%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP564-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 07:30:22 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 23 unt; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 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 : 45 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(divide(VAR_0,inverse(VAR_1)),VAR_2),divide(VAR_0,VAR_2)) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(divide(A,inverse(B)),C),divide(A,C)) = B,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = divide(VAR_0,inverse(VAR_1)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(clausify,[status(thm)],[multiply]) ).
fof(prove_these_axioms_4,axiom,
multiply(a,b) != multiply(b,a),
file('theBenchmark.p',prove_these_axioms_4) ).
cnf(c_3,plain,
multiply(a,b) != multiply(b,a),
inference(clausify,[status(thm)],[prove_these_axioms_4]) ).
cnf(c_102,plain,
divide(a,inverse(b)) != multiply(b,a),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_4,plain,
divide(a,inverse(b)) != divide(b,inverse(a)),
inference(paramod,[status(thm)],[c_2,c_102]) ).
cnf(c_5,plain,
divide(A,divide(divide(B,inverse(A)),divide(B,inverse(C)))) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_6,plain,
divide(divide(divide(divide(divide(A,inverse(B)),C),inverse(D)),divide(A,C)),B) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_103,plain,
divide(divide(A,divide(divide(divide(B,inverse(inverse(C))),D),divide(B,D))),A) = C,
inference(paramod,[status(thm)],[c_6,c_6]) ).
cnf(c_16,plain,
divide(divide(A,inverse(B)),A) = B,
inference(paramod,[status(thm)],[c_1,c_103]) ).
cnf(c_18,plain,
divide(divide(A,B),divide(divide(inverse(C),inverse(A)),B)) = C,
inference(paramod,[status(thm)],[c_16,c_1]) ).
cnf(c_19,plain,
divide(A,divide(B,B)) = A,
inference(paramod,[status(thm)],[c_16,c_1]) ).
cnf(c_28,plain,
divide(divide(A,A),inverse(B)) = B,
inference(paramod,[status(thm)],[c_19,c_16]) ).
cnf(c_104,plain,
divide(A,divide(A,divide(divide(B,B),inverse(C)))) = C,
inference(paramod,[status(thm)],[c_28,c_5]) ).
cnf(c_31,plain,
divide(A,divide(A,B)) = B,
inference(paramod,[status(thm)],[c_28,c_104]) ).
cnf(c_53,plain,
divide(divide(A,A),B) = inverse(B),
inference(paramod,[status(thm)],[c_28,c_31]) ).
cnf(c_89,plain,
divide(A,divide(divide(inverse(B),inverse(divide(C,inverse(A)))),C)) = B,
inference(paramod,[status(thm)],[c_16,c_18]) ).
cnf(c_105,plain,
divide(a,divide(divide(A,A),b)) != divide(b,inverse(a)),
inference(paramod,[status(thm)],[c_53,c_4]) ).
cnf(c_100,plain,
divide(b,inverse(a)) != divide(a,divide(divide(A,A),b)),
inference(copy,[status(thm)],[c_105]) ).
cnf(c_106,plain,
B = divide(A,divide(divide(inverse(B),inverse(divide(C,inverse(A)))),C)),
inference(copy,[status(thm)],[c_89]) ).
cnf(c_101,plain,
$false,
inference(resolve,[status(thm)],[c_100,c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP564-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n013.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Fri Sep 25 14:59:21 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 686987 was started by sandbox2 on n013,
% 0.18/0.44 % Fri Sep 25 14:59:21 2026
% 0.18/0.44 % 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).
% 0.18/0.47
% 0.18/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.47
% 0.18/0.47 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.18/0.47 % Length of proof is 15.
% 0.18/0.47 % Level of proof is 8.
% 0.18/0.47 % Maximum clause weight is 17.000.
% 0.18/0.47 % Given clauses 15.
% 0.18/0.47
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------