%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP431-1 : 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 07:29:32 AM UTC 2026
% Result : Unsatisfiable 1.25s 0.61s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 2
% Syntax : Number of formulae : 81 ( 81 unt; 0 def)
% Number of atoms : 81 ( 80 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 12 ( 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 : 289 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : multiply(VAR_0,inverse(multiply(VAR_1,multiply(multiply(multiply(VAR_2,inverse(VAR_2)),inverse(multiply(VAR_3,VAR_1))),VAR_0)))) = VAR_3,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A)))) = 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,
multiply(A,inverse(multiply(inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),E))),multiply(multiply(multiply(F,inverse(F)),inverse(D)),A)))) = E,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_4,plain,
multiply(A,inverse(multiply(multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,D))),multiply(E,inverse(E))),multiply(C,A)))) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_5,plain,
multiply(inverse(multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,A))),multiply(multiply(D,inverse(D)),inverse(multiply(E,F)))))),inverse(multiply(F,C))) = E,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_7,plain,
multiply(A,inverse(multiply(multiply(multiply(multiply(B,inverse(B)),inverse(C)),multiply(D,inverse(D))),multiply(E,A)))) = inverse(multiply(F,multiply(multiply(multiply(V6,inverse(V6)),inverse(multiply(C,F))),E))),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_1222,plain,
multiply(A,inverse(multiply(multiply(B,multiply(C,inverse(C))),multiply(D,A)))) = multiply(multiply(multiply(E,inverse(E)),inverse(multiply(B,D))),multiply(F,inverse(F))),
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_18,plain,
multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,C))),multiply(D,inverse(D))) = multiply(E,inverse(multiply(multiply(B,multiply(F,inverse(F))),multiply(C,E)))),
inference(copy,[status(thm)],[c_1222]) ).
cnf(c_33,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,multiply(C,inverse(multiply(multiply(D,multiply(E,inverse(E))),multiply(B,C))))))) = D,
inference(paramod,[status(thm)],[c_18,c_1]) ).
cnf(c_95,plain,
multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(C,multiply(D,inverse(D))),multiply(A,B)))))),inverse(multiply(inverse(E),C))) = E,
inference(paramod,[status(thm)],[c_33,c_1]) ).
cnf(c_1223,plain,
multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(C,multiply(D,inverse(D))),multiply(A,B)))))),inverse(multiply(inverse(multiply(E,multiply(multiply(multiply(F,inverse(F)),inverse(multiply(multiply(V6,inverse(V6)),E))),V7))),C))) = V7,
inference(paramod,[status(thm)],[c_33,c_3]) ).
cnf(c_101,plain,
multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(multiply(C,inverse(C)),A))),D)) = D,
inference(paramod,[status(thm)],[c_95,c_1223]) ).
cnf(c_154,plain,
multiply(A,inverse(A)) = multiply(B,inverse(B)),
inference(paramod,[status(thm)],[c_101,c_1]) ).
cnf(c_1224,plain,
multiply(A,B) = inverse(multiply(C,multiply(multiply(multiply(D,inverse(D)),inverse(multiply(B,C))),multiply(multiply(E,inverse(E)),inverse(multiply(multiply(F,inverse(F)),A)))))),
inference(paramod,[status(thm)],[c_1,c_101]) ).
cnf(c_157,plain,
inverse(multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,A))),multiply(multiply(D,inverse(D)),inverse(multiply(multiply(E,inverse(E)),F)))))) = multiply(F,C),
inference(copy,[status(thm)],[c_1224]) ).
cnf(c_196,plain,
multiply(A,inverse(multiply(inverse(B),multiply(multiply(C,inverse(C)),A)))) = B,
inference(paramod,[status(thm)],[c_154,c_1]) ).
cnf(c_202,plain,
multiply(A,inverse(multiply(multiply(multiply(B,inverse(B)),multiply(C,inverse(C))),multiply(D,A)))) = inverse(D),
inference(paramod,[status(thm)],[c_154,c_4]) ).
cnf(c_216,plain,
multiply(inverse(multiply(A,inverse(A))),multiply(multiply(B,inverse(B)),C)) = C,
inference(paramod,[status(thm)],[c_154,c_101]) ).
cnf(c_245,plain,
multiply(inverse(multiply(A,inverse(A))),inverse(multiply(inverse(B),multiply(C,inverse(C))))) = B,
inference(paramod,[status(thm)],[c_154,c_196]) ).
