%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU096+1 : 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 : n006.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 08:45:00 AM UTC 2026
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 9 unt; 0 def)
% Number of atoms : 55 ( 5 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 50 ( 16 ~; 12 |; 14 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t147_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( subset(A,relation_rng(B))
=> relation_image(B,relation_inverse_image(B,A)) = A ) ),
file('theBenchmark.p',t147_funct_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(t27_finset_1,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( finite(relation_inverse_image(B,A))
& subset(A,relation_rng(B)) )
=> finite(A) ) ),
file('theBenchmark.p',t27_finset_1) ).
fof(t27_finset_1_neg,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( finite(relation_inverse_image(B,A))
& subset(A,relation_rng(B)) )
=> finite(A) ) ),
inference(assume_negation,[status(cth)],[t27_finset_1]) ).
cnf(c_104,plain,
( relation_image(A,relation_inverse_image(A,B)) = B
| ~ subset(B,relation_rng(A))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t147_funct_1]) ).
cnf(c_105,plain,
( finite(relation_image(A,B))
| ~ finite(B)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t17_finset_1]) ).
fof(nnf_58,plain,
? [A,B] :
( ~ finite(A)
& finite(relation_inverse_image(B,A))
& subset(A,relation_rng(B))
& function(B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[t27_finset_1_neg]) ).
fof(sk_t27_finset_1_neg,plain,
( ~ finite(sK1)
& finite(relation_inverse_image(sK0,sK1))
& subset(sK1,relation_rng(sK0))
& function(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_58]) ).
cnf(c_106,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t27_finset_1_neg]) ).
cnf(c_178,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t27_finset_1_neg]) ).
cnf(c_179,negated_conjecture,
subset(sK1,relation_rng(sK0)),
inference(split_conjunct,[status(thm)],[sk_t27_finset_1_neg]) ).
cnf(c_180,negated_conjecture,
finite(relation_inverse_image(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_t27_finset_1_neg]) ).
cnf(c_181,negated_conjecture,
~ finite(sK1),
inference(split_conjunct,[status(thm)],[sk_t27_finset_1_neg]) ).
cnf(c_228,negated_conjecture,
( finite(relation_image(sK0,A))
| ~ finite(A)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_106,c_105]) ).
cnf(c_229,negated_conjecture,
( finite(relation_image(sK0,A))
| ~ finite(A) ),
inference(resolve,[status(thm)],[c_178,c_228]) ).
cnf(c_230,negated_conjecture,
( relation_image(sK0,relation_inverse_image(sK0,A)) = A
| ~ subset(A,relation_rng(sK0))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_106,c_104]) ).
cnf(c_231,negated_conjecture,
( relation_image(sK0,relation_inverse_image(sK0,A)) = A
| ~ subset(A,relation_rng(sK0)) ),
inference(resolve,[status(thm)],[c_178,c_230]) ).
cnf(c_393,plain,
finite(relation_image(sK0,relation_inverse_image(sK0,sK1))),
inference(resolve,[status(thm)],[c_229,c_180]) ).
cnf(c_395,plain,
relation_image(sK0,relation_inverse_image(sK0,sK1)) = sK1,
inference(resolve,[status(thm)],[c_231,c_179]) ).
cnf(c_398,plain,
finite(sK1),
inference(paramod,[status(thm)],[c_395,c_393]) ).
cnf(c_397,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_181,c_398]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU096+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.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 : Sat Sep 26 08:35:41 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 833165 was started by sandbox on n006,
% 0.08/0.36 % Sat Sep 26 08:35:41 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 0.12/0.40
% 0.12/0.40 % SZS status Theorem for theBenchmark
% 0.12/0.40
% 0.12/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.12/0.40 % Length of proof is 17.
% 0.12/0.40 % Level of proof is 5.
% 0.12/0.40 % Maximum clause weight is 26.000.
% 0.12/0.40 % Given clauses 94.
% 0.12/0.40
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------