%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP421-1 : 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 07:29:15 AM UTC 2026
% Result : Unsatisfiable 0.95s 0.61s
% Output : CNFRefutation 0.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 18 ( 18 unt; 0 def)
% Number of atoms : 18 ( 17 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 50 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : inverse(multiply(inverse(multiply(VAR_0,inverse(multiply(inverse(VAR_1),multiply(inverse(VAR_2),inverse(multiply(inverse(VAR_2),VAR_2))))))),multiply(VAR_0,VAR_2))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,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_837,plain,
inverse(multiply(inverse(multiply(A,inverse(multiply(B,multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C))) = multiply(inverse(multiply(D,inverse(multiply(inverse(B),multiply(inverse(E),inverse(multiply(inverse(E),E))))))),multiply(D,E)),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_4,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C)) = inverse(multiply(inverse(multiply(D,inverse(multiply(B,multiply(inverse(E),inverse(multiply(inverse(E),E))))))),multiply(D,E))),
inference(copy,[status(thm)],[c_837]) ).
cnf(c_838,plain,
inverse(multiply(inverse(multiply(A,B)),multiply(A,C))) = multiply(inverse(C),inverse(multiply(inverse(B),multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C)))))))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_5,plain,
multiply(inverse(A),inverse(multiply(inverse(B),multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A)))))))) = inverse(multiply(inverse(multiply(C,B)),multiply(C,A))),
inference(copy,[status(thm)],[c_838]) ).
cnf(c_7,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(B)),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C)) = B,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_10,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(A,B)),multiply(A,C)))),multiply(inverse(C),inverse(multiply(inverse(C),C))))) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_53,plain,
multiply(inverse(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,C)))),multiply(inverse(C),inverse(multiply(inverse(C),C)))) = B,
inference(paramod,[status(thm)],[c_5,c_7]) ).
cnf(c_58,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(paramod,[status(thm)],[c_10,c_7]) ).
cnf(c_839,plain,
multiply(A,multiply(inverse(inverse(multiply(inverse(multiply(B,A)),multiply(B,C)))),D)) = multiply(inverse(multiply(E,multiply(inverse(C),inverse(multiply(inverse(C),C))))),multiply(E,D)),
inference(paramod,[status(thm)],[c_10,c_58]) ).
cnf(c_78,plain,
multiply(inverse(multiply(A,multiply(inverse(B),inverse(multiply(inverse(B),B))))),multiply(A,C)) = multiply(D,multiply(inverse(inverse(multiply(inverse(multiply(E,D)),multiply(E,B)))),C)),
inference(copy,[status(thm)],[c_839]) ).
cnf(c_804,plain,
multiply(inverse(multiply(A,multiply(inverse(B),inverse(multiply(inverse(B),B))))),multiply(A,multiply(inverse(B),inverse(multiply(inverse(B),B))))) = multiply(inverse(C),C),
inference(paramod,[status(thm)],[c_53,c_78]) ).
cnf(c_840,plain,
multiply(inverse(multiply(A,multiply(inverse(B),inverse(multiply(inverse(B),B))))),multiply(A,multiply(inverse(B),inverse(multiply(inverse(B),B))))) != multiply(inverse(a1),a1),
inference(paramod,[status(thm)],[c_804,c_3]) ).
cnf(c_836,plain,
$false,
inference(resolve,[status(thm)],[c_804,c_840]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP421-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:53:02 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 500642 was started by sandbox on n014,
% 0.09/0.35 % Fri Sep 25 14:53:02 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.95/0.61
% 0.95/0.61 % SZS status Unsatisfiable for theBenchmark
% 0.95/0.61
% 0.95/0.61 % Proof 1 at 0.18 (+ 0.06) seconds.
% 0.95/0.61 % Length of proof is 12.
% 0.95/0.61 % Level of proof is 6.
% 0.95/0.61 % Maximum clause weight is 94.000.
% 0.95/0.61 % Given clauses 37.
% 0.95/0.61
% 0.95/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------