TSTP Solution File: GRP558-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP558-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 10:42:20 EDT 2022
% Result : Unsatisfiable 0.21s 0.40s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 29
% Syntax : Number of clauses : 102 ( 56 unt; 0 nHn; 55 RR)
% Number of literals : 170 ( 169 equ; 70 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 214 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(A,inverse(divide(divide(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( $equal(multiply(A,B),divide(A,inverse(B))) )],[multiply,refute_0_3]) ).
cnf(refute_0_5,plain,
divide(A,inverse(divide(divide(B,C),divide(A,C)))) = multiply(A,divide(divide(B,C),divide(A,C))),
inference(subst,[],[refute_0_4:[bind(B,$fot(divide(divide(B,C),divide(A,C))))]]) ).
cnf(refute_0_6,plain,
( divide(A,inverse(divide(divide(B,C),divide(A,C)))) != B
| divide(A,inverse(divide(divide(B,C),divide(A,C)))) != multiply(A,divide(divide(B,C),divide(A,C)))
| multiply(A,divide(divide(B,C),divide(A,C))) = B ),
introduced(tautology,[equality,[$cnf( $equal(divide(A,inverse(divide(divide(B,C),divide(A,C)))),B) ),[0],$fot(multiply(A,divide(divide(B,C),divide(A,C))))]]) ).
cnf(refute_0_7,plain,
( divide(A,inverse(divide(divide(B,C),divide(A,C)))) != B
| multiply(A,divide(divide(B,C),divide(A,C))) = B ),
inference(resolve,[$cnf( $equal(divide(A,inverse(divide(divide(B,C),divide(A,C)))),multiply(A,divide(divide(B,C),divide(A,C)))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
multiply(A,divide(divide(B,C),divide(A,C))) = B,
inference(resolve,[$cnf( $equal(divide(A,inverse(divide(divide(B,C),divide(A,C)))),B) )],[single_axiom,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(X_2,divide(divide(X_3,inverse(B)),divide(X_2,inverse(B)))) = X_3,
inference(subst,[],[refute_0_8:[bind(A,$fot(X_2)),bind(B,$fot(X_3)),bind(C,$fot(inverse(B)))]]) ).
cnf(refute_0_10,plain,
multiply(X_2,B) = divide(X_2,inverse(B)),
inference(subst,[],[multiply:[bind(A,$fot(X_2))]]) ).
cnf(refute_0_11,plain,
( multiply(X_2,B) != divide(X_2,inverse(B))
| divide(X_2,inverse(B)) = multiply(X_2,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(X_2,B))),bind(Y,$fot(divide(X_2,inverse(B))))]]) ).
cnf(refute_0_12,plain,
divide(X_2,inverse(B)) = multiply(X_2,B),
inference(resolve,[$cnf( $equal(multiply(X_2,B),divide(X_2,inverse(B))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( multiply(X_2,divide(divide(X_3,inverse(B)),divide(X_2,inverse(B)))) != X_3
| divide(X_2,inverse(B)) != multiply(X_2,B)
| multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))) = X_3 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_2,divide(divide(X_3,inverse(B)),divide(X_2,inverse(B)))),X_3) ),[0,1,1],$fot(multiply(X_2,B))]]) ).
cnf(refute_0_14,plain,
( multiply(X_2,divide(divide(X_3,inverse(B)),divide(X_2,inverse(B)))) != X_3
| multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))) = X_3 ),
inference(resolve,[$cnf( $equal(divide(X_2,inverse(B)),multiply(X_2,B)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))) = X_3,
inference(resolve,[$cnf( $equal(multiply(X_2,divide(divide(X_3,inverse(B)),divide(X_2,inverse(B)))),X_3) )],[refute_0_9,refute_0_14]) ).
cnf(refute_0_16,plain,
divide(X_3,inverse(B)) = multiply(X_3,B),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_3))]]) ).
cnf(refute_0_17,plain,
divide(divide(X_3,inverse(B)),multiply(X_2,B)) = divide(divide(X_3,inverse(B)),multiply(X_2,B)),
introduced(tautology,[refl,[$fot(divide(divide(X_3,inverse(B)),multiply(X_2,B)))]]) ).
