TSTP Solution File: GRP554-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP554-1 : 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 10:42:19 EDT 2022
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 32
% Syntax : Number of clauses : 120 ( 65 unt; 0 nHn; 67 RR)
% Number of literals : 201 ( 200 equ; 84 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 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 : 263 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(divide(A,inverse(divide(B,divide(A,C)))),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,
multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B) = divide(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),inverse(B)),
inference(subst,[],[multiply:[bind(A,$fot(multiply(X_2,divide(X_3,divide(X_2,inverse(B))))))]]) ).
cnf(refute_0_1,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_2,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_3,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( multiply(A,B) != divide(A,inverse(B))
| divide(A,inverse(B)) = multiply(A,B) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(divide(A,inverse(B))))]]) ).
cnf(refute_0_5,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),divide(A,inverse(B))) )],[multiply,refute_0_4]) ).
cnf(refute_0_6,plain,
divide(A,inverse(divide(B,divide(A,C)))) = multiply(A,divide(B,divide(A,C))),
inference(subst,[],[refute_0_5:[bind(B,$fot(divide(B,divide(A,C))))]]) ).
cnf(refute_0_7,plain,
divide(divide(A,inverse(divide(B,divide(A,C)))),C) = divide(divide(A,inverse(divide(B,divide(A,C)))),C),
introduced(tautology,[refl,[$fot(divide(divide(A,inverse(divide(B,divide(A,C)))),C))]]) ).
cnf(refute_0_8,plain,
( divide(A,inverse(divide(B,divide(A,C)))) != multiply(A,divide(B,divide(A,C)))
| divide(divide(A,inverse(divide(B,divide(A,C)))),C) != divide(divide(A,inverse(divide(B,divide(A,C)))),C)
| divide(divide(A,inverse(divide(B,divide(A,C)))),C) = divide(multiply(A,divide(B,divide(A,C))),C) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(A,inverse(divide(B,divide(A,C)))),C),divide(divide(A,inverse(divide(B,divide(A,C)))),C)) ),[1,0],$fot(multiply(A,divide(B,divide(A,C))))]]) ).
cnf(refute_0_9,plain,
( divide(A,inverse(divide(B,divide(A,C)))) != multiply(A,divide(B,divide(A,C)))
| divide(divide(A,inverse(divide(B,divide(A,C)))),C) = divide(multiply(A,divide(B,divide(A,C))),C) ),
inference(resolve,[$cnf( $equal(divide(divide(A,inverse(divide(B,divide(A,C)))),C),divide(divide(A,inverse(divide(B,divide(A,C)))),C)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
divide(divide(A,inverse(divide(B,divide(A,C)))),C) = divide(multiply(A,divide(B,divide(A,C))),C),
inference(resolve,[$cnf( $equal(divide(A,inverse(divide(B,divide(A,C)))),multiply(A,divide(B,divide(A,C)))) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( divide(divide(A,inverse(divide(B,divide(A,C)))),C) != B
| divide(divide(A,inverse(divide(B,divide(A,C)))),C) != divide(multiply(A,divide(B,divide(A,C))),C)
| divide(multiply(A,divide(B,divide(A,C))),C) = B ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(A,inverse(divide(B,divide(A,C)))),C),B) ),[0],$fot(divide(multiply(A,divide(B,divide(A,C))),C))]]) ).
cnf(refute_0_12,plain,
( divide(divide(A,inverse(divide(B,divide(A,C)))),C) != B
| divide(multiply(A,divide(B,divide(A,C))),C) = B ),
inference(resolve,[$cnf( $equal(divide(divide(A,inverse(divide(B,divide(A,C)))),C),divide(multiply(A,divide(B,divide(A,C))),C)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
divide(multiply(A,divide(B,divide(A,C))),C) = B,
inference(resolve,[$cnf( $equal(divide(divide(A,inverse(divide(B,divide(A,C)))),C),B) )],[single_axiom,refute_0_12]) ).
cnf(refute_0_14,plain,
divide(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),inverse(B)) = X_3,
inference(subst,[],[refute_0_13:[bind(A,$fot(X_2)),bind(B,$fot(X_3)),bind(C,$fot(inverse(B)))]]) ).
cnf(refute_0_15,plain,
( multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B) != divide(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),inverse(B))
| divide(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),inverse(B)) != X_3
| multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B) = X_3 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B),X_3) ),[0],$fot(divide(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),inverse(B)))]]) ).
