%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP548-1 : 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 : n014.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 07:30:20 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 32 unt; 0 def)
% Number of atoms : 32 ( 31 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(identity,divide(VAR_0,VAR_1)),divide(divide(VAR_1,VAR_2),VAR_0)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = divide(VAR_0,divide(identity,VAR_1)),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = divide(A,divide(identity,B)),
inference(clausify,[status(thm)],[multiply]) ).
fof(identity,axiom,
! [VAR_0] : identity = divide(VAR_0,VAR_0),
file('theBenchmark.p',identity) ).
cnf(c_4,plain,
identity = divide(A,A),
inference(clausify,[status(thm)],[identity]) ).
cnf(c_5,plain,
divide(A,A) = identity,
inference(copy,[status(thm)],[c_4]) ).
fof(prove_these_axioms_4,axiom,
multiply(a,b) != multiply(b,a),
file('theBenchmark.p',prove_these_axioms_4) ).
cnf(c_6,plain,
multiply(a,b) != multiply(b,a),
inference(clausify,[status(thm)],[prove_these_axioms_4]) ).
cnf(c_77,plain,
divide(a,divide(identity,b)) != multiply(b,a),
inference(paramod,[status(thm)],[c_2,c_6]) ).
cnf(c_78,plain,
divide(a,divide(identity,b)) != divide(b,divide(identity,a)),
inference(paramod,[status(thm)],[c_2,c_77]) ).
cnf(c_7,plain,
divide(b,divide(identity,a)) != divide(a,divide(identity,b)),
inference(copy,[status(thm)],[c_78]) ).
cnf(c_10,plain,
divide(divide(identity,divide(divide(divide(A,B),C),identity)),B) = divide(C,A),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_79,plain,
divide(divide(identity,identity),divide(divide(A,B),A)) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_11,plain,
divide(identity,divide(divide(A,B),A)) = B,
inference(paramod,[status(thm)],[c_5,c_79]) ).
cnf(c_80,plain,
divide(divide(identity,divide(divide(A,B),A)),identity) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_13,plain,
divide(A,identity) = A,
inference(paramod,[status(thm)],[c_11,c_80]) ).
cnf(c_14,plain,
divide(divide(identity,divide(divide(A,B),C)),B) = divide(C,A),
inference(paramod,[status(thm)],[c_13,c_10]) ).
cnf(c_28,plain,
divide(divide(identity,divide(identity,A)),divide(A,B)) = B,
inference(paramod,[status(thm)],[c_13,c_1]) ).
cnf(c_35,plain,
divide(identity,divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_5,c_11]) ).
cnf(c_81,plain,
divide(identity,divide(A,identity)) = divide(divide(B,A),B),
inference(paramod,[status(thm)],[c_11,c_11]) ).
cnf(c_82,plain,
divide(identity,A) = divide(divide(B,A),B),
inference(paramod,[status(thm)],[c_13,c_81]) ).
cnf(c_41,plain,
divide(divide(A,B),A) = divide(identity,B),
inference(copy,[status(thm)],[c_82]) ).
cnf(c_43,plain,
divide(A,divide(A,B)) = B,
inference(paramod,[status(thm)],[c_35,c_28]) ).
cnf(c_54,plain,
divide(divide(A,B),divide(identity,B)) = A,
inference(paramod,[status(thm)],[c_41,c_43]) ).
cnf(c_83,plain,
divide(A,B) = divide(identity,divide(B,A)),
inference(paramod,[status(thm)],[c_43,c_41]) ).
cnf(c_55,plain,
divide(identity,divide(A,B)) = divide(B,A),
inference(copy,[status(thm)],[c_83]) ).
cnf(c_68,plain,
divide(divide(identity,A),B) = divide(divide(identity,B),A),
inference(paramod,[status(thm)],[c_54,c_14]) ).
cnf(c_84,plain,
divide(b,divide(identity,a)) != divide(identity,divide(divide(identity,b),a)),
inference(paramod,[status(thm)],[c_55,c_7]) ).
cnf(c_85,plain,
divide(b,divide(identity,a)) != divide(identity,divide(divide(identity,a),b)),
inference(paramod,[status(thm)],[c_68,c_84]) ).
cnf(c_75,plain,
divide(identity,divide(divide(identity,a),b)) != divide(b,divide(identity,a)),
inference(copy,[status(thm)],[c_85]) ).
cnf(c_76,plain,
$false,
inference(resolve,[status(thm)],[c_75,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP548-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 14:59:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 518668 was started by sandbox2 on n014,
% 0.11/0.38 % Fri Sep 25 14:59:33 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.15/0.41
% 0.15/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.41
% 0.15/0.41 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.15/0.41 % Length of proof is 19.
% 0.15/0.41 % Level of proof is 9.
% 0.15/0.41 % Maximum clause weight is 15.000.
% 0.15/0.41 % Given clauses 14.
% 0.15/0.41
% 0.15/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------