cnf(refute_0_18,plain,
( divide(X_3,inverse(B)) != multiply(X_3,B)
| divide(divide(X_3,inverse(B)),multiply(X_2,B)) != divide(divide(X_3,inverse(B)),multiply(X_2,B))
| divide(divide(X_3,inverse(B)),multiply(X_2,B)) = divide(multiply(X_3,B),multiply(X_2,B)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X_3,inverse(B)),multiply(X_2,B)),divide(divide(X_3,inverse(B)),multiply(X_2,B))) ),[1,0],$fot(multiply(X_3,B))]]) ).
cnf(refute_0_19,plain,
( divide(X_3,inverse(B)) != multiply(X_3,B)
| divide(divide(X_3,inverse(B)),multiply(X_2,B)) = divide(multiply(X_3,B),multiply(X_2,B)) ),
inference(resolve,[$cnf( $equal(divide(divide(X_3,inverse(B)),multiply(X_2,B)),divide(divide(X_3,inverse(B)),multiply(X_2,B))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
divide(divide(X_3,inverse(B)),multiply(X_2,B)) = divide(multiply(X_3,B),multiply(X_2,B)),
inference(resolve,[$cnf( $equal(divide(X_3,inverse(B)),multiply(X_3,B)) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))) = multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))),
introduced(tautology,[refl,[$fot(multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))))]]) ).
cnf(refute_0_22,plain,
( multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))) != multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B)))
| divide(divide(X_3,inverse(B)),multiply(X_2,B)) != divide(multiply(X_3,B),multiply(X_2,B))
| multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))) = multiply(X_2,divide(multiply(X_3,B),multiply(X_2,B))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))),multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B)))) ),[1,1],$fot(divide(multiply(X_3,B),multiply(X_2,B)))]]) ).
cnf(refute_0_23,plain,
( divide(divide(X_3,inverse(B)),multiply(X_2,B)) != divide(multiply(X_3,B),multiply(X_2,B))
| multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))) = multiply(X_2,divide(multiply(X_3,B),multiply(X_2,B))) ),
inference(resolve,[$cnf( $equal(multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))),multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B)))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))) = multiply(X_2,divide(multiply(X_3,B),multiply(X_2,B))),
inference(resolve,[$cnf( $equal(divide(divide(X_3,inverse(B)),multiply(X_2,B)),divide(multiply(X_3,B),multiply(X_2,B))) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
( multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))) != X_3
| multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))) != multiply(X_2,divide(multiply(X_3,B),multiply(X_2,B)))
| multiply(X_2,divide(multiply(X_3,B),multiply(X_2,B))) = X_3 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))),X_3) ),[0],$fot(multiply(X_2,divide(multiply(X_3,B),multiply(X_2,B))))]]) ).
cnf(refute_0_26,plain,
( multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))) != X_3
| multiply(X_2,divide(multiply(X_3,B),multiply(X_2,B))) = X_3 ),
inference(resolve,[$cnf( $equal(multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))),multiply(X_2,divide(multiply(X_3,B),multiply(X_2,B)))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(X_2,divide(multiply(X_3,B),multiply(X_2,B))) = X_3,
inference(resolve,[$cnf( $equal(multiply(X_2,divide(divide(X_3,inverse(B)),multiply(X_2,B))),X_3) )],[refute_0_15,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(X_2,divide(multiply(X_3,divide(multiply(X_7,X_5),multiply(X_3,X_5))),multiply(X_2,divide(multiply(X_7,X_5),multiply(X_3,X_5))))) = X_3,
inference(subst,[],[refute_0_27:[bind(B,$fot(divide(multiply(X_7,X_5),multiply(X_3,X_5))))]]) ).
cnf(refute_0_29,plain,
multiply(X_3,divide(multiply(X_7,X_5),multiply(X_3,X_5))) = X_7,
inference(subst,[],[refute_0_27:[bind(B,$fot(X_5)),bind(X_2,$fot(X_3)),bind(X_3,$fot(X_7))]]) ).
