%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP510-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 : Sat Jul 16 10:42:02 EDT 2022
% Result : Unsatisfiable 0.37s 0.56s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 50
% Syntax : Number of clauses : 196 ( 101 unt; 0 nHn; 103 RR)
% Number of literals : 337 ( 336 equ; 144 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 456 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2 ).
cnf(refute_0_0,plain,
multiply(multiply(multiply(multiply(multiply(X_0,X_1),X_2),B),inverse(multiply(X_0,X_2))),inverse(multiply(multiply(multiply(X_0,X_1),X_2),inverse(multiply(X_0,X_2))))) = B,
inference(subst,[],[single_axiom:[bind(A,$fot(multiply(multiply(X_0,X_1),X_2))),bind(C,$fot(inverse(multiply(X_0,X_2))))]]) ).
cnf(refute_0_1,plain,
multiply(multiply(multiply(X_0,X_1),X_2),inverse(multiply(X_0,X_2))) = X_1,
inference(subst,[],[single_axiom:[bind(A,$fot(X_0)),bind(B,$fot(X_1)),bind(C,$fot(X_2))]]) ).
cnf(refute_0_2,plain,
( multiply(multiply(multiply(X_0,X_1),X_2),inverse(multiply(X_0,X_2))) != X_1
| multiply(multiply(multiply(multiply(multiply(X_0,X_1),X_2),B),inverse(multiply(X_0,X_2))),inverse(multiply(multiply(multiply(X_0,X_1),X_2),inverse(multiply(X_0,X_2))))) != B
| multiply(multiply(multiply(multiply(multiply(X_0,X_1),X_2),B),inverse(multiply(X_0,X_2))),inverse(X_1)) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(multiply(multiply(multiply(X_0,X_1),X_2),B),inverse(multiply(X_0,X_2))),inverse(multiply(multiply(multiply(X_0,X_1),X_2),inverse(multiply(X_0,X_2))))),B) ),[0,1,0],$fot(X_1)]]) ).
cnf(refute_0_3,plain,
( multiply(multiply(multiply(multiply(multiply(X_0,X_1),X_2),B),inverse(multiply(X_0,X_2))),inverse(multiply(multiply(multiply(X_0,X_1),X_2),inverse(multiply(X_0,X_2))))) != B
| multiply(multiply(multiply(multiply(multiply(X_0,X_1),X_2),B),inverse(multiply(X_0,X_2))),inverse(X_1)) = B ),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(X_0,X_1),X_2),inverse(multiply(X_0,X_2))),X_1) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(multiply(multiply(multiply(multiply(X_0,X_1),X_2),B),inverse(multiply(X_0,X_2))),inverse(X_1)) = B,
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(multiply(multiply(X_0,X_1),X_2),B),inverse(multiply(X_0,X_2))),inverse(multiply(multiply(multiply(X_0,X_1),X_2),inverse(multiply(X_0,X_2))))),B) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(multiply(multiply(multiply(multiply(X_0,X_1),inverse(X_15)),inverse(multiply(X_0,X_1))),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)) = inverse(multiply(X_0,X_1)),
inference(subst,[],[refute_0_4:[bind(B,$fot(inverse(multiply(X_0,X_1)))),bind(X_2,$fot(inverse(X_15)))]]) ).
cnf(refute_0_6,plain,
multiply(multiply(multiply(multiply(multiply(X_0,X_1),X_2),inverse(multiply(X_0,X_2))),C),inverse(multiply(multiply(multiply(X_0,X_1),X_2),C))) = inverse(multiply(X_0,X_2)),
inference(subst,[],[single_axiom:[bind(A,$fot(multiply(multiply(X_0,X_1),X_2))),bind(B,$fot(inverse(multiply(X_0,X_2))))]]) ).
cnf(refute_0_7,plain,
( multiply(multiply(multiply(X_0,X_1),X_2),inverse(multiply(X_0,X_2))) != X_1
| multiply(multiply(multiply(multiply(multiply(X_0,X_1),X_2),inverse(multiply(X_0,X_2))),C),inverse(multiply(multiply(multiply(X_0,X_1),X_2),C))) != inverse(multiply(X_0,X_2))
| multiply(multiply(X_1,C),inverse(multiply(multiply(multiply(X_0,X_1),X_2),C))) = inverse(multiply(X_0,X_2)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(multiply(multiply(multiply(X_0,X_1),X_2),inverse(multiply(X_0,X_2))),C),inverse(multiply(multiply(multiply(X_0,X_1),X_2),C))),inverse(multiply(X_0,X_2))) ),[0,0,0],$fot(X_1)]]) ).
cnf(refute_0_8,plain,
( multiply(multiply(multiply(multiply(multiply(X_0,X_1),X_2),inverse(multiply(X_0,X_2))),C),inverse(multiply(multiply(multiply(X_0,X_1),X_2),C))) != inverse(multiply(X_0,X_2))
| multiply(multiply(X_1,C),inverse(multiply(multiply(multiply(X_0,X_1),X_2),C))) = inverse(multiply(X_0,X_2)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(X_0,X_1),X_2),inverse(multiply(X_0,X_2))),X_1) )],[refute_0_1,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(multiply(X_1,C),inverse(multiply(multiply(multiply(X_0,X_1),X_2),C))) = inverse(multiply(X_0,X_2)),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(multiply(multiply(X_0,X_1),X_2),inverse(multiply(X_0,X_2))),C),inverse(multiply(multiply(multiply(X_0,X_1),X_2),C))),inverse(multiply(X_0,X_2))) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
multiply(multiply(X_1,inverse(X_12)),inverse(multiply(multiply(multiply(multiply(multiply(X_11,X_12),X_13),X_1),inverse(multiply(X_11,X_13))),inverse(X_12)))) = inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13)))),
inference(subst,[],[refute_0_9:[bind(C,$fot(inverse(X_12))),bind(X_0,$fot(multiply(multiply(X_11,X_12),X_13))),bind(X_2,$fot(inverse(multiply(X_11,X_13))))]]) ).
cnf(refute_0_11,plain,
multiply(multiply(multiply(multiply(multiply(X_11,X_12),X_13),X_1),inverse(multiply(X_11,X_13))),inverse(X_12)) = X_1,
inference(subst,[],[refute_0_4:[bind(B,$fot(X_1)),bind(X_0,$fot(X_11)),bind(X_1,$fot(X_12)),bind(X_2,$fot(X_13))]]) ).
cnf(refute_0_12,plain,
( multiply(multiply(X_1,inverse(X_12)),inverse(multiply(multiply(multiply(multiply(multiply(X_11,X_12),X_13),X_1),inverse(multiply(X_11,X_13))),inverse(X_12)))) != inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13))))
| multiply(multiply(multiply(multiply(multiply(X_11,X_12),X_13),X_1),inverse(multiply(X_11,X_13))),inverse(X_12)) != X_1
| multiply(multiply(X_1,inverse(X_12)),inverse(X_1)) = inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_1,inverse(X_12)),inverse(multiply(multiply(multiply(multiply(multiply(X_11,X_12),X_13),X_1),inverse(multiply(X_11,X_13))),inverse(X_12)))),inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13))))) ),[0,1,0],$fot(X_1)]]) ).
cnf(refute_0_13,plain,
( multiply(multiply(X_1,inverse(X_12)),inverse(multiply(multiply(multiply(multiply(multiply(X_11,X_12),X_13),X_1),inverse(multiply(X_11,X_13))),inverse(X_12)))) != inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13))))
| multiply(multiply(X_1,inverse(X_12)),inverse(X_1)) = inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13)))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(multiply(multiply(X_11,X_12),X_13),X_1),inverse(multiply(X_11,X_13))),inverse(X_12)),X_1) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
multiply(multiply(X_1,inverse(X_12)),inverse(X_1)) = inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13)))),
inference(resolve,[$cnf( $equal(multiply(multiply(X_1,inverse(X_12)),inverse(multiply(multiply(multiply(multiply(multiply(X_11,X_12),X_13),X_1),inverse(multiply(X_11,X_13))),inverse(X_12)))),inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13))))) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13))) = X_12,
inference(subst,[],[single_axiom:[bind(A,$fot(X_11)),bind(B,$fot(X_12)),bind(C,$fot(X_13))]]) ).
