TSTP Solution File: GRP562-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP562-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 10:42:22 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 47
% Syntax : Number of clauses : 166 ( 89 unt; 0 nHn; 83 RR)
% Number of literals : 280 ( 279 equ; 117 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 417 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(divide(divide(A,inverse(B)),C),divide(A,C)) = B ).
cnf(multiply,axiom,
multiply(A,B) = divide(A,inverse(B)) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2 ).
cnf(refute_0_0,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_1,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_2,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( multiply(A,B) != divide(A,inverse(B))
| divide(A,inverse(B)) = multiply(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(divide(A,inverse(B))))]]) ).
cnf(refute_0_4,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),divide(A,inverse(B))) )],[multiply,refute_0_3]) ).
cnf(refute_0_5,plain,
divide(divide(A,inverse(B)),C) = divide(divide(A,inverse(B)),C),
introduced(tautology,[refl,[$fot(divide(divide(A,inverse(B)),C))]]) ).
cnf(refute_0_6,plain,
( divide(A,inverse(B)) != multiply(A,B)
| divide(divide(A,inverse(B)),C) != divide(divide(A,inverse(B)),C)
| divide(divide(A,inverse(B)),C) = divide(multiply(A,B),C) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(A,inverse(B)),C),divide(divide(A,inverse(B)),C)) ),[1,0],$fot(multiply(A,B))]]) ).
cnf(refute_0_7,plain,
( divide(A,inverse(B)) != multiply(A,B)
| divide(divide(A,inverse(B)),C) = divide(multiply(A,B),C) ),
inference(resolve,[$cnf( $equal(divide(divide(A,inverse(B)),C),divide(divide(A,inverse(B)),C)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
divide(divide(A,inverse(B)),C) = divide(multiply(A,B),C),
inference(resolve,[$cnf( $equal(divide(A,inverse(B)),multiply(A,B)) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
divide(divide(divide(A,inverse(B)),C),divide(A,C)) = divide(divide(divide(A,inverse(B)),C),divide(A,C)),
introduced(tautology,[refl,[$fot(divide(divide(divide(A,inverse(B)),C),divide(A,C)))]]) ).
cnf(refute_0_10,plain,
( divide(divide(A,inverse(B)),C) != divide(multiply(A,B),C)
| divide(divide(divide(A,inverse(B)),C),divide(A,C)) != divide(divide(divide(A,inverse(B)),C),divide(A,C))
| divide(divide(divide(A,inverse(B)),C),divide(A,C)) = divide(divide(multiply(A,B),C),divide(A,C)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(A,inverse(B)),C),divide(A,C)),divide(divide(divide(A,inverse(B)),C),divide(A,C))) ),[1,0],$fot(divide(multiply(A,B),C))]]) ).
cnf(refute_0_11,plain,
( divide(divide(A,inverse(B)),C) != divide(multiply(A,B),C)
| divide(divide(divide(A,inverse(B)),C),divide(A,C)) = divide(divide(multiply(A,B),C),divide(A,C)) ),
inference(resolve,[$cnf( $equal(divide(divide(divide(A,inverse(B)),C),divide(A,C)),divide(divide(divide(A,inverse(B)),C),divide(A,C))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
divide(divide(divide(A,inverse(B)),C),divide(A,C)) = divide(divide(multiply(A,B),C),divide(A,C)),
inference(resolve,[$cnf( $equal(divide(divide(A,inverse(B)),C),divide(multiply(A,B),C)) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
( divide(divide(divide(A,inverse(B)),C),divide(A,C)) != B
| divide(divide(divide(A,inverse(B)),C),divide(A,C)) != divide(divide(multiply(A,B),C),divide(A,C))
| divide(divide(multiply(A,B),C),divide(A,C)) = B ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(A,inverse(B)),C),divide(A,C)),B) ),[0],$fot(divide(divide(multiply(A,B),C),divide(A,C)))]]) ).
cnf(refute_0_14,plain,
( divide(divide(divide(A,inverse(B)),C),divide(A,C)) != B
| divide(divide(multiply(A,B),C),divide(A,C)) = B ),
inference(resolve,[$cnf( $equal(divide(divide(divide(A,inverse(B)),C),divide(A,C)),divide(divide(multiply(A,B),C),divide(A,C))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
divide(divide(multiply(A,B),C),divide(A,C)) = B,
inference(resolve,[$cnf( $equal(divide(divide(divide(A,inverse(B)),C),divide(A,C)),B) )],[single_axiom,refute_0_14]) ).
cnf(refute_0_16,plain,
divide(divide(multiply(multiply(X_6,X_7),B),multiply(X_6,B)),divide(multiply(X_6,X_7),multiply(X_6,B))) = B,
inference(subst,[],[refute_0_15:[bind(A,$fot(multiply(X_6,X_7))),bind(C,$fot(multiply(X_6,B)))]]) ).
cnf(refute_0_17,plain,
divide(divide(multiply(X_2,X_3),inverse(B)),divide(X_2,inverse(B))) = X_3,
inference(subst,[],[refute_0_15:[bind(A,$fot(X_2)),bind(B,$fot(X_3)),bind(C,$fot(inverse(B)))]]) ).
cnf(refute_0_18,plain,
multiply(X_2,B) = divide(X_2,inverse(B)),
inference(subst,[],[multiply:[bind(A,$fot(X_2))]]) ).
cnf(refute_0_19,plain,
( multiply(X_2,B) != divide(X_2,inverse(B))
| divide(X_2,inverse(B)) = multiply(X_2,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(X_2,B))),bind(Y,$fot(divide(X_2,inverse(B))))]]) ).
cnf(refute_0_20,plain,
divide(X_2,inverse(B)) = multiply(X_2,B),
inference(resolve,[$cnf( $equal(multiply(X_2,B),divide(X_2,inverse(B))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( divide(X_2,inverse(B)) != multiply(X_2,B)
| divide(divide(multiply(X_2,X_3),inverse(B)),divide(X_2,inverse(B))) != X_3
| divide(divide(multiply(X_2,X_3),inverse(B)),multiply(X_2,B)) = X_3 ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(multiply(X_2,X_3),inverse(B)),divide(X_2,inverse(B))),X_3) ),[0,1],$fot(multiply(X_2,B))]]) ).
