%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP443-1 : TPTP v9.3.1. Released v2.6.0.
% 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 07:29:44 AM UTC 2026
% Result : Unsatisfiable 7.00s 1.35s
% Output : CNFRefutation 7.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 2
% Syntax : Number of formulae : 101 ( 101 unt; 0 def)
% Number of atoms : 101 ( 100 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 378 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : inverse(multiply(VAR_0,multiply(VAR_1,multiply(multiply(VAR_2,inverse(VAR_2)),inverse(multiply(VAR_3,multiply(VAR_0,VAR_1))))))) = VAR_3,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
inverse(multiply(A,multiply(B,multiply(multiply(C,inverse(C)),inverse(multiply(D,multiply(A,B))))))) = D,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(prove_these_axioms_2,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c_2,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(clausify,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_3,plain,
inverse(multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,multiply(D,A)))),multiply(multiply(E,inverse(E)),C)))) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_4,plain,
inverse(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,D)))),multiply(multiply(multiply(E,inverse(E)),B),multiply(multiply(F,inverse(F)),C)))) = D,
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_2923,plain,
inverse(multiply(multiply(multiply(A,inverse(A)),B),multiply(multiply(multiply(C,inverse(C)),D),multiply(multiply(E,inverse(E)),F)))) = multiply(multiply(V6,inverse(V6)),inverse(multiply(B,multiply(D,F)))),
inference(paramod,[status(thm)],[c_3,c_3]) ).
cnf(c_5,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,D)))) = inverse(multiply(multiply(multiply(E,inverse(E)),B),multiply(multiply(multiply(F,inverse(F)),C),multiply(multiply(V6,inverse(V6)),D)))),
inference(copy,[status(thm)],[c_2923]) ).
cnf(c_6,plain,
inverse(multiply(A,multiply(B,inverse(multiply(multiply(multiply(C,inverse(C)),D),multiply(multiply(multiply(E,inverse(E)),A),multiply(multiply(F,inverse(F)),B))))))) = D,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_7,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,inverse(multiply(D,multiply(multiply(multiply(E,inverse(E)),B),multiply(multiply(F,inverse(F)),C)))))))) = D,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_9,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(multiply(B,multiply(C,D))),multiply(B,C)))) = D,
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_10,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,D)))) = multiply(multiply(E,inverse(E)),inverse(multiply(B,multiply(C,D)))),
inference(paramod,[status(thm)],[c_5,c_5]) ).
cnf(c_2924,plain,
multiply(multiply(A,inverse(A)),B) = multiply(multiply(C,inverse(C)),inverse(multiply(D,multiply(E,multiply(multiply(F,inverse(F)),inverse(multiply(B,multiply(D,E)))))))),
inference(paramod,[status(thm)],[c_1,c_10]) ).
cnf(c_12,plain,
multiply(multiply(A,inverse(A)),B) = multiply(multiply(C,inverse(C)),B),
inference(paramod,[status(thm)],[c_1,c_2924]) ).
cnf(c_2925,plain,
inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(multiply(multiply(D,inverse(D)),inverse(multiply(E,multiply(multiply(F,inverse(F)),inverse(multiply(A,multiply(B,C))))))),multiply(multiply(V6,inverse(V6)),E)))) = multiply(V7,inverse(V7)),
inference(paramod,[status(thm)],[c_10,c_3]) ).
cnf(c_13,plain,
multiply(A,inverse(A)) = multiply(B,inverse(B)),
inference(paramod,[status(thm)],[c_3,c_2925]) ).
cnf(c_15,plain,
inverse(multiply(A,multiply(inverse(A),multiply(multiply(B,inverse(B)),inverse(multiply(C,multiply(D,inverse(D)))))))) = C,
inference(paramod,[status(thm)],[c_13,c_1]) ).
cnf(c_16,plain,
multiply(multiply(A,multiply(B,multiply(multiply(C,inverse(C)),inverse(multiply(D,multiply(A,B)))))),D) = multiply(E,inverse(E)),
inference(paramod,[status(thm)],[c_1,c_13]) ).
