%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU243+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:51:28 PM UTC 2026
% Result : Theorem 4.75s 1.09s
% Output : Proof 4.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 3
% Syntax : Number of formulae : 59 ( 5 unt; 0 def)
% Number of atoms : 221 ( 44 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 246 ( 84 ~; 126 |; 28 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 64 ( 0 sgn 23 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_well_founded_in(A,B)
<=> ! [C] :
~ ( ! [D] :
~ ( disjoint(fiber(A,D),C)
& in(D,C) )
& C != empty_set
& subset(C,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_wellord1) ).
fof(f5_nnf,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ! [D] :
( ~ disjoint(fiber(A,D),C)
| ~ in(D,C) )
& C != empty_set
& subset(C,B) )
| is_well_founded_in(A,B) )
& ( ! [C] :
( ? [D] :
( disjoint(fiber(A,D),C)
& in(D,C) )
| C = empty_set
| ~ subset(C,B) )
| ~ is_well_founded_in(A,B) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C,D] :
( ( ( ( ( ~ disjoint(fiber(A,D),sk3(A,B))
| ~ in(D,sk3(A,B)) )
& sk3(A,B) != empty_set
& subset(sk3(A,B),B) )
| is_well_founded_in(A,B) )
& ( ( disjoint(fiber(A,sk2(A,B,C)),C)
& in(sk2(A,B,C),C) )
| C = empty_set
| ~ subset(C,B)
| ~ is_well_founded_in(A,B) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f5_nnf]) ).
cnf(c12,plain,
( disjoint(fiber(X0,sk2(X0,X1,X2)),X2)
| X2 = empty_set
| ~ subset(X2,X1)
| ~ is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f33,conjecture,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_wellord1) ).
fof(f33_neg,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> is_well_founded_in(A,relation_field(A)) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f33_nnf,plain,
? [A] :
( ( ( is_well_founded_in(A,relation_field(A))
& ~ well_founded_relation(A) )
| ( ~ is_well_founded_in(A,relation_field(A))
& well_founded_relation(A) ) )
& relation(A) ),
inference(nnf_transformation,[status(thm)],[f33_neg]) ).
fof(f33_sk,plain,
( ( ( is_well_founded_in(sk10,relation_field(sk10))
& ~ well_founded_relation(sk10) )
| ( ~ is_well_founded_in(sk10,relation_field(sk10))
& well_founded_relation(sk10) ) )
& relation(sk10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f33_nnf]) ).
cnf(c49,plain,
relation(sk10),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(p100,plain,
( disjoint(fiber(sk10,sk2(sk10,X0,X1)),X1)
| X1 = empty_set
| ~ subset(X1,X0)
| ~ is_well_founded_in(sk10,X0) ),
inference(resolution,[status(thm)],[c12,c49]) ).
cnf(c51,plain,
( is_well_founded_in(sk10,relation_field(sk10))
| well_founded_relation(sk10) ),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(p112,plain,
( well_founded_relation(sk10)
| disjoint(fiber(sk10,sk2(sk10,relation_field(sk10),X0)),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sk10)) ),
inference(resolution,[status(thm)],[p100,c51]) ).
fof(f4,axiom,
! [A] :
( relation(A)
=> ( well_founded_relation(A)
<=> ! [B] :
~ ( ! [C] :
~ ( disjoint(fiber(A,C),B)
& in(C,B) )
& B != empty_set
& subset(B,relation_field(A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_wellord1) ).
fof(f4_nnf,plain,
! [A] :
( ( ( ? [B] :
( ! [C] :
( ~ disjoint(fiber(A,C),B)
| ~ in(C,B) )
& B != empty_set
& subset(B,relation_field(A)) )
| well_founded_relation(A) )
& ( ! [B] :
( ? [C] :
( disjoint(fiber(A,C),B)
& in(C,B) )
| B = empty_set
| ~ subset(B,relation_field(A)) )
| ~ well_founded_relation(A) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] :
( ( ( ( ( ~ disjoint(fiber(A,C),sk1(A))
| ~ in(C,sk1(A)) )
& sk1(A) != empty_set
& subset(sk1(A),relation_field(A)) )
| well_founded_relation(A) )
& ( ( disjoint(fiber(A,sk0(A,B)),B)
& in(sk0(A,B),B) )
| B = empty_set
| ~ subset(B,relation_field(A))
| ~ well_founded_relation(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f4_nnf]) ).
cnf(c8,plain,
( subset(sk1(X0),relation_field(X0))
| well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p79,plain,
( subset(sk1(sk10),relation_field(sk10))
| well_founded_relation(sk10) ),
inference(resolution,[status(thm)],[c8,c49]) ).
