%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP475-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:29:50 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.47s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 3
% Syntax : Number of formulae : 64 ( 64 unt; 0 def)
% Number of atoms : 64 ( 63 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 294 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : divide(inverse(divide(divide(divide(VAR_0,VAR_1),VAR_2),divide(VAR_3,VAR_2))),divide(VAR_1,VAR_0)) = VAR_3,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(inverse(divide(divide(divide(A,B),C),divide(D,C))),divide(B,A)) = D,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = divide(VAR_0,inverse(VAR_1)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(clausify,[status(thm)],[multiply]) ).
fof(prove_these_axioms_1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('theBenchmark.p',prove_these_axioms_1) ).
cnf(c_3,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(clausify,[status(thm)],[prove_these_axioms_1]) ).
cnf(c_380,plain,
divide(inverse(a1),inverse(a1)) != multiply(inverse(b1),b1),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_381,plain,
divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1)),
inference(paramod,[status(thm)],[c_2,c_380]) ).
cnf(c_4,plain,
divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)),
inference(copy,[status(thm)],[c_381]) ).
cnf(c_5,plain,
divide(inverse(divide(divide(A,B),divide(C,B))),divide(divide(D,E),inverse(divide(divide(divide(E,D),F),divide(A,F))))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_382,plain,
divide(inverse(divide(divide(divide(A,B),divide(C,D)),E)),divide(B,A)) = inverse(divide(divide(divide(D,C),F),divide(E,F))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
inverse(divide(divide(divide(A,B),C),divide(D,C))) = divide(inverse(divide(divide(divide(E,F),divide(B,A)),D)),divide(F,E)),
inference(copy,[status(thm)],[c_382]) ).
cnf(c_7,plain,
divide(inverse(divide(divide(divide(divide(A,B),inverse(divide(divide(divide(B,A),C),divide(D,C)))),E),divide(F,E))),D) = F,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_11,plain,
divide(divide(inverse(divide(divide(divide(A,B),divide(C,D)),E)),divide(B,A)),divide(C,D)) = E,
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_13,plain,
inverse(divide(divide(divide(A,B),C),divide(divide(D,divide(B,A)),C))) = D,
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_22,plain,
divide(A,divide(divide(B,C),inverse(divide(divide(divide(C,B),D),divide(divide(E,F),D))))) = divide(A,divide(F,E)),
inference(paramod,[status(thm)],[c_13,c_5]) ).
cnf(c_383,plain,
divide(divide(inverse(divide(divide(divide(A,B),C),D)),divide(B,A)),divide(inverse(divide(divide(divide(E,F),V6),divide(C,V6))),divide(F,E))) = D,
inference(paramod,[status(thm)],[c_1,c_11]) ).
cnf(c_44,plain,
divide(divide(inverse(divide(divide(divide(A,B),C),D)),divide(B,A)),C) = D,
inference(paramod,[status(thm)],[c_1,c_383]) ).
cnf(c_57,plain,
divide(inverse(divide(divide(divide(A,B),C),D)),divide(B,A)) = divide(inverse(divide(divide(divide(E,F),C),D)),divide(F,E)),
inference(paramod,[status(thm)],[c_44,c_1]) ).
cnf(c_121,plain,
divide(inverse(divide(divide(divide(A,B),inverse(divide(divide(divide(C,D),E),divide(divide(F,V6),E)))),divide(V6,F))),divide(B,A)) = divide(D,C),
inference(paramod,[status(thm)],[c_22,c_1]) ).
cnf(c_384,plain,
divide(divide(inverse(divide(divide(divide(A,B),C),divide(D,E))),divide(B,A)),C) = divide(divide(F,V6),inverse(divide(divide(divide(V6,F),V7),divide(divide(E,D),V7)))),
inference(paramod,[status(thm)],[c_22,c_44]) ).
cnf(c_385,plain,
divide(D,E) = divide(divide(F,V6),inverse(divide(divide(divide(V6,F),V7),divide(divide(E,D),V7)))),
inference(paramod,[status(thm)],[c_44,c_384]) ).
cnf(c_133,plain,
divide(divide(A,B),inverse(divide(divide(divide(B,A),C),divide(divide(D,E),C)))) = divide(E,D),
inference(copy,[status(thm)],[c_385]) ).
cnf(c_386,plain,
divide(inverse(divide(divide(A,B),C)),divide(D,E)) = divide(inverse(divide(divide(divide(F,V6),inverse(divide(divide(divide(D,E),V7),divide(divide(B,A),V7)))),C)),divide(V6,F)),
inference(paramod,[status(thm)],[c_133,c_57]) ).
cnf(c_171,plain,
divide(inverse(divide(divide(divide(A,B),inverse(divide(divide(divide(C,D),E),divide(divide(F,V6),E)))),V7)),divide(B,A)) = divide(inverse(divide(divide(V6,F),V7)),divide(C,D)),
inference(copy,[status(thm)],[c_386]) ).
