%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU177+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 02:51:14 PM UTC 2026
% Result : Theorem 27.22s 4.37s
% Output : Proof 27.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 6 unt; 0 def)
% Number of atoms : 94 ( 14 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 115 ( 44 ~; 39 |; 22 &)
% ( 4 <=>; 6 =>; 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 : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 59 ( 6 sgn 30 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f20,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f20_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)],[f20]) ).
fof(f20_sk,plain,
! [A,B,C,D] :
( ( ( ( in(ordered_pair(sk24(A,B),sk23(A,B)),A)
& ~ in(sk23(A,B),B) )
| ( ~ in(ordered_pair(D,sk23(A,B)),A)
& in(sk23(A,B),B) )
| B = relation_rng(A) )
& ( ( ( ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ( in(ordered_pair(sk22(A,B,C),C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk22,sk23,sk24])],[f20_nnf]) ).
cnf(c105,plain,
( ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
fof(f93,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_rng(C))
& in(A,relation_dom(C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f93_neg,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_rng(C))
& in(A,relation_dom(C)) ) ) ),
inference(negated_conjecture,[status(cth)],[f93]) ).
fof(f93_nnf,plain,
? [A,B,C] :
( ( ~ in(B,relation_rng(C))
| ~ in(A,relation_dom(C)) )
& in(ordered_pair(A,B),C)
& relation(C) ),
inference(nnf_transformation,[status(thm)],[f93_neg]) ).
fof(f93_sk,plain,
( ( ~ in(sk35,relation_rng(sk36))
| ~ in(sk34,relation_dom(sk36)) )
& in(ordered_pair(sk34,sk35),sk36)
& relation(sk36) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk34,sk35,sk36])],[f93_nnf]) ).
cnf(c207,plain,
relation(sk36),
inference(cnf_transformation,[status(esa)],[f93_sk]) ).
cnf(p2091,plain,
( ~ in(ordered_pair(X2,X1),sk36)
| in(X1,X0)
| X0 != relation_rng(sk36) ),
inference(resolution,[status(thm)],[c105,c207]) ).
cnf(p2093,plain,
( ~ in(ordered_pair(X1,X0),sk36)
| in(X0,relation_rng(sk36)) ),
inference(equality_resolution,[status(thm)],[p2091]) ).
cnf(c208,plain,
in(ordered_pair(sk34,sk35),sk36),
inference(cnf_transformation,[status(esa)],[f93_sk]) ).
cnf(p2098,plain,
in(sk35,relation_rng(sk36)),
inference(resolution,[status(thm)],[p2093,c208]) ).
fof(f16,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f16_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)],[f16]) ).
fof(f16_sk,plain,
! [A,B,C,D] :
( ( ( ( in(ordered_pair(sk16(A,B),sk17(A,B)),A)
& ~ in(sk16(A,B),B) )
| ( ~ in(ordered_pair(sk16(A,B),D),A)
& in(sk16(A,B),B) )
| B = relation_dom(A) )
& ( ( ( ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( in(ordered_pair(C,sk15(A,B,C)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk15,sk16,sk17])],[f16_nnf]) ).
cnf(c80,plain,
( ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p1415,plain,
( ~ in(ordered_pair(X1,X2),sk36)
| in(X1,X0)
| X0 != relation_dom(sk36) ),
inference(resolution,[status(thm)],[c80,c207]) ).
cnf(p1417,plain,
( ~ in(ordered_pair(X0,X1),sk36)
| in(X0,relation_dom(sk36)) ),
inference(equality_resolution,[status(thm)],[p1415]) ).
cnf(p1422,plain,
in(sk34,relation_dom(sk36)),
inference(resolution,[status(thm)],[p1417,c208]) ).
cnf(c209,plain,
( ~ in(sk35,relation_rng(sk36))
| ~ in(sk34,relation_dom(sk36)) ),
inference(cnf_transformation,[status(esa)],[f93_sk]) ).
cnf(p1425,plain,
~ in(sk35,relation_rng(sk36)),
inference(resolution,[status(thm)],[p1422,c209]) ).
cnf(p2123,plain,
$false,
inference(resolution,[status(thm)],[p2098,p1425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU177+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 13:07:09 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 27.22/4.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.22/4.37 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------