%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP434-1 : 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 07:29:32 AM UTC 2026
% Result : Unsatisfiable 1.03s 0.70s
% Output : CNFRefutation 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 2
% Syntax : Number of formulae : 49 ( 49 unt; 0 def)
% Number of atoms : 49 ( 48 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 11 ( 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 : 155 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(VAR_0,VAR_1),VAR_2)),VAR_0),VAR_1),multiply(VAR_3,inverse(VAR_3)))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),multiply(D,inverse(D)))) = 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,
inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),multiply(D,inverse(D)))) = multiply(E,inverse(E)),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
multiply(A,inverse(A)) = multiply(B,inverse(B)),
inference(paramod,[status(thm)],[c_3,c_3]) ).
cnf(c_7,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,inverse(A)),B)),C),inverse(C)),multiply(D,inverse(D)))) = B,
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_8,plain,
inverse(multiply(multiply(multiply(inverse(multiply(A,inverse(A))),B),C),multiply(D,inverse(D)))) = inverse(multiply(B,C)),
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_1291,plain,
inverse(multiply(multiply(multiply(inverse(multiply(A,inverse(A))),B),inverse(B)),multiply(C,inverse(C)))) = inverse(multiply(D,inverse(D))),
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_21,plain,
inverse(multiply(A,inverse(A))) = inverse(multiply(B,inverse(B))),
inference(paramod,[status(thm)],[c_8,c_1291]) ).
cnf(c_28,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))) = multiply(C,inverse(C)),
inference(paramod,[status(thm)],[c_21,c_6]) ).
cnf(c_33,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,inverse(A)),B)),multiply(C,inverse(C))),inverse(multiply(D,inverse(D)))),multiply(E,inverse(E)))) = B,
inference(paramod,[status(thm)],[c_28,c_1]) ).
cnf(c_1292,plain,
inverse(multiply(multiply(multiply(inverse(multiply(A,inverse(A))),multiply(inverse(multiply(B,inverse(B))),C)),inverse(C)),multiply(D,inverse(D)))) = multiply(E,inverse(E)),
inference(paramod,[status(thm)],[c_28,c_3]) ).
cnf(c_39,plain,
inverse(multiply(multiply(inverse(multiply(A,inverse(A))),B),inverse(B))) = multiply(C,inverse(C)),
inference(paramod,[status(thm)],[c_8,c_1292]) ).
cnf(c_1293,plain,
inverse(multiply(multiply(A,inverse(A)),multiply(B,inverse(B)))) = inverse(multiply(inverse(inverse(multiply(C,inverse(C)))),inverse(multiply(D,inverse(D))))),
inference(paramod,[status(thm)],[c_28,c_8]) ).
cnf(c_45,plain,
inverse(multiply(inverse(inverse(multiply(A,inverse(A)))),inverse(multiply(B,inverse(B))))) = inverse(multiply(multiply(C,inverse(C)),multiply(D,inverse(D)))),
inference(copy,[status(thm)],[c_1293]) ).
cnf(c_1294,plain,
inverse(multiply(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))),C),multiply(D,inverse(D)))) = inverse(multiply(inverse(inverse(multiply(E,inverse(E)))),C)),
inference(paramod,[status(thm)],[c_28,c_8]) ).
cnf(c_46,plain,
inverse(multiply(inverse(inverse(multiply(A,inverse(A)))),B)) = inverse(multiply(multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,inverse(D)))),B),multiply(E,inverse(E)))),
inference(copy,[status(thm)],[c_1294]) ).
cnf(c_53,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))) = multiply(multiply(C,inverse(C)),inverse(multiply(D,inverse(D)))),
inference(paramod,[status(thm)],[c_21,c_28]) ).
cnf(c_86,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))),C)),multiply(D,inverse(D))),inverse(multiply(E,inverse(E)))),multiply(F,inverse(F)))) = C,
inference(paramod,[status(thm)],[c_53,c_1]) ).
cnf(c_98,plain,
inverse(multiply(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))),C),multiply(D,inverse(D)))) = inverse(C),
inference(paramod,[status(thm)],[c_39,c_1]) ).
cnf(c_145,plain,
inverse(multiply(inverse(inverse(multiply(A,inverse(A)))),B)) = inverse(B),
inference(paramod,[status(thm)],[c_98,c_46]) ).
cnf(c_148,plain,
inverse(inverse(multiply(A,inverse(A)))) = inverse(multiply(multiply(B,inverse(B)),multiply(C,inverse(C)))),
inference(paramod,[status(thm)],[c_145,c_45]) ).
cnf(c_191,plain,
multiply(inverse(multiply(A,inverse(A))),inverse(multiply(multiply(B,inverse(B)),multiply(C,inverse(C))))) = multiply(D,inverse(D)),
inference(paramod,[status(thm)],[c_148,c_6]) ).
cnf(c_240,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_148,c_148]) ).
cnf(c_287,plain,
inverse(multiply(inverse(multiply(multiply(A,inverse(A)),multiply(B,inverse(B)))),C)) = inverse(C),
inference(paramod,[status(thm)],[c_148,c_145]) ).
