%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU101+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 : n014.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 02:50:56 PM UTC 2026
% Result : Theorem 66.56s 15.34s
% Output : Proof 66.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 59 ( 9 unt; 0 def)
% Number of atoms : 190 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 198 ( 67 ~; 89 |; 32 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 34 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A] :
( diff_closed(A)
<=> ! [B,C] :
( ( in(C,A)
& in(B,A) )
=> in(set_difference(B,C),A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_finsub_1) ).
fof(f7_nnf,plain,
! [A] :
( ( ? [B,C] :
( ~ in(set_difference(B,C),A)
& in(C,A)
& in(B,A) )
| diff_closed(A) )
& ( ! [B,C] :
( in(set_difference(B,C),A)
| ~ in(C,A)
| ~ in(B,A) )
| ~ diff_closed(A) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C] :
( ( ( ~ in(set_difference(sk2(A),sk3(A)),A)
& in(sk3(A),A)
& in(sk2(A),A) )
| diff_closed(A) )
& ( in(set_difference(B,C),A)
| ~ in(C,A)
| ~ in(B,A)
| ~ diff_closed(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f7_nnf]) ).
cnf(c12,plain,
( in(sk2(X0),X0)
| diff_closed(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f27,conjecture,
! [A] :
( preboolean(A)
<=> ! [B,C] :
( ( in(C,A)
& in(B,A) )
=> ( in(set_difference(B,C),A)
& in(set_union2(B,C),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_finsub_1) ).
fof(f27_neg,negated_conjecture,
~ ! [A] :
( preboolean(A)
<=> ! [B,C] :
( ( in(C,A)
& in(B,A) )
=> ( in(set_difference(B,C),A)
& in(set_union2(B,C),A) ) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f27_nnf,plain,
? [A] :
( ( ! [B,C] :
( ( in(set_difference(B,C),A)
& in(set_union2(B,C),A) )
| ~ in(C,A)
| ~ in(B,A) )
& ~ preboolean(A) )
| ( ? [B,C] :
( ( ~ in(set_difference(B,C),A)
| ~ in(set_union2(B,C),A) )
& in(C,A)
& in(B,A) )
& preboolean(A) ) ),
inference(nnf_transformation,[status(thm)],[f27_neg]) ).
fof(f27_sk,plain,
! [B,C] :
( ( ( ( in(set_difference(B,C),sk14)
& in(set_union2(B,C),sk14) )
| ~ in(C,sk14)
| ~ in(B,sk14) )
& ~ preboolean(sk14) )
| ( ( ~ in(set_difference(sk15,sk16),sk14)
| ~ in(set_union2(sk15,sk16),sk14) )
& in(sk16,sk14)
& in(sk15,sk14)
& preboolean(sk14) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk14,sk15,sk16])],[f27_nnf]) ).
cnf(c58,plain,
( in(set_difference(X1,X2),sk14)
| ~ in(X2,sk14)
| ~ in(X1,sk14)
| preboolean(sk14) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p216,plain,
( in(set_difference(sk2(sk14),X0),sk14)
| ~ in(X0,sk14)
| preboolean(sk14)
| diff_closed(sk14) ),
inference(resolution,[status(thm)],[c12,c58]) ).
cnf(c13,plain,
( in(sk3(X0),X0)
| diff_closed(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p495,plain,
( diff_closed(sk14)
| in(set_difference(sk2(sk14),sk3(sk14)),sk14)
| preboolean(sk14)
| diff_closed(sk14) ),
inference(resolution,[status(thm)],[p216,c13]) ).
cnf(p603,plain,
( in(set_difference(sk2(sk14),sk3(sk14)),sk14)
| preboolean(sk14)
| diff_closed(sk14) ),
inference(factoring,[status(thm)],[p495]) ).
cnf(c14,plain,
( ~ in(set_difference(sk2(X0),sk3(X0)),X0)
| diff_closed(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p617,plain,
( diff_closed(sk14)
| preboolean(sk14)
| diff_closed(sk14) ),
inference(resolution,[status(thm)],[p603,c14]) ).
cnf(p618,plain,
( preboolean(sk14)
| diff_closed(sk14) ),
inference(factoring,[status(thm)],[p617]) ).
fof(f6,axiom,
! [A] :
( cup_closed(A)
<=> ! [B,C] :
( ( in(C,A)
& in(B,A) )
=> in(set_union2(B,C),A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_finsub_1) ).
fof(f6_nnf,plain,
! [A] :
( ( ? [B,C] :
( ~ in(set_union2(B,C),A)
& in(C,A)
& in(B,A) )
| cup_closed(A) )
& ( ! [B,C] :
( in(set_union2(B,C),A)
| ~ in(C,A)
| ~ in(B,A) )
| ~ cup_closed(A) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C] :
( ( ( ~ in(set_union2(sk0(A),sk1(A)),A)
& in(sk1(A),A)
& in(sk0(A),A) )
| cup_closed(A) )
& ( in(set_union2(B,C),A)
| ~ in(C,A)
| ~ in(B,A)
| ~ cup_closed(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f6_nnf]) ).
cnf(c8,plain,
( in(sk0(X0),X0)
| cup_closed(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(c57,plain,
( in(set_union2(X1,X2),sk14)
| ~ in(X2,sk14)
| ~ in(X1,sk14)
| preboolean(sk14) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p107,plain,
( in(set_union2(sk0(sk14),X0),sk14)
| ~ in(X0,sk14)
| preboolean(sk14)
| cup_closed(sk14) ),
inference(resolution,[status(thm)],[c8,c57]) ).