cnf(refute_0_16,plain,
inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13)))) = inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13)))),
introduced(tautology,[refl,[$fot(inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13)))))]]) ).
cnf(refute_0_17,plain,
( multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13))) != X_12
| inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13)))) != inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13))))
| inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13)))) = inverse(X_12) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13)))),inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13))))) ),[1,0],$fot(X_12)]]) ).
cnf(refute_0_18,plain,
( multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13))) != X_12
| inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13)))) = inverse(X_12) ),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13)))),inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13))))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13)))) = inverse(X_12),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13))),X_12) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
( multiply(multiply(X_1,inverse(X_12)),inverse(X_1)) != inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13))))
| inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13)))) != inverse(X_12)
| multiply(multiply(X_1,inverse(X_12)),inverse(X_1)) = inverse(X_12) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(X_1,inverse(X_12)),inverse(X_1)),inverse(X_12)) ),[0],$fot(inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13)))))]]) ).
cnf(refute_0_21,plain,
( multiply(multiply(X_1,inverse(X_12)),inverse(X_1)) != inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13))))
| multiply(multiply(X_1,inverse(X_12)),inverse(X_1)) = inverse(X_12) ),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13)))),inverse(X_12)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
multiply(multiply(X_1,inverse(X_12)),inverse(X_1)) = inverse(X_12),
inference(resolve,[$cnf( $equal(multiply(multiply(X_1,inverse(X_12)),inverse(X_1)),inverse(multiply(multiply(multiply(X_11,X_12),X_13),inverse(multiply(X_11,X_13))))) )],[refute_0_14,refute_0_21]) ).
cnf(refute_0_23,plain,
multiply(multiply(multiply(X_0,X_1),inverse(X_15)),inverse(multiply(X_0,X_1))) = inverse(X_15),
inference(subst,[],[refute_0_22:[bind(X_1,$fot(multiply(X_0,X_1))),bind(X_12,$fot(X_15))]]) ).
cnf(refute_0_24,plain,
( multiply(multiply(multiply(X_0,X_1),inverse(X_15)),inverse(multiply(X_0,X_1))) != inverse(X_15)
| multiply(multiply(multiply(multiply(multiply(X_0,X_1),inverse(X_15)),inverse(multiply(X_0,X_1))),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)) != inverse(multiply(X_0,X_1))
| multiply(multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)) = inverse(multiply(X_0,X_1)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(multiply(multiply(multiply(X_0,X_1),inverse(X_15)),inverse(multiply(X_0,X_1))),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)),inverse(multiply(X_0,X_1))) ),[0,0,0],$fot(inverse(X_15))]]) ).
cnf(refute_0_25,plain,
( multiply(multiply(multiply(multiply(multiply(X_0,X_1),inverse(X_15)),inverse(multiply(X_0,X_1))),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)) != inverse(multiply(X_0,X_1))
| multiply(multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)) = inverse(multiply(X_0,X_1)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(X_0,X_1),inverse(X_15)),inverse(multiply(X_0,X_1))),inverse(X_15)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
multiply(multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)) = inverse(multiply(X_0,X_1)),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(multiply(multiply(X_0,X_1),inverse(X_15)),inverse(multiply(X_0,X_1))),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)),inverse(multiply(X_0,X_1))) )],[refute_0_5,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(multiply(multiply(X_12,inverse(X_15)),inverse(X_12)),inverse(multiply(X_12,inverse(X_15)))) = inverse(X_12),
inference(subst,[],[refute_0_22:[bind(X_1,$fot(multiply(X_12,inverse(X_15))))]]) ).
cnf(refute_0_28,plain,
multiply(multiply(X_12,inverse(X_15)),inverse(X_12)) = inverse(X_15),
inference(subst,[],[refute_0_22:[bind(X_1,$fot(X_12)),bind(X_12,$fot(X_15))]]) ).
cnf(refute_0_29,plain,
( multiply(multiply(X_12,inverse(X_15)),inverse(X_12)) != inverse(X_15)
| multiply(multiply(multiply(X_12,inverse(X_15)),inverse(X_12)),inverse(multiply(X_12,inverse(X_15)))) != inverse(X_12)
| multiply(inverse(X_15),inverse(multiply(X_12,inverse(X_15)))) = inverse(X_12) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(multiply(X_12,inverse(X_15)),inverse(X_12)),inverse(multiply(X_12,inverse(X_15)))),inverse(X_12)) ),[0,0],$fot(inverse(X_15))]]) ).
cnf(refute_0_30,plain,
( multiply(multiply(multiply(X_12,inverse(X_15)),inverse(X_12)),inverse(multiply(X_12,inverse(X_15)))) != inverse(X_12)
| multiply(inverse(X_15),inverse(multiply(X_12,inverse(X_15)))) = inverse(X_12) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_12,inverse(X_15)),inverse(X_12)),inverse(X_15)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
multiply(inverse(X_15),inverse(multiply(X_12,inverse(X_15)))) = inverse(X_12),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(X_12,inverse(X_15)),inverse(X_12)),inverse(multiply(X_12,inverse(X_15)))),inverse(X_12)) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))) = inverse(X_0),
inference(subst,[],[refute_0_31:[bind(X_12,$fot(X_0))]]) ).
cnf(refute_0_33,plain,
multiply(multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)) = multiply(multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)),
introduced(tautology,[refl,[$fot(multiply(multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)))]]) ).
cnf(refute_0_34,plain,
( multiply(multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)) != multiply(multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1))
| multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))) != inverse(X_0)
| multiply(multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)) = multiply(inverse(X_0),inverse(X_1)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)),multiply(multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1))) ),[1,0],$fot(inverse(X_0))]]) ).
cnf(refute_0_35,plain,
( multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))) != inverse(X_0)
| multiply(multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)) = multiply(inverse(X_0),inverse(X_1)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)),multiply(multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
multiply(multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)) = multiply(inverse(X_0),inverse(X_1)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))),inverse(X_0)) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
( multiply(multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)) != multiply(inverse(X_0),inverse(X_1))
| multiply(multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)) != inverse(multiply(X_0,X_1))
| multiply(inverse(X_0),inverse(X_1)) = inverse(multiply(X_0,X_1)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)),inverse(multiply(X_0,X_1))) ),[0],$fot(multiply(inverse(X_0),inverse(X_1)))]]) ).
cnf(refute_0_38,plain,
( multiply(multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)) != inverse(multiply(X_0,X_1))
| multiply(inverse(X_0),inverse(X_1)) = inverse(multiply(X_0,X_1)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)),multiply(inverse(X_0),inverse(X_1))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
multiply(inverse(X_0),inverse(X_1)) = inverse(multiply(X_0,X_1)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_15),inverse(multiply(X_0,inverse(X_15)))),inverse(X_1)),inverse(multiply(X_0,X_1))) )],[refute_0_26,refute_0_38]) ).
cnf(refute_0_40,plain,
multiply(inverse(inverse(X_18)),inverse(inverse(X_19))) = inverse(multiply(inverse(X_18),inverse(X_19))),
inference(subst,[],[refute_0_39:[bind(X_0,$fot(inverse(X_18))),bind(X_1,$fot(inverse(X_19)))]]) ).
cnf(refute_0_41,plain,
multiply(inverse(X_18),inverse(X_19)) = inverse(multiply(X_18,X_19)),
inference(subst,[],[refute_0_39:[bind(X_0,$fot(X_18)),bind(X_1,$fot(X_19))]]) ).
cnf(refute_0_42,plain,
( multiply(inverse(X_18),inverse(X_19)) != inverse(multiply(X_18,X_19))
| multiply(inverse(inverse(X_18)),inverse(inverse(X_19))) != inverse(multiply(inverse(X_18),inverse(X_19)))
| multiply(inverse(inverse(X_18)),inverse(inverse(X_19))) = inverse(inverse(multiply(X_18,X_19))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_18)),inverse(inverse(X_19))),inverse(multiply(inverse(X_18),inverse(X_19)))) ),[1,0],$fot(inverse(multiply(X_18,X_19)))]]) ).
