%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP452-1 : 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 : n001.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 07:29:45 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 43 ( 43 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(divide(VAR_0,VAR_0),divide(VAR_0,divide(VAR_1,divide(divide(divide(VAR_0,VAR_0),VAR_0),VAR_2)))),VAR_2) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(divide(A,A),divide(A,divide(B,divide(divide(divide(A,A),A),C)))),C) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,VAR_1) = divide(VAR_0,divide(divide(VAR_2,VAR_2),VAR_1)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
inference(clausify,[status(thm)],[multiply]) ).
cnf(c_3,plain,
divide(A,divide(divide(B,B),C)) = multiply(A,C),
inference(copy,[status(thm)],[c_2]) ).
fof(inverse,axiom,
! [VAR_0,VAR_1] : inverse(VAR_0) = divide(divide(VAR_1,VAR_1),VAR_0),
file('theBenchmark.p',inverse) ).
cnf(c_4,plain,
inverse(A) = divide(divide(B,B),A),
inference(clausify,[status(thm)],[inverse]) ).
cnf(c_5,plain,
divide(divide(A,A),B) = inverse(B),
inference(copy,[status(thm)],[c_4]) ).
fof(prove_these_axioms_2,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c_6,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(clausify,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_117,plain,
divide(A,inverse(C)) = multiply(A,C),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_7,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(copy,[status(thm)],[c_117]) ).
cnf(c_118,plain,
divide(divide(divide(A,A),divide(A,divide(B,divide(inverse(A),C)))),C) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_8,plain,
divide(inverse(divide(A,divide(B,divide(inverse(A),C)))),C) = B,
inference(paramod,[status(thm)],[c_5,c_118]) ).
cnf(c_119,plain,
multiply(divide(inverse(b2),inverse(b2)),a2) != a2,
inference(paramod,[status(thm)],[c_7,c_6]) ).
cnf(c_120,plain,
divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2,
inference(paramod,[status(thm)],[c_7,c_119]) ).
cnf(c_9,plain,
inverse(inverse(a2)) != a2,
inference(paramod,[status(thm)],[c_5,c_120]) ).
cnf(c_10,plain,
divide(inverse(divide(A,A)),B) = inverse(B),
inference(paramod,[status(thm)],[c_5,c_5]) ).
cnf(c_11,plain,
divide(inverse(divide(A,inverse(divide(inverse(A),B)))),B) = divide(C,C),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_121,plain,
divide(inverse(inverse(divide(A,divide(inverse(divide(B,B)),C)))),C) = A,
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_12,plain,
divide(inverse(inverse(divide(A,inverse(B)))),B) = A,
inference(paramod,[status(thm)],[c_10,c_121]) ).
cnf(c_13,plain,
divide(inverse(divide(divide(A,divide(B,divide(inverse(A),C))),divide(D,B))),C) = D,
inference(paramod,[status(thm)],[c_8,c_8]) ).
cnf(c_122,plain,
divide(inverse(inverse(A)),B) = inverse(inverse(divide(A,inverse(inverse(B))))),
inference(paramod,[status(thm)],[c_12,c_12]) ).
cnf(c_27,plain,
inverse(inverse(divide(A,inverse(inverse(B))))) = divide(inverse(inverse(A)),B),
inference(copy,[status(thm)],[c_122]) ).
cnf(c_40,plain,
divide(A,A) = divide(B,B),
inference(paramod,[status(thm)],[c_11,c_11]) ).
cnf(c_123,plain,
divide(A,A) = inverse(divide(B,B)),
inference(paramod,[status(thm)],[c_40,c_5]) ).
cnf(c_43,plain,
inverse(divide(A,A)) = divide(B,B),
inference(copy,[status(thm)],[c_123]) ).
cnf(c_45,plain,
divide(inverse(divide(A,divide(B,B))),C) = divide(inverse(A),C),
inference(paramod,[status(thm)],[c_40,c_8]) ).
cnf(c_50,plain,
inverse(divide(A,A)) = inverse(divide(B,B)),
inference(paramod,[status(thm)],[c_43,c_5]) ).
cnf(c_124,plain,
inverse(divide(A,A)) = inverse(inverse(divide(B,B))),
inference(paramod,[status(thm)],[c_43,c_10]) ).
cnf(c_54,plain,
inverse(inverse(divide(A,A))) = inverse(divide(B,B)),
inference(copy,[status(thm)],[c_124]) ).
cnf(c_62,plain,
divide(inverse(inverse(divide(A,inverse(divide(B,B))))),divide(C,C)) = A,
inference(paramod,[status(thm)],[c_50,c_12]) ).
cnf(c_125,plain,
divide(inverse(divide(divide(A,divide(B,divide(inverse(A),C))),divide(D,D))),C) = inverse(divide(E,inverse(divide(inverse(E),B)))),
inference(paramod,[status(thm)],[c_11,c_13]) ).
cnf(c_126,plain,
divide(inverse(divide(A,divide(B,divide(inverse(A),C)))),C) = inverse(divide(E,inverse(divide(inverse(E),B)))),
inference(paramod,[status(thm)],[c_45,c_125]) ).
cnf(c_127,plain,
B = inverse(divide(E,inverse(divide(inverse(E),B)))),
inference(paramod,[status(thm)],[c_8,c_126]) ).
cnf(c_77,plain,
inverse(divide(A,inverse(divide(inverse(A),B)))) = B,
inference(copy,[status(thm)],[c_127]) ).
cnf(c_128,plain,
divide(inverse(inverse(divide(A,inverse(inverse(divide(B,B)))))),divide(C,C)) = A,
inference(paramod,[status(thm)],[c_54,c_12]) ).
cnf(c_96,plain,
divide(divide(inverse(inverse(A)),divide(B,B)),divide(C,C)) = A,
inference(paramod,[status(thm)],[c_27,c_128]) ).
cnf(c_104,plain,
inverse(divide(A,inverse(divide(B,B)))) = inverse(A),
inference(paramod,[status(thm)],[c_40,c_77]) ).
cnf(c_113,plain,
divide(inverse(inverse(A)),divide(B,B)) = A,
inference(paramod,[status(thm)],[c_104,c_62]) ).
cnf(c_114,plain,
divide(A,divide(B,B)) = A,
inference(paramod,[status(thm)],[c_113,c_96]) ).
cnf(c_115,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_114,c_113]) ).
cnf(c_116,plain,
$false,
inference(resolve,[status(thm)],[c_115,c_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP452-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 15:00:55 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3606332 was started by sandbox on n001,
% 0.09/0.37 % Fri Sep 25 15:00:55 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.41
% 0.14/0.41 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.14/0.41
% 0.14/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.41
% 0.14/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.14/0.41 % Length of proof is 27.
% 0.14/0.41 % Level of proof is 11.
% 0.14/0.41 % Maximum clause weight is 94.000.
% 0.14/0.41 % Given clauses 18.
% 0.14/0.41
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------