%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET600+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 02:43:33 PM UTC 2026
% Result : Theorem 12.46s 2.17s
% Output : Proof 12.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 7
% Syntax : Number of formulae : 83 ( 20 unt; 0 def)
% Number of atoms : 220 ( 70 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 220 ( 83 ~; 97 |; 31 &)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 102 ( 15 sgn 46 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f0_nnf,plain,
! [B,C,D] :
( ( ( ~ member(D,C)
& ~ member(D,B) )
| member(D,union(B,C)) )
& ( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [D,B,C] :
( ( ( ~ member(D,C)
& ~ member(D,B) )
| member(D,union(B,C)) )
& ( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p26,plain,
( member(X0,X1)
| ~ member(X0,union(X1,X1)) ),
inference(factoring,[status(thm)],[c0]) ).
fof(f6,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
fof(f6_nnf,plain,
! [B] :
( ( ? [C] : member(C,B)
| empty(B) )
& ( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [B,C] :
( ( member(sk1(B),B)
| empty(B) )
& ( ~ member(C,B)
| ~ empty(B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f6_nnf]) ).
cnf(c13,plain,
( member(sk1(X0),X0)
| empty(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p65,plain,
( empty(union(X0,X0))
| member(sk1(union(X0,X0)),X0) ),
inference(resolution,[status(thm)],[p26,c13]) ).
fof(f1,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f1_nnf,plain,
! [B] : ~ member(B,empty_set),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B] : ~ member(B,empty_set),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c3,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p228,plain,
empty(union(empty_set,empty_set)),
inference(resolution,[status(thm)],[p65,c3]) ).
cnf(c12,plain,
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p240,plain,
~ member(X0,union(empty_set,empty_set)),
inference(resolution,[status(thm)],[p228,c12]) ).
fof(f7,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f7_nnf,plain,
! [B,C] :
( ( ? [D] :
( ( member(D,C)
& ~ member(D,B) )
| ( ~ member(D,C)
& member(D,B) ) )
| B = C )
& ( ! [D] :
( ( ~ member(D,C)
| member(D,B) )
& ( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [B,C,D] :
( ( ( member(sk2(B,C),C)
& ~ member(sk2(B,C),B) )
| ( ~ member(sk2(B,C),C)
& member(sk2(B,C),B) )
| B = C )
& ( ( ( ~ member(D,C)
| member(D,B) )
& ( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f7_nnf]) ).
cnf(c17,plain,
( member(sk2(X0,X1),X1)
| member(sk2(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p84,plain,
( member(sk2(X0,empty_set),X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[c17,c3]) ).
cnf(p249,plain,
union(empty_set,empty_set) = empty_set,
inference(resolution,[status(thm)],[p240,p84]) ).
cnf(c1,plain,
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p36,plain,
( member(sk1(X0),union(X0,X1))
| empty(X0) ),
inference(resolution,[status(thm)],[c13,c1]) ).
fof(f4,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f4_nnf,plain,
! [B,C] :
( ( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [B,C,D] :
( ( ( ~ member(sk0(B,C),C)
& member(sk0(B,C),B) )
| subset(B,C) )
& ( member(D,C)
| ~ member(D,B)
| ~ subset(B,C) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f4_nnf]) ).
cnf(c8,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f2,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f2_nnf,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c4,plain,
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f8,conjecture,
! [B,C] :
( union(B,C) = empty_set
<=> ( C = empty_set
& B = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th59) ).
fof(f8_neg,negated_conjecture,
~ ! [B,C] :
( union(B,C) = empty_set
<=> ( C = empty_set
& B = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [B,C] :
( ( C = empty_set
& B = empty_set
& union(B,C) != empty_set )
| ( ( C != empty_set
| B != empty_set )
& union(B,C) = empty_set ) ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
( ( sk4 = empty_set
& sk3 = empty_set
& union(sk3,sk4) != empty_set )
| ( ( sk4 != empty_set
| sk3 != empty_set )
& union(sk3,sk4) = empty_set ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f8_nnf]) ).
cnf(c21,plain,
( sk3 = empty_set
| union(sk3,sk4) = empty_set ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p27,plain,
( sk3 = empty_set
| subset(union(sk3,sk4),empty_set) ),
inference(resolution,[status(thm)],[c4,c21]) ).
cnf(p38,plain,
( sk3 = empty_set
| member(X0,empty_set)
| ~ member(X0,union(sk3,sk4)) ),
inference(resolution,[status(thm)],[c8,p27]) ).
cnf(p40,plain,
( empty(union(sk3,sk4))
| sk3 = empty_set
| member(sk1(union(sk3,sk4)),empty_set) ),
inference(resolution,[status(thm)],[p38,c13]) ).
cnf(p44,plain,
( empty(union(sk3,sk4))
| sk3 = empty_set ),
inference(resolution,[status(thm)],[p40,c3]) ).
cnf(p45,plain,
( ~ member(X0,union(sk3,sk4))
| sk3 = empty_set ),
inference(resolution,[status(thm)],[p44,c12]) ).
cnf(p71,plain,
( sk3 = empty_set
| empty(sk3) ),
inference(resolution,[status(thm)],[p36,p45]) ).
