%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP567-1 : 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 07:30:23 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 5
% Syntax : Number of formulae : 80 ( 80 unt; 0 def)
% Number of atoms : 80 ( 79 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 25 ( 25 ~; 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 : 107 ( 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(identity,VAR_2))),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(identity,C))),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_155,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_155]) ).
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_156,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_157,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_156]) ).
cnf(c_158,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_157]) ).
cnf(c_159,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_158]) ).
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_159]) ).
cnf(c_160,plain,
double_divide(double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(double_divide(D,B),double_divide(identity,double_divide(identity,identity)))),double_divide(identity,identity)) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_8,plain,
double_divide(double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(double_divide(D,B),identity)),double_divide(identity,identity)) = D,
inference(paramod,[status(thm)],[c_5,c_160]) ).
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(identity,C))),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_161,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_161]) ).
cnf(c_162,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(double_divide(B,double_divide(double_divide(C,double_divide(B,D)),double_divide(identity,D))),double_divide(double_divide(A,C),identity)),
inference(paramod,[status(thm)],[c_8,c_1]) ).
cnf(c_14,plain,
double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(double_divide(D,B),identity)) = double_divide(double_divide(identity,double_divide(D,double_divide(identity,identity))),double_divide(identity,identity)),
inference(copy,[status(thm)],[c_162]) ).
cnf(c_27,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_30,plain,
double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(double_divide(D,B),identity)) = double_divide(D,identity),
inference(paramod,[status(thm)],[c_27,c_14]) ).
cnf(c_163,plain,
double_divide(A,identity) = double_divide(B,double_divide(double_divide(A,double_divide(B,C)),double_divide(identity,C))),
inference(paramod,[status(thm)],[c_27,c_9]) ).
cnf(c_31,plain,
double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))) = double_divide(B,identity),
inference(copy,[status(thm)],[c_163]) ).
cnf(c_32,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(B,A),identity)) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_31,c_30]) ).
cnf(c_37,plain,
double_divide(identity,identity) = identity,
inference(paramod,[status(thm)],[c_32,c_5]) ).
cnf(c_164,plain,
double_divide(double_divide(double_divide(identity,identity),identity),double_divide(A,identity)) = double_divide(double_divide(A,identity),identity),
inference(paramod,[status(thm)],[c_11,c_32]) ).
cnf(c_165,plain,
double_divide(double_divide(identity,identity),double_divide(A,identity)) = double_divide(double_divide(A,identity),identity),
inference(paramod,[status(thm)],[c_37,c_164]) ).
cnf(c_166,plain,
double_divide(identity,double_divide(A,identity)) = double_divide(double_divide(A,identity),identity),
inference(paramod,[status(thm)],[c_37,c_165]) ).
cnf(c_39,plain,
double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(A,identity)),
inference(copy,[status(thm)],[c_166]) ).
cnf(c_167,plain,
double_divide(double_divide(double_divide(double_divide(A,B),identity),identity),double_divide(double_divide(A,identity),identity)) = double_divide(double_divide(B,identity),identity),
inference(paramod,[status(thm)],[c_32,c_32]) ).
cnf(c_168,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),identity)),double_divide(double_divide(A,identity),identity)) = double_divide(double_divide(B,identity),identity),
inference(paramod,[status(thm)],[c_39,c_167]) ).
cnf(c_169,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),identity)),double_divide(identity,double_divide(A,identity))) = double_divide(double_divide(B,identity),identity),
inference(paramod,[status(thm)],[c_39,c_168]) ).
cnf(c_40,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),identity)),double_divide(identity,double_divide(A,identity))) = double_divide(identity,double_divide(B,identity)),
inference(paramod,[status(thm)],[c_39,c_169]) ).
cnf(c_170,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(paramod,[status(thm)],[c_37,c_11]) ).
cnf(c_48,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(paramod,[status(thm)],[c_39,c_170]) ).
cnf(c_171,plain,
double_divide(double_divide(A,B),double_divide(identity,double_divide(A,identity))) = double_divide(identity,double_divide(B,identity)),
inference(paramod,[status(thm)],[c_48,c_40]) ).
cnf(c_172,plain,
double_divide(double_divide(A,B),A) = double_divide(identity,double_divide(B,identity)),
inference(paramod,[status(thm)],[c_48,c_171]) ).
cnf(c_51,plain,
double_divide(double_divide(A,B),A) = B,
inference(paramod,[status(thm)],[c_48,c_172]) ).
cnf(c_52,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(paramod,[status(thm)],[c_48,c_39]) ).
cnf(c_173,plain,
double_divide(identity,double_divide(double_divide(A,identity),identity)) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_37,c_32]) ).
cnf(c_53,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_52,c_173]) ).
cnf(c_59,plain,
double_divide(double_divide(A,identity),double_divide(identity,double_divide(B,A))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_53,c_32]) ).
cnf(c_174,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_53,c_7]) ).
cnf(c_175,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_53,c_174]) ).
cnf(c_176,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_53,c_175]) ).
cnf(c_60,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_53,c_176]) ).
cnf(c_63,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_53,c_48]) ).
cnf(c_71,plain,
double_divide(double_divide(A,B),double_divide(double_divide(C,B),double_divide(identity,A))) = double_divide(C,identity),
inference(paramod,[status(thm)],[c_51,c_31]) ).