cnf(c_182,plain,
divide(inverse(divide(divide(A,B),divide(A,B))),divide(C,D)) = divide(D,C),
inference(paramod,[status(thm)],[c_171,c_121]) ).
cnf(c_387,plain,
divide(inverse(divide(A,divide(inverse(divide(divide(divide(B,C),D),divide(A,D))),divide(C,B)))),divide(E,F)) = divide(F,E),
inference(paramod,[status(thm)],[c_1,c_182]) ).
cnf(c_186,plain,
divide(inverse(divide(A,A)),divide(B,C)) = divide(C,B),
inference(paramod,[status(thm)],[c_1,c_387]) ).
cnf(c_388,plain,
divide(inverse(divide(divide(divide(divide(A,B),inverse(divide(divide(divide(B,A),C),divide(D,C)))),divide(E,F)),divide(F,E))),D) = inverse(divide(V6,V6)),
inference(paramod,[status(thm)],[c_186,c_7]) ).
cnf(c_259,plain,
inverse(divide(A,A)) = divide(inverse(divide(divide(divide(divide(B,C),inverse(divide(divide(divide(C,B),D),divide(E,D)))),divide(F,V6)),divide(V6,F))),E),
inference(copy,[status(thm)],[c_388]) ).
cnf(c_389,plain,
divide(divide(A,B),inverse(divide(divide(divide(B,A),C),divide(divide(D,E),C)))) = divide(divide(E,D),inverse(divide(F,F))),
inference(paramod,[status(thm)],[c_186,c_133]) ).
cnf(c_390,plain,
divide(E,D) = divide(divide(E,D),inverse(divide(F,F))),
inference(paramod,[status(thm)],[c_133,c_389]) ).
cnf(c_274,plain,
divide(divide(A,B),inverse(divide(C,C))) = divide(A,B),
inference(copy,[status(thm)],[c_390]) ).
cnf(c_391,plain,
divide(A,inverse(divide(B,B))) = divide(inverse(divide(divide(divide(C,D),E),divide(A,E))),divide(D,C)),
inference(paramod,[status(thm)],[c_1,c_274]) ).
cnf(c_278,plain,
divide(A,inverse(divide(B,B))) = A,
inference(paramod,[status(thm)],[c_1,c_391]) ).
cnf(c_392,plain,
divide(inverse(divide(divide(A,B),divide(C,inverse(divide(D,D))))),divide(divide(E,F),inverse(divide(divide(divide(F,E),V6),divide(divide(A,B),V6))))) = C,
inference(paramod,[status(thm)],[c_274,c_5]) ).
cnf(c_393,plain,
divide(inverse(divide(divide(A,B),C)),divide(divide(E,F),inverse(divide(divide(divide(F,E),V6),divide(divide(A,B),V6))))) = C,
inference(paramod,[status(thm)],[c_278,c_392]) ).
cnf(c_279,plain,
divide(inverse(divide(divide(A,B),C)),divide(B,A)) = C,
inference(paramod,[status(thm)],[c_133,c_393]) ).
cnf(c_394,plain,
inverse(divide(divide(A,B),divide(C,inverse(divide(D,D))))) = divide(inverse(divide(divide(divide(E,F),divide(B,A)),C)),divide(F,E)),
inference(paramod,[status(thm)],[c_274,c_6]) ).
cnf(c_395,plain,
inverse(divide(divide(A,B),C)) = divide(inverse(divide(divide(divide(E,F),divide(B,A)),C)),divide(F,E)),
inference(paramod,[status(thm)],[c_278,c_394]) ).
cnf(c_282,plain,
divide(inverse(divide(divide(divide(A,B),divide(C,D)),E)),divide(B,A)) = inverse(divide(divide(D,C),E)),
inference(copy,[status(thm)],[c_395]) ).
cnf(c_396,plain,
inverse(divide(divide(divide(A,B),C),divide(D,C))) = divide(inverse(divide(divide(divide(E,F),divide(B,A)),D)),divide(inverse(divide(V6,V6)),divide(E,F))),
inference(paramod,[status(thm)],[c_274,c_6]) ).
cnf(c_397,plain,
inverse(divide(divide(divide(A,B),C),divide(D,C))) = divide(inverse(divide(divide(divide(E,F),divide(B,A)),D)),divide(F,E)),
inference(paramod,[status(thm)],[c_186,c_396]) ).
cnf(c_283,plain,
inverse(divide(divide(divide(A,B),C),divide(D,C))) = inverse(divide(divide(A,B),D)),
inference(paramod,[status(thm)],[c_282,c_397]) ).
