%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP488-1 : 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 : n005.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 07:29:52 AM UTC 2026
% Result : Unsatisfiable 0.15s 5.47s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 5
% Syntax : Number of formulae : 59 ( 59 unt; 0 def)
% Number of atoms : 59 ( 58 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 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 : 63 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(VAR_0,double_divide(double_divide(double_divide(identity,double_divide(double_divide(VAR_0,identity),double_divide(VAR_1,VAR_2))),VAR_1),identity)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),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_51,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_51]) ).
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(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),identity)),B),identity)) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_9,plain,
double_divide(A,double_divide(double_divide(double_divide(identity,identity),double_divide(A,identity)),identity)) = identity,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_10,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(identity,A))),double_divide(double_divide(A,B),identity)) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_1,c_8]) ).
cnf(c_52,plain,
double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),identity)),B),identity)) = double_divide(double_divide(double_divide(identity,identity),double_divide(B,identity)),identity),
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_53,plain,
double_divide(B,identity) = double_divide(double_divide(double_divide(identity,identity),double_divide(B,identity)),identity),
inference(paramod,[status(thm)],[c_8,c_52]) ).
cnf(c_14,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(A,identity)),identity) = double_divide(A,identity),
inference(copy,[status(thm)],[c_53]) ).
cnf(c_17,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity,
inference(paramod,[status(thm)],[c_5,c_9]) ).
cnf(c_54,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(identity,identity)),identity) = identity,
inference(paramod,[status(thm)],[c_10,c_5]) ).
cnf(c_19,plain,
double_divide(identity,identity) = identity,
inference(paramod,[status(thm)],[c_17,c_54]) ).
cnf(c_55,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,identity),identity)),double_divide(double_divide(double_divide(identity,identity),A),identity)) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_56,plain,
double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(double_divide(identity,identity),A),identity)) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_19,c_55]) ).
cnf(c_57,plain,
double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,identity),A),identity)) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_19,c_56]) ).
cnf(c_58,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,identity),A),identity)) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_19,c_57]) ).
cnf(c_20,plain,
double_divide(identity,double_divide(double_divide(identity,A),identity)) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_19,c_58]) ).
cnf(c_26,plain,
double_divide(double_divide(identity,double_divide(A,identity)),identity) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_19,c_14]) ).
cnf(c_30,plain,
double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(A,B))),A),identity)) = B,
inference(paramod,[status(thm)],[c_19,c_1]) ).
cnf(c_59,plain,
double_divide(identity,double_divide(double_divide(A,identity),identity)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),identity)),A),identity),identity),
inference(paramod,[status(thm)],[c_8,c_20]) ).
cnf(c_60,plain,
double_divide(identity,double_divide(double_divide(A,identity),identity)) = double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),A),identity),identity),
inference(paramod,[status(thm)],[c_19,c_59]) ).
cnf(c_61,plain,
double_divide(identity,double_divide(double_divide(A,identity),identity)) = double_divide(double_divide(double_divide(double_divide(identity,identity),A),identity),identity),
inference(paramod,[status(thm)],[c_19,c_60]) ).
cnf(c_62,plain,
double_divide(identity,double_divide(double_divide(A,identity),identity)) = double_divide(double_divide(double_divide(identity,A),identity),identity),
inference(paramod,[status(thm)],[c_19,c_61]) ).
cnf(c_33,plain,
double_divide(double_divide(double_divide(identity,A),identity),identity) = double_divide(identity,double_divide(double_divide(A,identity),identity)),
inference(copy,[status(thm)],[c_62]) ).
cnf(c_63,plain,
double_divide(A,identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(B,A))),B),identity),
inference(paramod,[status(thm)],[c_1,c_26]) ).
cnf(c_64,plain,
double_divide(A,identity) = double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(B,A))),B),identity),
inference(paramod,[status(thm)],[c_19,c_63]) ).
cnf(c_37,plain,
double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(A,B))),A),identity) = double_divide(B,identity),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_65,plain,
double_divide(double_divide(A,identity),identity) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),identity)),A),identity),
inference(paramod,[status(thm)],[c_8,c_26]) ).
