%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP065-1 : 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 : 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 07:26:55 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 4
% Syntax : Number of formulae : 77 ( 63 unt; 0 def)
% Number of atoms : 103 ( 102 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 70 ( 44 ~; 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 : 150 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(divide(VAR_0,VAR_0),divide(VAR_0,divide(VAR_1,divide(divide(divide(VAR_0,VAR_0),VAR_0),VAR_2)))),VAR_2) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(divide(A,A),divide(A,divide(B,divide(divide(divide(A,A),A),C)))),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]) ).
cnf(c_3,plain,
divide(A,divide(divide(B,B),C)) = multiply(A,C),
inference(copy,[status(thm)],[c_2]) ).
fof(inverse,axiom,
! [VAR_0,VAR_1] : inverse(VAR_0) = divide(divide(VAR_1,VAR_1),VAR_0),
file('theBenchmark.p',inverse) ).
cnf(c_4,plain,
inverse(A) = divide(divide(B,B),A),
inference(clausify,[status(thm)],[inverse]) ).
cnf(c_5,plain,
divide(divide(A,A),B) = inverse(B),
inference(copy,[status(thm)],[c_4]) ).
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_6,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_7,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_6]) ).
cnf(c_142,plain,
divide(A,inverse(C)) = multiply(A,C),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_8,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(copy,[status(thm)],[c_142]) ).
cnf(c_143,plain,
divide(divide(divide(A,A),divide(A,divide(B,divide(inverse(A),C)))),C) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_9,plain,
divide(inverse(divide(A,divide(B,divide(inverse(A),C)))),C) = B,
inference(paramod,[status(thm)],[c_5,c_143]) ).
cnf(c_144,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_8,c_7]) ).
cnf(c_145,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_8,c_144]) ).
cnf(c_146,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_8,c_145]) ).
cnf(c_147,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_8,c_146]) ).
cnf(c_148,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_5,c_147]) ).
cnf(c_149,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_8,c_148]) ).
cnf(c_150,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_8,c_149]) ).
cnf(c_151,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_8,c_150]) ).
cnf(c_10,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_8,c_151]) ).
cnf(c_11,plain,
divide(inverse(divide(A,A)),B) = inverse(B),
inference(paramod,[status(thm)],[c_5,c_5]) ).
cnf(c_12,plain,
divide(inverse(divide(A,inverse(divide(inverse(A),B)))),B) = divide(C,C),
inference(paramod,[status(thm)],[c_5,c_9]) ).
cnf(c_152,plain,
divide(inverse(inverse(divide(A,divide(inverse(divide(B,B)),C)))),C) = A,
inference(paramod,[status(thm)],[c_5,c_9]) ).
cnf(c_13,plain,
divide(inverse(inverse(divide(A,inverse(B)))),B) = A,
inference(paramod,[status(thm)],[c_11,c_152]) ).
cnf(c_14,plain,
divide(inverse(divide(divide(A,divide(B,divide(inverse(A),C))),divide(D,B))),C) = D,
inference(paramod,[status(thm)],[c_9,c_9]) ).
cnf(c_153,plain,
divide(inverse(divide(A,B)),C) = inverse(inverse(divide(B,inverse(divide(inverse(A),C))))),
inference(paramod,[status(thm)],[c_13,c_9]) ).
cnf(c_24,plain,
inverse(inverse(divide(A,inverse(divide(inverse(B),C))))) = divide(inverse(divide(B,A)),C),
inference(copy,[status(thm)],[c_153]) ).
cnf(c_154,plain,
divide(inverse(inverse(A)),B) = inverse(inverse(divide(A,inverse(inverse(B))))),
inference(paramod,[status(thm)],[c_13,c_13]) ).
cnf(c_28,plain,
inverse(inverse(divide(A,inverse(inverse(B))))) = divide(inverse(inverse(A)),B),
inference(copy,[status(thm)],[c_154]) ).