cnf(c14,plain,
( member(X2,X1)
| ~ member(X2,X0)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p76,plain,
( member(X0,empty_set)
| ~ member(X0,sk3)
| empty(sk3) ),
inference(resolution,[status(thm)],[p71,c14]) ).
cnf(p96,plain,
( empty(sk3)
| member(sk1(sk3),empty_set)
| empty(sk3) ),
inference(resolution,[status(thm)],[p76,c13]) ).
cnf(p104,plain,
( member(sk1(sk3),empty_set)
| empty(sk3) ),
inference(factoring,[status(thm)],[p96]) ).
cnf(p105,plain,
empty(sk3),
inference(resolution,[status(thm)],[p104,c3]) ).
cnf(p106,plain,
~ member(X0,sk3),
inference(resolution,[status(thm)],[p105,c12]) ).
cnf(c9,plain,
( member(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p107,plain,
subset(sk3,X0),
inference(resolution,[status(thm)],[p106,c9]) ).
cnf(p47,plain,
subset(empty_set,X0),
inference(resolution,[status(thm)],[c9,c3]) ).
cnf(c6,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p64,plain,
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(resolution,[status(thm)],[p47,c6]) ).
cnf(p113,plain,
empty_set = sk3,
inference(resolution,[status(thm)],[p107,p64]) ).
cnf(c22,plain,
( sk4 = empty_set
| union(sk3,sk4) = empty_set ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p28,plain,
( sk4 = empty_set
| subset(union(sk3,sk4),empty_set) ),
inference(resolution,[status(thm)],[c4,c22]) ).
cnf(p39,plain,
( sk4 = empty_set
| member(X0,empty_set)
| ~ member(X0,union(sk3,sk4)) ),
inference(resolution,[status(thm)],[c8,p28]) ).
cnf(p41,plain,
( empty(union(sk3,sk4))
| sk4 = empty_set
| member(sk1(union(sk3,sk4)),empty_set) ),
inference(resolution,[status(thm)],[p39,c13]) ).
cnf(p54,plain,
( empty(union(sk3,sk4))
| sk4 = empty_set ),
inference(resolution,[status(thm)],[p41,c3]) ).
cnf(p55,plain,
( ~ member(X0,union(sk3,sk4))
| sk4 = empty_set ),
inference(resolution,[status(thm)],[p54,c12]) ).
cnf(p125,plain,
( ~ member(X0,union(empty_set,sk4))
| sk4 = empty_set ),
inference(superposition,[status(thm)],[p113,p55]) ).
cnf(c2,plain,
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p37,plain,
( member(sk1(X0),union(X1,X0))
| empty(X0) ),
inference(resolution,[status(thm)],[c13,c2]) ).
cnf(p154,plain,
( empty(sk4)
| sk4 = empty_set ),
inference(resolution,[status(thm)],[p125,p37]) ).
cnf(p156,plain,
( member(X0,empty_set)
| ~ member(X0,sk4)
| empty(sk4) ),
inference(resolution,[status(thm)],[p154,c14]) ).
cnf(p174,plain,
( empty(sk4)
| member(sk1(sk4),empty_set)
| empty(sk4) ),
inference(resolution,[status(thm)],[p156,c13]) ).
cnf(p182,plain,
( member(sk1(sk4),empty_set)
| empty(sk4) ),
inference(factoring,[status(thm)],[p174]) ).
cnf(p183,plain,
empty(sk4),
inference(resolution,[status(thm)],[p182,c3]) ).
cnf(p187,plain,
~ member(X0,sk4),
inference(resolution,[status(thm)],[p183,c12]) ).
cnf(p188,plain,
subset(sk4,X0),
inference(resolution,[status(thm)],[p187,c9]) ).
cnf(p195,plain,
( ~ subset(X0,sk4)
| sk4 = X0 ),
inference(resolution,[status(thm)],[p188,c6]) ).
cnf(p205,plain,
sk4 = empty_set,
inference(resolution,[status(thm)],[p195,p47]) ).
cnf(p110,plain,
( ~ subset(X0,sk3)
| sk3 = X0 ),
inference(resolution,[status(thm)],[p107,c6]) ).
cnf(p131,plain,
sk3 = empty_set,
inference(resolution,[status(thm)],[p110,p47]) ).
cnf(c23,plain,
( union(sk3,sk4) != empty_set
| sk4 != empty_set
| sk3 != empty_set ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p132,plain,
( union(empty_set,sk4) != empty_set
| sk4 != empty_set
| empty_set != empty_set ),
inference(demodulation,[status(thm)],[p131,c23]) ).
cnf(p206,plain,
( union(empty_set,empty_set) != empty_set
| empty_set != empty_set
| empty_set != empty_set ),
inference(demodulation,[status(thm)],[p205,p132]) ).
cnf(p207,plain,
( union(empty_set,empty_set) != empty_set
| empty_set != empty_set ),
inference(factoring,[status(thm)],[p206]) ).
cnf(p208,plain,
union(empty_set,empty_set) != empty_set,
inference(equality_resolution,[status(thm)],[p207]) ).
cnf(p250,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[p249,p208]) ).
cnf(p251,plain,
$false,
inference(equality_resolution,[status(thm)],[p250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET600+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 11:24:13 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 12.46/2.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.46/2.17 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------