%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP571-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 07:30:23 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 5
% Syntax : Number of formulae : 79 ( 79 unt; 0 def)
% Number of atoms : 79 ( 78 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 16 ( 16 ~; 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 126 ( 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(VAR_1,double_divide(VAR_0,VAR_2)),double_divide(VAR_2,identity))),double_divide(identity,identity)) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(C,identity))),double_divide(identity,identity)) = B,
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_586,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_586]) ).
fof(prove_these_axioms_3,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('theBenchmark.p',prove_these_axioms_3) ).
cnf(c_6,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(clausify,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_587,plain,
multiply(double_divide(double_divide(b3,a3),identity),c3) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_6]) ).
cnf(c_588,plain,
double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_587]) ).
cnf(c_589,plain,
double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != multiply(a3,double_divide(double_divide(c3,b3),identity)),
inference(paramod,[status(thm)],[c_2,c_588]) ).
cnf(c_590,plain,
double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),
inference(paramod,[status(thm)],[c_2,c_589]) ).
cnf(c_7,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),
inference(copy,[status(thm)],[c_590]) ).
cnf(c_8,plain,
double_divide(double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(C,identity))),double_divide(double_divide(D,B),double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_9,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(A,double_divide(B,C)),double_divide(C,identity))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_591,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(identity,identity))),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_11,plain,
double_divide(double_divide(A,identity),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_5,c_591]) ).
cnf(c_592,plain,
double_divide(double_divide(double_divide(A,double_divide(double_divide(identity,double_divide(A,B)),double_divide(B,identity))),identity),double_divide(identity,identity)) = identity,
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_19,plain,
double_divide(A,double_divide(double_divide(identity,double_divide(A,B)),double_divide(B,identity))) = identity,
inference(paramod,[status(thm)],[c_11,c_592]) ).
cnf(c_23,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_11,c_1]) ).
cnf(c_593,plain,
double_divide(A,identity) = double_divide(B,double_divide(double_divide(A,double_divide(B,C)),double_divide(C,identity))),
inference(paramod,[status(thm)],[c_23,c_9]) ).
cnf(c_28,plain,
double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(C,identity))) = double_divide(B,identity),
inference(copy,[status(thm)],[c_593]) ).
cnf(c_34,plain,
double_divide(identity,identity) = identity,
inference(paramod,[status(thm)],[c_28,c_19]) ).
cnf(c_594,plain,
double_divide(double_divide(B,identity),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_28,c_1]) ).
cnf(c_37,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(paramod,[status(thm)],[c_34,c_594]) ).
cnf(c_595,plain,
double_divide(A,double_divide(double_divide(B,identity),double_divide(double_divide(A,identity),identity))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_5,c_28]) ).
cnf(c_48,plain,
double_divide(A,double_divide(double_divide(B,identity),A)) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_37,c_595]) ).
cnf(c_596,plain,
double_divide(identity,double_divide(double_divide(A,identity),double_divide(identity,identity))) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_34,c_28]) ).
cnf(c_597,plain,
double_divide(identity,double_divide(double_divide(A,identity),identity)) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_34,c_596]) ).
cnf(c_49,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_37,c_597]) ).
cnf(c_598,plain,
double_divide(A,double_divide(double_divide(B,double_divide(A,identity)),identity)) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_34,c_28]) ).
cnf(c_50,plain,
double_divide(A,double_divide(identity,double_divide(B,double_divide(A,identity)))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_49,c_598]) ).
cnf(c_599,plain,
double_divide(A,double_divide(double_divide(double_divide(B,identity),double_divide(A,C)),double_divide(C,identity))) = B,
inference(paramod,[status(thm)],[c_37,c_28]) ).
cnf(c_600,plain,
double_divide(double_divide(B,identity),identity) = B,
inference(paramod,[status(thm)],[c_28,c_599]) ).
cnf(c_53,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(paramod,[status(thm)],[c_49,c_600]) ).
cnf(c_601,plain,
double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),
inference(paramod,[status(thm)],[c_49,c_7]) ).
cnf(c_602,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),
inference(paramod,[status(thm)],[c_49,c_601]) ).
cnf(c_603,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(double_divide(c3,double_divide(identity,double_divide(b3,a3))),identity),
inference(paramod,[status(thm)],[c_49,c_602]) ).
cnf(c_58,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))),
inference(paramod,[status(thm)],[c_49,c_603]) ).
cnf(c_604,plain,
double_divide(identity,double_divide(double_divide(A,B),double_divide(double_divide(B,identity),identity))) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_53,c_28]) ).
cnf(c_605,plain,
double_divide(identity,double_divide(double_divide(A,B),double_divide(identity,double_divide(B,identity)))) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_49,c_604]) ).
cnf(c_65,plain,
double_divide(identity,double_divide(double_divide(A,B),B)) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_53,c_605]) ).
cnf(c_66,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_49,c_53]) ).
cnf(c_606,plain,
double_divide(identity,double_divide(A,identity)) = double_divide(double_divide(A,B),B),
inference(paramod,[status(thm)],[c_65,c_66]) ).
cnf(c_607,plain,
A = double_divide(double_divide(A,B),B),
inference(paramod,[status(thm)],[c_53,c_606]) ).
cnf(c_81,plain,
double_divide(double_divide(A,B),B) = A,
inference(copy,[status(thm)],[c_607]) ).
cnf(c_82,plain,
double_divide(double_divide(A,B),double_divide(double_divide(C,A),double_divide(B,identity))) = double_divide(C,identity),
inference(paramod,[status(thm)],[c_81,c_28]) ).
