%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP095-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 5
% Syntax : Number of formulae : 81 ( 48 unt; 0 def)
% Number of atoms : 154 ( 153 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 183 ( 110 ~; 73 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(identity,VAR_0),divide(divide(divide(VAR_1,VAR_0),VAR_2),VAR_1)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = divide(VAR_0,divide(identity,VAR_1)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = divide(A,divide(identity,B)),
inference(clausify,[status(thm)],[multiply]) ).
fof(inverse,axiom,
! [VAR_0] : inverse(VAR_0) = divide(identity,VAR_0),
file('theBenchmark.p',inverse) ).
cnf(c_3,plain,
inverse(A) = divide(identity,A),
inference(clausify,[status(thm)],[inverse]) ).
fof(identity,axiom,
! [VAR_0] : identity = divide(VAR_0,VAR_0),
file('theBenchmark.p',identity) ).
cnf(c_4,plain,
identity = divide(A,A),
inference(clausify,[status(thm)],[identity]) ).
cnf(c_5,plain,
divide(A,A) = identity,
inference(copy,[status(thm)],[c_4]) ).
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_6,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_105,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(divide(identity,a1),a1) != multiply(inverse(b1),b1) ),
inference(paramod,[status(thm)],[c_3,c_6]) ).
cnf(c_106,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(divide(identity,a1),divide(identity,a1)) != multiply(inverse(b1),b1) ),
inference(paramod,[status(thm)],[c_2,c_105]) ).
cnf(c_107,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| identity != multiply(inverse(b1),b1) ),
inference(paramod,[status(thm)],[c_5,c_106]) ).
cnf(c_108,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| identity != multiply(divide(identity,b1),b1) ),
inference(paramod,[status(thm)],[c_3,c_107]) ).
cnf(c_109,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| identity != divide(divide(identity,b1),divide(identity,b1)) ),
inference(paramod,[status(thm)],[c_2,c_108]) ).
cnf(c_110,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_5,c_109]) ).
cnf(c_111,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(divide(identity,b2),b2),a2) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_3,c_110]) ).
cnf(c_112,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(divide(divide(identity,b2),divide(identity,b2)),a2) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_2,c_111]) ).
cnf(c_113,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_5,c_112]) ).
cnf(c_114,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| divide(identity,divide(identity,a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_2,c_113]) ).
cnf(c_115,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(divide(a3,divide(identity,b3)),c3) != multiply(a3,multiply(b3,c3))
| divide(identity,divide(identity,a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_2,c_114]) ).
cnf(c_116,plain,
( multiply(a4,b4) != multiply(b4,a4)
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != multiply(a3,multiply(b3,c3))
| divide(identity,divide(identity,a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_2,c_115]) ).
cnf(c_117,plain,
( multiply(a4,b4) != multiply(b4,a4)
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != multiply(a3,divide(b3,divide(identity,c3)))
| divide(identity,divide(identity,a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_2,c_116]) ).
cnf(c_118,plain,
( multiply(a4,b4) != multiply(b4,a4)
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(identity,divide(identity,a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_2,c_117]) ).
cnf(c_119,plain,
( divide(a4,divide(identity,b4)) != multiply(b4,a4)
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(identity,divide(identity,a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_2,c_118]) ).
cnf(c_120,plain,
( divide(a4,divide(identity,b4)) != divide(b4,divide(identity,a4))
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(identity,divide(identity,a2)) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_2,c_119]) ).
cnf(c_121,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(identity,divide(identity,a2)) != a2
| identity != identity ),
inference(copy,[status(thm)],[c_120]) ).
cnf(c_7,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(identity,divide(identity,a2)) != a2 ),
inference(copy,[status(thm)],[c_121]) ).
cnf(c_122,plain,
divide(divide(identity,A),divide(B,identity)) = divide(divide(divide(C,A),B),C),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_9,plain,
divide(divide(divide(A,B),C),A) = divide(divide(identity,B),divide(C,identity)),
inference(copy,[status(thm)],[c_122]) ).
cnf(c_11,plain,
divide(divide(identity,A),divide(divide(identity,A),divide(B,identity))) = B,
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_123,plain,
divide(divide(identity,A),B) = divide(divide(identity,B),divide(A,identity)),
inference(paramod,[status(thm)],[c_5,c_9]) ).
