0_104,plain,
multiply(multiply(X_29,X_28,inverse(X_28)),X_27,X_28) = multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28)),
inference(subst,[],[refute_0_30:[bind(X_10,$fot(inverse(X_28))),bind(X_11,$fot(X_27)),bind(X_12,$fot(X_28)),bind(X_8,$fot(X_29))]]) ).
cnf(refute_0_105,plain,
multiply(X_29,X_28,inverse(X_28)) = X_29,
inference(subst,[],[right_inverse:[bind(X,$fot(X_29)),bind(Y,$fot(X_28))]]) ).
cnf(refute_0_106,plain,
( multiply(X_29,X_28,inverse(X_28)) != X_29
| multiply(multiply(X_29,X_28,inverse(X_28)),X_27,X_28) != multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28))
| multiply(X_29,X_27,X_28) = multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_29,X_28,inverse(X_28)),X_27,X_28),multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28))) ),[0,0],$fot(X_29)]]) ).
cnf(refute_0_107,plain,
( multiply(multiply(X_29,X_28,inverse(X_28)),X_27,X_28) != multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28))
| multiply(X_29,X_27,X_28) = multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28)) ),
inference(resolve,[$cnf( $equal(multiply(X_29,X_28,inverse(X_28)),X_29) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
multiply(X_29,X_27,X_28) = multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_29,X_28,inverse(X_28)),X_27,X_28),multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28))) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
multiply(X_28,inverse(X_28),X_27) = X_27,
inference(subst,[],[refute_0_94:[bind(X_21,$fot(X_27)),bind(X_29,$fot(X_28))]]) ).
cnf(refute_0_110,plain,
multiply(X_10,X_11,multiply(X_8,X_10,multiply(inverse(X_10),X_8,X_60))) = multiply(X_8,X_10,multiply(X_10,X_11,multiply(inverse(X_10),X_8,X_60))),
inference(subst,[],[refute_0_80:[bind(X_12,$fot(multiply(inverse(X_10),X_8,X_60)))]]) ).
cnf(refute_0_111,plain,
multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12)) = multiply(X_8,X_9,X_10),
inference(subst,[],[ternary_multiply_2:[bind(X,$fot(multiply(X_8,X_9,X_10))),bind(Y,$fot(multiply(X_8,X_9,X_12)))]]) ).
cnf(refute_0_112,plain,
multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12)) = multiply(X_8,X_9,multiply(X_10,multiply(X_8,X_9,X_10),X_12)),
inference(subst,[],[associativity:[bind(V,$fot(X_8)),bind(W,$fot(X_9)),bind(X,$fot(X_10)),bind(Y,$fot(multiply(X_8,X_9,X_10))),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_113,plain,
( multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12)) != multiply(X_8,X_9,X_10)
| multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12)) != multiply(X_8,X_9,multiply(X_10,multiply(X_8,X_9,X_10),X_12))
| multiply(X_8,X_9,multiply(X_10,multiply(X_8,X_9,X_10),X_12)) = multiply(X_8,X_9,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12)),multiply(X_8,X_9,X_10)) ),[0],$fot(multiply(X_8,X_9,multiply(X_10,multiply(X_8,X_9,X_10),X_12)))]]) ).
cnf(refute_0_114,plain,
( multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12)) != multiply(X_8,X_9,X_10)
| multiply(X_8,X_9,multiply(X_10,multiply(X_8,X_9,X_10),X_12)) = multiply(X_8,X_9,X_10) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12)),multiply(X_8,X_9,multiply(X_10,multiply(X_8,X_9,X_10),X_12))) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
multiply(X_8,X_9,multiply(X_10,multiply(X_8,X_9,X_10),X_12)) = multiply(X_8,X_9,X_10),
inference(resolve,[$cnf( $equal(multiply(multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_10),multiply(X_8,X_9,X_12)),multiply(X_8,X_9,X_10)) )],[refute_0_111,refute_0_114]) ).
cnf(refute_0_116,plain,
multiply(X_17,X_18,multiply(inverse(X_18),multiply(X_17,X_18,inverse(X_18)),X_16)) = multiply(X_17,X_18,inverse(X_18)),
inference(subst,[],[refute_0_115:[bind(X_10,$fot(inverse(X_18))),bind(X_12,$fot(X_16)),bind(X_8,$fot(X_17)),bind(X_9,$fot(X_18))]]) ).
cnf(refute_0_117,plain,
multiply(X_17,X_18,inverse(X_18)) = X_17,
inference(subst,[],[right_inverse:[bind(X,$fot(X_17)),bind(Y,$fot(X_18))]]) ).
cnf(refute_0_118,plain,
( multiply(X_17,X_18,inverse(X_18)) != X_17
| multiply(X_17,X_18,multiply(inverse(X_18),multiply(X_17,X_18,inverse(X_18)),X_16)) != multiply(X_17,X_18,inverse(X_18))
| multiply(X_17,X_18,multiply(inverse(X_18),X_17,X_16)) = multiply(X_17,X_18,inverse(X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_17,X_18,multiply(inverse(X_18),multiply(X_17,X_18,inverse(X_18)),X_16)),multiply(X_17,X_18,inverse(X_18))) ),[0,2,1],$fot(X_17)]]) ).
cnf(refute_0_119,plain,
( multiply(X_17,X_18,multiply(inverse(X_18),multiply(X_17,X_18,inverse(X_18)),X_16)) != multiply(X_17,X_18,inverse(X_18))
| multiply(X_17,X_18,multiply(inverse(X_18),X_17,X_16)) = multiply(X_17,X_18,inverse(X_18)) ),
inference(resolve,[$cnf( $equal(multiply(X_17,X_18,inverse(X_18)),X_17) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
multiply(X_17,X_18,multiply(inverse(X_18),X_17,X_16)) = multiply(X_17,X_18,inverse(X_18)),
inference(resolve,[$cnf( $equal(multiply(X_17,X_18,multiply(inverse(X_18),multiply(X_17,X_18,inverse(X_18)),X_16)),multiply(X_17,X_18,inverse(X_18))) )],[refute_0_116,refute_0_119]) ).
cnf(refute_0_121,plain,
( multiply(X_17,X_18,inverse(X_18)) != X_17
| multiply(X_17,X_18,multiply(inverse(X_18),X_17,X_16)) != multiply(X_17,X_18,inverse(X_18))
| multiply(X_17,X_18,multiply(inverse(X_18),X_17,X_16)) = X_17 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_17,X_18,multiply(inverse(X_18),X_17,X_16)),multiply(X_17,X_18,inverse(X_18))) ),[1],$fot(X_17)]]) ).
cnf(refute_0_122,plain,
( multiply(X_17,X_18,multiply(inverse(X_18),X_17,X_16)) != multiply(X_17,X_18,inverse(X_18))
| multiply(X_17,X_18,multiply(inverse(X_18),X_17,X_16)) = X_17 ),
inference(resolve,[$cnf( $equal(multiply(X_17,X_18,inverse(X_18)),X_17) )],[refute_0_117,refute_0_121]) ).
cnf(refute_0_123,plain,
multiply(X_17,X_18,multiply(inverse(X_18),X_17,X_16)) = X_17,
inference(resolve,[$cnf( $equal(multiply(X_17,X_18,multiply(inverse(X_18),X_17,X_16)),multiply(X_17,X_18,inverse(X_18))) )],[refute_0_120,refute_0_122]) ).
