%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP404-1 : 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 : n014.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 07:28:47 AM UTC 2026
% Result : Unsatisfiable 39.00s 16.01s
% Output : CNFRefutation 39.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 2
% Syntax : Number of formulae : 59 ( 59 unt; 0 def)
% Number of atoms : 59 ( 58 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 15 ( 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 : 213 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,inverse(multiply(inverse(multiply(inverse(multiply(VAR_0,VAR_1)),VAR_2)),inverse(multiply(VAR_1,multiply(inverse(VAR_1),VAR_1)))))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),inverse(multiply(B,multiply(inverse(B),B)))))) = C,
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(inverse(B),C)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),inverse(multiply(D,multiply(inverse(D),D))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),inverse(multiply(D,multiply(inverse(D),D)))))),inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),inverse(multiply(D,multiply(inverse(D),D))))))))))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_10557,plain,
multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,multiply(inverse(C),C)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,C)),D)),B)),inverse(multiply(D,multiply(inverse(D),D))))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_4,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D)),inverse(multiply(C,multiply(inverse(C),C))))) = multiply(A,inverse(multiply(inverse(D),inverse(multiply(B,multiply(inverse(B),B)))))),
inference(copy,[status(thm)],[c_10557]) ).
cnf(c_13,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(C),inverse(multiply(B,multiply(inverse(B),B))))))) = C,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_10558,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),inverse(multiply(B,multiply(inverse(B),B))))))),D)),multiply(inverse(C),E))),inverse(multiply(D,multiply(inverse(D),D))))) = E,
inference(paramod,[status(thm)],[c_3,c_4]) ).
cnf(c_15,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(A),C))),inverse(multiply(B,multiply(inverse(B),B))))) = C,
inference(paramod,[status(thm)],[c_1,c_10558]) ).
cnf(c_10559,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(inverse(D),B)),multiply(inverse(D),C)),
inference(paramod,[status(thm)],[c_15,c_13]) ).
cnf(c_45,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(inverse(A),C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(copy,[status(thm)],[c_10559]) ).
cnf(c_10560,plain,
inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(C),D)),multiply(inverse(C),A))),inverse(multiply(D,multiply(inverse(D),D))))),E))),inverse(multiply(B,multiply(inverse(B),B))))) = E,
inference(paramod,[status(thm)],[c_15,c_15]) ).
cnf(c_46,plain,
inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(B,multiply(inverse(B),B))))) = C,
inference(paramod,[status(thm)],[c_15,c_10560]) ).
cnf(c_10561,plain,
multiply(inverse(A),multiply(inverse(multiply(B,C)),D)) = multiply(inverse(multiply(E,multiply(B,inverse(multiply(inverse(A),inverse(multiply(C,multiply(inverse(C),C)))))))),multiply(E,D)),
inference(paramod,[status(thm)],[c_13,c_45]) ).
cnf(c_86,plain,
multiply(inverse(multiply(A,multiply(B,inverse(multiply(inverse(C),inverse(multiply(D,multiply(inverse(D),D)))))))),multiply(A,E)) = multiply(inverse(C),multiply(inverse(multiply(B,D)),E)),
inference(copy,[status(thm)],[c_10561]) ).
cnf(c_89,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(paramod,[status(thm)],[c_45,c_45]) ).
cnf(c_100,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),D)),inverse(multiply(multiply(B,C),multiply(inverse(multiply(E,C)),multiply(E,C))))))) = D,
inference(paramod,[status(thm)],[c_89,c_1]) ).
cnf(c_124,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E))) = multiply(inverse(multiply(F,C)),multiply(F,multiply(A,E))),
inference(paramod,[status(thm)],[c_89,c_89]) ).
cnf(c_10562,plain,
multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),D)) = multiply(inverse(multiply(E,inverse(multiply(C,multiply(inverse(C),C))))),multiply(E,D)),
inference(paramod,[status(thm)],[c_46,c_89]) ).
cnf(c_141,plain,
multiply(inverse(multiply(A,inverse(multiply(B,multiply(inverse(B),B))))),multiply(A,C)) = multiply(D,multiply(inverse(multiply(inverse(multiply(E,B)),multiply(E,D))),C)),
inference(copy,[status(thm)],[c_10562]) ).