cnf(refute_0_16,plain,
( multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B) != divide(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),inverse(B))
| multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B) = X_3 ),
inference(resolve,[$cnf( $equal(divide(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),inverse(B)),X_3) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B) = X_3,
inference(resolve,[$cnf( $equal(multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B),divide(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),inverse(B))) )],[refute_0_0,refute_0_16]) ).
cnf(refute_0_18,plain,
divide(X_2,inverse(B)) = multiply(X_2,B),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_2))]]) ).
cnf(refute_0_19,plain,
divide(X_3,divide(X_2,inverse(B))) = divide(X_3,divide(X_2,inverse(B))),
introduced(tautology,[refl,[$fot(divide(X_3,divide(X_2,inverse(B))))]]) ).
cnf(refute_0_20,plain,
( divide(X_2,inverse(B)) != multiply(X_2,B)
| divide(X_3,divide(X_2,inverse(B))) != divide(X_3,divide(X_2,inverse(B)))
| divide(X_3,divide(X_2,inverse(B))) = divide(X_3,multiply(X_2,B)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_3,divide(X_2,inverse(B))),divide(X_3,divide(X_2,inverse(B)))) ),[1,1],$fot(multiply(X_2,B))]]) ).
cnf(refute_0_21,plain,
( divide(X_2,inverse(B)) != multiply(X_2,B)
| divide(X_3,divide(X_2,inverse(B))) = divide(X_3,multiply(X_2,B)) ),
inference(resolve,[$cnf( $equal(divide(X_3,divide(X_2,inverse(B))),divide(X_3,divide(X_2,inverse(B)))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
divide(X_3,divide(X_2,inverse(B))) = divide(X_3,multiply(X_2,B)),
inference(resolve,[$cnf( $equal(divide(X_2,inverse(B)),multiply(X_2,B)) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
multiply(X_2,divide(X_3,divide(X_2,inverse(B)))) = multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),
introduced(tautology,[refl,[$fot(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))))]]) ).
cnf(refute_0_24,plain,
( multiply(X_2,divide(X_3,divide(X_2,inverse(B)))) != multiply(X_2,divide(X_3,divide(X_2,inverse(B))))
| divide(X_3,divide(X_2,inverse(B))) != divide(X_3,multiply(X_2,B))
| multiply(X_2,divide(X_3,divide(X_2,inverse(B)))) = multiply(X_2,divide(X_3,multiply(X_2,B))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),multiply(X_2,divide(X_3,divide(X_2,inverse(B))))) ),[1,1],$fot(divide(X_3,multiply(X_2,B)))]]) ).
cnf(refute_0_25,plain,
( divide(X_3,divide(X_2,inverse(B))) != divide(X_3,multiply(X_2,B))
| multiply(X_2,divide(X_3,divide(X_2,inverse(B)))) = multiply(X_2,divide(X_3,multiply(X_2,B))) ),
inference(resolve,[$cnf( $equal(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),multiply(X_2,divide(X_3,divide(X_2,inverse(B))))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
multiply(X_2,divide(X_3,divide(X_2,inverse(B)))) = multiply(X_2,divide(X_3,multiply(X_2,B))),
inference(resolve,[$cnf( $equal(divide(X_3,divide(X_2,inverse(B))),divide(X_3,multiply(X_2,B))) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B) = multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B),
introduced(tautology,[refl,[$fot(multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B))]]) ).
cnf(refute_0_28,plain,
( multiply(X_2,divide(X_3,divide(X_2,inverse(B)))) != multiply(X_2,divide(X_3,multiply(X_2,B)))
| multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B) != multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B)
| multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B) = multiply(multiply(X_2,divide(X_3,multiply(X_2,B))),B) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B),multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B)) ),[1,0],$fot(multiply(X_2,divide(X_3,multiply(X_2,B))))]]) ).
cnf(refute_0_29,plain,
( multiply(X_2,divide(X_3,divide(X_2,inverse(B)))) != multiply(X_2,divide(X_3,multiply(X_2,B)))
| multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B) = multiply(multiply(X_2,divide(X_3,multiply(X_2,B))),B) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B),multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B) = multiply(multiply(X_2,divide(X_3,multiply(X_2,B))),B),
inference(resolve,[$cnf( $equal(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),multiply(X_2,divide(X_3,multiply(X_2,B)))) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
( multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B) != X_3
| multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B) != multiply(multiply(X_2,divide(X_3,multiply(X_2,B))),B)
| multiply(multiply(X_2,divide(X_3,multiply(X_2,B))),B) = X_3 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B),X_3) ),[0],$fot(multiply(multiply(X_2,divide(X_3,multiply(X_2,B))),B))]]) ).