cnf(refute_0_30,plain,
( multiply(X_2,divide(multiply(X_3,divide(multiply(X_7,X_5),multiply(X_3,X_5))),multiply(X_2,divide(multiply(X_7,X_5),multiply(X_3,X_5))))) != X_3
| multiply(X_3,divide(multiply(X_7,X_5),multiply(X_3,X_5))) != X_7
| multiply(X_2,divide(X_7,multiply(X_2,divide(multiply(X_7,X_5),multiply(X_3,X_5))))) = X_3 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_2,divide(multiply(X_3,divide(multiply(X_7,X_5),multiply(X_3,X_5))),multiply(X_2,divide(multiply(X_7,X_5),multiply(X_3,X_5))))),X_3) ),[0,1,0],$fot(X_7)]]) ).
cnf(refute_0_31,plain,
( multiply(X_2,divide(multiply(X_3,divide(multiply(X_7,X_5),multiply(X_3,X_5))),multiply(X_2,divide(multiply(X_7,X_5),multiply(X_3,X_5))))) != X_3
| multiply(X_2,divide(X_7,multiply(X_2,divide(multiply(X_7,X_5),multiply(X_3,X_5))))) = X_3 ),
inference(resolve,[$cnf( $equal(multiply(X_3,divide(multiply(X_7,X_5),multiply(X_3,X_5))),X_7) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
multiply(X_2,divide(X_7,multiply(X_2,divide(multiply(X_7,X_5),multiply(X_3,X_5))))) = X_3,
inference(resolve,[$cnf( $equal(multiply(X_2,divide(multiply(X_3,divide(multiply(X_7,X_5),multiply(X_3,X_5))),multiply(X_2,divide(multiply(X_7,X_5),multiply(X_3,X_5))))),X_3) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
multiply(X_9,divide(X_11,multiply(X_9,divide(multiply(X_11,X_10),multiply(X_9,X_10))))) = X_9,
inference(subst,[],[refute_0_32:[bind(X_2,$fot(X_9)),bind(X_3,$fot(X_9)),bind(X_5,$fot(X_10)),bind(X_7,$fot(X_11))]]) ).
cnf(refute_0_34,plain,
multiply(X_9,divide(multiply(X_11,X_10),multiply(X_9,X_10))) = X_11,
inference(subst,[],[refute_0_27:[bind(B,$fot(X_10)),bind(X_2,$fot(X_9)),bind(X_3,$fot(X_11))]]) ).
cnf(refute_0_35,plain,
( multiply(X_9,divide(X_11,multiply(X_9,divide(multiply(X_11,X_10),multiply(X_9,X_10))))) != X_9
| multiply(X_9,divide(multiply(X_11,X_10),multiply(X_9,X_10))) != X_11
| multiply(X_9,divide(X_11,X_11)) = X_9 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_9,divide(X_11,multiply(X_9,divide(multiply(X_11,X_10),multiply(X_9,X_10))))),X_9) ),[0,1,1],$fot(X_11)]]) ).
cnf(refute_0_36,plain,
( multiply(X_9,divide(X_11,multiply(X_9,divide(multiply(X_11,X_10),multiply(X_9,X_10))))) != X_9
| multiply(X_9,divide(X_11,X_11)) = X_9 ),
inference(resolve,[$cnf( $equal(multiply(X_9,divide(multiply(X_11,X_10),multiply(X_9,X_10))),X_11) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
multiply(X_9,divide(X_11,X_11)) = X_9,
inference(resolve,[$cnf( $equal(multiply(X_9,divide(X_11,multiply(X_9,divide(multiply(X_11,X_10),multiply(X_9,X_10))))),X_9) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
multiply(inverse(divide(divide(X_11,X_11),X_33)),divide(X_11,X_11)) = inverse(divide(divide(X_11,X_11),X_33)),
inference(subst,[],[refute_0_37:[bind(X_9,$fot(inverse(divide(divide(X_11,X_11),X_33))))]]) ).
