%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP479-1 : TPTP v9.3.1. Released v2.6.0.
% 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 07:29:50 AM UTC 2026
% Result : Unsatisfiable 4.24s 1.06s
% Output : CNFRefutation 4.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 3
% Syntax : Number of formulae : 85 ( 85 unt; 0 def)
% Number of atoms : 85 ( 84 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 371 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : divide(inverse(divide(divide(divide(VAR_0,VAR_0),VAR_1),divide(VAR_2,divide(VAR_1,VAR_3)))),VAR_3) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(inverse(divide(divide(divide(A,A),B),divide(C,divide(B,D)))),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_2,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c_3,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(clausify,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_1870,plain,
multiply(divide(inverse(b2),inverse(b2)),a2) != a2,
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_4,plain,
divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2,
inference(paramod,[status(thm)],[c_2,c_1870]) ).
cnf(c_5,plain,
divide(inverse(divide(divide(divide(A,A),inverse(divide(divide(divide(B,B),C),divide(D,divide(C,E))))),divide(F,D))),E) = F,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_1871,plain,
divide(inverse(divide(divide(divide(A,A),B),C)),D) = inverse(divide(divide(divide(E,E),F),divide(C,divide(F,divide(B,D))))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
inverse(divide(divide(divide(A,A),B),divide(C,divide(B,divide(D,E))))) = divide(inverse(divide(divide(divide(F,F),D),C)),E),
inference(copy,[status(thm)],[c_1871]) ).
cnf(c_14,plain,
divide(divide(inverse(divide(divide(divide(A,A),B),C)),D),divide(B,D)) = C,
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_1872,plain,
inverse(divide(divide(divide(A,A),B),divide(divide(C,D),divide(B,divide(inverse(divide(divide(divide(E,E),F),divide(D,divide(F,V6)))),V6))))) = C,
inference(paramod,[status(thm)],[c_6,c_5]) ).
cnf(c_25,plain,
inverse(divide(divide(divide(A,A),B),divide(divide(C,D),divide(B,D)))) = C,
inference(paramod,[status(thm)],[c_1,c_1872]) ).
cnf(c_37,plain,
divide(inverse(divide(A,divide(B,divide(divide(C,inverse(divide(divide(divide(D,D),C),A))),E)))),E) = B,
inference(paramod,[status(thm)],[c_14,c_1]) ).
cnf(c_1873,plain,
inverse(divide(divide(divide(A,A),B),C)) = divide(inverse(divide(divide(divide(D,D),E),divide(inverse(divide(divide(divide(F,F),B),C)),divide(E,V6)))),V6),
inference(paramod,[status(thm)],[c_14,c_6]) ).
cnf(c_47,plain,
inverse(divide(divide(divide(A,A),B),C)) = inverse(divide(divide(divide(D,D),B),C)),
inference(paramod,[status(thm)],[c_1,c_1873]) ).
cnf(c_52,plain,
divide(divide(inverse(divide(A,B)),C),divide(divide(D,inverse(divide(divide(divide(E,E),D),A))),C)) = B,
inference(paramod,[status(thm)],[c_14,c_14]) ).
cnf(c_62,plain,
divide(divide(A,B),divide(C,B)) = divide(divide(A,D),divide(C,D)),
inference(paramod,[status(thm)],[c_25,c_14]) ).
cnf(c_65,plain,
divide(inverse(divide(divide(divide(A,B),divide(C,B)),divide(D,divide(divide(C,A),E)))),E) = D,
inference(paramod,[status(thm)],[c_62,c_1]) ).
cnf(c_81,plain,
divide(divide(inverse(divide(divide(divide(A,B),divide(C,B)),D)),E),divide(divide(C,A),E)) = D,
inference(paramod,[status(thm)],[c_62,c_14]) ).
cnf(c_82,plain,
divide(divide(inverse(divide(divide(divide(A,A),B),divide(C,B))),D),divide(E,D)) = divide(C,E),
inference(paramod,[status(thm)],[c_62,c_14]) ).
cnf(c_85,plain,
inverse(divide(divide(divide(A,B),divide(C,B)),divide(divide(D,E),divide(divide(C,A),E)))) = D,
inference(paramod,[status(thm)],[c_62,c_25]) ).
cnf(c_422,plain,
inverse(divide(divide(divide(divide(A,B),C),divide(divide(inverse(divide(divide(divide(D,D),E),divide(F,E))),B),C)),divide(divide(V6,V7),divide(divide(F,A),V7)))) = V6,
inference(paramod,[status(thm)],[c_82,c_85]) ).
cnf(c_424,plain,
inverse(divide(divide(divide(A,B),divide(C,B)),divide(D,divide(C,A)))) = inverse(divide(divide(divide(E,E),F),divide(D,F))),
inference(paramod,[status(thm)],[c_82,c_85]) ).
