%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP589-1 : 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 : n004.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 07:30:26 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 17 unt; 0 def)
% Number of atoms : 17 ( 16 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(inverse(double_divide(double_divide(VAR_0,VAR_1),inverse(double_divide(VAR_0,inverse(VAR_2))))),VAR_1) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B) = C,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = inverse(double_divide(VAR_1,VAR_0)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = inverse(double_divide(B,A)),
inference(clausify,[status(thm)],[multiply]) ).
fof(prove_these_axioms_1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('theBenchmark.p',prove_these_axioms_1) ).
cnf(c_3,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(clausify,[status(thm)],[prove_these_axioms_1]) ).
cnf(c_41,plain,
inverse(double_divide(a1,inverse(a1))) != multiply(inverse(b1),b1),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_42,plain,
inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))),
inference(paramod,[status(thm)],[c_2,c_41]) ).
cnf(c_4,plain,
inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1))),
inference(copy,[status(thm)],[c_42]) ).
cnf(c_5,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(B,C),inverse(double_divide(B,inverse(A))))),inverse(D))))),C) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_10,plain,
double_divide(inverse(double_divide(A,inverse(A))),inverse(B)) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_43,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(inverse(double_divide(B,inverse(B))),inverse(C))))),inverse(A)) = C,
inference(paramod,[status(thm)],[c_10,c_1]) ).
cnf(c_13,plain,
double_divide(inverse(double_divide(A,inverse(B))),inverse(A)) = B,
inference(paramod,[status(thm)],[c_10,c_43]) ).
cnf(c_18,plain,
double_divide(inverse(inverse(double_divide(A,inverse(A)))),inverse(B)) = B,
inference(paramod,[status(thm)],[c_10,c_10]) ).
cnf(c_25,plain,
double_divide(inverse(A),inverse(inverse(double_divide(B,inverse(B))))) = A,
inference(paramod,[status(thm)],[c_10,c_13]) ).
cnf(c_39,plain,
inverse(double_divide(A,inverse(A))) = inverse(double_divide(B,inverse(B))),
inference(paramod,[status(thm)],[c_25,c_18]) ).
cnf(c_40,plain,
$false,
inference(resolve,[status(thm)],[c_39,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP589-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n004.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 15:01:06 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 3486723 was started by sandbox on n004,
% 0.12/0.38 % Fri Sep 25 15:01:06 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 0.12/0.39
% 0.12/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.39
% 0.12/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.12/0.39 % Length of proof is 11.
% 0.12/0.39 % Level of proof is 6.
% 0.12/0.39 % Maximum clause weight is 21.000.
% 0.12/0.39 % Given clauses 8.
% 0.12/0.39
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------