%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET902+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 : n008.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 02:44:15 PM UTC 2026
% Result : Theorem 0.14s 5.79s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 22 unt; 0 def)
% Number of atoms : 88 ( 74 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 89 ( 41 ~; 25 |; 22 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 2 sgn 24 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,conjecture,
! [A,B,C] :
~ ( ~ ( C = empty_set
& B = singleton(A) )
& ~ ( C = singleton(A)
& B = empty_set )
& ~ ( C = singleton(A)
& B = singleton(A) )
& singleton(A) = set_union2(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_zfmisc_1) ).
fof(f10_neg,negated_conjecture,
~ ! [A,B,C] :
~ ( ~ ( C = empty_set
& B = singleton(A) )
& ~ ( C = singleton(A)
& B = empty_set )
& ~ ( C = singleton(A)
& B = singleton(A) )
& singleton(A) = set_union2(B,C) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f10_nnf,plain,
? [A,B,C] :
( ( C != empty_set
| B != singleton(A) )
& ( C != singleton(A)
| B != empty_set )
& ( C != singleton(A)
| B != singleton(A) )
& singleton(A) = set_union2(B,C) ),
inference(nnf_transformation,[status(thm)],[f10_neg]) ).
fof(f10_sk,plain,
( ( sk4 != empty_set
| sk3 != singleton(sk2) )
& ( sk4 != singleton(sk2)
| sk3 != empty_set )
& ( sk4 != singleton(sk2)
| sk3 != singleton(sk2) )
& singleton(sk2) = set_union2(sk3,sk4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f10_nnf]) ).
cnf(c13,plain,
( sk4 != singleton(sk2)
| sk3 != singleton(sk2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f6,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f6_nnf,plain,
! [A,B] :
( ( ( A != singleton(B)
& A != empty_set )
| subset(A,singleton(B)) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B] :
( ( ( A != singleton(B)
& A != empty_set )
| subset(A,singleton(B)) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( X0 = singleton(X1)
| X0 = empty_set
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(c12,plain,
singleton(sk2) = set_union2(sk3,sk4),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f0_nnf,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p18,plain,
set_union2(sk3,sk4) = singleton(sk2),
inference(superposition,[status(thm)],[c12,c0]) ).
fof(f11,axiom,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f11_nnf,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c16,plain,
subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p19,plain,
subset(sk3,singleton(sk2)),
inference(superposition,[status(thm)],[p18,c16]) ).
cnf(p25,plain,
( sk3 = singleton(sk2)
| sk3 = empty_set ),
inference(resolution,[status(thm)],[c6,p19]) ).
cnf(p44,plain,
( sk3 = empty_set
| sk4 != singleton(sk2) ),
inference(resolution,[status(thm)],[c13,p25]) ).
cnf(p17,plain,
subset(X0,set_union2(X1,X0)),
inference(superposition,[status(thm)],[c0,c16]) ).
cnf(p20,plain,
subset(sk4,singleton(sk2)),
inference(superposition,[status(thm)],[p18,p17]) ).
cnf(p26,plain,
( sk4 = singleton(sk2)
| sk4 = empty_set ),
inference(resolution,[status(thm)],[c6,p20]) ).
cnf(p52,plain,
( sk4 = empty_set
| sk3 = empty_set ),
inference(resolution,[status(thm)],[p44,p26]) ).
cnf(c15,plain,
( sk4 != empty_set
| sk3 != singleton(sk2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p33,plain,
( sk4 != empty_set
| sk3 = empty_set ),
inference(resolution,[status(thm)],[p25,c15]) ).
cnf(p55,plain,
( sk3 = empty_set
| sk3 = empty_set ),
inference(resolution,[status(thm)],[p52,p33]) ).
cnf(p56,plain,
sk3 = empty_set,
inference(factoring,[status(thm)],[p55]) ).
cnf(c14,plain,
( sk4 != singleton(sk2)
| sk3 != empty_set ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p58,plain,
( sk4 != singleton(sk2)
| empty_set != empty_set ),
inference(demodulation,[status(thm)],[p56,c14]) ).
cnf(p62,plain,
sk4 != singleton(sk2),
inference(equality_resolution,[status(thm)],[p58]) ).
cnf(p63,plain,
sk4 = empty_set,
inference(resolution,[status(thm)],[p62,p26]) ).
cnf(p60,plain,
set_union2(empty_set,sk4) = singleton(sk2),
inference(demodulation,[status(thm)],[p56,p18]) ).
cnf(p65,plain,
set_union2(empty_set,empty_set) = singleton(sk2),
inference(demodulation,[status(thm)],[p63,p60]) ).
cnf(p67,plain,
singleton(sk2) = empty_set,
inference(superposition,[status(thm)],[p65,c0]) ).
cnf(p66,plain,
empty_set != singleton(sk2),
inference(demodulation,[status(thm)],[p63,p62]) ).
cnf(p69,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[p67,p66]) ).
cnf(p71,plain,
$false,
inference(equality_resolution,[status(thm)],[p69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET902+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.36 % Computer : n008.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Thu Sep 24 12:21:48 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/5.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.79 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------