%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU303+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 08:45:45 AM UTC 2026
% Result : Theorem 0.08s 0.41s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 8 unt; 0 def)
% Number of atoms : 41 ( 3 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 35 ( 12 ~; 7 |; 9 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn 5 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t146_relat_1,axiom,
! [A] :
( relation(A)
=> relation_image(A,relation_dom(A)) = relation_rng(A) ),
file('theBenchmark.p',t146_relat_1) ).
fof(t17_finset_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( finite(A)
=> finite(relation_image(B,A)) ) ),
file('theBenchmark.p',t17_finset_1) ).
fof(t26_finset_1,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( finite(relation_dom(A))
=> finite(relation_rng(A)) ) ),
file('theBenchmark.p',t26_finset_1) ).
fof(t26_finset_1_neg,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( finite(relation_dom(A))
=> finite(relation_rng(A)) ) ),
inference(assume_negation,[status(cth)],[t26_finset_1]) ).
cnf(c_110,plain,
( finite(relation_image(A,B))
| ~ finite(B)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t17_finset_1]) ).
fof(nnf_61,plain,
? [A] :
( ~ finite(relation_rng(A))
& finite(relation_dom(A))
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[t26_finset_1_neg]) ).
fof(sk_t26_finset_1_neg,plain,
( ~ finite(relation_rng(sK0))
& finite(relation_dom(sK0))
& function(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_61]) ).
cnf(c_111,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t26_finset_1_neg]) ).
cnf(c_182,plain,
( relation_rng(A) = relation_image(A,relation_dom(A))
| ~ relation(A) ),
inference(clausify,[status(thm)],[t146_relat_1]) ).
cnf(c_190,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t26_finset_1_neg]) ).
cnf(c_191,negated_conjecture,
finite(relation_dom(sK0)),
inference(split_conjunct,[status(thm)],[sk_t26_finset_1_neg]) ).
cnf(c_192,negated_conjecture,
~ finite(relation_rng(sK0)),
inference(split_conjunct,[status(thm)],[sk_t26_finset_1_neg]) ).
cnf(c_239,negated_conjecture,
( finite(relation_image(sK0,A))
| ~ finite(A)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_111,c_110]) ).
cnf(c_240,negated_conjecture,
( finite(relation_image(sK0,A))
| ~ finite(A) ),
inference(resolve,[status(thm)],[c_190,c_239]) ).
cnf(c_341,plain,
relation_rng(sK0) = relation_image(sK0,relation_dom(sK0)),
inference(resolve,[status(thm)],[c_190,c_182]) ).
cnf(c_342,negated_conjecture,
~ finite(relation_image(sK0,relation_dom(sK0))),
inference(paramod,[status(thm)],[c_341,c_192]) ).
cnf(c_371,negated_conjecture,
finite(relation_image(sK0,relation_dom(sK0))),
inference(resolve,[status(thm)],[c_240,c_191]) ).
cnf(c_370,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_342,c_371]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU303+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n018.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 09:11:22 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 69558 was started by sandbox on n018,
% 0.08/0.36 % Sat Sep 26 09:11:22 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 0.08/0.41
% 0.08/0.41 % SZS status Theorem for theBenchmark
% 0.08/0.41
% 0.08/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.08/0.41 % Length of proof is 14.
% 0.08/0.41 % Level of proof is 4.
% 0.08/0.41 % Maximum clause weight is 9.000.
% 0.08/0.41 % Given clauses 95.
% 0.08/0.41
% 0.08/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------