%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP070-1 : 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 : n008.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 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 78 ( 65 unt; 0 def)
% Number of atoms : 102 ( 101 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 63 ( 39 ~; 24 |; 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 217 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : divide(divide(VAR_0,VAR_0),divide(VAR_1,divide(divide(VAR_2,divide(VAR_3,VAR_1)),inverse(VAR_3)))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(A,A),divide(B,divide(divide(C,divide(D,B)),inverse(D)))) = C,
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(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(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_117,plain,
( 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_118,plain,
( 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_117]) ).
cnf(c_119,plain,
( 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_118]) ).
cnf(c_120,plain,
( 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_119]) ).
cnf(c_121,plain,
( 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_120]) ).
cnf(c_122,plain,
( 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_121]) ).
cnf(c_123,plain,
( 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_122]) ).
cnf(c_124,plain,
( 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_123]) ).
cnf(c_4,plain,
( 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(divide(A,A),divide(divide(B,divide(divide(C,divide(D,B)),inverse(D))),divide(divide(E,C),inverse(divide(F,F))))) = E,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
divide(divide(A,A),divide(divide(divide(B,divide(C,D)),inverse(C)),divide(B,inverse(D)))) = divide(E,E),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_8,plain,
divide(A,A) = divide(B,B),
inference(paramod,[status(thm)],[c_6,c_6]) ).
cnf(c_9,plain,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2 ),
inference(resolve,[status(thm)],[c_8,c_4]) ).
cnf(c_11,plain,
divide(divide(A,A),divide(B,divide(divide(C,C),inverse(D)))) = divide(D,B),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_22,plain,
divide(A,divide(divide(B,B),inverse(A))) = divide(C,C),
inference(paramod,[status(thm)],[c_11,c_8]) ).
cnf(c_125,plain,
divide(divide(A,A),divide(inverse(B),divide(divide(C,C),inverse(divide(D,D))))) = B,
inference(paramod,[status(thm)],[c_22,c_1]) ).
cnf(c_27,plain,
divide(divide(A,A),inverse(B)) = B,
inference(paramod,[status(thm)],[c_11,c_125]) ).
cnf(c_126,plain,
divide(divide(A,A),divide(B,divide(divide(C,divide(divide(D,D),inverse(C))),inverse(E)))) = divide(E,B),
inference(paramod,[status(thm)],[c_22,c_1]) ).
cnf(c_127,plain,
divide(divide(A,A),divide(B,divide(divide(C,C),inverse(E)))) = divide(E,B),
inference(paramod,[status(thm)],[c_27,c_126]) ).
cnf(c_29,plain,
divide(divide(A,A),divide(B,C)) = divide(C,B),
inference(paramod,[status(thm)],[c_27,c_127]) ).
cnf(c_128,plain,
divide(divide(A,A),divide(divide(divide(divide(B,B),inverse(C)),divide(divide(D,divide(E,E)),inverse(C))),divide(divide(F,D),inverse(divide(V6,V6))))) = F,
inference(paramod,[status(thm)],[c_22,c_5]) ).
cnf(c_129,plain,
divide(divide(A,A),divide(divide(C,divide(divide(D,divide(E,E)),inverse(C))),divide(divide(F,D),inverse(divide(V6,V6))))) = F,
inference(paramod,[status(thm)],[c_27,c_128]) ).
cnf(c_30,plain,
divide(divide(divide(A,B),inverse(divide(C,C))),divide(D,divide(divide(B,divide(E,E)),inverse(D)))) = A,
inference(paramod,[status(thm)],[c_29,c_129]) ).
cnf(c_130,plain,
divide(divide(A,A),divide(divide(B,B),divide(divide(C,divide(D,D)),inverse(divide(E,E))))) = C,
inference(paramod,[status(thm)],[c_22,c_5]) ).
cnf(c_131,plain,
divide(divide(A,A),divide(inverse(divide(E,E)),divide(C,divide(D,D)))) = C,
inference(paramod,[status(thm)],[c_29,c_130]) ).
cnf(c_32,plain,
divide(divide(A,divide(B,B)),inverse(divide(C,C))) = A,
inference(paramod,[status(thm)],[c_29,c_131]) ).
cnf(c_132,plain,
divide(divide(A,A),divide(divide(B,divide(divide(divide(divide(C,C),inverse(D)),divide(E,B)),inverse(E))),divide(divide(F,F),inverse(divide(V6,V6))))) = D,
inference(paramod,[status(thm)],[c_22,c_5]) ).
