TSTP Solution File: GRP525-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP525-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 10:42:08 EDT 2022
% Result : Unsatisfiable 0.13s 0.40s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 27
% Syntax : Number of clauses : 99 ( 55 unt; 0 nHn; 42 RR)
% Number of literals : 161 ( 160 equ; 64 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 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 : 212 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(A,divide(divide(A,B),divide(C,B))) = C ).
cnf(multiply,axiom,
multiply(A,B) = divide(A,divide(divide(C,C),B)) ).
cnf(inverse,axiom,
inverse(A) = divide(divide(B,B),A) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ).
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( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( inverse(A) != divide(divide(B,B),A)
| divide(divide(B,B),A) = inverse(A) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(A))),bind(Y,$fot(divide(divide(B,B),A)))]]) ).
cnf(refute_0_4,plain,
divide(divide(B,B),A) = inverse(A),
inference(resolve,[$cnf( $equal(inverse(A),divide(divide(B,B),A)) )],[inverse,refute_0_3]) ).
cnf(refute_0_5,plain,
divide(divide(C,C),B) = inverse(B),
inference(subst,[],[refute_0_4:[bind(A,$fot(B)),bind(B,$fot(C))]]) ).
cnf(refute_0_6,plain,
divide(A,divide(divide(C,C),B)) = divide(A,divide(divide(C,C),B)),
introduced(tautology,[refl,[$fot(divide(A,divide(divide(C,C),B)))]]) ).
cnf(refute_0_7,plain,
( divide(A,divide(divide(C,C),B)) != divide(A,divide(divide(C,C),B))
| divide(divide(C,C),B) != inverse(B)
| divide(A,divide(divide(C,C),B)) = divide(A,inverse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(A,divide(divide(C,C),B)),divide(A,divide(divide(C,C),B))) ),[1,1],$fot(inverse(B))]]) ).
cnf(refute_0_8,plain,
( divide(divide(C,C),B) != inverse(B)
| divide(A,divide(divide(C,C),B)) = divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(divide(A,divide(divide(C,C),B)),divide(A,divide(divide(C,C),B))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
divide(A,divide(divide(C,C),B)) = divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(divide(divide(C,C),B),inverse(B)) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( multiply(A,B) != divide(A,divide(divide(C,C),B))
| divide(A,divide(divide(C,C),B)) != divide(A,inverse(B))
| multiply(A,B) = divide(A,inverse(B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(A,B),divide(A,inverse(B))) ),[0],$fot(divide(A,divide(divide(C,C),B)))]]) ).
cnf(refute_0_11,plain,
( multiply(A,B) != divide(A,divide(divide(C,C),B))
| multiply(A,B) = divide(A,inverse(B)) ),
inference(resolve,[$cnf( $equal(divide(A,divide(divide(C,C),B)),divide(A,inverse(B))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(resolve,[$cnf( $equal(multiply(A,B),divide(A,divide(divide(C,C),B))) )],[multiply,refute_0_11]) ).
cnf(refute_0_13,plain,
multiply(inverse(X_19),X_19) = divide(inverse(X_19),inverse(X_19)),
inference(subst,[],[refute_0_12:[bind(A,$fot(inverse(X_19))),bind(B,$fot(X_19))]]) ).
cnf(refute_0_14,plain,
divide(X_7,divide(divide(X_7,X_7),divide(X_8,X_7))) = X_8,
inference(subst,[],[single_axiom:[bind(A,$fot(X_7)),bind(B,$fot(X_7)),bind(C,$fot(X_8))]]) ).
cnf(refute_0_15,plain,
inverse(divide(X_8,X_7)) = divide(divide(X_7,X_7),divide(X_8,X_7)),
inference(subst,[],[inverse:[bind(A,$fot(divide(X_8,X_7))),bind(B,$fot(X_7))]]) ).