cnf(refute_0_124,plain,
multiply(X_8,X_10,multiply(inverse(X_10),X_8,X_60)) = X_8,
inference(subst,[],[refute_0_123:[bind(X_16,$fot(X_60)),bind(X_17,$fot(X_8)),bind(X_18,$fot(X_10))]]) ).
cnf(refute_0_125,plain,
( multiply(X_10,X_11,multiply(X_8,X_10,multiply(inverse(X_10),X_8,X_60))) != multiply(X_8,X_10,multiply(X_10,X_11,multiply(inverse(X_10),X_8,X_60)))
| multiply(X_8,X_10,multiply(inverse(X_10),X_8,X_60)) != X_8
| multiply(X_10,X_11,X_8) = multiply(X_8,X_10,multiply(X_10,X_11,multiply(inverse(X_10),X_8,X_60))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_10,X_11,multiply(X_8,X_10,multiply(inverse(X_10),X_8,X_60))),multiply(X_8,X_10,multiply(X_10,X_11,multiply(inverse(X_10),X_8,X_60)))) ),[0,2],$fot(X_8)]]) ).
cnf(refute_0_126,plain,
( multiply(X_10,X_11,multiply(X_8,X_10,multiply(inverse(X_10),X_8,X_60))) != multiply(X_8,X_10,multiply(X_10,X_11,multiply(inverse(X_10),X_8,X_60)))
| multiply(X_10,X_11,X_8) = multiply(X_8,X_10,multiply(X_10,X_11,multiply(inverse(X_10),X_8,X_60))) ),
inference(resolve,[$cnf( $equal(multiply(X_8,X_10,multiply(inverse(X_10),X_8,X_60)),X_8) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
multiply(X_10,X_11,X_8) = multiply(X_8,X_10,multiply(X_10,X_11,multiply(inverse(X_10),X_8,X_60))),
inference(resolve,[$cnf( $equal(multiply(X_10,X_11,multiply(X_8,X_10,multiply(inverse(X_10),X_8,X_60))),multiply(X_8,X_10,multiply(X_10,X_11,multiply(inverse(X_10),X_8,X_60)))) )],[refute_0_110,refute_0_126]) ).
cnf(refute_0_128,plain,
multiply(X_8,multiply(X_8,X_10,X_10),X_11) = multiply(X_8,multiply(X_8,X_10,X_10),X_11),
introduced(tautology,[refl,[$fot(multiply(X_8,multiply(X_8,X_10,X_10),X_11))]]) ).
cnf(refute_0_129,plain,
( multiply(X_8,X_10,X_10) != X_10
| multiply(X_8,multiply(X_8,X_10,X_10),X_11) != multiply(X_8,multiply(X_8,X_10,X_10),X_11)
| multiply(X_8,multiply(X_8,X_10,X_10),X_11) = multiply(X_8,X_10,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_8,multiply(X_8,X_10,X_10),X_11),multiply(X_8,multiply(X_8,X_10,X_10),X_11)) ),[1,1],$fot(X_10)]]) ).
cnf(refute_0_130,plain,
( multiply(X_8,X_10,X_10) != X_10
| multiply(X_8,multiply(X_8,X_10,X_10),X_11) = multiply(X_8,X_10,X_11) ),
inference(resolve,[$cnf( $equal(multiply(X_8,multiply(X_8,X_10,X_10),X_11),multiply(X_8,multiply(X_8,X_10,X_10),X_11)) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
multiply(X_8,multiply(X_8,X_10,X_10),X_11) = multiply(X_8,X_10,X_11),
inference(resolve,[$cnf( $equal(multiply(X_8,X_10,X_10),X_10) )],[refute_0_77,refute_0_130]) ).
cnf(refute_0_132,plain,
multiply(multiply(V,W,X),Y,multiply(V,W,multiply(inverse(W),V,X_60))) = multiply(V,W,multiply(X,Y,multiply(inverse(W),V,X_60))),
inference(subst,[],[associativity:[bind(Z,$fot(multiply(inverse(W),V,X_60)))]]) ).
cnf(refute_0_133,plain,
multiply(V,W,multiply(inverse(W),V,X_60)) = V,
inference(subst,[],[refute_0_123:[bind(X_16,$fot(X_60)),bind(X_17,$fot(V)),bind(X_18,$fot(W))]]) ).
cnf(refute_0_134,plain,
( multiply(V,W,multiply(inverse(W),V,X_60)) != V
| multiply(multiply(V,W,X),Y,multiply(V,W,multiply(inverse(W),V,X_60))) != multiply(V,W,multiply(X,Y,multiply(inverse(W),V,X_60)))
| multiply(multiply(V,W,X),Y,V) = multiply(V,W,multiply(X,Y,multiply(inverse(W),V,X_60))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(V,W,X),Y,multiply(V,W,multiply(inverse(W),V,X_60))),multiply(V,W,multiply(X,Y,multiply(inverse(W),V,X_60)))) ),[0,2],$fot(V)]]) ).
cnf(refute_0_135,plain,
( multiply(multiply(V,W,X),Y,multiply(V,W,multiply(inverse(W),V,X_60))) != multiply(V,W,multiply(X,Y,multiply(inverse(W),V,X_60)))
| multiply(multiply(V,W,X),Y,V) = multiply(V,W,multiply(X,Y,multiply(inverse(W),V,X_60))) ),
inference(resolve,[$cnf( $equal(multiply(V,W,multiply(inverse(W),V,X_60)),V) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
multiply(multiply(V,W,X),Y,V) = multiply(V,W,multiply(X,Y,multiply(inverse(W),V,X_60))),
inference(resolve,[$cnf( $equal(multiply(multiply(V,W,X),Y,multiply(V,W,multiply(inverse(W),V,X_60))),multiply(V,W,multiply(X,Y,multiply(inverse(W),V,X_60)))) )],[refute_0_132,refute_0_135]) ).
cnf(refute_0_137,plain,
multiply(multiply(inverse(inverse(X_22)),X_29,X_60),X_22,multiply(X_29,inverse(X_22),multiply(inverse(inverse(X_22)),X_29,X_60))) = multiply(inverse(inverse(X_22)),X_29,X_60),
inference(subst,[],[refute_0_74:[bind(X_21,$fot(multiply(inverse(inverse(X_22)),X_29,X_60)))]]) ).
cnf(refute_0_138,plain,
multiply(X_29,inverse(X_22),multiply(inverse(inverse(X_22)),X_29,X_60)) = X_29,
inference(subst,[],[refute_0_123:[bind(X_16,$fot(X_60)),bind(X_17,$fot(X_29)),bind(X_18,$fot(inverse(X_22)))]]) ).
cnf(refute_0_139,plain,
( multiply(X_29,inverse(X_22),multiply(inverse(inverse(X_22)),X_29,X_60)) != X_29
| multiply(multiply(inverse(inverse(X_22)),X_29,X_60),X_22,multiply(X_29,inverse(X_22),multiply(inverse(inverse(X_22)),X_29,X_60))) != multiply(inverse(inverse(X_22)),X_29,X_60)
| multiply(multiply(inverse(inverse(X_22)),X_29,X_60),X_22,X_29) = multiply(inverse(inverse(X_22)),X_29,X_60) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(inverse(X_22)),X_29,X_60),X_22,multiply(X_29,inverse(X_22),multiply(inverse(inverse(X_22)),X_29,X_60))),multiply(inverse(inverse(X_22)),X_29,X_60)) ),[0,2],$fot(X_29)]]) ).