cnf(refute_0_22,plain,
( divide(divide(multiply(X_2,X_3),inverse(B)),divide(X_2,inverse(B))) != X_3
| divide(divide(multiply(X_2,X_3),inverse(B)),multiply(X_2,B)) = X_3 ),
inference(resolve,[$cnf( $equal(divide(X_2,inverse(B)),multiply(X_2,B)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
divide(divide(multiply(X_2,X_3),inverse(B)),multiply(X_2,B)) = X_3,
inference(resolve,[$cnf( $equal(divide(divide(multiply(X_2,X_3),inverse(B)),divide(X_2,inverse(B))),X_3) )],[refute_0_17,refute_0_22]) ).
cnf(refute_0_24,plain,
divide(multiply(X_2,X_3),inverse(B)) = multiply(multiply(X_2,X_3),B),
inference(subst,[],[refute_0_4:[bind(A,$fot(multiply(X_2,X_3)))]]) ).
cnf(refute_0_25,plain,
divide(divide(multiply(X_2,X_3),inverse(B)),multiply(X_2,B)) = divide(divide(multiply(X_2,X_3),inverse(B)),multiply(X_2,B)),
introduced(tautology,[refl,[$fot(divide(divide(multiply(X_2,X_3),inverse(B)),multiply(X_2,B)))]]) ).
cnf(refute_0_26,plain,
( divide(multiply(X_2,X_3),inverse(B)) != multiply(multiply(X_2,X_3),B)
| divide(divide(multiply(X_2,X_3),inverse(B)),multiply(X_2,B)) != divide(divide(multiply(X_2,X_3),inverse(B)),multiply(X_2,B))
| divide(divide(multiply(X_2,X_3),inverse(B)),multiply(X_2,B)) = divide(multiply(multiply(X_2,X_3),B),multiply(X_2,B)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(multiply(X_2,X_3),inverse(B)),multiply(X_2,B)),divide(divide(multiply(X_2,X_3),inverse(B)),multiply(X_2,B))) ),[1,0],$fot(multiply(multiply(X_2,X_3),B))]]) ).
cnf(refute_0_27,plain,
( divide(multiply(X_2,X_3),inverse(B)) != multiply(multiply(X_2,X_3),B)
| divide(divide(multiply(X_2,X_3),inverse(B)),multiply(X_2,B)) = divide(multiply(multiply(X_2,X_3),B),multiply(X_2,B)) ),
inference(resolve,[$cnf( $equal(divide(divide(multiply(X_2,X_3),inverse(B)),multiply(X_2,B)),divide(divide(multiply(X_2,X_3),inverse(B)),multiply(X_2,B))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
divide(divide(multiply(X_2,X_3),inverse(B)),multiply(X_2,B)) = divide(multiply(multiply(X_2,X_3),B),multiply(X_2,B)),
inference(resolve,[$cnf( $equal(divide(multiply(X_2,X_3),inverse(B)),multiply(multiply(X_2,X_3),B)) )],[refute_0_24,refute_0_27]) ).
cnf(refute_0_29,plain,
( divide(divide(multiply(X_2,X_3),inverse(B)),multiply(X_2,B)) != X_3
| divide(divide(multiply(X_2,X_3),inverse(B)),multiply(X_2,B)) != divide(multiply(multiply(X_2,X_3),B),multiply(X_2,B))
| divide(multiply(multiply(X_2,X_3),B),multiply(X_2,B)) = X_3 ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(multiply(X_2,X_3),inverse(B)),multiply(X_2,B)),X_3) ),[0],$fot(divide(multiply(multiply(X_2,X_3),B),multiply(X_2,B)))]]) ).
cnf(refute_0_30,plain,
( divide(divide(multiply(X_2,X_3),inverse(B)),multiply(X_2,B)) != X_3
| divide(multiply(multiply(X_2,X_3),B),multiply(X_2,B)) = X_3 ),
inference(resolve,[$cnf( $equal(divide(divide(multiply(X_2,X_3),inverse(B)),multiply(X_2,B)),divide(multiply(multiply(X_2,X_3),B),multiply(X_2,B))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
divide(multiply(multiply(X_2,X_3),B),multiply(X_2,B)) = X_3,
inference(resolve,[$cnf( $equal(divide(divide(multiply(X_2,X_3),inverse(B)),multiply(X_2,B)),X_3) )],[refute_0_23,refute_0_30]) ).
cnf(refute_0_32,plain,
divide(multiply(multiply(X_6,X_7),B),multiply(X_6,B)) = X_7,
inference(subst,[],[refute_0_31:[bind(X_2,$fot(X_6)),bind(X_3,$fot(X_7))]]) ).
cnf(refute_0_33,plain,
( divide(multiply(multiply(X_6,X_7),B),multiply(X_6,B)) != X_7
| divide(divide(multiply(multiply(X_6,X_7),B),multiply(X_6,B)),divide(multiply(X_6,X_7),multiply(X_6,B))) != B
| divide(X_7,divide(multiply(X_6,X_7),multiply(X_6,B))) = B ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(multiply(multiply(X_6,X_7),B),multiply(X_6,B)),divide(multiply(X_6,X_7),multiply(X_6,B))),B) ),[0,0],$fot(X_7)]]) ).
cnf(refute_0_34,plain,
( divide(divide(multiply(multiply(X_6,X_7),B),multiply(X_6,B)),divide(multiply(X_6,X_7),multiply(X_6,B))) != B
| divide(X_7,divide(multiply(X_6,X_7),multiply(X_6,B))) = B ),
inference(resolve,[$cnf( $equal(divide(multiply(multiply(X_6,X_7),B),multiply(X_6,B)),X_7) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
divide(X_7,divide(multiply(X_6,X_7),multiply(X_6,B))) = B,
inference(resolve,[$cnf( $equal(divide(divide(multiply(multiply(X_6,X_7),B),multiply(X_6,B)),divide(multiply(X_6,X_7),multiply(X_6,B))),B) )],[refute_0_16,refute_0_34]) ).
cnf(refute_0_36,plain,
divide(X_7,divide(multiply(inverse(X_35),X_7),multiply(inverse(X_35),multiply(inverse(X_35),X_7)))) = multiply(inverse(X_35),X_7),
inference(subst,[],[refute_0_35:[bind(B,$fot(multiply(inverse(X_35),X_7))),bind(X_6,$fot(inverse(X_35)))]]) ).
