%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET903+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 : n013.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 5.31s 16.13s
% Output : Proof 5.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 12 unt; 0 def)
% Number of atoms : 74 ( 73 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 76 ( 30 ~; 22 |; 24 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 37 ( 3 sgn 21 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,conjecture,
! [A,B,C] :
~ ( C != empty_set
& B != empty_set
& B != C
& singleton(A) = set_union2(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_zfmisc_1) ).
fof(f8_neg,negated_conjecture,
~ ! [A,B,C] :
~ ( C != empty_set
& B != empty_set
& B != C
& singleton(A) = set_union2(B,C) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [A,B,C] :
( C != empty_set
& B != empty_set
& B != C
& singleton(A) = set_union2(B,C) ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
( sk4 != empty_set
& sk3 != empty_set
& sk3 != sk4
& singleton(sk2) = set_union2(sk3,sk4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f8_nnf]) ).
cnf(c15,plain,
singleton(sk2) = set_union2(sk3,sk4),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/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(p19,plain,
set_union2(sk3,sk4) = singleton(sk2),
inference(superposition,[status(thm)],[c15,c0]) ).
fof(f7,axiom,
! [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/sandbox2/benchmark/theBenchmark.p',t43_zfmisc_1) ).
fof(f7_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)],[f7]) ).
fof(f7_sk,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(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( X1 = singleton(X0)
| X1 = empty_set
| X1 = singleton(X0)
| singleton(X0) != set_union2(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p22,plain,
( X1 = empty_set
| X1 = singleton(X0)
| singleton(X0) != set_union2(X1,X2) ),
inference(factoring,[status(thm)],[c7]) ).
cnf(p25,plain,
( X2 = empty_set
| X2 = singleton(X0)
| singleton(X0) != set_union2(X1,X2) ),
inference(superposition,[status(thm)],[c0,p22]) ).
cnf(p52,plain,
( sk4 = empty_set
| sk4 = singleton(X0)
| singleton(X0) != singleton(sk2) ),
inference(superposition,[status(thm)],[p19,p25]) ).
cnf(p53,plain,
( sk4 = empty_set
| sk4 = singleton(sk2) ),
inference(equality_resolution,[status(thm)],[p52]) ).
cnf(p26,plain,
( sk3 = empty_set
| sk3 = singleton(X0)
| singleton(X0) != singleton(sk2) ),
inference(superposition,[status(thm)],[p19,p22]) ).
cnf(p28,plain,
( sk3 = empty_set
| sk3 = singleton(sk2) ),
inference(equality_resolution,[status(thm)],[p26]) ).
cnf(p63,plain,
( sk3 = empty_set
| sk3 = sk4
| sk4 = empty_set ),
inference(superposition,[status(thm)],[p53,p28]) ).
cnf(c18,plain,
sk4 != empty_set,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p71,plain,
( sk3 = empty_set
| sk3 = sk4 ),
inference(resolution,[status(thm)],[p63,c18]) ).
cnf(c16,plain,
sk3 != sk4,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p73,plain,
sk3 = empty_set,
inference(resolution,[status(thm)],[p71,c16]) ).
cnf(c17,plain,
sk3 != empty_set,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p75,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[p73,c17]) ).
cnf(p81,plain,
$false,
inference(equality_resolution,[status(thm)],[p75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET903+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/15.38 % Computer : n013.cluster.edu
% 0.10/15.38 % Model : x86_64 x86_64
% 0.10/15.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.38 % Memory : 8046.5625MB
% 0.10/15.38 % OS : Linux 6.8.0-71-generic
% 0.10/15.39 % CPULimit : 300
% 0.10/15.39 % WCLimit : 300
% 0.10/15.39 % DateTime : Thu Sep 24 12:20:53 UTC 2026
% 0.10/15.39 % CPUTime :
% 0.10/15.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.31/16.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.31/16.13 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------