cnf(refute_0_39,plain,
multiply(X_2,divide(multiply(X_3,divide(X_20,X_20)),multiply(X_2,divide(X_20,X_20)))) = X_3,
inference(subst,[],[refute_0_27:[bind(B,$fot(divide(X_20,X_20)))]]) ).
cnf(refute_0_40,plain,
multiply(X_3,divide(X_20,X_20)) = X_3,
inference(subst,[],[refute_0_37:[bind(X_11,$fot(X_20)),bind(X_9,$fot(X_3))]]) ).
cnf(refute_0_41,plain,
( multiply(X_2,divide(multiply(X_3,divide(X_20,X_20)),multiply(X_2,divide(X_20,X_20)))) != X_3
| multiply(X_3,divide(X_20,X_20)) != X_3
| multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))) = X_3 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_2,divide(multiply(X_3,divide(X_20,X_20)),multiply(X_2,divide(X_20,X_20)))),X_3) ),[0,1,0],$fot(X_3)]]) ).
cnf(refute_0_42,plain,
( multiply(X_2,divide(multiply(X_3,divide(X_20,X_20)),multiply(X_2,divide(X_20,X_20)))) != X_3
| multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))) = X_3 ),
inference(resolve,[$cnf( $equal(multiply(X_3,divide(X_20,X_20)),X_3) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))) = X_3,
inference(resolve,[$cnf( $equal(multiply(X_2,divide(multiply(X_3,divide(X_20,X_20)),multiply(X_2,divide(X_20,X_20)))),X_3) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
multiply(X_2,divide(X_20,X_20)) = X_2,
inference(subst,[],[refute_0_37:[bind(X_11,$fot(X_20)),bind(X_9,$fot(X_2))]]) ).
cnf(refute_0_45,plain,
divide(X_3,multiply(X_2,divide(X_20,X_20))) = divide(X_3,multiply(X_2,divide(X_20,X_20))),
introduced(tautology,[refl,[$fot(divide(X_3,multiply(X_2,divide(X_20,X_20))))]]) ).
cnf(refute_0_46,plain,
( multiply(X_2,divide(X_20,X_20)) != X_2
| divide(X_3,multiply(X_2,divide(X_20,X_20))) != divide(X_3,multiply(X_2,divide(X_20,X_20)))
| divide(X_3,multiply(X_2,divide(X_20,X_20))) = divide(X_3,X_2) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_3,multiply(X_2,divide(X_20,X_20))),divide(X_3,multiply(X_2,divide(X_20,X_20)))) ),[1,1],$fot(X_2)]]) ).
cnf(refute_0_47,plain,
( multiply(X_2,divide(X_20,X_20)) != X_2
| divide(X_3,multiply(X_2,divide(X_20,X_20))) = divide(X_3,X_2) ),
inference(resolve,[$cnf( $equal(divide(X_3,multiply(X_2,divide(X_20,X_20))),divide(X_3,multiply(X_2,divide(X_20,X_20)))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
divide(X_3,multiply(X_2,divide(X_20,X_20))) = divide(X_3,X_2),
inference(resolve,[$cnf( $equal(multiply(X_2,divide(X_20,X_20)),X_2) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))) = multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))),
introduced(tautology,[refl,[$fot(multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))))]]) ).
cnf(refute_0_50,plain,
( multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))) != multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20))))
| divide(X_3,multiply(X_2,divide(X_20,X_20))) != divide(X_3,X_2)
| multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))) = multiply(X_2,divide(X_3,X_2)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))),multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20))))) ),[1,1],$fot(divide(X_3,X_2))]]) ).
cnf(refute_0_51,plain,
( divide(X_3,multiply(X_2,divide(X_20,X_20))) != divide(X_3,X_2)
| multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))) = multiply(X_2,divide(X_3,X_2)) ),
inference(resolve,[$cnf( $equal(multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))),multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20))))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))) = multiply(X_2,divide(X_3,X_2)),
inference(resolve,[$cnf( $equal(divide(X_3,multiply(X_2,divide(X_20,X_20))),divide(X_3,X_2)) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
( multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))) != X_3
| multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))) != multiply(X_2,divide(X_3,X_2))
| multiply(X_2,divide(X_3,X_2)) = X_3 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))),X_3) ),[0],$fot(multiply(X_2,divide(X_3,X_2)))]]) ).