cnf(c_1874,plain,
divide(inverse(divide(A,divide(B,divide(C,inverse(divide(divide(divide(D,D),C),A)))))),E) = divide(inverse(divide(divide(divide(F,F),V6),divide(B,V6))),E),
inference(paramod,[status(thm)],[c_82,c_37]) ).
cnf(c_510,plain,
divide(inverse(divide(divide(divide(A,A),B),divide(C,B))),D) = divide(inverse(divide(E,divide(C,divide(F,inverse(divide(divide(divide(V6,V6),F),E)))))),D),
inference(copy,[status(thm)],[c_1874]) ).
cnf(c_1875,plain,
divide(A,B) = divide(A,divide(C,inverse(divide(divide(divide(D,D),C),divide(divide(E,E),B))))),
inference(paramod,[status(thm)],[c_52,c_82]) ).
cnf(c_567,plain,
divide(A,divide(B,inverse(divide(divide(divide(C,C),B),divide(divide(D,D),E))))) = divide(A,E),
inference(copy,[status(thm)],[c_1875]) ).
cnf(c_1876,plain,
divide(divide(inverse(divide(divide(divide(A,A),B),C)),D),divide(B,D)) = divide(E,inverse(divide(divide(divide(F,F),E),divide(divide(V6,V6),C)))),
inference(paramod,[status(thm)],[c_567,c_14]) ).
cnf(c_1877,plain,
C = divide(E,inverse(divide(divide(divide(F,F),E),divide(divide(V6,V6),C)))),
inference(paramod,[status(thm)],[c_14,c_1876]) ).
cnf(c_701,plain,
divide(A,inverse(divide(divide(divide(B,B),A),divide(divide(C,C),D)))) = D,
inference(copy,[status(thm)],[c_1877]) ).
cnf(c_714,plain,
divide(inverse(divide(divide(divide(A,B),divide(C,B)),divide(D,E))),inverse(divide(divide(divide(F,F),divide(C,A)),divide(divide(V6,V6),E)))) = D,
inference(paramod,[status(thm)],[c_567,c_65]) ).
cnf(c_744,plain,
divide(inverse(divide(divide(divide(A,A),B),divide(C,divide(D,D)))),B) = C,
inference(paramod,[status(thm)],[c_701,c_5]) ).
cnf(c_1878,plain,
inverse(divide(A,B)) = inverse(divide(divide(divide(C,C),inverse(divide(divide(divide(D,D),divide(E,E)),divide(divide(F,F),A)))),B)),
inference(paramod,[status(thm)],[c_701,c_47]) ).
cnf(c_765,plain,
inverse(divide(divide(divide(A,A),inverse(divide(divide(divide(B,B),divide(C,C)),divide(divide(D,D),E)))),F)) = inverse(divide(E,F)),
inference(copy,[status(thm)],[c_1878]) ).
cnf(c_1879,plain,
divide(divide(inverse(A),B),divide(divide(C,D),B)) = inverse(divide(divide(divide(E,E),divide(divide(D,F),divide(C,F))),divide(divide(V6,V6),A))),
inference(paramod,[status(thm)],[c_701,c_81]) ).
cnf(c_769,plain,
inverse(divide(divide(divide(A,A),divide(divide(B,C),divide(D,C))),divide(divide(E,E),F))) = divide(divide(inverse(F),V6),divide(divide(D,B),V6)),
inference(copy,[status(thm)],[c_1879]) ).
cnf(c_825,plain,
divide(inverse(divide(divide(divide(A,A),B),divide(divide(C,D),divide(E,D)))),B) = divide(C,E),
inference(paramod,[status(thm)],[c_62,c_744]) ).
cnf(c_1880,plain,
divide(inverse(divide(divide(divide(A,B),divide(C,B)),D)),E) = inverse(divide(divide(divide(F,F),divide(divide(C,A),E)),divide(D,divide(V6,V6)))),
inference(paramod,[status(thm)],[c_744,c_65]) ).
cnf(c_835,plain,
inverse(divide(divide(divide(A,A),divide(divide(B,C),D)),divide(E,divide(F,F)))) = divide(inverse(divide(divide(divide(C,V6),divide(B,V6)),E)),D),
inference(copy,[status(thm)],[c_1880]) ).
cnf(c_843,plain,
divide(A,divide(B,divide(C,C))) = divide(A,B),
inference(paramod,[status(thm)],[c_744,c_82]) ).
cnf(c_1881,plain,
divide(divide(inverse(divide(divide(divide(A,A),B),divide(inverse(divide(divide(divide(C,C),D),divide(E,divide(F,F)))),B))),V6),divide(D,V6)) = E,
inference(paramod,[status(thm)],[c_744,c_82]) ).