cnf(refute_0_32,plain,
( multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B) != X_3
| multiply(multiply(X_2,divide(X_3,multiply(X_2,B))),B) = X_3 ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B),multiply(multiply(X_2,divide(X_3,multiply(X_2,B))),B)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
multiply(multiply(X_2,divide(X_3,multiply(X_2,B))),B) = X_3,
inference(resolve,[$cnf( $equal(multiply(multiply(X_2,divide(X_3,divide(X_2,inverse(B)))),B),X_3) )],[refute_0_17,refute_0_32]) ).
cnf(refute_0_34,plain,
multiply(multiply(X_6,divide(multiply(A,divide(B,divide(A,multiply(X_6,X_5)))),multiply(X_6,X_5))),X_5) = multiply(A,divide(B,divide(A,multiply(X_6,X_5)))),
inference(subst,[],[refute_0_33:[bind(B,$fot(X_5)),bind(X_2,$fot(X_6)),bind(X_3,$fot(multiply(A,divide(B,divide(A,multiply(X_6,X_5))))))]]) ).
cnf(refute_0_35,plain,
divide(multiply(A,divide(B,divide(A,multiply(X_6,X_5)))),multiply(X_6,X_5)) = B,
inference(subst,[],[refute_0_13:[bind(C,$fot(multiply(X_6,X_5)))]]) ).
cnf(refute_0_36,plain,
( multiply(multiply(X_6,divide(multiply(A,divide(B,divide(A,multiply(X_6,X_5)))),multiply(X_6,X_5))),X_5) != multiply(A,divide(B,divide(A,multiply(X_6,X_5))))
| divide(multiply(A,divide(B,divide(A,multiply(X_6,X_5)))),multiply(X_6,X_5)) != B
| multiply(multiply(X_6,B),X_5) = multiply(A,divide(B,divide(A,multiply(X_6,X_5)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_6,divide(multiply(A,divide(B,divide(A,multiply(X_6,X_5)))),multiply(X_6,X_5))),X_5),multiply(A,divide(B,divide(A,multiply(X_6,X_5))))) ),[0,0,1],$fot(B)]]) ).
cnf(refute_0_37,plain,
( multiply(multiply(X_6,divide(multiply(A,divide(B,divide(A,multiply(X_6,X_5)))),multiply(X_6,X_5))),X_5) != multiply(A,divide(B,divide(A,multiply(X_6,X_5))))
| multiply(multiply(X_6,B),X_5) = multiply(A,divide(B,divide(A,multiply(X_6,X_5)))) ),
inference(resolve,[$cnf( $equal(divide(multiply(A,divide(B,divide(A,multiply(X_6,X_5)))),multiply(X_6,X_5)),B) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
multiply(multiply(X_6,B),X_5) = multiply(A,divide(B,divide(A,multiply(X_6,X_5)))),
inference(resolve,[$cnf( $equal(multiply(multiply(X_6,divide(multiply(A,divide(B,divide(A,multiply(X_6,X_5)))),multiply(X_6,X_5))),X_5),multiply(A,divide(B,divide(A,multiply(X_6,X_5))))) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
multiply(multiply(multiply(X_6,divide(X_7,multiply(X_6,B))),divide(X_3,multiply(multiply(X_6,divide(X_7,multiply(X_6,B))),B))),B) = X_3,
inference(subst,[],[refute_0_33:[bind(X_2,$fot(multiply(X_6,divide(X_7,multiply(X_6,B)))))]]) ).
cnf(refute_0_40,plain,
multiply(multiply(X_6,divide(X_7,multiply(X_6,B))),B) = X_7,
inference(subst,[],[refute_0_33:[bind(X_2,$fot(X_6)),bind(X_3,$fot(X_7))]]) ).
cnf(refute_0_41,plain,
( multiply(multiply(X_6,divide(X_7,multiply(X_6,B))),B) != X_7
| multiply(multiply(multiply(X_6,divide(X_7,multiply(X_6,B))),divide(X_3,multiply(multiply(X_6,divide(X_7,multiply(X_6,B))),B))),B) != X_3
| multiply(multiply(multiply(X_6,divide(X_7,multiply(X_6,B))),divide(X_3,X_7)),B) = X_3 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(multiply(X_6,divide(X_7,multiply(X_6,B))),divide(X_3,multiply(multiply(X_6,divide(X_7,multiply(X_6,B))),B))),B),X_3) ),[0,0,1,1],$fot(X_7)]]) ).