cnf(c_17,plain,
inverse(multiply(inverse(A),multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,multiply(D,inverse(D))))),multiply(multiply(E,inverse(E)),C)))) = A,
inference(paramod,[status(thm)],[c_13,c_3]) ).
cnf(c_20,plain,
inverse(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,inverse(C))))),multiply(multiply(multiply(D,inverse(D)),B),multiply(multiply(E,inverse(E)),F)))) = inverse(F),
inference(paramod,[status(thm)],[c_13,c_4]) ).
cnf(c_48,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))) = multiply(C,inverse(C)),
inference(paramod,[status(thm)],[c_12,c_13]) ).
cnf(c_2926,plain,
inverse(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,inverse(C))))),multiply(multiply(multiply(D,inverse(D)),B),multiply(multiply(E,inverse(E)),multiply(F,inverse(F)))))) = inverse(multiply(V6,inverse(V6))),
inference(paramod,[status(thm)],[c_48,c_4]) ).
cnf(c_60,plain,
inverse(multiply(A,inverse(A))) = inverse(multiply(B,inverse(B))),
inference(paramod,[status(thm)],[c_20,c_2926]) ).
cnf(c_170,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(multiply(B,multiply(C,inverse(C)))),multiply(B,D)))) = inverse(D),
inference(paramod,[status(thm)],[c_13,c_9]) ).
cnf(c_261,plain,
inverse(multiply(A,multiply(B,inverse(B)))) = inverse(multiply(A,multiply(C,inverse(C)))),
inference(paramod,[status(thm)],[c_170,c_1]) ).
cnf(c_266,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(multiply(B,multiply(C,inverse(C)))),multiply(D,inverse(D))))) = inverse(inverse(B)),
inference(paramod,[status(thm)],[c_13,c_170]) ).
cnf(c_2927,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(multiply(multiply(B,inverse(B)),multiply(C,inverse(C)))),multiply(D,inverse(D))))) = inverse(inverse(multiply(E,inverse(E)))),
inference(paramod,[status(thm)],[c_48,c_170]) ).
cnf(c_269,plain,
inverse(inverse(multiply(A,inverse(A)))) = inverse(inverse(multiply(B,inverse(B)))),
inference(paramod,[status(thm)],[c_266,c_2927]) ).
cnf(c_353,plain,
inverse(multiply(multiply(A,inverse(A)),multiply(B,inverse(B)))) = inverse(multiply(multiply(C,inverse(C)),multiply(D,inverse(D)))),
inference(paramod,[status(thm)],[c_12,c_261]) ).
cnf(c_905,plain,
inverse(multiply(A,multiply(inverse(A),B))) = inverse(multiply(C,multiply(inverse(C),B))),
inference(paramod,[status(thm)],[c_9,c_15]) ).
cnf(c_909,plain,
inverse(multiply(A,multiply(inverse(A),inverse(inverse(B))))) = inverse(multiply(B,multiply(C,inverse(C)))),
inference(paramod,[status(thm)],[c_170,c_15]) ).
cnf(c_934,plain,
multiply(multiply(A,multiply(inverse(A),B)),inverse(multiply(C,multiply(inverse(C),B)))) = multiply(D,inverse(D)),
inference(paramod,[status(thm)],[c_905,c_13]) ).
cnf(c_2928,plain,
inverse(multiply(inverse(multiply(A,multiply(inverse(A),B))),multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,multiply(E,inverse(E))))),multiply(multiply(F,inverse(F)),D)))) = multiply(V6,multiply(inverse(V6),B)),
inference(paramod,[status(thm)],[c_934,c_3]) ).
cnf(c_1215,plain,
multiply(A,multiply(inverse(A),B)) = multiply(C,multiply(inverse(C),B)),
inference(paramod,[status(thm)],[c_17,c_2928]) ).
cnf(c_2929,plain,
multiply(A,multiply(B,inverse(B))) = multiply(C,multiply(inverse(C),inverse(inverse(A)))),
inference(paramod,[status(thm)],[c_13,c_1215]) ).
