%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU187+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 : n016.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 02:51:16 PM UTC 2026
% Result : Theorem 0.14s 5.89s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 9 unt; 0 def)
% Number of atoms : 115 ( 36 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 125 ( 48 ~; 49 |; 22 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-3 aty)
% Number of variables : 52 ( 1 sgn 30 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,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(f4_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)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C,D] :
( ( ( ( in(ordered_pair(sk5(A,B),sk4(A,B)),A)
& ~ in(sk4(A,B),B) )
| ( ~ in(ordered_pair(D,sk4(A,B)),A)
& in(sk4(A,B),B) )
| B = relation_rng(A) )
& ( ( ( ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ( in(ordered_pair(sk3(A,B,C),C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4,sk5])],[f4_nnf]) ).
cnf(c12,plain,
( in(ordered_pair(sk5(X0,X1),sk4(X0,X1)),X0)
| in(sk4(X0,X1),X1)
| X1 = relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f18,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f18_nnf,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c29,plain,
relation(empty_set),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p106,plain,
( in(ordered_pair(sk5(empty_set,X0),sk4(empty_set,X0)),empty_set)
| in(sk4(empty_set,X0),X0)
| X0 = relation_rng(empty_set) ),
inference(resolution,[status(thm)],[c12,c29]) ).
fof(f30,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f30_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c46,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(p291,plain,
( ~ empty(empty_set)
| in(sk4(empty_set,X0),X0)
| X0 = relation_rng(empty_set) ),
inference(resolution,[status(thm)],[p106,c46]) ).
fof(f14,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f14_nnf,plain,
empty(empty_set),
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c24,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(p313,plain,
( in(sk4(empty_set,X0),X0)
| X0 = relation_rng(empty_set) ),
inference(resolution,[status(thm)],[p291,c24]) ).
cnf(p315,plain,
( ~ empty(X0)
| X0 = relation_rng(empty_set) ),
inference(resolution,[status(thm)],[p313,c46]) ).
cnf(p343,plain,
empty_set = relation_rng(empty_set),
inference(resolution,[status(thm)],[p315,c24]) ).
fof(f3,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(f3_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)],[f3]) ).
fof(f3_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])],[f3_nnf]) ).
cnf(c6,plain,
( in(ordered_pair(sk1(X0,X1),sk2(X0,X1)),X0)
| in(sk1(X0,X1),X1)
| X1 = relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p63,plain,
( in(ordered_pair(sk1(empty_set,X0),sk2(empty_set,X0)),empty_set)
| in(sk1(empty_set,X0),X0)
| X0 = relation_dom(empty_set) ),
inference(resolution,[status(thm)],[c6,c29]) ).
cnf(p214,plain,
( ~ empty(empty_set)
| in(sk1(empty_set,X0),X0)
| X0 = relation_dom(empty_set) ),
inference(resolution,[status(thm)],[p63,c46]) ).
cnf(p218,plain,
( in(sk1(empty_set,X0),X0)
| X0 = relation_dom(empty_set) ),
inference(resolution,[status(thm)],[p214,c24]) ).
cnf(p220,plain,
( ~ empty(X0)
| X0 = relation_dom(empty_set) ),
inference(resolution,[status(thm)],[p218,c46]) ).
cnf(p223,plain,
empty_set = relation_dom(empty_set),
inference(resolution,[status(thm)],[p220,c24]) ).
fof(f28,conjecture,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
fof(f28_neg,negated_conjecture,
~ ( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f28_nnf,plain,
( relation_rng(empty_set) != empty_set
| relation_dom(empty_set) != empty_set ),
inference(nnf_transformation,[status(thm)],[f28_neg]) ).
fof(f28_sk,plain,
( relation_rng(empty_set) != empty_set
| relation_dom(empty_set) != empty_set ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c44,plain,
( relation_rng(empty_set) != empty_set
| relation_dom(empty_set) != empty_set ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p224,plain,
( relation_rng(empty_set) != empty_set
| empty_set != empty_set ),
inference(superposition,[status(thm)],[p223,c44]) ).
cnf(p234,plain,
relation_rng(empty_set) != empty_set,
inference(equality_resolution,[status(thm)],[p224]) ).
cnf(p346,plain,
empty_set != empty_set,
inference(superposition,[status(thm)],[p343,p234]) ).
cnf(p350,plain,
$false,
inference(equality_resolution,[status(thm)],[p346]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU187+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/5.37 % Computer : n016.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 13:11:18 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/5.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/5.89 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------