cnf(refute_0_54,plain,
( multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))) != X_3
| multiply(X_2,divide(X_3,X_2)) = X_3 ),
inference(resolve,[$cnf( $equal(multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))),multiply(X_2,divide(X_3,X_2))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
multiply(X_2,divide(X_3,X_2)) = X_3,
inference(resolve,[$cnf( $equal(multiply(X_2,divide(X_3,multiply(X_2,divide(X_20,X_20)))),X_3) )],[refute_0_43,refute_0_54]) ).
cnf(refute_0_56,plain,
multiply(inverse(B),divide(X_23,inverse(B))) = X_23,
inference(subst,[],[refute_0_55:[bind(X_2,$fot(inverse(B))),bind(X_3,$fot(X_23))]]) ).
cnf(refute_0_57,plain,
multiply(X_23,B) = divide(X_23,inverse(B)),
inference(subst,[],[multiply:[bind(A,$fot(X_23))]]) ).
cnf(refute_0_58,plain,
( multiply(X_23,B) != divide(X_23,inverse(B))
| divide(X_23,inverse(B)) = multiply(X_23,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(X_23,B))),bind(Y,$fot(divide(X_23,inverse(B))))]]) ).
cnf(refute_0_59,plain,
divide(X_23,inverse(B)) = multiply(X_23,B),
inference(resolve,[$cnf( $equal(multiply(X_23,B),divide(X_23,inverse(B))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( multiply(inverse(B),divide(X_23,inverse(B))) != X_23
| divide(X_23,inverse(B)) != multiply(X_23,B)
| multiply(inverse(B),multiply(X_23,B)) = X_23 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(B),divide(X_23,inverse(B))),X_23) ),[0,1],$fot(multiply(X_23,B))]]) ).
cnf(refute_0_61,plain,
( multiply(inverse(B),divide(X_23,inverse(B))) != X_23
| multiply(inverse(B),multiply(X_23,B)) = X_23 ),
inference(resolve,[$cnf( $equal(divide(X_23,inverse(B)),multiply(X_23,B)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
multiply(inverse(B),multiply(X_23,B)) = X_23,
inference(resolve,[$cnf( $equal(multiply(inverse(B),divide(X_23,inverse(B))),X_23) )],[refute_0_56,refute_0_61]) ).
cnf(refute_0_63,plain,
multiply(inverse(divide(X_3,X_31)),multiply(X_31,divide(X_3,X_31))) = X_31,
inference(subst,[],[refute_0_62:[bind(B,$fot(divide(X_3,X_31))),bind(X_23,$fot(X_31))]]) ).
cnf(refute_0_64,plain,
multiply(X_31,divide(X_3,X_31)) = X_3,
inference(subst,[],[refute_0_55:[bind(X_2,$fot(X_31))]]) ).
cnf(refute_0_65,plain,
( multiply(X_31,divide(X_3,X_31)) != X_3
| multiply(inverse(divide(X_3,X_31)),multiply(X_31,divide(X_3,X_31))) != X_31
| multiply(inverse(divide(X_3,X_31)),X_3) = X_31 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(divide(X_3,X_31)),multiply(X_31,divide(X_3,X_31))),X_31) ),[0,1],$fot(X_3)]]) ).
cnf(refute_0_66,plain,
( multiply(inverse(divide(X_3,X_31)),multiply(X_31,divide(X_3,X_31))) != X_31
| multiply(inverse(divide(X_3,X_31)),X_3) = X_31 ),
inference(resolve,[$cnf( $equal(multiply(X_31,divide(X_3,X_31)),X_3) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
multiply(inverse(divide(X_3,X_31)),X_3) = X_31,
inference(resolve,[$cnf( $equal(multiply(inverse(divide(X_3,X_31)),multiply(X_31,divide(X_3,X_31))),X_31) )],[refute_0_63,refute_0_66]) ).