cnf(refute_0_140,plain,
( multiply(multiply(inverse(inverse(X_22)),X_29,X_60),X_22,multiply(X_29,inverse(X_22),multiply(inverse(inverse(X_22)),X_29,X_60))) != multiply(inverse(inverse(X_22)),X_29,X_60)
| multiply(multiply(inverse(inverse(X_22)),X_29,X_60),X_22,X_29) = multiply(inverse(inverse(X_22)),X_29,X_60) ),
inference(resolve,[$cnf( $equal(multiply(X_29,inverse(X_22),multiply(inverse(inverse(X_22)),X_29,X_60)),X_29) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
multiply(multiply(inverse(inverse(X_22)),X_29,X_60),X_22,X_29) = multiply(inverse(inverse(X_22)),X_29,X_60),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(inverse(X_22)),X_29,X_60),X_22,multiply(X_29,inverse(X_22),multiply(inverse(inverse(X_22)),X_29,X_60))),multiply(inverse(inverse(X_22)),X_29,X_60)) )],[refute_0_137,refute_0_140]) ).
cnf(refute_0_142,plain,
multiply(multiply(X_11,X_12,X_10),X_11,X_12) = multiply(X_11,X_12,multiply(X_10,X_11,X_12)),
inference(subst,[],[refute_0_30:[bind(X_8,$fot(X_11))]]) ).
cnf(refute_0_143,plain,
multiply(X_11,X_12,multiply(X_10,X_11,X_12)) = multiply(X_10,X_11,multiply(X_11,X_12,X_12)),
inference(subst,[],[refute_0_80:[bind(X_10,$fot(X_11)),bind(X_11,$fot(X_12)),bind(X_8,$fot(X_10))]]) ).
cnf(refute_0_144,plain,
( multiply(X_11,X_12,multiply(X_10,X_11,X_12)) != multiply(X_10,X_11,multiply(X_11,X_12,X_12))
| multiply(multiply(X_11,X_12,X_10),X_11,X_12) != multiply(X_11,X_12,multiply(X_10,X_11,X_12))
| multiply(multiply(X_11,X_12,X_10),X_11,X_12) = multiply(X_10,X_11,multiply(X_11,X_12,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_11,X_12,X_10),X_11,X_12),multiply(X_11,X_12,multiply(X_10,X_11,X_12))) ),[1],$fot(multiply(X_10,X_11,multiply(X_11,X_12,X_12)))]]) ).
cnf(refute_0_145,plain,
( multiply(multiply(X_11,X_12,X_10),X_11,X_12) != multiply(X_11,X_12,multiply(X_10,X_11,X_12))
| multiply(multiply(X_11,X_12,X_10),X_11,X_12) = multiply(X_10,X_11,multiply(X_11,X_12,X_12)) ),
inference(resolve,[$cnf( $equal(multiply(X_11,X_12,multiply(X_10,X_11,X_12)),multiply(X_10,X_11,multiply(X_11,X_12,X_12))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
multiply(multiply(X_11,X_12,X_10),X_11,X_12) = multiply(X_10,X_11,multiply(X_11,X_12,X_12)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_11,X_12,X_10),X_11,X_12),multiply(X_11,X_12,multiply(X_10,X_11,X_12))) )],[refute_0_142,refute_0_145]) ).
cnf(refute_0_147,plain,
( multiply(multiply(X_11,X_12,X_10),X_11,X_12) != multiply(X_10,X_11,multiply(X_11,X_12,X_12))
| multiply(multiply(X_11,X_12,X_10),X_11,X_12) != multiply(X_11,X_12,multiply(X_10,X_11,X_12))
| multiply(X_11,X_12,multiply(X_10,X_11,X_12)) = multiply(X_10,X_11,multiply(X_11,X_12,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_11,X_12,X_10),X_11,X_12),multiply(X_10,X_11,multiply(X_11,X_12,X_12))) ),[0],$fot(multiply(X_11,X_12,multiply(X_10,X_11,X_12)))]]) ).
cnf(refute_0_148,plain,
( multiply(multiply(X_11,X_12,X_10),X_11,X_12) != multiply(X_10,X_11,multiply(X_11,X_12,X_12))
| multiply(X_11,X_12,multiply(X_10,X_11,X_12)) = multiply(X_10,X_11,multiply(X_11,X_12,X_12)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_11,X_12,X_10),X_11,X_12),multiply(X_11,X_12,multiply(X_10,X_11,X_12))) )],[refute_0_142,refute_0_147]) ).
cnf(refute_0_149,plain,
multiply(X_11,X_12,X_12) = X_12,
inference(subst,[],[ternary_multiply_1:[bind(X,$fot(X_12)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_150,plain,
multiply(X_10,X_11,multiply(X_11,X_12,X_12)) = multiply(X_10,X_11,multiply(X_11,X_12,X_12)),
introduced(tautology,[refl,[$fot(multiply(X_10,X_11,multiply(X_11,X_12,X_12)))]]) ).
cnf(refute_0_151,plain,
( multiply(X_10,X_11,multiply(X_11,X_12,X_12)) != multiply(X_10,X_11,multiply(X_11,X_12,X_12))
| multiply(X_11,X_12,X_12) != X_12
| multiply(X_10,X_11,multiply(X_11,X_12,X_12)) = multiply(X_10,X_11,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_10,X_11,multiply(X_11,X_12,X_12)),multiply(X_10,X_11,multiply(X_11,X_12,X_12))) ),[1,2],$fot(X_12)]]) ).
cnf(refute_0_152,plain,
( multiply(X_11,X_12,X_12) != X_12
| multiply(X_10,X_11,multiply(X_11,X_12,X_12)) = multiply(X_10,X_11,X_12) ),
inference(resolve,[$cnf( $equal(multiply(X_10,X_11,multiply(X_11,X_12,X_12)),multiply(X_10,X_11,multiply(X_11,X_12,X_12))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
multiply(X_10,X_11,multiply(X_11,X_12,X_12)) = multiply(X_10,X_11,X_12),
inference(resolve,[$cnf( $equal(multiply(X_11,X_12,X_12),X_12) )],[refute_0_149,refute_0_152]) ).
cnf(refute_0_154,plain,
( multiply(X_10,X_11,multiply(X_11,X_12,X_12)) != multiply(X_10,X_11,X_12)
| multiply(X_11,X_12,multiply(X_10,X_11,X_12)) != multiply(X_10,X_11,multiply(X_11,X_12,X_12))
| multiply(X_11,X_12,multiply(X_10,X_11,X_12)) = multiply(X_10,X_11,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_11,X_12,multiply(X_10,X_11,X_12)),multiply(X_10,X_11,multiply(X_11,X_12,X_12))) ),[1],$fot(multiply(X_10,X_11,X_12))]]) ).
