%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP498-1 : 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 : n018.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 07:29:53 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.43s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 5
% Syntax : Number of formulae : 98 ( 98 unt; 0 def)
% Number of atoms : 98 ( 97 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 : 147 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(double_divide(identity,double_divide(VAR_0,double_divide(VAR_1,identity))),double_divide(double_divide(VAR_1,double_divide(VAR_2,VAR_0)),identity)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),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_205,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_205]) ).
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_206,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_207,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_206]) ).
cnf(c_208,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_207]) ).
cnf(c_209,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_208]) ).
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_209]) ).
cnf(c_8,plain,
double_divide(double_divide(identity,identity),double_divide(double_divide(A,double_divide(B,A)),identity)) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_9,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,identity))),double_divide(double_divide(B,identity),identity)) = A,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_10,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_210,plain,
identity = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_11,plain,
double_divide(identity,identity) = identity,
inference(copy,[status(thm)],[c_210]) ).
cnf(c_12,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),identity) = A,
inference(paramod,[status(thm)],[c_11,c_10]) ).
cnf(c_13,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(B,A)),identity)) = B,
inference(paramod,[status(thm)],[c_11,c_8]) ).
cnf(c_15,plain,
double_divide(double_divide(identity,double_divide(A,identity)),double_divide(double_divide(identity,double_divide(B,A)),identity)) = B,
inference(paramod,[status(thm)],[c_11,c_1]) ).
cnf(c_19,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),double_divide(double_divide(A,B),identity)) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(paramod,[status(thm)],[c_12,c_1]) ).
cnf(c_22,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,identity),identity)) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_12,c_9]) ).
cnf(c_211,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,identity),B)),double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(B,identity))),identity),identity)) = A,
inference(paramod,[status(thm)],[c_12,c_9]) ).
cnf(c_23,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,identity),B)),double_divide(B,identity)) = A,
inference(paramod,[status(thm)],[c_12,c_211]) ).
cnf(c_25,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))) = A,
inference(paramod,[status(thm)],[c_22,c_9]) ).
cnf(c_212,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(A,identity)) = double_divide(B,double_divide(A,B)),
inference(paramod,[status(thm)],[c_13,c_1]) ).
cnf(c_213,plain,
double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(A,identity)) = double_divide(B,double_divide(A,B)),
inference(paramod,[status(thm)],[c_11,c_212]) ).
cnf(c_214,plain,
double_divide(double_divide(identity,identity),double_divide(A,identity)) = double_divide(B,double_divide(A,B)),
inference(paramod,[status(thm)],[c_11,c_213]) ).
cnf(c_28,plain,
double_divide(identity,double_divide(A,identity)) = double_divide(B,double_divide(A,B)),
inference(paramod,[status(thm)],[c_11,c_214]) ).
cnf(c_35,plain,
double_divide(A,double_divide(identity,A)) = identity,
inference(paramod,[status(thm)],[c_28,c_5]) ).
cnf(c_215,plain,
double_divide(identity,double_divide(A,identity)) = double_divide(double_divide(A,identity),identity),
inference(paramod,[status(thm)],[c_5,c_28]) ).
cnf(c_36,plain,
double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(A,identity)),
inference(copy,[status(thm)],[c_215]) ).
cnf(c_38,plain,
double_divide(A,double_divide(double_divide(B,double_divide(C,B)),A)) = C,
inference(paramod,[status(thm)],[c_28,c_13]) ).
cnf(c_41,plain,
double_divide(A,double_divide(B,A)) = double_divide(C,double_divide(B,C)),
inference(paramod,[status(thm)],[c_28,c_28]) ).
cnf(c_44,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = A,
inference(paramod,[status(thm)],[c_36,c_25]) ).
cnf(c_45,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(identity,double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_36,c_22]) ).
cnf(c_216,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),double_divide(B,identity))),double_divide(double_divide(B,identity),identity)) = A,
inference(paramod,[status(thm)],[c_35,c_1]) ).
cnf(c_217,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),double_divide(B,identity))),double_divide(identity,double_divide(B,identity))) = A,
inference(paramod,[status(thm)],[c_36,c_216]) ).
cnf(c_46,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))) = A,
inference(paramod,[status(thm)],[c_45,c_217]) ).
cnf(c_218,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),double_divide(double_divide(A,double_divide(identity,double_divide(B,identity))),identity)) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_36,c_1]) ).
cnf(c_219,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(B,identity)),identity))) = double_divide(B,identity),
inference(paramod,[status(thm)],[c_19,c_218]) ).
cnf(c_48,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_38,c_219]) ).
