%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP098-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 07:27:19 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.48s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 3
% Syntax : Number of formulae : 53 ( 29 unt; 0 def)
% Number of atoms : 108 ( 107 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 136 ( 81 ~; 55 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(divide(VAR_0,inverse(VAR_1)),VAR_2),divide(VAR_0,VAR_2)) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(divide(A,inverse(B)),C),divide(A,C)) = B,
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,axiom,
( multiply(a4,b4) != multiply(b4,a4)
| 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_3,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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_175,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| divide(inverse(a1),inverse(a1)) != multiply(inverse(b1),b1) ),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_176,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1)) ),
inference(paramod,[status(thm)],[c_2,c_175]) ).
cnf(c_177,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(divide(inverse(b2),inverse(b2)),a2) != a2
| divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1)) ),
inference(paramod,[status(thm)],[c_2,c_176]) ).
cnf(c_178,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2
| divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1)) ),
inference(paramod,[status(thm)],[c_2,c_177]) ).
cnf(c_179,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(divide(a3,inverse(b3)),c3) != multiply(a3,multiply(b3,c3))
| divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2
| divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1)) ),
inference(paramod,[status(thm)],[c_2,c_178]) ).
cnf(c_180,plain,
( multiply(a4,b4) != multiply(b4,a4)
| divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,multiply(b3,c3))
| divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2
| divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1)) ),
inference(paramod,[status(thm)],[c_2,c_179]) ).
cnf(c_181,plain,
( multiply(a4,b4) != multiply(b4,a4)
| divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,divide(b3,inverse(c3)))
| divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2
| divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1)) ),
inference(paramod,[status(thm)],[c_2,c_180]) ).
cnf(c_182,plain,
( multiply(a4,b4) != multiply(b4,a4)
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2
| divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1)) ),
inference(paramod,[status(thm)],[c_2,c_181]) ).
cnf(c_183,plain,
( divide(a4,inverse(b4)) != multiply(b4,a4)
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2
| divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1)) ),
inference(paramod,[status(thm)],[c_2,c_182]) ).
cnf(c_184,plain,
( divide(a4,inverse(b4)) != divide(b4,inverse(a4))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2
| divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1)) ),
inference(paramod,[status(thm)],[c_2,c_183]) ).
cnf(c_185,plain,
( divide(a4,inverse(b4)) != divide(b4,inverse(a4))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(copy,[status(thm)],[c_184]) ).
cnf(c_4,plain,
( divide(a4,inverse(b4)) != divide(b4,inverse(a4))
| divide(a3,inverse(divide(b3,inverse(c3)))) != divide(divide(a3,inverse(b3)),inverse(c3))
| divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(copy,[status(thm)],[c_185]) ).
cnf(c_5,plain,
divide(A,divide(divide(B,inverse(A)),divide(B,inverse(C)))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
divide(divide(divide(divide(divide(A,inverse(B)),C),inverse(D)),divide(A,C)),B) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_186,plain,
divide(divide(A,divide(divide(divide(B,inverse(inverse(C))),D),divide(B,D))),A) = C,
inference(paramod,[status(thm)],[c_6,c_6]) ).
cnf(c_16,plain,
divide(divide(A,inverse(B)),A) = B,
inference(paramod,[status(thm)],[c_1,c_186]) ).
cnf(c_19,plain,
divide(A,divide(B,B)) = A,
inference(paramod,[status(thm)],[c_16,c_1]) ).
cnf(c_28,plain,
divide(divide(A,A),inverse(B)) = B,
inference(paramod,[status(thm)],[c_19,c_16]) ).
cnf(c_187,plain,
( divide(a4,inverse(b4)) != divide(b4,inverse(a4))
| divide(a3,inverse(divide(b3,inverse(c3)))) != divide(divide(a3,inverse(b3)),inverse(c3))
| a2 != a2
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_28,c_4]) ).
cnf(c_29,plain,
( divide(a4,inverse(b4)) != divide(b4,inverse(a4))
| divide(a3,inverse(divide(b3,inverse(c3)))) != divide(divide(a3,inverse(b3)),inverse(c3))
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(copy,[status(thm)],[c_187]) ).
cnf(c_188,plain,
divide(divide(divide(divide(A,A),inverse(B)),inverse(C)),C) = B,
inference(paramod,[status(thm)],[c_28,c_1]) ).
cnf(c_31,plain,
divide(divide(A,inverse(B)),B) = A,
inference(paramod,[status(thm)],[c_28,c_188]) ).
cnf(c_189,plain,
divide(A,divide(A,divide(divide(B,B),inverse(C)))) = C,
inference(paramod,[status(thm)],[c_28,c_5]) ).
cnf(c_32,plain,
divide(A,divide(A,B)) = B,
inference(paramod,[status(thm)],[c_28,c_189]) ).
cnf(c_53,plain,
divide(A,A) = divide(B,B),
inference(paramod,[status(thm)],[c_19,c_32]) ).