cnf(refute_0_16,plain,
( inverse(divide(X_8,X_7)) != divide(divide(X_7,X_7),divide(X_8,X_7))
| divide(divide(X_7,X_7),divide(X_8,X_7)) = inverse(divide(X_8,X_7)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(divide(X_8,X_7)))),bind(Y,$fot(divide(divide(X_7,X_7),divide(X_8,X_7))))]]) ).
cnf(refute_0_17,plain,
divide(divide(X_7,X_7),divide(X_8,X_7)) = inverse(divide(X_8,X_7)),
inference(resolve,[$cnf( $equal(inverse(divide(X_8,X_7)),divide(divide(X_7,X_7),divide(X_8,X_7))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( divide(X_7,divide(divide(X_7,X_7),divide(X_8,X_7))) != X_8
| divide(divide(X_7,X_7),divide(X_8,X_7)) != inverse(divide(X_8,X_7))
| divide(X_7,inverse(divide(X_8,X_7))) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_7,divide(divide(X_7,X_7),divide(X_8,X_7))),X_8) ),[0,1],$fot(inverse(divide(X_8,X_7)))]]) ).
cnf(refute_0_19,plain,
( divide(X_7,divide(divide(X_7,X_7),divide(X_8,X_7))) != X_8
| divide(X_7,inverse(divide(X_8,X_7))) = X_8 ),
inference(resolve,[$cnf( $equal(divide(divide(X_7,X_7),divide(X_8,X_7)),inverse(divide(X_8,X_7))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
divide(X_7,inverse(divide(X_8,X_7))) = X_8,
inference(resolve,[$cnf( $equal(divide(X_7,divide(divide(X_7,X_7),divide(X_8,X_7))),X_8) )],[refute_0_14,refute_0_19]) ).
cnf(refute_0_21,plain,
( multiply(A,B) != divide(A,inverse(B))
| divide(A,inverse(B)) = multiply(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(A,B))),bind(Y,$fot(divide(A,inverse(B))))]]) ).
cnf(refute_0_22,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(resolve,[$cnf( $equal(multiply(A,B),divide(A,inverse(B))) )],[refute_0_12,refute_0_21]) ).
cnf(refute_0_23,plain,
divide(X_7,inverse(divide(X_8,X_7))) = multiply(X_7,divide(X_8,X_7)),
inference(subst,[],[refute_0_22:[bind(A,$fot(X_7)),bind(B,$fot(divide(X_8,X_7)))]]) ).
cnf(refute_0_24,plain,
( divide(X_7,inverse(divide(X_8,X_7))) != X_8
| divide(X_7,inverse(divide(X_8,X_7))) != multiply(X_7,divide(X_8,X_7))
| multiply(X_7,divide(X_8,X_7)) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(divide(X_7,inverse(divide(X_8,X_7))),X_8) ),[0],$fot(multiply(X_7,divide(X_8,X_7)))]]) ).
cnf(refute_0_25,plain,
( divide(X_7,inverse(divide(X_8,X_7))) != X_8
| multiply(X_7,divide(X_8,X_7)) = X_8 ),
inference(resolve,[$cnf( $equal(divide(X_7,inverse(divide(X_8,X_7))),multiply(X_7,divide(X_8,X_7))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
multiply(X_7,divide(X_8,X_7)) = X_8,
inference(resolve,[$cnf( $equal(divide(X_7,inverse(divide(X_8,X_7))),X_8) )],[refute_0_20,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(X_9,divide(divide(B,B),X_9)) = divide(B,B),
inference(subst,[],[refute_0_26:[bind(X_7,$fot(X_9)),bind(X_8,$fot(divide(B,B)))]]) ).
cnf(refute_0_28,plain,
inverse(X_9) = divide(divide(B,B),X_9),
inference(subst,[],[inverse:[bind(A,$fot(X_9))]]) ).
cnf(refute_0_29,plain,
( inverse(X_9) != divide(divide(B,B),X_9)
| divide(divide(B,B),X_9) = inverse(X_9) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(inverse(X_9))),bind(Y,$fot(divide(divide(B,B),X_9)))]]) ).