cnf(c_10563,plain,
multiply(inverse(A),multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(inverse(multiply(E,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(F,C)),V6)),A)),inverse(multiply(V6,multiply(inverse(V6),V6))))))),multiply(E,multiply(F,D))),
inference(paramod,[status(thm)],[c_1,c_124]) ).
cnf(c_10564,plain,
multiply(inverse(A),multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(inverse(multiply(E,multiply(F,inverse(multiply(inverse(A),inverse(multiply(C,multiply(inverse(C),C)))))))),multiply(E,multiply(F,D))),
inference(paramod,[status(thm)],[c_4,c_10563]) ).
cnf(c_211,plain,
multiply(inverse(A),multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(inverse(A),multiply(inverse(multiply(E,C)),multiply(E,D))),
inference(paramod,[status(thm)],[c_86,c_10564]) ).
cnf(c_10565,plain,
multiply(A,multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(E,F)),multiply(E,A))),inverse(multiply(F,multiply(inverse(F),F))))),multiply(inverse(multiply(V6,C)),multiply(V6,D))),
inference(paramod,[status(thm)],[c_46,c_211]) ).
cnf(c_354,plain,
multiply(A,multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(A,multiply(inverse(multiply(E,C)),multiply(E,D))),
inference(paramod,[status(thm)],[c_46,c_10565]) ).
cnf(c_10566,plain,
multiply(inverse(multiply(A,B)),inverse(multiply(C,inverse(multiply(multiply(A,C),multiply(inverse(multiply(D,C)),multiply(D,C))))))) = inverse(multiply(B,multiply(inverse(B),B))),
inference(paramod,[status(thm)],[c_46,c_100]) ).
cnf(c_483,plain,
inverse(multiply(A,multiply(inverse(A),A))) = multiply(inverse(multiply(B,A)),inverse(multiply(C,inverse(multiply(multiply(B,C),multiply(inverse(multiply(D,C)),multiply(D,C))))))),
inference(copy,[status(thm)],[c_10566]) ).
cnf(c_745,plain,
multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),D)) = multiply(E,multiply(inverse(multiply(inverse(multiply(F,C)),multiply(F,E))),D)),
inference(paramod,[status(thm)],[c_46,c_141]) ).
cnf(c_2469,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),inverse(multiply(B,multiply(inverse(B),B)))) = C,
inference(paramod,[status(thm)],[c_483,c_13]) ).
cnf(c_2771,plain,
multiply(inverse(A),A) = multiply(B,multiply(inverse(multiply(inverse(multiply(C,D)),multiply(C,B))),inverse(multiply(D,multiply(inverse(D),D))))),
inference(paramod,[status(thm)],[c_2469,c_745]) ).
cnf(c_10567,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(B,multiply(inverse(B),B))))) = multiply(C,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(D,E)),multiply(D,inverse(multiply(inverse(multiply(C,F)),B))))),inverse(multiply(E,multiply(inverse(E),E))))),inverse(multiply(F,multiply(inverse(F),F)))))),
inference(paramod,[status(thm)],[c_2771,c_4]) ).
cnf(c_10568,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(B,multiply(inverse(B),B))))) = multiply(C,inverse(multiply(inverse(multiply(inverse(multiply(C,F)),B)),inverse(multiply(F,multiply(inverse(F),F)))))),
inference(paramod,[status(thm)],[c_2469,c_10567]) ).
cnf(c_2855,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(B,multiply(inverse(B),B))))) = B,
inference(paramod,[status(thm)],[c_1,c_10568]) ).
cnf(c_3154,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(paramod,[status(thm)],[c_2469,c_2771]) ).
cnf(c_3169,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),inverse(multiply(B,multiply(inverse(D),D)))))) = C,
inference(paramod,[status(thm)],[c_3154,c_1]) ).
cnf(c_3170,plain,
multiply(multiply(inverse(A),A),a2) != a2,
inference(paramod,[status(thm)],[c_3154,c_2]) ).
cnf(c_10569,plain,
multiply(A,multiply(inverse(B),B)) = multiply(A,multiply(inverse(multiply(C,D)),multiply(C,D))),
inference(paramod,[status(thm)],[c_3154,c_354]) ).
cnf(c_3213,plain,
multiply(A,multiply(inverse(multiply(B,C)),multiply(B,C))) = multiply(A,multiply(inverse(D),D)),
inference(copy,[status(thm)],[c_10569]) ).
cnf(c_3313,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(B),multiply(inverse(inverse(B)),inverse(B))))) = B,
inference(paramod,[status(thm)],[c_3154,c_2469]) ).