cnf(c9,plain,
( in(sk1(X0),X0)
| cup_closed(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p377,plain,
( cup_closed(sk14)
| in(set_union2(sk0(sk14),sk1(sk14)),sk14)
| preboolean(sk14)
| cup_closed(sk14) ),
inference(resolution,[status(thm)],[p107,c9]) ).
cnf(p562,plain,
( in(set_union2(sk0(sk14),sk1(sk14)),sk14)
| preboolean(sk14)
| cup_closed(sk14) ),
inference(factoring,[status(thm)],[p377]) ).
cnf(c10,plain,
( ~ in(set_union2(sk0(X0),sk1(X0)),X0)
| cup_closed(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p576,plain,
( cup_closed(sk14)
| preboolean(sk14)
| cup_closed(sk14) ),
inference(resolution,[status(thm)],[p562,c10]) ).
cnf(p581,plain,
( preboolean(sk14)
| cup_closed(sk14) ),
inference(factoring,[status(thm)],[p576]) ).
fof(f4,axiom,
! [A] :
( ( diff_closed(A)
& cup_closed(A) )
=> preboolean(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finsub_1) ).
fof(f4_nnf,plain,
! [A] :
( preboolean(A)
| ~ diff_closed(A)
| ~ cup_closed(A) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A] :
( preboolean(A)
| ~ diff_closed(A)
| ~ cup_closed(A) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c5,plain,
( preboolean(X0)
| ~ diff_closed(X0)
| ~ cup_closed(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p582,plain,
( preboolean(sk14)
| ~ diff_closed(sk14)
| preboolean(sk14) ),
inference(resolution,[status(thm)],[p581,c5]) ).
cnf(p583,plain,
( ~ diff_closed(sk14)
| preboolean(sk14) ),
inference(factoring,[status(thm)],[p582]) ).
cnf(p619,plain,
( preboolean(sk14)
| preboolean(sk14) ),
inference(resolution,[status(thm)],[p618,p583]) ).
cnf(p620,plain,
preboolean(sk14),
inference(factoring,[status(thm)],[p619]) ).
fof(f2,axiom,
! [A] :
( preboolean(A)
=> ( diff_closed(A)
& cup_closed(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finsub_1) ).
fof(f2_nnf,plain,
! [A] :
( ( diff_closed(A)
& cup_closed(A) )
| ~ preboolean(A) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A] :
( ( diff_closed(A)
& cup_closed(A) )
| ~ preboolean(A) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c3,plain,
( diff_closed(X0)
| ~ preboolean(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p624,plain,
diff_closed(sk14),
inference(resolution,[status(thm)],[p620,c3]) ).
cnf(c11,plain,
( in(set_difference(X1,X2),X0)
| ~ in(X2,X0)
| ~ in(X1,X0)
| ~ diff_closed(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p626,plain,
( in(set_difference(X0,X1),sk14)
| ~ in(X1,sk14)
| ~ in(X0,sk14) ),
inference(resolution,[status(thm)],[p624,c11]) ).
cnf(c59,plain,
( ~ preboolean(sk14)
| in(sk15,sk14) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p621,plain,
in(sk15,sk14),
inference(resolution,[status(thm)],[p620,c59]) ).
cnf(p726,plain,
( in(set_difference(sk15,X0),sk14)
| ~ in(X0,sk14) ),
inference(resolution,[status(thm)],[p626,p621]) ).
cnf(c62,plain,
( ~ preboolean(sk14)
| in(sk16,sk14) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p622,plain,
in(sk16,sk14),
inference(resolution,[status(thm)],[p620,c62]) ).
cnf(p806,plain,
in(set_difference(sk15,sk16),sk14),
inference(resolution,[status(thm)],[p726,p622]) ).
cnf(c2,plain,
( cup_closed(X0)
| ~ preboolean(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p623,plain,
cup_closed(sk14),
inference(resolution,[status(thm)],[p620,c2]) ).
cnf(c7,plain,
( in(set_union2(X1,X2),X0)
| ~ in(X2,X0)
| ~ in(X1,X0)
| ~ cup_closed(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p625,plain,
( in(set_union2(X0,X1),sk14)
| ~ in(X1,sk14)
| ~ in(X0,sk14) ),
inference(resolution,[status(thm)],[p623,c7]) ).
cnf(p632,plain,
( in(set_union2(sk15,X0),sk14)
| ~ in(X0,sk14) ),
inference(resolution,[status(thm)],[p625,p621]) ).
cnf(p634,plain,
in(set_union2(sk15,sk16),sk14),
inference(resolution,[status(thm)],[p632,p622]) ).
cnf(c65,plain,
( ~ preboolean(sk14)
| ~ in(set_difference(sk15,sk16),sk14)
| ~ in(set_union2(sk15,sk16),sk14) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p635,plain,
( ~ preboolean(sk14)
| ~ in(set_difference(sk15,sk16),sk14) ),
inference(resolution,[status(thm)],[p634,c65]) ).
cnf(p833,plain,
~ preboolean(sk14),
inference(resolution,[status(thm)],[p806,p635]) ).
cnf(p839,plain,
$false,
inference(resolution,[status(thm)],[p833,p620]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU101+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/5.63 % Computer : n014.cluster.edu
% 0.14/5.63 % Model : x86_64 x86_64
% 0.14/5.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.63 % Memory : 8046.5625MB
% 0.14/5.63 % OS : Linux 6.8.0-71-generic
% 0.14/5.63 % CPULimit : 300
% 0.14/5.63 % WCLimit : 300
% 0.14/5.63 % DateTime : Thu Sep 24 12:44:53 UTC 2026
% 0.14/5.63 % CPUTime :
% 0.14/5.63 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 66.56/15.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 66.56/15.34 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------