%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP079-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 07:27:07 AM UTC 2026
% Result : Unsatisfiable 0.75s 0.53s
% Output : CNFRefutation 0.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 5
% Syntax : Number of formulae : 91 ( 77 unt; 0 def)
% Number of atoms : 118 ( 117 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 77 ( 50 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(double_divide(identity,VAR_0),double_divide(double_divide(double_divide(VAR_1,VAR_2),double_divide(identity,identity)),double_divide(VAR_0,VAR_2))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = 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_136,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_136]) ).
fof(prove_these_axioms,axiom,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
file('theBenchmark.p',prove_these_axioms) ).
cnf(c_6,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
inference(clausify,[status(thm)],[prove_these_axioms]) ).
cnf(c_137,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(double_divide(a1,identity),a1) != identity ),
inference(paramod,[status(thm)],[c_3,c_6]) ).
cnf(c_138,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| double_divide(double_divide(a1,double_divide(a1,identity)),identity) != identity ),
inference(paramod,[status(thm)],[c_2,c_137]) ).
cnf(c_139,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| double_divide(identity,identity) != identity ),
inference(paramod,[status(thm)],[c_5,c_138]) ).
cnf(c_140,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(identity,identity) != identity ),
inference(paramod,[status(thm)],[c_2,c_139]) ).
cnf(c_141,plain,
( multiply(double_divide(double_divide(b3,a3),identity),c3) != multiply(a3,multiply(b3,c3))
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(identity,identity) != identity ),
inference(paramod,[status(thm)],[c_2,c_140]) ).
cnf(c_142,plain,
( double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != multiply(a3,multiply(b3,c3))
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(identity,identity) != identity ),
inference(paramod,[status(thm)],[c_2,c_141]) ).
cnf(c_143,plain,
( double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != multiply(a3,double_divide(double_divide(c3,b3),identity))
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(identity,identity) != identity ),
inference(paramod,[status(thm)],[c_2,c_142]) ).
cnf(c_144,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)
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(identity,identity) != identity ),
inference(paramod,[status(thm)],[c_2,c_143]) ).
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)
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(identity,identity) != identity ),
inference(copy,[status(thm)],[c_144]) ).
cnf(c_8,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,B),double_divide(identity,identity)),double_divide(double_divide(identity,identity),B))) = A,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_145,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(A,double_divide(B,identity)))) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_9,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(A,double_divide(B,identity)))) = B,
inference(paramod,[status(thm)],[c_5,c_145]) ).
cnf(c_10,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,double_divide(A,identity)),double_divide(identity,identity)),identity)) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_146,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(A,identity)))) = A,
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_12,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(identity,identity),double_divide(A,identity)))) = A,
inference(paramod,[status(thm)],[c_5,c_146]) ).
cnf(c_13,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(double_divide(identity,identity),identity)),double_divide(identity,identity)),identity)) = A,
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_14,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(B,double_divide(identity,identity)),double_divide(A,double_divide(identity,double_divide(C,double_divide(B,identity)))))) = double_divide(identity,C),
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_15,plain,
double_divide(double_divide(identity,A),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_5,c_9]) ).
cnf(c_19,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(B,double_divide(identity,identity)),double_divide(A,double_divide(identity,identity)))) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_15,c_1]) ).
cnf(c_21,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(double_divide(double_divide(B,double_divide(identity,identity)),double_divide(identity,identity)),A)) = B,
inference(paramod,[status(thm)],[c_15,c_1]) ).
cnf(c_147,plain,
double_divide(identity,double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_15]) ).
cnf(c_148,plain,
identity = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_147]) ).
cnf(c_22,plain,
double_divide(identity,identity) = identity,
inference(copy,[status(thm)],[c_148]) ).
cnf(c_149,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(identity,identity)),double_divide(double_divide(identity,identity),double_divide(identity,identity)))) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_15,c_8]) ).
cnf(c_150,plain,
double_divide(identity,double_divide(double_divide(A,identity),double_divide(double_divide(identity,identity),double_divide(identity,identity)))) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_22,c_149]) ).
