%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP578-1 : 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 : n020.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 07:30:24 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 30 unt; 0 def)
% Number of atoms : 30 ( 29 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 : 9 ( 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 : 40 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(double_divide(VAR_0,double_divide(double_divide(double_divide(VAR_1,VAR_0),VAR_2),double_divide(VAR_1,identity))),double_divide(identity,identity)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) = C,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = double_divide(double_divide(VAR_1,VAR_0),identity),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = double_divide(double_divide(B,A),identity),
inference(clausify,[status(thm)],[multiply]) ).
fof(inverse,axiom,
! [VAR_0] : inverse(VAR_0) = double_divide(VAR_0,identity),
file('theBenchmark.p',inverse) ).
cnf(c_3,plain,
inverse(A) = double_divide(A,identity),
inference(clausify,[status(thm)],[inverse]) ).
fof(identity,axiom,
! [VAR_0] : identity = double_divide(VAR_0,inverse(VAR_0)),
file('theBenchmark.p',identity) ).
cnf(c_4,plain,
identity = double_divide(A,inverse(A)),
inference(clausify,[status(thm)],[identity]) ).
cnf(c_77,plain,
identity = double_divide(A,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_3,c_4]) ).
cnf(c_5,plain,
double_divide(A,double_divide(A,identity)) = identity,
inference(copy,[status(thm)],[c_77]) ).
fof(prove_these_axioms_2,axiom,
multiply(identity,a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c_6,plain,
multiply(identity,a2) != a2,
inference(clausify,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_7,plain,
double_divide(double_divide(a2,identity),identity) != a2,
inference(paramod,[status(thm)],[c_2,c_6]) ).
cnf(c_8,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(A,B),double_divide(double_divide(C,double_divide(double_divide(double_divide(D,C),A),double_divide(D,identity))),identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_11,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,B),double_divide(A,identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_21,plain,
double_divide(double_divide(double_divide(identity,identity),identity),double_divide(identity,identity)) = double_divide(double_divide(double_divide(A,B),B),double_divide(A,identity)),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_29,plain,
double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_5,c_11]) ).
cnf(c_35,plain,
double_divide(double_divide(double_divide(identity,identity),identity),double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_29]) ).
cnf(c_78,plain,
double_divide(identity,identity) = double_divide(double_divide(double_divide(A,B),B),double_divide(A,identity)),
inference(paramod,[status(thm)],[c_35,c_21]) ).
cnf(c_39,plain,
double_divide(double_divide(double_divide(A,B),B),double_divide(A,identity)) = double_divide(identity,identity),
inference(copy,[status(thm)],[c_78]) ).
cnf(c_42,plain,
double_divide(double_divide(A,double_divide(identity,identity)),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_39,c_1]) ).
cnf(c_79,plain,
double_divide(A,double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(double_divide(C,B),A),double_divide(C,identity))),
inference(paramod,[status(thm)],[c_1,c_42]) ).
cnf(c_55,plain,
double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))) = double_divide(C,double_divide(identity,identity)),
inference(copy,[status(thm)],[c_79]) ).
cnf(c_80,plain,
double_divide(double_divide(A,double_divide(identity,identity)),double_divide(double_divide(A,double_divide(identity,identity)),identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_42,c_39]) ).
cnf(c_81,plain,
identity = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_80]) ).
cnf(c_61,plain,
double_divide(identity,identity) = identity,
inference(copy,[status(thm)],[c_81]) ).
cnf(c_82,plain,
double_divide(double_divide(C,double_divide(identity,identity)),double_divide(identity,identity)) = C,
inference(paramod,[status(thm)],[c_55,c_1]) ).
cnf(c_83,plain,
double_divide(double_divide(C,identity),double_divide(identity,identity)) = C,
inference(paramod,[status(thm)],[c_61,c_82]) ).
cnf(c_75,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(paramod,[status(thm)],[c_61,c_83]) ).
cnf(c_76,plain,
$false,
inference(resolve,[status(thm)],[c_75,c_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP578-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 15:01:48 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 3215141 was started by sandbox on n020,
% 0.13/0.36 % Fri Sep 25 15:01:48 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 18.
% 0.13/0.38 % Level of proof is 9.
% 0.13/0.38 % Maximum clause weight is 27.000.
% 0.13/0.38 % Given clauses 10.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------