cnf(refute_0_155,plain,
( multiply(X_11,X_12,multiply(X_10,X_11,X_12)) != multiply(X_10,X_11,multiply(X_11,X_12,X_12))
| multiply(X_11,X_12,multiply(X_10,X_11,X_12)) = multiply(X_10,X_11,X_12) ),
inference(resolve,[$cnf( $equal(multiply(X_10,X_11,multiply(X_11,X_12,X_12)),multiply(X_10,X_11,X_12)) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
( multiply(multiply(X_11,X_12,X_10),X_11,X_12) != multiply(X_10,X_11,multiply(X_11,X_12,X_12))
| multiply(X_11,X_12,multiply(X_10,X_11,X_12)) = multiply(X_10,X_11,X_12) ),
inference(resolve,[$cnf( $equal(multiply(X_11,X_12,multiply(X_10,X_11,X_12)),multiply(X_10,X_11,multiply(X_11,X_12,X_12))) )],[refute_0_148,refute_0_155]) ).
cnf(refute_0_157,plain,
multiply(X_11,X_12,multiply(X_10,X_11,X_12)) = multiply(X_10,X_11,X_12),
inference(resolve,[$cnf( $equal(multiply(multiply(X_11,X_12,X_10),X_11,X_12),multiply(X_10,X_11,multiply(X_11,X_12,X_12))) )],[refute_0_146,refute_0_156]) ).
cnf(refute_0_158,plain,
multiply(X_22,X_29,multiply(X_60,X_22,X_29)) = multiply(X_60,X_22,X_29),
inference(subst,[],[refute_0_157:[bind(X_10,$fot(X_60)),bind(X_11,$fot(X_22)),bind(X_12,$fot(X_29))]]) ).
cnf(refute_0_159,plain,
multiply(X,inverse(X),inverse(inverse(X))) = X,
inference(subst,[],[right_inverse:[bind(Y,$fot(inverse(X)))]]) ).
cnf(refute_0_160,plain,
multiply(X,inverse(X),inverse(inverse(X))) = inverse(inverse(X)),
inference(subst,[],[refute_0_94:[bind(X_21,$fot(inverse(inverse(X)))),bind(X_29,$fot(X))]]) ).
cnf(refute_0_161,plain,
( multiply(X,inverse(X),inverse(inverse(X))) != X
| multiply(X,inverse(X),inverse(inverse(X))) != inverse(inverse(X))
| inverse(inverse(X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,inverse(X),inverse(inverse(X))),X) ),[0],$fot(inverse(inverse(X)))]]) ).
cnf(refute_0_162,plain,
( multiply(X,inverse(X),inverse(inverse(X))) != X
| inverse(inverse(X)) = X ),
inference(resolve,[$cnf( $equal(multiply(X,inverse(X),inverse(inverse(X))),inverse(inverse(X))) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
inverse(inverse(X)) = X,
inference(resolve,[$cnf( $equal(multiply(X,inverse(X),inverse(inverse(X))),X) )],[refute_0_159,refute_0_162]) ).
cnf(refute_0_164,plain,
inverse(inverse(X_22)) = X_22,
inference(subst,[],[refute_0_163:[bind(X,$fot(X_22))]]) ).
cnf(refute_0_165,plain,
multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29)) = multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29)),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29)))]]) ).
cnf(refute_0_166,plain,
( inverse(inverse(X_22)) != X_22
| multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29)) != multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29))
| multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29)) = multiply(X_22,X_29,multiply(X_60,X_22,X_29)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29)),multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29))) ),[1,0],$fot(X_22)]]) ).
cnf(refute_0_167,plain,
( inverse(inverse(X_22)) != X_22
| multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29)) = multiply(X_22,X_29,multiply(X_60,X_22,X_29)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29)),multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29)) = multiply(X_22,X_29,multiply(X_60,X_22,X_29)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_22)),X_22) )],[refute_0_164,refute_0_167]) ).
cnf(refute_0_169,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_170,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_68,refute_0_169]) ).
cnf(refute_0_171,plain,
( multiply(X_22,X_29,multiply(X_60,X_22,X_29)) != multiply(X_60,X_22,X_29)
| multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29)) != multiply(X_22,X_29,multiply(X_60,X_22,X_29))
| multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29)) = multiply(X_60,X_22,X_29) ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29)))),bind(Y0,$fot(multiply(X_22,X_29,multiply(X_60,X_22,X_29)))),bind(Z0,$fot(multiply(X_60,X_22,X_29)))]]) ).
cnf(refute_0_172,plain,
( multiply(X_22,X_29,multiply(X_60,X_22,X_29)) != multiply(X_60,X_22,X_29)
| multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29)) = multiply(X_60,X_22,X_29) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29)),multiply(X_22,X_29,multiply(X_60,X_22,X_29))) )],[refute_0_168,refute_0_171]) ).
cnf(refute_0_173,plain,
multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29)) = multiply(X_60,X_22,X_29),
inference(resolve,[$cnf( $equal(multiply(X_22,X_29,multiply(X_60,X_22,X_29)),multiply(X_60,X_22,X_29)) )],[refute_0_158,refute_0_172]) ).
cnf(refute_0_174,plain,
multiply(multiply(inverse(inverse(X_22)),X_29,X_60),X_22,X_29) = multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29)),
inference(subst,[],[refute_0_30:[bind(X_10,$fot(X_60)),bind(X_11,$fot(X_22)),bind(X_12,$fot(X_29)),bind(X_8,$fot(inverse(inverse(X_22))))]]) ).
cnf(refute_0_175,plain,
( multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29)) != multiply(X_60,X_22,X_29)
| multiply(multiply(inverse(inverse(X_22)),X_29,X_60),X_22,X_29) != multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29))
| multiply(multiply(inverse(inverse(X_22)),X_29,X_60),X_22,X_29) = multiply(X_60,X_22,X_29) ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(multiply(multiply(inverse(inverse(X_22)),X_29,X_60),X_22,X_29))),bind(Y0,$fot(multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29)))),bind(Z0,$fot(multiply(X_60,X_22,X_29)))]]) ).
cnf(refute_0_176,plain,
( multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29)) != multiply(X_60,X_22,X_29)
| multiply(multiply(inverse(inverse(X_22)),X_29,X_60),X_22,X_29) = multiply(X_60,X_22,X_29) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(inverse(X_22)),X_29,X_60),X_22,X_29),multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29))) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
multiply(multiply(inverse(inverse(X_22)),X_29,X_60),X_22,X_29) = multiply(X_60,X_22,X_29),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_22)),X_29,multiply(X_60,X_22,X_29)),multiply(X_60,X_22,X_29)) )],[refute_0_173,refute_0_176]) ).
cnf(refute_0_178,plain,
( multiply(multiply(inverse(inverse(X_22)),X_29,X_60),X_22,X_29) != multiply(X_60,X_22,X_29)
| multiply(multiply(inverse(inverse(X_22)),X_29,X_60),X_22,X_29) != multiply(inverse(inverse(X_22)),X_29,X_60)
| multiply(X_60,X_22,X_29) = multiply(inverse(inverse(X_22)),X_29,X_60) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(inverse(X_22)),X_29,X_60),X_22,X_29),multiply(inverse(inverse(X_22)),X_29,X_60)) ),[0],$fot(multiply(X_60,X_22,X_29))]]) ).
cnf(refute_0_179,plain,
( multiply(multiply(inverse(inverse(X_22)),X_29,X_60),X_22,X_29) != multiply(inverse(inverse(X_22)),X_29,X_60)
| multiply(X_60,X_22,X_29) = multiply(inverse(inverse(X_22)),X_29,X_60) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(inverse(X_22)),X_29,X_60),X_22,X_29),multiply(X_60,X_22,X_29)) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
multiply(inverse(inverse(X_22)),X_29,X_60) = multiply(inverse(inverse(X_22)),X_29,X_60),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(X_22)),X_29,X_60))]]) ).