cnf(c_41,plain,
divide(A,A) = divide(B,B),
inference(paramod,[status(thm)],[c_12,c_12]) ).
cnf(c_44,plain,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| inverse(inverse(a2)) != a2 ),
inference(resolve,[status(thm)],[c_41,c_10]) ).
cnf(c_155,plain,
divide(A,A) = inverse(divide(B,B)),
inference(paramod,[status(thm)],[c_41,c_5]) ).
cnf(c_45,plain,
inverse(divide(A,A)) = divide(B,B),
inference(copy,[status(thm)],[c_155]) ).
cnf(c_47,plain,
divide(inverse(divide(A,divide(B,B))),C) = divide(inverse(A),C),
inference(paramod,[status(thm)],[c_41,c_9]) ).
cnf(c_52,plain,
inverse(divide(A,A)) = inverse(divide(B,B)),
inference(paramod,[status(thm)],[c_45,c_5]) ).
cnf(c_156,plain,
multiply(A,divide(B,B)) = divide(A,divide(C,C)),
inference(paramod,[status(thm)],[c_45,c_8]) ).
cnf(c_53,plain,
divide(A,inverse(divide(B,B))) = divide(A,divide(C,C)),
inference(paramod,[status(thm)],[c_8,c_156]) ).
cnf(c_157,plain,
inverse(divide(A,A)) = inverse(inverse(divide(B,B))),
inference(paramod,[status(thm)],[c_45,c_11]) ).
cnf(c_56,plain,
inverse(inverse(divide(A,A))) = inverse(divide(B,B)),
inference(copy,[status(thm)],[c_157]) ).
cnf(c_64,plain,
divide(inverse(inverse(divide(A,inverse(divide(B,B))))),divide(C,C)) = A,
inference(paramod,[status(thm)],[c_52,c_13]) ).
cnf(c_158,plain,
divide(inverse(divide(divide(A,divide(B,divide(inverse(A),C))),divide(D,D))),C) = inverse(divide(E,inverse(divide(inverse(E),B)))),
inference(paramod,[status(thm)],[c_12,c_14]) ).
cnf(c_159,plain,
divide(inverse(divide(A,divide(B,divide(inverse(A),C)))),C) = inverse(divide(E,inverse(divide(inverse(E),B)))),
inference(paramod,[status(thm)],[c_47,c_158]) ).
cnf(c_160,plain,
B = inverse(divide(E,inverse(divide(inverse(E),B)))),
inference(paramod,[status(thm)],[c_9,c_159]) ).
cnf(c_79,plain,
inverse(divide(A,inverse(divide(inverse(A),B)))) = B,
inference(copy,[status(thm)],[c_160]) ).
cnf(c_81,plain,
divide(inverse(divide(divide(A,divide(B,inverse(divide(C,C)))),divide(D,B))),inverse(A)) = D,
inference(paramod,[status(thm)],[c_45,c_14]) ).
cnf(c_161,plain,
divide(inverse(inverse(divide(A,inverse(inverse(divide(B,B)))))),divide(C,C)) = A,
inference(paramod,[status(thm)],[c_56,c_13]) ).
cnf(c_98,plain,
divide(divide(inverse(inverse(A)),divide(B,B)),divide(C,C)) = A,
inference(paramod,[status(thm)],[c_28,c_161]) ).
cnf(c_99,plain,
divide(A,inverse(inverse(inverse(divide(B,B))))) = divide(A,divide(C,C)),
inference(paramod,[status(thm)],[c_11,c_53]) ).
cnf(c_104,plain,
divide(inverse(A),divide(inverse(B),A)) = B,
inference(paramod,[status(thm)],[c_79,c_13]) ).
cnf(c_106,plain,
inverse(divide(A,inverse(divide(B,B)))) = inverse(A),
inference(paramod,[status(thm)],[c_41,c_79]) ).
cnf(c_115,plain,
divide(inverse(inverse(A)),divide(B,B)) = A,
inference(paramod,[status(thm)],[c_106,c_64]) ).
