%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP063-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 07:26:54 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.48s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 4
% Syntax : Number of formulae : 71 ( 57 unt; 0 def)
% Number of atoms : 97 ( 96 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 67 ( 41 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 129 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(VAR_0,divide(divide(divide(divide(VAR_0,VAR_0),VAR_1),VAR_2),divide(divide(divide(VAR_0,VAR_0),VAR_0),VAR_2))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(A,divide(divide(divide(divide(A,A),B),C),divide(divide(divide(A,A),A),C))) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,VAR_1) = divide(VAR_0,divide(divide(VAR_2,VAR_2),VAR_1)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
inference(clausify,[status(thm)],[multiply]) ).
fof(inverse,axiom,
! [VAR_0,VAR_1] : inverse(VAR_0) = divide(divide(VAR_1,VAR_1),VAR_0),
file('theBenchmark.p',inverse) ).
cnf(c_3,plain,
inverse(A) = divide(divide(B,B),A),
inference(clausify,[status(thm)],[inverse]) ).
cnf(c_4,plain,
divide(divide(A,A),B) = inverse(B),
inference(copy,[status(thm)],[c_3]) ).
fof(prove_these_axioms,axiom,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('theBenchmark.p',prove_these_axioms) ).
cnf(c_5,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(clausify,[status(thm)],[prove_these_axioms]) ).
cnf(c_6,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ),
inference(copy,[status(thm)],[c_5]) ).
cnf(c_7,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_256,plain,
divide(A,divide(divide(inverse(B),C),divide(divide(divide(A,A),A),C))) = B,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_8,plain,
divide(A,divide(divide(inverse(B),C),divide(inverse(A),C))) = B,
inference(paramod,[status(thm)],[c_4,c_256]) ).
cnf(c_257,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| divide(inverse(b1),inverse(b1)) != multiply(inverse(a1),a1) ),
inference(paramod,[status(thm)],[c_7,c_6]) ).
cnf(c_258,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_7,c_257]) ).
cnf(c_259,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(divide(inverse(b2),inverse(b2)),a2) != a2
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_7,c_258]) ).
cnf(c_260,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_7,c_259]) ).
cnf(c_261,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_4,c_260]) ).
cnf(c_262,plain,
( multiply(divide(a3,inverse(b3)),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_7,c_261]) ).
cnf(c_263,plain,
( divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_7,c_262]) ).
cnf(c_264,plain,
( divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,divide(b3,inverse(c3)))
| inverse(inverse(a2)) != a2
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_7,c_263]) ).
cnf(c_9,plain,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| inverse(inverse(a2)) != a2
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_7,c_264]) ).
cnf(c_10,plain,
divide(inverse(divide(A,A)),B) = inverse(B),
inference(paramod,[status(thm)],[c_4,c_4]) ).
cnf(c_265,plain,
A = inverse(divide(divide(inverse(A),B),divide(inverse(divide(C,C)),B))),
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_266,plain,
A = inverse(divide(divide(inverse(A),B),inverse(B))),
inference(paramod,[status(thm)],[c_10,c_265]) ).
cnf(c_11,plain,
inverse(divide(divide(inverse(A),B),inverse(B))) = A,
inference(copy,[status(thm)],[c_266]) ).
cnf(c_12,plain,
divide(A,inverse(divide(inverse(A),inverse(B)))) = B,
inference(paramod,[status(thm)],[c_4,c_8]) ).
cnf(c_13,plain,
divide(A,divide(B,divide(inverse(A),divide(divide(inverse(B),C),divide(inverse(inverse(D)),C))))) = D,
inference(paramod,[status(thm)],[c_8,c_8]) ).
cnf(c_14,plain,
divide(A,divide(divide(inverse(B),divide(divide(inverse(C),D),divide(inverse(inverse(A)),D))),C)) = B,
inference(paramod,[status(thm)],[c_8,c_8]) ).
cnf(c_15,plain,
divide(inverse(inverse(divide(A,A))),B) = inverse(B),
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_18,plain,
inverse(inverse(inverse(inverse(A)))) = A,
inference(paramod,[status(thm)],[c_4,c_11]) ).
cnf(c_22,plain,
inverse(divide(inverse(A),inverse(A))) = divide(B,B),
inference(paramod,[status(thm)],[c_10,c_11]) ).
cnf(c_30,plain,
divide(inverse(inverse(inverse(A))),inverse(divide(A,inverse(B)))) = B,
inference(paramod,[status(thm)],[c_18,c_12]) ).
cnf(c_267,plain,
divide(A,inverse(B)) = divide(inverse(inverse(A)),inverse(B)),
inference(paramod,[status(thm)],[c_12,c_12]) ).
cnf(c_32,plain,
divide(inverse(inverse(A)),inverse(B)) = divide(A,inverse(B)),
inference(copy,[status(thm)],[c_267]) ).
cnf(c_33,plain,
divide(inverse(A),inverse(divide(A,inverse(B)))) = B,
inference(paramod,[status(thm)],[c_32,c_30]) ).
cnf(c_268,plain,
divide(A,divide(B,divide(inverse(A),inverse(divide(inverse(inverse(C)),inverse(B)))))) = C,
inference(paramod,[status(thm)],[c_4,c_13]) ).
cnf(c_34,plain,
divide(A,divide(B,divide(inverse(A),inverse(divide(C,inverse(B)))))) = C,
inference(paramod,[status(thm)],[c_32,c_268]) ).
