%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP449-1 : 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 : n011.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 07:29:44 AM UTC 2026
% Result : Unsatisfiable 0.05s 0.43s
% Output : CNFRefutation 0.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 26 unt; 0 def)
% Number of atoms : 26 ( 25 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 : 6 ( 2 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 : 47 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(VAR_0,divide(divide(divide(divide(VAR_1,VAR_1),VAR_1),VAR_2),divide(divide(divide(VAR_1,VAR_1),VAR_0),VAR_2))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(A,divide(divide(divide(divide(B,B),B),C),divide(divide(divide(B,B),A),C))) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,VAR_1) = divide(VAR_0,divide(divide(VAR_2,VAR_2),VAR_1)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
inference(clausify,[status(thm)],[multiply]) ).
fof(inverse,axiom,
! [VAR_0,VAR_1] : inverse(VAR_0) = divide(divide(VAR_1,VAR_1),VAR_0),
file('theBenchmark.p',inverse) ).
cnf(c_3,plain,
inverse(A) = divide(divide(B,B),A),
inference(clausify,[status(thm)],[inverse]) ).
cnf(c_4,plain,
divide(divide(A,A),B) = inverse(B),
inference(copy,[status(thm)],[c_3]) ).
fof(prove_these_axioms_2,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c_5,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(clausify,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_6,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_51,plain,
divide(A,divide(divide(inverse(B),C),divide(divide(divide(B,B),A),C))) = B,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_7,plain,
divide(A,divide(divide(inverse(B),C),divide(inverse(A),C))) = B,
inference(paramod,[status(thm)],[c_4,c_51]) ).
cnf(c_52,plain,
multiply(divide(inverse(b2),inverse(b2)),a2) != a2,
inference(paramod,[status(thm)],[c_6,c_5]) ).
cnf(c_53,plain,
divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2,
inference(paramod,[status(thm)],[c_6,c_52]) ).
cnf(c_8,plain,
inverse(inverse(a2)) != a2,
inference(paramod,[status(thm)],[c_4,c_53]) ).
cnf(c_9,plain,
divide(inverse(divide(A,A)),B) = inverse(B),
inference(paramod,[status(thm)],[c_4,c_4]) ).
cnf(c_54,plain,
A = inverse(divide(divide(inverse(A),B),divide(inverse(divide(C,C)),B))),
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_55,plain,
A = inverse(divide(divide(inverse(A),B),inverse(B))),
inference(paramod,[status(thm)],[c_9,c_54]) ).
cnf(c_10,plain,
inverse(divide(divide(inverse(A),B),inverse(B))) = A,
inference(copy,[status(thm)],[c_55]) ).
cnf(c_11,plain,
divide(A,inverse(divide(inverse(A),inverse(B)))) = B,
inference(paramod,[status(thm)],[c_4,c_7]) ).
cnf(c_21,plain,
inverse(divide(inverse(A),inverse(A))) = divide(B,B),
inference(paramod,[status(thm)],[c_9,c_10]) ).
cnf(c_40,plain,
inverse(divide(divide(inverse(A),divide(inverse(B),inverse(B))),divide(C,C))) = A,
inference(paramod,[status(thm)],[c_21,c_10]) ).
cnf(c_43,plain,
divide(A,divide(B,B)) = A,
inference(paramod,[status(thm)],[c_21,c_11]) ).
cnf(c_56,plain,
inverse(divide(inverse(A),divide(C,C))) = A,
inference(paramod,[status(thm)],[c_43,c_40]) ).
cnf(c_49,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_43,c_56]) ).
cnf(c_50,plain,
$false,
inference(resolve,[status(thm)],[c_49,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP449-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.40 % Computer : n011.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 14:54:43 UTC 2026
% 0.05/0.41 % CPUTime :
% 0.05/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/0.41 % Process 2292507 was started by sandbox on n011,
% 0.05/0.41 % Fri Sep 25 14:54:43 2026
% 0.05/0.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.05/0.42
% 0.05/0.42 % From the command line: assign(max_seconds, 300).
% 0.05/0.43
% 0.05/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.05/0.43
% 0.05/0.43 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.05/0.43 % Length of proof is 16.
% 0.05/0.43 % Level of proof is 7.
% 0.05/0.43 % Maximum clause weight is 84.000.
% 0.05/0.43 % Given clauses 8.
% 0.05/0.43
% 0.05/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------