cnf(refute_0_30,plain,
divide(divide(B,B),X_9) = inverse(X_9),
inference(resolve,[$cnf( $equal(inverse(X_9),divide(divide(B,B),X_9)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( multiply(X_9,divide(divide(B,B),X_9)) != divide(B,B)
| divide(divide(B,B),X_9) != inverse(X_9)
| multiply(X_9,inverse(X_9)) = divide(B,B) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_9,divide(divide(B,B),X_9)),divide(B,B)) ),[0,1],$fot(inverse(X_9))]]) ).
cnf(refute_0_32,plain,
( multiply(X_9,divide(divide(B,B),X_9)) != divide(B,B)
| multiply(X_9,inverse(X_9)) = divide(B,B) ),
inference(resolve,[$cnf( $equal(divide(divide(B,B),X_9),inverse(X_9)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
multiply(X_9,inverse(X_9)) = divide(B,B),
inference(resolve,[$cnf( $equal(multiply(X_9,divide(divide(B,B),X_9)),divide(B,B)) )],[refute_0_27,refute_0_32]) ).
cnf(refute_0_34,plain,
multiply(X_9,inverse(X_9)) = divide(inverse(X_19),inverse(X_19)),
inference(subst,[],[refute_0_33:[bind(B,$fot(inverse(X_19)))]]) ).
cnf(refute_0_35,plain,
( multiply(X_9,inverse(X_9)) != divide(inverse(X_19),inverse(X_19))
| divide(inverse(X_19),inverse(X_19)) = multiply(X_9,inverse(X_9)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(X_9,inverse(X_9)))),bind(Y,$fot(divide(inverse(X_19),inverse(X_19))))]]) ).
cnf(refute_0_36,plain,
divide(inverse(X_19),inverse(X_19)) = multiply(X_9,inverse(X_9)),
inference(resolve,[$cnf( $equal(multiply(X_9,inverse(X_9)),divide(inverse(X_19),inverse(X_19))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( multiply(inverse(X_19),X_19) != divide(inverse(X_19),inverse(X_19))
| divide(inverse(X_19),inverse(X_19)) != multiply(X_9,inverse(X_9))
| multiply(inverse(X_19),X_19) = multiply(X_9,inverse(X_9)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_19),X_19),multiply(X_9,inverse(X_9))) ),[0],$fot(divide(inverse(X_19),inverse(X_19)))]]) ).
cnf(refute_0_38,plain,
( multiply(inverse(X_19),X_19) != divide(inverse(X_19),inverse(X_19))
| multiply(inverse(X_19),X_19) = multiply(X_9,inverse(X_9)) ),
inference(resolve,[$cnf( $equal(divide(inverse(X_19),inverse(X_19)),multiply(X_9,inverse(X_9))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
multiply(inverse(X_19),X_19) = multiply(X_9,inverse(X_9)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_19),X_19),divide(inverse(X_19),inverse(X_19))) )],[refute_0_13,refute_0_38]) ).
cnf(refute_0_40,plain,
multiply(X_18,inverse(X_7)) = divide(X_18,inverse(inverse(X_7))),
inference(subst,[],[refute_0_12:[bind(A,$fot(X_18)),bind(B,$fot(inverse(X_7)))]]) ).
cnf(refute_0_41,plain,
inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))) = divide(divide(B,B),divide(divide(divide(B,B),X_7),divide(X_8,X_7))),
inference(subst,[],[inverse:[bind(A,$fot(divide(divide(divide(B,B),X_7),divide(X_8,X_7))))]]) ).
cnf(refute_0_42,plain,
divide(divide(B,B),divide(divide(divide(B,B),X_7),divide(X_8,X_7))) = X_8,
inference(subst,[],[single_axiom:[bind(A,$fot(divide(B,B))),bind(B,$fot(X_7)),bind(C,$fot(X_8))]]) ).