cnf(c_12,plain,
divide(divide(identity,A),divide(B,identity)) = divide(divide(identity,B),A),
inference(copy,[status(thm)],[c_123]) ).
cnf(c_124,plain,
divide(identity,divide(divide(identity,identity),divide(A,identity))) = A,
inference(paramod,[status(thm)],[c_5,c_11]) ).
cnf(c_16,plain,
divide(identity,divide(identity,divide(A,identity))) = A,
inference(paramod,[status(thm)],[c_5,c_124]) ).
cnf(c_125,plain,
divide(divide(A,B),identity) = divide(divide(identity,divide(identity,divide(A,identity))),divide(B,identity)),
inference(paramod,[status(thm)],[c_16,c_9]) ).
cnf(c_19,plain,
divide(divide(A,B),identity) = divide(A,divide(B,identity)),
inference(paramod,[status(thm)],[c_16,c_125]) ).
cnf(c_126,plain,
divide(A,divide(divide(identity,divide(identity,divide(A,identity))),divide(B,identity))) = B,
inference(paramod,[status(thm)],[c_16,c_11]) ).
cnf(c_21,plain,
divide(A,divide(A,divide(B,identity))) = B,
inference(paramod,[status(thm)],[c_16,c_126]) ).
cnf(c_127,plain,
divide(divide(A,identity),identity) = A,
inference(paramod,[status(thm)],[c_5,c_21]) ).
cnf(c_128,plain,
divide(A,divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_19,c_127]) ).
cnf(c_24,plain,
divide(A,identity) = A,
inference(paramod,[status(thm)],[c_5,c_128]) ).
cnf(c_129,plain,
divide(divide(A,B),C) = divide(divide(identity,divide(C,divide(A,identity))),divide(B,identity)),
inference(paramod,[status(thm)],[c_21,c_9]) ).
cnf(c_130,plain,
divide(divide(A,B),C) = divide(divide(identity,divide(C,A)),divide(B,identity)),
inference(paramod,[status(thm)],[c_24,c_129]) ).
cnf(c_131,plain,
divide(divide(A,B),C) = divide(divide(identity,divide(C,A)),B),
inference(paramod,[status(thm)],[c_24,c_130]) ).
cnf(c_25,plain,
divide(divide(identity,divide(A,B)),C) = divide(divide(B,C),A),
inference(copy,[status(thm)],[c_131]) ).
cnf(c_31,plain,
divide(A,divide(A,B)) = B,
inference(paramod,[status(thm)],[c_24,c_21]) ).
cnf(c_34,plain,
divide(divide(identity,A),B) = divide(divide(identity,B),A),
inference(paramod,[status(thm)],[c_24,c_12]) ).
cnf(c_132,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_31,c_7]) ).
cnf(c_37,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(copy,[status(thm)],[c_132]) ).
cnf(c_133,plain,
divide(divide(A,identity),B) = divide(identity,divide(B,A)),
inference(paramod,[status(thm)],[c_25,c_24]) ).
cnf(c_134,plain,
divide(A,B) = divide(identity,divide(B,A)),
inference(paramod,[status(thm)],[c_24,c_133]) ).
cnf(c_41,plain,
divide(identity,divide(A,B)) = divide(B,A),
inference(copy,[status(thm)],[c_134]) ).
cnf(c_135,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(divide(identity,divide(divide(identity,c3),a3)),divide(identity,b3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(paramod,[status(thm)],[c_25,c_37]) ).
cnf(c_136,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(divide(identity,divide(divide(identity,a3),c3)),divide(identity,b3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(paramod,[status(thm)],[c_34,c_135]) ).
cnf(c_137,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(divide(identity,divide(identity,b3)),divide(divide(identity,a3),c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(paramod,[status(thm)],[c_34,c_136]) ).
cnf(c_47,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(b3,divide(divide(identity,a3),c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(paramod,[status(thm)],[c_31,c_137]) ).
cnf(c_138,plain,
multiply(A,divide(B,C)) = divide(A,divide(C,B)),
inference(paramod,[status(thm)],[c_41,c_2]) ).
cnf(c_57,plain,
divide(A,divide(identity,divide(B,C))) = divide(A,divide(C,B)),
inference(paramod,[status(thm)],[c_2,c_138]) ).
cnf(c_139,plain,
divide(divide(identity,divide(A,B)),C) = divide(divide(divide(B,A),C),identity),
inference(paramod,[status(thm)],[c_41,c_25]) ).
