%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU212+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 02:51:21 PM UTC 2026
% Result : Theorem 25.54s 13.70s
% Output : Proof 25.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 8 unt; 0 def)
% Number of atoms : 142 ( 40 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 173 ( 66 ~; 65 |; 30 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 58 ( 3 sgn 27 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f5_nnf,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
& ~ in(C,B) )
| ( ! [D] : ~ in(ordered_pair(C,D),A)
& in(C,B) ) )
| B = relation_dom(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C,D] :
( ( ( ( in(ordered_pair(sk1(A,B),sk2(A,B)),A)
& ~ in(sk1(A,B),B) )
| ( ~ in(ordered_pair(sk1(A,B),D),A)
& in(sk1(A,B),B) )
| B = relation_dom(A) )
& ( ( ( ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( in(ordered_pair(C,sk0(A,B,C)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f5_nnf]) ).
cnf(c9,plain,
( ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f34,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
fof(f34_neg,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f34_nnf,plain,
? [A,B,C] :
( ( ( B = apply(C,A)
& in(A,relation_dom(C))
& ~ in(ordered_pair(A,B),C) )
| ( ( B != apply(C,A)
| ~ in(A,relation_dom(C)) )
& in(ordered_pair(A,B),C) ) )
& function(C)
& relation(C) ),
inference(nnf_transformation,[status(thm)],[f34_neg]) ).
fof(f34_sk,plain,
( ( ( sk13 = apply(sk14,sk12)
& in(sk12,relation_dom(sk14))
& ~ in(ordered_pair(sk12,sk13),sk14) )
| ( ( sk13 != apply(sk14,sk12)
| ~ in(sk12,relation_dom(sk14)) )
& in(ordered_pair(sk12,sk13),sk14) ) )
& function(sk14)
& relation(sk14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12,sk13,sk14])],[f34_nnf]) ).
cnf(c53,plain,
relation(sk14),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p115,plain,
( ~ in(ordered_pair(X1,X2),sk14)
| in(X1,X0)
| X0 != relation_dom(sk14) ),
inference(resolution,[status(thm)],[c9,c53]) ).
cnf(p120,plain,
( ~ in(ordered_pair(X0,X1),sk14)
| in(X0,relation_dom(sk14)) ),
inference(equality_resolution,[status(thm)],[p115]) ).
cnf(c56,plain,
( in(sk12,relation_dom(sk14))
| in(ordered_pair(sk12,sk13),sk14) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p122,plain,
( in(sk12,relation_dom(sk14))
| in(sk12,relation_dom(sk14)) ),
inference(resolution,[status(thm)],[p120,c56]) ).
cnf(p123,plain,
in(sk12,relation_dom(sk14)),
inference(factoring,[status(thm)],[p122]) ).
fof(f4,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( ( ~ in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> C = empty_set ) )
& ( in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f4_nnf,plain,
! [A] :
( ! [B,C] :
( ( ( ( C != empty_set
| C = apply(A,B) )
& ( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ( ( ( ~ in(ordered_pair(B,C),A)
| C = apply(A,B) )
& ( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] :
( ( ( ( ( C != empty_set
| C = apply(A,B) )
& ( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ( ( ( ~ in(ordered_pair(B,C),A)
| C = apply(A,B) )
& ( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c5,plain,
( ~ in(ordered_pair(X1,X2),X0)
| X2 = apply(X0,X1)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p75,plain,
( ~ in(ordered_pair(X0,X1),sk14)
| X1 = apply(sk14,X0)
| ~ in(X0,relation_dom(sk14))
| ~ function(sk14) ),
inference(resolution,[status(thm)],[c5,c53]) ).
cnf(c54,plain,
function(sk14),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p78,plain,
( ~ in(ordered_pair(X0,X1),sk14)
| X1 = apply(sk14,X0)
| ~ in(X0,relation_dom(sk14)) ),
inference(resolution,[status(thm)],[p75,c54]) ).
cnf(p128,plain,
( ~ in(ordered_pair(sk12,X0),sk14)
| X0 = apply(sk14,sk12) ),
inference(resolution,[status(thm)],[p123,p78]) ).
cnf(c57,plain,
( sk13 = apply(sk14,sk12)
| in(ordered_pair(sk12,sk13),sk14) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p136,plain,
( sk13 = apply(sk14,sk12)
| sk13 = apply(sk14,sk12) ),
inference(resolution,[status(thm)],[p128,c57]) ).
cnf(p137,plain,
sk13 = apply(sk14,sk12),
inference(factoring,[status(thm)],[p136]) ).
cnf(c58,plain,
( ~ in(ordered_pair(sk12,sk13),sk14)
| sk13 != apply(sk14,sk12)
| ~ in(sk12,relation_dom(sk14)) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p125,plain,
( ~ in(ordered_pair(sk12,sk13),sk14)
| sk13 != apply(sk14,sk12) ),
inference(resolution,[status(thm)],[p123,c58]) ).
cnf(p140,plain,
~ in(ordered_pair(sk12,sk13),sk14),
inference(resolution,[status(thm)],[p137,p125]) ).
cnf(c4,plain,
( in(ordered_pair(X1,X2),X0)
| X2 != apply(X0,X1)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p68,plain,
( in(ordered_pair(X0,X1),sk14)
| X1 != apply(sk14,X0)
| ~ in(X0,relation_dom(sk14))
| ~ function(sk14) ),
inference(resolution,[status(thm)],[c4,c53]) ).
cnf(p71,plain,
( in(ordered_pair(X0,apply(sk14,X0)),sk14)
| ~ in(X0,relation_dom(sk14))
| ~ function(sk14) ),
inference(equality_resolution,[status(thm)],[p68]) ).
cnf(p73,plain,
( in(ordered_pair(X0,apply(sk14,X0)),sk14)
| ~ in(X0,relation_dom(sk14)) ),
inference(resolution,[status(thm)],[p71,c54]) ).
cnf(p126,plain,
in(ordered_pair(sk12,apply(sk14,sk12)),sk14),
inference(resolution,[status(thm)],[p123,p73]) ).
cnf(p138,plain,
in(ordered_pair(sk12,sk13),sk14),
inference(superposition,[status(thm)],[p137,p126]) ).
cnf(p148,plain,
$false,
inference(resolution,[status(thm)],[p140,p138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU212+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/10.39 % Computer : n017.cluster.edu
% 0.09/10.39 % Model : x86_64 x86_64
% 0.09/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.39 % Memory : 8046.5625MB
% 0.09/10.39 % OS : Linux 6.8.0-71-generic
% 0.09/10.39 % CPULimit : 300
% 0.09/10.39 % WCLimit : 300
% 0.09/10.39 % DateTime : Thu Sep 24 13:07:41 UTC 2026
% 0.09/10.39 % CPUTime :
% 0.09/10.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 25.54/13.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.54/13.70 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------