cnf(c_50,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,A)))) = A,
inference(paramod,[status(thm)],[c_48,c_46]) ).
cnf(c_61,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),double_divide(identity,double_divide(A,B))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(paramod,[status(thm)],[c_48,c_19]) ).
cnf(c_63,plain,
double_divide(double_divide(identity,double_divide(A,identity)),double_divide(identity,double_divide(identity,double_divide(B,A)))) = B,
inference(paramod,[status(thm)],[c_48,c_15]) ).
cnf(c_220,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_48,c_7]) ).
cnf(c_221,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_48,c_220]) ).
cnf(c_222,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_48,c_221]) ).
cnf(c_64,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_48,c_222]) ).
cnf(c_65,plain,
multiply(A,B) = double_divide(identity,double_divide(B,A)),
inference(paramod,[status(thm)],[c_48,c_2]) ).
cnf(c_66,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(identity,double_divide(B,double_divide(C,A)))) = C,
inference(paramod,[status(thm)],[c_48,c_1]) ).
cnf(c_67,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(A,identity)) = identity,
inference(paramod,[status(thm)],[c_11,c_23]) ).
cnf(c_69,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,identity),B)),double_divide(identity,B)) = A,
inference(paramod,[status(thm)],[c_48,c_23]) ).
cnf(c_223,plain,
double_divide(double_divide(identity,A),identity) = double_divide(B,double_divide(A,B)),
inference(paramod,[status(thm)],[c_35,c_41]) ).
cnf(c_71,plain,
double_divide(identity,double_divide(identity,A)) = double_divide(B,double_divide(A,B)),
inference(paramod,[status(thm)],[c_48,c_223]) ).
cnf(c_79,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),B)))) = double_divide(double_divide(B,identity),A),
inference(paramod,[status(thm)],[c_23,c_71]) ).
cnf(c_224,plain,
double_divide(identity,double_divide(identity,A)) = double_divide(double_divide(B,A),double_divide(identity,double_divide(identity,B))),
inference(paramod,[status(thm)],[c_71,c_71]) ).
cnf(c_86,plain,
double_divide(double_divide(A,B),double_divide(identity,double_divide(identity,A))) = double_divide(identity,double_divide(identity,B)),
inference(copy,[status(thm)],[c_224]) ).
cnf(c_225,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,A)))) = double_divide(double_divide(A,identity),identity),
inference(paramod,[status(thm)],[c_67,c_71]) ).
cnf(c_226,plain,
A = double_divide(double_divide(A,identity),identity),
inference(paramod,[status(thm)],[c_50,c_225]) ).
cnf(c_227,plain,
A = double_divide(identity,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_48,c_226]) ).
cnf(c_91,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(copy,[status(thm)],[c_227]) ).
cnf(c_96,plain,
double_divide(A,double_divide(identity,double_divide(identity,double_divide(B,A)))) = B,
inference(paramod,[status(thm)],[c_91,c_63]) ).
cnf(c_228,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(A,B))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(paramod,[status(thm)],[c_91,c_61]) ).
cnf(c_98,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(A,B))) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_91,c_228]) ).
cnf(c_102,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_91,c_44]) ).
cnf(c_103,plain,
double_divide(A,double_divide(B,A)) = B,
inference(paramod,[status(thm)],[c_102,c_96]) ).
cnf(c_229,plain,
double_divide(double_divide(A,B),A) = double_divide(identity,double_divide(identity,B)),
inference(paramod,[status(thm)],[c_102,c_86]) ).
cnf(c_105,plain,
double_divide(double_divide(A,B),A) = B,
inference(paramod,[status(thm)],[c_102,c_229]) ).
cnf(c_106,plain,
double_divide(identity,double_divide(double_divide(A,identity),B)) = double_divide(double_divide(B,identity),A),
inference(paramod,[status(thm)],[c_102,c_79]) ).
cnf(c_110,plain,
double_divide(double_divide(double_divide(A,identity),B),double_divide(identity,A)) = B,
inference(paramod,[status(thm)],[c_106,c_69]) ).
cnf(c_118,plain,
double_divide(A,double_divide(identity,double_divide(B,double_divide(C,identity)))) = double_divide(identity,double_divide(C,double_divide(A,B))),
inference(paramod,[status(thm)],[c_66,c_105]) ).
cnf(c_119,plain,
double_divide(double_divide(identity,A),B) = double_divide(double_divide(A,identity),B),
inference(paramod,[status(thm)],[c_110,c_103]) ).
cnf(c_230,plain,
multiply(A,double_divide(identity,B)) = double_divide(identity,double_divide(double_divide(B,identity),A)),
inference(paramod,[status(thm)],[c_119,c_65]) ).