cnf(c_177,plain,
double_divide(A,double_divide(A,B)) = double_divide(double_divide(identity,B),identity),
inference(paramod,[status(thm)],[c_51,c_31]) ).
cnf(c_178,plain,
double_divide(A,double_divide(A,B)) = double_divide(identity,double_divide(identity,B)),
inference(paramod,[status(thm)],[c_53,c_177]) ).
cnf(c_73,plain,
double_divide(A,double_divide(A,B)) = B,
inference(paramod,[status(thm)],[c_63,c_178]) ).
cnf(c_76,plain,
double_divide(A,B) = double_divide(B,A),
inference(paramod,[status(thm)],[c_73,c_51]) ).
cnf(c_179,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_76,c_60]) ).
cnf(c_180,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_76,c_179]) ).
cnf(c_181,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_76,c_180]) ).
cnf(c_80,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_181]) ).
cnf(c_83,plain,
double_divide(double_divide(A,identity),double_divide(B,identity)) = double_divide(identity,double_divide(B,A)),
inference(paramod,[status(thm)],[c_59,c_73]) ).
cnf(c_86,plain,
double_divide(double_divide(identity,A),double_divide(B,identity)) = double_divide(identity,double_divide(B,A)),
inference(paramod,[status(thm)],[c_76,c_83]) ).
cnf(c_182,plain,
double_divide(A,double_divide(B,identity)) = double_divide(identity,double_divide(B,double_divide(identity,A))),
inference(paramod,[status(thm)],[c_73,c_86]) ).
cnf(c_88,plain,
double_divide(identity,double_divide(A,double_divide(identity,B))) = double_divide(B,double_divide(A,identity)),
inference(copy,[status(thm)],[c_182]) ).
cnf(c_183,plain,
double_divide(double_divide(a3,b3),double_divide(c3,identity)) != double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_88,c_80]) ).
cnf(c_184,plain,
double_divide(double_divide(a3,b3),double_divide(identity,c3)) != double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_76,c_183]) ).
cnf(c_185,plain,
double_divide(double_divide(identity,c3),double_divide(a3,b3)) != double_divide(identity,double_divide(a3,double_divide(identity,double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_76,c_184]) ).
cnf(c_186,plain,
double_divide(double_divide(identity,c3),double_divide(a3,b3)) != double_divide(double_divide(b3,c3),double_divide(a3,identity)),
inference(paramod,[status(thm)],[c_88,c_185]) ).
cnf(c_187,plain,
double_divide(double_divide(identity,c3),double_divide(a3,b3)) != double_divide(double_divide(b3,c3),double_divide(identity,a3)),
inference(paramod,[status(thm)],[c_76,c_186]) ).
cnf(c_90,plain,
double_divide(double_divide(identity,c3),double_divide(a3,b3)) != double_divide(double_divide(identity,a3),double_divide(b3,c3)),
inference(paramod,[status(thm)],[c_76,c_187]) ).
cnf(c_188,plain,
double_divide(double_divide(A,B),double_divide(C,identity)) = double_divide(double_divide(C,B),double_divide(identity,A)),
inference(paramod,[status(thm)],[c_71,c_73]) ).
cnf(c_102,plain,
double_divide(double_divide(A,B),double_divide(identity,C)) = double_divide(double_divide(C,B),double_divide(A,identity)),
inference(copy,[status(thm)],[c_188]) ).
cnf(c_189,plain,
double_divide(double_divide(A,B),double_divide(C,identity)) = double_divide(double_divide(identity,A),double_divide(C,B)),
inference(paramod,[status(thm)],[c_102,c_76]) ).
cnf(c_124,plain,
double_divide(double_divide(identity,A),double_divide(B,C)) = double_divide(double_divide(A,C),double_divide(B,identity)),
inference(copy,[status(thm)],[c_189]) ).
cnf(c_190,plain,
double_divide(double_divide(c3,b3),double_divide(a3,identity)) != double_divide(double_divide(identity,a3),double_divide(b3,c3)),
inference(paramod,[status(thm)],[c_124,c_90]) ).
cnf(c_191,plain,
double_divide(double_divide(b3,c3),double_divide(a3,identity)) != double_divide(double_divide(identity,a3),double_divide(b3,c3)),
inference(paramod,[status(thm)],[c_76,c_190]) ).
cnf(c_192,plain,
double_divide(double_divide(b3,c3),double_divide(identity,a3)) != double_divide(double_divide(identity,a3),double_divide(b3,c3)),
inference(paramod,[status(thm)],[c_76,c_191]) ).
cnf(c_193,plain,
double_divide(double_divide(identity,a3),double_divide(b3,c3)) != double_divide(double_divide(identity,a3),double_divide(b3,c3)),
inference(paramod,[status(thm)],[c_76,c_192]) ).
cnf(c_154,plain,
$false,
inference(copy,[status(thm)],[c_193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP567-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.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
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 15:00:17 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 3773887 was started by sandbox on n005,
% 0.11/0.36 % Fri Sep 25 15:00:17 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 0.11/0.41
% 0.11/0.41 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.11/0.41
% 0.11/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.41
% 0.11/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.11/0.41 % Length of proof is 36.
% 0.11/0.41 % Level of proof is 17.
% 0.11/0.41 % Maximum clause weight is 81.000.
% 0.11/0.41 % Given clauses 31.
% 0.11/0.41
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------