%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP527-1 : 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 : n019.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 07:30:17 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 40 unt; 0 def)
% Number of atoms : 40 ( 39 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 12 ( 12 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 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 : 68 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(VAR_0,divide(divide(VAR_0,VAR_1),divide(VAR_2,VAR_1))) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(A,divide(divide(A,B),divide(C,B))) = C,
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]) ).
fof(inverse,axiom,
! [VAR_0,VAR_1] : inverse(VAR_0) = divide(divide(VAR_1,VAR_1),VAR_0),
file('theBenchmark.p',inverse) ).
cnf(c_3,plain,
inverse(A) = divide(divide(B,B),A),
inference(clausify,[status(thm)],[inverse]) ).
cnf(c_4,plain,
divide(divide(A,A),B) = inverse(B),
inference(copy,[status(thm)],[c_3]) ).
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_5,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(clausify,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_6,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_73,plain,
multiply(divide(a3,inverse(b3)),c3) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_6,c_5]) ).
cnf(c_74,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_6,c_73]) ).
cnf(c_75,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != multiply(a3,divide(b3,inverse(c3))),
inference(paramod,[status(thm)],[c_6,c_74]) ).
cnf(c_7,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(paramod,[status(thm)],[c_6,c_75]) ).
cnf(c_8,plain,
divide(A,divide(B,divide(C,divide(divide(A,D),divide(B,D))))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_76,plain,
divide(A,B) = divide(divide(A,divide(B,C)),C),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_10,plain,
divide(divide(A,divide(B,C)),C) = divide(A,B),
inference(copy,[status(thm)],[c_76]) ).
cnf(c_13,plain,
divide(A,inverse(divide(B,A))) = B,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_18,plain,
divide(A,divide(B,B)) = A,
inference(paramod,[status(thm)],[c_1,c_8]) ).
cnf(c_77,plain,
divide(A,divide(A,divide(B,divide(C,C)))) = B,
inference(paramod,[status(thm)],[c_18,c_1]) ).
cnf(c_26,plain,
divide(A,divide(A,B)) = B,
inference(paramod,[status(thm)],[c_18,c_77]) ).
cnf(c_78,plain,
A = inverse(divide(divide(B,B),A)),
inference(paramod,[status(thm)],[c_26,c_4]) ).
cnf(c_79,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_4,c_78]) ).
cnf(c_36,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_79]) ).
cnf(c_37,plain,
divide(divide(A,B),A) = inverse(B),
inference(paramod,[status(thm)],[c_10,c_4]) ).
cnf(c_41,plain,
divide(divide(A,divide(B,C)),D) = divide(A,divide(B,divide(C,D))),
inference(paramod,[status(thm)],[c_10,c_10]) ).
cnf(c_80,plain,
divide(divide(A,B),C) = divide(divide(A,divide(B,divide(D,C))),D),
inference(paramod,[status(thm)],[c_10,c_10]) ).
cnf(c_81,plain,
divide(divide(A,B),C) = divide(A,divide(B,divide(divide(D,C),D))),
inference(paramod,[status(thm)],[c_41,c_80]) ).
cnf(c_42,plain,
divide(divide(A,B),C) = divide(A,divide(B,inverse(C))),
inference(paramod,[status(thm)],[c_37,c_81]) ).
cnf(c_43,plain,
divide(A,divide(B,inverse(A))) = inverse(B),
inference(paramod,[status(thm)],[c_42,c_37]) ).
cnf(c_82,plain,
divide(a3,divide(inverse(b3),inverse(inverse(c3)))) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(paramod,[status(thm)],[c_42,c_7]) ).
cnf(c_44,plain,
divide(a3,divide(inverse(b3),c3)) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(paramod,[status(thm)],[c_36,c_82]) ).
cnf(c_83,plain,
divide(A,B) = inverse(divide(B,A)),
inference(paramod,[status(thm)],[c_13,c_26]) ).
cnf(c_45,plain,
inverse(divide(A,B)) = divide(B,A),
inference(copy,[status(thm)],[c_83]) ).
cnf(c_50,plain,
divide(a3,inverse(divide(c3,inverse(b3)))) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(paramod,[status(thm)],[c_45,c_44]) ).
cnf(c_84,plain,
divide(a3,inverse(divide(c3,inverse(b3)))) != inverse(divide(inverse(divide(b3,inverse(c3))),a3)),
inference(paramod,[status(thm)],[c_45,c_50]) ).
cnf(c_62,plain,
inverse(divide(inverse(divide(b3,inverse(c3))),a3)) != divide(a3,inverse(divide(c3,inverse(b3)))),
inference(copy,[status(thm)],[c_84]) ).
cnf(c_66,plain,
divide(A,inverse(B)) = divide(B,inverse(A)),
inference(paramod,[status(thm)],[c_43,c_26]) ).
cnf(c_71,plain,
inverse(divide(inverse(divide(b3,inverse(c3))),a3)) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(paramod,[status(thm)],[c_66,c_62]) ).
cnf(c_72,plain,
$false,
inference(resolve,[status(thm)],[c_71,c_45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP527-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n019.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Fri Sep 25 14:58:51 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 3042444 was started by sandbox2 on n019,
% 0.18/0.45 % Fri Sep 25 14:58:51 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.48
% 0.18/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.48
% 0.18/0.48 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.18/0.48 % Length of proof is 24.
% 0.18/0.48 % Level of proof is 9.
% 0.18/0.48 % Maximum clause weight is 16.000.
% 0.18/0.48 % Given clauses 23.
% 0.18/0.48
% 0.18/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------