cnf(refute_0_42,plain,
( multiply(multiply(multiply(X_6,divide(X_7,multiply(X_6,B))),divide(X_3,multiply(multiply(X_6,divide(X_7,multiply(X_6,B))),B))),B) != X_3
| multiply(multiply(multiply(X_6,divide(X_7,multiply(X_6,B))),divide(X_3,X_7)),B) = X_3 ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_6,divide(X_7,multiply(X_6,B))),B),X_7) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
multiply(multiply(multiply(X_6,divide(X_7,multiply(X_6,B))),divide(X_3,X_7)),B) = X_3,
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(X_6,divide(X_7,multiply(X_6,B))),divide(X_3,multiply(multiply(X_6,divide(X_7,multiply(X_6,B))),B))),B),X_3) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
multiply(multiply(multiply(X_14,divide(X_15,multiply(X_14,divide(X_13,X_15)))),divide(X_13,X_15)),divide(X_13,X_15)) = X_13,
inference(subst,[],[refute_0_43:[bind(B,$fot(divide(X_13,X_15))),bind(X_3,$fot(X_13)),bind(X_6,$fot(X_14)),bind(X_7,$fot(X_15))]]) ).
cnf(refute_0_45,plain,
multiply(multiply(X_14,divide(X_15,multiply(X_14,divide(X_13,X_15)))),divide(X_13,X_15)) = X_15,
inference(subst,[],[refute_0_33:[bind(B,$fot(divide(X_13,X_15))),bind(X_2,$fot(X_14)),bind(X_3,$fot(X_15))]]) ).
cnf(refute_0_46,plain,
( multiply(multiply(X_14,divide(X_15,multiply(X_14,divide(X_13,X_15)))),divide(X_13,X_15)) != X_15
| multiply(multiply(multiply(X_14,divide(X_15,multiply(X_14,divide(X_13,X_15)))),divide(X_13,X_15)),divide(X_13,X_15)) != X_13
| multiply(X_15,divide(X_13,X_15)) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(multiply(X_14,divide(X_15,multiply(X_14,divide(X_13,X_15)))),divide(X_13,X_15)),divide(X_13,X_15)),X_13) ),[0,0],$fot(X_15)]]) ).
cnf(refute_0_47,plain,
( multiply(multiply(multiply(X_14,divide(X_15,multiply(X_14,divide(X_13,X_15)))),divide(X_13,X_15)),divide(X_13,X_15)) != X_13
| multiply(X_15,divide(X_13,X_15)) = X_13 ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_14,divide(X_15,multiply(X_14,divide(X_13,X_15)))),divide(X_13,X_15)),X_15) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
multiply(X_15,divide(X_13,X_15)) = X_13,
inference(resolve,[$cnf( $equal(multiply(multiply(multiply(X_14,divide(X_15,multiply(X_14,divide(X_13,X_15)))),divide(X_13,X_15)),divide(X_13,X_15)),X_13) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
multiply(X_17,divide(multiply(A,divide(B,divide(A,X_17))),X_17)) = multiply(A,divide(B,divide(A,X_17))),
inference(subst,[],[refute_0_48:[bind(X_13,$fot(multiply(A,divide(B,divide(A,X_17))))),bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_50,plain,
divide(multiply(A,divide(B,divide(A,X_17))),X_17) = B,
inference(subst,[],[refute_0_13:[bind(C,$fot(X_17))]]) ).
cnf(refute_0_51,plain,
( multiply(X_17,divide(multiply(A,divide(B,divide(A,X_17))),X_17)) != multiply(A,divide(B,divide(A,X_17)))
| divide(multiply(A,divide(B,divide(A,X_17))),X_17) != B
| multiply(X_17,B) = multiply(A,divide(B,divide(A,X_17))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_17,divide(multiply(A,divide(B,divide(A,X_17))),X_17)),multiply(A,divide(B,divide(A,X_17)))) ),[0,1],$fot(B)]]) ).
cnf(refute_0_52,plain,
( multiply(X_17,divide(multiply(A,divide(B,divide(A,X_17))),X_17)) != multiply(A,divide(B,divide(A,X_17)))
| multiply(X_17,B) = multiply(A,divide(B,divide(A,X_17))) ),
inference(resolve,[$cnf( $equal(divide(multiply(A,divide(B,divide(A,X_17))),X_17),B) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
multiply(X_17,B) = multiply(A,divide(B,divide(A,X_17))),
inference(resolve,[$cnf( $equal(multiply(X_17,divide(multiply(A,divide(B,divide(A,X_17))),X_17)),multiply(A,divide(B,divide(A,X_17)))) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
( multiply(X_17,B) != multiply(A,divide(B,divide(A,X_17)))
| multiply(A,divide(B,divide(A,X_17))) = multiply(X_17,B) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(multiply(X_17,B))),bind(Y,$fot(multiply(A,divide(B,divide(A,X_17)))))]]) ).