cnf(refute_0_37,plain,
divide(divide(multiply(divide(multiply(X_2,X_3),X_4),B),divide(X_2,X_4)),divide(divide(multiply(X_2,X_3),X_4),divide(X_2,X_4))) = B,
inference(subst,[],[refute_0_15:[bind(A,$fot(divide(multiply(X_2,X_3),X_4))),bind(C,$fot(divide(X_2,X_4)))]]) ).
cnf(refute_0_38,plain,
divide(divide(multiply(X_2,X_3),X_4),divide(X_2,X_4)) = X_3,
inference(subst,[],[refute_0_15:[bind(A,$fot(X_2)),bind(B,$fot(X_3)),bind(C,$fot(X_4))]]) ).
cnf(refute_0_39,plain,
( divide(divide(multiply(X_2,X_3),X_4),divide(X_2,X_4)) != X_3
| divide(divide(multiply(divide(multiply(X_2,X_3),X_4),B),divide(X_2,X_4)),divide(divide(multiply(X_2,X_3),X_4),divide(X_2,X_4))) != B
| divide(divide(multiply(divide(multiply(X_2,X_3),X_4),B),divide(X_2,X_4)),X_3) = B ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(multiply(divide(multiply(X_2,X_3),X_4),B),divide(X_2,X_4)),divide(divide(multiply(X_2,X_3),X_4),divide(X_2,X_4))),B) ),[0,1],$fot(X_3)]]) ).
cnf(refute_0_40,plain,
( divide(divide(multiply(divide(multiply(X_2,X_3),X_4),B),divide(X_2,X_4)),divide(divide(multiply(X_2,X_3),X_4),divide(X_2,X_4))) != B
| divide(divide(multiply(divide(multiply(X_2,X_3),X_4),B),divide(X_2,X_4)),X_3) = B ),
inference(resolve,[$cnf( $equal(divide(divide(multiply(X_2,X_3),X_4),divide(X_2,X_4)),X_3) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
divide(divide(multiply(divide(multiply(X_2,X_3),X_4),B),divide(X_2,X_4)),X_3) = B,
inference(resolve,[$cnf( $equal(divide(divide(multiply(divide(multiply(X_2,X_3),X_4),B),divide(X_2,X_4)),divide(divide(multiply(X_2,X_3),X_4),divide(X_2,X_4))),B) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
divide(divide(multiply(divide(multiply(multiply(multiply(X_30,inverse(B)),X_29),X_3),multiply(X_30,X_29)),B),divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3) = B,
inference(subst,[],[refute_0_41:[bind(X_2,$fot(multiply(multiply(X_30,inverse(B)),X_29))),bind(X_4,$fot(multiply(X_30,X_29)))]]) ).
cnf(refute_0_43,plain,
multiply(divide(multiply(multiply(multiply(X_17,inverse(B)),X_16),X_15),multiply(X_17,X_16)),B) = divide(divide(multiply(multiply(multiply(X_17,inverse(B)),X_16),X_15),multiply(X_17,X_16)),inverse(B)),
inference(subst,[],[multiply:[bind(A,$fot(divide(multiply(multiply(multiply(X_17,inverse(B)),X_16),X_15),multiply(X_17,X_16))))]]) ).
cnf(refute_0_44,plain,
divide(divide(multiply(multiply(multiply(X_6,X_7),X_5),B),multiply(X_6,X_5)),divide(multiply(multiply(X_6,X_7),X_5),multiply(X_6,X_5))) = B,
inference(subst,[],[refute_0_15:[bind(A,$fot(multiply(multiply(X_6,X_7),X_5))),bind(C,$fot(multiply(X_6,X_5)))]]) ).
cnf(refute_0_45,plain,
divide(multiply(multiply(X_6,X_7),X_5),multiply(X_6,X_5)) = X_7,
inference(subst,[],[refute_0_31:[bind(B,$fot(X_5)),bind(X_2,$fot(X_6)),bind(X_3,$fot(X_7))]]) ).
cnf(refute_0_46,plain,
( divide(multiply(multiply(X_6,X_7),X_5),multiply(X_6,X_5)) != X_7
| divide(divide(multiply(multiply(multiply(X_6,X_7),X_5),B),multiply(X_6,X_5)),divide(multiply(multiply(X_6,X_7),X_5),multiply(X_6,X_5))) != B
| divide(divide(multiply(multiply(multiply(X_6,X_7),X_5),B),multiply(X_6,X_5)),X_7) = B ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(multiply(multiply(multiply(X_6,X_7),X_5),B),multiply(X_6,X_5)),divide(multiply(multiply(X_6,X_7),X_5),multiply(X_6,X_5))),B) ),[0,1],$fot(X_7)]]) ).
cnf(refute_0_47,plain,
( divide(divide(multiply(multiply(multiply(X_6,X_7),X_5),B),multiply(X_6,X_5)),divide(multiply(multiply(X_6,X_7),X_5),multiply(X_6,X_5))) != B
| divide(divide(multiply(multiply(multiply(X_6,X_7),X_5),B),multiply(X_6,X_5)),X_7) = B ),
inference(resolve,[$cnf( $equal(divide(multiply(multiply(X_6,X_7),X_5),multiply(X_6,X_5)),X_7) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
divide(divide(multiply(multiply(multiply(X_6,X_7),X_5),B),multiply(X_6,X_5)),X_7) = B,
inference(resolve,[$cnf( $equal(divide(divide(multiply(multiply(multiply(X_6,X_7),X_5),B),multiply(X_6,X_5)),divide(multiply(multiply(X_6,X_7),X_5),multiply(X_6,X_5))),B) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
divide(divide(multiply(multiply(multiply(X_17,inverse(B)),X_16),X_15),multiply(X_17,X_16)),inverse(B)) = X_15,
inference(subst,[],[refute_0_48:[bind(B,$fot(X_15)),bind(X_5,$fot(X_16)),bind(X_6,$fot(X_17)),bind(X_7,$fot(inverse(B)))]]) ).
cnf(refute_0_50,plain,
( multiply(divide(multiply(multiply(multiply(X_17,inverse(B)),X_16),X_15),multiply(X_17,X_16)),B) != divide(divide(multiply(multiply(multiply(X_17,inverse(B)),X_16),X_15),multiply(X_17,X_16)),inverse(B))
| divide(divide(multiply(multiply(multiply(X_17,inverse(B)),X_16),X_15),multiply(X_17,X_16)),inverse(B)) != X_15
| multiply(divide(multiply(multiply(multiply(X_17,inverse(B)),X_16),X_15),multiply(X_17,X_16)),B) = X_15 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(divide(multiply(multiply(multiply(X_17,inverse(B)),X_16),X_15),multiply(X_17,X_16)),B),X_15) ),[0],$fot(divide(divide(multiply(multiply(multiply(X_17,inverse(B)),X_16),X_15),multiply(X_17,X_16)),inverse(B)))]]) ).
