%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU251+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 : n015.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 02:51:30 PM UTC 2026
% Result : Theorem 70.65s 10.84s
% Output : Proof 70.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 5 unt; 0 def)
% Number of atoms : 144 ( 30 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 166 ( 64 ~; 68 |; 24 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 110 ( 7 sgn 42 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f6_nnf,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk1(A,B),B)
& in(sk1(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f6_nnf]) ).
cnf(c17,plain,
( in(sk1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
fof(f14,axiom,
! [A,B] :
( relation(A)
=> relation(relation_restriction(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f14_nnf,plain,
! [A,B] :
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B] :
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c26,plain,
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
fof(f31,conjecture,
! [A,B,C] :
( relation(C)
=> subset(fiber(relation_restriction(C,A),B),fiber(C,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_wellord1) ).
fof(f31_neg,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> subset(fiber(relation_restriction(C,A),B),fiber(C,B)) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f31_nnf,plain,
? [A,B,C] :
( ~ subset(fiber(relation_restriction(C,A),B),fiber(C,B))
& relation(C) ),
inference(nnf_transformation,[status(thm)],[f31_neg]) ).
fof(f31_sk,plain,
( ~ subset(fiber(relation_restriction(sk10,sk8),sk9),fiber(sk10,sk9))
& relation(sk10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9,sk10])],[f31_nnf]) ).
cnf(c50,plain,
relation(sk10),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p96,plain,
relation(relation_restriction(sk10,X0)),
inference(resolution,[status(thm)],[c26,c50]) ).
fof(f5,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = fiber(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(ordered_pair(D,B),A)
& D != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_wellord1) ).
fof(f5_nnf,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( in(ordered_pair(D,B),A)
& D != B
& ~ in(D,C) )
| ( ( ~ in(ordered_pair(D,B),A)
| D = B )
& in(D,C) ) )
| C = fiber(A,B) )
& ( ! [D] :
( ( ~ in(ordered_pair(D,B),A)
| D = B
| in(D,C) )
& ( ( in(ordered_pair(D,B),A)
& D != B )
| ~ in(D,C) ) )
| C != fiber(A,B) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,C,B,D] :
( ( ( ( in(ordered_pair(sk0(A,B,C),B),A)
& sk0(A,B,C) != B
& ~ in(sk0(A,B,C),C) )
| ( ( ~ in(ordered_pair(sk0(A,B,C),B),A)
| sk0(A,B,C) = B )
& in(sk0(A,B,C),C) )
| C = fiber(A,B) )
& ( ( ( ~ in(ordered_pair(D,B),A)
| D = B
| in(D,C) )
& ( ( in(ordered_pair(D,B),A)
& D != B )
| ~ in(D,C) ) )
| C != fiber(A,B) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f5_nnf]) ).
cnf(c8,plain,
( in(ordered_pair(X3,X1),X0)
| ~ in(X3,X2)
| X2 != fiber(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p102,plain,
( in(ordered_pair(X3,X2),relation_restriction(sk10,X1))
| ~ in(X3,X0)
| X0 != fiber(relation_restriction(sk10,X1),X2) ),
inference(resolution,[status(thm)],[p96,c8]) ).
cnf(p182,plain,
( in(ordered_pair(X0,X2),relation_restriction(sk10,X1))
| ~ in(X0,fiber(relation_restriction(sk10,X1),X2)) ),
inference(equality_resolution,[status(thm)],[p102]) ).
cnf(p200,plain,
( in(ordered_pair(sk1(fiber(relation_restriction(sk10,X0),X1),X2),X1),relation_restriction(sk10,X0))
| subset(fiber(relation_restriction(sk10,X0),X1),X2) ),
inference(resolution,[status(thm)],[c17,p182]) ).