cnf(refute_0_68,plain,
multiply(inverse(divide(divide(X_11,X_11),X_33)),divide(X_11,X_11)) = X_33,
inference(subst,[],[refute_0_67:[bind(X_3,$fot(divide(X_11,X_11))),bind(X_31,$fot(X_33))]]) ).
cnf(refute_0_69,plain,
( multiply(inverse(divide(divide(X_11,X_11),X_33)),divide(X_11,X_11)) != X_33
| multiply(inverse(divide(divide(X_11,X_11),X_33)),divide(X_11,X_11)) != inverse(divide(divide(X_11,X_11),X_33))
| X_33 = inverse(divide(divide(X_11,X_11),X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(divide(divide(X_11,X_11),X_33)),divide(X_11,X_11)),inverse(divide(divide(X_11,X_11),X_33))) ),[0],$fot(X_33)]]) ).
cnf(refute_0_70,plain,
( multiply(inverse(divide(divide(X_11,X_11),X_33)),divide(X_11,X_11)) != inverse(divide(divide(X_11,X_11),X_33))
| X_33 = inverse(divide(divide(X_11,X_11),X_33)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(divide(X_11,X_11),X_33)),divide(X_11,X_11)),X_33) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
X_33 = inverse(divide(divide(X_11,X_11),X_33)),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(divide(X_11,X_11),X_33)),divide(X_11,X_11)),inverse(divide(divide(X_11,X_11),X_33))) )],[refute_0_38,refute_0_70]) ).
cnf(refute_0_72,plain,
( X_33 != inverse(divide(divide(X_11,X_11),X_33))
| inverse(divide(divide(X_11,X_11),X_33)) = X_33 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_33)),bind(Y,$fot(inverse(divide(divide(X_11,X_11),X_33))))]]) ).
cnf(refute_0_73,plain,
inverse(divide(divide(X_11,X_11),X_33)) = X_33,
inference(resolve,[$cnf( $equal(X_33,inverse(divide(divide(X_11,X_11),X_33))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
inverse(divide(divide(b2,b2),a2)) = a2,
inference(subst,[],[refute_0_73:[bind(X_11,$fot(b2)),bind(X_33,$fot(a2))]]) ).
cnf(refute_0_75,plain,
multiply(inverse(B),multiply(inverse(divide(B,X_33)),B)) = inverse(divide(B,X_33)),
inference(subst,[],[refute_0_62:[bind(X_23,$fot(inverse(divide(B,X_33))))]]) ).
cnf(refute_0_76,plain,
multiply(inverse(divide(B,X_33)),B) = X_33,
inference(subst,[],[refute_0_67:[bind(X_3,$fot(B)),bind(X_31,$fot(X_33))]]) ).
cnf(refute_0_77,plain,
( multiply(inverse(B),multiply(inverse(divide(B,X_33)),B)) != inverse(divide(B,X_33))
| multiply(inverse(divide(B,X_33)),B) != X_33
| multiply(inverse(B),X_33) = inverse(divide(B,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(B),multiply(inverse(divide(B,X_33)),B)),inverse(divide(B,X_33))) ),[0,1],$fot(X_33)]]) ).
cnf(refute_0_78,plain,
( multiply(inverse(B),multiply(inverse(divide(B,X_33)),B)) != inverse(divide(B,X_33))
| multiply(inverse(B),X_33) = inverse(divide(B,X_33)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(B,X_33)),B),X_33) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
multiply(inverse(B),X_33) = inverse(divide(B,X_33)),
inference(resolve,[$cnf( $equal(multiply(inverse(B),multiply(inverse(divide(B,X_33)),B)),inverse(divide(B,X_33))) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
multiply(inverse(divide(b2,b2)),a2) = inverse(divide(divide(b2,b2),a2)),
inference(subst,[],[refute_0_79:[bind(B,$fot(divide(b2,b2))),bind(X_33,$fot(a2))]]) ).
cnf(refute_0_81,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_82,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_81]) ).
