%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP599-1 : 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 : 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 07:30:27 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.40s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 3
% Syntax : Number of formulae : 53 ( 53 unt; 0 def)
% Number of atoms : 53 ( 52 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 : 11 ( 2 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 : 89 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(double_divide(VAR_0,VAR_1),inverse(double_divide(VAR_0,inverse(double_divide(inverse(VAR_2),VAR_1))))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(inverse(C),B))))) = C,
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_127,plain,
multiply(inverse(double_divide(b3,a3)),c3) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_128,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_127]) ).
cnf(c_129,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != multiply(a3,inverse(double_divide(c3,b3))),
inference(paramod,[status(thm)],[c_2,c_128]) ).
cnf(c_130,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_129]) ).
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_130]) ).
cnf(c_5,plain,
double_divide(A,inverse(double_divide(double_divide(B,C),inverse(double_divide(inverse(D),inverse(double_divide(B,inverse(double_divide(inverse(A),C))))))))) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_131,plain,
double_divide(A,inverse(double_divide(double_divide(double_divide(B,C),inverse(double_divide(B,inverse(double_divide(inverse(inverse(D)),C))))),inverse(A)))) = D,
inference(paramod,[status(thm)],[c_5,c_5]) ).
cnf(c_9,plain,
double_divide(A,inverse(double_divide(inverse(B),inverse(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_131]) ).
cnf(c_10,plain,
double_divide(A,inverse(double_divide(B,inverse(double_divide(inverse(C),inverse(double_divide(inverse(A),inverse(B)))))))) = C,
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_12,plain,
double_divide(double_divide(A,inverse(A)),inverse(B)) = B,
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_20,plain,
double_divide(inverse(A),inverse(double_divide(B,inverse(B)))) = A,
inference(paramod,[status(thm)],[c_12,c_9]) ).
cnf(c_132,plain,
double_divide(A,inverse(double_divide(inverse(A),inverse(double_divide(inverse(B),inverse(double_divide(C,inverse(C)))))))) = B,
inference(paramod,[status(thm)],[c_20,c_1]) ).
cnf(c_21,plain,
double_divide(A,inverse(double_divide(inverse(A),inverse(B)))) = B,
inference(paramod,[status(thm)],[c_20,c_132]) ).
cnf(c_28,plain,
double_divide(double_divide(A,inverse(B)),inverse(B)) = A,
inference(paramod,[status(thm)],[c_21,c_1]) ).
cnf(c_32,plain,
double_divide(A,inverse(double_divide(double_divide(inverse(inverse(B)),C),inverse(double_divide(inverse(A),C))))) = B,
inference(paramod,[status(thm)],[c_21,c_5]) ).
cnf(c_33,plain,
double_divide(A,inverse(double_divide(B,inverse(double_divide(inverse(A),C))))) = double_divide(B,C),
inference(paramod,[status(thm)],[c_21,c_5]) ).
cnf(c_133,plain,
double_divide(double_divide(inverse(inverse(A)),inverse(B)),inverse(B)) = A,
inference(paramod,[status(thm)],[c_21,c_9]) ).
cnf(c_35,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_28,c_133]) ).
cnf(c_134,plain,
double_divide(A,inverse(B)) = double_divide(inverse(B),inverse(inverse(A))),
inference(paramod,[status(thm)],[c_9,c_21]) ).
cnf(c_135,plain,
double_divide(A,inverse(B)) = double_divide(inverse(B),A),
inference(paramod,[status(thm)],[c_35,c_134]) ).
cnf(c_36,plain,
double_divide(inverse(A),B) = double_divide(B,inverse(A)),
inference(copy,[status(thm)],[c_135]) ).
cnf(c_136,plain,
double_divide(A,inverse(double_divide(double_divide(B,C),inverse(double_divide(inverse(A),C))))) = B,
inference(paramod,[status(thm)],[c_35,c_32]) ).
cnf(c_39,plain,
double_divide(double_divide(A,B),B) = A,
inference(paramod,[status(thm)],[c_33,c_136]) ).
cnf(c_137,plain,
inverse(double_divide(a3,inverse(double_divide(c3,b3)))) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))),
inference(paramod,[status(thm)],[c_36,c_4]) ).
cnf(c_51,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(a3,inverse(double_divide(c3,b3)))),
inference(copy,[status(thm)],[c_137]) ).