cnf(c_270,plain,
multiply(inverse(multiply(A,inverse(A))),multiply(B,inverse(B))) = inverse(multiply(C,inverse(C))),
inference(paramod,[status(thm)],[c_154,c_216]) ).
cnf(c_1225,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(multiply(B,inverse(B))),multiply(multiply(C,inverse(C)),inverse(multiply(multiply(D,multiply(E,inverse(E))),inverse(multiply(F,inverse(F))))))))) = D,
inference(paramod,[status(thm)],[c_270,c_33]) ).
cnf(c_392,plain,
multiply(multiply(A,inverse(A)),inverse(inverse(multiply(multiply(B,multiply(C,inverse(C))),inverse(multiply(D,inverse(D))))))) = B,
inference(paramod,[status(thm)],[c_216,c_1225]) ).
cnf(c_408,plain,
inverse(multiply(A,inverse(A))) = inverse(multiply(B,inverse(B))),
inference(paramod,[status(thm)],[c_270,c_216]) ).
cnf(c_441,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))) = multiply(C,inverse(C)),
inference(paramod,[status(thm)],[c_408,c_154]) ).
cnf(c_1226,plain,
multiply(inverse(multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,A))),multiply(multiply(D,inverse(D)),inverse(multiply(multiply(E,inverse(E)),inverse(multiply(F,inverse(F))))))))),inverse(multiply(inverse(V6),C))) = V6,
inference(paramod,[status(thm)],[c_441,c_5]) ).
cnf(c_470,plain,
multiply(multiply(inverse(multiply(A,inverse(A))),B),inverse(multiply(inverse(C),B))) = C,
inference(paramod,[status(thm)],[c_157,c_1226]) ).
cnf(c_1227,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(multiply(C,multiply(multiply(multiply(D,inverse(D)),inverse(multiply(E,C))),B)))))) = multiply(multiply(F,inverse(F)),inverse(E)),
inference(paramod,[status(thm)],[c_7,c_33]) ).
cnf(c_537,plain,
multiply(multiply(A,inverse(A)),inverse(B)) = multiply(multiply(C,inverse(C)),inverse(B)),
inference(paramod,[status(thm)],[c_1,c_1227]) ).
cnf(c_642,plain,
multiply(A,inverse(multiply(inverse(inverse(multiply(B,inverse(B)))),multiply(C,A)))) = inverse(C),
inference(paramod,[status(thm)],[c_470,c_1]) ).
cnf(c_685,plain,
multiply(A,inverse(multiply(inverse(B),inverse(multiply(inverse(A),multiply(C,inverse(C))))))) = B,
inference(paramod,[status(thm)],[c_245,c_470]) ).
cnf(c_693,plain,
multiply(multiply(inverse(multiply(A,inverse(A))),inverse(inverse(B))),inverse(multiply(multiply(C,inverse(C)),inverse(multiply(D,inverse(D)))))) = B,
inference(paramod,[status(thm)],[c_441,c_470]) ).
cnf(c_1228,plain,
multiply(multiply(multiply(A,inverse(A)),inverse(multiply(multiply(B,inverse(B)),inverse(C)))),multiply(D,inverse(D))) = multiply(E,inverse(multiply(multiply(multiply(F,inverse(F)),multiply(V6,inverse(V6))),multiply(inverse(C),E)))),
inference(paramod,[status(thm)],[c_537,c_18]) ).
cnf(c_708,plain,
multiply(multiply(multiply(A,inverse(A)),inverse(multiply(multiply(B,inverse(B)),inverse(C)))),multiply(D,inverse(D))) = inverse(inverse(C)),
inference(paramod,[status(thm)],[c_202,c_1228]) ).
cnf(c_1229,plain,
multiply(A,inverse(B)) = multiply(multiply(C,inverse(C)),inverse(multiply(B,inverse(A)))),
inference(paramod,[status(thm)],[c_1,c_685]) ).
cnf(c_784,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(C)))) = multiply(C,inverse(B)),
inference(copy,[status(thm)],[c_1229]) ).
cnf(c_1230,plain,
multiply(A,B) = inverse(multiply(inverse(B),inverse(multiply(inverse(multiply(multiply(C,inverse(C)),inverse(multiply(multiply(D,inverse(D)),A)))),multiply(E,inverse(E)))))),
inference(paramod,[status(thm)],[c_685,c_101]) ).
cnf(c_806,plain,
inverse(multiply(inverse(A),inverse(multiply(inverse(multiply(multiply(B,inverse(B)),inverse(multiply(multiply(C,inverse(C)),D)))),multiply(E,inverse(E)))))) = multiply(D,A),
inference(copy,[status(thm)],[c_1230]) ).