cnf(c_1882,plain,
divide(divide(inverse(divide(divide(divide(A,A),B),divide(inverse(divide(divide(divide(C,C),D),E)),B))),V6),divide(D,V6)) = E,
inference(paramod,[status(thm)],[c_843,c_1881]) ).
cnf(c_845,plain,
divide(inverse(divide(divide(divide(A,A),B),C)),B) = C,
inference(paramod,[status(thm)],[c_82,c_1882]) ).
cnf(c_1883,plain,
divide(inverse(divide(divide(divide(A,A),B),divide(C,divide(D,inverse(divide(divide(divide(E,E),F),divide(D,F))))))),B) = C,
inference(paramod,[status(thm)],[c_82,c_744]) ).
cnf(c_848,plain,
divide(A,divide(B,inverse(divide(divide(divide(C,C),D),divide(B,D))))) = A,
inference(paramod,[status(thm)],[c_845,c_1883]) ).
cnf(c_1884,plain,
divide(inverse(divide(divide(divide(A,A),B),C)),B) = inverse(divide(D,divide(C,divide(divide(E,inverse(divide(divide(divide(F,F),E),D))),divide(V6,V6))))),
inference(paramod,[status(thm)],[c_37,c_744]) ).
cnf(c_1885,plain,
C = inverse(divide(D,divide(C,divide(divide(E,inverse(divide(divide(divide(F,F),E),D))),divide(V6,V6))))),
inference(paramod,[status(thm)],[c_845,c_1884]) ).
cnf(c_1886,plain,
C = inverse(divide(D,divide(C,divide(E,inverse(divide(divide(divide(F,F),E),D)))))),
inference(paramod,[status(thm)],[c_843,c_1885]) ).
cnf(c_866,plain,
inverse(divide(A,divide(B,divide(C,inverse(divide(divide(divide(D,D),C),A)))))) = B,
inference(copy,[status(thm)],[c_1886]) ).
cnf(c_1887,plain,
divide(inverse(divide(divide(divide(A,A),B),C)),B) = inverse(divide(divide(divide(D,D),divide(E,E)),divide(C,divide(F,F)))),
inference(paramod,[status(thm)],[c_744,c_744]) ).
cnf(c_1888,plain,
C = inverse(divide(divide(divide(D,D),divide(E,E)),divide(C,divide(F,F)))),
inference(paramod,[status(thm)],[c_845,c_1887]) ).
cnf(c_1889,plain,
C = inverse(divide(divide(divide(D,D),divide(E,E)),C)),
inference(paramod,[status(thm)],[c_843,c_1888]) ).
cnf(c_876,plain,
inverse(divide(divide(divide(A,A),divide(B,B)),C)) = C,
inference(copy,[status(thm)],[c_1889]) ).
cnf(c_883,plain,
inverse(divide(divide(divide(A,A),divide(divide(B,C),D)),E)) = divide(inverse(divide(divide(divide(C,F),divide(B,F)),E)),D),
inference(paramod,[status(thm)],[c_843,c_835]) ).
cnf(c_910,plain,
divide(divide(A,B),divide(C,B)) = divide(A,C),
inference(paramod,[status(thm)],[c_845,c_825]) ).
cnf(c_1890,plain,
divide(inverse(divide(divide(A,A),C)),D) = divide(inverse(divide(E,divide(C,divide(F,inverse(divide(divide(divide(V6,V6),F),E)))))),D),
inference(paramod,[status(thm)],[c_910,c_510]) ).
cnf(c_921,plain,
divide(inverse(divide(divide(A,A),B)),C) = divide(B,C),
inference(paramod,[status(thm)],[c_866,c_1890]) ).
cnf(c_1891,plain,
inverse(divide(divide(divide(divide(A,B),C),divide(divide(inverse(divide(divide(D,D),F)),B),C)),divide(divide(V6,V7),divide(divide(F,A),V7)))) = V6,
inference(paramod,[status(thm)],[c_910,c_422]) ).
cnf(c_1892,plain,
inverse(divide(divide(divide(divide(A,B),C),divide(divide(F,B),C)),divide(divide(V6,V7),divide(divide(F,A),V7)))) = V6,
inference(paramod,[status(thm)],[c_921,c_1891]) ).
cnf(c_1893,plain,
inverse(divide(divide(divide(A,B),divide(F,B)),divide(divide(V6,V7),divide(divide(F,A),V7)))) = V6,
inference(paramod,[status(thm)],[c_910,c_1892]) ).
cnf(c_1894,plain,
inverse(divide(divide(A,F),divide(divide(V6,V7),divide(divide(F,A),V7)))) = V6,
inference(paramod,[status(thm)],[c_910,c_1893]) ).