cnf(refute_0_51,plain,
( multiply(divide(multiply(multiply(multiply(X_17,inverse(B)),X_16),X_15),multiply(X_17,X_16)),B) != divide(divide(multiply(multiply(multiply(X_17,inverse(B)),X_16),X_15),multiply(X_17,X_16)),inverse(B))
| multiply(divide(multiply(multiply(multiply(X_17,inverse(B)),X_16),X_15),multiply(X_17,X_16)),B) = X_15 ),
inference(resolve,[$cnf( $equal(divide(divide(multiply(multiply(multiply(X_17,inverse(B)),X_16),X_15),multiply(X_17,X_16)),inverse(B)),X_15) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
multiply(divide(multiply(multiply(multiply(X_17,inverse(B)),X_16),X_15),multiply(X_17,X_16)),B) = X_15,
inference(resolve,[$cnf( $equal(multiply(divide(multiply(multiply(multiply(X_17,inverse(B)),X_16),X_15),multiply(X_17,X_16)),B),divide(divide(multiply(multiply(multiply(X_17,inverse(B)),X_16),X_15),multiply(X_17,X_16)),inverse(B))) )],[refute_0_43,refute_0_51]) ).
cnf(refute_0_53,plain,
multiply(divide(multiply(multiply(multiply(X_30,inverse(B)),X_29),X_3),multiply(X_30,X_29)),B) = X_3,
inference(subst,[],[refute_0_52:[bind(X_15,$fot(X_3)),bind(X_16,$fot(X_29)),bind(X_17,$fot(X_30))]]) ).
cnf(refute_0_54,plain,
( multiply(divide(multiply(multiply(multiply(X_30,inverse(B)),X_29),X_3),multiply(X_30,X_29)),B) != X_3
| divide(divide(multiply(divide(multiply(multiply(multiply(X_30,inverse(B)),X_29),X_3),multiply(X_30,X_29)),B),divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3) != B
| divide(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3) = B ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(multiply(divide(multiply(multiply(multiply(X_30,inverse(B)),X_29),X_3),multiply(X_30,X_29)),B),divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3),B) ),[0,0,0],$fot(X_3)]]) ).
cnf(refute_0_55,plain,
( divide(divide(multiply(divide(multiply(multiply(multiply(X_30,inverse(B)),X_29),X_3),multiply(X_30,X_29)),B),divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3) != B
| divide(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3) = B ),
inference(resolve,[$cnf( $equal(multiply(divide(multiply(multiply(multiply(X_30,inverse(B)),X_29),X_3),multiply(X_30,X_29)),B),X_3) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
divide(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3) = B,
inference(resolve,[$cnf( $equal(divide(divide(multiply(divide(multiply(multiply(multiply(X_30,inverse(B)),X_29),X_3),multiply(X_30,X_29)),B),divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3),B) )],[refute_0_42,refute_0_55]) ).
cnf(refute_0_57,plain,
divide(X_3,inverse(B)) = multiply(X_3,B),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_58,plain,
divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29)) = inverse(B),
inference(subst,[],[refute_0_31:[bind(B,$fot(X_29)),bind(X_2,$fot(X_30)),bind(X_3,$fot(inverse(B)))]]) ).
cnf(refute_0_59,plain,
divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))) = divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),
introduced(tautology,[refl,[$fot(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))))]]) ).
cnf(refute_0_60,plain,
( divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))) != divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29)))
| divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29)) != inverse(B)
| divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))) = divide(X_3,inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29)))) ),[1,1],$fot(inverse(B))]]) ).
cnf(refute_0_61,plain,
( divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29)) != inverse(B)
| divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))) = divide(X_3,inverse(B)) ),
inference(resolve,[$cnf( $equal(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29)))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))) = divide(X_3,inverse(B)),
inference(resolve,[$cnf( $equal(divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29)),inverse(B)) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_64,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_63]) ).
cnf(refute_0_65,plain,
( divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))) != divide(X_3,inverse(B))
| divide(X_3,inverse(B)) != multiply(X_3,B)
| divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))) = multiply(X_3,B) ),
inference(subst,[],[refute_0_64:[bind(X,$fot(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))))),bind(Y,$fot(divide(X_3,inverse(B)))),bind(Z,$fot(multiply(X_3,B)))]]) ).
cnf(refute_0_66,plain,
( divide(X_3,inverse(B)) != multiply(X_3,B)
| divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))) = multiply(X_3,B) ),
inference(resolve,[$cnf( $equal(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),divide(X_3,inverse(B))) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))) = multiply(X_3,B),
inference(resolve,[$cnf( $equal(divide(X_3,inverse(B)),multiply(X_3,B)) )],[refute_0_57,refute_0_66]) ).
cnf(refute_0_68,plain,
divide(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3) = divide(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3),
introduced(tautology,[refl,[$fot(divide(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3))]]) ).
cnf(refute_0_69,plain,
( divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))) != multiply(X_3,B)
| divide(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3) != divide(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3)
| divide(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3) = divide(multiply(X_3,B),X_3) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3),divide(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3)) ),[1,0],$fot(multiply(X_3,B))]]) ).
cnf(refute_0_70,plain,
( divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))) != multiply(X_3,B)
| divide(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3) = divide(multiply(X_3,B),X_3) ),
inference(resolve,[$cnf( $equal(divide(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3),divide(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
divide(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3) = divide(multiply(X_3,B),X_3),
inference(resolve,[$cnf( $equal(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),multiply(X_3,B)) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
( divide(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3) != B
| divide(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3) != divide(multiply(X_3,B),X_3)
| divide(multiply(X_3,B),X_3) = B ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3),B) ),[0],$fot(divide(multiply(X_3,B),X_3))]]) ).
cnf(refute_0_73,plain,
( divide(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3) != B
| divide(multiply(X_3,B),X_3) = B ),
inference(resolve,[$cnf( $equal(divide(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3),divide(multiply(X_3,B),X_3)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
divide(multiply(X_3,B),X_3) = B,
inference(resolve,[$cnf( $equal(divide(divide(X_3,divide(multiply(multiply(X_30,inverse(B)),X_29),multiply(X_30,X_29))),X_3),B) )],[refute_0_56,refute_0_73]) ).