cnf(c_1293,plain,
multiply(A,multiply(inverse(A),inverse(inverse(B)))) = multiply(B,multiply(C,inverse(C))),
inference(copy,[status(thm)],[c_2929]) ).
cnf(c_1370,plain,
multiply(multiply(multiply(A,inverse(A)),multiply(B,inverse(B))),multiply(inverse(multiply(multiply(C,inverse(C)),multiply(D,inverse(D)))),inverse(inverse(E)))) = multiply(E,multiply(F,inverse(F))),
inference(paramod,[status(thm)],[c_353,c_1293]) ).
cnf(c_2930,plain,
multiply(A,multiply(inverse(A),inverse(inverse(multiply(B,multiply(C,multiply(multiply(D,inverse(D)),inverse(multiply(multiply(E,inverse(E)),multiply(B,C)))))))))) = multiply(F,inverse(F)),
inference(paramod,[status(thm)],[c_16,c_1293]) ).
cnf(c_1488,plain,
multiply(A,multiply(inverse(A),inverse(multiply(B,inverse(B))))) = multiply(C,inverse(C)),
inference(paramod,[status(thm)],[c_1,c_2930]) ).
cnf(c_1493,plain,
inverse(multiply(inverse(A),multiply(inverse(multiply(B,inverse(B))),multiply(multiply(C,inverse(C)),inverse(multiply(D,inverse(D))))))) = A,
inference(paramod,[status(thm)],[c_1488,c_1]) ).
cnf(c_1500,plain,
inverse(multiply(inverse(multiply(A,inverse(A))),multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,inverse(C)))),multiply(multiply(D,inverse(D)),E)))) = inverse(E),
inference(paramod,[status(thm)],[c_1488,c_3]) ).
cnf(c_2931,plain,
inverse(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,inverse(C))))),multiply(multiply(multiply(D,inverse(D)),B),multiply(multiply(E,inverse(E)),F)))) = multiply(inverse(F),inverse(multiply(V6,inverse(V6)))),
inference(paramod,[status(thm)],[c_1488,c_4]) ).
cnf(c_2932,plain,
inverse(F) = multiply(inverse(F),inverse(multiply(V6,inverse(V6)))),
inference(paramod,[status(thm)],[c_20,c_2931]) ).
cnf(c_1507,plain,
multiply(inverse(A),inverse(multiply(B,inverse(B)))) = inverse(A),
inference(copy,[status(thm)],[c_2932]) ).
cnf(c_2933,plain,
multiply(A,inverse(multiply(B,inverse(B)))) = inverse(multiply(C,multiply(D,multiply(multiply(E,inverse(E)),inverse(multiply(A,multiply(C,D))))))),
inference(paramod,[status(thm)],[c_1,c_1507]) ).
cnf(c_1532,plain,
multiply(A,inverse(multiply(B,inverse(B)))) = A,
inference(paramod,[status(thm)],[c_1,c_2933]) ).
cnf(c_1558,plain,
inverse(multiply(inverse(multiply(A,inverse(A))),multiply(multiply(B,inverse(B)),multiply(multiply(C,inverse(C)),D)))) = inverse(D),
inference(paramod,[status(thm)],[c_1532,c_1500]) ).
cnf(c_1559,plain,
inverse(multiply(inverse(A),multiply(inverse(multiply(B,inverse(B))),multiply(C,inverse(C))))) = A,
inference(paramod,[status(thm)],[c_1532,c_1493]) ).
cnf(c_1570,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(multiply(B,C)),multiply(B,C)))) = inverse(multiply(D,inverse(D))),
inference(paramod,[status(thm)],[c_1532,c_9]) ).
cnf(c_2934,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(B),multiply(multiply(C,inverse(C)),inverse(multiply(D,multiply(E,inverse(multiply(B,multiply(multiply(multiply(F,inverse(F)),D),multiply(multiply(V6,inverse(V6)),E))))))))))) = inverse(multiply(V7,inverse(V7))),
inference(paramod,[status(thm)],[c_7,c_1570]) ).