cnf(refute_0_55,plain,
multiply(A,divide(B,divide(A,X_17))) = multiply(X_17,B),
inference(resolve,[$cnf( $equal(multiply(X_17,B),multiply(A,divide(B,divide(A,X_17)))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
multiply(A,divide(B,divide(A,multiply(X_6,X_5)))) = multiply(multiply(X_6,X_5),B),
inference(subst,[],[refute_0_55:[bind(X_17,$fot(multiply(X_6,X_5)))]]) ).
cnf(refute_0_57,plain,
( multiply(A,divide(B,divide(A,multiply(X_6,X_5)))) != multiply(multiply(X_6,X_5),B)
| multiply(multiply(X_6,B),X_5) != multiply(A,divide(B,divide(A,multiply(X_6,X_5))))
| multiply(multiply(X_6,B),X_5) = multiply(multiply(X_6,X_5),B) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_6,B),X_5),multiply(A,divide(B,divide(A,multiply(X_6,X_5))))) ),[1],$fot(multiply(multiply(X_6,X_5),B))]]) ).
cnf(refute_0_58,plain,
( multiply(multiply(X_6,B),X_5) != multiply(A,divide(B,divide(A,multiply(X_6,X_5))))
| multiply(multiply(X_6,B),X_5) = multiply(multiply(X_6,X_5),B) ),
inference(resolve,[$cnf( $equal(multiply(A,divide(B,divide(A,multiply(X_6,X_5)))),multiply(multiply(X_6,X_5),B)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
multiply(multiply(X_6,B),X_5) = multiply(multiply(X_6,X_5),B),
inference(resolve,[$cnf( $equal(multiply(multiply(X_6,B),X_5),multiply(A,divide(B,divide(A,multiply(X_6,X_5))))) )],[refute_0_38,refute_0_58]) ).
cnf(refute_0_60,plain,
( multiply(multiply(X_6,B),X_5) != multiply(multiply(X_6,X_5),B)
| multiply(multiply(X_6,X_5),B) = multiply(multiply(X_6,B),X_5) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(multiply(multiply(X_6,B),X_5))),bind(Y,$fot(multiply(multiply(X_6,X_5),B)))]]) ).
cnf(refute_0_61,plain,
multiply(multiply(X_6,X_5),B) = multiply(multiply(X_6,B),X_5),
inference(resolve,[$cnf( $equal(multiply(multiply(X_6,B),X_5),multiply(multiply(X_6,X_5),B)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
multiply(multiply(inverse(b2),b2),a2) = multiply(multiply(inverse(b2),a2),b2),
inference(subst,[],[refute_0_61:[bind(B,$fot(a2)),bind(X_5,$fot(b2)),bind(X_6,$fot(inverse(b2)))]]) ).
cnf(refute_0_63,plain,
( multiply(multiply(inverse(b2),a2),b2) != a2
| multiply(multiply(inverse(b2),b2),a2) != multiply(multiply(inverse(b2),a2),b2)
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),multiply(multiply(inverse(b2),a2),b2)) ),[1],$fot(a2)]]) ).
cnf(refute_0_64,plain,
( multiply(multiply(inverse(b2),a2),b2) != a2
| multiply(multiply(inverse(b2),b2),a2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),multiply(multiply(inverse(b2),a2),b2)) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
multiply(multiply(inverse(b2),a2),b2) != a2,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),b2),a2),a2) )],[refute_0_64,prove_these_axioms_2]) ).
cnf(refute_0_66,plain,
multiply(inverse(divide(B,X_21)),B) = divide(inverse(divide(B,X_21)),inverse(B)),
inference(subst,[],[multiply:[bind(A,$fot(inverse(divide(B,X_21))))]]) ).
cnf(refute_0_67,plain,
multiply(inverse(B),divide(X_16,inverse(B))) = X_16,
inference(subst,[],[refute_0_48:[bind(X_13,$fot(X_16)),bind(X_15,$fot(inverse(B)))]]) ).
cnf(refute_0_68,plain,
multiply(X_16,B) = divide(X_16,inverse(B)),
inference(subst,[],[multiply:[bind(A,$fot(X_16))]]) ).
cnf(refute_0_69,plain,
( multiply(X_16,B) != divide(X_16,inverse(B))
| divide(X_16,inverse(B)) = multiply(X_16,B) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(multiply(X_16,B))),bind(Y,$fot(divide(X_16,inverse(B))))]]) ).