cnf(refute_0_181,plain,
( inverse(inverse(X_22)) != X_22
| multiply(inverse(inverse(X_22)),X_29,X_60) != multiply(inverse(inverse(X_22)),X_29,X_60)
| multiply(inverse(inverse(X_22)),X_29,X_60) = multiply(X_22,X_29,X_60) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_22)),X_29,X_60),multiply(inverse(inverse(X_22)),X_29,X_60)) ),[1,0],$fot(X_22)]]) ).
cnf(refute_0_182,plain,
( inverse(inverse(X_22)) != X_22
| multiply(inverse(inverse(X_22)),X_29,X_60) = multiply(X_22,X_29,X_60) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_22)),X_29,X_60),multiply(inverse(inverse(X_22)),X_29,X_60)) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
multiply(inverse(inverse(X_22)),X_29,X_60) = multiply(X_22,X_29,X_60),
inference(resolve,[$cnf( $equal(inverse(inverse(X_22)),X_22) )],[refute_0_164,refute_0_182]) ).
cnf(refute_0_184,plain,
( multiply(X_60,X_22,X_29) != multiply(inverse(inverse(X_22)),X_29,X_60)
| multiply(inverse(inverse(X_22)),X_29,X_60) != multiply(X_22,X_29,X_60)
| multiply(X_60,X_22,X_29) = multiply(X_22,X_29,X_60) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_60,X_22,X_29),multiply(X_22,X_29,X_60)) ),[0],$fot(multiply(inverse(inverse(X_22)),X_29,X_60))]]) ).
cnf(refute_0_185,plain,
( multiply(X_60,X_22,X_29) != multiply(inverse(inverse(X_22)),X_29,X_60)
| multiply(X_60,X_22,X_29) = multiply(X_22,X_29,X_60) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_22)),X_29,X_60),multiply(X_22,X_29,X_60)) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
( multiply(multiply(inverse(inverse(X_22)),X_29,X_60),X_22,X_29) != multiply(inverse(inverse(X_22)),X_29,X_60)
| multiply(X_60,X_22,X_29) = multiply(X_22,X_29,X_60) ),
inference(resolve,[$cnf( $equal(multiply(X_60,X_22,X_29),multiply(inverse(inverse(X_22)),X_29,X_60)) )],[refute_0_179,refute_0_185]) ).
cnf(refute_0_187,plain,
multiply(X_60,X_22,X_29) = multiply(X_22,X_29,X_60),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(inverse(X_22)),X_29,X_60),X_22,X_29),multiply(inverse(inverse(X_22)),X_29,X_60)) )],[refute_0_141,refute_0_186]) ).
cnf(refute_0_188,plain,
( multiply(X_60,X_22,X_29) != multiply(X_22,X_29,X_60)
| multiply(X_22,X_29,X_60) = multiply(X_60,X_22,X_29) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(multiply(X_60,X_22,X_29))),bind(Y0,$fot(multiply(X_22,X_29,X_60)))]]) ).
cnf(refute_0_189,plain,
multiply(X_22,X_29,X_60) = multiply(X_60,X_22,X_29),
inference(resolve,[$cnf( $equal(multiply(X_60,X_22,X_29),multiply(X_22,X_29,X_60)) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
multiply(multiply(V,W,X),Y,V) = multiply(V,multiply(V,W,X),Y),
inference(subst,[],[refute_0_189:[bind(X_22,$fot(multiply(V,W,X))),bind(X_29,$fot(Y)),bind(X_60,$fot(V))]]) ).
cnf(refute_0_191,plain,
( multiply(multiply(V,W,X),Y,V) != multiply(V,W,multiply(X,Y,multiply(inverse(W),V,X_60)))
| multiply(multiply(V,W,X),Y,V) != multiply(V,multiply(V,W,X),Y)
| multiply(V,multiply(V,W,X),Y) = multiply(V,W,multiply(X,Y,multiply(inverse(W),V,X_60))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(V,W,X),Y,V),multiply(V,W,multiply(X,Y,multiply(inverse(W),V,X_60)))) ),[0],$fot(multiply(V,multiply(V,W,X),Y))]]) ).
cnf(refute_0_192,plain,
( multiply(multiply(V,W,X),Y,V) != multiply(V,W,multiply(X,Y,multiply(inverse(W),V,X_60)))
| multiply(V,multiply(V,W,X),Y) = multiply(V,W,multiply(X,Y,multiply(inverse(W),V,X_60))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(V,W,X),Y,V),multiply(V,multiply(V,W,X),Y)) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
multiply(V,multiply(V,W,X),Y) = multiply(V,W,multiply(X,Y,multiply(inverse(W),V,X_60))),
inference(resolve,[$cnf( $equal(multiply(multiply(V,W,X),Y,V),multiply(V,W,multiply(X,Y,multiply(inverse(W),V,X_60)))) )],[refute_0_136,refute_0_192]) ).
cnf(refute_0_194,plain,
( multiply(V,multiply(V,W,X),Y) != multiply(V,W,multiply(X,Y,multiply(inverse(W),V,X_60)))
| multiply(V,W,multiply(X,Y,multiply(inverse(W),V,X_60))) = multiply(V,multiply(V,W,X),Y) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(multiply(V,multiply(V,W,X),Y))),bind(Y0,$fot(multiply(V,W,multiply(X,Y,multiply(inverse(W),V,X_60)))))]]) ).
cnf(refute_0_195,plain,
multiply(V,W,multiply(X,Y,multiply(inverse(W),V,X_60))) = multiply(V,multiply(V,W,X),Y),
inference(resolve,[$cnf( $equal(multiply(V,multiply(V,W,X),Y),multiply(V,W,multiply(X,Y,multiply(inverse(W),V,X_60)))) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
multiply(X_8,X_10,multiply(X_10,X_11,multiply(inverse(X_10),X_8,X_60))) = multiply(X_8,multiply(X_8,X_10,X_10),X_11),
inference(subst,[],[refute_0_195:[bind(V,$fot(X_8)),bind(W,$fot(X_10)),bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_197,plain,
( multiply(X_8,X_10,multiply(X_10,X_11,multiply(inverse(X_10),X_8,X_60))) != multiply(X_8,multiply(X_8,X_10,X_10),X_11)
| multiply(X_8,multiply(X_8,X_10,X_10),X_11) != multiply(X_8,X_10,X_11)
| multiply(X_8,X_10,multiply(X_10,X_11,multiply(inverse(X_10),X_8,X_60))) = multiply(X_8,X_10,X_11) ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(multiply(X_8,X_10,multiply(X_10,X_11,multiply(inverse(X_10),X_8,X_60))))),bind(Y0,$fot(multiply(X_8,multiply(X_8,X_10,X_10),X_11))),bind(Z0,$fot(multiply(X_8,X_10,X_11)))]]) ).
cnf(refute_0_198,plain,
( multiply(X_8,multiply(X_8,X_10,X_10),X_11) != multiply(X_8,X_10,X_11)
| multiply(X_8,X_10,multiply(X_10,X_11,multiply(inverse(X_10),X_8,X_60))) = multiply(X_8,X_10,X_11) ),
inference(resolve,[$cnf( $equal(multiply(X_8,X_10,multiply(X_10,X_11,multiply(inverse(X_10),X_8,X_60))),multiply(X_8,multiply(X_8,X_10,X_10),X_11)) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
multiply(X_8,X_10,multiply(X_10,X_11,multiply(inverse(X_10),X_8,X_60))) = multiply(X_8,X_10,X_11),
inference(resolve,[$cnf( $equal(multiply(X_8,multiply(X_8,X_10,X_10),X_11),multiply(X_8,X_10,X_11)) )],[refute_0_131,refute_0_198]) ).
