%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP097-1 : 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 : n019.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 0.17s 0.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 3
% Syntax : Number of formulae : 84 ( 60 unt; 0 def)
% Number of atoms : 141 ( 140 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 141 ( 84 ~; 57 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 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 : 161 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(VAR_0,inverse(divide(divide(VAR_1,VAR_2),divide(VAR_0,VAR_2)))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(A,inverse(divide(divide(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_114,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_115,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_114]) ).
cnf(c_116,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_115]) ).
cnf(c_117,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_116]) ).
cnf(c_118,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_117]) ).
cnf(c_119,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_118]) ).
cnf(c_120,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_119]) ).
cnf(c_121,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_120]) ).
cnf(c_122,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_121]) ).
cnf(c_123,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_122]) ).
cnf(c_124,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_123]) ).
cnf(c_4,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| 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_124]) ).
cnf(c_5,plain,
divide(A,inverse(divide(B,divide(A,inverse(divide(divide(B,C),divide(D,C))))))) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
divide(A,inverse(divide(divide(B,inverse(divide(divide(C,D),divide(A,D)))),C))) = B,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_10,plain,
divide(A,inverse(divide(B,B))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_125,plain,
divide(A,inverse(divide(B,divide(A,inverse(divide(C,C)))))) = B,
inference(paramod,[status(thm)],[c_10,c_1]) ).
cnf(c_11,plain,
divide(A,inverse(divide(B,A))) = B,
inference(paramod,[status(thm)],[c_10,c_125]) ).
cnf(c_20,plain,
divide(inverse(divide(A,A)),inverse(B)) = B,
inference(paramod,[status(thm)],[c_10,c_11]) ).
cnf(c_21,plain,
divide(inverse(divide(A,B)),inverse(A)) = B,
inference(paramod,[status(thm)],[c_11,c_11]) ).
cnf(c_126,plain,
divide(A,A) = inverse(divide(B,B)),
inference(paramod,[status(thm)],[c_20,c_10]) ).
cnf(c_27,plain,
inverse(divide(A,A)) = divide(B,B),
inference(copy,[status(thm)],[c_126]) ).
cnf(c_29,plain,
divide(A,divide(B,B)) = A,
inference(paramod,[status(thm)],[c_27,c_1]) ).
cnf(c_127,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| divide(inverse(divide(A,A)),inverse(a2)) != a2
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_27,c_4]) ).
cnf(c_128,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| a2 != a2
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(paramod,[status(thm)],[c_20,c_127]) ).
cnf(c_31,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) ),
inference(copy,[status(thm)],[c_128]) ).
cnf(c_35,plain,
divide(divide(A,A),inverse(B)) = B,
inference(paramod,[status(thm)],[c_27,c_20]) ).
cnf(c_36,plain,
divide(A,A) = divide(B,B),
inference(paramod,[status(thm)],[c_27,c_27]) ).
cnf(c_38,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))) ),
inference(resolve,[status(thm)],[c_36,c_31]) ).
cnf(c_47,plain,
divide(A,inverse(divide(divide(B,C),B))) = divide(A,C),
inference(paramod,[status(thm)],[c_11,c_6]) ).
cnf(c_129,plain,
divide(A,inverse(divide(divide(B,B),C))) = inverse(divide(divide(C,D),divide(A,D))),
inference(paramod,[status(thm)],[c_36,c_6]) ).
cnf(c_52,plain,
inverse(divide(divide(A,B),divide(C,B))) = divide(C,inverse(divide(divide(D,D),A))),
inference(copy,[status(thm)],[c_129]) ).
cnf(c_130,plain,
divide(inverse(A),inverse(B)) = inverse(divide(divide(A,C),divide(B,C))),
inference(paramod,[status(thm)],[c_1,c_21]) ).
cnf(c_59,plain,
inverse(divide(divide(A,B),divide(C,B))) = divide(inverse(A),inverse(C)),
inference(copy,[status(thm)],[c_130]) ).
cnf(c_131,plain,
divide(inverse(A),inverse(B)) = inverse(divide(A,B)),
inference(paramod,[status(thm)],[c_21,c_11]) ).
cnf(c_65,plain,
inverse(divide(A,B)) = divide(inverse(A),inverse(B)),
inference(copy,[status(thm)],[c_131]) ).
cnf(c_132,plain,
divide(A,inverse(divide(B,C))) = inverse(divide(divide(divide(C,D),divide(A,D)),B)),
inference(paramod,[status(thm)],[c_21,c_6]) ).