cnf(refute_0_70,plain,
divide(X_16,inverse(B)) = multiply(X_16,B),
inference(resolve,[$cnf( $equal(multiply(X_16,B),divide(X_16,inverse(B))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( multiply(inverse(B),divide(X_16,inverse(B))) != X_16
| divide(X_16,inverse(B)) != multiply(X_16,B)
| multiply(inverse(B),multiply(X_16,B)) = X_16 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(B),divide(X_16,inverse(B))),X_16) ),[0,1],$fot(multiply(X_16,B))]]) ).
cnf(refute_0_72,plain,
( multiply(inverse(B),divide(X_16,inverse(B))) != X_16
| multiply(inverse(B),multiply(X_16,B)) = X_16 ),
inference(resolve,[$cnf( $equal(divide(X_16,inverse(B)),multiply(X_16,B)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
multiply(inverse(B),multiply(X_16,B)) = X_16,
inference(resolve,[$cnf( $equal(multiply(inverse(B),divide(X_16,inverse(B))),X_16) )],[refute_0_67,refute_0_72]) ).
cnf(refute_0_74,plain,
multiply(inverse(divide(X_13,X_19)),multiply(X_19,divide(X_13,X_19))) = X_19,
inference(subst,[],[refute_0_73:[bind(B,$fot(divide(X_13,X_19))),bind(X_16,$fot(X_19))]]) ).
cnf(refute_0_75,plain,
multiply(X_19,divide(X_13,X_19)) = X_13,
inference(subst,[],[refute_0_48:[bind(X_15,$fot(X_19))]]) ).
cnf(refute_0_76,plain,
( multiply(X_19,divide(X_13,X_19)) != X_13
| multiply(inverse(divide(X_13,X_19)),multiply(X_19,divide(X_13,X_19))) != X_19
| multiply(inverse(divide(X_13,X_19)),X_13) = X_19 ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(divide(X_13,X_19)),multiply(X_19,divide(X_13,X_19))),X_19) ),[0,1],$fot(X_13)]]) ).
cnf(refute_0_77,plain,
( multiply(inverse(divide(X_13,X_19)),multiply(X_19,divide(X_13,X_19))) != X_19
| multiply(inverse(divide(X_13,X_19)),X_13) = X_19 ),
inference(resolve,[$cnf( $equal(multiply(X_19,divide(X_13,X_19)),X_13) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
multiply(inverse(divide(X_13,X_19)),X_13) = X_19,
inference(resolve,[$cnf( $equal(multiply(inverse(divide(X_13,X_19)),multiply(X_19,divide(X_13,X_19))),X_19) )],[refute_0_74,refute_0_77]) ).
cnf(refute_0_79,plain,
multiply(inverse(divide(B,X_21)),B) = X_21,
inference(subst,[],[refute_0_78:[bind(X_13,$fot(B)),bind(X_19,$fot(X_21))]]) ).
cnf(refute_0_80,plain,
( multiply(inverse(divide(B,X_21)),B) != X_21
| multiply(inverse(divide(B,X_21)),B) != divide(inverse(divide(B,X_21)),inverse(B))
| X_21 = divide(inverse(divide(B,X_21)),inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(divide(B,X_21)),B),divide(inverse(divide(B,X_21)),inverse(B))) ),[0],$fot(X_21)]]) ).
cnf(refute_0_81,plain,
( multiply(inverse(divide(B,X_21)),B) != divide(inverse(divide(B,X_21)),inverse(B))
| X_21 = divide(inverse(divide(B,X_21)),inverse(B)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(B,X_21)),B),X_21) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
X_21 = divide(inverse(divide(B,X_21)),inverse(B)),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(B,X_21)),B),divide(inverse(divide(B,X_21)),inverse(B))) )],[refute_0_66,refute_0_81]) ).
cnf(refute_0_83,plain,
multiply(inverse(B),multiply(inverse(divide(B,X_21)),B)) = inverse(divide(B,X_21)),
inference(subst,[],[refute_0_73:[bind(X_16,$fot(inverse(divide(B,X_21))))]]) ).
cnf(refute_0_84,plain,
( multiply(inverse(B),multiply(inverse(divide(B,X_21)),B)) != inverse(divide(B,X_21))
| multiply(inverse(divide(B,X_21)),B) != X_21
| multiply(inverse(B),X_21) = inverse(divide(B,X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(B),multiply(inverse(divide(B,X_21)),B)),inverse(divide(B,X_21))) ),[0,1],$fot(X_21)]]) ).