cnf(c_151,plain,
double_divide(identity,double_divide(double_divide(A,identity),double_divide(identity,double_divide(identity,identity)))) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_22,c_150]) ).
cnf(c_152,plain,
double_divide(identity,double_divide(double_divide(A,identity),double_divide(identity,identity))) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_22,c_151]) ).
cnf(c_23,plain,
double_divide(identity,double_divide(double_divide(A,identity),identity)) = double_divide(identity,A),
inference(paramod,[status(thm)],[c_22,c_152]) ).
cnf(c_153,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(identity,identity)),double_divide(identity,identity)),identity)) = A,
inference(paramod,[status(thm)],[c_15,c_8]) ).
cnf(c_154,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,identity),double_divide(identity,identity)),identity)) = A,
inference(paramod,[status(thm)],[c_22,c_153]) ).
cnf(c_155,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),identity)) = A,
inference(paramod,[status(thm)],[c_22,c_154]) ).
cnf(c_25,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(paramod,[status(thm)],[c_23,c_155]) ).
cnf(c_156,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(double_divide(double_divide(B,identity),double_divide(identity,identity)),A)) = B,
inference(paramod,[status(thm)],[c_22,c_21]) ).
cnf(c_28,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(double_divide(double_divide(B,identity),identity),A)) = B,
inference(paramod,[status(thm)],[c_22,c_156]) ).
cnf(c_157,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(B,identity),double_divide(A,double_divide(identity,identity)))) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_22,c_19]) ).
cnf(c_29,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(B,identity),double_divide(A,identity))) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_22,c_157]) ).
cnf(c_34,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(B,identity),double_divide(A,double_divide(identity,double_divide(C,double_divide(B,identity)))))) = double_divide(identity,C),
inference(paramod,[status(thm)],[c_22,c_14]) ).
cnf(c_158,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(identity,identity)),double_divide(identity,identity)),identity)) = A,
inference(paramod,[status(thm)],[c_22,c_13]) ).
cnf(c_159,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,identity),double_divide(identity,identity)),identity)) = A,
inference(paramod,[status(thm)],[c_22,c_158]) ).
cnf(c_160,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),identity)) = A,
inference(paramod,[status(thm)],[c_22,c_159]) ).
cnf(c_35,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(paramod,[status(thm)],[c_25,c_160]) ).
cnf(c_161,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = A,
inference(paramod,[status(thm)],[c_22,c_12]) ).
cnf(c_36,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_25,c_161]) ).
cnf(c_162,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,double_divide(A,identity)),identity),identity)) = B,
inference(paramod,[status(thm)],[c_22,c_10]) ).
cnf(c_37,plain,
double_divide(double_divide(identity,A),double_divide(B,double_divide(A,identity))) = B,
inference(paramod,[status(thm)],[c_35,c_162]) ).
cnf(c_163,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)
| double_divide(double_divide(a2,identity),identity) != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_22,c_7]) ).
cnf(c_164,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)
| a2 != a2
| identity != identity ),
inference(paramod,[status(thm)],[c_35,c_163]) ).
cnf(c_165,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)
| a2 != a2 ),
inference(copy,[status(thm)],[c_164]) ).
cnf(c_38,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_165]) ).
cnf(c_39,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),identity),double_divide(A,C))) = B,
inference(paramod,[status(thm)],[c_22,c_1]) ).
cnf(c_166,plain,
double_divide(A,double_divide(double_divide(double_divide(B,identity),identity),A)) = B,
inference(paramod,[status(thm)],[c_36,c_28]) ).
cnf(c_40,plain,
double_divide(A,double_divide(B,A)) = B,
inference(paramod,[status(thm)],[c_35,c_166]) ).
cnf(c_167,plain,
double_divide(B,identity) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_37,c_29]) ).
cnf(c_41,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(copy,[status(thm)],[c_167]) ).
cnf(c_43,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(identity,double_divide(B,C)),double_divide(A,C))) = B,
inference(paramod,[status(thm)],[c_41,c_39]) ).
cnf(c_168,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_41,c_38]) ).
cnf(c_169,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_41,c_168]) ).
cnf(c_170,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_41,c_169]) ).
