%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU303+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 : Fri Sep 25 02:51:39 PM UTC 2026
% Result : Theorem 22.47s 3.39s
% Output : Proof 22.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 17 unt; 0 def)
% Number of atoms : 57 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 18 ~; 12 |; 9 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-4 aty)
% Number of variables : 18 ( 0 sgn 11 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( finite(A)
=> finite(relation_image(B,A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_finset_1) ).
fof(f6_nnf,plain,
! [A,B] :
( finite(relation_image(B,A))
| ~ finite(A)
| ~ function(B)
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [B,A] :
( finite(relation_image(B,A))
| ~ finite(A)
| ~ function(B)
| ~ relation(B) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c7,plain,
( finite(relation_image(X1,X0))
| ~ finite(X0)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi4,axiom,
ifeq(relation(X0),true,ifeq(function(X0),true,ifeq(finite(X1),true,finite(relation_image(X0,X1)),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
fof(f7,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( finite(relation_dom(A))
=> finite(relation_rng(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finset_1) ).
fof(f7_neg,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( finite(relation_dom(A))
=> finite(relation_rng(A)) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f7_nnf,plain,
? [A] :
( ~ finite(relation_rng(A))
& finite(relation_dom(A))
& function(A)
& relation(A) ),
inference(nnf_transformation,[status(thm)],[f7_neg]) ).
fof(f7_sk,plain,
( ~ finite(relation_rng(sk1))
& finite(relation_dom(sk1))
& function(sk1)
& relation(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f7_nnf]) ).
cnf(c8,plain,
relation(sk1),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi5,negated_conjecture,
relation(sk1) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(c9,plain,
function(sk1),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi6,negated_conjecture,
function(sk1) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(c10,plain,
finite(relation_dom(sk1)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,negated_conjecture,
finite(relation_dom(sk1)) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t6,plain,
finite(relation_image(sk1,relation_dom(sk1))) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi5,hi6,hi7]) ).
fof(f5,axiom,
! [A] :
( relation(A)
=> relation_image(A,relation_dom(A)) = relation_rng(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_relat_1) ).
fof(f5_nnf,plain,
! [A] :
( relation_image(A,relation_dom(A)) = relation_rng(A)
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] :
( relation_image(A,relation_dom(A)) = relation_rng(A)
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c6,plain,
( relation_image(X0,relation_dom(X0)) = relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi3,axiom,
ifeq(relation(X0),true,relation_image(X0,relation_dom(X0)),relation_rng(X0)) = relation_rng(X0),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t9,plain,
relation_image(sk1,relation_dom(sk1)) = relation_rng(sk1),
inference(hyper_resolution,[status(thm)],[hi3,hi5]) ).
cnf(t257,plain,
relation_image(sk1,relation_dom(sk1)) = relation_rng(sk1),
inference(orient,[status(thm)],[t9]) ).
cnf(t445,plain,
finite(relation_rng(sk1)) = true,
inference(step,[status(thm)],[t6,t257]) ).
cnf(t381,plain,
finite(relation_rng(sk1)) = true,
inference(orient,[status(thm)],[t445]) ).
cnf(c11,plain,
~ finite(relation_rng(sk1)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(goal_0,negated_conjecture,
finite(relation_rng(sk1)) != true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t381]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU303+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 13:36:43 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 22.47/3.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.47/3.39 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------