cnf(refute_0_85,plain,
( multiply(inverse(B),multiply(inverse(divide(B,X_21)),B)) != inverse(divide(B,X_21))
| multiply(inverse(B),X_21) = inverse(divide(B,X_21)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(B,X_21)),B),X_21) )],[refute_0_79,refute_0_84]) ).
cnf(refute_0_86,plain,
multiply(inverse(B),X_21) = inverse(divide(B,X_21)),
inference(resolve,[$cnf( $equal(multiply(inverse(B),multiply(inverse(divide(B,X_21)),B)),inverse(divide(B,X_21))) )],[refute_0_83,refute_0_85]) ).
cnf(refute_0_87,plain,
multiply(inverse(divide(B,X_21)),B) = inverse(divide(divide(B,X_21),B)),
inference(subst,[],[refute_0_86:[bind(B,$fot(divide(B,X_21))),bind(X_21,$fot(B))]]) ).
cnf(refute_0_88,plain,
divide(inverse(divide(B,X_21)),inverse(B)) = multiply(inverse(divide(B,X_21)),B),
inference(subst,[],[refute_0_5:[bind(A,$fot(inverse(divide(B,X_21))))]]) ).
cnf(refute_0_89,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_90,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_3,refute_0_89]) ).
cnf(refute_0_91,plain,
( multiply(inverse(divide(B,X_21)),B) != inverse(divide(divide(B,X_21),B))
| divide(inverse(divide(B,X_21)),inverse(B)) != multiply(inverse(divide(B,X_21)),B)
| divide(inverse(divide(B,X_21)),inverse(B)) = inverse(divide(divide(B,X_21),B)) ),
inference(subst,[],[refute_0_90:[bind(X,$fot(divide(inverse(divide(B,X_21)),inverse(B)))),bind(Y,$fot(multiply(inverse(divide(B,X_21)),B))),bind(Z,$fot(inverse(divide(divide(B,X_21),B))))]]) ).
cnf(refute_0_92,plain,
( multiply(inverse(divide(B,X_21)),B) != inverse(divide(divide(B,X_21),B))
| divide(inverse(divide(B,X_21)),inverse(B)) = inverse(divide(divide(B,X_21),B)) ),
inference(resolve,[$cnf( $equal(divide(inverse(divide(B,X_21)),inverse(B)),multiply(inverse(divide(B,X_21)),B)) )],[refute_0_88,refute_0_91]) ).
cnf(refute_0_93,plain,
divide(inverse(divide(B,X_21)),inverse(B)) = inverse(divide(divide(B,X_21),B)),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(B,X_21)),B),inverse(divide(divide(B,X_21),B))) )],[refute_0_87,refute_0_92]) ).
cnf(refute_0_94,plain,
( X_21 != divide(inverse(divide(B,X_21)),inverse(B))
| divide(inverse(divide(B,X_21)),inverse(B)) != inverse(divide(divide(B,X_21),B))
| X_21 = inverse(divide(divide(B,X_21),B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_21,inverse(divide(divide(B,X_21),B))) ),[0],$fot(divide(inverse(divide(B,X_21)),inverse(B)))]]) ).
cnf(refute_0_95,plain,
( X_21 != divide(inverse(divide(B,X_21)),inverse(B))
| X_21 = inverse(divide(divide(B,X_21),B)) ),
inference(resolve,[$cnf( $equal(divide(inverse(divide(B,X_21)),inverse(B)),inverse(divide(divide(B,X_21),B))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
X_21 = inverse(divide(divide(B,X_21),B)),
inference(resolve,[$cnf( $equal(X_21,divide(inverse(divide(B,X_21)),inverse(B))) )],[refute_0_82,refute_0_95]) ).
cnf(refute_0_97,plain,
( X_21 != inverse(divide(divide(B,X_21),B))
| inverse(divide(divide(B,X_21),B)) = X_21 ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_21)),bind(Y,$fot(inverse(divide(divide(B,X_21),B))))]]) ).
cnf(refute_0_98,plain,
inverse(divide(divide(B,X_21),B)) = X_21,
inference(resolve,[$cnf( $equal(X_21,inverse(divide(divide(B,X_21),B))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
inverse(divide(divide(b2,a2),b2)) = a2,
inference(subst,[],[refute_0_98:[bind(B,$fot(b2)),bind(X_21,$fot(a2))]]) ).
cnf(refute_0_100,plain,
multiply(inverse(divide(b2,a2)),b2) = inverse(divide(divide(b2,a2),b2)),
inference(subst,[],[refute_0_86:[bind(B,$fot(divide(b2,a2))),bind(X_21,$fot(b2))]]) ).