cnf(p114,plain,
( well_founded_relation(sk10)
| well_founded_relation(sk10)
| disjoint(fiber(sk10,sk2(sk10,relation_field(sk10),sk1(sk10))),sk1(sk10))
| sk1(sk10) = empty_set ),
inference(resolution,[status(thm)],[p112,p79]) ).
cnf(p125,plain,
( well_founded_relation(sk10)
| disjoint(fiber(sk10,sk2(sk10,relation_field(sk10),sk1(sk10))),sk1(sk10))
| sk1(sk10) = empty_set ),
inference(factoring,[status(thm)],[p114]) ).
cnf(c11,plain,
( in(sk2(X0,X1,X2),X2)
| X2 = empty_set
| ~ subset(X2,X1)
| ~ is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p91,plain,
( in(sk2(sk10,X0,X1),X1)
| X1 = empty_set
| ~ subset(X1,X0)
| ~ is_well_founded_in(sk10,X0) ),
inference(resolution,[status(thm)],[c11,c49]) ).
cnf(p95,plain,
( well_founded_relation(sk10)
| in(sk2(sk10,relation_field(sk10),X0),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sk10)) ),
inference(resolution,[status(thm)],[p91,c51]) ).
cnf(p97,plain,
( well_founded_relation(sk10)
| well_founded_relation(sk10)
| in(sk2(sk10,relation_field(sk10),sk1(sk10)),sk1(sk10))
| sk1(sk10) = empty_set ),
inference(resolution,[status(thm)],[p95,p79]) ).
cnf(p104,plain,
( well_founded_relation(sk10)
| in(sk2(sk10,relation_field(sk10),sk1(sk10)),sk1(sk10))
| sk1(sk10) = empty_set ),
inference(factoring,[status(thm)],[p97]) ).
cnf(c10,plain,
( ~ disjoint(fiber(X0,X2),sk1(X0))
| ~ in(X2,sk1(X0))
| well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p87,plain,
( ~ disjoint(fiber(sk10,X0),sk1(sk10))
| ~ in(X0,sk1(sk10))
| well_founded_relation(sk10) ),
inference(resolution,[status(thm)],[c10,c49]) ).
cnf(p106,plain,
( ~ disjoint(fiber(sk10,sk2(sk10,relation_field(sk10),sk1(sk10))),sk1(sk10))
| well_founded_relation(sk10)
| well_founded_relation(sk10)
| sk1(sk10) = empty_set ),
inference(resolution,[status(thm)],[p104,p87]) ).
cnf(p120,plain,
( ~ disjoint(fiber(sk10,sk2(sk10,relation_field(sk10),sk1(sk10))),sk1(sk10))
| well_founded_relation(sk10)
| sk1(sk10) = empty_set ),
inference(factoring,[status(thm)],[p106]) ).
cnf(p127,plain,
( well_founded_relation(sk10)
| sk1(sk10) = empty_set
| well_founded_relation(sk10)
| sk1(sk10) = empty_set ),
inference(resolution,[status(thm)],[p125,p120]) ).
cnf(p136,plain,
( well_founded_relation(sk10)
| well_founded_relation(sk10)
| sk1(sk10) = empty_set ),
inference(factoring,[status(thm)],[p127]) ).
cnf(p138,plain,
( well_founded_relation(sk10)
| sk1(sk10) = empty_set ),
inference(factoring,[status(thm)],[p136]) ).
cnf(c9,plain,
( sk1(X0) != empty_set
| well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p83,plain,
( sk1(sk10) != empty_set
| well_founded_relation(sk10) ),
inference(resolution,[status(thm)],[c9,c49]) ).
cnf(p140,plain,
( well_founded_relation(sk10)
| well_founded_relation(sk10) ),
inference(resolution,[status(thm)],[p138,p83]) ).
cnf(p141,plain,
well_founded_relation(sk10),
inference(factoring,[status(thm)],[p140]) ).
cnf(c6,plain,
( in(sk0(X0,X1),X1)
| X1 = empty_set
| ~ subset(X1,relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p63,plain,
( in(sk0(sk10,X0),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sk10))
| ~ well_founded_relation(sk10) ),
inference(resolution,[status(thm)],[c6,c49]) ).
cnf(p143,plain,
( in(sk0(sk10,X0),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sk10)) ),
inference(resolution,[status(thm)],[p141,p63]) ).
cnf(c13,plain,
( subset(sk3(X0,X1),X1)
| is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p108,plain,
( subset(sk3(sk10,X0),X0)
| is_well_founded_in(sk10,X0) ),
inference(resolution,[status(thm)],[c13,c49]) ).