cnf(refute_0_43,plain,
( multiply(inverse(inverse(X_18)),inverse(inverse(X_19))) != inverse(multiply(inverse(X_18),inverse(X_19)))
| multiply(inverse(inverse(X_18)),inverse(inverse(X_19))) = inverse(inverse(multiply(X_18,X_19))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_18),inverse(X_19)),inverse(multiply(X_18,X_19))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
multiply(inverse(inverse(X_18)),inverse(inverse(X_19))) = inverse(inverse(multiply(X_18,X_19))),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_18)),inverse(inverse(X_19))),inverse(multiply(inverse(X_18),inverse(X_19)))) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
multiply(multiply(multiply(multiply(X_0,X_1),B),inverse(multiply(X_0,B))),inverse(multiply(multiply(X_0,X_1),inverse(multiply(X_0,B))))) = B,
inference(subst,[],[single_axiom:[bind(A,$fot(multiply(X_0,X_1))),bind(C,$fot(inverse(multiply(X_0,B))))]]) ).
cnf(refute_0_46,plain,
multiply(multiply(multiply(X_0,X_1),B),inverse(multiply(X_0,B))) = X_1,
inference(subst,[],[single_axiom:[bind(A,$fot(X_0)),bind(B,$fot(X_1)),bind(C,$fot(B))]]) ).
cnf(refute_0_47,plain,
( multiply(multiply(multiply(X_0,X_1),B),inverse(multiply(X_0,B))) != X_1
| multiply(multiply(multiply(multiply(X_0,X_1),B),inverse(multiply(X_0,B))),inverse(multiply(multiply(X_0,X_1),inverse(multiply(X_0,B))))) != B
| multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(multiply(X_0,B))))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(multiply(multiply(X_0,X_1),B),inverse(multiply(X_0,B))),inverse(multiply(multiply(X_0,X_1),inverse(multiply(X_0,B))))),B) ),[0,0],$fot(X_1)]]) ).
cnf(refute_0_48,plain,
( multiply(multiply(multiply(multiply(X_0,X_1),B),inverse(multiply(X_0,B))),inverse(multiply(multiply(X_0,X_1),inverse(multiply(X_0,B))))) != B
| multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(multiply(X_0,B))))) = B ),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(X_0,X_1),B),inverse(multiply(X_0,B))),X_1) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(multiply(X_0,B))))) = B,
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(multiply(X_0,X_1),B),inverse(multiply(X_0,B))),inverse(multiply(multiply(X_0,X_1),inverse(multiply(X_0,B))))),B) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(multiply(X_0,inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3))))))))) = inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3)))),
inference(subst,[],[refute_0_49:[bind(B,$fot(inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3))))))]]) ).
cnf(refute_0_51,plain,
multiply(X_0,inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3))))) = X_3,
inference(subst,[],[refute_0_49:[bind(B,$fot(X_3)),bind(X_0,$fot(X_4)),bind(X_1,$fot(X_0))]]) ).
cnf(refute_0_52,plain,
( multiply(X_0,inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3))))) != X_3
| multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(multiply(X_0,inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3))))))))) != inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3))))
| multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(X_3)))) = inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(multiply(X_0,inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3))))))))),inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3))))) ),[0,1,0,1,0],$fot(X_3)]]) ).
cnf(refute_0_53,plain,
( multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(multiply(X_0,inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3))))))))) != inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3))))
| multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(X_3)))) = inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3)))) ),
inference(resolve,[$cnf( $equal(multiply(X_0,inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3))))),X_3) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(X_3)))) = inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3)))),
inference(resolve,[$cnf( $equal(multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(multiply(X_0,inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3))))))))),inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3))))) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
multiply(multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))),inverse(multiply(multiply(A,B),C))) = inverse(multiply(A,C)),
inference(subst,[],[refute_0_22:[bind(X_1,$fot(multiply(multiply(A,B),C))),bind(X_12,$fot(multiply(A,C)))]]) ).
cnf(refute_0_56,plain,
( multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) != B
| multiply(multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))),inverse(multiply(multiply(A,B),C))) != inverse(multiply(A,C))
| multiply(B,inverse(multiply(multiply(A,B),C))) = inverse(multiply(A,C)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))),inverse(multiply(multiply(A,B),C))),inverse(multiply(A,C))) ),[0,0],$fot(B)]]) ).
cnf(refute_0_57,plain,
( multiply(multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))),inverse(multiply(multiply(A,B),C))) != inverse(multiply(A,C))
| multiply(B,inverse(multiply(multiply(A,B),C))) = inverse(multiply(A,C)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))),B) )],[single_axiom,refute_0_56]) ).
cnf(refute_0_58,plain,
multiply(B,inverse(multiply(multiply(A,B),C))) = inverse(multiply(A,C)),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))),inverse(multiply(multiply(A,B),C))),inverse(multiply(A,C))) )],[refute_0_55,refute_0_57]) ).
cnf(refute_0_59,plain,
multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(X_3)))) = inverse(multiply(X_0,inverse(X_3))),
inference(subst,[],[refute_0_58:[bind(A,$fot(X_0)),bind(B,$fot(X_1)),bind(C,$fot(inverse(X_3)))]]) ).
cnf(refute_0_60,plain,
( multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(X_3)))) != inverse(multiply(X_0,inverse(X_3)))
| multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(X_3)))) != inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3))))
| inverse(multiply(X_0,inverse(X_3))) = inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(X_3)))),inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3))))) ),[0],$fot(inverse(multiply(X_0,inverse(X_3))))]]) ).
cnf(refute_0_61,plain,
( multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(X_3)))) != inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3))))
| inverse(multiply(X_0,inverse(X_3))) = inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3)))) ),
inference(resolve,[$cnf( $equal(multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(X_3)))),inverse(multiply(X_0,inverse(X_3)))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
multiply(multiply(X_14,inverse(multiply(multiply(X_0,X_14),inverse(multiply(X_0,B))))),inverse(X_14)) = inverse(multiply(multiply(X_0,X_14),inverse(multiply(X_0,B)))),
inference(subst,[],[refute_0_22:[bind(X_1,$fot(X_14)),bind(X_12,$fot(multiply(multiply(X_0,X_14),inverse(multiply(X_0,B)))))]]) ).
cnf(refute_0_63,plain,
multiply(X_14,inverse(multiply(multiply(X_0,X_14),inverse(multiply(X_0,B))))) = B,
inference(subst,[],[refute_0_49:[bind(X_1,$fot(X_14))]]) ).
cnf(refute_0_64,plain,
( multiply(X_14,inverse(multiply(multiply(X_0,X_14),inverse(multiply(X_0,B))))) != B
| multiply(multiply(X_14,inverse(multiply(multiply(X_0,X_14),inverse(multiply(X_0,B))))),inverse(X_14)) != inverse(multiply(multiply(X_0,X_14),inverse(multiply(X_0,B))))
| multiply(B,inverse(X_14)) = inverse(multiply(multiply(X_0,X_14),inverse(multiply(X_0,B)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_14,inverse(multiply(multiply(X_0,X_14),inverse(multiply(X_0,B))))),inverse(X_14)),inverse(multiply(multiply(X_0,X_14),inverse(multiply(X_0,B))))) ),[0,0],$fot(B)]]) ).
cnf(refute_0_65,plain,
( multiply(multiply(X_14,inverse(multiply(multiply(X_0,X_14),inverse(multiply(X_0,B))))),inverse(X_14)) != inverse(multiply(multiply(X_0,X_14),inverse(multiply(X_0,B))))
| multiply(B,inverse(X_14)) = inverse(multiply(multiply(X_0,X_14),inverse(multiply(X_0,B)))) ),
inference(resolve,[$cnf( $equal(multiply(X_14,inverse(multiply(multiply(X_0,X_14),inverse(multiply(X_0,B))))),B) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
multiply(B,inverse(X_14)) = inverse(multiply(multiply(X_0,X_14),inverse(multiply(X_0,B)))),
inference(resolve,[$cnf( $equal(multiply(multiply(X_14,inverse(multiply(multiply(X_0,X_14),inverse(multiply(X_0,B))))),inverse(X_14)),inverse(multiply(multiply(X_0,X_14),inverse(multiply(X_0,B))))) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_68,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_69,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( multiply(B,inverse(X_14)) != inverse(multiply(multiply(X_0,X_14),inverse(multiply(X_0,B))))
| inverse(multiply(multiply(X_0,X_14),inverse(multiply(X_0,B)))) = multiply(B,inverse(X_14)) ),
inference(subst,[],[refute_0_69:[bind(X,$fot(multiply(B,inverse(X_14)))),bind(Y,$fot(inverse(multiply(multiply(X_0,X_14),inverse(multiply(X_0,B))))))]]) ).
