%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP425-1 : 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 : n018.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 07:29:25 AM UTC 2026
% Result : Unsatisfiable 3.47s 1.09s
% Output : CNFRefutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of formulae : 46 ( 46 unt; 0 def)
% Number of atoms : 46 ( 45 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 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 : 141 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(inverse(multiply(inverse(multiply(VAR_0,inverse(multiply(inverse(VAR_1),VAR_2)))),multiply(VAR_0,inverse(VAR_2)))),inverse(multiply(inverse(VAR_2),VAR_2))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),C)))),multiply(A,inverse(C)))),inverse(multiply(inverse(C),C))) = B,
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(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(inverse(C),C)))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))) = multiply(inverse(multiply(D,inverse(multiply(inverse(B),C)))),multiply(D,inverse(C))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_5,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),inverse(multiply(inverse(C),C)))),C)))),multiply(A,inverse(C))) = B,
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_6,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(inverse(C),C)))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C)))))),inverse(multiply(inverse(C),C))) = B,
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_8,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(B),C)))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(multiply(inverse(B),C)))),multiply(D,inverse(C))),
inference(paramod,[status(thm)],[c_3,c_3]) ).
cnf(c_9,plain,
multiply(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,inverse(D)))))),inverse(multiply(inverse(multiply(C,inverse(D))),multiply(C,inverse(D))))) = multiply(C,inverse(multiply(inverse(multiply(inverse(B),inverse(multiply(inverse(D),D)))),D))),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_712,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,inverse(D))))) = multiply(inverse(multiply(E,inverse(multiply(inverse(multiply(C,inverse(multiply(inverse(multiply(inverse(B),inverse(multiply(inverse(D),D)))),D)))),multiply(C,inverse(D)))))),multiply(E,inverse(multiply(C,inverse(D))))),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_12,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,inverse(D))))) = multiply(inverse(multiply(E,inverse(B))),multiply(E,inverse(multiply(C,inverse(D))))),
inference(paramod,[status(thm)],[c_5,c_712]) ).
cnf(c_713,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(multiply(inverse(multiply(inverse(multiply(E,inverse(multiply(inverse(C),F)))),multiply(E,inverse(F)))),inverse(multiply(inverse(F),F)))))),
inference(paramod,[status(thm)],[c_1,c_12]) ).
cnf(c_15,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(C))),
inference(paramod,[status(thm)],[c_1,c_713]) ).
cnf(c_714,plain,
multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(B,inverse(C))),multiply(B,inverse(D)))))),multiply(A,inverse(multiply(E,inverse(D)))))),inverse(multiply(inverse(multiply(E,inverse(D))),multiply(E,inverse(D))))) = multiply(E,inverse(C)),
inference(paramod,[status(thm)],[c_15,c_1]) ).
cnf(c_17,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),multiply(B,inverse(D)))),inverse(multiply(inverse(D),D)))),D))) = multiply(A,inverse(C)),
inference(paramod,[status(thm)],[c_9,c_714]) ).
cnf(c_715,plain,
multiply(inverse(A),multiply(inverse(multiply(inverse(multiply(B,inverse(multiply(inverse(A),C)))),multiply(B,inverse(C)))),inverse(D))) = multiply(inverse(multiply(E,inverse(multiply(inverse(C),C)))),multiply(E,inverse(D))),
inference(paramod,[status(thm)],[c_1,c_15]) ).
cnf(c_19,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(C))) = multiply(inverse(D),multiply(inverse(multiply(inverse(multiply(E,inverse(multiply(inverse(D),B)))),multiply(E,inverse(B)))),inverse(C))),
inference(copy,[status(thm)],[c_715]) ).
cnf(c_26,plain,
multiply(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C)))),inverse(multiply(inverse(C),C))) = multiply(inverse(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(C)))),inverse(multiply(inverse(C),C))),
inference(paramod,[status(thm)],[c_17,c_1]) ).
cnf(c_716,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(inverse(C),C)))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C)))))),inverse(multiply(inverse(C),C))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(E)))),inverse(multiply(inverse(E),E)))),E),
inference(paramod,[status(thm)],[c_17,c_6]) ).
cnf(c_717,plain,
B = multiply(inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(E)))),inverse(multiply(inverse(E),E)))),E),
inference(paramod,[status(thm)],[c_6,c_716]) ).
cnf(c_33,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C)))),inverse(multiply(inverse(C),C)))),C) = B,
inference(copy,[status(thm)],[c_717]) ).
cnf(c_37,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(multiply(inverse(B),B)))) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_1,c_19]) ).
cnf(c_718,plain,
multiply(inverse(A),multiply(inverse(multiply(inverse(multiply(B,inverse(multiply(inverse(A),C)))),multiply(B,inverse(C)))),inverse(multiply(inverse(C),C)))) = multiply(inverse(D),D),
inference(paramod,[status(thm)],[c_1,c_37]) ).
cnf(c_44,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(paramod,[status(thm)],[c_1,c_718]) ).
