%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP550-1 : 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 : n002.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 0.43s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 29 unt; 0 def)
% Number of atoms : 29 ( 28 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : divide(divide(identity,VAR_0),divide(divide(divide(VAR_1,VAR_0),VAR_2),VAR_1)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = 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(inverse,axiom,
! [VAR_0] : inverse(VAR_0) = divide(identity,VAR_0),
file('theBenchmark.p',inverse) ).
cnf(c_3,plain,
inverse(A) = divide(identity,A),
inference(clausify,[status(thm)],[inverse]) ).
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(multiply(inverse(b2),b2),a2) != a2,
file('theBenchmark.p',prove_these_axioms_2) ).
cnf(c_6,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(clausify,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_33,plain,
multiply(multiply(divide(identity,b2),b2),a2) != a2,
inference(paramod,[status(thm)],[c_3,c_6]) ).
cnf(c_34,plain,
multiply(divide(divide(identity,b2),divide(identity,b2)),a2) != a2,
inference(paramod,[status(thm)],[c_2,c_33]) ).
cnf(c_35,plain,
multiply(identity,a2) != a2,
inference(paramod,[status(thm)],[c_5,c_34]) ).
cnf(c_7,plain,
divide(identity,divide(identity,a2)) != a2,
inference(paramod,[status(thm)],[c_2,c_35]) ).
cnf(c_36,plain,
divide(divide(identity,A),divide(B,identity)) = 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,B),divide(C,identity)),
inference(copy,[status(thm)],[c_36]) ).
cnf(c_11,plain,
divide(divide(identity,A),divide(divide(identity,A),divide(B,identity))) = B,
inference(paramod,[status(thm)],[c_9,c_1]) ).
cnf(c_37,plain,
divide(identity,divide(divide(identity,identity),divide(A,identity))) = A,
inference(paramod,[status(thm)],[c_5,c_11]) ).
cnf(c_16,plain,
divide(identity,divide(identity,divide(A,identity))) = A,
inference(paramod,[status(thm)],[c_5,c_37]) ).
cnf(c_38,plain,
divide(divide(A,B),identity) = divide(divide(identity,divide(identity,divide(A,identity))),divide(B,identity)),
inference(paramod,[status(thm)],[c_16,c_9]) ).
cnf(c_19,plain,
divide(divide(A,B),identity) = divide(A,divide(B,identity)),
inference(paramod,[status(thm)],[c_16,c_38]) ).
cnf(c_39,plain,
divide(A,divide(divide(identity,divide(identity,divide(A,identity))),divide(B,identity))) = B,
inference(paramod,[status(thm)],[c_16,c_11]) ).
cnf(c_21,plain,
divide(A,divide(A,divide(B,identity))) = B,
inference(paramod,[status(thm)],[c_16,c_39]) ).
cnf(c_40,plain,
divide(divide(A,identity),identity) = A,
inference(paramod,[status(thm)],[c_5,c_21]) ).
cnf(c_41,plain,
divide(A,divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_19,c_40]) ).
cnf(c_24,plain,
divide(A,identity) = A,
inference(paramod,[status(thm)],[c_5,c_41]) ).
cnf(c_31,plain,
divide(A,divide(A,B)) = B,
inference(paramod,[status(thm)],[c_24,c_21]) ).
cnf(c_32,plain,
$false,
inference(resolve,[status(thm)],[c_31,c_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP550-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.40 % Computer : n002.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Fri Sep 25 15:02:05 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.41 % Process 3583439 was started by sandbox on n002,
% 0.15/0.41 % Fri Sep 25 15:02:05 2026
% 0.15/0.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.42
% 0.15/0.42 % From the command line: assign(max_seconds, 300).
% 0.15/0.43
% 0.15/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.43
% 0.15/0.43 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.15/0.43 % Length of proof is 15.
% 0.15/0.43 % Level of proof is 7.
% 0.15/0.43 % Maximum clause weight is 15.000.
% 0.15/0.43 % Given clauses 9.
% 0.15/0.43
% 0.15/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------