TSTP Solution File: GRP466-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP466-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 10:40:49 EDT 2022
% Result : Unsatisfiable 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of clauses : 47 ( 27 unt; 0 nHn; 21 RR)
% Number of literals : 76 ( 75 equ; 31 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 : 140 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))) = C ).
cnf(multiply,axiom,
multiply(A,B) = divide(A,inverse(B)) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ).
cnf(refute_0_0,plain,
multiply(inverse(B),B) = divide(inverse(B),inverse(B)),
inference(subst,[],[multiply:[bind(A,$fot(inverse(B)))]]) ).
cnf(refute_0_1,plain,
X = X,
introduced(tautology,[refl,[$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( $equal(multiply(A,B),divide(A,inverse(B))) )],[multiply,refute_0_4]) ).
cnf(refute_0_6,plain,
divide(divide(C,divide(D,B)),inverse(D)) = multiply(divide(C,divide(D,B)),D),
inference(subst,[],[refute_0_5:[bind(A,$fot(divide(C,divide(D,B)))),bind(B,$fot(D))]]) ).
cnf(refute_0_7,plain,
divide(B,divide(divide(C,divide(D,B)),inverse(D))) = divide(B,divide(divide(C,divide(D,B)),inverse(D))),
introduced(tautology,[refl,[$fot(divide(B,divide(divide(C,divide(D,B)),inverse(D))))]]) ).
cnf(refute_0_8,plain,
( divide(B,divide(divide(C,divide(D,B)),inverse(D))) != divide(B,divide(divide(C,divide(D,B)),inverse(D)))
| divide(divide(C,divide(D,B)),inverse(D)) != multiply(divide(C,divide(D,B)),D)
| divide(B,divide(divide(C,divide(D,B)),inverse(D))) = divide(B,multiply(divide(C,divide(D,B)),D)) ),
introduced(tautology,[equality,[$cnf( $equal(divide(B,divide(divide(C,divide(D,B)),inverse(D))),divide(B,divide(divide(C,divide(D,B)),inverse(D)))) ),[1,1],$fot(multiply(divide(C,divide(D,B)),D))]]) ).
cnf(refute_0_9,plain,
( divide(divide(C,divide(D,B)),inverse(D)) != multiply(divide(C,divide(D,B)),D)
| divide(B,divide(divide(C,divide(D,B)),inverse(D))) = divide(B,multiply(divide(C,divide(D,B)),D)) ),
inference(resolve,[$cnf( $equal(divide(B,divide(divide(C,divide(D,B)),inverse(D))),divide(B,divide(divide(C,divide(D,B)),inverse(D)))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
divide(B,divide(divide(C,divide(D,B)),inverse(D))) = divide(B,multiply(divide(C,divide(D,B)),D)),
inference(resolve,[$cnf( $equal(divide(divide(C,divide(D,B)),inverse(D)),multiply(divide(C,divide(D,B)),D)) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))) = divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))),
introduced(tautology,[refl,[$fot(divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))))]]) ).
cnf(refute_0_12,plain,
( divide(B,divide(divide(C,divide(D,B)),inverse(D))) != divide(B,multiply(divide(C,divide(D,B)),D))
| divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))) != divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D))))
| divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))) = divide(divide(A,A),divide(B,multiply(divide(C,divide(D,B)),D))) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))),divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D))))) ),[1,1],$fot(divide(B,multiply(divide(C,divide(D,B)),D)))]]) ).
cnf(refute_0_13,plain,
( divide(B,divide(divide(C,divide(D,B)),inverse(D))) != divide(B,multiply(divide(C,divide(D,B)),D))
| divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))) = divide(divide(A,A),divide(B,multiply(divide(C,divide(D,B)),D))) ),
inference(resolve,[$cnf( $equal(divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))),divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D))))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))) = divide(divide(A,A),divide(B,multiply(divide(C,divide(D,B)),D))),
inference(resolve,[$cnf( $equal(divide(B,divide(divide(C,divide(D,B)),inverse(D))),divide(B,multiply(divide(C,divide(D,B)),D))) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
( divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))) != C
| divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))) != divide(divide(A,A),divide(B,multiply(divide(C,divide(D,B)),D)))
| divide(divide(A,A),divide(B,multiply(divide(C,divide(D,B)),D))) = C ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))),C) ),[0],$fot(divide(divide(A,A),divide(B,multiply(divide(C,divide(D,B)),D))))]]) ).
cnf(refute_0_16,plain,
( divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))) != C
| divide(divide(A,A),divide(B,multiply(divide(C,divide(D,B)),D))) = C ),
inference(resolve,[$cnf( $equal(divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))),divide(divide(A,A),divide(B,multiply(divide(C,divide(D,B)),D)))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
divide(divide(A,A),divide(B,multiply(divide(C,divide(D,B)),D))) = C,
inference(resolve,[$cnf( $equal(divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))),C) )],[single_axiom,refute_0_16]) ).