cnf(c_58,plain,
divide(divide(identity,divide(A,B)),C) = divide(divide(B,A),C),
inference(paramod,[status(thm)],[c_24,c_139]) ).
cnf(c_63,plain,
divide(divide(identity,divide(A,B)),C) = divide(identity,divide(A,divide(B,C))),
inference(paramod,[status(thm)],[c_41,c_25]) ).
cnf(c_70,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(b3,divide(identity,divide(c3,divide(identity,a3)))) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(paramod,[status(thm)],[c_41,c_47]) ).
cnf(c_140,plain,
divide(identity,divide(A,divide(B,C))) = divide(divide(B,A),C),
inference(paramod,[status(thm)],[c_63,c_58]) ).
cnf(c_76,plain,
divide(divide(A,B),C) = divide(identity,divide(B,divide(A,C))),
inference(copy,[status(thm)],[c_140]) ).
cnf(c_141,plain,
divide(A,divide(identity,divide(B,divide(C,D)))) = divide(A,divide(divide(identity,divide(D,C)),B)),
inference(paramod,[status(thm)],[c_57,c_57]) ).
cnf(c_142,plain,
divide(A,divide(identity,divide(B,divide(C,D)))) = divide(A,divide(identity,divide(divide(D,C),divide(identity,B)))),
inference(paramod,[status(thm)],[c_76,c_141]) ).
cnf(c_143,plain,
divide(A,divide(identity,divide(B,divide(C,D)))) = divide(A,divide(identity,divide(identity,divide(C,divide(D,divide(identity,B)))))),
inference(paramod,[status(thm)],[c_76,c_142]) ).
cnf(c_98,plain,
divide(A,divide(identity,divide(B,divide(C,D)))) = divide(A,divide(C,divide(D,divide(identity,B)))),
inference(paramod,[status(thm)],[c_31,c_143]) ).
cnf(c_144,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(identity,divide(divide(identity,divide(c3,divide(identity,a3))),b3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(paramod,[status(thm)],[c_41,c_70]) ).
cnf(c_145,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(identity,divide(identity,divide(divide(c3,divide(identity,a3)),divide(identity,b3)))) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(paramod,[status(thm)],[c_76,c_144]) ).
cnf(c_146,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(identity,divide(identity,divide(identity,divide(divide(identity,a3),divide(c3,divide(identity,b3)))))) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(paramod,[status(thm)],[c_76,c_145]) ).
cnf(c_147,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(identity,divide(identity,divide(identity,divide(identity,divide(a3,divide(identity,divide(c3,divide(identity,b3)))))))) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(paramod,[status(thm)],[c_76,c_146]) ).
cnf(c_148,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(identity,divide(identity,divide(a3,divide(identity,divide(c3,divide(identity,b3)))))) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(paramod,[status(thm)],[c_31,c_147]) ).
cnf(c_149,plain,
( divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4))
| divide(a3,divide(identity,divide(c3,divide(identity,b3)))) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(paramod,[status(thm)],[c_31,c_148]) ).
cnf(c_103,plain,
divide(b4,divide(identity,a4)) != divide(a4,divide(identity,b4)),
inference(resolve,[status(thm)],[c_98,c_149]) ).
cnf(c_150,plain,
divide(identity,divide(divide(identity,a4),b4)) != divide(a4,divide(identity,b4)),
inference(paramod,[status(thm)],[c_41,c_103]) ).
cnf(c_151,plain,
divide(identity,divide(identity,divide(a4,divide(identity,b4)))) != divide(a4,divide(identity,b4)),
inference(paramod,[status(thm)],[c_76,c_150]) ).
cnf(c_152,plain,
divide(a4,divide(identity,b4)) != divide(a4,divide(identity,b4)),
inference(paramod,[status(thm)],[c_31,c_151]) ).
cnf(c_104,plain,
$false,
inference(copy,[status(thm)],[c_152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP095-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n002.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 14:24:34 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.14/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.36 % Process 3484648 was started by sandbox on n002,
% 0.14/0.36 % Fri Sep 25 14:24:34 2026
% 0.14/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.38
% 0.14/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.38
% 0.14/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/0.38 % Length of proof is 28.
% 0.14/0.38 % Level of proof is 12.
% 0.14/0.38 % Maximum clause weight is 37.000.
% 0.14/0.38 % Given clauses 20.
% 0.14/0.38
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------