cnf(c_269,plain,
inverse(divide(A,inverse(inverse(inverse(inverse(A)))))) = divide(B,B),
inference(paramod,[status(thm)],[c_18,c_22]) ).
cnf(c_47,plain,
inverse(divide(A,A)) = divide(B,B),
inference(paramod,[status(thm)],[c_18,c_269]) ).
cnf(c_270,plain,
inverse(inverse(inverse(inverse(divide(A,A))))) = divide(B,B),
inference(paramod,[status(thm)],[c_15,c_22]) ).
cnf(c_49,plain,
divide(A,A) = divide(B,B),
inference(paramod,[status(thm)],[c_18,c_270]) ).
cnf(c_51,plain,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| inverse(inverse(a2)) != a2 ),
inference(resolve,[status(thm)],[c_49,c_9]) ).
cnf(c_52,plain,
inverse(divide(A,A)) = inverse(divide(B,B)),
inference(paramod,[status(thm)],[c_47,c_4]) ).
cnf(c_271,plain,
multiply(A,divide(B,B)) = divide(A,divide(C,C)),
inference(paramod,[status(thm)],[c_47,c_7]) ).
cnf(c_53,plain,
divide(A,inverse(divide(B,B))) = divide(A,divide(C,C)),
inference(paramod,[status(thm)],[c_7,c_271]) ).
cnf(c_71,plain,
divide(A,divide(divide(inverse(B),inverse(divide(C,C))),inverse(A))) = B,
inference(paramod,[status(thm)],[c_47,c_14]) ).
cnf(c_272,plain,
divide(inverse(inverse(A)),inverse(divide(B,B))) = A,
inference(paramod,[status(thm)],[c_49,c_33]) ).
cnf(c_78,plain,
divide(A,inverse(divide(B,B))) = A,
inference(paramod,[status(thm)],[c_32,c_272]) ).
cnf(c_273,plain,
divide(inverse(inverse(A)),inverse(divide(B,B))) = A,
inference(paramod,[status(thm)],[c_52,c_33]) ).
cnf(c_82,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_78,c_273]) ).
cnf(c_83,plain,
divide(A,divide(inverse(B),inverse(A))) = B,
inference(paramod,[status(thm)],[c_78,c_71]) ).
cnf(c_274,plain,
A = divide(A,divide(C,C)),
inference(paramod,[status(thm)],[c_78,c_53]) ).
cnf(c_86,plain,
divide(A,divide(B,B)) = A,
inference(copy,[status(thm)],[c_274]) ).
cnf(c_275,plain,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_82,c_51]) ).
cnf(c_94,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(copy,[status(thm)],[c_275]) ).
cnf(c_118,plain,
divide(A,divide(B,inverse(A))) = inverse(B),
inference(paramod,[status(thm)],[c_82,c_83]) ).
cnf(c_276,plain,
divide(divide(A,inverse(B)),divide(B,divide(C,C))) = A,
inference(paramod,[status(thm)],[c_49,c_34]) ).
cnf(c_122,plain,
divide(divide(A,inverse(B)),B) = A,
inference(paramod,[status(thm)],[c_86,c_276]) ).
cnf(c_277,plain,
multiply(divide(A,inverse(inverse(B))),B) = A,
inference(paramod,[status(thm)],[c_122,c_7]) ).
cnf(c_278,plain,
multiply(divide(A,B),B) = A,
inference(paramod,[status(thm)],[c_82,c_277]) ).
cnf(c_125,plain,
divide(divide(A,B),inverse(B)) = A,
inference(paramod,[status(thm)],[c_7,c_278]) ).
cnf(c_279,plain,
divide(A,B) = inverse(divide(B,inverse(inverse(A)))),
inference(paramod,[status(thm)],[c_122,c_118]) ).
cnf(c_280,plain,
divide(A,B) = inverse(divide(B,A)),
inference(paramod,[status(thm)],[c_82,c_279]) ).
cnf(c_126,plain,
inverse(divide(A,B)) = divide(B,A),
inference(copy,[status(thm)],[c_280]) ).
cnf(c_143,plain,
divide(inverse(divide(inverse(A),B)),A) = B,
inference(paramod,[status(thm)],[c_126,c_122]) ).
cnf(c_281,plain,
divide(divide(inverse(inverse(divide(A,inverse(B)))),C),divide(B,C)) = A,
inference(paramod,[status(thm)],[c_143,c_34]) ).
cnf(c_160,plain,
divide(divide(divide(A,inverse(B)),C),divide(B,C)) = A,
inference(paramod,[status(thm)],[c_82,c_281]) ).
cnf(c_282,plain,
divide(A,inverse(divide(B,C))) = divide(divide(A,inverse(B)),C),
inference(paramod,[status(thm)],[c_160,c_125]) ).
cnf(c_254,plain,
divide(divide(A,inverse(B)),C) = divide(A,inverse(divide(B,C))),
inference(copy,[status(thm)],[c_282]) ).
cnf(c_255,plain,
$false,
inference(resolve,[status(thm)],[c_254,c_94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP063-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n007.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Fri Sep 25 14:18:53 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 1185466 was started by sandbox on n007,
% 0.16/0.42 % Fri Sep 25 14:18:53 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.42
% 0.16/0.42 % From the command line: assign(max_seconds, 300).
% 0.16/0.48
% 0.16/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.48
% 0.16/0.48 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.16/0.48 % Length of proof is 40.
% 0.16/0.48 % Level of proof is 14.
% 0.16/0.48 % Maximum clause weight is 31.000.
% 0.16/0.48 % Given clauses 49.
% 0.16/0.48
% 0.16/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------