%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU161+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 02:51:10 PM UTC 2026
% Result : Theorem 14.01s 2.25s
% Output : Proof 14.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 80 ( 32 unt; 0 def)
% Number of atoms : 187 ( 44 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 224 ( 117 ~; 59 |; 39 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-4 aty)
% Number of variables : 143 ( 9 sgn 99 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f37,lemma,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
fof(f37_nnf,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c106,plain,
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(hi72,axiom,
ifeq(in(X0,X1),true,set_union2(singleton(X0),X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c106]) ).
fof(f75,conjecture,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
fof(f75_neg,negated_conjecture,
~ ! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
inference(negated_conjecture,[status(cth)],[f75]) ).
fof(f75_nnf,plain,
? [A,B] :
( set_union2(singleton(A),B) != B
& in(A,B) ),
inference(nnf_transformation,[status(thm)],[f75_neg]) ).
fof(f75_sk,plain,
( set_union2(singleton(sk20),sk21) != sk21
& in(sk20,sk21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21])],[f75_nnf]) ).
cnf(c162,plain,
in(sk20,sk21),
inference(cnf_transformation,[status(esa)],[f75_sk]) ).
cnf(hi123,negated_conjecture,
in(sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c162]) ).
fof(f81,lemma,
! [A] : unordered_pair(A,A) = singleton(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f81_nnf,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(nnf_transformation,[status(thm)],[f81]) ).
fof(f81_sk,plain,
! [A] : unordered_pair(A,A) = singleton(A),
inference(skolemisation,[status(esa)],[f81_nnf]) ).
cnf(c170,plain,
unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f81_sk]) ).
cnf(hi8,axiom,
unordered_pair(X0,X0) = singleton(X0),
inference(equality_encoding,[status(esa)],[c170]) ).
cnf(h326,plain,
set_union2(unordered_pair(sk20,sk20),sk21) = sk21,
inference(hyper_resolution,[status(thm)],[hi72,hi123,hi8]) ).
cnf(c163,plain,
set_union2(singleton(sk20),sk21) != sk21,
inference(cnf_transformation,[status(esa)],[f75_sk]) ).
cnf(hi147,negated_conjecture,
ifeq(set_union2(singleton(sk20),sk21),sk21,false,true) = true,
inference(equality_encoding,[status(esa)],[c163]) ).
cnf(t1,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi147,h326,hi8]) ).
cnf(t882,plain,
false = true,
inference(orient,[status(thm)],[t1]) ).
fof(f0,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f0_nnf,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f1,axiom,
! [A,B] :
( proper_subset(A,B)
=> ~ proper_subset(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(f1_nnf,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f7,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f7_nnf,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B] :
( ( in(sk1(A),A)
| A = empty_set )
& ( ~ in(B,A)
| A != empty_set ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f7_nnf]) ).
cnf(c14,plain,
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f15,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f15_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( ~ in(D,B)
& in(D,A)
& ~ in(D,C) )
| ( ( in(D,B)
| ~ in(D,A) )
& in(D,C) ) )
| C = set_difference(A,B) )
& ( ! [D] :
( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [C,A,B,D] :
( ( ( ~ in(sk15(A,B,C),B)
& in(sk15(A,B,C),A)
& ~ in(sk15(A,B,C),C) )
| ( ( in(sk15(A,B,C),B)
| ~ in(sk15(A,B,C),A) )
& in(sk15(A,B,C),C) )
| C = set_difference(A,B) )
& ( ( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk15])],[f15_nnf]) ).
cnf(c74,plain,
( ~ in(X3,X1)
| ~ in(X3,X2)
| X2 != set_difference(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
fof(f18,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f18_nnf,plain,
! [A,B] :
( ( A = B
| ~ subset(A,B)
| proper_subset(A,B) )
& ( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A,B] :
( ( A = B
| ~ subset(A,B)
| proper_subset(A,B) )
& ( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c86,plain,
( X0 != X1
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f30,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(f30_nnf,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c99,plain,
~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f35,axiom,
! [A,B] : ~ proper_subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(f35_nnf,plain,
! [A,B] : ~ proper_subset(A,A),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
! [A] : ~ proper_subset(A,A),
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c104,plain,
~ proper_subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
fof(f36,lemma,
! [A] : singleton(A) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f36_nnf,plain,
! [A] : singleton(A) != empty_set,
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
! [A] : singleton(A) != empty_set,
inference(skolemisation,[status(esa)],[f36_nnf]) ).
cnf(c105,plain,
singleton(X0) != empty_set,
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
fof(f38,lemma,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f38_nnf,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c107,plain,
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
fof(f47,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f47_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f47]) ).
fof(f47_sk,plain,
~ empty(sk17),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk17])],[f47_nnf]) ).
cnf(c122,plain,
~ empty(sk17),
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
fof(f71,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f71_nnf,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ( ? [C] :
( in(C,B)
& in(C,A) )
| disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f71]) ).
fof(f71_sk,plain,
! [A,B,C] :
( ( ~ disjoint(A,B)
| ~ in(C,B)
| ~ in(C,A) )
& ( ( in(sk19(A,B),B)
& in(sk19(A,B),A) )
| disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk19])],[f71_nnf]) ).
cnf(c158,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f71_sk]) ).
fof(f78,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f78_nnf,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( ? [C] : in(C,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f78]) ).
fof(f78_sk,plain,
! [A,B,C] :
( ( ~ disjoint(A,B)
| ~ in(C,set_intersection2(A,B)) )
& ( in(sk22(A,B),set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk22])],[f78_nnf]) ).
cnf(c167,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f78_sk]) ).
fof(f79,lemma,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(f79_nnf,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f79]) ).
fof(f79_sk,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f79_nnf]) ).
cnf(c168,plain,
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f79_sk]) ).
fof(f84,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f84_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f84]) ).
fof(f84_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f84_nnf]) ).
cnf(c173,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f84_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c14,c74,c86,c99,c104,c105,c107,c122,c158,c163,c167,c168,c173]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t882]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU161+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:59:41 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 14.01/2.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.01/2.25 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------