cnf(refute_0_101,plain,
( multiply(inverse(divide(b2,a2)),b2) != inverse(divide(divide(b2,a2),b2))
| inverse(divide(divide(b2,a2),b2)) != a2
| multiply(inverse(divide(b2,a2)),b2) = a2 ),
inference(subst,[],[refute_0_90:[bind(X,$fot(multiply(inverse(divide(b2,a2)),b2))),bind(Y,$fot(inverse(divide(divide(b2,a2),b2)))),bind(Z,$fot(a2))]]) ).
cnf(refute_0_102,plain,
( inverse(divide(divide(b2,a2),b2)) != a2
| multiply(inverse(divide(b2,a2)),b2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(inverse(divide(b2,a2)),b2),inverse(divide(divide(b2,a2),b2))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
multiply(inverse(divide(b2,a2)),b2) = a2,
inference(resolve,[$cnf( $equal(inverse(divide(divide(b2,a2),b2)),a2) )],[refute_0_99,refute_0_102]) ).
cnf(refute_0_104,plain,
multiply(inverse(b2),a2) = inverse(divide(b2,a2)),
inference(subst,[],[refute_0_86:[bind(B,$fot(b2)),bind(X_21,$fot(a2))]]) ).
cnf(refute_0_105,plain,
multiply(multiply(inverse(b2),a2),b2) = multiply(multiply(inverse(b2),a2),b2),
introduced(tautology,[refl,[$fot(multiply(multiply(inverse(b2),a2),b2))]]) ).
cnf(refute_0_106,plain,
( multiply(multiply(inverse(b2),a2),b2) != multiply(multiply(inverse(b2),a2),b2)
| multiply(inverse(b2),a2) != inverse(divide(b2,a2))
| multiply(multiply(inverse(b2),a2),b2) = multiply(inverse(divide(b2,a2)),b2) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(inverse(b2),a2),b2),multiply(multiply(inverse(b2),a2),b2)) ),[1,0],$fot(inverse(divide(b2,a2)))]]) ).
cnf(refute_0_107,plain,
( multiply(inverse(b2),a2) != inverse(divide(b2,a2))
| multiply(multiply(inverse(b2),a2),b2) = multiply(inverse(divide(b2,a2)),b2) ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),a2),b2),multiply(multiply(inverse(b2),a2),b2)) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
multiply(multiply(inverse(b2),a2),b2) = multiply(inverse(divide(b2,a2)),b2),
inference(resolve,[$cnf( $equal(multiply(inverse(b2),a2),inverse(divide(b2,a2))) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
( multiply(multiply(inverse(b2),a2),b2) != multiply(inverse(divide(b2,a2)),b2)
| multiply(inverse(divide(b2,a2)),b2) != a2
| multiply(multiply(inverse(b2),a2),b2) = a2 ),
inference(subst,[],[refute_0_90:[bind(X,$fot(multiply(multiply(inverse(b2),a2),b2))),bind(Y,$fot(multiply(inverse(divide(b2,a2)),b2))),bind(Z,$fot(a2))]]) ).
cnf(refute_0_110,plain,
( multiply(inverse(divide(b2,a2)),b2) != a2
| multiply(multiply(inverse(b2),a2),b2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),a2),b2),multiply(inverse(divide(b2,a2)),b2)) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
multiply(multiply(inverse(b2),a2),b2) = a2,
inference(resolve,[$cnf( $equal(multiply(inverse(divide(b2,a2)),b2),a2) )],[refute_0_103,refute_0_110]) ).
cnf(refute_0_112,plain,
( multiply(multiply(inverse(b2),a2),b2) != a2
| a2 != a2
| multiply(multiply(inverse(b2),a2),b2) = a2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(inverse(b2),a2),b2),a2) ),[0],$fot(a2)]]) ).
cnf(refute_0_113,plain,
( a2 != a2
| multiply(multiply(inverse(b2),a2),b2) = a2 ),
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),a2),b2),a2) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
a2 != a2,
inference(resolve,[$cnf( $equal(multiply(multiply(inverse(b2),a2),b2),a2) )],[refute_0_113,refute_0_65]) ).
cnf(refute_0_115,plain,
a2 = a2,
introduced(tautology,[refl,[$fot(a2)]]) ).
cnf(refute_0_116,plain,
$false,
inference(resolve,[$cnf( $equal(a2,a2) )],[refute_0_115,refute_0_114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP554-1 : TPTP v8.1.0. Released v2.6.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n019.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 09:22:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.40
%------------------------------------------------------------------------------