cnf(c_53,plain,
double_divide(A,inverse(double_divide(B,inverse(A)))) = inverse(B),
inference(paramod,[status(thm)],[c_35,c_9]) ).
cnf(c_138,plain,
double_divide(A,B) = double_divide(B,inverse(inverse(A))),
inference(paramod,[status(thm)],[c_35,c_36]) ).
cnf(c_62,plain,
double_divide(A,B) = double_divide(B,A),
inference(paramod,[status(thm)],[c_35,c_138]) ).
cnf(c_139,plain,
inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != inverse(double_divide(a3,inverse(double_divide(c3,b3)))),
inference(paramod,[status(thm)],[c_62,c_51]) ).
cnf(c_63,plain,
inverse(double_divide(c3,inverse(double_divide(a3,b3)))) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_62,c_139]) ).
cnf(c_64,plain,
double_divide(A,double_divide(B,A)) = B,
inference(paramod,[status(thm)],[c_62,c_39]) ).
cnf(c_69,plain,
double_divide(A,double_divide(A,B)) = B,
inference(paramod,[status(thm)],[c_62,c_64]) ).
cnf(c_140,plain,
double_divide(A,B) = inverse(double_divide(C,inverse(double_divide(inverse(B),inverse(double_divide(inverse(A),inverse(C))))))),
inference(paramod,[status(thm)],[c_10,c_69]) ).
cnf(c_77,plain,
inverse(double_divide(A,inverse(double_divide(inverse(B),inverse(double_divide(inverse(C),inverse(A))))))) = double_divide(C,B),
inference(copy,[status(thm)],[c_140]) ).
cnf(c_141,plain,
double_divide(A,inverse(B)) = inverse(double_divide(B,inverse(A))),
inference(paramod,[status(thm)],[c_53,c_69]) ).
cnf(c_81,plain,
inverse(double_divide(A,inverse(B))) = double_divide(B,inverse(A)),
inference(copy,[status(thm)],[c_141]) ).
cnf(c_142,plain,
inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,inverse(inverse(C))))))) = double_divide(C,B),
inference(paramod,[status(thm)],[c_81,c_77]) ).
cnf(c_143,plain,
inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))) = double_divide(C,B),
inference(paramod,[status(thm)],[c_35,c_142]) ).
cnf(c_144,plain,
double_divide(double_divide(inverse(B),double_divide(A,C)),inverse(A)) = double_divide(C,B),
inference(paramod,[status(thm)],[c_81,c_143]) ).
cnf(c_84,plain,
double_divide(inverse(A),double_divide(inverse(B),double_divide(A,C))) = double_divide(C,B),
inference(paramod,[status(thm)],[c_62,c_144]) ).
cnf(c_145,plain,
double_divide(double_divide(a3,b3),inverse(c3)) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_81,c_63]) ).
cnf(c_146,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != inverse(double_divide(a3,inverse(double_divide(b3,c3)))),
inference(paramod,[status(thm)],[c_62,c_145]) ).
cnf(c_147,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(double_divide(b3,c3),inverse(a3)),
inference(paramod,[status(thm)],[c_81,c_146]) ).
cnf(c_90,plain,
double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(a3),double_divide(b3,c3)),
inference(paramod,[status(thm)],[c_62,c_147]) ).
cnf(c_125,plain,
double_divide(inverse(A),double_divide(B,C)) = double_divide(inverse(C),double_divide(A,B)),
inference(paramod,[status(thm)],[c_84,c_69]) ).
cnf(c_148,plain,
double_divide(inverse(a3),double_divide(b3,c3)) != double_divide(inverse(c3),double_divide(a3,b3)),
inference(copy,[status(thm)],[c_90]) ).
cnf(c_126,plain,
$false,
inference(resolve,[status(thm)],[c_125,c_148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP599-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 15:01:17 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 3777292 was started by sandbox2 on n005,
% 0.08/0.37 % Fri Sep 25 15:01:17 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.40
% 0.08/0.40 % Assigning unary symbol inverse kb_weight 0 and highest precedence (7).
% 0.08/0.40
% 0.08/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.40
% 0.08/0.40 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.08/0.40 % Length of proof is 28.
% 0.08/0.40 % Level of proof is 15.
% 0.08/0.40 % Maximum clause weight is 78.000.
% 0.08/0.40 % Given clauses 26.
% 0.08/0.40
% 0.08/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------