cnf(c_3350,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(B,multiply(inverse(C),C))))) = B,
inference(paramod,[status(thm)],[c_3154,c_2855]) ).
cnf(c_3553,plain,
multiply(A,multiply(inverse(B),B)) = multiply(A,multiply(inverse(C),C)),
inference(paramod,[status(thm)],[c_3154,c_3213]) ).
cnf(c_3606,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),B)) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_3553,c_3154]) ).
cnf(c_10570,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(inverse(B),B)),multiply(inverse(C),C))))) = inverse(multiply(inverse(D),D)),
inference(paramod,[status(thm)],[c_3606,c_3350]) ).
cnf(c_3713,plain,
inverse(multiply(inverse(A),A)) = inverse(multiply(inverse(B),B)),
inference(paramod,[status(thm)],[c_3350,c_10570]) ).
cnf(c_3725,plain,
inverse(multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),B))) = inverse(multiply(inverse(C),C)),
inference(paramod,[status(thm)],[c_3553,c_3713]) ).
cnf(c_3956,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(B),multiply(inverse(C),C)))) = B,
inference(paramod,[status(thm)],[c_3154,c_3313]) ).
cnf(c_3960,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(B),B))) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_3606,c_3313]) ).
cnf(c_5991,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(B),B)),C)),inverse(multiply(multiply(inverse(D),D),multiply(inverse(E),E)))))) = C,
inference(paramod,[status(thm)],[c_3606,c_3169]) ).
cnf(c_10571,plain,
multiply(inverse(A),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(A,multiply(inverse(C),C)))))) = inverse(multiply(inverse(D),D)),
inference(paramod,[status(thm)],[c_3960,c_3169]) ).
cnf(c_10572,plain,
multiply(inverse(A),A) = inverse(multiply(inverse(D),D)),
inference(paramod,[status(thm)],[c_3350,c_10571]) ).
cnf(c_5997,plain,
inverse(multiply(inverse(A),A)) = multiply(inverse(B),B),
inference(copy,[status(thm)],[c_10572]) ).
cnf(c_6104,plain,
multiply(inverse(multiply(inverse(A),A)),a2) != a2,
inference(paramod,[status(thm)],[c_5997,c_3170]) ).
cnf(c_6261,plain,
inverse(multiply(multiply(inverse(A),A),multiply(inverse(B),B))) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_5997,c_5997]) ).
cnf(c_6827,plain,
multiply(inverse(multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),B))),a2) != a2,
inference(paramod,[status(thm)],[c_3553,c_6104]) ).
cnf(c_8838,plain,
multiply(inverse(multiply(inverse(multiply(inverse(A),A)),multiply(inverse(multiply(inverse(multiply(inverse(B),B)),multiply(inverse(C),C))),multiply(inverse(D),D)))),a2) != a2,
inference(paramod,[status(thm)],[c_3725,c_6827]) ).
cnf(c_10339,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(B),inverse(multiply(multiply(inverse(C),C),multiply(inverse(D),D)))))) = B,
inference(paramod,[status(thm)],[c_6261,c_3956]) ).
cnf(c_10555,plain,
multiply(inverse(multiply(inverse(A),A)),B) = B,
inference(paramod,[status(thm)],[c_10339,c_5991]) ).
cnf(c_10556,plain,
$false,
inference(resolve,[status(thm)],[c_10555,c_8838]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP404-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.37 % Computer : n014.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.37 % CPULimit : 300
% 0.10/10.37 % WCLimit : 300
% 0.10/10.37 % DateTime : Fri Sep 25 14:52:13 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/10.38 % Process 498440 was started by sandbox on n014,
% 0.10/10.38 % Fri Sep 25 14:52:13 2026
% 0.10/10.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/10.38
% 0.10/10.38 % From the command line: assign(max_seconds, 300).
% 39.00/16.01
% 39.00/16.01 % SZS status Unsatisfiable for theBenchmark
% 39.00/16.01
% 39.00/16.01 % Proof 1 at 4.79 (+ 0.80) seconds.
% 39.00/16.01 % Length of proof is 41.
% 39.00/16.01 % Level of proof is 18.
% 39.00/16.01 % Maximum clause weight is 63.000.
% 39.00/16.01 % Given clauses 122.
% 39.00/16.01
% 39.00/16.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------