%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP536-1 : 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 : 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 07:30:19 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(VAR_0,divide(divide(VAR_0,VAR_1),VAR_2)),VAR_1) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(A,divide(divide(A,B),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(prove_these_axioms_4,axiom,
multiply(a,b) != multiply(b,a),
file('theBenchmark.p',prove_these_axioms_4) ).
cnf(c_7,plain,
multiply(a,b) != multiply(b,a),
inference(clausify,[status(thm)],[prove_these_axioms_4]) ).
cnf(c_8,plain,
multiply(b,a) != multiply(a,b),
inference(copy,[status(thm)],[c_7]) ).
cnf(c_10,plain,
divide(divide(A,B),divide(divide(A,C),B)) = C,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_82,plain,
divide(b,divide(divide(A,A),a)) != multiply(a,b),
inference(paramod,[status(thm)],[c_2,c_8]) ).
cnf(c_33,plain,
multiply(a,b) != divide(b,divide(divide(A,A),a)),
inference(copy,[status(thm)],[c_82]) ).
cnf(c_59,plain,
divide(A,divide(divide(divide(B,divide(divide(B,C),A)),D),C)) = D,
inference(paramod,[status(thm)],[c_1,c_10]) ).
cnf(c_83,plain,
divide(a,divide(divide(A,A),b)) != divide(b,divide(divide(B,B),a)),
inference(paramod,[status(thm)],[c_2,c_33]) ).
cnf(c_80,plain,
divide(b,divide(divide(A,A),a)) != divide(a,divide(divide(B,B),b)),
inference(copy,[status(thm)],[c_83]) ).
cnf(c_81,plain,
$false,
inference(resolve,[status(thm)],[c_80,c_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP536-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n001.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 15:04:55 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.46 % Process 3617284 was started by sandbox2 on n001,
% 0.18/0.46 % Fri Sep 25 15:04:55 2026
% 0.18/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % 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 0.01 (+ 0.00) seconds.
% 0.18/0.48 % Length of proof is 9.
% 0.18/0.48 % Level of proof is 4.
% 0.18/0.48 % Maximum clause weight is 50.000.
% 0.18/0.48 % Given clauses 8.
% 0.18/0.48
% 0.18/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------