%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU180+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 : n005.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 02:51:15 PM UTC 2026
% Result : Theorem 33.73s 5.44s
% Output : Proof 33.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 14 unt; 0 def)
% Number of atoms : 158 ( 32 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 185 ( 71 ~; 67 |; 34 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-3 aty)
% Number of variables : 98 ( 8 sgn 51 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f5_nnf,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(D,C),A)
& ~ in(C,B) )
| ( ! [D] : ~ in(ordered_pair(D,C),A)
& in(C,B) ) )
| B = relation_rng(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C,D] :
( ( ( ( in(ordered_pair(sk6(A,B),sk5(A,B)),A)
& ~ in(sk5(A,B),B) )
| ( ~ in(ordered_pair(D,sk5(A,B)),A)
& in(sk5(A,B),B) )
| B = relation_rng(A) )
& ( ( ( ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ( in(ordered_pair(sk4(A,B,C),C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6])],[f5_nnf]) ).
cnf(c19,plain,
( ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p168,plain,
( ~ in(ordered_pair(X2,X1),X0)
| in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[status(thm)],[c19]) ).
fof(f32,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_field(C))
& in(A,relation_field(C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f32_neg,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_field(C))
& in(A,relation_field(C)) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f32_nnf,plain,
? [A,B,C] :
( ( ~ in(B,relation_field(C))
| ~ in(A,relation_field(C)) )
& in(ordered_pair(A,B),C)
& relation(C) ),
inference(nnf_transformation,[status(thm)],[f32_neg]) ).
fof(f32_sk,plain,
( ( ~ in(sk12,relation_field(sk13))
| ~ in(sk11,relation_field(sk13)) )
& in(ordered_pair(sk11,sk12),sk13)
& relation(sk13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11,sk12,sk13])],[f32_nnf]) ).
cnf(c51,plain,
relation(sk13),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p631,plain,
( ~ in(ordered_pair(X1,X0),sk13)
| in(X0,relation_rng(sk13)) ),
inference(resolution,[status(thm)],[p168,c51]) ).
cnf(c52,plain,
in(ordered_pair(sk11,sk12),sk13),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p642,plain,
in(sk12,relation_rng(sk13)),
inference(resolution,[status(thm)],[p631,c52]) ).
fof(f7,axiom,
! [A] :
( relation(A)
=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
fof(f7_nnf,plain,
! [A] :
( relation_field(A) = set_union2(relation_dom(A),relation_rng(A))
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A] :
( relation_field(A) = set_union2(relation_dom(A),relation_rng(A))
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c25,plain,
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p205,plain,
relation_field(sk13) = set_union2(relation_dom(sk13),relation_rng(sk13)),
inference(resolution,[status(thm)],[c25,c51]) ).
fof(f2,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f2_nnf,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p207,plain,
set_union2(relation_dom(sk13),relation_rng(sk13)) = relation_field(sk13),
inference(superposition,[status(thm)],[p205,c2]) ).
fof(f3,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f3_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( in(D,B)
| in(D,A) )
& ~ in(D,C) )
| ( ~ in(D,B)
& ~ in(D,A)
& in(D,C) ) )
| C = set_union2(A,B) )
& ( ! [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [C,A,B,D] :
( ( ( ( in(sk0(A,B,C),B)
| in(sk0(A,B,C),A) )
& ~ in(sk0(A,B,C),C) )
| ( ~ in(sk0(A,B,C),B)
& ~ in(sk0(A,B,C),A)
& in(sk0(A,B,C),C) )
| C = set_union2(A,B) )
& ( ( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f3_nnf]) ).
cnf(c5,plain,
( ~ in(X3,X1)
| in(X3,X2)
| X2 != set_union2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p210,plain,
( ~ in(X1,relation_rng(sk13))
| in(X1,X0)
| X0 != relation_field(sk13) ),
inference(superposition,[status(thm)],[p207,c5]) ).
cnf(p272,plain,
( ~ in(X0,relation_rng(sk13))
| in(X0,relation_field(sk13)) ),
inference(equality_resolution,[status(thm)],[p210]) ).
cnf(p650,plain,
in(sk12,relation_field(sk13)),
inference(resolution,[status(thm)],[p642,p272]) ).
fof(f4,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(f4_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)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C,D] :
( ( ( ( in(ordered_pair(sk2(A,B),sk3(A,B)),A)
& ~ in(sk2(A,B),B) )
| ( ~ in(ordered_pair(sk2(A,B),D),A)
& in(sk2(A,B),B) )
| B = relation_dom(A) )
& ( ( ( ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( in(ordered_pair(C,sk1(A,B,C)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3])],[f4_nnf]) ).
cnf(c13,plain,
( ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p124,plain,
( ~ in(ordered_pair(X1,X2),sk13)
| in(X1,X0)
| X0 != relation_dom(sk13) ),
inference(resolution,[status(thm)],[c13,c51]) ).
cnf(p353,plain,
( ~ in(ordered_pair(X0,X1),sk13)
| in(X0,relation_dom(sk13)) ),
inference(equality_resolution,[status(thm)],[p124]) ).
cnf(p354,plain,
in(sk11,relation_dom(sk13)),
inference(resolution,[status(thm)],[p353,c52]) ).
cnf(c4,plain,
( ~ in(X3,X0)
| in(X3,X2)
| X2 != set_union2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p209,plain,
( ~ in(X1,relation_dom(sk13))
| in(X1,X0)
| X0 != relation_field(sk13) ),
inference(superposition,[status(thm)],[p207,c4]) ).
cnf(p265,plain,
( ~ in(X0,relation_dom(sk13))
| in(X0,relation_field(sk13)) ),
inference(equality_resolution,[status(thm)],[p209]) ).
cnf(p360,plain,
in(sk11,relation_field(sk13)),
inference(resolution,[status(thm)],[p354,p265]) ).
cnf(c53,plain,
( ~ in(sk12,relation_field(sk13))
| ~ in(sk11,relation_field(sk13)) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p363,plain,
~ in(sk12,relation_field(sk13)),
inference(resolution,[status(thm)],[p360,c53]) ).
cnf(p655,plain,
$false,
inference(resolution,[status(thm)],[p650,p363]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU180+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.42 % Computer : n005.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Thu Sep 24 13:04:33 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 33.73/5.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.73/5.44 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------