cnf(c_133,plain,
divide(A,divide(inverse(B),inverse(C))) = inverse(divide(divide(divide(C,D),divide(A,D)),B)),
inference(paramod,[status(thm)],[c_65,c_132]) ).
cnf(c_134,plain,
divide(A,divide(inverse(B),inverse(C))) = divide(inverse(divide(divide(C,D),divide(A,D))),inverse(B)),
inference(paramod,[status(thm)],[c_65,c_133]) ).
cnf(c_135,plain,
divide(A,divide(inverse(B),inverse(C))) = divide(divide(inverse(divide(C,D)),inverse(divide(A,D))),inverse(B)),
inference(paramod,[status(thm)],[c_65,c_134]) ).
cnf(c_136,plain,
divide(A,divide(inverse(B),inverse(C))) = divide(divide(divide(inverse(C),inverse(D)),inverse(divide(A,D))),inverse(B)),
inference(paramod,[status(thm)],[c_65,c_135]) ).
cnf(c_137,plain,
divide(A,divide(inverse(B),inverse(C))) = divide(divide(divide(inverse(C),inverse(D)),divide(inverse(A),inverse(D))),inverse(B)),
inference(paramod,[status(thm)],[c_65,c_136]) ).
cnf(c_66,plain,
divide(divide(divide(inverse(A),inverse(B)),divide(inverse(C),inverse(B))),inverse(D)) = divide(C,divide(inverse(D),inverse(A))),
inference(copy,[status(thm)],[c_137]) ).
cnf(c_138,plain,
divide(inverse(divide(A,B)),inverse(divide(C,B))) = divide(C,inverse(divide(divide(D,D),A))),
inference(paramod,[status(thm)],[c_65,c_52]) ).
cnf(c_139,plain,
divide(divide(inverse(A),inverse(B)),inverse(divide(C,B))) = divide(C,inverse(divide(divide(D,D),A))),
inference(paramod,[status(thm)],[c_65,c_138]) ).
cnf(c_140,plain,
divide(divide(inverse(A),inverse(B)),divide(inverse(C),inverse(B))) = divide(C,inverse(divide(divide(D,D),A))),
inference(paramod,[status(thm)],[c_65,c_139]) ).
cnf(c_141,plain,
divide(divide(inverse(A),inverse(B)),divide(inverse(C),inverse(B))) = divide(C,divide(inverse(divide(D,D)),inverse(A))),
inference(paramod,[status(thm)],[c_65,c_140]) ).
cnf(c_142,plain,
divide(divide(inverse(A),inverse(B)),divide(inverse(C),inverse(B))) = divide(C,divide(divide(inverse(D),inverse(D)),inverse(A))),
inference(paramod,[status(thm)],[c_65,c_141]) ).
cnf(c_71,plain,
divide(divide(inverse(A),inverse(B)),divide(inverse(C),inverse(B))) = divide(C,A),
inference(paramod,[status(thm)],[c_35,c_142]) ).
cnf(c_143,plain,
divide(A,divide(inverse(divide(B,C)),inverse(divide(A,C)))) = B,
inference(paramod,[status(thm)],[c_65,c_1]) ).
cnf(c_144,plain,
divide(A,divide(divide(inverse(B),inverse(C)),inverse(divide(A,C)))) = B,
inference(paramod,[status(thm)],[c_65,c_143]) ).
cnf(c_145,plain,
divide(A,divide(divide(inverse(B),inverse(C)),divide(inverse(A),inverse(C)))) = B,
inference(paramod,[status(thm)],[c_65,c_144]) ).
cnf(c_76,plain,
divide(A,divide(A,B)) = B,
inference(paramod,[status(thm)],[c_71,c_145]) ).
cnf(c_146,plain,
divide(inverse(divide(A,B)),inverse(divide(C,B))) = divide(inverse(A),inverse(C)),
inference(paramod,[status(thm)],[c_65,c_59]) ).
cnf(c_147,plain,
divide(divide(inverse(A),inverse(B)),inverse(divide(C,B))) = divide(inverse(A),inverse(C)),
inference(paramod,[status(thm)],[c_65,c_146]) ).
cnf(c_148,plain,
divide(divide(inverse(A),inverse(B)),divide(inverse(C),inverse(B))) = divide(inverse(A),inverse(C)),
inference(paramod,[status(thm)],[c_65,c_147]) ).
cnf(c_149,plain,
divide(C,A) = divide(inverse(A),inverse(C)),
inference(paramod,[status(thm)],[c_71,c_148]) ).
cnf(c_82,plain,
divide(inverse(A),inverse(B)) = divide(B,A),
inference(copy,[status(thm)],[c_149]) ).
