%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP064-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 62 ( 47 unt; 0 def)
% Number of atoms : 90 ( 89 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 74 ( 46 ~; 28 |; 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 : 104 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(VAR_0,divide(divide(divide(divide(VAR_1,VAR_1),VAR_1),VAR_2),divide(divide(divide(VAR_1,VAR_1),VAR_0),VAR_2))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(A,divide(divide(divide(divide(B,B),B),C),divide(divide(divide(B,B),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_226,plain,
divide(A,divide(divide(inverse(B),C),divide(divide(divide(B,B),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_226]) ).
cnf(c_227,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_228,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_227]) ).
cnf(c_229,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_228]) ).
cnf(c_230,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_229]) ).
cnf(c_231,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_230]) ).
cnf(c_232,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_231]) ).
cnf(c_233,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_232]) ).
cnf(c_234,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_233]) ).
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_234]) ).
cnf(c_10,plain,
divide(inverse(divide(A,A)),B) = inverse(B),
inference(paramod,[status(thm)],[c_4,c_4]) ).
cnf(c_235,plain,
A = inverse(divide(divide(inverse(A),B),divide(inverse(divide(C,C)),B))),
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_236,plain,
A = inverse(divide(divide(inverse(A),B),inverse(B))),
inference(paramod,[status(thm)],[c_10,c_235]) ).
cnf(c_11,plain,
inverse(divide(divide(inverse(A),B),inverse(B))) = A,
inference(copy,[status(thm)],[c_236]) ).
cnf(c_12,plain,
divide(A,inverse(divide(inverse(A),inverse(B)))) = B,
inference(paramod,[status(thm)],[c_4,c_8]) ).
cnf(c_22,plain,
inverse(divide(inverse(A),inverse(A))) = divide(B,B),
inference(paramod,[status(thm)],[c_10,c_11]) ).
cnf(c_25,plain,
divide(A,divide(B,divide(inverse(A),inverse(divide(inverse(inverse(C)),inverse(B)))))) = C,
inference(paramod,[status(thm)],[c_12,c_8]) ).
cnf(c_26,plain,
divide(A,divide(divide(inverse(B),inverse(divide(inverse(inverse(A)),inverse(C)))),C)) = B,
inference(paramod,[status(thm)],[c_12,c_8]) ).
cnf(c_237,plain,
divide(A,inverse(B)) = divide(inverse(inverse(A)),inverse(B)),
inference(paramod,[status(thm)],[c_12,c_12]) ).
cnf(c_30,plain,
divide(inverse(inverse(A)),inverse(B)) = divide(A,inverse(B)),
inference(copy,[status(thm)],[c_237]) ).
cnf(c_32,plain,
divide(A,divide(divide(inverse(B),inverse(divide(A,inverse(C)))),C)) = B,
inference(paramod,[status(thm)],[c_30,c_26]) ).
cnf(c_33,plain,
divide(A,divide(B,divide(inverse(A),inverse(divide(C,inverse(B)))))) = C,
inference(paramod,[status(thm)],[c_30,c_25]) ).
cnf(c_238,plain,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| inverse(inverse(a2)) != a2
| inverse(divide(inverse(A),inverse(A))) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_22,c_9]) ).
cnf(c_39,plain,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| inverse(inverse(a2)) != a2 ),
inference(resolve,[status(thm)],[c_22,c_238]) ).
cnf(c_42,plain,
inverse(divide(divide(inverse(A),divide(inverse(B),inverse(B))),divide(C,C))) = A,
inference(paramod,[status(thm)],[c_22,c_11]) ).
cnf(c_45,plain,
divide(A,divide(B,B)) = A,
inference(paramod,[status(thm)],[c_22,c_12]) ).
cnf(c_48,plain,
divide(A,A) = divide(B,B),
inference(paramod,[status(thm)],[c_22,c_22]) ).