cnf(refute_0_43,plain,
( divide(divide(B,B),divide(divide(divide(B,B),X_7),divide(X_8,X_7))) != X_8
| inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))) != divide(divide(B,B),divide(divide(divide(B,B),X_7),divide(X_8,X_7)))
| inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))),divide(divide(B,B),divide(divide(divide(B,B),X_7),divide(X_8,X_7)))) ),[1],$fot(X_8)]]) ).
cnf(refute_0_44,plain,
( inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))) != divide(divide(B,B),divide(divide(divide(B,B),X_7),divide(X_8,X_7)))
| inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))) = X_8 ),
inference(resolve,[$cnf( $equal(divide(divide(B,B),divide(divide(divide(B,B),X_7),divide(X_8,X_7))),X_8) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))) = X_8,
inference(resolve,[$cnf( $equal(inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))),divide(divide(B,B),divide(divide(divide(B,B),X_7),divide(X_8,X_7)))) )],[refute_0_41,refute_0_44]) ).
cnf(refute_0_46,plain,
divide(divide(B,B),X_7) = inverse(X_7),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_7))]]) ).
cnf(refute_0_47,plain,
divide(divide(divide(B,B),X_7),divide(X_8,X_7)) = divide(divide(divide(B,B),X_7),divide(X_8,X_7)),
introduced(tautology,[refl,[$fot(divide(divide(divide(B,B),X_7),divide(X_8,X_7)))]]) ).
cnf(refute_0_48,plain,
( divide(divide(B,B),X_7) != inverse(X_7)
| divide(divide(divide(B,B),X_7),divide(X_8,X_7)) != divide(divide(divide(B,B),X_7),divide(X_8,X_7))
| divide(divide(divide(B,B),X_7),divide(X_8,X_7)) = divide(inverse(X_7),divide(X_8,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(B,B),X_7),divide(X_8,X_7)),divide(divide(divide(B,B),X_7),divide(X_8,X_7))) ),[1,0],$fot(inverse(X_7))]]) ).
cnf(refute_0_49,plain,
( divide(divide(B,B),X_7) != inverse(X_7)
| divide(divide(divide(B,B),X_7),divide(X_8,X_7)) = divide(inverse(X_7),divide(X_8,X_7)) ),
inference(resolve,[$cnf( $equal(divide(divide(divide(B,B),X_7),divide(X_8,X_7)),divide(divide(divide(B,B),X_7),divide(X_8,X_7))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
divide(divide(divide(B,B),X_7),divide(X_8,X_7)) = divide(inverse(X_7),divide(X_8,X_7)),
inference(resolve,[$cnf( $equal(divide(divide(B,B),X_7),inverse(X_7)) )],[refute_0_46,refute_0_49]) ).
cnf(refute_0_51,plain,
inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))) = inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))),
introduced(tautology,[refl,[$fot(inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))))]]) ).
cnf(refute_0_52,plain,
( divide(divide(divide(B,B),X_7),divide(X_8,X_7)) != divide(inverse(X_7),divide(X_8,X_7))
| inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))) != inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7)))
| inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))) = inverse(divide(inverse(X_7),divide(X_8,X_7))) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))),inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7)))) ),[1,0],$fot(divide(inverse(X_7),divide(X_8,X_7)))]]) ).
cnf(refute_0_53,plain,
( divide(divide(divide(B,B),X_7),divide(X_8,X_7)) != divide(inverse(X_7),divide(X_8,X_7))
| inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))) = inverse(divide(inverse(X_7),divide(X_8,X_7))) ),
inference(resolve,[$cnf( $equal(inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))),inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7)))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))) = inverse(divide(inverse(X_7),divide(X_8,X_7))),
inference(resolve,[$cnf( $equal(divide(divide(divide(B,B),X_7),divide(X_8,X_7)),divide(inverse(X_7),divide(X_8,X_7))) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
( inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))) != X_8
| inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))) != inverse(divide(inverse(X_7),divide(X_8,X_7)))
| inverse(divide(inverse(X_7),divide(X_8,X_7))) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))),X_8) ),[0],$fot(inverse(divide(inverse(X_7),divide(X_8,X_7))))]]) ).
