%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET628+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 02:43:39 PM UTC 2026
% Result : Theorem 4.28s 16.39s
% Output : Proof 4.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 11 unt; 0 def)
% Number of atoms : 124 ( 18 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 129 ( 51 ~; 50 |; 21 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 64 ( 4 sgn 34 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f2_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)],[f2]) ).
fof(f2_sk,plain,
! [B,C,D] :
( ( ( member(sk1(B,C),C)
& ~ member(sk1(B,C),B) )
| ( ~ member(sk1(B,C),C)
& member(sk1(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,[sk1])],[f2_nnf]) ).
cnf(c7,plain,
( member(sk1(X0,X1),X1)
| member(sk1(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f0,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(f0_nnf,plain,
! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ( ? [D] :
( member(D,C)
& member(D,B) )
| ~ intersect(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C,D] :
( ( ~ member(D,C)
| ~ member(D,B)
| intersect(B,C) )
& ( ( member(sk0(B,C),C)
& member(sk0(B,C),B) )
| ~ intersect(B,C) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c2,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p22,plain,
( ~ member(X1,X0)
| intersect(X0,X0) ),
inference(factoring,[status(thm)],[c2]) ).
fof(f5,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_defn) ).
fof(f5_nnf,plain,
! [B] :
( ( ? [C] : member(C,B)
| empty(B) )
& ( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [B,C] :
( ( member(sk2(B),B)
| empty(B) )
& ( ~ member(C,B)
| ~ empty(B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f5_nnf]) ).
cnf(c14,plain,
( member(sk2(X0),X0)
| empty(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p25,plain,
( empty(X0)
| intersect(X0,X0) ),
inference(resolution,[status(thm)],[p22,c14]) ).
fof(f3,axiom,
! [B,C] :
( not_equal(B,C)
<=> B != C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_equal_defn) ).
fof(f3_nnf,plain,
! [B,C] :
( ( B = C
| not_equal(B,C) )
& ( B != C
| ~ not_equal(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B,C] :
( ( B = C
| not_equal(B,C) )
& ( B != C
| ~ not_equal(B,C) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c11,plain,
( X0 = X1
| not_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f6,conjecture,
! [B] :
( intersect(B,B)
<=> not_equal(B,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th110) ).
fof(f6_neg,negated_conjecture,
~ ! [B] :
( intersect(B,B)
<=> not_equal(B,empty_set) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
? [B] :
( ( not_equal(B,empty_set)
& ~ intersect(B,B) )
| ( ~ not_equal(B,empty_set)
& intersect(B,B) ) ),
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
( ( not_equal(sk3,empty_set)
& ~ intersect(sk3,sk3) )
| ( ~ not_equal(sk3,empty_set)
& intersect(sk3,sk3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f6_nnf]) ).
cnf(c17,plain,
( ~ intersect(sk3,sk3)
| ~ not_equal(sk3,empty_set) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p21,plain,
( ~ intersect(sk3,sk3)
| sk3 = empty_set ),
inference(resolution,[status(thm)],[c11,c17]) ).
cnf(p27,plain,
( sk3 = empty_set
| empty(sk3) ),
inference(resolution,[status(thm)],[p25,p21]) ).
cnf(c4,plain,
( member(X2,X1)
| ~ member(X2,X0)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p28,plain,
( member(X0,empty_set)
| ~ member(X0,sk3)
| empty(sk3) ),
inference(resolution,[status(thm)],[p27,c4]) ).
cnf(p29,plain,
( empty(sk3)
| member(sk2(sk3),empty_set)
| empty(sk3) ),
inference(resolution,[status(thm)],[p28,c14]) ).
cnf(p30,plain,
( member(sk2(sk3),empty_set)
| empty(sk3) ),
inference(factoring,[status(thm)],[p29]) ).
fof(f1,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox2/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(p31,plain,
empty(sk3),
inference(resolution,[status(thm)],[p30,c3]) ).
cnf(c13,plain,
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p32,plain,
~ member(X0,sk3),
inference(resolution,[status(thm)],[p31,c13]) ).
cnf(p40,plain,
( member(sk1(sk3,X0),X0)
| sk3 = X0 ),
inference(resolution,[status(thm)],[c7,p32]) ).
cnf(p42,plain,
sk3 = empty_set,
inference(resolution,[status(thm)],[p40,c3]) ).
cnf(c16,plain,
( not_equal(sk3,empty_set)
| intersect(sk3,sk3) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p43,plain,
( not_equal(empty_set,empty_set)
| intersect(empty_set,empty_set) ),
inference(demodulation,[status(thm)],[p42,c16]) ).
cnf(c10,plain,
( X0 != X1
| ~ not_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p19,plain,
~ not_equal(X0,X0),
inference(equality_resolution,[status(thm)],[c10]) ).
cnf(p45,plain,
intersect(empty_set,empty_set),
inference(resolution,[status(thm)],[p43,p19]) ).
cnf(c0,plain,
( member(sk0(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p46,plain,
member(sk0(empty_set,empty_set),empty_set),
inference(resolution,[status(thm)],[p45,c0]) ).
cnf(p47,plain,
$false,
inference(resolution,[status(thm)],[p46,c3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET628+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/15.63 % CPULimit : 300
% 0.09/15.63 % WCLimit : 300
% 0.09/15.63 % DateTime : Thu Sep 24 11:30:28 UTC 2026
% 0.09/15.64 % CPUTime :
% 0.09/15.64 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.28/16.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.28/16.39 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------