cnf(refute_0_18,plain,
divide(divide(X_2,X_2),divide(multiply(divide(C,divide(D,X_5)),D),multiply(divide(divide(A,A),divide(X_5,multiply(divide(C,divide(D,X_5)),D))),X_5))) = divide(A,A),
inference(subst,[],[refute_0_17:[bind(A,$fot(X_2)),bind(B,$fot(multiply(divide(C,divide(D,X_5)),D))),bind(C,$fot(divide(A,A))),bind(D,$fot(X_5))]]) ).
cnf(refute_0_19,plain,
divide(divide(A,A),divide(X_5,multiply(divide(C,divide(D,X_5)),D))) = C,
inference(subst,[],[refute_0_17:[bind(B,$fot(X_5))]]) ).
cnf(refute_0_20,plain,
( divide(divide(A,A),divide(X_5,multiply(divide(C,divide(D,X_5)),D))) != C
| divide(divide(X_2,X_2),divide(multiply(divide(C,divide(D,X_5)),D),multiply(divide(divide(A,A),divide(X_5,multiply(divide(C,divide(D,X_5)),D))),X_5))) != divide(A,A)
| divide(divide(X_2,X_2),divide(multiply(divide(C,divide(D,X_5)),D),multiply(C,X_5))) = divide(A,A) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X_2,X_2),divide(multiply(divide(C,divide(D,X_5)),D),multiply(divide(divide(A,A),divide(X_5,multiply(divide(C,divide(D,X_5)),D))),X_5))),divide(A,A)) ),[0,1,1,0],$fot(C)]]) ).
cnf(refute_0_21,plain,
( divide(divide(X_2,X_2),divide(multiply(divide(C,divide(D,X_5)),D),multiply(divide(divide(A,A),divide(X_5,multiply(divide(C,divide(D,X_5)),D))),X_5))) != divide(A,A)
| divide(divide(X_2,X_2),divide(multiply(divide(C,divide(D,X_5)),D),multiply(C,X_5))) = divide(A,A) ),
inference(resolve,[$cnf( $equal(divide(divide(A,A),divide(X_5,multiply(divide(C,divide(D,X_5)),D))),C) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
divide(divide(X_2,X_2),divide(multiply(divide(C,divide(D,X_5)),D),multiply(C,X_5))) = divide(A,A),
inference(resolve,[$cnf( $equal(divide(divide(X_2,X_2),divide(multiply(divide(C,divide(D,X_5)),D),multiply(divide(divide(A,A),divide(X_5,multiply(divide(C,divide(D,X_5)),D))),X_5))),divide(A,A)) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
divide(divide(A,A),divide(multiply(divide(X_4,divide(X_5,D)),X_5),multiply(divide(divide(X_2,X_2),divide(D,multiply(divide(X_4,divide(X_5,D)),X_5))),D))) = divide(X_2,X_2),
inference(subst,[],[refute_0_17:[bind(B,$fot(multiply(divide(X_4,divide(X_5,D)),X_5))),bind(C,$fot(divide(X_2,X_2)))]]) ).
cnf(refute_0_24,plain,
divide(divide(X_2,X_2),divide(D,multiply(divide(X_4,divide(X_5,D)),X_5))) = X_4,
inference(subst,[],[refute_0_17:[bind(A,$fot(X_2)),bind(B,$fot(D)),bind(C,$fot(X_4)),bind(D,$fot(X_5))]]) ).
cnf(refute_0_25,plain,
( divide(divide(A,A),divide(multiply(divide(X_4,divide(X_5,D)),X_5),multiply(divide(divide(X_2,X_2),divide(D,multiply(divide(X_4,divide(X_5,D)),X_5))),D))) != divide(X_2,X_2)
| divide(divide(X_2,X_2),divide(D,multiply(divide(X_4,divide(X_5,D)),X_5))) != X_4
| divide(divide(A,A),divide(multiply(divide(X_4,divide(X_5,D)),X_5),multiply(X_4,D))) = divide(X_2,X_2) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(A,A),divide(multiply(divide(X_4,divide(X_5,D)),X_5),multiply(divide(divide(X_2,X_2),divide(D,multiply(divide(X_4,divide(X_5,D)),X_5))),D))),divide(X_2,X_2)) ),[0,1,1,0],$fot(X_4)]]) ).
cnf(refute_0_26,plain,
( divide(divide(A,A),divide(multiply(divide(X_4,divide(X_5,D)),X_5),multiply(divide(divide(X_2,X_2),divide(D,multiply(divide(X_4,divide(X_5,D)),X_5))),D))) != divide(X_2,X_2)
| divide(divide(A,A),divide(multiply(divide(X_4,divide(X_5,D)),X_5),multiply(X_4,D))) = divide(X_2,X_2) ),
inference(resolve,[$cnf( $equal(divide(divide(X_2,X_2),divide(D,multiply(divide(X_4,divide(X_5,D)),X_5))),X_4) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
divide(divide(A,A),divide(multiply(divide(X_4,divide(X_5,D)),X_5),multiply(X_4,D))) = divide(X_2,X_2),
inference(resolve,[$cnf( $equal(divide(divide(A,A),divide(multiply(divide(X_4,divide(X_5,D)),X_5),multiply(divide(divide(X_2,X_2),divide(D,multiply(divide(X_4,divide(X_5,D)),X_5))),D))),divide(X_2,X_2)) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
divide(divide(X_2,X_2),divide(multiply(divide(C,divide(D,X_5)),D),multiply(C,X_5))) = divide(X_2,X_2),
inference(subst,[],[refute_0_27:[bind(A,$fot(X_2)),bind(D,$fot(X_5)),bind(X_4,$fot(C)),bind(X_5,$fot(D))]]) ).