cnf(c_398,plain,
inverse(divide(divide(divide(A,B),C),divide(inverse(divide(D,D)),C))) = divide(inverse(divide(divide(E,F),divide(B,A))),divide(F,E)),
inference(paramod,[status(thm)],[c_274,c_6]) ).
cnf(c_399,plain,
inverse(divide(divide(A,B),inverse(divide(D,D)))) = divide(inverse(divide(divide(E,F),divide(B,A))),divide(F,E)),
inference(paramod,[status(thm)],[c_283,c_398]) ).
cnf(c_400,plain,
inverse(divide(A,B)) = divide(inverse(divide(divide(E,F),divide(B,A))),divide(F,E)),
inference(paramod,[status(thm)],[c_278,c_399]) ).
cnf(c_284,plain,
inverse(divide(A,B)) = divide(B,A),
inference(paramod,[status(thm)],[c_279,c_400]) ).
cnf(c_401,plain,
divide(inverse(divide(divide(divide(A,B),inverse(divide(C,C))),D)),divide(B,A)) = D,
inference(paramod,[status(thm)],[c_274,c_44]) ).
cnf(c_402,plain,
divide(inverse(divide(divide(divide(A,B),divide(C,C)),D)),divide(B,A)) = D,
inference(paramod,[status(thm)],[c_284,c_401]) ).
cnf(c_304,plain,
divide(divide(A,divide(divide(B,C),divide(D,D))),divide(C,B)) = A,
inference(paramod,[status(thm)],[c_284,c_402]) ).
cnf(c_403,plain,
divide(inverse(divide(divide(divide(A,B),C),divide(D,C))),divide(B,A)) = D,
inference(paramod,[status(thm)],[c_274,c_7]) ).
cnf(c_311,plain,
divide(divide(divide(A,B),divide(divide(C,D),B)),divide(D,C)) = A,
inference(paramod,[status(thm)],[c_284,c_403]) ).
cnf(c_404,plain,
divide(inverse(divide(divide(A,B),C)),divide(B,A)) = divide(inverse(divide(divide(divide(D,E),inverse(divide(F,F))),C)),divide(E,D)),
inference(paramod,[status(thm)],[c_274,c_57]) ).
cnf(c_405,plain,
divide(divide(C,divide(A,B)),divide(B,A)) = divide(inverse(divide(divide(divide(D,E),inverse(divide(F,F))),C)),divide(E,D)),
inference(paramod,[status(thm)],[c_284,c_404]) ).
cnf(c_406,plain,
divide(divide(C,divide(A,B)),divide(B,A)) = divide(inverse(divide(divide(divide(D,E),divide(F,F)),C)),divide(E,D)),
inference(paramod,[status(thm)],[c_284,c_405]) ).
cnf(c_407,plain,
divide(divide(C,divide(A,B)),divide(B,A)) = divide(divide(C,divide(divide(D,E),divide(F,F))),divide(E,D)),
inference(paramod,[status(thm)],[c_284,c_406]) ).
cnf(c_324,plain,
divide(divide(A,divide(B,C)),divide(C,B)) = A,
inference(paramod,[status(thm)],[c_304,c_407]) ).
cnf(c_408,plain,
divide(A,A) = divide(inverse(divide(divide(divide(divide(B,C),inverse(divide(divide(divide(C,B),D),divide(E,D)))),divide(F,V6)),divide(V6,F))),E),
inference(paramod,[status(thm)],[c_284,c_259]) ).
cnf(c_409,plain,
divide(A,A) = divide(inverse(divide(divide(divide(divide(B,C),divide(divide(E,D),divide(divide(C,B),D))),divide(F,V6)),divide(V6,F))),E),
inference(paramod,[status(thm)],[c_284,c_408]) ).
cnf(c_410,plain,
divide(A,A) = divide(inverse(divide(divide(B,C),divide(divide(E,D),divide(divide(C,B),D)))),E),
inference(paramod,[status(thm)],[c_324,c_409]) ).
cnf(c_411,plain,
divide(A,A) = divide(divide(divide(divide(E,D),divide(divide(C,B),D)),divide(B,C)),E),
inference(paramod,[status(thm)],[c_284,c_410]) ).
cnf(c_378,plain,
divide(A,A) = divide(B,B),
inference(paramod,[status(thm)],[c_311,c_411]) ).
cnf(c_379,plain,
$false,
inference(resolve,[status(thm)],[c_378,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP475-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n007.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 14:53:54 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 1277386 was started by sandbox2 on n007,
% 0.07/0.35 % Fri Sep 25 14:53:54 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 0.12/0.47
% 0.12/0.47 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.12/0.47
% 0.12/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.47
% 0.12/0.47 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.12/0.47 % Length of proof is 29.
% 0.12/0.47 % Level of proof is 16.
% 0.12/0.47 % Maximum clause weight is 97.000.
% 0.12/0.47 % Given clauses 20.
% 0.12/0.47
% 0.12/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------