cnf(c_1231,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(B),inverse(inverse(multiply(C,inverse(C))))))) = B,
inference(paramod,[status(thm)],[c_216,c_685]) ).
cnf(c_810,plain,
multiply(inverse(multiply(A,inverse(A))),inverse(inverse(B))) = B,
inference(paramod,[status(thm)],[c_784,c_1231]) ).
cnf(c_837,plain,
multiply(multiply(A,inverse(multiply(B,inverse(B)))),multiply(C,inverse(C))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_784,c_708]) ).
cnf(c_1232,plain,
multiply(B,inverse(multiply(multiply(C,inverse(C)),inverse(multiply(D,inverse(D)))))) = B,
inference(paramod,[status(thm)],[c_810,c_693]) ).
cnf(c_840,plain,
multiply(A,inverse(multiply(B,inverse(B)))) = A,
inference(paramod,[status(thm)],[c_784,c_1232]) ).
cnf(c_871,plain,
multiply(A,multiply(B,inverse(B))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_840,c_837]) ).
cnf(c_884,plain,
multiply(multiply(A,inverse(A)),inverse(inverse(multiply(B,multiply(C,inverse(C)))))) = B,
inference(paramod,[status(thm)],[c_840,c_392]) ).
cnf(c_1233,plain,
inverse(inverse(multiply(multiply(A,inverse(A)),inverse(multiply(B,C))))) = multiply(D,inverse(multiply(multiply(B,multiply(E,inverse(E))),multiply(C,D)))),
inference(paramod,[status(thm)],[c_871,c_18]) ).
cnf(c_1051,plain,
multiply(A,inverse(multiply(multiply(B,multiply(C,inverse(C))),multiply(D,A)))) = inverse(inverse(multiply(multiply(E,inverse(E)),inverse(multiply(B,D))))),
inference(copy,[status(thm)],[c_1233]) ).
cnf(c_1052,plain,
multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,C))),multiply(D,inverse(D))) = multiply(E,inverse(multiply(inverse(inverse(B)),multiply(C,E)))),
inference(paramod,[status(thm)],[c_871,c_18]) ).
cnf(c_1054,plain,
multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,C))),multiply(D,inverse(D))) = multiply(inverse(C),inverse(inverse(inverse(multiply(B,multiply(E,inverse(E))))))),
inference(paramod,[status(thm)],[c_871,c_18]) ).
cnf(c_1234,plain,
multiply(inverse(multiply(A,inverse(A))),inverse(inverse(inverse(inverse(B))))) = B,
inference(paramod,[status(thm)],[c_871,c_196]) ).
cnf(c_1080,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_810,c_1234]) ).
cnf(c_1085,plain,
multiply(inverse(multiply(A,inverse(A))),multiply(multiply(inverse(B),multiply(B,multiply(C,inverse(C)))),D)) = D,
inference(paramod,[status(thm)],[c_871,c_216]) ).
cnf(c_1235,plain,
multiply(A,multiply(multiply(B,inverse(B)),inverse(multiply(C,inverse(C))))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_408,c_871]) ).
cnf(c_1236,plain,
multiply(A,multiply(B,inverse(B))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_840,c_1235]) ).
cnf(c_1108,plain,
multiply(A,multiply(B,inverse(B))) = A,
inference(paramod,[status(thm)],[c_1080,c_1236]) ).
cnf(c_1237,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(inverse(inverse(multiply(B,inverse(B)))),inverse(inverse(C))))) = inverse(C),
inference(paramod,[status(thm)],[c_871,c_642]) ).
cnf(c_1238,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(multiply(B,inverse(B)),inverse(inverse(C))))) = inverse(C),
inference(paramod,[status(thm)],[c_1080,c_1237]) ).
cnf(c_1125,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(multiply(B,inverse(B)),C))) = inverse(C),
inference(paramod,[status(thm)],[c_1080,c_1238]) ).
cnf(c_1239,plain,
inverse(multiply(inverse(A),inverse(multiply(inverse(inverse(D)),multiply(E,inverse(E)))))) = multiply(D,A),
inference(paramod,[status(thm)],[c_1125,c_806]) ).
cnf(c_1240,plain,
inverse(multiply(inverse(A),inverse(multiply(D,multiply(E,inverse(E)))))) = multiply(D,A),
inference(paramod,[status(thm)],[c_1080,c_1239]) ).
cnf(c_1140,plain,
inverse(multiply(inverse(A),inverse(B))) = multiply(B,A),
inference(paramod,[status(thm)],[c_1108,c_1240]) ).
