%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP409-1 : 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 : n017.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 07:29:08 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 19 unt; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 60 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(inverse(multiply(VAR_0,inverse(multiply(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(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(inverse(C),C))) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(prove_these_axioms_1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('theBenchmark.p',prove_these_axioms_1) ).
cnf(c_2,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(clausify,[status(thm)],[prove_these_axioms_1]) ).
cnf(c_3,plain,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
inference(copy,[status(thm)],[c_2]) ).
cnf(c_112,plain,
multiply(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(B,C)))),multiply(D,inverse(C))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_4,plain,
multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))) = multiply(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),
inference(copy,[status(thm)],[c_112]) ).
cnf(c_10,plain,
multiply(inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),C))),C)))),multiply(A,inverse(C))) = B,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_14,plain,
multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(multiply(B,C)))),multiply(D,inverse(C))),
inference(paramod,[status(thm)],[c_4,c_4]) ).
cnf(c_113,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(multiply(B,inverse(multiply(inverse(D),D))),D)))),multiply(C,inverse(D)))))),multiply(E,inverse(multiply(C,inverse(D))))),
inference(paramod,[status(thm)],[c_10,c_14]) ).
cnf(c_39,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_10,c_113]) ).
cnf(c_114,plain,
multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(multiply(multiply(inverse(multiply(E,inverse(multiply(C,F)))),multiply(E,inverse(F))),inverse(multiply(inverse(F),F)))))),
inference(paramod,[status(thm)],[c_1,c_39]) ).
cnf(c_43,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_114]) ).
cnf(c_115,plain,
multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(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_43]) ).
cnf(c_56,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(B),B)))),multiply(A,inverse(C))) = multiply(inverse(D),multiply(multiply(inverse(multiply(E,inverse(multiply(D,B)))),multiply(E,inverse(B))),inverse(C))),
inference(copy,[status(thm)],[c_115]) ).
cnf(c_72,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_56]) ).
cnf(c_116,plain,
multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C))),inverse(multiply(inverse(C),C)))) = multiply(inverse(D),D),
inference(paramod,[status(thm)],[c_1,c_72]) ).
cnf(c_110,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(paramod,[status(thm)],[c_1,c_116]) ).
cnf(c_111,plain,
$false,
inference(resolve,[status(thm)],[c_110,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP409-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.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 14:47:47 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 2555858 was started by sandbox on n017,
% 0.13/0.36 % Fri Sep 25 14:47:47 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.44
% 0.13/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.44
% 0.13/0.44 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.13/0.44 % Length of proof is 12.
% 0.13/0.44 % Level of proof is 8.
% 0.13/0.44 % Maximum clause weight is 67.000.
% 0.13/0.44 % Given clauses 14.
% 0.13/0.44
% 0.13/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------