cnf(refute_0_71,plain,
inverse(multiply(multiply(X_0,X_14),inverse(multiply(X_0,B)))) = multiply(B,inverse(X_14)),
inference(resolve,[$cnf( $equal(multiply(B,inverse(X_14)),inverse(multiply(multiply(X_0,X_14),inverse(multiply(X_0,B))))) )],[refute_0_66,refute_0_70]) ).
cnf(refute_0_72,plain,
inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3)))) = multiply(X_3,inverse(X_0)),
inference(subst,[],[refute_0_71:[bind(B,$fot(X_3)),bind(X_0,$fot(X_4)),bind(X_14,$fot(X_0))]]) ).
cnf(refute_0_73,plain,
( inverse(multiply(X_0,inverse(X_3))) != inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3))))
| inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3)))) != multiply(X_3,inverse(X_0))
| inverse(multiply(X_0,inverse(X_3))) = multiply(X_3,inverse(X_0)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(multiply(X_0,inverse(X_3))),multiply(X_3,inverse(X_0))) ),[0],$fot(inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3)))))]]) ).
cnf(refute_0_74,plain,
( inverse(multiply(X_0,inverse(X_3))) != inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3))))
| inverse(multiply(X_0,inverse(X_3))) = multiply(X_3,inverse(X_0)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3)))),multiply(X_3,inverse(X_0))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
( multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(X_3)))) != inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3))))
| inverse(multiply(X_0,inverse(X_3))) = multiply(X_3,inverse(X_0)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_0,inverse(X_3))),inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3))))) )],[refute_0_61,refute_0_74]) ).
cnf(refute_0_76,plain,
inverse(multiply(X_0,inverse(X_3))) = multiply(X_3,inverse(X_0)),
inference(resolve,[$cnf( $equal(multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(X_3)))),inverse(multiply(multiply(X_4,X_0),inverse(multiply(X_4,X_3))))) )],[refute_0_54,refute_0_75]) ).
cnf(refute_0_77,plain,
inverse(multiply(inverse(X_18),inverse(X_19))) = multiply(X_19,inverse(inverse(X_18))),
inference(subst,[],[refute_0_76:[bind(X_0,$fot(inverse(X_18))),bind(X_3,$fot(X_19))]]) ).
cnf(refute_0_78,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_79,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_69,refute_0_78]) ).
cnf(refute_0_80,plain,
( multiply(inverse(inverse(X_18)),inverse(inverse(X_19))) != inverse(multiply(inverse(X_18),inverse(X_19)))
| inverse(multiply(inverse(X_18),inverse(X_19))) != multiply(X_19,inverse(inverse(X_18)))
| multiply(inverse(inverse(X_18)),inverse(inverse(X_19))) = multiply(X_19,inverse(inverse(X_18))) ),
inference(subst,[],[refute_0_79:[bind(X,$fot(multiply(inverse(inverse(X_18)),inverse(inverse(X_19))))),bind(Y,$fot(inverse(multiply(inverse(X_18),inverse(X_19))))),bind(Z,$fot(multiply(X_19,inverse(inverse(X_18)))))]]) ).
cnf(refute_0_81,plain,
( inverse(multiply(inverse(X_18),inverse(X_19))) != multiply(X_19,inverse(inverse(X_18)))
| multiply(inverse(inverse(X_18)),inverse(inverse(X_19))) = multiply(X_19,inverse(inverse(X_18))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_18)),inverse(inverse(X_19))),inverse(multiply(inverse(X_18),inverse(X_19)))) )],[refute_0_40,refute_0_80]) ).
cnf(refute_0_82,plain,
multiply(inverse(inverse(X_18)),inverse(inverse(X_19))) = multiply(X_19,inverse(inverse(X_18))),
inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_18),inverse(X_19))),multiply(X_19,inverse(inverse(X_18)))) )],[refute_0_77,refute_0_81]) ).
cnf(refute_0_83,plain,
( multiply(inverse(inverse(X_18)),inverse(inverse(X_19))) != multiply(X_19,inverse(inverse(X_18)))
| multiply(inverse(inverse(X_18)),inverse(inverse(X_19))) != inverse(inverse(multiply(X_18,X_19)))
| multiply(X_19,inverse(inverse(X_18))) = inverse(inverse(multiply(X_18,X_19))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_18)),inverse(inverse(X_19))),inverse(inverse(multiply(X_18,X_19)))) ),[0],$fot(multiply(X_19,inverse(inverse(X_18))))]]) ).
cnf(refute_0_84,plain,
( multiply(inverse(inverse(X_18)),inverse(inverse(X_19))) != inverse(inverse(multiply(X_18,X_19)))
| multiply(X_19,inverse(inverse(X_18))) = inverse(inverse(multiply(X_18,X_19))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_18)),inverse(inverse(X_19))),multiply(X_19,inverse(inverse(X_18)))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
multiply(X_19,inverse(inverse(X_18))) = inverse(inverse(multiply(X_18,X_19))),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_18)),inverse(inverse(X_19))),inverse(inverse(multiply(X_18,X_19)))) )],[refute_0_44,refute_0_84]) ).
cnf(refute_0_86,plain,
multiply(inverse(X_0),inverse(inverse(multiply(X_0,B)))) = inverse(inverse(multiply(multiply(X_0,B),inverse(X_0)))),
inference(subst,[],[refute_0_85:[bind(X_18,$fot(multiply(X_0,B))),bind(X_19,$fot(inverse(X_0)))]]) ).
cnf(refute_0_87,plain,
multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(multiply(X_0,B))))) = inverse(multiply(X_0,inverse(multiply(X_0,B)))),
inference(subst,[],[refute_0_58:[bind(A,$fot(X_0)),bind(B,$fot(X_1)),bind(C,$fot(inverse(multiply(X_0,B))))]]) ).
cnf(refute_0_88,plain,
( multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(multiply(X_0,B))))) != B
| multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(multiply(X_0,B))))) != inverse(multiply(X_0,inverse(multiply(X_0,B))))
| inverse(multiply(X_0,inverse(multiply(X_0,B)))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(multiply(X_0,B))))),B) ),[0],$fot(inverse(multiply(X_0,inverse(multiply(X_0,B)))))]]) ).
cnf(refute_0_89,plain,
( multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(multiply(X_0,B))))) != B
| inverse(multiply(X_0,inverse(multiply(X_0,B)))) = B ),
inference(resolve,[$cnf( $equal(multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(multiply(X_0,B))))),inverse(multiply(X_0,inverse(multiply(X_0,B))))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
inverse(multiply(X_0,inverse(multiply(X_0,B)))) = B,
inference(resolve,[$cnf( $equal(multiply(X_1,inverse(multiply(multiply(X_0,X_1),inverse(multiply(X_0,B))))),B) )],[refute_0_49,refute_0_89]) ).
cnf(refute_0_91,plain,
inverse(multiply(X_0,inverse(multiply(X_0,B)))) = multiply(multiply(X_0,B),inverse(X_0)),
inference(subst,[],[refute_0_76:[bind(X_3,$fot(multiply(X_0,B)))]]) ).
cnf(refute_0_92,plain,
( inverse(multiply(X_0,inverse(multiply(X_0,B)))) != B
| inverse(multiply(X_0,inverse(multiply(X_0,B)))) != multiply(multiply(X_0,B),inverse(X_0))
| multiply(multiply(X_0,B),inverse(X_0)) = B ),
introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_0,inverse(multiply(X_0,B)))),B) ),[0],$fot(multiply(multiply(X_0,B),inverse(X_0)))]]) ).
cnf(refute_0_93,plain,
( inverse(multiply(X_0,inverse(multiply(X_0,B)))) != B
| multiply(multiply(X_0,B),inverse(X_0)) = B ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_0,inverse(multiply(X_0,B)))),multiply(multiply(X_0,B),inverse(X_0))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
multiply(multiply(X_0,B),inverse(X_0)) = B,
inference(resolve,[$cnf( $equal(inverse(multiply(X_0,inverse(multiply(X_0,B)))),B) )],[refute_0_90,refute_0_93]) ).