cnf(c_44,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_41,c_170]) ).
cnf(c_171,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,identity)))))) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_22,c_34]) ).
cnf(c_172,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(A,double_divide(identity,double_divide(B,identity))))) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_22,c_171]) ).
cnf(c_52,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(A,B))) = double_divide(identity,B),
inference(paramod,[status(thm)],[c_40,c_172]) ).
cnf(c_60,plain,
double_divide(double_divide(A,B),A) = B,
inference(paramod,[status(thm)],[c_40,c_40]) ).
cnf(c_67,plain,
double_divide(A,double_divide(identity,B)) = double_divide(A,double_divide(B,identity)),
inference(paramod,[status(thm)],[c_37,c_60]) ).
cnf(c_69,plain,
double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,A))) = B,
inference(paramod,[status(thm)],[c_67,c_40]) ).
cnf(c_173,plain,
double_divide(A,double_divide(identity,B)) = double_divide(double_divide(identity,double_divide(A,C)),double_divide(B,C)),
inference(paramod,[status(thm)],[c_43,c_60]) ).
cnf(c_80,plain,
double_divide(double_divide(identity,double_divide(A,B)),double_divide(C,B)) = double_divide(A,double_divide(identity,C)),
inference(copy,[status(thm)],[c_173]) ).
cnf(c_90,plain,
double_divide(double_divide(identity,A),double_divide(identity,B)) = double_divide(identity,double_divide(B,A)),
inference(paramod,[status(thm)],[c_40,c_52]) ).
cnf(c_174,plain,
double_divide(double_divide(identity,double_divide(A,identity)),double_divide(identity,B)) = double_divide(identity,double_divide(B,double_divide(identity,A))),
inference(paramod,[status(thm)],[c_69,c_52]) ).
cnf(c_175,plain,
double_divide(A,double_divide(identity,B)) = double_divide(identity,double_divide(B,double_divide(identity,A))),
inference(paramod,[status(thm)],[c_40,c_174]) ).
cnf(c_92,plain,
double_divide(identity,double_divide(A,double_divide(identity,B))) = double_divide(B,double_divide(identity,A)),
inference(copy,[status(thm)],[c_175]) ).
cnf(c_96,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(double_divide(b3,a3),double_divide(identity,c3)),
inference(paramod,[status(thm)],[c_92,c_44]) ).
cnf(c_176,plain,
double_divide(double_divide(identity,A),B) = double_divide(identity,double_divide(double_divide(identity,B),A)),
inference(paramod,[status(thm)],[c_36,c_90]) ).
cnf(c_98,plain,
double_divide(identity,double_divide(double_divide(identity,A),B)) = double_divide(double_divide(identity,B),A),
inference(copy,[status(thm)],[c_176]) ).
cnf(c_177,plain,
double_divide(double_divide(identity,a3),double_divide(c3,b3)) != double_divide(double_divide(b3,a3),double_divide(identity,c3)),
inference(paramod,[status(thm)],[c_98,c_96]) ).
cnf(c_100,plain,
double_divide(double_divide(b3,a3),double_divide(identity,c3)) != double_divide(double_divide(identity,a3),double_divide(c3,b3)),
inference(copy,[status(thm)],[c_177]) ).
cnf(c_134,plain,
double_divide(double_divide(identity,A),double_divide(B,C)) = double_divide(double_divide(C,A),double_divide(identity,B)),
inference(paramod,[status(thm)],[c_60,c_80]) ).
cnf(c_178,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_100]) ).
cnf(c_135,plain,
$false,
inference(resolve,[status(thm)],[c_134,c_178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP079-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n002.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 14:24:04 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 3483090 was started by sandbox on n002,
% 0.16/0.42 % Fri Sep 25 14:24:04 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 0.75/0.53
% 0.75/0.53 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 0.75/0.53
% 0.75/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.75/0.53
% 0.75/0.53 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.75/0.53 % Length of proof is 43.
% 0.75/0.53 % Level of proof is 15.
% 0.75/0.53 % Maximum clause weight is 98.000.
% 0.75/0.53 % Given clauses 36.
% 0.75/0.53
% 0.75/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------