cnf(c_133,plain,
divide(divide(A,A),divide(divide(B,divide(divide(D,divide(E,B)),inverse(E))),divide(divide(F,F),inverse(divide(V6,V6))))) = D,
inference(paramod,[status(thm)],[c_27,c_132]) ).
cnf(c_134,plain,
divide(divide(A,A),divide(divide(B,divide(divide(D,divide(E,B)),inverse(E))),divide(V6,V6))) = D,
inference(paramod,[status(thm)],[c_27,c_133]) ).
cnf(c_135,plain,
divide(divide(V6,V6),divide(B,divide(divide(D,divide(E,B)),inverse(E)))) = D,
inference(paramod,[status(thm)],[c_29,c_134]) ).
cnf(c_33,plain,
divide(divide(divide(A,divide(B,C)),inverse(B)),C) = A,
inference(paramod,[status(thm)],[c_29,c_135]) ).
cnf(c_136,plain,
divide(divide(A,A),divide(divide(divide(B,B),inverse(divide(C,C))),divide(D,inverse(inverse(D))))) = divide(E,E),
inference(paramod,[status(thm)],[c_22,c_6]) ).
cnf(c_137,plain,
divide(divide(A,A),divide(divide(C,C),divide(D,inverse(inverse(D))))) = divide(E,E),
inference(paramod,[status(thm)],[c_27,c_136]) ).
cnf(c_138,plain,
divide(divide(A,A),divide(inverse(inverse(D)),D)) = divide(E,E),
inference(paramod,[status(thm)],[c_29,c_137]) ).
cnf(c_37,plain,
divide(A,inverse(inverse(A))) = divide(B,B),
inference(paramod,[status(thm)],[c_29,c_138]) ).
cnf(c_139,plain,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| a2 != a2 ),
inference(paramod,[status(thm)],[c_27,c_9]) ).
cnf(c_44,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(copy,[status(thm)],[c_139]) ).
cnf(c_140,plain,
divide(divide(A,A),B) = divide(inverse(B),divide(C,C)),
inference(paramod,[status(thm)],[c_27,c_29]) ).
cnf(c_50,plain,
divide(inverse(A),divide(B,B)) = divide(divide(C,C),A),
inference(copy,[status(thm)],[c_140]) ).
cnf(c_141,plain,
divide(divide(A,A),divide(B,B)) = divide(inverse(inverse(C)),C),
inference(paramod,[status(thm)],[c_37,c_29]) ).
cnf(c_142,plain,
divide(B,B) = divide(inverse(inverse(C)),C),
inference(paramod,[status(thm)],[c_29,c_141]) ).
cnf(c_51,plain,
divide(inverse(inverse(A)),A) = divide(B,B),
inference(copy,[status(thm)],[c_142]) ).
cnf(c_75,plain,
divide(divide(inverse(inverse(A)),A),divide(B,C)) = divide(C,B),
inference(paramod,[status(thm)],[c_51,c_29]) ).
cnf(c_143,plain,
divide(divide(divide(A,divide(B,B)),inverse(divide(C,C))),divide(D,divide(divide(E,E),inverse(D)))) = A,
inference(paramod,[status(thm)],[c_8,c_30]) ).
cnf(c_144,plain,
divide(A,divide(D,divide(divide(E,E),inverse(D)))) = A,
inference(paramod,[status(thm)],[c_32,c_143]) ).
cnf(c_85,plain,
divide(A,divide(B,B)) = A,
inference(paramod,[status(thm)],[c_27,c_144]) ).
cnf(c_145,plain,
divide(divide(A,A),divide(B,divide(divide(C,divide(D,D)),inverse(B)))) = C,
inference(paramod,[status(thm)],[c_27,c_30]) ).
cnf(c_146,plain,
divide(divide(A,A),divide(B,divide(C,inverse(B)))) = C,
inference(paramod,[status(thm)],[c_85,c_145]) ).
cnf(c_87,plain,
divide(divide(A,inverse(B)),B) = A,
inference(paramod,[status(thm)],[c_29,c_146]) ).
cnf(c_147,plain,
divide(divide(divide(A,divide(B,B)),inverse(divide(C,C))),divide(D,D)) = A,
inference(paramod,[status(thm)],[c_27,c_30]) ).