cnf(refute_0_29,plain,
( divide(divide(X_2,X_2),divide(multiply(divide(C,divide(D,X_5)),D),multiply(C,X_5))) != divide(A,A)
| divide(divide(X_2,X_2),divide(multiply(divide(C,divide(D,X_5)),D),multiply(C,X_5))) != divide(X_2,X_2)
| divide(X_2,X_2) = divide(A,A) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(X_2,X_2),divide(multiply(divide(C,divide(D,X_5)),D),multiply(C,X_5))),divide(A,A)) ),[0],$fot(divide(X_2,X_2))]]) ).
cnf(refute_0_30,plain,
( divide(divide(X_2,X_2),divide(multiply(divide(C,divide(D,X_5)),D),multiply(C,X_5))) != divide(A,A)
| divide(X_2,X_2) = divide(A,A) ),
inference(resolve,[$cnf( $equal(divide(divide(X_2,X_2),divide(multiply(divide(C,divide(D,X_5)),D),multiply(C,X_5))),divide(X_2,X_2)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
divide(X_2,X_2) = divide(A,A),
inference(resolve,[$cnf( $equal(divide(divide(X_2,X_2),divide(multiply(divide(C,divide(D,X_5)),D),multiply(C,X_5))),divide(A,A)) )],[refute_0_22,refute_0_30]) ).
cnf(refute_0_32,plain,
divide(inverse(B),inverse(B)) = divide(X_6,X_6),
inference(subst,[],[refute_0_31:[bind(A,$fot(X_6)),bind(X_2,$fot(inverse(B)))]]) ).
cnf(refute_0_33,plain,
( multiply(inverse(B),B) != divide(inverse(B),inverse(B))
| divide(inverse(B),inverse(B)) != divide(X_6,X_6)
| multiply(inverse(B),B) = divide(X_6,X_6) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(B),B),divide(X_6,X_6)) ),[0],$fot(divide(inverse(B),inverse(B)))]]) ).
cnf(refute_0_34,plain,
( multiply(inverse(B),B) != divide(inverse(B),inverse(B))
| multiply(inverse(B),B) = divide(X_6,X_6) ),
inference(resolve,[$cnf( $equal(divide(inverse(B),inverse(B)),divide(X_6,X_6)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
multiply(inverse(B),B) = divide(X_6,X_6),
inference(resolve,[$cnf( $equal(multiply(inverse(B),B),divide(inverse(B),inverse(B))) )],[refute_0_0,refute_0_34]) ).
cnf(refute_0_36,plain,
multiply(inverse(a1),a1) = divide(X_9,X_9),
inference(subst,[],[refute_0_35:[bind(B,$fot(a1)),bind(X_6,$fot(X_9))]]) ).
cnf(refute_0_37,plain,
( multiply(inverse(a1),a1) != divide(X_9,X_9)
| divide(X_9,X_9) != multiply(inverse(b1),b1)
| multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)) ),[0],$fot(divide(X_9,X_9))]]) ).
cnf(refute_0_38,plain,
( divide(X_9,X_9) != multiply(inverse(b1),b1)
| multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),divide(X_9,X_9)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
divide(X_9,X_9) != multiply(inverse(b1),b1),
inference(resolve,[$cnf( $equal(multiply(inverse(a1),a1),multiply(inverse(b1),b1)) )],[refute_0_38,prove_these_axioms_1]) ).
cnf(refute_0_40,plain,
( multiply(inverse(B),B) != divide(X_6,X_6)
| divide(X_6,X_6) = multiply(inverse(B),B) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(multiply(inverse(B),B))),bind(Y,$fot(divide(X_6,X_6)))]]) ).
cnf(refute_0_41,plain,
divide(X_6,X_6) = multiply(inverse(B),B),
inference(resolve,[$cnf( $equal(multiply(inverse(B),B),divide(X_6,X_6)) )],[refute_0_35,refute_0_40]) ).
cnf(refute_0_42,plain,
divide(X_9,X_9) = multiply(inverse(b1),b1),
inference(subst,[],[refute_0_41:[bind(B,$fot(b1)),bind(X_6,$fot(X_9))]]) ).
cnf(refute_0_43,plain,
$false,
inference(resolve,[$cnf( $equal(divide(X_9,X_9),multiply(inverse(b1),b1)) )],[refute_0_42,refute_0_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP466-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 09:38:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------