%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP458-1 : TPTP v9.3.1. Released v2.6.0.
% 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 07:29:46 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.37s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 41 unt; 0 def)
% Number of atoms : 41 ( 40 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 11 ( 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 : 72 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(divide(VAR_0,VAR_0),divide(VAR_0,divide(VAR_1,divide(divide(identity,VAR_0),VAR_2)))),VAR_2) = VAR_1,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),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_2,axiom,
multiply(identity,a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c_6,plain,
multiply(identity,a2) != a2,
inference(clausify,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_7,plain,
divide(identity,divide(identity,a2)) != a2,
inference(paramod,[status(thm)],[c_2,c_6]) ).
cnf(c_8,plain,
divide(divide(identity,divide(A,divide(B,divide(divide(identity,A),C)))),C) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_9,plain,
divide(divide(identity,divide(identity,divide(A,divide(identity,B)))),B) = A,
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_12,plain,
divide(divide(identity,divide(divide(A,divide(B,divide(divide(identity,A),C))),divide(D,B))),C) = D,
inference(paramod,[status(thm)],[c_8,c_8]) ).
cnf(c_14,plain,
divide(divide(identity,divide(identity,divide(A,identity))),identity) = A,
inference(paramod,[status(thm)],[c_5,c_9]) ).
cnf(c_16,plain,
divide(divide(identity,divide(A,B)),C) = divide(identity,divide(identity,divide(B,divide(identity,divide(divide(identity,A),C))))),
inference(paramod,[status(thm)],[c_9,c_8]) ).
cnf(c_53,plain,
divide(identity,divide(identity,divide(divide(A,identity),divide(identity,divide(divide(identity,identity),identity))))) = A,
inference(paramod,[status(thm)],[c_16,c_14]) ).
cnf(c_54,plain,
divide(identity,divide(identity,divide(divide(A,identity),divide(identity,divide(identity,identity))))) = A,
inference(paramod,[status(thm)],[c_5,c_53]) ).
cnf(c_55,plain,
divide(identity,divide(identity,divide(divide(A,identity),divide(identity,identity)))) = A,
inference(paramod,[status(thm)],[c_5,c_54]) ).
cnf(c_19,plain,
divide(identity,divide(identity,divide(divide(A,identity),identity))) = A,
inference(paramod,[status(thm)],[c_5,c_55]) ).
cnf(c_56,plain,
divide(identity,divide(identity,divide(divide(D,B),divide(identity,divide(divide(identity,divide(A,divide(B,divide(divide(identity,A),C)))),C))))) = D,
inference(paramod,[status(thm)],[c_16,c_12]) ).
cnf(c_21,plain,
divide(identity,divide(identity,divide(divide(A,B),divide(identity,divide(identity,divide(identity,divide(divide(B,divide(divide(identity,C),D)),divide(identity,divide(divide(identity,C),D))))))))) = A,
inference(paramod,[status(thm)],[c_16,c_56]) ).
cnf(c_24,plain,
divide(identity,divide(identity,divide(divide(A,divide(divide(identity,B),C)),divide(identity,divide(divide(identity,B),C))))) = A,
inference(paramod,[status(thm)],[c_16,c_8]) ).
cnf(c_25,plain,
divide(identity,divide(identity,divide(divide(A,B),divide(identity,B)))) = A,
inference(paramod,[status(thm)],[c_24,c_21]) ).
cnf(c_26,plain,
divide(identity,divide(identity,divide(identity,divide(identity,A)))) = A,
inference(paramod,[status(thm)],[c_5,c_25]) ).
cnf(c_57,plain,
divide(identity,divide(identity,A)) = divide(divide(A,identity),identity),
inference(paramod,[status(thm)],[c_19,c_26]) ).
cnf(c_31,plain,
divide(divide(A,identity),identity) = divide(identity,divide(identity,A)),
inference(copy,[status(thm)],[c_57]) ).
