%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET908+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 02:44:16 PM UTC 2026
% Result : Theorem 25.96s 3.75s
% Output : Proof 25.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 16 unt; 0 def)
% Number of atoms : 102 ( 44 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 112 ( 44 ~; 41 |; 22 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 64 ( 4 sgn 37 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f4_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( in(D,B)
| in(D,A) )
& ~ in(D,C) )
| ( ~ in(D,B)
& ~ in(D,A)
& in(D,C) ) )
| C = set_union2(A,B) )
& ( ! [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [C,A,B,D] :
( ( ( ( in(sk2(A,B,C),B)
| in(sk2(A,B,C),A) )
& ~ in(sk2(A,B,C),C) )
| ( ~ in(sk2(A,B,C),B)
& ~ in(sk2(A,B,C),A)
& in(sk2(A,B,C),C) )
| C = set_union2(A,B) )
& ( ( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f4_nnf]) ).
cnf(c11,plain,
( ~ in(X3,X0)
| in(X3,X2)
| X2 != set_union2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f11,conjecture,
! [A,B] : set_union2(singleton(A),B) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_zfmisc_1) ).
fof(f11_neg,negated_conjecture,
~ ! [A,B] : set_union2(singleton(A),B) != empty_set,
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
? [A,B] : set_union2(singleton(A),B) = empty_set,
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
set_union2(singleton(sk5),sk6) = empty_set,
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5,sk6])],[f11_nnf]) ).
cnf(c25,plain,
set_union2(singleton(sk5),sk6) = empty_set,
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
fof(f1,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f1_nnf,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p28,plain,
empty_set = set_union2(sk6,singleton(sk5)),
inference(superposition,[status(thm)],[c25,c1]) ).
cnf(p82,plain,
( ~ in(X0,sk6)
| in(X0,empty_set) ),
inference(resolution,[status(thm)],[c11,p28]) ).
fof(f3,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f3_nnf,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( ( in(sk1(A),A)
| A = empty_set )
& ( ~ in(B,A)
| A != empty_set ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f3_nnf]) ).
cnf(c9,plain,
( in(sk1(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p86,plain,
( sk6 = empty_set
| in(sk1(sk6),empty_set) ),
inference(resolution,[status(thm)],[p82,c9]) ).
cnf(c8,plain,
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p30,plain,
~ in(X0,empty_set),
inference(equality_resolution,[status(thm)],[c8]) ).
cnf(p89,plain,
sk6 = empty_set,
inference(resolution,[status(thm)],[p86,p30]) ).
cnf(p92,plain,
empty_set = set_union2(empty_set,singleton(sk5)),
inference(demodulation,[status(thm)],[p89,p28]) ).
cnf(c12,plain,
( ~ in(X3,X1)
| in(X3,X2)
| X2 != set_union2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p99,plain,
( ~ in(X0,singleton(sk5))
| in(X0,empty_set) ),
inference(resolution,[status(thm)],[p92,c12]) ).
fof(f2,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f2_nnf,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
& ~ in(C,B) )
| ( C != A
& in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,A,C] :
( ( ( sk0(A,B) = A
& ~ in(sk0(A,B),B) )
| ( sk0(A,B) != A
& in(sk0(A,B),B) )
| B = singleton(A) )
& ( ( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c3,plain,
( X2 != X0
| in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p33,plain,
( X0 != X1
| in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c3]) ).
cnf(p39,plain,
in(X0,singleton(X0)),
inference(equality_resolution,[status(thm)],[p33]) ).
cnf(p102,plain,
in(sk5,empty_set),
inference(resolution,[status(thm)],[p99,p39]) ).
cnf(p105,plain,
$false,
inference(resolution,[status(thm)],[p102,p30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET908+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n015.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 12:24:57 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 25.96/3.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.96/3.75 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------