%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET636+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 : n002.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 02:43:41 PM UTC 2026
% Result : Theorem 32.56s 10.08s
% Output : Proof 32.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 58 ( 12 unt; 0 def)
% Number of atoms : 156 ( 16 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 159 ( 61 ~; 64 |; 26 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 96 ( 5 sgn 45 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,conjecture,
! [B,C] :
( disjoint(B,C)
<=> intersection(B,C) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th118) ).
fof(f11_neg,negated_conjecture,
~ ! [B,C] :
( disjoint(B,C)
<=> intersection(B,C) = empty_set ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
? [B,C] :
( ( intersection(B,C) = empty_set
& ~ disjoint(B,C) )
| ( intersection(B,C) != empty_set
& disjoint(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
( ( intersection(sk4,sk5) = empty_set
& ~ disjoint(sk4,sk5) )
| ( intersection(sk4,sk5) != empty_set
& disjoint(sk4,sk5) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5])],[f11_nnf]) ).
cnf(c27,plain,
( intersection(sk4,sk5) = empty_set
| disjoint(sk4,sk5) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
fof(f9,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
fof(f9_nnf,plain,
! [B] :
( ( ? [C] : member(C,B)
| empty(B) )
& ( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [B,C] :
( ( member(sk2(B),B)
| empty(B) )
& ( ~ member(C,B)
| ~ empty(B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f9_nnf]) ).
cnf(c19,plain,
( member(sk2(X0),X0)
| empty(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
fof(f0,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f0_nnf,plain,
! [B,C,D] :
( ( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [D,B,C] :
( ( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p32,plain,
( member(sk2(intersection(X0,X1)),X0)
| empty(intersection(X0,X1)) ),
inference(resolution,[status(thm)],[c19,c0]) ).
fof(f1,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
fof(f1_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)],[f1]) ).
fof(f1_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])],[f1_nnf]) ).
cnf(c5,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p87,plain,
( ~ member(sk2(intersection(X0,X1)),X2)
| intersect(X0,X2)
| empty(intersection(X0,X1)) ),
inference(resolution,[status(thm)],[p32,c5]) ).
cnf(c1,plain,
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p33,plain,
( member(sk2(intersection(X0,X1)),X1)
| empty(intersection(X0,X1)) ),
inference(resolution,[status(thm)],[c19,c1]) ).
cnf(p784,plain,
( empty(intersection(X0,X1))
| intersect(X0,X1)
| empty(intersection(X0,X1)) ),
inference(resolution,[status(thm)],[p87,p33]) ).
cnf(p1760,plain,
( intersect(X0,X1)
| empty(intersection(X0,X1)) ),
inference(factoring,[status(thm)],[p784]) ).
cnf(c18,plain,
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p1761,plain,
( ~ member(X2,intersection(X0,X1))
| intersect(X0,X1) ),
inference(resolution,[status(thm)],[p1760,c18]) ).
fof(f10,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f10_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)],[f10]) ).
fof(f10_sk,plain,
! [B,C,D] :
( ( ( member(sk3(B,C),C)
& ~ member(sk3(B,C),B) )
| ( ~ member(sk3(B,C),C)
& member(sk3(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,[sk3])],[f10_nnf]) ).
cnf(c23,plain,
( member(sk3(X0,X1),X1)
| member(sk3(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f2,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f2_nnf,plain,
! [B] : ~ member(B,empty_set),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B] : ~ member(B,empty_set),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c6,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p101,plain,
( member(sk3(X0,empty_set),X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[c23,c6]) ).
cnf(p1781,plain,
( intersection(X0,X1) = empty_set
| intersect(X0,X1) ),
inference(resolution,[status(thm)],[p1761,p101]) ).
cnf(c28,plain,
( ~ disjoint(sk4,sk5)
| intersection(sk4,sk5) != empty_set ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p1896,plain,
( ~ disjoint(sk4,sk5)
| intersect(sk4,sk5) ),
inference(resolution,[status(thm)],[p1781,c28]) ).
fof(f3,axiom,
! [B,C] :
( disjoint(B,C)
<=> ~ intersect(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).
fof(f3_nnf,plain,
! [B,C] :
( ( intersect(B,C)
| disjoint(B,C) )
& ( ~ intersect(B,C)
| ~ disjoint(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B,C] :
( ( intersect(B,C)
| disjoint(B,C) )
& ( ~ intersect(B,C)
| ~ disjoint(B,C) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c8,plain,
( intersect(X0,X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p1897,plain,
( intersect(sk4,sk5)
| intersect(sk4,sk5) ),
inference(resolution,[status(thm)],[p1896,c8]) ).
cnf(p1898,plain,
intersect(sk4,sk5),
inference(factoring,[status(thm)],[p1897]) ).
cnf(c3,plain,
( member(sk0(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p1904,plain,
member(sk0(sk4,sk5),sk4),
inference(resolution,[status(thm)],[p1898,c3]) ).
cnf(c2,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p1908,plain,
( ~ member(sk0(sk4,sk5),X0)
| member(sk0(sk4,sk5),intersection(sk4,X0)) ),
inference(resolution,[status(thm)],[p1904,c2]) ).
cnf(c4,plain,
( member(sk0(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p1905,plain,
member(sk0(sk4,sk5),sk5),
inference(resolution,[status(thm)],[p1898,c4]) ).
cnf(p3602,plain,
member(sk0(sk4,sk5),intersection(sk4,sk5)),
inference(resolution,[status(thm)],[p1908,p1905]) ).
cnf(p1909,plain,
( ~ member(sk0(sk4,sk5),X0)
| intersect(sk4,X0) ),
inference(resolution,[status(thm)],[p1904,c5]) ).
cnf(p3610,plain,
intersect(sk4,intersection(sk4,sk5)),
inference(resolution,[status(thm)],[p3602,p1909]) ).
cnf(p3616,plain,
( intersect(sk4,empty_set)
| disjoint(sk4,sk5) ),
inference(superposition,[status(thm)],[c27,p3610]) ).
cnf(c7,plain,
( ~ intersect(X0,X1)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p3634,plain,
( ~ intersect(sk4,sk5)
| intersect(sk4,empty_set) ),
inference(resolution,[status(thm)],[p3616,c7]) ).
cnf(p3660,plain,
intersect(sk4,empty_set),
inference(resolution,[status(thm)],[p3634,p1898]) ).
cnf(p3663,plain,
member(sk0(sk4,empty_set),empty_set),
inference(resolution,[status(thm)],[p3660,c4]) ).
cnf(p3680,plain,
$false,
inference(resolution,[status(thm)],[p3663,c6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET636+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.36 % Computer : n002.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Thu Sep 24 11:34:54 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 32.56/10.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.56/10.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------