cnf(refute_0_75,plain,
divide(multiply(multiply(inverse(B),X_34),B),multiply(inverse(B),X_34)) = B,
inference(subst,[],[refute_0_74:[bind(X_3,$fot(multiply(inverse(B),X_34)))]]) ).
cnf(refute_0_76,plain,
multiply(multiply(inverse(B),X_31),B) = divide(multiply(inverse(B),X_31),inverse(B)),
inference(subst,[],[multiply:[bind(A,$fot(multiply(inverse(B),X_31)))]]) ).
cnf(refute_0_77,plain,
divide(multiply(inverse(B),X_31),inverse(B)) = X_31,
inference(subst,[],[refute_0_74:[bind(B,$fot(X_31)),bind(X_3,$fot(inverse(B)))]]) ).
cnf(refute_0_78,plain,
( multiply(multiply(inverse(B),X_31),B) != divide(multiply(inverse(B),X_31),inverse(B))
| divide(multiply(inverse(B),X_31),inverse(B)) != X_31
| multiply(multiply(inverse(B),X_31),B) = X_31 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(inverse(B),X_31),B),X_31) ),[0],$fot(divide(multiply(inverse(B),X_31),inverse(B)))]]) ).
cnf(refute_0_79,plain,
( multiply(multiply(inverse(B),X_31),B) != divide(multiply(inverse(B),X_31),inverse(B))
| multiply(multiply(inverse(B),X_31),B) = X_31 ),
inference(resolve,[$cnf( $equal(divide(multiply(inverse(B),X_31),inverse(B)),X_31) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
multiply(multiply(inverse(B),X_31),B) = X_31,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(B),X_31),B),divide(multiply(inverse(B),X_31),inverse(B))) )],[refute_0_76,refute_0_79]) ).
cnf(refute_0_81,plain,
multiply(multiply(inverse(B),X_34),B) = X_34,
inference(subst,[],[refute_0_80:[bind(X_31,$fot(X_34))]]) ).
cnf(refute_0_82,plain,
( multiply(multiply(inverse(B),X_34),B) != X_34
| divide(multiply(multiply(inverse(B),X_34),B),multiply(inverse(B),X_34)) != B
| divide(X_34,multiply(inverse(B),X_34)) = B ),
introduced(tautology,[equality,[$cnf( $equal(divide(multiply(multiply(inverse(B),X_34),B),multiply(inverse(B),X_34)),B) ),[0,0],$fot(X_34)]]) ).
cnf(refute_0_83,plain,
( divide(multiply(multiply(inverse(B),X_34),B),multiply(inverse(B),X_34)) != B
| divide(X_34,multiply(inverse(B),X_34)) = B ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(B),X_34),B),X_34) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
divide(X_34,multiply(inverse(B),X_34)) = B,
inference(resolve,[$cnf( $equal(divide(multiply(multiply(inverse(B),X_34),B),multiply(inverse(B),X_34)),B) )],[refute_0_75,refute_0_83]) ).
cnf(refute_0_85,plain,
divide(multiply(inverse(X_35),X_7),multiply(inverse(X_35),multiply(inverse(X_35),X_7))) = X_35,
inference(subst,[],[refute_0_84:[bind(B,$fot(X_35)),bind(X_34,$fot(multiply(inverse(X_35),X_7)))]]) ).
cnf(refute_0_86,plain,
( divide(X_7,divide(multiply(inverse(X_35),X_7),multiply(inverse(X_35),multiply(inverse(X_35),X_7)))) != multiply(inverse(X_35),X_7)
| divide(multiply(inverse(X_35),X_7),multiply(inverse(X_35),multiply(inverse(X_35),X_7))) != X_35
| divide(X_7,X_35) = multiply(inverse(X_35),X_7) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_7,divide(multiply(inverse(X_35),X_7),multiply(inverse(X_35),multiply(inverse(X_35),X_7)))),multiply(inverse(X_35),X_7)) ),[0,1],$fot(X_35)]]) ).
cnf(refute_0_87,plain,
( divide(X_7,divide(multiply(inverse(X_35),X_7),multiply(inverse(X_35),multiply(inverse(X_35),X_7)))) != multiply(inverse(X_35),X_7)
| divide(X_7,X_35) = multiply(inverse(X_35),X_7) ),
inference(resolve,[$cnf( $equal(divide(multiply(inverse(X_35),X_7),multiply(inverse(X_35),multiply(inverse(X_35),X_7))),X_35) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
divide(X_7,X_35) = multiply(inverse(X_35),X_7),
inference(resolve,[$cnf( $equal(divide(X_7,divide(multiply(inverse(X_35),X_7),multiply(inverse(X_35),multiply(inverse(X_35),X_7)))),multiply(inverse(X_35),X_7)) )],[refute_0_36,refute_0_87]) ).
cnf(refute_0_89,plain,
( divide(X_7,X_35) != multiply(inverse(X_35),X_7)
| multiply(inverse(X_35),X_7) = divide(X_7,X_35) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(divide(X_7,X_35))),bind(Y,$fot(multiply(inverse(X_35),X_7)))]]) ).
cnf(refute_0_90,plain,
multiply(inverse(X_35),X_7) = divide(X_7,X_35),
inference(resolve,[$cnf( $equal(divide(X_7,X_35),multiply(inverse(X_35),X_7)) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
multiply(inverse(b2),b2) = divide(b2,b2),
inference(subst,[],[refute_0_90:[bind(X_35,$fot(b2)),bind(X_7,$fot(b2))]]) ).
cnf(refute_0_92,plain,
multiply(multiply(inverse(b2),b2),a2) = multiply(multiply(inverse(b2),b2),a2),
introduced(tautology,[refl,[$fot(multiply(multiply(inverse(b2),b2),a2))]]) ).
cnf(refute_0_93,plain,
( multiply(multiply(inverse(b2),b2),a2) != multiply(multiply(inverse(b2),b2),a2)
| multiply(inverse(b2),b2) != divide(b2,b2)
| multiply(multiply(inverse(b2),b2),a2) = multiply(divide(b2,b2),a2) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),multiply(multiply(inverse(b2),b2),a2)) ),[1,0],$fot(divide(b2,b2))]]) ).
