%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU112+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 02:50:57 PM UTC 2026
% Result : Theorem 26.89s 4.35s
% Output : Proof 26.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 18 unt; 0 def)
% Number of atoms : 40 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 14 ~; 10 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 4 sgn 31 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f39,axiom,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(f39_nnf,plain,
! [A,B,C] :
( subset(set_union2(A,C),B)
| ~ subset(C,B)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [A,B,C] :
( subset(set_union2(A,C),B)
| ~ subset(C,B)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c67,plain,
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
fof(f29,axiom,
! [A,B] :
( subset(A,B)
=> subset(finite_subsets(A),finite_subsets(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_finsub_1) ).
fof(f29_nnf,plain,
! [A,B] :
( subset(finite_subsets(A),finite_subsets(B))
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [A,B] :
( subset(finite_subsets(A),finite_subsets(B))
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c56,plain,
( subset(finite_subsets(X0),finite_subsets(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
fof(f37,axiom,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f37_nnf,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c65,plain,
subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(p106,plain,
subset(finite_subsets(X0),finite_subsets(set_union2(X0,X1))),
inference(resolution,[status(thm)],[c56,c65]) ).
cnf(p189,plain,
( subset(set_union2(finite_subsets(X1),X0),finite_subsets(set_union2(X1,X2)))
| ~ subset(X0,finite_subsets(set_union2(X1,X2))) ),
inference(resolution,[status(thm)],[c67,p106]) ).
fof(f6,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/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(c7,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p81,plain,
subset(X0,set_union2(X1,X0)),
inference(superposition,[status(thm)],[c7,c65]) ).
cnf(p108,plain,
subset(finite_subsets(X0),finite_subsets(set_union2(X1,X0))),
inference(resolution,[status(thm)],[c56,p81]) ).
cnf(p1439,plain,
subset(set_union2(finite_subsets(X0),finite_subsets(X1)),finite_subsets(set_union2(X0,X1))),
inference(resolution,[status(thm)],[p189,p108]) ).
fof(f30,conjecture,
! [A,B] : subset(set_union2(finite_subsets(A),finite_subsets(B)),finite_subsets(set_union2(A,B))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_finsub_1) ).
fof(f30_neg,negated_conjecture,
~ ! [A,B] : subset(set_union2(finite_subsets(A),finite_subsets(B)),finite_subsets(set_union2(A,B))),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f30_nnf,plain,
? [A,B] : ~ subset(set_union2(finite_subsets(A),finite_subsets(B)),finite_subsets(set_union2(A,B))),
inference(nnf_transformation,[status(thm)],[f30_neg]) ).
fof(f30_sk,plain,
~ subset(set_union2(finite_subsets(sk10),finite_subsets(sk11)),finite_subsets(set_union2(sk10,sk11))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10,sk11])],[f30_nnf]) ).
cnf(c57,plain,
~ subset(set_union2(finite_subsets(sk10),finite_subsets(sk11)),finite_subsets(set_union2(sk10,sk11))),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(p1989,plain,
$false,
inference(resolution,[status(thm)],[p1439,c57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU112+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 12:42:00 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 26.89/4.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.89/4.35 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------