cnf(refute_0_56,plain,
( inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))) != X_8
| inverse(divide(inverse(X_7),divide(X_8,X_7))) = X_8 ),
inference(resolve,[$cnf( $equal(inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))),inverse(divide(inverse(X_7),divide(X_8,X_7)))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
inverse(divide(inverse(X_7),divide(X_8,X_7))) = X_8,
inference(resolve,[$cnf( $equal(inverse(divide(divide(divide(B,B),X_7),divide(X_8,X_7))),X_8) )],[refute_0_45,refute_0_56]) ).
cnf(refute_0_58,plain,
inverse(divide(inverse(X_7),divide(X_7,X_7))) = X_7,
inference(subst,[],[refute_0_57:[bind(X_8,$fot(X_7))]]) ).
cnf(refute_0_59,plain,
multiply(X_16,inverse(X_16)) = divide(X_7,X_7),
inference(subst,[],[refute_0_33:[bind(B,$fot(X_7)),bind(X_9,$fot(X_16))]]) ).
cnf(refute_0_60,plain,
( multiply(X_16,inverse(X_16)) != divide(X_7,X_7)
| divide(X_7,X_7) = multiply(X_16,inverse(X_16)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(X_16,inverse(X_16)))),bind(Y,$fot(divide(X_7,X_7)))]]) ).
cnf(refute_0_61,plain,
divide(X_7,X_7) = multiply(X_16,inverse(X_16)),
inference(resolve,[$cnf( $equal(multiply(X_16,inverse(X_16)),divide(X_7,X_7)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
( divide(X_7,X_7) != multiply(X_16,inverse(X_16))
| inverse(divide(inverse(X_7),divide(X_7,X_7))) != X_7
| inverse(divide(inverse(X_7),multiply(X_16,inverse(X_16)))) = X_7 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(inverse(X_7),divide(X_7,X_7))),X_7) ),[0,0,1],$fot(multiply(X_16,inverse(X_16)))]]) ).
cnf(refute_0_63,plain,
( inverse(divide(inverse(X_7),divide(X_7,X_7))) != X_7
| inverse(divide(inverse(X_7),multiply(X_16,inverse(X_16)))) = X_7 ),
inference(resolve,[$cnf( $equal(divide(X_7,X_7),multiply(X_16,inverse(X_16))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
inverse(divide(inverse(X_7),multiply(X_16,inverse(X_16)))) = X_7,
inference(resolve,[$cnf( $equal(inverse(divide(inverse(X_7),divide(X_7,X_7))),X_7) )],[refute_0_58,refute_0_63]) ).
cnf(refute_0_65,plain,
divide(C,divide(divide(C,B),divide(C,B))) = C,
inference(subst,[],[single_axiom:[bind(A,$fot(C))]]) ).
cnf(refute_0_66,plain,
multiply(X_16,inverse(X_16)) = divide(divide(C,B),divide(C,B)),
inference(subst,[],[refute_0_33:[bind(B,$fot(divide(C,B))),bind(X_9,$fot(X_16))]]) ).
cnf(refute_0_67,plain,
( multiply(X_16,inverse(X_16)) != divide(divide(C,B),divide(C,B))
| divide(divide(C,B),divide(C,B)) = multiply(X_16,inverse(X_16)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(X_16,inverse(X_16)))),bind(Y,$fot(divide(divide(C,B),divide(C,B))))]]) ).
cnf(refute_0_68,plain,
divide(divide(C,B),divide(C,B)) = multiply(X_16,inverse(X_16)),
inference(resolve,[$cnf( $equal(multiply(X_16,inverse(X_16)),divide(divide(C,B),divide(C,B))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
( divide(C,divide(divide(C,B),divide(C,B))) != C
| divide(divide(C,B),divide(C,B)) != multiply(X_16,inverse(X_16))
| divide(C,multiply(X_16,inverse(X_16))) = C ),
introduced(tautology,[equality,[$cnf( $equal(divide(C,divide(divide(C,B),divide(C,B))),C) ),[0,1],$fot(multiply(X_16,inverse(X_16)))]]) ).