cnf(refute_0_94,plain,
( multiply(inverse(b2),b2) != divide(b2,b2)
| multiply(multiply(inverse(b2),b2),a2) = multiply(divide(b2,b2),a2) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),multiply(multiply(inverse(b2),b2),a2)) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
multiply(multiply(inverse(b2),b2),a2) = multiply(divide(b2,b2),a2),
inference(resolve,[$cnf( $equal(multiply(inverse(b2),b2),divide(b2,b2)) )],[refute_0_91,refute_0_94]) ).
cnf(refute_0_96,plain,
( multiply(multiply(inverse(b2),b2),a2) != multiply(divide(b2,b2),a2)
| multiply(divide(b2,b2),a2) != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(inverse(b2),b2),a2),a2) ),[0],$fot(multiply(divide(b2,b2),a2))]]) ).
cnf(refute_0_97,plain,
( multiply(divide(b2,b2),a2) != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),multiply(divide(b2,b2),a2)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
multiply(divide(b2,b2),a2) != a2,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),a2) )],[refute_0_97,prove_these_axioms_2]) ).
cnf(refute_0_99,plain,
divide(divide(multiply(divide(multiply(X_2,X_3),B),B),divide(X_2,B)),X_3) = B,
inference(subst,[],[refute_0_41:[bind(X_4,$fot(B))]]) ).
cnf(refute_0_100,plain,
multiply(inverse(B),X_31) = divide(X_31,B),
inference(subst,[],[refute_0_90:[bind(X_35,$fot(B)),bind(X_7,$fot(X_31))]]) ).
cnf(refute_0_101,plain,
multiply(multiply(inverse(B),X_31),B) = multiply(multiply(inverse(B),X_31),B),
introduced(tautology,[refl,[$fot(multiply(multiply(inverse(B),X_31),B))]]) ).
cnf(refute_0_102,plain,
( multiply(multiply(inverse(B),X_31),B) != multiply(multiply(inverse(B),X_31),B)
| multiply(inverse(B),X_31) != divide(X_31,B)
| multiply(multiply(inverse(B),X_31),B) = multiply(divide(X_31,B),B) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(B),X_31),B),multiply(multiply(inverse(B),X_31),B)) ),[1,0],$fot(divide(X_31,B))]]) ).
cnf(refute_0_103,plain,
( multiply(inverse(B),X_31) != divide(X_31,B)
| multiply(multiply(inverse(B),X_31),B) = multiply(divide(X_31,B),B) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(B),X_31),B),multiply(multiply(inverse(B),X_31),B)) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
multiply(multiply(inverse(B),X_31),B) = multiply(divide(X_31,B),B),
inference(resolve,[$cnf( $equal(multiply(inverse(B),X_31),divide(X_31,B)) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
( multiply(multiply(inverse(B),X_31),B) != X_31
| multiply(multiply(inverse(B),X_31),B) != multiply(divide(X_31,B),B)
| multiply(divide(X_31,B),B) = X_31 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(B),X_31),B),X_31) ),[0],$fot(multiply(divide(X_31,B),B))]]) ).
cnf(refute_0_106,plain,
( multiply(multiply(inverse(B),X_31),B) != X_31
| multiply(divide(X_31,B),B) = X_31 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(B),X_31),B),multiply(divide(X_31,B),B)) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
multiply(divide(X_31,B),B) = X_31,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(B),X_31),B),X_31) )],[refute_0_80,refute_0_106]) ).
cnf(refute_0_108,plain,
multiply(divide(multiply(X_2,X_3),B),B) = multiply(X_2,X_3),
inference(subst,[],[refute_0_107:[bind(X_31,$fot(multiply(X_2,X_3)))]]) ).
cnf(refute_0_109,plain,
( multiply(divide(multiply(X_2,X_3),B),B) != multiply(X_2,X_3)
| divide(divide(multiply(divide(multiply(X_2,X_3),B),B),divide(X_2,B)),X_3) != B
| divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3) = B ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(multiply(divide(multiply(X_2,X_3),B),B),divide(X_2,B)),X_3),B) ),[0,0,0],$fot(multiply(X_2,X_3))]]) ).
cnf(refute_0_110,plain,
( divide(divide(multiply(divide(multiply(X_2,X_3),B),B),divide(X_2,B)),X_3) != B
| divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3) = B ),
inference(resolve,[$cnf( $equal(multiply(divide(multiply(X_2,X_3),B),B),multiply(X_2,X_3)) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3) = B,
inference(resolve,[$cnf( $equal(divide(divide(multiply(divide(multiply(X_2,X_3),B),B),divide(X_2,B)),X_3),B) )],[refute_0_99,refute_0_110]) ).
cnf(refute_0_112,plain,
multiply(divide(divide(multiply(A,B),C),divide(A,C)),divide(A,C)) = divide(multiply(A,B),C),
inference(subst,[],[refute_0_107:[bind(B,$fot(divide(A,C))),bind(X_31,$fot(divide(multiply(A,B),C)))]]) ).
cnf(refute_0_113,plain,
( multiply(divide(divide(multiply(A,B),C),divide(A,C)),divide(A,C)) != divide(multiply(A,B),C)
| divide(divide(multiply(A,B),C),divide(A,C)) != B
| multiply(B,divide(A,C)) = divide(multiply(A,B),C) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(divide(divide(multiply(A,B),C),divide(A,C)),divide(A,C)),divide(multiply(A,B),C)) ),[0,0],$fot(B)]]) ).
cnf(refute_0_114,plain,
( multiply(divide(divide(multiply(A,B),C),divide(A,C)),divide(A,C)) != divide(multiply(A,B),C)
| multiply(B,divide(A,C)) = divide(multiply(A,B),C) ),
inference(resolve,[$cnf( $equal(divide(divide(multiply(A,B),C),divide(A,C)),B) )],[refute_0_15,refute_0_113]) ).
cnf(refute_0_115,plain,
multiply(B,divide(A,C)) = divide(multiply(A,B),C),
inference(resolve,[$cnf( $equal(multiply(divide(divide(multiply(A,B),C),divide(A,C)),divide(A,C)),divide(multiply(A,B),C)) )],[refute_0_112,refute_0_114]) ).
cnf(refute_0_116,plain,
( multiply(B,divide(A,C)) != divide(multiply(A,B),C)
| divide(multiply(A,B),C) = multiply(B,divide(A,C)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(B,divide(A,C)))),bind(Y,$fot(divide(multiply(A,B),C)))]]) ).
