%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT019-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 06:56:00 AM UTC 2026
% Result : Unsatisfiable 0.18s 5.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 9 unt; 0 def)
% Number of atoms : 13 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 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 : 5 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(codomain_composition,axiom,
! [VAR_0] : compose(VAR_0,codomain(VAR_0)) = VAR_0,
file('theBenchmark.p',codomain_composition) ).
cnf(c_4,plain,
compose(A,codomain(A)) = A,
inference(clausify,[status(thm)],[codomain_composition]) ).
fof(equality_to_c1_and_c2_1,axiom,
! [VAR_0] :
( c1 = VAR_0
| c2 != VAR_0 ),
file('theBenchmark.p',equality_to_c1_and_c2_1) ).
cnf(c_9,plain,
( c1 = A
| c2 != A ),
inference(clausify,[status(thm)],[equality_to_c1_and_c2_1]) ).
fof(prove_c1_equals_c2,axiom,
c2 != c1,
file('theBenchmark.p',prove_c1_equals_c2) ).
cnf(c_11,plain,
c2 != c1,
inference(clausify,[status(thm)],[prove_c1_equals_c2]) ).
cnf(c_26,plain,
A = compose(A,codomain(A)),
inference(copy,[status(thm)],[c_4]) ).
cnf(c_27,plain,
c1 = compose(c2,codomain(c2)),
inference(resolve,[status(thm)],[c_9,c_26]) ).
cnf(c_28,plain,
c1 = c2,
inference(paramod,[status(thm)],[c_4,c_27]) ).
cnf(c_24,plain,
c2 = c1,
inference(copy,[status(thm)],[c_28]) ).
cnf(c_25,plain,
$false,
inference(resolve,[status(thm)],[c_24,c_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT019-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/5.44 % Computer : n010.cluster.edu
% 0.18/5.44 % Model : x86_64 x86_64
% 0.18/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.44 % Memory : 8046.5625MB
% 0.18/5.44 % OS : Linux 6.8.0-71-generic
% 0.18/5.44 % CPULimit : 300
% 0.18/5.44 % WCLimit : 300
% 0.18/5.45 % DateTime : Sat Sep 26 22:50:53 UTC 2026
% 0.18/5.45 % CPUTime :
% 0.18/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.45 % Process 221201 was started by sandbox on n010,
% 0.18/5.45 % Sat Sep 26 22:50:53 2026
% 0.18/5.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/5.46
% 0.18/5.46 % From the command line: assign(max_seconds, 300).
% 0.18/5.47
% 0.18/5.47 % SZS status Unsatisfiable for theBenchmark
% 0.18/5.47
% 0.18/5.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/5.47 % Length of proof is 5.
% 0.18/5.47 % Level of proof is 2.
% 0.18/5.47 % Maximum clause weight is 6.000.
% 0.18/5.47 % Given clauses 8.
% 0.18/5.47
% 0.18/5.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------