cnf(c_62,plain,
( divide(a4,inverse(b4)) != divide(b4,inverse(a4))
| divide(a3,inverse(divide(b3,inverse(c3)))) != divide(divide(a3,inverse(b3)),inverse(c3)) ),
inference(resolve,[status(thm)],[c_53,c_29]) ).
cnf(c_190,plain,
divide(A,divide(A,inverse(inverse(B)))) = B,
inference(paramod,[status(thm)],[c_31,c_16]) ).
cnf(c_68,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_32,c_190]) ).
cnf(c_88,plain,
divide(divide(A,B),A) = inverse(B),
inference(paramod,[status(thm)],[c_68,c_16]) ).
cnf(c_89,plain,
divide(divide(A,B),inverse(B)) = A,
inference(paramod,[status(thm)],[c_68,c_31]) ).
cnf(c_118,plain,
divide(A,divide(divide(B,inverse(A)),C)) = inverse(divide(B,C)),
inference(paramod,[status(thm)],[c_1,c_88]) ).
cnf(c_191,plain,
divide(A,B) = inverse(divide(B,A)),
inference(paramod,[status(thm)],[c_32,c_88]) ).
cnf(c_123,plain,
inverse(divide(A,B)) = divide(B,A),
inference(copy,[status(thm)],[c_191]) ).
cnf(c_124,plain,
divide(inverse(A),B) = divide(inverse(B),A),
inference(paramod,[status(thm)],[c_88,c_31]) ).
cnf(c_137,plain,
divide(A,divide(divide(B,inverse(A)),C)) = divide(C,B),
inference(paramod,[status(thm)],[c_123,c_118]) ).
cnf(c_192,plain,
( divide(a4,inverse(b4)) != divide(b4,inverse(a4))
| divide(a3,divide(inverse(c3),b3)) != divide(divide(a3,inverse(b3)),inverse(c3)) ),
inference(paramod,[status(thm)],[c_123,c_62]) ).
cnf(c_193,plain,
( divide(a4,inverse(b4)) != divide(b4,inverse(a4))
| divide(a3,divide(inverse(b3),c3)) != divide(divide(a3,inverse(b3)),inverse(c3)) ),
inference(paramod,[status(thm)],[c_124,c_192]) ).
cnf(c_146,plain,
( divide(a4,inverse(b4)) != divide(b4,inverse(a4))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(b3),c3)) ),
inference(copy,[status(thm)],[c_193]) ).
cnf(c_151,plain,
divide(A,inverse(B)) = divide(B,inverse(A)),
inference(paramod,[status(thm)],[c_16,c_89]) ).
cnf(c_194,plain,
( divide(a4,inverse(b4)) != divide(b4,inverse(a4))
| divide(divide(b3,inverse(a3)),inverse(c3)) != divide(a3,divide(inverse(b3),c3)) ),
inference(paramod,[status(thm)],[c_151,c_146]) ).
cnf(c_195,plain,
( divide(a4,inverse(b4)) != divide(b4,inverse(a4))
| divide(c3,inverse(divide(b3,inverse(a3)))) != divide(a3,divide(inverse(b3),c3)) ),
inference(paramod,[status(thm)],[c_151,c_194]) ).
cnf(c_196,plain,
( divide(a4,inverse(b4)) != divide(b4,inverse(a4))
| divide(c3,divide(inverse(a3),b3)) != divide(a3,divide(inverse(b3),c3)) ),
inference(paramod,[status(thm)],[c_123,c_195]) ).
cnf(c_197,plain,
( divide(b4,inverse(a4)) != divide(b4,inverse(a4))
| divide(c3,divide(inverse(a3),b3)) != divide(a3,divide(inverse(b3),c3)) ),
inference(paramod,[status(thm)],[c_151,c_196]) ).
cnf(c_155,plain,
divide(c3,divide(inverse(a3),b3)) != divide(a3,divide(inverse(b3),c3)),
inference(copy,[status(thm)],[c_197]) ).
cnf(c_173,plain,
divide(c3,divide(inverse(a3),b3)) != divide(a3,divide(divide(divide(A,b3),A),c3)),
inference(paramod,[status(thm)],[c_88,c_155]) ).
cnf(c_198,plain,
divide(C,B) = divide(A,divide(divide(B,inverse(A)),C)),
inference(copy,[status(thm)],[c_137]) ).
cnf(c_174,plain,
$false,
inference(resolve,[status(thm)],[c_173,c_198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP098-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n001.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 14:27:55 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 3507856 was started by sandbox2 on n001,
% 0.16/0.42 % Fri Sep 25 14:27:55 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/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 26.
% 0.16/0.48 % Level of proof is 12.
% 0.16/0.48 % Maximum clause weight is 45.000.
% 0.16/0.48 % Given clauses 22.
% 0.16/0.48
% 0.16/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------