%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP544-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 5.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 34 unt; 0 def)
% Number of atoms : 34 ( 33 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; 3 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(identity,divide(divide(divide(VAR_0,VAR_1),VAR_2),VAR_0)),VAR_2) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B,
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_46,plain,
divide(a,divide(identity,b)) != multiply(b,a),
inference(paramod,[status(thm)],[c_2,c_6]) ).
cnf(c_47,plain,
divide(a,divide(identity,b)) != divide(b,divide(identity,a)),
inference(paramod,[status(thm)],[c_2,c_46]) ).
cnf(c_7,plain,
divide(b,divide(identity,a)) != divide(a,divide(identity,b)),
inference(copy,[status(thm)],[c_47]) ).
cnf(c_48,plain,
divide(divide(identity,divide(A,identity)),B) = divide(divide(divide(C,A),B),C),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_9,plain,
divide(divide(divide(A,B),C),A) = divide(divide(identity,divide(B,identity)),C),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_49,plain,
divide(divide(identity,divide(divide(A,B),divide(identity,divide(divide(divide(C,A),D),C)))),B) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_10,plain,
divide(divide(identity,divide(divide(A,B),divide(identity,divide(divide(identity,divide(A,identity)),C)))),B) = C,
inference(paramod,[status(thm)],[c_9,c_49]) ).
cnf(c_11,plain,
divide(divide(identity,divide(divide(identity,divide(A,identity)),B)),B) = A,
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_50,plain,
divide(divide(identity,A),B) = divide(divide(identity,divide(B,identity)),A),
inference(paramod,[status(thm)],[c_5,c_9]) ).
cnf(c_12,plain,
divide(divide(identity,divide(A,identity)),B) = divide(divide(identity,B),A),
inference(copy,[status(thm)],[c_50]) ).
cnf(c_51,plain,
divide(divide(identity,identity),divide(divide(identity,divide(identity,identity)),A)) = A,
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_52,plain,
divide(identity,divide(divide(identity,divide(identity,identity)),A)) = A,
inference(paramod,[status(thm)],[c_5,c_51]) ).
cnf(c_53,plain,
divide(identity,divide(divide(identity,identity),A)) = A,
inference(paramod,[status(thm)],[c_5,c_52]) ).
cnf(c_19,plain,
divide(identity,divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_5,c_53]) ).
cnf(c_54,plain,
divide(divide(identity,identity),divide(identity,divide(A,identity))) = A,
inference(paramod,[status(thm)],[c_5,c_11]) ).
cnf(c_55,plain,
divide(identity,divide(identity,divide(A,identity))) = A,
inference(paramod,[status(thm)],[c_5,c_54]) ).
cnf(c_23,plain,
divide(A,identity) = A,
inference(paramod,[status(thm)],[c_19,c_55]) ).
cnf(c_37,plain,
divide(divide(identity,A),B) = divide(divide(identity,B),A),
inference(paramod,[status(thm)],[c_23,c_12]) ).
cnf(c_56,plain,
multiply(divide(identity,A),B) = divide(divide(identity,divide(identity,B)),A),
inference(paramod,[status(thm)],[c_37,c_2]) ).
cnf(c_57,plain,
divide(divide(identity,A),divide(identity,B)) = divide(divide(identity,divide(identity,B)),A),
inference(paramod,[status(thm)],[c_2,c_56]) ).
cnf(c_43,plain,
divide(divide(identity,A),divide(identity,B)) = divide(B,A),
inference(paramod,[status(thm)],[c_19,c_57]) ).
cnf(c_58,plain,
multiply(A,B) = divide(divide(identity,divide(identity,B)),divide(identity,A)),
inference(paramod,[status(thm)],[c_43,c_2]) ).
cnf(c_59,plain,
divide(A,divide(identity,B)) = divide(divide(identity,divide(identity,B)),divide(identity,A)),
inference(paramod,[status(thm)],[c_2,c_58]) ).
cnf(c_44,plain,
divide(A,divide(identity,B)) = divide(B,divide(identity,A)),
inference(paramod,[status(thm)],[c_19,c_59]) ).
cnf(c_45,plain,
$false,
inference(resolve,[status(thm)],[c_44,c_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP544-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n005.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Fri Sep 25 14:59:07 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 3770955 was started by sandbox on n005,
% 0.10/5.38 % Fri Sep 25 14:59:07 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.39
% 0.10/5.39 % From the command line: assign(max_seconds, 300).
% 0.15/5.40
% 0.15/5.40 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.40
% 0.15/5.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/5.40 % Length of proof is 16.
% 0.15/5.40 % Level of proof is 8.
% 0.15/5.40 % Maximum clause weight is 94.000.
% 0.15/5.40 % Given clauses 13.
% 0.15/5.40
% 0.15/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------