cnf(c_482,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,inverse(A)),B)),inverse(multiply(C,inverse(C)))),inverse(multiply(multiply(D,inverse(D)),multiply(E,inverse(E))))),multiply(F,inverse(F)))) = B,
inference(paramod,[status(thm)],[c_191,c_1]) ).
cnf(c_1295,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,inverse(A)),multiply(B,inverse(B)))),C),inverse(C)),multiply(D,inverse(D)))) = inverse(multiply(multiply(E,inverse(E)),multiply(F,inverse(F)))),
inference(paramod,[status(thm)],[c_287,c_240]) ).
cnf(c_1296,plain,
multiply(B,inverse(B)) = inverse(multiply(multiply(E,inverse(E)),multiply(F,inverse(F)))),
inference(paramod,[status(thm)],[c_7,c_1295]) ).
cnf(c_727,plain,
inverse(multiply(multiply(A,inverse(A)),multiply(B,inverse(B)))) = multiply(C,inverse(C)),
inference(copy,[status(thm)],[c_1296]) ).
cnf(c_1297,plain,
inverse(multiply(inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,inverse(A)),multiply(B,inverse(B)))),C),inverse(C)),multiply(D,inverse(D)))),E)) = inverse(E),
inference(paramod,[status(thm)],[c_287,c_287]) ).
cnf(c_756,plain,
inverse(multiply(multiply(A,inverse(A)),B)) = inverse(B),
inference(paramod,[status(thm)],[c_7,c_1297]) ).
cnf(c_783,plain,
inverse(multiply(A,inverse(A))) = multiply(B,inverse(B)),
inference(paramod,[status(thm)],[c_756,c_727]) ).
cnf(c_1298,plain,
inverse(multiply(multiply(multiply(inverse(B),inverse(multiply(C,inverse(C)))),inverse(multiply(multiply(D,inverse(D)),multiply(E,inverse(E))))),multiply(F,inverse(F)))) = B,
inference(paramod,[status(thm)],[c_756,c_482]) ).
cnf(c_883,plain,
inverse(multiply(multiply(multiply(inverse(A),inverse(multiply(B,inverse(B)))),inverse(multiply(C,inverse(C)))),multiply(D,inverse(D)))) = A,
inference(paramod,[status(thm)],[c_756,c_1298]) ).
cnf(c_973,plain,
inverse(multiply(multiply(multiply(inverse(A),multiply(B,inverse(B))),inverse(multiply(C,inverse(C)))),multiply(D,inverse(D)))) = A,
inference(paramod,[status(thm)],[c_756,c_33]) ).
cnf(c_976,plain,
multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))),C) = C,
inference(paramod,[status(thm)],[c_973,c_86]) ).
cnf(c_1000,plain,
inverse(multiply(A,multiply(B,inverse(B)))) = inverse(A),
inference(paramod,[status(thm)],[c_976,c_98]) ).
cnf(c_1022,plain,
inverse(multiply(multiply(inverse(A),inverse(multiply(B,inverse(B)))),inverse(multiply(C,inverse(C))))) = A,
inference(paramod,[status(thm)],[c_1000,c_883]) ).
cnf(c_1157,plain,
inverse(multiply(A,inverse(multiply(B,inverse(B))))) = inverse(A),
inference(paramod,[status(thm)],[c_783,c_1000]) ).
cnf(c_1299,plain,
inverse(multiply(inverse(A),inverse(multiply(B,inverse(B))))) = A,
inference(paramod,[status(thm)],[c_1157,c_1022]) ).
cnf(c_1163,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_1157,c_1299]) ).
cnf(c_1252,plain,
multiply(inverse(A),A) = multiply(B,inverse(B)),
inference(paramod,[status(thm)],[c_1163,c_6]) ).
cnf(c_1300,plain,
inverse(inverse(A)) = multiply(multiply(B,inverse(B)),A),
inference(paramod,[status(thm)],[c_756,c_1163]) ).
cnf(c_1301,plain,
A = multiply(multiply(B,inverse(B)),A),
inference(paramod,[status(thm)],[c_1163,c_1300]) ).
cnf(c_1264,plain,
multiply(multiply(A,inverse(A)),B) = B,
inference(copy,[status(thm)],[c_1301]) ).
cnf(c_1302,plain,
multiply(multiply(A,inverse(A)),a2) != a2,
inference(paramod,[status(thm)],[c_1252,c_2]) ).
cnf(c_1303,plain,
a2 != a2,
inference(paramod,[status(thm)],[c_1264,c_1302]) ).
cnf(c_1290,plain,
$false,
inference(copy,[status(thm)],[c_1303]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP434-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n014.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 14:53:47 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 502251 was started by sandbox on n014,
% 0.16/0.43 % Fri Sep 25 14:53:47 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 1.03/0.70
% 1.03/0.70 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 1.03/0.70
% 1.03/0.70 % SZS status Unsatisfiable for theBenchmark
% 1.03/0.70
% 1.03/0.70 % Proof 1 at 0.18 (+ 0.07) seconds.
% 1.03/0.70 % Length of proof is 34.
% 1.03/0.70 % Level of proof is 18.
% 1.03/0.70 % Maximum clause weight is 99.000.
% 1.03/0.70 % Given clauses 29.
% 1.03/0.70
% 1.03/0.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------