cnf(refute_0_95,plain,
( multiply(multiply(X_0,B),inverse(X_0)) != B
| multiply(inverse(X_0),inverse(inverse(multiply(X_0,B)))) != inverse(inverse(multiply(multiply(X_0,B),inverse(X_0))))
| multiply(inverse(X_0),inverse(inverse(multiply(X_0,B)))) = inverse(inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_0),inverse(inverse(multiply(X_0,B)))),inverse(inverse(multiply(multiply(X_0,B),inverse(X_0))))) ),[1,0,0],$fot(B)]]) ).
cnf(refute_0_96,plain,
( multiply(inverse(X_0),inverse(inverse(multiply(X_0,B)))) != inverse(inverse(multiply(multiply(X_0,B),inverse(X_0))))
| multiply(inverse(X_0),inverse(inverse(multiply(X_0,B)))) = inverse(inverse(B)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_0,B),inverse(X_0)),B) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
multiply(inverse(X_0),inverse(inverse(multiply(X_0,B)))) = inverse(inverse(B)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_0),inverse(inverse(multiply(X_0,B)))),inverse(inverse(multiply(multiply(X_0,B),inverse(X_0))))) )],[refute_0_86,refute_0_96]) ).
cnf(refute_0_98,plain,
inverse(multiply(multiply(X_0,B),inverse(X_0))) = multiply(X_0,inverse(multiply(X_0,B))),
inference(subst,[],[refute_0_76:[bind(X_0,$fot(multiply(X_0,B))),bind(X_3,$fot(X_0))]]) ).
cnf(refute_0_99,plain,
inverse(inverse(multiply(multiply(X_0,B),inverse(X_0)))) = inverse(inverse(multiply(multiply(X_0,B),inverse(X_0)))),
introduced(tautology,[refl,[$fot(inverse(inverse(multiply(multiply(X_0,B),inverse(X_0)))))]]) ).
cnf(refute_0_100,plain,
( inverse(multiply(multiply(X_0,B),inverse(X_0))) != multiply(X_0,inverse(multiply(X_0,B)))
| inverse(inverse(multiply(multiply(X_0,B),inverse(X_0)))) != inverse(inverse(multiply(multiply(X_0,B),inverse(X_0))))
| inverse(inverse(multiply(multiply(X_0,B),inverse(X_0)))) = inverse(multiply(X_0,inverse(multiply(X_0,B)))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(multiply(multiply(X_0,B),inverse(X_0)))),inverse(inverse(multiply(multiply(X_0,B),inverse(X_0))))) ),[1,0],$fot(multiply(X_0,inverse(multiply(X_0,B))))]]) ).
cnf(refute_0_101,plain,
( inverse(multiply(multiply(X_0,B),inverse(X_0))) != multiply(X_0,inverse(multiply(X_0,B)))
| inverse(inverse(multiply(multiply(X_0,B),inverse(X_0)))) = inverse(multiply(X_0,inverse(multiply(X_0,B)))) ),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(multiply(X_0,B),inverse(X_0)))),inverse(inverse(multiply(multiply(X_0,B),inverse(X_0))))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
inverse(inverse(multiply(multiply(X_0,B),inverse(X_0)))) = inverse(multiply(X_0,inverse(multiply(X_0,B)))),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X_0,B),inverse(X_0))),multiply(X_0,inverse(multiply(X_0,B)))) )],[refute_0_98,refute_0_101]) ).
cnf(refute_0_103,plain,
( inverse(multiply(X_0,inverse(multiply(X_0,B)))) != B
| inverse(inverse(multiply(multiply(X_0,B),inverse(X_0)))) != inverse(multiply(X_0,inverse(multiply(X_0,B))))
| inverse(inverse(multiply(multiply(X_0,B),inverse(X_0)))) = B ),
inference(subst,[],[refute_0_79:[bind(X,$fot(inverse(inverse(multiply(multiply(X_0,B),inverse(X_0)))))),bind(Y,$fot(inverse(multiply(X_0,inverse(multiply(X_0,B)))))),bind(Z,$fot(B))]]) ).
cnf(refute_0_104,plain,
( inverse(multiply(X_0,inverse(multiply(X_0,B)))) != B
| inverse(inverse(multiply(multiply(X_0,B),inverse(X_0)))) = B ),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(multiply(X_0,B),inverse(X_0)))),inverse(multiply(X_0,inverse(multiply(X_0,B))))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
inverse(inverse(multiply(multiply(X_0,B),inverse(X_0)))) = B,
inference(resolve,[$cnf( $equal(inverse(multiply(X_0,inverse(multiply(X_0,B)))),B) )],[refute_0_90,refute_0_104]) ).
cnf(refute_0_106,plain,
( multiply(inverse(X_0),inverse(inverse(multiply(X_0,B)))) != inverse(inverse(multiply(multiply(X_0,B),inverse(X_0))))
| inverse(inverse(multiply(multiply(X_0,B),inverse(X_0)))) != B
| multiply(inverse(X_0),inverse(inverse(multiply(X_0,B)))) = B ),
inference(subst,[],[refute_0_79:[bind(X,$fot(multiply(inverse(X_0),inverse(inverse(multiply(X_0,B)))))),bind(Y,$fot(inverse(inverse(multiply(multiply(X_0,B),inverse(X_0)))))),bind(Z,$fot(B))]]) ).
cnf(refute_0_107,plain,
( inverse(inverse(multiply(multiply(X_0,B),inverse(X_0)))) != B
| multiply(inverse(X_0),inverse(inverse(multiply(X_0,B)))) = B ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_0),inverse(inverse(multiply(X_0,B)))),inverse(inverse(multiply(multiply(X_0,B),inverse(X_0))))) )],[refute_0_86,refute_0_106]) ).
cnf(refute_0_108,plain,
multiply(inverse(X_0),inverse(inverse(multiply(X_0,B)))) = B,
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(multiply(X_0,B),inverse(X_0)))),B) )],[refute_0_105,refute_0_107]) ).
cnf(refute_0_109,plain,
( multiply(inverse(X_0),inverse(inverse(multiply(X_0,B)))) != B
| multiply(inverse(X_0),inverse(inverse(multiply(X_0,B)))) != inverse(inverse(B))
| B = inverse(inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_0),inverse(inverse(multiply(X_0,B)))),inverse(inverse(B))) ),[0],$fot(B)]]) ).
cnf(refute_0_110,plain,
( multiply(inverse(X_0),inverse(inverse(multiply(X_0,B)))) != inverse(inverse(B))
| B = inverse(inverse(B)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_0),inverse(inverse(multiply(X_0,B)))),B) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
B = inverse(inverse(B)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_0),inverse(inverse(multiply(X_0,B)))),inverse(inverse(B))) )],[refute_0_97,refute_0_110]) ).
cnf(refute_0_112,plain,
( B != inverse(inverse(B))
| inverse(inverse(B)) = B ),
inference(subst,[],[refute_0_69:[bind(X,$fot(B)),bind(Y,$fot(inverse(inverse(B))))]]) ).
cnf(refute_0_113,plain,
inverse(inverse(B)) = B,
inference(resolve,[$cnf( $equal(B,inverse(inverse(B))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
inverse(inverse(X_18)) = X_18,
inference(subst,[],[refute_0_113:[bind(B,$fot(X_18))]]) ).
cnf(refute_0_115,plain,
multiply(X_19,inverse(inverse(X_18))) = multiply(X_19,inverse(inverse(X_18))),
introduced(tautology,[refl,[$fot(multiply(X_19,inverse(inverse(X_18))))]]) ).
cnf(refute_0_116,plain,
( multiply(X_19,inverse(inverse(X_18))) != multiply(X_19,inverse(inverse(X_18)))
| inverse(inverse(X_18)) != X_18
| multiply(X_19,inverse(inverse(X_18))) = multiply(X_19,X_18) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_19,inverse(inverse(X_18))),multiply(X_19,inverse(inverse(X_18)))) ),[1,1],$fot(X_18)]]) ).
cnf(refute_0_117,plain,
( inverse(inverse(X_18)) != X_18
| multiply(X_19,inverse(inverse(X_18))) = multiply(X_19,X_18) ),
inference(resolve,[$cnf( $equal(multiply(X_19,inverse(inverse(X_18))),multiply(X_19,inverse(inverse(X_18)))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
multiply(X_19,inverse(inverse(X_18))) = multiply(X_19,X_18),
inference(resolve,[$cnf( $equal(inverse(inverse(X_18)),X_18) )],[refute_0_114,refute_0_117]) ).