cnf(c_1604,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(B),B))) = inverse(multiply(C,inverse(C))),
inference(paramod,[status(thm)],[c_7,c_2934]) ).
cnf(c_1753,plain,
inverse(multiply(multiply(A,inverse(A)),multiply(multiply(multiply(B,inverse(B)),inverse(multiply(inverse(C),C))),multiply(multiply(D,inverse(D)),inverse(multiply(E,multiply(F,inverse(F)))))))) = E,
inference(paramod,[status(thm)],[c_1604,c_15]) ).
cnf(c_1780,plain,
multiply(A,multiply(multiply(B,inverse(B)),inverse(multiply(inverse(C),C)))) = A,
inference(paramod,[status(thm)],[c_1604,c_1532]) ).
cnf(c_1782,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(B),B))) = multiply(multiply(C,inverse(C)),inverse(multiply(inverse(D),D))),
inference(paramod,[status(thm)],[c_1604,c_1604]) ).
cnf(c_1816,plain,
multiply(A,multiply(multiply(B,inverse(B)),inverse(multiply(multiply(multiply(C,inverse(C)),inverse(multiply(inverse(D),D))),multiply(E,inverse(E)))))) = A,
inference(paramod,[status(thm)],[c_1604,c_1780]) ).
cnf(c_1832,plain,
multiply(A,inverse(multiply(multiply(inverse(B),multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,multiply(E,inverse(E))))),multiply(multiply(F,inverse(F)),D))),B))) = A,
inference(paramod,[status(thm)],[c_17,c_1532]) ).
cnf(c_1835,plain,
multiply(A,multiply(multiply(B,inverse(B)),multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,multiply(E,inverse(E))))),multiply(multiply(F,inverse(F)),D)))) = A,
inference(paramod,[status(thm)],[c_17,c_1780]) ).
cnf(c_2935,plain,
inverse(multiply(A,multiply(B,inverse(multiply(multiply(multiply(C,inverse(C)),inverse(multiply(inverse(D),D))),multiply(multiply(multiply(E,inverse(E)),A),multiply(multiply(F,inverse(F)),B))))))) = inverse(multiply(inverse(V6),V6)),
inference(paramod,[status(thm)],[c_1782,c_6]) ).
cnf(c_1841,plain,
inverse(multiply(inverse(A),A)) = inverse(multiply(inverse(B),B)),
inference(paramod,[status(thm)],[c_6,c_2935]) ).
cnf(c_2936,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,multiply(D,inverse(D))))),multiply(multiply(E,inverse(E)),C)))) = multiply(inverse(F),F),
inference(paramod,[status(thm)],[c_1841,c_17]) ).
cnf(c_1941,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(paramod,[status(thm)],[c_17,c_2936]) ).
cnf(c_1952,plain,
multiply(multiply(inverse(A),A),a2) != a2,
inference(paramod,[status(thm)],[c_1941,c_2]) ).
cnf(c_1960,plain,
multiply(inverse(multiply(A,inverse(A))),multiply(B,inverse(B))) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_60,c_1941]) ).
cnf(c_2937,plain,
multiply(inverse(inverse(multiply(A,inverse(A)))),inverse(multiply(B,inverse(B)))) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_269,c_1941]) ).
cnf(c_2938,plain,
inverse(inverse(multiply(A,inverse(A)))) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_1532,c_2937]) ).
cnf(c_1965,plain,
multiply(inverse(A),A) = inverse(inverse(multiply(B,inverse(B)))),
inference(copy,[status(thm)],[c_2938]) ).
cnf(c_1982,plain,
multiply(A,multiply(inverse(B),B)) = multiply(C,multiply(inverse(C),A)),
inference(paramod,[status(thm)],[c_1941,c_1215]) ).
cnf(c_2027,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(multiply(B,multiply(inverse(C),C))),multiply(D,inverse(D))))) = B,
inference(paramod,[status(thm)],[c_1982,c_9]) ).