cnf(refute_0_200,plain,
( multiply(X_10,X_11,X_8) != multiply(X_8,X_10,multiply(X_10,X_11,multiply(inverse(X_10),X_8,X_60)))
| multiply(X_8,X_10,multiply(X_10,X_11,multiply(inverse(X_10),X_8,X_60))) != multiply(X_8,X_10,X_11)
| multiply(X_10,X_11,X_8) = multiply(X_8,X_10,X_11) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_10,X_11,X_8),multiply(X_8,X_10,X_11)) ),[0],$fot(multiply(X_8,X_10,multiply(X_10,X_11,multiply(inverse(X_10),X_8,X_60))))]]) ).
cnf(refute_0_201,plain,
( multiply(X_10,X_11,X_8) != multiply(X_8,X_10,multiply(X_10,X_11,multiply(inverse(X_10),X_8,X_60)))
| multiply(X_10,X_11,X_8) = multiply(X_8,X_10,X_11) ),
inference(resolve,[$cnf( $equal(multiply(X_8,X_10,multiply(X_10,X_11,multiply(inverse(X_10),X_8,X_60))),multiply(X_8,X_10,X_11)) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
multiply(X_10,X_11,X_8) = multiply(X_8,X_10,X_11),
inference(resolve,[$cnf( $equal(multiply(X_10,X_11,X_8),multiply(X_8,X_10,multiply(X_10,X_11,multiply(inverse(X_10),X_8,X_60)))) )],[refute_0_127,refute_0_201]) ).
cnf(refute_0_203,plain,
multiply(inverse(X_28),X_27,X_28) = multiply(X_28,inverse(X_28),X_27),
inference(subst,[],[refute_0_202:[bind(X_10,$fot(inverse(X_28))),bind(X_11,$fot(X_27)),bind(X_8,$fot(X_28))]]) ).
cnf(refute_0_204,plain,
( multiply(X_28,inverse(X_28),X_27) != X_27
| multiply(inverse(X_28),X_27,X_28) != multiply(X_28,inverse(X_28),X_27)
| multiply(inverse(X_28),X_27,X_28) = X_27 ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(multiply(inverse(X_28),X_27,X_28))),bind(Y0,$fot(multiply(X_28,inverse(X_28),X_27))),bind(Z0,$fot(X_27))]]) ).
cnf(refute_0_205,plain,
( multiply(X_28,inverse(X_28),X_27) != X_27
| multiply(inverse(X_28),X_27,X_28) = X_27 ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_28),X_27,X_28),multiply(X_28,inverse(X_28),X_27)) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
multiply(inverse(X_28),X_27,X_28) = X_27,
inference(resolve,[$cnf( $equal(multiply(X_28,inverse(X_28),X_27),X_27) )],[refute_0_109,refute_0_205]) ).
cnf(refute_0_207,plain,
multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28)) = multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28)),
introduced(tautology,[refl,[$fot(multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28)))]]) ).
cnf(refute_0_208,plain,
( multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28)) != multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28))
| multiply(inverse(X_28),X_27,X_28) != X_27
| multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28)) = multiply(X_29,X_28,X_27) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28)),multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28))) ),[1,2],$fot(X_27)]]) ).
cnf(refute_0_209,plain,
( multiply(inverse(X_28),X_27,X_28) != X_27
| multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28)) = multiply(X_29,X_28,X_27) ),
inference(resolve,[$cnf( $equal(multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28)),multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28))) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28)) = multiply(X_29,X_28,X_27),
inference(resolve,[$cnf( $equal(multiply(inverse(X_28),X_27,X_28),X_27) )],[refute_0_206,refute_0_209]) ).
cnf(refute_0_211,plain,
( multiply(X_29,X_27,X_28) != multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28))
| multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28)) != multiply(X_29,X_28,X_27)
| multiply(X_29,X_27,X_28) = multiply(X_29,X_28,X_27) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_29,X_27,X_28),multiply(X_29,X_28,X_27)) ),[0],$fot(multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28)))]]) ).
cnf(refute_0_212,plain,
( multiply(X_29,X_27,X_28) != multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28))
| multiply(X_29,X_27,X_28) = multiply(X_29,X_28,X_27) ),
inference(resolve,[$cnf( $equal(multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28)),multiply(X_29,X_28,X_27)) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
multiply(X_29,X_27,X_28) = multiply(X_29,X_28,X_27),
inference(resolve,[$cnf( $equal(multiply(X_29,X_27,X_28),multiply(X_29,X_28,multiply(inverse(X_28),X_27,X_28))) )],[refute_0_108,refute_0_212]) ).
cnf(refute_0_214,plain,
( multiply(X_29,X_27,X_28) != multiply(X_29,X_28,X_27)
| multiply(X_29,X_28,X_27) = multiply(X_29,X_27,X_28) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(multiply(X_29,X_27,X_28))),bind(Y0,$fot(multiply(X_29,X_28,X_27)))]]) ).
cnf(refute_0_215,plain,
multiply(X_29,X_28,X_27) = multiply(X_29,X_27,X_28),
inference(resolve,[$cnf( $equal(multiply(X_29,X_27,X_28),multiply(X_29,X_28,X_27)) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
multiply(e,g,f) = multiply(e,f,g),
inference(subst,[],[refute_0_215:[bind(X_27,$fot(f)),bind(X_28,$fot(g)),bind(X_29,$fot(e))]]) ).
cnf(refute_0_217,plain,
( multiply(X_10,X_11,X_8) != multiply(X_8,X_10,X_11)
| multiply(X_8,X_10,X_11) = multiply(X_10,X_11,X_8) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(multiply(X_10,X_11,X_8))),bind(Y0,$fot(multiply(X_8,X_10,X_11)))]]) ).
cnf(refute_0_218,plain,
multiply(X_8,X_10,X_11) = multiply(X_10,X_11,X_8),
inference(resolve,[$cnf( $equal(multiply(X_10,X_11,X_8),multiply(X_8,X_10,X_11)) )],[refute_0_202,refute_0_217]) ).
cnf(refute_0_219,plain,
multiply(f,e,g) = multiply(e,g,f),
inference(subst,[],[refute_0_218:[bind(X_10,$fot(e)),bind(X_11,$fot(g)),bind(X_8,$fot(f))]]) ).
cnf(refute_0_220,plain,
( multiply(e,g,f) != multiply(e,f,g)
| multiply(f,e,g) != multiply(e,g,f)
| multiply(f,e,g) = multiply(e,f,g) ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(multiply(f,e,g))),bind(Y0,$fot(multiply(e,g,f))),bind(Z0,$fot(multiply(e,f,g)))]]) ).
cnf(refute_0_221,plain,
( multiply(e,g,f) != multiply(e,f,g)
| multiply(f,e,g) = multiply(e,f,g) ),
inference(resolve,[$cnf( $equal(multiply(f,e,g),multiply(e,g,f)) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
multiply(f,e,g) = multiply(e,f,g),
inference(resolve,[$cnf( $equal(multiply(e,g,f),multiply(e,f,g)) )],[refute_0_216,refute_0_221]) ).