cnf(refute_0_119,plain,
( multiply(X_19,inverse(inverse(X_18))) != multiply(X_19,X_18)
| multiply(X_19,inverse(inverse(X_18))) != inverse(inverse(multiply(X_18,X_19)))
| multiply(X_19,X_18) = inverse(inverse(multiply(X_18,X_19))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_19,inverse(inverse(X_18))),inverse(inverse(multiply(X_18,X_19)))) ),[0],$fot(multiply(X_19,X_18))]]) ).
cnf(refute_0_120,plain,
( multiply(X_19,inverse(inverse(X_18))) != inverse(inverse(multiply(X_18,X_19)))
| multiply(X_19,X_18) = inverse(inverse(multiply(X_18,X_19))) ),
inference(resolve,[$cnf( $equal(multiply(X_19,inverse(inverse(X_18))),multiply(X_19,X_18)) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
inverse(inverse(multiply(X_18,X_19))) = multiply(X_18,X_19),
inference(subst,[],[refute_0_113:[bind(B,$fot(multiply(X_18,X_19)))]]) ).
cnf(refute_0_122,plain,
( multiply(X_19,X_18) != inverse(inverse(multiply(X_18,X_19)))
| inverse(inverse(multiply(X_18,X_19))) != multiply(X_18,X_19)
| multiply(X_19,X_18) = multiply(X_18,X_19) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_19,X_18),multiply(X_18,X_19)) ),[0],$fot(inverse(inverse(multiply(X_18,X_19))))]]) ).
cnf(refute_0_123,plain,
( multiply(X_19,X_18) != inverse(inverse(multiply(X_18,X_19)))
| multiply(X_19,X_18) = multiply(X_18,X_19) ),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_18,X_19))),multiply(X_18,X_19)) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
( multiply(X_19,inverse(inverse(X_18))) != inverse(inverse(multiply(X_18,X_19)))
| multiply(X_19,X_18) = multiply(X_18,X_19) ),
inference(resolve,[$cnf( $equal(multiply(X_19,X_18),inverse(inverse(multiply(X_18,X_19)))) )],[refute_0_120,refute_0_123]) ).
cnf(refute_0_125,plain,
multiply(X_19,X_18) = multiply(X_18,X_19),
inference(resolve,[$cnf( $equal(multiply(X_19,inverse(inverse(X_18))),inverse(inverse(multiply(X_18,X_19)))) )],[refute_0_85,refute_0_124]) ).
cnf(refute_0_126,plain,
( multiply(X_19,X_18) != multiply(X_18,X_19)
| multiply(X_18,X_19) = multiply(X_19,X_18) ),
inference(subst,[],[refute_0_69:[bind(X,$fot(multiply(X_19,X_18))),bind(Y,$fot(multiply(X_18,X_19)))]]) ).
cnf(refute_0_127,plain,
multiply(X_18,X_19) = multiply(X_19,X_18),
inference(resolve,[$cnf( $equal(multiply(X_19,X_18),multiply(X_18,X_19)) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
multiply(inverse(b2),b2) = multiply(b2,inverse(b2)),
inference(subst,[],[refute_0_127:[bind(X_18,$fot(inverse(b2))),bind(X_19,$fot(b2))]]) ).
cnf(refute_0_129,plain,
multiply(a2,multiply(inverse(b2),b2)) = multiply(a2,multiply(inverse(b2),b2)),
introduced(tautology,[refl,[$fot(multiply(a2,multiply(inverse(b2),b2)))]]) ).
cnf(refute_0_130,plain,
( multiply(a2,multiply(inverse(b2),b2)) != multiply(a2,multiply(inverse(b2),b2))
| multiply(inverse(b2),b2) != multiply(b2,inverse(b2))
| multiply(a2,multiply(inverse(b2),b2)) = multiply(a2,multiply(b2,inverse(b2))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(a2,multiply(inverse(b2),b2)),multiply(a2,multiply(inverse(b2),b2))) ),[1,1],$fot(multiply(b2,inverse(b2)))]]) ).
cnf(refute_0_131,plain,
( multiply(inverse(b2),b2) != multiply(b2,inverse(b2))
| multiply(a2,multiply(inverse(b2),b2)) = multiply(a2,multiply(b2,inverse(b2))) ),
inference(resolve,[$cnf( $equal(multiply(a2,multiply(inverse(b2),b2)),multiply(a2,multiply(inverse(b2),b2))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
multiply(a2,multiply(inverse(b2),b2)) = multiply(a2,multiply(b2,inverse(b2))),
inference(resolve,[$cnf( $equal(multiply(inverse(b2),b2),multiply(b2,inverse(b2))) )],[refute_0_128,refute_0_131]) ).
cnf(refute_0_133,plain,
multiply(multiply(inverse(b2),b2),a2) = multiply(a2,multiply(inverse(b2),b2)),
inference(subst,[],[refute_0_127:[bind(X_18,$fot(multiply(inverse(b2),b2))),bind(X_19,$fot(a2))]]) ).
cnf(refute_0_134,plain,
( multiply(multiply(inverse(b2),b2),a2) != multiply(a2,multiply(inverse(b2),b2))
| multiply(a2,multiply(inverse(b2),b2)) != multiply(a2,multiply(b2,inverse(b2)))
| multiply(multiply(inverse(b2),b2),a2) = multiply(a2,multiply(b2,inverse(b2))) ),
inference(subst,[],[refute_0_79:[bind(X,$fot(multiply(multiply(inverse(b2),b2),a2))),bind(Y,$fot(multiply(a2,multiply(inverse(b2),b2)))),bind(Z,$fot(multiply(a2,multiply(b2,inverse(b2)))))]]) ).
cnf(refute_0_135,plain,
( multiply(a2,multiply(inverse(b2),b2)) != multiply(a2,multiply(b2,inverse(b2)))
| multiply(multiply(inverse(b2),b2),a2) = multiply(a2,multiply(b2,inverse(b2))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),multiply(a2,multiply(inverse(b2),b2))) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
multiply(multiply(inverse(b2),b2),a2) = multiply(a2,multiply(b2,inverse(b2))),
inference(resolve,[$cnf( $equal(multiply(a2,multiply(inverse(b2),b2)),multiply(a2,multiply(b2,inverse(b2)))) )],[refute_0_132,refute_0_135]) ).
cnf(refute_0_137,plain,
( multiply(multiply(inverse(b2),b2),a2) != multiply(a2,multiply(b2,inverse(b2)))
| multiply(a2,multiply(b2,inverse(b2))) != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(inverse(b2),b2),a2),a2) ),[0],$fot(multiply(a2,multiply(b2,inverse(b2))))]]) ).
cnf(refute_0_138,plain,
( multiply(a2,multiply(b2,inverse(b2))) != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),multiply(a2,multiply(b2,inverse(b2)))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
multiply(a2,multiply(b2,inverse(b2))) != a2,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),a2) )],[refute_0_138,prove_these_axioms_2]) ).
cnf(refute_0_140,plain,
multiply(multiply(inverse(X_20),B),inverse(inverse(X_20))) = B,
inference(subst,[],[refute_0_94:[bind(X_0,$fot(inverse(X_20)))]]) ).
cnf(refute_0_141,plain,
multiply(multiply(inverse(X_20),B),inverse(inverse(X_20))) = inverse(inverse(multiply(X_20,multiply(inverse(X_20),B)))),
inference(subst,[],[refute_0_85:[bind(X_18,$fot(X_20)),bind(X_19,$fot(multiply(inverse(X_20),B)))]]) ).
cnf(refute_0_142,plain,
( multiply(multiply(inverse(X_20),B),inverse(inverse(X_20))) != B
| multiply(multiply(inverse(X_20),B),inverse(inverse(X_20))) != inverse(inverse(multiply(X_20,multiply(inverse(X_20),B))))
| inverse(inverse(multiply(X_20,multiply(inverse(X_20),B)))) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_20),B),inverse(inverse(X_20))),B) ),[0],$fot(inverse(inverse(multiply(X_20,multiply(inverse(X_20),B)))))]]) ).