cnf(refute_0_70,plain,
( divide(C,divide(divide(C,B),divide(C,B))) != C
| divide(C,multiply(X_16,inverse(X_16))) = C ),
inference(resolve,[$cnf( $equal(divide(divide(C,B),divide(C,B)),multiply(X_16,inverse(X_16))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
divide(C,multiply(X_16,inverse(X_16))) = C,
inference(resolve,[$cnf( $equal(divide(C,divide(divide(C,B),divide(C,B))),C) )],[refute_0_65,refute_0_70]) ).
cnf(refute_0_72,plain,
divide(inverse(X_7),multiply(X_16,inverse(X_16))) = inverse(X_7),
inference(subst,[],[refute_0_71:[bind(C,$fot(inverse(X_7)))]]) ).
cnf(refute_0_73,plain,
inverse(divide(inverse(X_7),multiply(X_16,inverse(X_16)))) = inverse(divide(inverse(X_7),multiply(X_16,inverse(X_16)))),
introduced(tautology,[refl,[$fot(inverse(divide(inverse(X_7),multiply(X_16,inverse(X_16)))))]]) ).
cnf(refute_0_74,plain,
( divide(inverse(X_7),multiply(X_16,inverse(X_16))) != inverse(X_7)
| inverse(divide(inverse(X_7),multiply(X_16,inverse(X_16)))) != inverse(divide(inverse(X_7),multiply(X_16,inverse(X_16))))
| inverse(divide(inverse(X_7),multiply(X_16,inverse(X_16)))) = inverse(inverse(X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(inverse(X_7),multiply(X_16,inverse(X_16)))),inverse(divide(inverse(X_7),multiply(X_16,inverse(X_16))))) ),[1,0],$fot(inverse(X_7))]]) ).
cnf(refute_0_75,plain,
( divide(inverse(X_7),multiply(X_16,inverse(X_16))) != inverse(X_7)
| inverse(divide(inverse(X_7),multiply(X_16,inverse(X_16)))) = inverse(inverse(X_7)) ),
inference(resolve,[$cnf( $equal(inverse(divide(inverse(X_7),multiply(X_16,inverse(X_16)))),inverse(divide(inverse(X_7),multiply(X_16,inverse(X_16))))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
inverse(divide(inverse(X_7),multiply(X_16,inverse(X_16)))) = inverse(inverse(X_7)),
inference(resolve,[$cnf( $equal(divide(inverse(X_7),multiply(X_16,inverse(X_16))),inverse(X_7)) )],[refute_0_72,refute_0_75]) ).
cnf(refute_0_77,plain,
( inverse(divide(inverse(X_7),multiply(X_16,inverse(X_16)))) != X_7
| inverse(divide(inverse(X_7),multiply(X_16,inverse(X_16)))) != inverse(inverse(X_7))
| inverse(inverse(X_7)) = X_7 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(divide(inverse(X_7),multiply(X_16,inverse(X_16)))),X_7) ),[0],$fot(inverse(inverse(X_7)))]]) ).
cnf(refute_0_78,plain,
( inverse(divide(inverse(X_7),multiply(X_16,inverse(X_16)))) != X_7
| inverse(inverse(X_7)) = X_7 ),
inference(resolve,[$cnf( $equal(inverse(divide(inverse(X_7),multiply(X_16,inverse(X_16)))),inverse(inverse(X_7))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
inverse(inverse(X_7)) = X_7,
inference(resolve,[$cnf( $equal(inverse(divide(inverse(X_7),multiply(X_16,inverse(X_16)))),X_7) )],[refute_0_64,refute_0_78]) ).