cnf(c_608,plain,
double_divide(A,double_divide(B,A)) = double_divide(double_divide(B,identity),identity),
inference(paramod,[status(thm)],[c_81,c_48]) ).
cnf(c_609,plain,
double_divide(A,double_divide(B,A)) = double_divide(identity,double_divide(B,identity)),
inference(paramod,[status(thm)],[c_49,c_608]) ).
cnf(c_85,plain,
double_divide(A,double_divide(B,A)) = B,
inference(paramod,[status(thm)],[c_53,c_609]) ).
cnf(c_610,plain,
double_divide(A,double_divide(B,identity)) = double_divide(double_divide(B,double_divide(identity,A)),identity),
inference(paramod,[status(thm)],[c_28,c_50]) ).
cnf(c_611,plain,
double_divide(A,double_divide(B,identity)) = double_divide(identity,double_divide(B,double_divide(identity,A))),
inference(paramod,[status(thm)],[c_49,c_610]) ).
cnf(c_89,plain,
double_divide(identity,double_divide(A,double_divide(identity,B))) = double_divide(B,double_divide(A,identity)),
inference(copy,[status(thm)],[c_611]) ).
cnf(c_612,plain,
double_divide(A,double_divide(double_divide(B,C),double_divide(double_divide(C,A),identity))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_85,c_28]) ).
cnf(c_92,plain,
double_divide(A,double_divide(double_divide(B,C),double_divide(identity,double_divide(C,A)))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_49,c_612]) ).
cnf(c_95,plain,
double_divide(A,double_divide(A,B)) = B,
inference(paramod,[status(thm)],[c_85,c_81]) ).
cnf(c_96,plain,
double_divide(A,B) = double_divide(B,A),
inference(paramod,[status(thm)],[c_81,c_85]) ).
cnf(c_613,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(b3,c3)),a3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))),
inference(paramod,[status(thm)],[c_96,c_58]) ).
cnf(c_614,plain,
double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))),
inference(paramod,[status(thm)],[c_96,c_613]) ).
cnf(c_615,plain,
double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(a3,b3)))),
inference(paramod,[status(thm)],[c_96,c_614]) ).
cnf(c_97,plain,
double_divide(identity,double_divide(c3,double_divide(identity,double_divide(a3,b3)))) != double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))),
inference(copy,[status(thm)],[c_615]) ).
cnf(c_616,plain,
double_divide(A,double_divide(B,identity)) = double_divide(double_divide(B,double_divide(A,C)),double_divide(C,identity)),
inference(paramod,[status(thm)],[c_28,c_95]) ).
cnf(c_100,plain,
double_divide(double_divide(A,double_divide(B,C)),double_divide(C,identity)) = double_divide(B,double_divide(A,identity)),
inference(copy,[status(thm)],[c_616]) ).
cnf(c_617,plain,
double_divide(identity,double_divide(A,double_divide(identity,B))) = double_divide(double_divide(A,identity),B),
inference(paramod,[status(thm)],[c_89,c_96]) ).
cnf(c_153,plain,
double_divide(double_divide(A,identity),B) = double_divide(identity,double_divide(A,double_divide(identity,B))),
inference(copy,[status(thm)],[c_617]) ).
cnf(c_220,plain,
double_divide(double_divide(A,B),double_divide(C,identity)) = double_divide(double_divide(C,A),double_divide(B,identity)),
inference(paramod,[status(thm)],[c_82,c_95]) ).
cnf(c_618,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(identity,double_divide(B,C)),identity)) = double_divide(double_divide(A,B),double_divide(C,identity)),
inference(paramod,[status(thm)],[c_92,c_100]) ).
cnf(c_619,plain,
double_divide(double_divide(A,identity),double_divide(identity,double_divide(identity,double_divide(B,C)))) = double_divide(double_divide(A,B),double_divide(C,identity)),
inference(paramod,[status(thm)],[c_96,c_618]) ).
cnf(c_620,plain,
double_divide(double_divide(A,identity),double_divide(B,C)) = double_divide(double_divide(A,B),double_divide(C,identity)),
inference(paramod,[status(thm)],[c_95,c_619]) ).
cnf(c_621,plain,
double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(double_divide(A,B),double_divide(C,identity)),
inference(paramod,[status(thm)],[c_153,c_620]) ).
cnf(c_539,plain,
double_divide(double_divide(A,B),double_divide(C,identity)) = double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))),
inference(copy,[status(thm)],[c_621]) ).
cnf(c_622,plain,
double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(double_divide(C,A),double_divide(B,identity)),
inference(paramod,[status(thm)],[c_539,c_220]) ).
cnf(c_584,plain,
double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(identity,double_divide(C,double_divide(identity,double_divide(A,B)))),
inference(paramod,[status(thm)],[c_539,c_622]) ).
cnf(c_623,plain,
double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(a3,b3)))),
inference(copy,[status(thm)],[c_97]) ).
cnf(c_585,plain,
$false,
inference(resolve,[status(thm)],[c_584,c_623]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP571-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 15:06:26 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 3622329 was started by sandbox2 on n001,
% 0.10/0.36 % Fri Sep 25 15:06:26 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.45
% 0.14/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.45
% 0.14/0.45 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.14/0.45 % Length of proof is 36.
% 0.14/0.45 % Level of proof is 16.
% 0.14/0.45 % Maximum clause weight is 27.000.
% 0.14/0.45 % Given clauses 59.
% 0.14/0.45
% 0.14/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------