cnf(refute_0_143,plain,
( multiply(multiply(inverse(X_20),B),inverse(inverse(X_20))) != B
| inverse(inverse(multiply(X_20,multiply(inverse(X_20),B)))) = B ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_20),B),inverse(inverse(X_20))),inverse(inverse(multiply(X_20,multiply(inverse(X_20),B))))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
inverse(inverse(multiply(X_20,multiply(inverse(X_20),B)))) = B,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_20),B),inverse(inverse(X_20))),B) )],[refute_0_140,refute_0_143]) ).
cnf(refute_0_145,plain,
inverse(inverse(multiply(X_20,multiply(inverse(X_20),B)))) = multiply(X_20,multiply(inverse(X_20),B)),
inference(subst,[],[refute_0_113:[bind(B,$fot(multiply(X_20,multiply(inverse(X_20),B))))]]) ).
cnf(refute_0_146,plain,
( inverse(inverse(multiply(X_20,multiply(inverse(X_20),B)))) != B
| inverse(inverse(multiply(X_20,multiply(inverse(X_20),B)))) != multiply(X_20,multiply(inverse(X_20),B))
| multiply(X_20,multiply(inverse(X_20),B)) = B ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(multiply(X_20,multiply(inverse(X_20),B)))),B) ),[0],$fot(multiply(X_20,multiply(inverse(X_20),B)))]]) ).
cnf(refute_0_147,plain,
( inverse(inverse(multiply(X_20,multiply(inverse(X_20),B)))) != B
| multiply(X_20,multiply(inverse(X_20),B)) = B ),
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_20,multiply(inverse(X_20),B)))),multiply(X_20,multiply(inverse(X_20),B))) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
multiply(X_20,multiply(inverse(X_20),B)) = B,
inference(resolve,[$cnf( $equal(inverse(inverse(multiply(X_20,multiply(inverse(X_20),B)))),B) )],[refute_0_144,refute_0_147]) ).
cnf(refute_0_149,plain,
multiply(X_20,multiply(inverse(X_20),inverse(inverse(X_20)))) = inverse(inverse(X_20)),
inference(subst,[],[refute_0_148:[bind(B,$fot(inverse(inverse(X_20))))]]) ).
cnf(refute_0_150,plain,
multiply(multiply(multiply(A,inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3))))),C),inverse(multiply(A,C))) = inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3)))),
inference(subst,[],[single_axiom:[bind(B,$fot(inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3))))))]]) ).
cnf(refute_0_151,plain,
multiply(A,inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3))))) = X_3,
inference(subst,[],[refute_0_49:[bind(B,$fot(X_3)),bind(X_0,$fot(X_4)),bind(X_1,$fot(A))]]) ).
cnf(refute_0_152,plain,
( multiply(A,inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3))))) != X_3
| multiply(multiply(multiply(A,inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3))))),C),inverse(multiply(A,C))) != inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3))))
| multiply(multiply(X_3,C),inverse(multiply(A,C))) = inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(multiply(A,inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3))))),C),inverse(multiply(A,C))),inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3))))) ),[0,0,0],$fot(X_3)]]) ).
cnf(refute_0_153,plain,
( multiply(multiply(multiply(A,inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3))))),C),inverse(multiply(A,C))) != inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3))))
| multiply(multiply(X_3,C),inverse(multiply(A,C))) = inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3)))) ),
inference(resolve,[$cnf( $equal(multiply(A,inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3))))),X_3) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
multiply(multiply(X_3,C),inverse(multiply(A,C))) = inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3)))),
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(A,inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3))))),C),inverse(multiply(A,C))),inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3))))) )],[refute_0_150,refute_0_153]) ).
cnf(refute_0_155,plain,
inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3)))) = multiply(X_3,inverse(A)),
inference(subst,[],[refute_0_71:[bind(B,$fot(X_3)),bind(X_0,$fot(X_4)),bind(X_14,$fot(A))]]) ).
cnf(refute_0_156,plain,
( multiply(multiply(X_3,C),inverse(multiply(A,C))) != inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3))))
| inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3)))) != multiply(X_3,inverse(A))
| multiply(multiply(X_3,C),inverse(multiply(A,C))) = multiply(X_3,inverse(A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(X_3,C),inverse(multiply(A,C))),multiply(X_3,inverse(A))) ),[0],$fot(inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3)))))]]) ).
cnf(refute_0_157,plain,
( multiply(multiply(X_3,C),inverse(multiply(A,C))) != inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3))))
| multiply(multiply(X_3,C),inverse(multiply(A,C))) = multiply(X_3,inverse(A)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3)))),multiply(X_3,inverse(A))) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
multiply(multiply(X_3,C),inverse(multiply(A,C))) = multiply(X_3,inverse(A)),
inference(resolve,[$cnf( $equal(multiply(multiply(X_3,C),inverse(multiply(A,C))),inverse(multiply(multiply(X_4,A),inverse(multiply(X_4,X_3))))) )],[refute_0_154,refute_0_157]) ).
cnf(refute_0_159,plain,
multiply(multiply(inverse(X_0),multiply(X_0,B)),inverse(multiply(X_42,multiply(X_0,B)))) = multiply(inverse(X_0),inverse(X_42)),
inference(subst,[],[refute_0_158:[bind(A,$fot(X_42)),bind(C,$fot(multiply(X_0,B))),bind(X_3,$fot(inverse(X_0)))]]) ).
cnf(refute_0_160,plain,
multiply(multiply(X_0,B),inverse(X_0)) = multiply(inverse(X_0),multiply(X_0,B)),
inference(subst,[],[refute_0_127:[bind(X_18,$fot(multiply(X_0,B))),bind(X_19,$fot(inverse(X_0)))]]) ).
cnf(refute_0_161,plain,
( multiply(multiply(X_0,B),inverse(X_0)) != B
| multiply(multiply(X_0,B),inverse(X_0)) != multiply(inverse(X_0),multiply(X_0,B))
| multiply(inverse(X_0),multiply(X_0,B)) = B ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_0,B),inverse(X_0)),B) ),[0],$fot(multiply(inverse(X_0),multiply(X_0,B)))]]) ).
cnf(refute_0_162,plain,
( multiply(multiply(X_0,B),inverse(X_0)) != B
| multiply(inverse(X_0),multiply(X_0,B)) = B ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_0,B),inverse(X_0)),multiply(inverse(X_0),multiply(X_0,B))) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
multiply(inverse(X_0),multiply(X_0,B)) = B,
inference(resolve,[$cnf( $equal(multiply(multiply(X_0,B),inverse(X_0)),B) )],[refute_0_94,refute_0_162]) ).
cnf(refute_0_164,plain,
( multiply(multiply(inverse(X_0),multiply(X_0,B)),inverse(multiply(X_42,multiply(X_0,B)))) != multiply(inverse(X_0),inverse(X_42))
| multiply(inverse(X_0),multiply(X_0,B)) != B
| multiply(B,inverse(multiply(X_42,multiply(X_0,B)))) = multiply(inverse(X_0),inverse(X_42)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(X_0),multiply(X_0,B)),inverse(multiply(X_42,multiply(X_0,B)))),multiply(inverse(X_0),inverse(X_42))) ),[0,0],$fot(B)]]) ).
cnf(refute_0_165,plain,
( multiply(multiply(inverse(X_0),multiply(X_0,B)),inverse(multiply(X_42,multiply(X_0,B)))) != multiply(inverse(X_0),inverse(X_42))
| multiply(B,inverse(multiply(X_42,multiply(X_0,B)))) = multiply(inverse(X_0),inverse(X_42)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_0),multiply(X_0,B)),B) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
multiply(B,inverse(multiply(X_42,multiply(X_0,B)))) = multiply(inverse(X_0),inverse(X_42)),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(X_0),multiply(X_0,B)),inverse(multiply(X_42,multiply(X_0,B)))),multiply(inverse(X_0),inverse(X_42))) )],[refute_0_159,refute_0_165]) ).
cnf(refute_0_167,plain,
multiply(inverse(X_0),inverse(X_42)) = inverse(multiply(X_0,X_42)),
inference(subst,[],[refute_0_39:[bind(X_1,$fot(X_42))]]) ).