cnf(refute_0_80,plain,
( multiply(X_18,inverse(X_7)) != divide(X_18,inverse(inverse(X_7)))
| inverse(inverse(X_7)) != X_7
| multiply(X_18,inverse(X_7)) = divide(X_18,X_7) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_18,inverse(X_7)),divide(X_18,inverse(inverse(X_7)))) ),[1,1],$fot(X_7)]]) ).
cnf(refute_0_81,plain,
( multiply(X_18,inverse(X_7)) != divide(X_18,inverse(inverse(X_7)))
| multiply(X_18,inverse(X_7)) = divide(X_18,X_7) ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_7)),X_7) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
multiply(X_18,inverse(X_7)) = divide(X_18,X_7),
inference(resolve,[$cnf( $equal(multiply(X_18,inverse(X_7)),divide(X_18,inverse(inverse(X_7)))) )],[refute_0_40,refute_0_81]) ).
cnf(refute_0_83,plain,
multiply(X_9,inverse(X_9)) = divide(X_9,X_9),
inference(subst,[],[refute_0_82:[bind(X_18,$fot(X_9)),bind(X_7,$fot(X_9))]]) ).
cnf(refute_0_84,plain,
( multiply(X_9,inverse(X_9)) != divide(X_9,X_9)
| multiply(inverse(X_19),X_19) != multiply(X_9,inverse(X_9))
| multiply(inverse(X_19),X_19) = divide(X_9,X_9) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_19),X_19),multiply(X_9,inverse(X_9))) ),[1],$fot(divide(X_9,X_9))]]) ).
cnf(refute_0_85,plain,
( multiply(inverse(X_19),X_19) != multiply(X_9,inverse(X_9))
| multiply(inverse(X_19),X_19) = divide(X_9,X_9) ),
inference(resolve,[$cnf( $equal(multiply(X_9,inverse(X_9)),divide(X_9,X_9)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
multiply(inverse(X_19),X_19) = divide(X_9,X_9),
inference(resolve,[$cnf( $equal(multiply(inverse(X_19),X_19),multiply(X_9,inverse(X_9))) )],[refute_0_39,refute_0_85]) ).
cnf(refute_0_87,plain,
multiply(inverse(a1),a1) = divide(X_27,X_27),
inference(subst,[],[refute_0_86:[bind(X_19,$fot(a1)),bind(X_9,$fot(X_27))]]) ).
cnf(refute_0_88,plain,
( multiply(inverse(a1),a1) != divide(X_27,X_27)
| divide(X_27,X_27) != multiply(inverse(b1),b1)
| multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)) ),[0],$fot(divide(X_27,X_27))]]) ).
cnf(refute_0_89,plain,
( divide(X_27,X_27) != multiply(inverse(b1),b1)
| multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),divide(X_27,X_27)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
divide(X_27,X_27) != multiply(inverse(b1),b1),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)) )],[refute_0_89,prove_these_axioms_1]) ).
cnf(refute_0_91,plain,
( multiply(inverse(X_19),X_19) != divide(X_9,X_9)
| divide(X_9,X_9) = multiply(inverse(X_19),X_19) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(multiply(inverse(X_19),X_19))),bind(Y,$fot(divide(X_9,X_9)))]]) ).
cnf(refute_0_92,plain,
divide(X_9,X_9) = multiply(inverse(X_19),X_19),
inference(resolve,[$cnf( $equal(multiply(inverse(X_19),X_19),divide(X_9,X_9)) )],[refute_0_86,refute_0_91]) ).
cnf(refute_0_93,plain,
divide(X_27,X_27) = multiply(inverse(b1),b1),
inference(subst,[],[refute_0_92:[bind(X_19,$fot(b1)),bind(X_9,$fot(X_27))]]) ).
cnf(refute_0_94,plain,
$false,
inference(resolve,[$cnf( $equal(divide(X_27,X_27),multiply(inverse(b1),b1)) )],[refute_0_93,refute_0_90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP525-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 08:59:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.40
% 0.13/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.42
%------------------------------------------------------------------------------