cnf(c_1241,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,C))) = multiply(inverse(C),inverse(inverse(inverse(multiply(B,multiply(E,inverse(E))))))),
inference(paramod,[status(thm)],[c_1108,c_1054]) ).
cnf(c_1242,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,C))) = multiply(inverse(C),inverse(inverse(inverse(B)))),
inference(paramod,[status(thm)],[c_1108,c_1241]) ).
cnf(c_1151,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,C))) = multiply(inverse(C),inverse(B)),
inference(paramod,[status(thm)],[c_1080,c_1242]) ).
cnf(c_1243,plain,
multiply(multiply(inverse(C),inverse(B)),multiply(D,inverse(D))) = multiply(E,inverse(multiply(inverse(inverse(B)),multiply(C,E)))),
inference(paramod,[status(thm)],[c_1151,c_1052]) ).
cnf(c_1244,plain,
multiply(inverse(C),inverse(B)) = multiply(E,inverse(multiply(inverse(inverse(B)),multiply(C,E)))),
inference(paramod,[status(thm)],[c_1108,c_1243]) ).
cnf(c_1245,plain,
multiply(inverse(C),inverse(B)) = multiply(E,inverse(multiply(B,multiply(C,E)))),
inference(paramod,[status(thm)],[c_1080,c_1244]) ).
cnf(c_1152,plain,
multiply(A,inverse(multiply(B,multiply(C,A)))) = multiply(inverse(C),inverse(B)),
inference(copy,[status(thm)],[c_1245]) ).
cnf(c_1246,plain,
multiply(A,inverse(multiply(B,multiply(D,A)))) = inverse(inverse(multiply(multiply(E,inverse(E)),inverse(multiply(B,D))))),
inference(paramod,[status(thm)],[c_1108,c_1051]) ).
cnf(c_1247,plain,
multiply(inverse(D),inverse(B)) = inverse(inverse(multiply(multiply(E,inverse(E)),inverse(multiply(B,D))))),
inference(paramod,[status(thm)],[c_1152,c_1246]) ).
cnf(c_1248,plain,
multiply(inverse(D),inverse(B)) = inverse(inverse(multiply(inverse(D),inverse(B)))),
inference(paramod,[status(thm)],[c_1151,c_1247]) ).
cnf(c_1249,plain,
multiply(inverse(D),inverse(B)) = inverse(multiply(B,D)),
inference(paramod,[status(thm)],[c_1140,c_1248]) ).
cnf(c_1153,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(copy,[status(thm)],[c_1249]) ).
cnf(c_1250,plain,
multiply(multiply(A,inverse(A)),inverse(inverse(B))) = B,
inference(paramod,[status(thm)],[c_1108,c_884]) ).
cnf(c_1182,plain,
multiply(multiply(A,inverse(A)),B) = B,
inference(paramod,[status(thm)],[c_1080,c_1250]) ).
cnf(c_1251,plain,
multiply(multiply(inverse(inverse(A)),inverse(A)),multiply(multiply(inverse(B),multiply(B,multiply(C,inverse(C)))),D)) = D,
inference(paramod,[status(thm)],[c_1153,c_1085]) ).
cnf(c_1252,plain,
multiply(multiply(A,inverse(A)),multiply(multiply(inverse(B),multiply(B,multiply(C,inverse(C)))),D)) = D,
inference(paramod,[status(thm)],[c_1080,c_1251]) ).
cnf(c_1253,plain,
multiply(multiply(A,inverse(A)),multiply(multiply(inverse(B),B),D)) = D,
inference(paramod,[status(thm)],[c_1108,c_1252]) ).
cnf(c_1220,plain,
multiply(multiply(inverse(A),A),B) = B,
inference(paramod,[status(thm)],[c_1182,c_1253]) ).
cnf(c_1221,plain,
$false,
inference(resolve,[status(thm)],[c_1220,c_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP431-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 25 14:53:49 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 3032017 was started by sandbox2 on n019,
% 0.11/0.38 % Fri Sep 25 14:53:49 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 1.25/0.61
% 1.25/0.61 % SZS status Unsatisfiable for theBenchmark
% 1.25/0.61
% 1.25/0.61 % Proof 1 at 0.18 (+ 0.03) seconds.
% 1.25/0.61 % Length of proof is 47.
% 1.25/0.61 % Level of proof is 23.
% 1.25/0.61 % Maximum clause weight is 34.000.
% 1.25/0.61 % Given clauses 25.
% 1.25/0.61
% 1.25/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------