cnf(c_58,plain,
divide(identity,divide(identity,A)) = divide(divide(A,B),divide(identity,B)),
inference(paramod,[status(thm)],[c_25,c_26]) ).
cnf(c_34,plain,
divide(divide(A,B),divide(identity,B)) = divide(identity,divide(identity,A)),
inference(copy,[status(thm)],[c_58]) ).
cnf(c_59,plain,
divide(divide(identity,divide(identity,divide(identity,A))),B) = divide(identity,divide(identity,divide(identity,divide(identity,divide(divide(identity,divide(A,identity)),B))))),
inference(paramod,[status(thm)],[c_31,c_16]) ).
cnf(c_60,plain,
divide(identity,divide(identity,divide(divide(identity,A),divide(identity,divide(divide(identity,identity),B))))) = divide(identity,divide(identity,divide(identity,divide(identity,divide(divide(identity,divide(A,identity)),B))))),
inference(paramod,[status(thm)],[c_16,c_59]) ).
cnf(c_61,plain,
divide(identity,divide(identity,divide(divide(identity,A),divide(identity,divide(identity,B))))) = divide(identity,divide(identity,divide(identity,divide(identity,divide(divide(identity,divide(A,identity)),B))))),
inference(paramod,[status(thm)],[c_5,c_60]) ).
cnf(c_62,plain,
divide(identity,divide(identity,divide(divide(identity,A),divide(identity,divide(identity,B))))) = divide(identity,divide(identity,divide(identity,divide(identity,divide(identity,divide(identity,divide(identity,divide(identity,divide(divide(identity,A),B))))))))),
inference(paramod,[status(thm)],[c_16,c_61]) ).
cnf(c_63,plain,
divide(identity,divide(identity,divide(divide(identity,A),divide(identity,divide(identity,B))))) = divide(identity,divide(identity,divide(identity,divide(identity,divide(divide(identity,A),B))))),
inference(paramod,[status(thm)],[c_26,c_62]) ).
cnf(c_38,plain,
divide(identity,divide(identity,divide(divide(identity,A),divide(identity,divide(identity,B))))) = divide(divide(identity,A),B),
inference(paramod,[status(thm)],[c_26,c_63]) ).
cnf(c_64,plain,
divide(divide(divide(identity,divide(identity,divide(identity,A))),B),divide(identity,B)) = divide(identity,A),
inference(paramod,[status(thm)],[c_26,c_34]) ).
cnf(c_65,plain,
divide(divide(identity,divide(identity,divide(divide(identity,A),divide(identity,divide(divide(identity,identity),B))))),divide(identity,B)) = divide(identity,A),
inference(paramod,[status(thm)],[c_16,c_64]) ).
cnf(c_66,plain,
divide(divide(identity,divide(identity,divide(divide(identity,A),divide(identity,divide(identity,B))))),divide(identity,B)) = divide(identity,A),
inference(paramod,[status(thm)],[c_5,c_65]) ).
cnf(c_67,plain,
divide(divide(divide(identity,A),B),divide(identity,B)) = divide(identity,A),
inference(paramod,[status(thm)],[c_38,c_66]) ).
cnf(c_41,plain,
divide(identity,divide(identity,divide(identity,A))) = divide(identity,A),
inference(paramod,[status(thm)],[c_34,c_67]) ).
cnf(c_51,plain,
divide(identity,divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_41,c_26]) ).
cnf(c_52,plain,
$false,
inference(resolve,[status(thm)],[c_51,c_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP458-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:55:02 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 3761483 was started by sandbox on n005,
% 0.08/0.35 % Fri Sep 25 14:55:02 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 0.08/0.37
% 0.08/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.37
% 0.08/0.37 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.08/0.37 % Length of proof is 22.
% 0.08/0.37 % Level of proof is 12.
% 0.08/0.37 % Maximum clause weight is 31.000.
% 0.08/0.37 % Given clauses 12.
% 0.08/0.37
% 0.08/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------