cnf(refute_0_168,plain,
( multiply(B,inverse(multiply(X_42,multiply(X_0,B)))) != multiply(inverse(X_0),inverse(X_42))
| multiply(inverse(X_0),inverse(X_42)) != inverse(multiply(X_0,X_42))
| multiply(B,inverse(multiply(X_42,multiply(X_0,B)))) = inverse(multiply(X_0,X_42)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(B,inverse(multiply(X_42,multiply(X_0,B)))),inverse(multiply(X_0,X_42))) ),[0],$fot(multiply(inverse(X_0),inverse(X_42)))]]) ).
cnf(refute_0_169,plain,
( multiply(B,inverse(multiply(X_42,multiply(X_0,B)))) != multiply(inverse(X_0),inverse(X_42))
| multiply(B,inverse(multiply(X_42,multiply(X_0,B)))) = inverse(multiply(X_0,X_42)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_0),inverse(X_42)),inverse(multiply(X_0,X_42))) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
multiply(B,inverse(multiply(X_42,multiply(X_0,B)))) = inverse(multiply(X_0,X_42)),
inference(resolve,[$cnf( $equal(multiply(B,inverse(multiply(X_42,multiply(X_0,B)))),multiply(inverse(X_0),inverse(X_42))) )],[refute_0_166,refute_0_169]) ).
cnf(refute_0_171,plain,
multiply(X_45,inverse(multiply(inverse(X_46),multiply(X_46,X_45)))) = inverse(multiply(X_46,inverse(X_46))),
inference(subst,[],[refute_0_170:[bind(B,$fot(X_45)),bind(X_0,$fot(X_46)),bind(X_42,$fot(inverse(X_46)))]]) ).
cnf(refute_0_172,plain,
multiply(inverse(X_46),multiply(X_46,X_45)) = X_45,
inference(subst,[],[refute_0_163:[bind(B,$fot(X_45)),bind(X_0,$fot(X_46))]]) ).
cnf(refute_0_173,plain,
( multiply(X_45,inverse(multiply(inverse(X_46),multiply(X_46,X_45)))) != inverse(multiply(X_46,inverse(X_46)))
| multiply(inverse(X_46),multiply(X_46,X_45)) != X_45
| multiply(X_45,inverse(X_45)) = inverse(multiply(X_46,inverse(X_46))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_45,inverse(multiply(inverse(X_46),multiply(X_46,X_45)))),inverse(multiply(X_46,inverse(X_46)))) ),[0,1,0],$fot(X_45)]]) ).
cnf(refute_0_174,plain,
( multiply(X_45,inverse(multiply(inverse(X_46),multiply(X_46,X_45)))) != inverse(multiply(X_46,inverse(X_46)))
| multiply(X_45,inverse(X_45)) = inverse(multiply(X_46,inverse(X_46))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_46),multiply(X_46,X_45)),X_45) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
multiply(X_45,inverse(X_45)) = inverse(multiply(X_46,inverse(X_46))),
inference(resolve,[$cnf( $equal(multiply(X_45,inverse(multiply(inverse(X_46),multiply(X_46,X_45)))),inverse(multiply(X_46,inverse(X_46)))) )],[refute_0_171,refute_0_174]) ).
cnf(refute_0_176,plain,
inverse(multiply(X_46,inverse(X_46))) = multiply(X_46,inverse(X_46)),
inference(subst,[],[refute_0_76:[bind(X_0,$fot(X_46)),bind(X_3,$fot(X_46))]]) ).
cnf(refute_0_177,plain,
( multiply(X_45,inverse(X_45)) != inverse(multiply(X_46,inverse(X_46)))
| inverse(multiply(X_46,inverse(X_46))) != multiply(X_46,inverse(X_46))
| multiply(X_45,inverse(X_45)) = multiply(X_46,inverse(X_46)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_45,inverse(X_45)),multiply(X_46,inverse(X_46))) ),[0],$fot(inverse(multiply(X_46,inverse(X_46))))]]) ).
cnf(refute_0_178,plain,
( multiply(X_45,inverse(X_45)) != inverse(multiply(X_46,inverse(X_46)))
| multiply(X_45,inverse(X_45)) = multiply(X_46,inverse(X_46)) ),
inference(resolve,[$cnf( $equal(inverse(multiply(X_46,inverse(X_46))),multiply(X_46,inverse(X_46))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
multiply(X_45,inverse(X_45)) = multiply(X_46,inverse(X_46)),
inference(resolve,[$cnf( $equal(multiply(X_45,inverse(X_45)),inverse(multiply(X_46,inverse(X_46)))) )],[refute_0_175,refute_0_178]) ).
cnf(refute_0_180,plain,
multiply(inverse(X_20),inverse(inverse(X_20))) = multiply(X_49,inverse(X_49)),
inference(subst,[],[refute_0_179:[bind(X_45,$fot(inverse(X_20))),bind(X_46,$fot(X_49))]]) ).
cnf(refute_0_181,plain,
( multiply(X_20,multiply(inverse(X_20),inverse(inverse(X_20)))) != inverse(inverse(X_20))
| multiply(inverse(X_20),inverse(inverse(X_20))) != multiply(X_49,inverse(X_49))
| multiply(X_20,multiply(X_49,inverse(X_49))) = inverse(inverse(X_20)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_20,multiply(inverse(X_20),inverse(inverse(X_20)))),inverse(inverse(X_20))) ),[0,1],$fot(multiply(X_49,inverse(X_49)))]]) ).
cnf(refute_0_182,plain,
( multiply(X_20,multiply(inverse(X_20),inverse(inverse(X_20)))) != inverse(inverse(X_20))
| multiply(X_20,multiply(X_49,inverse(X_49))) = inverse(inverse(X_20)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_20),inverse(inverse(X_20))),multiply(X_49,inverse(X_49))) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
multiply(X_20,multiply(X_49,inverse(X_49))) = inverse(inverse(X_20)),
inference(resolve,[$cnf( $equal(multiply(X_20,multiply(inverse(X_20),inverse(inverse(X_20)))),inverse(inverse(X_20))) )],[refute_0_149,refute_0_182]) ).
cnf(refute_0_184,plain,
inverse(inverse(X_20)) = X_20,
inference(subst,[],[refute_0_113:[bind(B,$fot(X_20))]]) ).
cnf(refute_0_185,plain,
( multiply(X_20,multiply(X_49,inverse(X_49))) != inverse(inverse(X_20))
| inverse(inverse(X_20)) != X_20
| multiply(X_20,multiply(X_49,inverse(X_49))) = X_20 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_20,multiply(X_49,inverse(X_49))),X_20) ),[0],$fot(inverse(inverse(X_20)))]]) ).
cnf(refute_0_186,plain,
( multiply(X_20,multiply(X_49,inverse(X_49))) != inverse(inverse(X_20))
| multiply(X_20,multiply(X_49,inverse(X_49))) = X_20 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_20)),X_20) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
multiply(X_20,multiply(X_49,inverse(X_49))) = X_20,
inference(resolve,[$cnf( $equal(multiply(X_20,multiply(X_49,inverse(X_49))),inverse(inverse(X_20))) )],[refute_0_183,refute_0_186]) ).
cnf(refute_0_188,plain,
multiply(a2,multiply(b2,inverse(b2))) = a2,
inference(subst,[],[refute_0_187:[bind(X_20,$fot(a2)),bind(X_49,$fot(b2))]]) ).
cnf(refute_0_189,plain,
( multiply(a2,multiply(b2,inverse(b2))) != a2
| a2 != a2
| multiply(a2,multiply(b2,inverse(b2))) = a2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a2,multiply(b2,inverse(b2))),a2) ),[0],$fot(a2)]]) ).
cnf(refute_0_190,plain,
( a2 != a2
| multiply(a2,multiply(b2,inverse(b2))) = a2 ),
inference(resolve,[$cnf( $equal(multiply(a2,multiply(b2,inverse(b2))),a2) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
a2 != a2,
inference(resolve,[$cnf( $equal(multiply(a2,multiply(b2,inverse(b2))),a2) )],[refute_0_190,refute_0_139]) ).
cnf(refute_0_192,plain,
a2 = a2,
introduced(tautology,[refl,[$fot(a2)]]) ).
cnf(refute_0_193,plain,
$false,
inference(resolve,[$cnf( $equal(a2,a2) )],[refute_0_192,refute_0_191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP510-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 10:11:09 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.37/0.56 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.37/0.56
% 0.37/0.56 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.37/0.59
%------------------------------------------------------------------------------