%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET873+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 : n018.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 02:44:12 PM UTC 2026
% Result : Theorem 44.93s 11.16s
% Output : Proof 44.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 14 unt; 0 def)
% Number of atoms : 62 ( 33 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 56 ( 23 ~; 18 |; 10 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 2 sgn 30 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,conjecture,
! [A,B] :
( set_union2(singleton(A),singleton(B)) = singleton(A)
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_zfmisc_1) ).
fof(f10_neg,negated_conjecture,
~ ! [A,B] :
( set_union2(singleton(A),singleton(B)) = singleton(A)
=> A = B ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f10_nnf,plain,
? [A,B] :
( A != B
& set_union2(singleton(A),singleton(B)) = singleton(A) ),
inference(nnf_transformation,[status(thm)],[f10_neg]) ).
fof(f10_sk,plain,
( sk3 != sk4
& set_union2(singleton(sk3),singleton(sk4)) = singleton(sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f10_nnf]) ).
cnf(c15,plain,
set_union2(singleton(sk3),singleton(sk4)) = singleton(sk3),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f1,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/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]) ).
fof(f6,axiom,
! [A,B] :
( subset(set_union2(singleton(A),B),B)
=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l21_zfmisc_1) ).
fof(f6_nnf,plain,
! [A,B] :
( in(A,B)
| ~ subset(set_union2(singleton(A),B),B) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B] :
( in(A,B)
| ~ subset(set_union2(singleton(A),B),B) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c11,plain,
( in(X0,X1)
| ~ subset(set_union2(singleton(X0),X1),X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p27,plain,
( in(X1,X0)
| ~ subset(set_union2(X0,singleton(X1)),X0) ),
inference(superposition,[status(thm)],[c1,c11]) ).
cnf(p35,plain,
( in(sk4,singleton(sk3))
| ~ subset(singleton(sk3),singleton(sk3)) ),
inference(superposition,[status(thm)],[c15,p27]) ).
fof(f9,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f9_nnf,plain,
! [A,B] : subset(A,A),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A] : subset(A,A),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c14,plain,
subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p36,plain,
in(sk4,singleton(sk3)),
inference(resolution,[status(thm)],[p35,c14]) ).
fof(f2,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/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(c2,plain,
( X2 = X0
| ~ in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p18,plain,
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p38,plain,
sk4 = sk3,
inference(resolution,[status(thm)],[p36,p18]) ).
cnf(c16,plain,
sk3 != sk4,
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p39,plain,
sk3 != sk3,
inference(demodulation,[status(thm)],[p38,c16]) ).
cnf(p40,plain,
$false,
inference(equality_resolution,[status(thm)],[p39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET873+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/5.37 % Computer : n018.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Thu Sep 24 12:20:39 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 44.93/11.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.93/11.16 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
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