cnf(c_66,plain,
double_divide(double_divide(A,identity),identity) = double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),A),identity),
inference(paramod,[status(thm)],[c_19,c_65]) ).
cnf(c_67,plain,
double_divide(double_divide(A,identity),identity) = double_divide(double_divide(double_divide(identity,identity),A),identity),
inference(paramod,[status(thm)],[c_19,c_66]) ).
cnf(c_68,plain,
double_divide(double_divide(A,identity),identity) = double_divide(double_divide(identity,A),identity),
inference(paramod,[status(thm)],[c_19,c_67]) ).
cnf(c_40,plain,
double_divide(double_divide(identity,A),identity) = double_divide(double_divide(A,identity),identity),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_69,plain,
double_divide(identity,double_divide(A,identity)) = double_divide(double_divide(A,identity),identity),
inference(paramod,[status(thm)],[c_26,c_20]) ).
cnf(c_41,plain,
double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(A,identity)),
inference(copy,[status(thm)],[c_69]) ).
cnf(c_70,plain,
double_divide(double_divide(A,identity),identity) = double_divide(double_divide(identity,A),identity),
inference(paramod,[status(thm)],[c_20,c_26]) ).
cnf(c_71,plain,
double_divide(identity,double_divide(A,identity)) = double_divide(double_divide(identity,A),identity),
inference(paramod,[status(thm)],[c_41,c_70]) ).
cnf(c_42,plain,
double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(A,identity)),
inference(copy,[status(thm)],[c_71]) ).
cnf(c_44,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(paramod,[status(thm)],[c_37,c_30]) ).
cnf(c_72,plain,
double_divide(double_divide(identity,double_divide(A,identity)),identity) = double_divide(identity,double_divide(double_divide(A,identity),identity)),
inference(paramod,[status(thm)],[c_42,c_33]) ).
cnf(c_73,plain,
double_divide(A,identity) = double_divide(identity,double_divide(double_divide(A,identity),identity)),
inference(paramod,[status(thm)],[c_44,c_72]) ).
cnf(c_74,plain,
double_divide(A,identity) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_41,c_73]) ).
cnf(c_75,plain,
double_divide(A,identity) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_44,c_74]) ).
cnf(c_46,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(copy,[status(thm)],[c_75]) ).
cnf(c_76,plain,
double_divide(double_divide(identity,a2),identity) != a2,
inference(paramod,[status(thm)],[c_46,c_7]) ).
cnf(c_48,plain,
double_divide(identity,double_divide(identity,a2)) != a2,
inference(paramod,[status(thm)],[c_46,c_76]) ).
cnf(c_77,plain,
double_divide(identity,double_divide(identity,A)) = double_divide(double_divide(A,identity),identity),
inference(paramod,[status(thm)],[c_46,c_40]) ).
cnf(c_78,plain,
double_divide(identity,double_divide(identity,A)) = double_divide(identity,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_46,c_77]) ).
cnf(c_49,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_44,c_78]) ).
cnf(c_50,plain,
$false,
inference(resolve,[status(thm)],[c_49,c_48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP488-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.43 % Computer : n005.cluster.edu
% 0.15/5.43 % Model : x86_64 x86_64
% 0.15/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.43 % Memory : 8046.5625MB
% 0.15/5.43 % OS : Linux 6.8.0-71-generic
% 0.15/5.43 % CPULimit : 300
% 0.15/5.43 % WCLimit : 300
% 0.15/5.43 % DateTime : Fri Sep 25 14:56:22 UTC 2026
% 0.15/5.43 % CPUTime :
% 0.15/5.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/5.44 % Process 3763261 was started by sandbox on n005,
% 0.15/5.44 % Fri Sep 25 14:56:22 2026
% 0.15/5.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/5.44
% 0.15/5.44 % From the command line: assign(max_seconds, 300).
% 0.15/5.47
% 0.15/5.47 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.47
% 0.15/5.47 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.15/5.47 % Length of proof is 26.
% 0.15/5.47 % Level of proof is 10.
% 0.15/5.47 % Maximum clause weight is 82.000.
% 0.15/5.47 % Given clauses 11.
% 0.15/5.47
% 0.15/5.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------