cnf(c_924,plain,
inverse(divide(divide(A,B),divide(C,divide(B,A)))) = C,
inference(paramod,[status(thm)],[c_910,c_1894]) ).
cnf(c_976,plain,
inverse(divide(divide(divide(A,A),divide(divide(B,B),C)),D)) = inverse(divide(C,D)),
inference(paramod,[status(thm)],[c_876,c_765]) ).
cnf(c_1895,plain,
inverse(divide(divide(A,C),divide(D,divide(C,A)))) = inverse(divide(divide(divide(E,E),F),divide(D,F))),
inference(paramod,[status(thm)],[c_910,c_424]) ).
cnf(c_1896,plain,
D = inverse(divide(divide(divide(E,E),F),divide(D,F))),
inference(paramod,[status(thm)],[c_924,c_1895]) ).
cnf(c_1897,plain,
D = inverse(divide(divide(E,E),D)),
inference(paramod,[status(thm)],[c_910,c_1896]) ).
cnf(c_984,plain,
inverse(divide(divide(A,A),B)) = B,
inference(copy,[status(thm)],[c_1897]) ).
cnf(c_1898,plain,
divide(A,divide(B,inverse(divide(divide(C,C),B)))) = A,
inference(paramod,[status(thm)],[c_910,c_848]) ).
cnf(c_985,plain,
divide(A,divide(B,B)) = A,
inference(paramod,[status(thm)],[c_984,c_1898]) ).
cnf(c_1007,plain,
inverse(divide(divide(divide(A,A),divide(divide(B,C),D)),E)) = divide(inverse(divide(divide(C,B),E)),D),
inference(paramod,[status(thm)],[c_910,c_883]) ).
cnf(c_1899,plain,
inverse(divide(divide(divide(A,A),divide(B,D)),divide(divide(E,E),F))) = divide(divide(inverse(F),V6),divide(divide(D,B),V6)),
inference(paramod,[status(thm)],[c_910,c_769]) ).
cnf(c_1023,plain,
inverse(divide(divide(divide(A,A),divide(B,C)),divide(divide(D,D),E))) = divide(inverse(E),divide(C,B)),
inference(paramod,[status(thm)],[c_910,c_1899]) ).
cnf(c_1900,plain,
divide(inverse(divide(divide(A,C),divide(D,E))),inverse(divide(divide(divide(F,F),divide(C,A)),divide(divide(V6,V6),E)))) = D,
inference(paramod,[status(thm)],[c_910,c_714]) ).
cnf(c_1031,plain,
divide(inverse(divide(divide(A,B),divide(C,D))),divide(inverse(D),divide(A,B))) = C,
inference(paramod,[status(thm)],[c_1023,c_1900]) ).
cnf(c_1901,plain,
divide(inverse(divide(divide(B,B),D)),C) = inverse(divide(C,D)),
inference(paramod,[status(thm)],[c_1007,c_976]) ).
cnf(c_1902,plain,
divide(D,C) = inverse(divide(C,D)),
inference(paramod,[status(thm)],[c_984,c_1901]) ).
cnf(c_1239,plain,
inverse(divide(A,B)) = divide(B,A),
inference(copy,[status(thm)],[c_1902]) ).
cnf(c_1903,plain,
divide(divide(divide(C,D),divide(A,B)),divide(inverse(D),divide(A,B))) = C,
inference(paramod,[status(thm)],[c_1239,c_1031]) ).
cnf(c_1247,plain,
divide(divide(A,B),inverse(B)) = A,
inference(paramod,[status(thm)],[c_910,c_1903]) ).
cnf(c_1861,plain,
inverse(A) = divide(divide(B,B),A),
inference(paramod,[status(thm)],[c_985,c_1239]) ).
cnf(c_1904,plain,
divide(divide(divide(divide(A,A),b2),inverse(b2)),inverse(a2)) != a2,
inference(paramod,[status(thm)],[c_1861,c_4]) ).
cnf(c_1868,plain,
divide(divide(A,A),inverse(a2)) != a2,
inference(paramod,[status(thm)],[c_1247,c_1904]) ).
cnf(c_1869,plain,
$false,
inference(resolve,[status(thm)],[c_1868,c_1247]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP479-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:56:29 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 1033707 was started by sandbox on n010,
% 0.09/0.35 % Fri Sep 25 14:56:29 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 4.24/1.06
% 4.24/1.06 % SZS status Unsatisfiable for theBenchmark
% 4.24/1.06
% 4.24/1.06 % Proof 1 at 0.58 (+ 0.11) seconds.
% 4.24/1.06 % Length of proof is 47.
% 4.24/1.06 % Level of proof is 17.
% 4.24/1.06 % Maximum clause weight is 33.000.
% 4.24/1.06 % Given clauses 28.
% 4.24/1.06
% 4.24/1.06 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------