cnf(refute_0_223,plain,
multiply(g,f,e) = multiply(f,e,g),
inference(subst,[],[refute_0_218:[bind(X_10,$fot(f)),bind(X_11,$fot(e)),bind(X_8,$fot(g))]]) ).
cnf(refute_0_224,plain,
( multiply(f,e,g) != multiply(e,f,g)
| multiply(g,f,e) != multiply(f,e,g)
| multiply(g,f,e) = multiply(e,f,g) ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(multiply(g,f,e))),bind(Y0,$fot(multiply(f,e,g))),bind(Z0,$fot(multiply(e,f,g)))]]) ).
cnf(refute_0_225,plain,
( multiply(f,e,g) != multiply(e,f,g)
| multiply(g,f,e) = multiply(e,f,g) ),
inference(resolve,[$cnf( $equal(multiply(g,f,e),multiply(f,e,g)) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
multiply(g,f,e) = multiply(e,f,g),
inference(resolve,[$cnf( $equal(multiply(f,e,g),multiply(e,f,g)) )],[refute_0_222,refute_0_225]) ).
cnf(refute_0_227,plain,
multiply(c,d,multiply(g,f,e)) = multiply(c,d,multiply(g,f,e)),
introduced(tautology,[refl,[$fot(multiply(c,d,multiply(g,f,e)))]]) ).
cnf(refute_0_228,plain,
( multiply(c,d,multiply(g,f,e)) != multiply(c,d,multiply(g,f,e))
| multiply(g,f,e) != multiply(e,f,g)
| multiply(c,d,multiply(g,f,e)) = multiply(c,d,multiply(e,f,g)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(c,d,multiply(g,f,e)),multiply(c,d,multiply(g,f,e))) ),[1,2],$fot(multiply(e,f,g))]]) ).
cnf(refute_0_229,plain,
( multiply(g,f,e) != multiply(e,f,g)
| multiply(c,d,multiply(g,f,e)) = multiply(c,d,multiply(e,f,g)) ),
inference(resolve,[$cnf( $equal(multiply(c,d,multiply(g,f,e)),multiply(c,d,multiply(g,f,e))) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
multiply(c,d,multiply(g,f,e)) = multiply(c,d,multiply(e,f,g)),
inference(resolve,[$cnf( $equal(multiply(g,f,e),multiply(e,f,g)) )],[refute_0_226,refute_0_229]) ).
cnf(refute_0_231,plain,
multiply(d,multiply(g,f,e),c) = multiply(c,d,multiply(g,f,e)),
inference(subst,[],[refute_0_202:[bind(X_10,$fot(d)),bind(X_11,$fot(multiply(g,f,e))),bind(X_8,$fot(c))]]) ).
cnf(refute_0_232,plain,
( multiply(c,d,multiply(g,f,e)) != multiply(c,d,multiply(e,f,g))
| multiply(d,multiply(g,f,e),c) != multiply(c,d,multiply(g,f,e))
| multiply(d,multiply(g,f,e),c) = multiply(c,d,multiply(e,f,g)) ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(multiply(d,multiply(g,f,e),c))),bind(Y0,$fot(multiply(c,d,multiply(g,f,e)))),bind(Z0,$fot(multiply(c,d,multiply(e,f,g))))]]) ).
cnf(refute_0_233,plain,
( multiply(c,d,multiply(g,f,e)) != multiply(c,d,multiply(e,f,g))
| multiply(d,multiply(g,f,e),c) = multiply(c,d,multiply(e,f,g)) ),
inference(resolve,[$cnf( $equal(multiply(d,multiply(g,f,e),c),multiply(c,d,multiply(g,f,e))) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
multiply(d,multiply(g,f,e),c) = multiply(c,d,multiply(e,f,g)),
inference(resolve,[$cnf( $equal(multiply(c,d,multiply(g,f,e)),multiply(c,d,multiply(e,f,g))) )],[refute_0_230,refute_0_233]) ).
cnf(refute_0_235,plain,
multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))) = multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))),
introduced(tautology,[refl,[$fot(multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))))]]) ).
cnf(refute_0_236,plain,
( multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))) != multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g))))
| multiply(d,multiply(g,f,e),c) != multiply(c,d,multiply(e,f,g))
| multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))) = multiply(b,multiply(c,d,multiply(e,f,g)),inverse(multiply(c,d,multiply(e,f,g)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))),multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g))))) ),[1,1],$fot(multiply(c,d,multiply(e,f,g)))]]) ).
cnf(refute_0_237,plain,
( multiply(d,multiply(g,f,e),c) != multiply(c,d,multiply(e,f,g))
| multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))) = multiply(b,multiply(c,d,multiply(e,f,g)),inverse(multiply(c,d,multiply(e,f,g)))) ),
inference(resolve,[$cnf( $equal(multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))),multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g))))) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))) = multiply(b,multiply(c,d,multiply(e,f,g)),inverse(multiply(c,d,multiply(e,f,g)))),
inference(resolve,[$cnf( $equal(multiply(d,multiply(g,f,e),c),multiply(c,d,multiply(e,f,g))) )],[refute_0_234,refute_0_237]) ).
cnf(refute_0_239,plain,
( multiply(b,multiply(c,d,multiply(e,f,g)),inverse(multiply(c,d,multiply(e,f,g)))) != b
| multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))) != multiply(b,multiply(c,d,multiply(e,f,g)),inverse(multiply(c,d,multiply(e,f,g))))
| multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))) = b ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))))),bind(Y0,$fot(multiply(b,multiply(c,d,multiply(e,f,g)),inverse(multiply(c,d,multiply(e,f,g)))))),bind(Z0,$fot(b))]]) ).
cnf(refute_0_240,plain,
( multiply(b,multiply(c,d,multiply(e,f,g)),inverse(multiply(c,d,multiply(e,f,g)))) != b
| multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))) = b ),
inference(resolve,[$cnf( $equal(multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))),multiply(b,multiply(c,d,multiply(e,f,g)),inverse(multiply(c,d,multiply(e,f,g))))) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))) = b,
inference(resolve,[$cnf( $equal(multiply(b,multiply(c,d,multiply(e,f,g)),inverse(multiply(c,d,multiply(e,f,g)))),b) )],[refute_0_103,refute_0_240]) ).
cnf(refute_0_242,plain,
multiply(multiply(X_8,inverse(X_10),X_10),X_11,inverse(X_10)) = multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10))),
inference(subst,[],[refute_0_30:[bind(X_12,$fot(inverse(X_10)))]]) ).
cnf(refute_0_243,plain,
multiply(X,inverse(X_39),inverse(inverse(X_39))) = X,
inference(subst,[],[right_inverse:[bind(Y,$fot(inverse(X_39)))]]) ).
cnf(refute_0_244,plain,
inverse(inverse(X_39)) = X_39,
inference(subst,[],[refute_0_163:[bind(X,$fot(X_39))]]) ).
cnf(refute_0_245,plain,
( inverse(inverse(X_39)) != X_39
| multiply(X,inverse(X_39),inverse(inverse(X_39))) != X
| multiply(X,inverse(X_39),X_39) = X ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,inverse(X_39),inverse(inverse(X_39))),X) ),[0,2],$fot(X_39)]]) ).