cnf(c_2939,plain,
multiply(multiply(inverse(inverse(multiply(A,inverse(A)))),inverse(multiply(B,inverse(B)))),a2) != a2,
inference(paramod,[status(thm)],[c_269,c_1952]) ).
cnf(c_2112,plain,
multiply(inverse(inverse(multiply(A,inverse(A)))),a2) != a2,
inference(paramod,[status(thm)],[c_1532,c_2939]) ).
cnf(c_2436,plain,
multiply(inverse(inverse(multiply(inverse(multiply(A,inverse(A))),multiply(inverse(B),B)))),a2) != a2,
inference(paramod,[status(thm)],[c_1965,c_2112]) ).
cnf(c_2940,plain,
inverse(multiply(inverse(multiply(A,inverse(A))),multiply(multiply(B,inverse(B)),multiply(multiply(C,inverse(C)),inverse(multiply(D,multiply(inverse(E),E))))))) = D,
inference(paramod,[status(thm)],[c_1960,c_1]) ).
cnf(c_2605,plain,
inverse(inverse(multiply(A,multiply(inverse(B),B)))) = A,
inference(paramod,[status(thm)],[c_1558,c_2940]) ).
cnf(c_2941,plain,
inverse(multiply(inverse(inverse(A)),multiply(inverse(multiply(B,inverse(B))),multiply(C,inverse(C))))) = inverse(multiply(A,multiply(D,inverse(D)))),
inference(paramod,[status(thm)],[c_1960,c_909]) ).
cnf(c_2942,plain,
inverse(A) = inverse(multiply(A,multiply(D,inverse(D)))),
inference(paramod,[status(thm)],[c_1559,c_2941]) ).
cnf(c_2659,plain,
inverse(multiply(A,multiply(B,inverse(B)))) = inverse(A),
inference(copy,[status(thm)],[c_2942]) ).
cnf(c_2696,plain,
multiply(inverse(multiply(A,inverse(A))),a2) != a2,
inference(paramod,[status(thm)],[c_2605,c_2436]) ).
cnf(c_2943,plain,
multiply(multiply(A,inverse(A)),inverse(inverse(multiply(B,multiply(inverse(C),C))))) = B,
inference(paramod,[status(thm)],[c_2659,c_2027]) ).
cnf(c_2847,plain,
multiply(multiply(A,inverse(A)),B) = B,
inference(paramod,[status(thm)],[c_2605,c_2943]) ).
cnf(c_2944,plain,
multiply(A,multiply(multiply(B,inverse(B)),multiply(multiply(multiply(C,inverse(C)),inverse(D)),multiply(multiply(F,inverse(F)),D)))) = A,
inference(paramod,[status(thm)],[c_2659,c_1835]) ).
cnf(c_2945,plain,
multiply(A,multiply(multiply(B,inverse(B)),multiply(inverse(D),multiply(multiply(F,inverse(F)),D)))) = A,
inference(paramod,[status(thm)],[c_2847,c_2944]) ).
cnf(c_2946,plain,
multiply(A,multiply(multiply(B,inverse(B)),multiply(inverse(D),D))) = A,
inference(paramod,[status(thm)],[c_2847,c_2945]) ).
cnf(c_2875,plain,
multiply(A,multiply(inverse(B),B)) = A,
inference(paramod,[status(thm)],[c_2847,c_2946]) ).
cnf(c_2947,plain,
multiply(A,inverse(multiply(multiply(inverse(B),multiply(multiply(multiply(C,inverse(C)),inverse(D)),multiply(multiply(F,inverse(F)),D))),B))) = A,
inference(paramod,[status(thm)],[c_2659,c_1832]) ).
cnf(c_2948,plain,
multiply(A,inverse(multiply(multiply(inverse(B),multiply(inverse(D),multiply(multiply(F,inverse(F)),D))),B))) = A,
inference(paramod,[status(thm)],[c_2847,c_2947]) ).
cnf(c_2949,plain,
multiply(A,inverse(multiply(multiply(inverse(B),multiply(inverse(D),D)),B))) = A,
inference(paramod,[status(thm)],[c_2847,c_2948]) ).