cnf(refute_0_117,plain,
divide(multiply(A,B),C) = multiply(B,divide(A,C)),
inference(resolve,[$cnf( $equal(multiply(B,divide(A,C)),divide(multiply(A,B),C)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
divide(multiply(X_3,B),X_3) = multiply(B,divide(X_3,X_3)),
inference(subst,[],[refute_0_117:[bind(A,$fot(X_3)),bind(C,$fot(X_3))]]) ).
cnf(refute_0_119,plain,
multiply(inverse(B),X_34) = divide(X_34,B),
inference(subst,[],[refute_0_90:[bind(X_35,$fot(B)),bind(X_7,$fot(X_34))]]) ).
cnf(refute_0_120,plain,
divide(X_34,multiply(inverse(B),X_34)) = divide(X_34,multiply(inverse(B),X_34)),
introduced(tautology,[refl,[$fot(divide(X_34,multiply(inverse(B),X_34)))]]) ).
cnf(refute_0_121,plain,
( multiply(inverse(B),X_34) != divide(X_34,B)
| divide(X_34,multiply(inverse(B),X_34)) != divide(X_34,multiply(inverse(B),X_34))
| divide(X_34,multiply(inverse(B),X_34)) = divide(X_34,divide(X_34,B)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_34,multiply(inverse(B),X_34)),divide(X_34,multiply(inverse(B),X_34))) ),[1,1],$fot(divide(X_34,B))]]) ).
cnf(refute_0_122,plain,
( multiply(inverse(B),X_34) != divide(X_34,B)
| divide(X_34,multiply(inverse(B),X_34)) = divide(X_34,divide(X_34,B)) ),
inference(resolve,[$cnf( $equal(divide(X_34,multiply(inverse(B),X_34)),divide(X_34,multiply(inverse(B),X_34))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
divide(X_34,multiply(inverse(B),X_34)) = divide(X_34,divide(X_34,B)),
inference(resolve,[$cnf( $equal(multiply(inverse(B),X_34),divide(X_34,B)) )],[refute_0_119,refute_0_122]) ).
cnf(refute_0_124,plain,
( divide(X_34,multiply(inverse(B),X_34)) != B
| divide(X_34,multiply(inverse(B),X_34)) != divide(X_34,divide(X_34,B))
| divide(X_34,divide(X_34,B)) = B ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_34,multiply(inverse(B),X_34)),B) ),[0],$fot(divide(X_34,divide(X_34,B)))]]) ).
cnf(refute_0_125,plain,
( divide(X_34,multiply(inverse(B),X_34)) != B
| divide(X_34,divide(X_34,B)) = B ),
inference(resolve,[$cnf( $equal(divide(X_34,multiply(inverse(B),X_34)),divide(X_34,divide(X_34,B))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
divide(X_34,divide(X_34,B)) = B,
inference(resolve,[$cnf( $equal(divide(X_34,multiply(inverse(B),X_34)),B) )],[refute_0_84,refute_0_125]) ).
cnf(refute_0_127,plain,
divide(X_2,divide(X_2,B)) = B,
inference(subst,[],[refute_0_126:[bind(X_34,$fot(X_2))]]) ).
cnf(refute_0_128,plain,
multiply(X_3,divide(X_2,divide(X_2,B))) = multiply(X_3,divide(X_2,divide(X_2,B))),
introduced(tautology,[refl,[$fot(multiply(X_3,divide(X_2,divide(X_2,B))))]]) ).
cnf(refute_0_129,plain,
( multiply(X_3,divide(X_2,divide(X_2,B))) != multiply(X_3,divide(X_2,divide(X_2,B)))
| divide(X_2,divide(X_2,B)) != B
| multiply(X_3,divide(X_2,divide(X_2,B))) = multiply(X_3,B) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_3,divide(X_2,divide(X_2,B))),multiply(X_3,divide(X_2,divide(X_2,B)))) ),[1,1],$fot(B)]]) ).
cnf(refute_0_130,plain,
( divide(X_2,divide(X_2,B)) != B
| multiply(X_3,divide(X_2,divide(X_2,B))) = multiply(X_3,B) ),
inference(resolve,[$cnf( $equal(multiply(X_3,divide(X_2,divide(X_2,B))),multiply(X_3,divide(X_2,divide(X_2,B)))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
multiply(X_3,divide(X_2,divide(X_2,B))) = multiply(X_3,B),
inference(resolve,[$cnf( $equal(divide(X_2,divide(X_2,B)),B) )],[refute_0_127,refute_0_130]) ).
cnf(refute_0_132,plain,
divide(multiply(X_2,X_3),divide(X_2,B)) = multiply(X_3,divide(X_2,divide(X_2,B))),
inference(subst,[],[refute_0_117:[bind(A,$fot(X_2)),bind(B,$fot(X_3)),bind(C,$fot(divide(X_2,B)))]]) ).
cnf(refute_0_133,plain,
( multiply(X_3,divide(X_2,divide(X_2,B))) != multiply(X_3,B)
| divide(multiply(X_2,X_3),divide(X_2,B)) != multiply(X_3,divide(X_2,divide(X_2,B)))
| divide(multiply(X_2,X_3),divide(X_2,B)) = multiply(X_3,B) ),
inference(subst,[],[refute_0_64:[bind(X,$fot(divide(multiply(X_2,X_3),divide(X_2,B)))),bind(Y,$fot(multiply(X_3,divide(X_2,divide(X_2,B))))),bind(Z,$fot(multiply(X_3,B)))]]) ).
cnf(refute_0_134,plain,
( multiply(X_3,divide(X_2,divide(X_2,B))) != multiply(X_3,B)
| divide(multiply(X_2,X_3),divide(X_2,B)) = multiply(X_3,B) ),
inference(resolve,[$cnf( $equal(divide(multiply(X_2,X_3),divide(X_2,B)),multiply(X_3,divide(X_2,divide(X_2,B)))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
divide(multiply(X_2,X_3),divide(X_2,B)) = multiply(X_3,B),
inference(resolve,[$cnf( $equal(multiply(X_3,divide(X_2,divide(X_2,B))),multiply(X_3,B)) )],[refute_0_131,refute_0_134]) ).
cnf(refute_0_136,plain,
divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3) = divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3),
introduced(tautology,[refl,[$fot(divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3))]]) ).
cnf(refute_0_137,plain,
( divide(multiply(X_2,X_3),divide(X_2,B)) != multiply(X_3,B)
| divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3) != divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3)
| divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3) = divide(multiply(X_3,B),X_3) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3),divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3)) ),[1,0],$fot(multiply(X_3,B))]]) ).