cnf(refute_0_246,plain,
( multiply(X,inverse(X_39),inverse(inverse(X_39))) != X
| multiply(X,inverse(X_39),X_39) = X ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_39)),X_39) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
multiply(X,inverse(X_39),X_39) = X,
inference(resolve,[$cnf( $equal(multiply(X,inverse(X_39),inverse(inverse(X_39))),X) )],[refute_0_243,refute_0_246]) ).
cnf(refute_0_248,plain,
multiply(X_8,inverse(X_10),X_10) = X_8,
inference(subst,[],[refute_0_247:[bind(X,$fot(X_8)),bind(X_39,$fot(X_10))]]) ).
cnf(refute_0_249,plain,
( multiply(X_8,inverse(X_10),X_10) != X_8
| multiply(multiply(X_8,inverse(X_10),X_10),X_11,inverse(X_10)) != multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10)))
| multiply(X_8,X_11,inverse(X_10)) = multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_8,inverse(X_10),X_10),X_11,inverse(X_10)),multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10)))) ),[0,0],$fot(X_8)]]) ).
cnf(refute_0_250,plain,
( multiply(multiply(X_8,inverse(X_10),X_10),X_11,inverse(X_10)) != multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10)))
| multiply(X_8,X_11,inverse(X_10)) = multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10))) ),
inference(resolve,[$cnf( $equal(multiply(X_8,inverse(X_10),X_10),X_8) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
multiply(X_8,X_11,inverse(X_10)) = multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10))),
inference(resolve,[$cnf( $equal(multiply(multiply(X_8,inverse(X_10),X_10),X_11,inverse(X_10)),multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10)))) )],[refute_0_242,refute_0_250]) ).
cnf(refute_0_252,plain,
multiply(inverse(Y),Y,X) = multiply(Y,X,inverse(Y)),
inference(subst,[],[refute_0_218:[bind(X_10,$fot(Y)),bind(X_11,$fot(X)),bind(X_8,$fot(inverse(Y)))]]) ).
cnf(refute_0_253,plain,
( multiply(inverse(Y),Y,X) != X
| multiply(inverse(Y),Y,X) != multiply(Y,X,inverse(Y))
| multiply(Y,X,inverse(Y)) = X ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(Y),Y,X),X) ),[0],$fot(multiply(Y,X,inverse(Y)))]]) ).
cnf(refute_0_254,plain,
( multiply(inverse(Y),Y,X) != X
| multiply(Y,X,inverse(Y)) = X ),
inference(resolve,[$cnf( $equal(multiply(inverse(Y),Y,X),multiply(Y,X,inverse(Y))) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
multiply(Y,X,inverse(Y)) = X,
inference(resolve,[$cnf( $equal(multiply(inverse(Y),Y,X),X) )],[left_inverse,refute_0_254]) ).
cnf(refute_0_256,plain,
multiply(X_10,X_11,inverse(X_10)) = X_11,
inference(subst,[],[refute_0_255:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_257,plain,
multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10))) = multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10))),
introduced(tautology,[refl,[$fot(multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10))))]]) ).
cnf(refute_0_258,plain,
( multiply(X_10,X_11,inverse(X_10)) != X_11
| multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10))) != multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10)))
| multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10))) = multiply(X_8,inverse(X_10),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10))),multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10)))) ),[1,2],$fot(X_11)]]) ).
cnf(refute_0_259,plain,
( multiply(X_10,X_11,inverse(X_10)) != X_11
| multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10))) = multiply(X_8,inverse(X_10),X_11) ),
inference(resolve,[$cnf( $equal(multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10))),multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10)))) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10))) = multiply(X_8,inverse(X_10),X_11),
inference(resolve,[$cnf( $equal(multiply(X_10,X_11,inverse(X_10)),X_11) )],[refute_0_256,refute_0_259]) ).
cnf(refute_0_261,plain,
( multiply(X_8,X_11,inverse(X_10)) != multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10)))
| multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10))) != multiply(X_8,inverse(X_10),X_11)
| multiply(X_8,X_11,inverse(X_10)) = multiply(X_8,inverse(X_10),X_11) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_8,X_11,inverse(X_10)),multiply(X_8,inverse(X_10),X_11)) ),[0],$fot(multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10))))]]) ).
cnf(refute_0_262,plain,
( multiply(X_8,X_11,inverse(X_10)) != multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10)))
| multiply(X_8,X_11,inverse(X_10)) = multiply(X_8,inverse(X_10),X_11) ),
inference(resolve,[$cnf( $equal(multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10))),multiply(X_8,inverse(X_10),X_11)) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
multiply(X_8,X_11,inverse(X_10)) = multiply(X_8,inverse(X_10),X_11),
inference(resolve,[$cnf( $equal(multiply(X_8,X_11,inverse(X_10)),multiply(X_8,inverse(X_10),multiply(X_10,X_11,inverse(X_10)))) )],[refute_0_251,refute_0_262]) ).
cnf(refute_0_264,plain,
( multiply(X_8,X_11,inverse(X_10)) != multiply(X_8,inverse(X_10),X_11)
| multiply(X_8,inverse(X_10),X_11) = multiply(X_8,X_11,inverse(X_10)) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(multiply(X_8,X_11,inverse(X_10)))),bind(Y0,$fot(multiply(X_8,inverse(X_10),X_11)))]]) ).
cnf(refute_0_265,plain,
multiply(X_8,inverse(X_10),X_11) = multiply(X_8,X_11,inverse(X_10)),
inference(resolve,[$cnf( $equal(multiply(X_8,X_11,inverse(X_10)),multiply(X_8,inverse(X_10),X_11)) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) = multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))),
inference(subst,[],[refute_0_265:[bind(X_10,$fot(multiply(c,d,multiply(e,f,g)))),bind(X_11,$fot(multiply(d,multiply(g,f,e),c))),bind(X_8,$fot(b))]]) ).
cnf(refute_0_267,plain,
( multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) != multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g))))
| multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))) != b
| multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) = b ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)))),bind(Y0,$fot(multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))))),bind(Z0,$fot(b))]]) ).
cnf(refute_0_268,plain,
( multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))) != b
| multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) = b ),
inference(resolve,[$cnf( $equal(multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)),multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g))))) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) = b,
inference(resolve,[$cnf( $equal(multiply(b,multiply(d,multiply(g,f,e),c),inverse(multiply(c,d,multiply(e,f,g)))),b) )],[refute_0_241,refute_0_268]) ).
cnf(refute_0_270,plain,
( b != b
| multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) != b
| multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) = b ),
introduced(tautology,[equality,[$cnf( $equal(multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)),b) ),[0,0],$fot(b)]]) ).
cnf(refute_0_271,plain,
( b != b
| multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) = b ),
inference(resolve,[$cnf( $equal(multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)),b) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
b != b,
inference(resolve,[$cnf( $equal(multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)),b) )],[refute_0_271,refute_0_102]) ).
cnf(refute_0_273,plain,
b = b,
introduced(tautology,[refl,[$fot(b)]]) ).
cnf(refute_0_274,plain,
$false,
inference(resolve,[$cnf( $equal(b,b) )],[refute_0_273,refute_0_272]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO034-1 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n018.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 : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 1 18:49:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.53/0.73 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.53/0.73
% 0.53/0.73 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.60/0.77
%------------------------------------------------------------------------------