cnf(c_116,plain,
divide(A,divide(B,B)) = A,
inference(paramod,[status(thm)],[c_115,c_98]) ).
cnf(c_117,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_116,c_115]) ).
cnf(c_162,plain,
divide(A,inverse(divide(B,B))) = divide(A,divide(C,C)),
inference(paramod,[status(thm)],[c_117,c_99]) ).
cnf(c_118,plain,
divide(A,inverse(divide(B,B))) = A,
inference(paramod,[status(thm)],[c_116,c_162]) ).
cnf(c_163,plain,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_117,c_44]) ).
cnf(c_128,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(copy,[status(thm)],[c_163]) ).
cnf(c_164,plain,
divide(A,inverse(divide(inverse(B),C))) = divide(inverse(divide(B,A)),C),
inference(paramod,[status(thm)],[c_117,c_24]) ).
cnf(c_129,plain,
divide(inverse(divide(A,B)),C) = divide(B,inverse(divide(inverse(A),C))),
inference(copy,[status(thm)],[c_164]) ).
cnf(c_165,plain,
divide(inverse(divide(divide(A,B),divide(D,B))),inverse(A)) = D,
inference(paramod,[status(thm)],[c_118,c_81]) ).
cnf(c_166,plain,
divide(divide(D,B),inverse(divide(inverse(divide(A,B)),inverse(A)))) = D,
inference(paramod,[status(thm)],[c_129,c_165]) ).
cnf(c_167,plain,
divide(divide(D,B),inverse(divide(B,inverse(divide(inverse(A),inverse(A)))))) = D,
inference(paramod,[status(thm)],[c_129,c_166]) ).
cnf(c_130,plain,
divide(divide(A,B),inverse(B)) = A,
inference(paramod,[status(thm)],[c_118,c_167]) ).
cnf(c_136,plain,
divide(inverse(A),divide(B,A)) = inverse(B),
inference(paramod,[status(thm)],[c_117,c_104]) ).
cnf(c_168,plain,
divide(inverse(inverse(A)),B) = inverse(divide(B,A)),
inference(paramod,[status(thm)],[c_130,c_136]) ).
cnf(c_169,plain,
divide(A,B) = inverse(divide(B,A)),
inference(paramod,[status(thm)],[c_117,c_168]) ).
cnf(c_139,plain,
inverse(divide(A,B)) = divide(B,A),
inference(copy,[status(thm)],[c_169]) ).
cnf(c_170,plain,
divide(divide(B,A),C) = divide(B,inverse(divide(inverse(A),C))),
inference(paramod,[status(thm)],[c_139,c_129]) ).
cnf(c_140,plain,
divide(divide(A,B),C) = divide(A,divide(C,inverse(B))),
inference(paramod,[status(thm)],[c_139,c_170]) ).
cnf(c_171,plain,
divide(a3,divide(inverse(c3),inverse(inverse(b3)))) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(paramod,[status(thm)],[c_140,c_128]) ).
cnf(c_172,plain,
divide(a3,divide(inverse(c3),b3)) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(paramod,[status(thm)],[c_117,c_171]) ).
cnf(c_173,plain,
divide(a3,divide(inverse(c3),b3)) != divide(a3,divide(inverse(c3),b3)),
inference(paramod,[status(thm)],[c_139,c_172]) ).
cnf(c_141,plain,
$false,
inference(copy,[status(thm)],[c_173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP065-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 14:21:14 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 947310 was started by sandbox on n010,
% 0.10/0.36 % Fri Sep 25 14:21:14 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.41
% 0.13/0.41 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 0.13/0.41
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.41
% 0.13/0.41 % Proof 1 at 0.02 (+ 0.02) seconds.
% 0.13/0.41 % Length of proof is 41.
% 0.13/0.41 % Level of proof is 15.
% 0.13/0.41 % Maximum clause weight is 94.000.
% 0.13/0.41 % Given clauses 26.
% 0.13/0.41
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------