cnf(c_150,plain,
divide(A,divide(inverse(divide(B,C)),inverse(B))) = divide(A,C),
inference(paramod,[status(thm)],[c_65,c_47]) ).
cnf(c_85,plain,
divide(A,divide(divide(inverse(B),inverse(C)),inverse(B))) = divide(A,C),
inference(paramod,[status(thm)],[c_65,c_150]) ).
cnf(c_87,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(b3),inverse(inverse(c3)))) ),
inference(paramod,[status(thm)],[c_65,c_38]) ).
cnf(c_89,plain,
divide(divide(A,B),inverse(C)) = divide(A,divide(inverse(C),inverse(B))),
inference(paramod,[status(thm)],[c_71,c_66]) ).
cnf(c_151,plain,
divide(A,divide(inverse(B),divide(inverse(B),inverse(inverse(C))))) = divide(A,C),
inference(paramod,[status(thm)],[c_89,c_85]) ).
cnf(c_90,plain,
divide(A,inverse(inverse(B))) = divide(A,B),
inference(paramod,[status(thm)],[c_76,c_151]) ).
cnf(c_152,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(a3,divide(inverse(c3),inverse(inverse(b3)))) != divide(a3,divide(inverse(b3),inverse(inverse(c3)))) ),
inference(paramod,[status(thm)],[c_89,c_87]) ).
cnf(c_153,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(a3,divide(inverse(c3),b3)) != divide(a3,divide(inverse(b3),inverse(inverse(c3)))) ),
inference(paramod,[status(thm)],[c_90,c_152]) ).
cnf(c_91,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(a3,divide(inverse(c3),b3)) != divide(a3,divide(inverse(b3),c3)) ),
inference(paramod,[status(thm)],[c_90,c_153]) ).
cnf(c_154,plain,
divide(inverse(divide(A,A)),inverse(B)) = B,
inference(paramod,[status(thm)],[c_82,c_29]) ).
cnf(c_155,plain,
divide(divide(inverse(A),inverse(A)),inverse(B)) = B,
inference(paramod,[status(thm)],[c_65,c_154]) ).
cnf(c_156,plain,
divide(inverse(A),divide(inverse(B),inverse(inverse(A)))) = B,
inference(paramod,[status(thm)],[c_89,c_155]) ).
cnf(c_101,plain,
divide(inverse(A),divide(inverse(B),A)) = B,
inference(paramod,[status(thm)],[c_90,c_156]) ).
cnf(c_107,plain,
divide(inverse(A),divide(B,A)) = inverse(B),
inference(paramod,[status(thm)],[c_82,c_76]) ).
cnf(c_108,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_107,c_101]) ).
cnf(c_157,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(a3,divide(inverse(b3),inverse(inverse(c3)))) != divide(a3,divide(inverse(b3),c3)) ),
inference(paramod,[status(thm)],[c_82,c_91]) ).
cnf(c_158,plain,
( divide(b4,inverse(a4)) != divide(a4,inverse(b4))
| divide(a3,divide(inverse(b3),c3)) != divide(a3,divide(inverse(b3),c3)) ),
inference(paramod,[status(thm)],[c_108,c_157]) ).
cnf(c_112,plain,
divide(b4,inverse(a4)) != divide(a4,inverse(b4)),
inference(copy,[status(thm)],[c_158]) ).
cnf(c_159,plain,
divide(inverse(inverse(a4)),inverse(b4)) != divide(a4,inverse(b4)),
inference(paramod,[status(thm)],[c_82,c_112]) ).
cnf(c_160,plain,
divide(a4,inverse(b4)) != divide(a4,inverse(b4)),
inference(paramod,[status(thm)],[c_108,c_159]) ).
cnf(c_113,plain,
$false,
inference(copy,[status(thm)],[c_160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP097-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n019.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 14:22:18 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.42 % Process 2941496 was started by sandbox2 on n019,
% 0.17/0.42 % Fri Sep 25 14:22:18 2026
% 0.17/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.43
% 0.17/0.43 % From the command line: assign(max_seconds, 300).
% 0.17/0.45
% 0.17/0.45 % Assigning unary symbol inverse kb_weight 0 and highest precedence (13).
% 0.17/0.45
% 0.17/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.45
% 0.17/0.45 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.17/0.45 % Length of proof is 34.
% 0.17/0.45 % Level of proof is 14.
% 0.17/0.45 % Maximum clause weight is 80.000.
% 0.17/0.45 % Given clauses 21.
% 0.17/0.45
% 0.17/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------