cnf(c_719,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(inverse(B),B)),multiply(inverse(B),B)))) = multiply(inverse(multiply(inverse(multiply(C,inverse(multiply(inverse(B),B)))),multiply(C,inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(multiply(inverse(B),B)),multiply(inverse(B),B)))),
inference(paramod,[status(thm)],[c_37,c_26]) ).
cnf(c_57,plain,
multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(multiply(inverse(B),B)),multiply(inverse(B),B)))) = multiply(inverse(multiply(inverse(C),C)),inverse(multiply(inverse(multiply(inverse(B),B)),multiply(inverse(B),B)))),
inference(copy,[status(thm)],[c_719]) ).
cnf(c_68,plain,
multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(C)))),inverse(multiply(inverse(C),C))) = C,
inference(paramod,[status(thm)],[c_44,c_1]) ).
cnf(c_72,plain,
multiply(multiply(inverse(A),A),a2) != a2,
inference(paramod,[status(thm)],[c_44,c_2]) ).
cnf(c_91,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(inverse(B)),inverse(C))) = multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(C))),
inference(paramod,[status(thm)],[c_44,c_15]) ).
cnf(c_720,plain,
multiply(inverse(B),B) = multiply(inverse(multiply(inverse(C),C)),inverse(multiply(inverse(multiply(inverse(B),B)),multiply(inverse(B),B)))),
inference(paramod,[status(thm)],[c_68,c_57]) ).
cnf(c_111,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(inverse(B),B)),multiply(inverse(B),B)))) = multiply(inverse(B),B),
inference(copy,[status(thm)],[c_720]) ).
cnf(c_112,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(inverse(B)),inverse(B))) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_91,c_44]) ).
cnf(c_118,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),B)) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_44,c_112]) ).
cnf(c_442,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(B),B))) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_44,c_111]) ).
cnf(c_475,plain,
multiply(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(B),B))),a2) != a2,
inference(paramod,[status(thm)],[c_442,c_72]) ).
cnf(c_477,plain,
multiply(inverse(multiply(inverse(A),A)),multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(C),C)))) = multiply(inverse(D),D),
inference(paramod,[status(thm)],[c_442,c_118]) ).
cnf(c_554,plain,
multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(B),B))) = multiply(inverse(multiply(inverse(C),C)),inverse(multiply(inverse(D),D))),
inference(paramod,[status(thm)],[c_442,c_442]) ).
cnf(c_660,plain,
multiply(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(inverse(B),B)),multiply(inverse(multiply(inverse(C),C)),inverse(multiply(inverse(D),D)))))),a2) != a2,
inference(paramod,[status(thm)],[c_477,c_475]) ).
cnf(c_694,plain,
multiply(inverse(multiply(inverse(A),A)),B) = B,
inference(paramod,[status(thm)],[c_442,c_33]) ).
cnf(c_721,plain,
multiply(inverse(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(B),B)))),C) = C,
inference(paramod,[status(thm)],[c_554,c_33]) ).
cnf(c_703,plain,
multiply(inverse(inverse(multiply(inverse(A),A))),B) = B,
inference(paramod,[status(thm)],[c_694,c_721]) ).
cnf(c_722,plain,
multiply(multiply(inverse(multiply(inverse(A),A)),inverse(multiply(inverse(multiply(inverse(B),B)),inverse(multiply(inverse(D),D))))),a2) != a2,
inference(paramod,[status(thm)],[c_694,c_660]) ).
cnf(c_723,plain,
multiply(multiply(inverse(multiply(inverse(A),A)),inverse(inverse(multiply(inverse(D),D)))),a2) != a2,
inference(paramod,[status(thm)],[c_694,c_722]) ).
cnf(c_724,plain,
multiply(inverse(inverse(multiply(inverse(D),D))),a2) != a2,
inference(paramod,[status(thm)],[c_694,c_723]) ).
cnf(c_725,plain,
a2 != a2,
inference(paramod,[status(thm)],[c_703,c_724]) ).
cnf(c_711,plain,
$false,
inference(copy,[status(thm)],[c_725]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP425-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.58 % Computer : n018.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Fri Sep 25 14:55:51 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.59 % Process 2232785 was started by sandbox on n018,
% 0.10/0.59 % Fri Sep 25 14:55:51 2026
% 0.10/0.59 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.59
% 0.10/0.59 % From the command line: assign(max_seconds, 300).
% 3.47/1.09
% 3.47/1.09 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 3.47/1.09
% 3.47/1.09 % SZS status Unsatisfiable for theBenchmark
% 3.47/1.09
% 3.47/1.09 % Proof 1 at 0.27 (+ 0.10) seconds.
% 3.47/1.09 % Length of proof is 30.
% 3.47/1.09 % Level of proof is 13.
% 3.47/1.09 % Maximum clause weight is 93.000.
% 3.47/1.09 % Given clauses 60.
% 3.47/1.09
% 3.47/1.09 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------