%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP611-1 : 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 : n004.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 07:30:29 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.46s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 37 ( 37 unt; 0 def)
% Number of atoms : 37 ( 36 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : inverse(double_divide(inverse(double_divide(inverse(double_divide(VAR_0,VAR_1)),VAR_2)),double_divide(VAR_0,VAR_2))) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C))) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = inverse(double_divide(VAR_1,VAR_0)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = inverse(double_divide(B,A)),
inference(clausify,[status(thm)],[multiply]) ).
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_3,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(clausify,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_430,plain,
multiply(inverse(double_divide(b3,a3)),c3) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_431,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_430]) ).
cnf(c_432,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != multiply(a3,inverse(double_divide(c3,b3))),
inference(paramod,[status(thm)],[c_2,c_431]) ).
cnf(c_433,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference(paramod,[status(thm)],[c_2,c_432]) ).
cnf(c_4,plain,
inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))),
inference(copy,[status(thm)],[c_433]) ).
cnf(c_5,plain,
inverse(double_divide(inverse(double_divide(A,B)),double_divide(inverse(double_divide(inverse(double_divide(C,A)),D)),B))) = double_divide(C,D),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),double_divide(B,C)))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_7,plain,
inverse(double_divide(inverse(double_divide(double_divide(A,B),C)),double_divide(inverse(double_divide(D,E)),C))) = double_divide(inverse(double_divide(inverse(double_divide(A,D)),B)),E),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_9,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(inverse(double_divide(B,inverse(double_divide(inverse(double_divide(C,A)),D)))),E)),double_divide(C,D)))) = double_divide(B,E),
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_10,plain,
inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,B))) = double_divide(inverse(double_divide(D,C)),double_divide(D,A)),
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_434,plain,
A = double_divide(B,inverse(double_divide(C,double_divide(inverse(double_divide(B,C)),A)))),
inference(paramod,[status(thm)],[c_6,c_5]) ).
cnf(c_18,plain,
double_divide(A,inverse(double_divide(B,double_divide(inverse(double_divide(A,B)),C)))) = C,
inference(copy,[status(thm)],[c_434]) ).
cnf(c_23,plain,
inverse(inverse(double_divide(inverse(double_divide(double_divide(A,B),C)),double_divide(inverse(double_divide(D,double_divide(A,B))),C)))) = D,
inference(paramod,[status(thm)],[c_7,c_1]) ).
cnf(c_41,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(B,C)))) = C,
inference(paramod,[status(thm)],[c_10,c_1]) ).
cnf(c_75,plain,
double_divide(inverse(double_divide(A,B)),double_divide(A,C)) = double_divide(inverse(double_divide(D,B)),double_divide(D,C)),
inference(paramod,[status(thm)],[c_10,c_10]) ).
cnf(c_435,plain,
inverse(double_divide(inverse(double_divide(A,B)),double_divide(inverse(double_divide(inverse(double_divide(C,A)),double_divide(C,D))),B))) = double_divide(E,double_divide(E,D)),
inference(paramod,[status(thm)],[c_75,c_5]) ).
cnf(c_125,plain,
double_divide(A,double_divide(A,B)) = double_divide(C,double_divide(C,B)),
inference(paramod,[status(thm)],[c_5,c_435]) ).
cnf(c_436,plain,
multiply(double_divide(A,B),A) = inverse(double_divide(C,double_divide(C,B))),
inference(paramod,[status(thm)],[c_125,c_2]) ).
cnf(c_155,plain,
inverse(double_divide(A,double_divide(A,B))) = inverse(double_divide(C,double_divide(C,B))),
inference(paramod,[status(thm)],[c_2,c_436]) ).
cnf(c_184,plain,
inverse(double_divide(inverse(double_divide(A,B)),C)) = inverse(double_divide(D,double_divide(D,double_divide(A,inverse(double_divide(B,C)))))),
inference(paramod,[status(thm)],[c_41,c_155]) ).
cnf(c_190,plain,
inverse(double_divide(inverse(double_divide(inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),C))),D)),double_divide(inverse(double_divide(inverse(C),E)),D))) = double_divide(B,E),
inference(paramod,[status(thm)],[c_18,c_5]) ).
cnf(c_203,plain,
inverse(double_divide(inverse(double_divide(inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),C))),D)),double_divide(E,D))) = double_divide(inverse(double_divide(B,E)),C),
inference(paramod,[status(thm)],[c_18,c_10]) ).
cnf(c_221,plain,
double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),C)))),B) = double_divide(A,C),
inference(paramod,[status(thm)],[c_203,c_190]) ).
cnf(c_326,plain,
inverse(double_divide(inverse(double_divide(A,B)),double_divide(inverse(double_divide(C,A)),D))) = double_divide(C,inverse(double_divide(inverse(B),D))),
inference(paramod,[status(thm)],[c_221,c_5]) ).
cnf(c_363,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(B,C)),double_divide(D,C)))) = double_divide(B,double_divide(D,A)),
inference(paramod,[status(thm)],[c_221,c_9]) ).
cnf(c_376,plain,
inverse(double_divide(A,inverse(double_divide(inverse(B),B)))) = A,
inference(paramod,[status(thm)],[c_326,c_23]) ).
cnf(c_437,plain,
inverse(double_divide(A,inverse(double_divide(B,double_divide(inverse(double_divide(inverse(double_divide(C,B)),D)),double_divide(C,D)))))) = A,
inference(paramod,[status(thm)],[c_1,c_376]) ).
cnf(c_438,plain,
inverse(double_divide(A,double_divide(inverse(double_divide(C,B)),double_divide(C,B)))) = A,
inference(paramod,[status(thm)],[c_363,c_437]) ).
cnf(c_380,plain,
double_divide(A,double_divide(A,B)) = B,
inference(paramod,[status(thm)],[c_363,c_438]) ).
cnf(c_428,plain,
inverse(double_divide(inverse(double_divide(A,B)),C)) = inverse(double_divide(A,inverse(double_divide(B,C)))),
inference(paramod,[status(thm)],[c_380,c_184]) ).
cnf(c_429,plain,
$false,
inference(resolve,[status(thm)],[c_428,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP611-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 15:02:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 3489045 was started by sandbox2 on n004,
% 0.12/0.36 % Fri Sep 25 15:02:06 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.46
% 0.12/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.46
% 0.12/0.46 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.12/0.46 % Length of proof is 25.
% 0.12/0.46 % Level of proof is 9.
% 0.12/0.46 % Maximum clause weight is 94.000.
% 0.12/0.46 % Given clauses 18.
% 0.12/0.46
% 0.12/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------