cnf(p146,plain,
( is_well_founded_in(sk10,relation_field(sk10))
| in(sk0(sk10,sk3(sk10,relation_field(sk10))),sk3(sk10,relation_field(sk10)))
| sk3(sk10,relation_field(sk10)) = empty_set ),
inference(resolution,[status(thm)],[p143,p108]) ).
cnf(c15,plain,
( ~ disjoint(fiber(X0,X3),sk3(X0,X1))
| ~ in(X3,sk3(X0,X1))
| is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p121,plain,
( ~ disjoint(fiber(sk10,X1),sk3(sk10,X0))
| ~ in(X1,sk3(sk10,X0))
| is_well_founded_in(sk10,X0) ),
inference(resolution,[status(thm)],[c15,c49]) ).
cnf(p162,plain,
( ~ disjoint(fiber(sk10,sk0(sk10,sk3(sk10,relation_field(sk10)))),sk3(sk10,relation_field(sk10)))
| is_well_founded_in(sk10,relation_field(sk10))
| is_well_founded_in(sk10,relation_field(sk10))
| sk3(sk10,relation_field(sk10)) = empty_set ),
inference(resolution,[status(thm)],[p146,p121]) ).
cnf(p175,plain,
( ~ disjoint(fiber(sk10,sk0(sk10,sk3(sk10,relation_field(sk10)))),sk3(sk10,relation_field(sk10)))
| is_well_founded_in(sk10,relation_field(sk10))
| sk3(sk10,relation_field(sk10)) = empty_set ),
inference(factoring,[status(thm)],[p162]) ).
cnf(c7,plain,
( disjoint(fiber(X0,sk0(X0,X1)),X1)
| X1 = empty_set
| ~ subset(X1,relation_field(X0))
| ~ well_founded_relation(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p67,plain,
( disjoint(fiber(sk10,sk0(sk10,X0)),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sk10))
| ~ well_founded_relation(sk10) ),
inference(resolution,[status(thm)],[c7,c49]) ).
cnf(p144,plain,
( disjoint(fiber(sk10,sk0(sk10,X0)),X0)
| X0 = empty_set
| ~ subset(X0,relation_field(sk10)) ),
inference(resolution,[status(thm)],[p141,p67]) ).
cnf(p156,plain,
( is_well_founded_in(sk10,relation_field(sk10))
| disjoint(fiber(sk10,sk0(sk10,sk3(sk10,relation_field(sk10)))),sk3(sk10,relation_field(sk10)))
| sk3(sk10,relation_field(sk10)) = empty_set ),
inference(resolution,[status(thm)],[p144,p108]) ).
cnf(p176,plain,
( is_well_founded_in(sk10,relation_field(sk10))
| sk3(sk10,relation_field(sk10)) = empty_set
| is_well_founded_in(sk10,relation_field(sk10))
| sk3(sk10,relation_field(sk10)) = empty_set ),
inference(resolution,[status(thm)],[p175,p156]) ).
cnf(p177,plain,
( is_well_founded_in(sk10,relation_field(sk10))
| is_well_founded_in(sk10,relation_field(sk10))
| sk3(sk10,relation_field(sk10)) = empty_set ),
inference(factoring,[status(thm)],[p176]) ).
cnf(p179,plain,
( is_well_founded_in(sk10,relation_field(sk10))
| sk3(sk10,relation_field(sk10)) = empty_set ),
inference(factoring,[status(thm)],[p177]) ).
cnf(c14,plain,
( sk3(X0,X1) != empty_set
| is_well_founded_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p115,plain,
( sk3(sk10,X0) != empty_set
| is_well_founded_in(sk10,X0) ),
inference(resolution,[status(thm)],[c14,c49]) ).
cnf(p181,plain,
( is_well_founded_in(sk10,relation_field(sk10))
| is_well_founded_in(sk10,relation_field(sk10)) ),
inference(resolution,[status(thm)],[p179,p115]) ).
cnf(p182,plain,
is_well_founded_in(sk10,relation_field(sk10)),
inference(factoring,[status(thm)],[p181]) ).
cnf(c52,plain,
( ~ well_founded_relation(sk10)
| ~ is_well_founded_in(sk10,relation_field(sk10)) ),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(p183,plain,
~ well_founded_relation(sk10),
inference(resolution,[status(thm)],[p182,c52]) ).
cnf(p186,plain,
$false,
inference(resolution,[status(thm)],[p183,p141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU243+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 13:23:08 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.75/1.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.75/1.09 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------