%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU230+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 02:51:25 PM UTC 2026
% Result : Theorem 25.81s 4.23s
% Output : Proof 25.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 22 unt; 0 def)
% Number of atoms : 34 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 17 ( 9 ~; 5 |; 2 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 36 ( 2 sgn 23 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f116,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f116_nnf,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(nnf_transformation,[status(thm)],[f116]) ).
fof(f116_sk,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(skolemisation,[status(esa)],[f116_nnf]) ).
cnf(c337,plain,
( in(X0,X1)
| ~ subset(singleton(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f116_sk]) ).
fof(f17,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f17_nnf,plain,
! [A] : succ(A) = set_union2(A,singleton(A)),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [A] : succ(A) = set_union2(A,singleton(A)),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c91,plain,
succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
fof(f6,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f6_nnf,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c8,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p890,plain,
set_union2(X0,singleton(X0)) = succ(X0),
inference(superposition,[status(thm)],[c91,c8]) ).
fof(f240,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f240_nnf,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(nnf_transformation,[status(thm)],[f240]) ).
fof(f240_sk,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(skolemisation,[status(esa)],[f240_nnf]) ).
cnf(c546,plain,
subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[status(esa)],[f240_sk]) ).
cnf(p882,plain,
subset(X0,set_union2(X1,X0)),
inference(superposition,[status(thm)],[c8,c546]) ).
cnf(p947,plain,
subset(singleton(X0),succ(X0)),
inference(superposition,[status(thm)],[p890,p882]) ).
cnf(p1039,plain,
in(X0,succ(X0)),
inference(resolution,[status(thm)],[c337,p947]) ).
fof(f142,conjecture,
! [A] : in(A,succ(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f142_neg,negated_conjecture,
~ ! [A] : in(A,succ(A)),
inference(negated_conjecture,[status(cth)],[f142]) ).
fof(f142_nnf,plain,
? [A] : ~ in(A,succ(A)),
inference(nnf_transformation,[status(thm)],[f142_neg]) ).
fof(f142_sk,plain,
~ in(sk74,succ(sk74)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk74])],[f142_nnf]) ).
cnf(c386,plain,
~ in(sk74,succ(sk74)),
inference(cnf_transformation,[status(esa)],[f142_sk]) ).
cnf(p1042,plain,
$false,
inference(resolution,[status(thm)],[p1039,c386]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU230+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 13:16:52 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 25.81/4.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.81/4.23 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------