cnf(c_148,plain,
divide(divide(A,inverse(divide(C,C))),divide(D,D)) = A,
inference(paramod,[status(thm)],[c_85,c_147]) ).
cnf(c_88,plain,
divide(A,inverse(divide(B,B))) = A,
inference(paramod,[status(thm)],[c_85,c_148]) ).
cnf(c_149,plain,
divide(divide(divide(A,A),inverse(divide(B,B))),divide(C,divide(divide(inverse(inverse(D)),divide(E,E)),inverse(C)))) = D,
inference(paramod,[status(thm)],[c_37,c_30]) ).
cnf(c_150,plain,
divide(divide(A,A),divide(C,divide(divide(inverse(inverse(D)),divide(E,E)),inverse(C)))) = D,
inference(paramod,[status(thm)],[c_88,c_149]) ).
cnf(c_151,plain,
divide(divide(A,A),divide(C,divide(inverse(inverse(D)),inverse(C)))) = D,
inference(paramod,[status(thm)],[c_85,c_150]) ).
cnf(c_152,plain,
divide(divide(inverse(inverse(D)),inverse(C)),C) = D,
inference(paramod,[status(thm)],[c_29,c_151]) ).
cnf(c_89,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_87,c_152]) ).
cnf(c_153,plain,
divide(divide(divide(A,B),inverse(divide(C,C))),divide(inverse(divide(B,divide(D,D))),divide(E,E))) = A,
inference(paramod,[status(thm)],[c_37,c_30]) ).
cnf(c_154,plain,
divide(divide(A,B),divide(inverse(divide(B,divide(D,D))),divide(E,E))) = A,
inference(paramod,[status(thm)],[c_88,c_153]) ).
cnf(c_155,plain,
divide(divide(A,B),divide(inverse(B),divide(E,E))) = A,
inference(paramod,[status(thm)],[c_85,c_154]) ).
cnf(c_90,plain,
divide(divide(A,B),inverse(B)) = A,
inference(paramod,[status(thm)],[c_85,c_155]) ).
cnf(c_156,plain,
inverse(A) = divide(divide(C,C),A),
inference(paramod,[status(thm)],[c_85,c_50]) ).
cnf(c_98,plain,
divide(divide(A,A),B) = inverse(B),
inference(copy,[status(thm)],[c_156]) ).
cnf(c_157,plain,
divide(divide(A,A),divide(B,C)) = divide(C,B),
inference(paramod,[status(thm)],[c_89,c_75]) ).
cnf(c_102,plain,
inverse(divide(A,B)) = divide(B,A),
inference(paramod,[status(thm)],[c_98,c_157]) ).
cnf(c_104,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(c3),b3)),
inference(paramod,[status(thm)],[c_102,c_44]) ).
cnf(c_158,plain,
divide(A,inverse(B)) = divide(divide(A,divide(C,B)),inverse(C)),
inference(paramod,[status(thm)],[c_33,c_90]) ).
cnf(c_112,plain,
divide(divide(A,divide(B,C)),inverse(B)) = divide(A,inverse(C)),
inference(copy,[status(thm)],[c_158]) ).
cnf(c_159,plain,
divide(divide(A,inverse(B)),C) = divide(divide(A,divide(D,divide(B,C))),inverse(D)),
inference(paramod,[status(thm)],[c_33,c_33]) ).
cnf(c_160,plain,
divide(divide(A,inverse(B)),C) = divide(A,inverse(divide(B,C))),
inference(paramod,[status(thm)],[c_112,c_159]) ).
cnf(c_115,plain,
divide(divide(A,inverse(B)),C) = divide(A,divide(C,B)),
inference(paramod,[status(thm)],[c_102,c_160]) ).
cnf(c_116,plain,
$false,
inference(resolve,[status(thm)],[c_115,c_104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP070-1 : 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 : n008.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 14:21:24 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1241732 was started by sandbox2 on n008,
% 0.09/0.37 % Fri Sep 25 14:21:24 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.15/0.44
% 0.15/0.44 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 0.15/0.44
% 0.15/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.44
% 0.15/0.44 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.15/0.44 % Length of proof is 31.
% 0.15/0.44 % Level of proof is 13.
% 0.15/0.44 % Maximum clause weight is 100.000.
% 0.15/0.44 % Given clauses 27.
% 0.15/0.44
% 0.15/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------