cnf(c_239,plain,
inverse(divide(inverse(A),divide(C,C))) = A,
inference(paramod,[status(thm)],[c_45,c_42]) ).
cnf(c_51,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_45,c_239]) ).
cnf(c_240,plain,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_51,c_39]) ).
cnf(c_52,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(copy,[status(thm)],[c_240]) ).
cnf(c_57,plain,
divide(A,inverse(divide(B,B))) = A,
inference(paramod,[status(thm)],[c_48,c_12]) ).
cnf(c_241,plain,
divide(inverse(A),divide(divide(inverse(B),inverse(divide(C,C))),A)) = B,
inference(paramod,[status(thm)],[c_48,c_32]) ).
cnf(c_76,plain,
divide(inverse(A),divide(inverse(B),A)) = B,
inference(paramod,[status(thm)],[c_57,c_241]) ).
cnf(c_77,plain,
divide(A,divide(divide(B,inverse(divide(A,inverse(C)))),C)) = inverse(B),
inference(paramod,[status(thm)],[c_51,c_32]) ).
cnf(c_242,plain,
divide(divide(A,inverse(B)),divide(B,divide(C,C))) = A,
inference(paramod,[status(thm)],[c_48,c_33]) ).
cnf(c_81,plain,
divide(divide(A,inverse(B)),B) = A,
inference(paramod,[status(thm)],[c_45,c_242]) ).
cnf(c_243,plain,
multiply(divide(A,inverse(inverse(B))),B) = A,
inference(paramod,[status(thm)],[c_81,c_7]) ).
cnf(c_244,plain,
multiply(divide(A,B),B) = A,
inference(paramod,[status(thm)],[c_51,c_243]) ).
cnf(c_84,plain,
divide(divide(A,B),inverse(B)) = A,
inference(paramod,[status(thm)],[c_7,c_244]) ).
cnf(c_87,plain,
divide(inverse(A),divide(B,A)) = inverse(B),
inference(paramod,[status(thm)],[c_51,c_76]) ).
cnf(c_245,plain,
divide(inverse(inverse(A)),B) = inverse(divide(B,A)),
inference(paramod,[status(thm)],[c_84,c_87]) ).
cnf(c_246,plain,
divide(A,B) = inverse(divide(B,A)),
inference(paramod,[status(thm)],[c_51,c_245]) ).
cnf(c_92,plain,
inverse(divide(A,B)) = divide(B,A),
inference(copy,[status(thm)],[c_246]) ).
cnf(c_102,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(c3),b3)),
inference(paramod,[status(thm)],[c_92,c_52]) ).
cnf(c_155,plain,
inverse(divide(inverse(c3),divide(a3,inverse(b3)))) != divide(a3,divide(inverse(c3),b3)),
inference(paramod,[status(thm)],[c_92,c_102]) ).
cnf(c_247,plain,
divide(A,divide(B,C)) = inverse(divide(B,inverse(inverse(divide(A,inverse(C)))))),
inference(paramod,[status(thm)],[c_81,c_77]) ).
cnf(c_248,plain,
divide(A,divide(B,C)) = inverse(divide(B,divide(A,inverse(C)))),
inference(paramod,[status(thm)],[c_51,c_247]) ).
cnf(c_224,plain,
inverse(divide(A,divide(B,inverse(C)))) = divide(B,divide(A,C)),
inference(copy,[status(thm)],[c_248]) ).
cnf(c_225,plain,
$false,
inference(resolve,[status(thm)],[c_224,c_155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP064-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:21:14 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 947320 was started by sandbox2 on n010,
% 0.09/0.36 % Fri Sep 25 14:21:14 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.40
% 0.14/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.40
% 0.14/0.40 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.14/0.40 % Length of proof is 35.
% 0.14/0.40 % Level of proof is 12.
% 0.14/0.40 % Maximum clause weight is 84.000.
% 0.14/0.40 % Given clauses 38.
% 0.14/0.40
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------