cnf(refute_0_138,plain,
( divide(multiply(X_2,X_3),divide(X_2,B)) != multiply(X_3,B)
| divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3) = divide(multiply(X_3,B),X_3) ),
inference(resolve,[$cnf( $equal(divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3),divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3)) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3) = divide(multiply(X_3,B),X_3),
inference(resolve,[$cnf( $equal(divide(multiply(X_2,X_3),divide(X_2,B)),multiply(X_3,B)) )],[refute_0_135,refute_0_138]) ).
cnf(refute_0_140,plain,
( divide(multiply(X_3,B),X_3) != multiply(B,divide(X_3,X_3))
| divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3) != divide(multiply(X_3,B),X_3)
| divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3) = multiply(B,divide(X_3,X_3)) ),
inference(subst,[],[refute_0_64:[bind(X,$fot(divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3))),bind(Y,$fot(divide(multiply(X_3,B),X_3))),bind(Z,$fot(multiply(B,divide(X_3,X_3))))]]) ).
cnf(refute_0_141,plain,
( divide(multiply(X_3,B),X_3) != multiply(B,divide(X_3,X_3))
| divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3) = multiply(B,divide(X_3,X_3)) ),
inference(resolve,[$cnf( $equal(divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3),divide(multiply(X_3,B),X_3)) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3) = multiply(B,divide(X_3,X_3)),
inference(resolve,[$cnf( $equal(divide(multiply(X_3,B),X_3),multiply(B,divide(X_3,X_3))) )],[refute_0_118,refute_0_141]) ).
cnf(refute_0_143,plain,
( divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3) != B
| divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3) != multiply(B,divide(X_3,X_3))
| multiply(B,divide(X_3,X_3)) = B ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3),B) ),[0],$fot(multiply(B,divide(X_3,X_3)))]]) ).
cnf(refute_0_144,plain,
( divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3) != B
| multiply(B,divide(X_3,X_3)) = B ),
inference(resolve,[$cnf( $equal(divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3),multiply(B,divide(X_3,X_3))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
multiply(B,divide(X_3,X_3)) = B,
inference(resolve,[$cnf( $equal(divide(divide(multiply(X_2,X_3),divide(X_2,B)),X_3),B) )],[refute_0_111,refute_0_144]) ).
cnf(refute_0_146,plain,
multiply(a2,divide(b2,b2)) = a2,
inference(subst,[],[refute_0_145:[bind(B,$fot(a2)),bind(X_3,$fot(b2))]]) ).
cnf(refute_0_147,plain,
multiply(divide(multiply(X_37,B),X_37),X_37) = multiply(X_37,B),
inference(subst,[],[refute_0_107:[bind(B,$fot(X_37)),bind(X_31,$fot(multiply(X_37,B)))]]) ).
cnf(refute_0_148,plain,
divide(multiply(X_37,B),X_37) = B,
inference(subst,[],[refute_0_74:[bind(X_3,$fot(X_37))]]) ).
cnf(refute_0_149,plain,
( multiply(divide(multiply(X_37,B),X_37),X_37) != multiply(X_37,B)
| divide(multiply(X_37,B),X_37) != B
| multiply(B,X_37) = multiply(X_37,B) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(divide(multiply(X_37,B),X_37),X_37),multiply(X_37,B)) ),[0,0],$fot(B)]]) ).
cnf(refute_0_150,plain,
( multiply(divide(multiply(X_37,B),X_37),X_37) != multiply(X_37,B)
| multiply(B,X_37) = multiply(X_37,B) ),
inference(resolve,[$cnf( $equal(divide(multiply(X_37,B),X_37),B) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
multiply(B,X_37) = multiply(X_37,B),
inference(resolve,[$cnf( $equal(multiply(divide(multiply(X_37,B),X_37),X_37),multiply(X_37,B)) )],[refute_0_147,refute_0_150]) ).
cnf(refute_0_152,plain,
( multiply(B,X_37) != multiply(X_37,B)
| multiply(X_37,B) = multiply(B,X_37) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(B,X_37))),bind(Y,$fot(multiply(X_37,B)))]]) ).
cnf(refute_0_153,plain,
multiply(X_37,B) = multiply(B,X_37),
inference(resolve,[$cnf( $equal(multiply(B,X_37),multiply(X_37,B)) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
multiply(divide(b2,b2),a2) = multiply(a2,divide(b2,b2)),
inference(subst,[],[refute_0_153:[bind(B,$fot(a2)),bind(X_37,$fot(divide(b2,b2)))]]) ).
cnf(refute_0_155,plain,
( multiply(divide(b2,b2),a2) != multiply(a2,divide(b2,b2))
| multiply(a2,divide(b2,b2)) != a2
| multiply(divide(b2,b2),a2) = a2 ),
inference(subst,[],[refute_0_64:[bind(X,$fot(multiply(divide(b2,b2),a2))),bind(Y,$fot(multiply(a2,divide(b2,b2)))),bind(Z,$fot(a2))]]) ).
cnf(refute_0_156,plain,
( multiply(a2,divide(b2,b2)) != a2
| multiply(divide(b2,b2),a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(divide(b2,b2),a2),multiply(a2,divide(b2,b2))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
multiply(divide(b2,b2),a2) = a2,
inference(resolve,[$cnf( $equal(multiply(a2,divide(b2,b2)),a2) )],[refute_0_146,refute_0_156]) ).
cnf(refute_0_158,plain,
( multiply(divide(b2,b2),a2) != a2
| a2 != a2
| multiply(divide(b2,b2),a2) = a2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(divide(b2,b2),a2),a2) ),[0],$fot(a2)]]) ).
cnf(refute_0_159,plain,
( a2 != a2
| multiply(divide(b2,b2),a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(divide(b2,b2),a2),a2) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
a2 != a2,
inference(resolve,[$cnf( $equal(multiply(divide(b2,b2),a2),a2) )],[refute_0_159,refute_0_98]) ).
cnf(refute_0_161,plain,
a2 = a2,
introduced(tautology,[refl,[$fot(a2)]]) ).
cnf(refute_0_162,plain,
$false,
inference(resolve,[$cnf( $equal(a2,a2) )],[refute_0_161,refute_0_160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP562-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 10:16:06 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.43 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.43
% 0.19/0.43 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.46
%------------------------------------------------------------------------------