cnf(c_2877,plain,
multiply(A,inverse(multiply(inverse(B),B))) = A,
inference(paramod,[status(thm)],[c_2875,c_2949]) ).
cnf(c_2950,plain,
multiply(A,multiply(multiply(B,inverse(B)),inverse(multiply(multiply(C,inverse(C)),multiply(E,inverse(E)))))) = A,
inference(paramod,[status(thm)],[c_2877,c_1816]) ).
cnf(c_2951,plain,
multiply(A,multiply(multiply(B,inverse(B)),inverse(multiply(E,inverse(E))))) = A,
inference(paramod,[status(thm)],[c_2847,c_2950]) ).
cnf(c_2892,plain,
multiply(A,multiply(B,inverse(B))) = A,
inference(paramod,[status(thm)],[c_1532,c_2951]) ).
cnf(c_2952,plain,
inverse(multiply(multiply(A,inverse(A)),multiply(multiply(B,inverse(B)),multiply(multiply(D,inverse(D)),inverse(multiply(E,multiply(F,inverse(F)))))))) = E,
inference(paramod,[status(thm)],[c_2877,c_1753]) ).
cnf(c_2953,plain,
inverse(multiply(multiply(A,inverse(A)),multiply(multiply(B,inverse(B)),multiply(multiply(D,inverse(D)),inverse(E))))) = E,
inference(paramod,[status(thm)],[c_2892,c_2952]) ).
cnf(c_2954,plain,
inverse(multiply(multiply(A,inverse(A)),multiply(multiply(B,inverse(B)),inverse(E)))) = E,
inference(paramod,[status(thm)],[c_2847,c_2953]) ).
cnf(c_2955,plain,
inverse(multiply(multiply(A,inverse(A)),inverse(E))) = E,
inference(paramod,[status(thm)],[c_2847,c_2954]) ).
cnf(c_2901,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_2847,c_2955]) ).
cnf(c_2956,plain,
multiply(multiply(A,inverse(A)),multiply(inverse(multiply(multiply(C,inverse(C)),multiply(D,inverse(D)))),inverse(inverse(E)))) = multiply(E,multiply(F,inverse(F))),
inference(paramod,[status(thm)],[c_2892,c_1370]) ).
cnf(c_2957,plain,
multiply(multiply(A,inverse(A)),multiply(inverse(multiply(C,inverse(C))),inverse(inverse(E)))) = multiply(E,multiply(F,inverse(F))),
inference(paramod,[status(thm)],[c_2892,c_2956]) ).
cnf(c_2958,plain,
multiply(multiply(A,inverse(A)),multiply(inverse(multiply(C,inverse(C))),E)) = multiply(E,multiply(F,inverse(F))),
inference(paramod,[status(thm)],[c_2901,c_2957]) ).
cnf(c_2959,plain,
multiply(inverse(multiply(C,inverse(C))),E) = multiply(E,multiply(F,inverse(F))),
inference(paramod,[status(thm)],[c_2847,c_2958]) ).
cnf(c_2921,plain,
multiply(inverse(multiply(A,inverse(A))),B) = B,
inference(paramod,[status(thm)],[c_2892,c_2959]) ).
cnf(c_2922,plain,
$false,
inference(resolve,[status(thm)],[c_2921,c_2696]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP443-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.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 14:54:48 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3034451 was started by sandbox2 on n019,
% 0.09/0.37 % Fri Sep 25 14:54:48 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 7.00/1.35
% 7.00/1.35 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 7.00/1.35
% 7.00/1.35 % SZS status Unsatisfiable for theBenchmark
% 7.00/1.35
% 7.00/1.35 % Proof 1 at 0.73 (+ 0.23) seconds.
% 7.00/1.35 % Length of proof is 62.
% 7.00/1.35 % Level of proof is 26.
% 7.00/1.35 % Maximum clause weight is 98.000.
% 7.00/1.35 % Given clauses 67.
% 7.00/1.35
% 7.00/1.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------