%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU198+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 02:51:18 PM UTC 2026
% Result : Theorem 25.95s 4.22s
% Output : Proof 25.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 4 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 60 ( 22 ~; 21 |; 11 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 22 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_rng(relation_rng_restriction(B,C)))
<=> ( in(A,relation_rng(C))
& in(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_relat_1) ).
fof(f21_nnf,plain,
! [A,B,C] :
( ( ( ~ in(A,relation_rng(C))
| ~ in(A,B)
| in(A,relation_rng(relation_rng_restriction(B,C))) )
& ( ( in(A,relation_rng(C))
& in(A,B) )
| ~ in(A,relation_rng(relation_rng_restriction(B,C))) ) )
| ~ relation(C) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [C,A,B] :
( ( ( ~ in(A,relation_rng(C))
| ~ in(A,B)
| in(A,relation_rng(relation_rng_restriction(B,C))) )
& ( ( in(A,relation_rng(C))
& in(A,B) )
| ~ in(A,relation_rng(relation_rng_restriction(B,C))) ) )
| ~ relation(C) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c29,plain,
( in(X0,X1)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ relation(X2) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
fof(f22,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t116_relat_1) ).
fof(f22_neg,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),A) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f22_nnf,plain,
? [A,B] :
( ~ subset(relation_rng(relation_rng_restriction(A,B)),A)
& relation(B) ),
inference(nnf_transformation,[status(thm)],[f22_neg]) ).
fof(f22_sk,plain,
( ~ subset(relation_rng(relation_rng_restriction(sk8,sk9)),sk8)
& relation(sk9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9])],[f22_nnf]) ).
cnf(c32,plain,
relation(sk9),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p89,plain,
( in(X0,X1)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,sk9))) ),
inference(resolution,[status(thm)],[c29,c32]) ).
fof(f2,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f2_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)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk0(A,B),B)
& in(sk0(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c3,plain,
( in(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p108,plain,
( subset(relation_rng(relation_rng_restriction(X0,sk9)),X1)
| in(sk0(relation_rng(relation_rng_restriction(X0,sk9)),X1),X0) ),
inference(resolution,[status(thm)],[p89,c3]) ).
cnf(c4,plain,
( ~ in(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p112,plain,
( subset(relation_rng(relation_rng_restriction(X0,sk9)),X0)
| subset(relation_rng(relation_rng_restriction(X0,sk9)),X0) ),
inference(resolution,[status(thm)],[p108,c4]) ).
cnf(p136,plain,
subset(relation_rng(relation_rng_restriction(X0,sk9)),X0),
inference(factoring,[status(thm)],[p112]) ).
cnf(c33,plain,
~ subset(relation_rng(relation_rng_restriction(sk8,sk9)),sk8),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p137,plain,
$false,
inference(resolution,[status(thm)],[p136,c33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU198+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.40 % Computer : n011.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Thu Sep 24 13:09:12 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 25.95/4.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.95/4.22 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------