cnf(c_231,plain,
double_divide(identity,double_divide(double_divide(identity,B),A)) = double_divide(identity,double_divide(double_divide(B,identity),A)),
inference(paramod,[status(thm)],[c_65,c_230]) ).
cnf(c_121,plain,
double_divide(identity,double_divide(double_divide(identity,A),B)) = double_divide(double_divide(B,identity),A),
inference(paramod,[status(thm)],[c_106,c_231]) ).
cnf(c_232,plain,
double_divide(double_divide(a3,identity),double_divide(c3,b3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))),
inference(paramod,[status(thm)],[c_121,c_64]) ).
cnf(c_233,plain,
double_divide(double_divide(identity,a3),double_divide(c3,b3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))),
inference(paramod,[status(thm)],[c_48,c_232]) ).
cnf(c_125,plain,
double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))) != double_divide(double_divide(identity,a3),double_divide(c3,b3)),
inference(copy,[status(thm)],[c_233]) ).
cnf(c_131,plain,
double_divide(double_divide(identity,A),double_divide(identity,B)) = double_divide(identity,double_divide(B,A)),
inference(paramod,[status(thm)],[c_103,c_98]) ).
cnf(c_234,plain,
double_divide(A,double_divide(identity,B)) = double_divide(identity,double_divide(B,double_divide(identity,A))),
inference(paramod,[status(thm)],[c_102,c_131]) ).
cnf(c_139,plain,
double_divide(identity,double_divide(A,double_divide(identity,B))) = double_divide(B,double_divide(identity,A)),
inference(copy,[status(thm)],[c_234]) ).
cnf(c_235,plain,
double_divide(A,double_divide(identity,B)) = double_divide(identity,double_divide(B,double_divide(A,identity))),
inference(paramod,[status(thm)],[c_103,c_131]) ).
cnf(c_140,plain,
double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(B,double_divide(identity,A)),
inference(copy,[status(thm)],[c_235]) ).
cnf(c_141,plain,
double_divide(double_divide(b3,a3),double_divide(identity,c3)) != double_divide(double_divide(identity,a3),double_divide(c3,b3)),
inference(paramod,[status(thm)],[c_139,c_125]) ).
cnf(c_236,plain,
double_divide(A,double_divide(C,double_divide(identity,B))) = double_divide(identity,double_divide(C,double_divide(A,B))),
inference(paramod,[status(thm)],[c_140,c_118]) ).
cnf(c_142,plain,
double_divide(identity,double_divide(A,double_divide(B,C))) = double_divide(B,double_divide(A,double_divide(identity,C))),
inference(copy,[status(thm)],[c_236]) ).
cnf(c_237,plain,
double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,C)))) = double_divide(double_divide(identity,C),double_divide(A,double_divide(identity,double_divide(identity,B)))),
inference(paramod,[status(thm)],[c_131,c_142]) ).
cnf(c_238,plain,
double_divide(double_divide(B,C),double_divide(identity,A)) = double_divide(double_divide(identity,C),double_divide(A,double_divide(identity,double_divide(identity,B)))),
inference(paramod,[status(thm)],[c_139,c_237]) ).
cnf(c_239,plain,
double_divide(double_divide(B,C),double_divide(identity,A)) = double_divide(double_divide(identity,C),double_divide(A,B)),
inference(paramod,[status(thm)],[c_102,c_238]) ).
cnf(c_203,plain,
double_divide(double_divide(identity,A),double_divide(B,C)) = double_divide(double_divide(C,A),double_divide(identity,B)),
inference(copy,[status(thm)],[c_239]) ).
cnf(c_240,plain,
double_divide(double_divide(identity,a3),double_divide(c3,b3)) != double_divide(double_divide(b3,a3),double_divide(identity,c3)),
inference(copy,[status(thm)],[c_141]) ).
cnf(c_204,plain,
$false,
inference(resolve,[status(thm)],[c_203,c_240]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP498-1 : 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 : n018.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 14:59:36 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2242344 was started by sandbox on n018,
% 0.10/0.37 % Fri Sep 25 14:59:36 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.15/0.43
% 0.15/0.43 % Assigning unary symbol inverse kb_weight 0 and highest precedence (8).
% 0.15/0.43
% 0.15/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.43
% 0.15/0.43 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.15/0.43 % Length of proof is 57.
% 0.15/0.43 % Level of proof is 17.
% 0.15/0.43 % Maximum clause weight is 81.000.
% 0.15/0.43 % Given clauses 50.
% 0.15/0.43
% 0.15/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------