fof(f29,axiom,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,cartesian_product2(B,B))
& in(A,C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
fof(f29_nnf,plain,
! [A,B,C] :
( ( ( ~ in(A,cartesian_product2(B,B))
| ~ in(A,C)
| in(A,relation_restriction(C,B)) )
& ( ( in(A,cartesian_product2(B,B))
& in(A,C) )
| ~ in(A,relation_restriction(C,B)) ) )
| ~ relation(C) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [C,A,B] :
( ( ( ~ in(A,cartesian_product2(B,B))
| ~ in(A,C)
| in(A,relation_restriction(C,B)) )
& ( ( in(A,cartesian_product2(B,B))
& in(A,C) )
| ~ in(A,relation_restriction(C,B)) ) )
| ~ relation(C) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c46,plain,
( in(X0,X2)
| ~ in(X0,relation_restriction(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p243,plain,
( in(X0,sk10)
| ~ in(X0,relation_restriction(sk10,X1)) ),
inference(resolution,[status(thm)],[c46,c50]) ).
cnf(p492,plain,
( in(ordered_pair(sk1(fiber(relation_restriction(sk10,X0),X1),X2),X1),sk10)
| subset(fiber(relation_restriction(sk10,X0),X1),X2) ),
inference(resolution,[status(thm)],[p200,p243]) ).
cnf(c9,plain,
( ~ in(ordered_pair(X3,X1),X0)
| X3 = X1
| in(X3,X2)
| X2 != fiber(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p91,plain,
( ~ in(ordered_pair(X2,X1),sk10)
| X2 = X1
| in(X2,X0)
| X0 != fiber(sk10,X1) ),
inference(resolution,[status(thm)],[c9,c50]) ).
cnf(p95,plain,
( ~ in(ordered_pair(X0,X1),sk10)
| X0 = X1
| in(X0,fiber(sk10,X1)) ),
inference(equality_resolution,[status(thm)],[p91]) ).
cnf(p501,plain,
( sk1(fiber(relation_restriction(sk10,X0),X1),X2) = X1
| in(sk1(fiber(relation_restriction(sk10,X0),X1),X2),fiber(sk10,X1))
| subset(fiber(relation_restriction(sk10,X0),X1),X2) ),
inference(resolution,[status(thm)],[p492,p95]) ).
cnf(c18,plain,
( ~ in(sk1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p3885,plain,
( subset(fiber(relation_restriction(sk10,X0),X1),fiber(sk10,X1))
| sk1(fiber(relation_restriction(sk10,X0),X1),fiber(sk10,X1)) = X1
| subset(fiber(relation_restriction(sk10,X0),X1),fiber(sk10,X1)) ),
inference(resolution,[status(thm)],[p501,c18]) ).
cnf(p9631,plain,
( sk1(fiber(relation_restriction(sk10,X0),X1),fiber(sk10,X1)) = X1
| subset(fiber(relation_restriction(sk10,X0),X1),fiber(sk10,X1)) ),
inference(factoring,[status(thm)],[p3885]) ).
cnf(c7,plain,
( X3 != X1
| ~ in(X3,X2)
| X2 != fiber(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p101,plain,
( X3 != X2
| ~ in(X3,X0)
| X0 != fiber(relation_restriction(sk10,X1),X2) ),
inference(resolution,[status(thm)],[p96,c7]) ).
cnf(p150,plain,
( X0 != X2
| ~ in(X0,fiber(relation_restriction(sk10,X1),X2)) ),
inference(equality_resolution,[status(thm)],[p101]) ).
cnf(p198,plain,
( sk1(fiber(relation_restriction(sk10,X0),X1),X2) != X1
| subset(fiber(relation_restriction(sk10,X0),X1),X2) ),
inference(resolution,[status(thm)],[c17,p150]) ).
cnf(p9660,plain,
( subset(fiber(relation_restriction(sk10,X0),X1),fiber(sk10,X1))
| subset(fiber(relation_restriction(sk10,X0),X1),fiber(sk10,X1)) ),
inference(resolution,[status(thm)],[p9631,p198]) ).
cnf(p9718,plain,
subset(fiber(relation_restriction(sk10,X0),X1),fiber(sk10,X1)),
inference(factoring,[status(thm)],[p9660]) ).
cnf(c51,plain,
~ subset(fiber(relation_restriction(sk10,sk8),sk9),fiber(sk10,sk9)),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p9719,plain,
$false,
inference(resolution,[status(thm)],[p9718,c51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU251+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n015.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 13:27:40 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 70.65/10.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 70.65/10.84 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------