cnf(refute_0_83,plain,
( multiply(inverse(divide(b2,b2)),a2) != inverse(divide(divide(b2,b2),a2))
| inverse(divide(divide(b2,b2),a2)) != a2
| multiply(inverse(divide(b2,b2)),a2) = a2 ),
inference(subst,[],[refute_0_82:[bind(X,$fot(multiply(inverse(divide(b2,b2)),a2))),bind(Y,$fot(inverse(divide(divide(b2,b2),a2)))),bind(Z,$fot(a2))]]) ).
cnf(refute_0_84,plain,
( inverse(divide(divide(b2,b2),a2)) != a2
| multiply(inverse(divide(b2,b2)),a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(b2,b2)),a2),inverse(divide(divide(b2,b2),a2))) )],[refute_0_80,refute_0_83]) ).
cnf(refute_0_85,plain,
multiply(inverse(divide(b2,b2)),a2) = a2,
inference(resolve,[$cnf( $equal(inverse(divide(divide(b2,b2),a2)),a2) )],[refute_0_74,refute_0_84]) ).
cnf(refute_0_86,plain,
multiply(inverse(b2),b2) = inverse(divide(b2,b2)),
inference(subst,[],[refute_0_79:[bind(B,$fot(b2)),bind(X_33,$fot(b2))]]) ).
cnf(refute_0_87,plain,
multiply(multiply(inverse(b2),b2),a2) = multiply(multiply(inverse(b2),b2),a2),
introduced(tautology,[refl,[$fot(multiply(multiply(inverse(b2),b2),a2))]]) ).
cnf(refute_0_88,plain,
( multiply(multiply(inverse(b2),b2),a2) != multiply(multiply(inverse(b2),b2),a2)
| multiply(inverse(b2),b2) != inverse(divide(b2,b2))
| multiply(multiply(inverse(b2),b2),a2) = multiply(inverse(divide(b2,b2)),a2) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),multiply(multiply(inverse(b2),b2),a2)) ),[1,0],$fot(inverse(divide(b2,b2)))]]) ).
cnf(refute_0_89,plain,
( multiply(inverse(b2),b2) != inverse(divide(b2,b2))
| multiply(multiply(inverse(b2),b2),a2) = multiply(inverse(divide(b2,b2)),a2) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),multiply(multiply(inverse(b2),b2),a2)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
multiply(multiply(inverse(b2),b2),a2) = multiply(inverse(divide(b2,b2)),a2),
inference(resolve,[$cnf( $equal(multiply(inverse(b2),b2),inverse(divide(b2,b2))) )],[refute_0_86,refute_0_89]) ).
cnf(refute_0_91,plain,
( multiply(multiply(inverse(b2),b2),a2) != multiply(inverse(divide(b2,b2)),a2)
| multiply(inverse(divide(b2,b2)),a2) != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
inference(subst,[],[refute_0_82:[bind(X,$fot(multiply(multiply(inverse(b2),b2),a2))),bind(Y,$fot(multiply(inverse(divide(b2,b2)),a2))),bind(Z,$fot(a2))]]) ).
cnf(refute_0_92,plain,
( multiply(inverse(divide(b2,b2)),a2) != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),multiply(inverse(divide(b2,b2)),a2)) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
multiply(multiply(inverse(b2),b2),a2) = a2,
inference(resolve,[$cnf( $equal(multiply(inverse(divide(b2,b2)),a2),a2) )],[refute_0_85,refute_0_92]) ).
cnf(refute_0_94,plain,
( multiply(multiply(inverse(b2),b2),a2) != a2
| a2 != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(inverse(b2),b2),a2),a2) ),[0],$fot(a2)]]) ).
cnf(refute_0_95,plain,
( a2 != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),a2) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
a2 != a2,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),a2) )],[refute_0_95,prove_these_axioms_2]) ).
cnf(refute_0_97,plain,
a2 = a2,
introduced(tautology,[refl,[$fot(a2)]]) ).
cnf(refute_0_98,plain,
$false,
inference(resolve,[$cnf( $equal(a2,a2) )],[refute_0_97,refute_0_96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP558-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 16:34:54 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.40
% 0.21/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.21/0.42
%------------------------------------------------------------------------------