%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU162+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 : n009.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 61.11s 9.32s
% Output : Proof 61.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 62 ( 32 unt; 0 def)
% Number of atoms : 100 ( 43 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 69 ( 31 ~; 25 |; 7 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 108 ( 5 sgn 64 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f87,lemma,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f87_nnf,plain,
! [A,B] :
( ( set_difference(A,B) != A
| disjoint(A,B) )
& ( set_difference(A,B) = A
| ~ disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f87]) ).
fof(f87_sk,plain,
! [A,B] :
( ( set_difference(A,B) != A
| disjoint(A,B) )
& ( set_difference(A,B) = A
| ~ disjoint(A,B) ) ),
inference(skolemisation,[status(esa)],[f87_nnf]) ).
cnf(c178,plain,
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f87_sk]) ).
fof(f39,lemma,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f39_nnf,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c108,plain,
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
fof(f49,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f49_nnf,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(nnf_transformation,[status(thm)],[f49]) ).
fof(f49_sk,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(skolemisation,[status(esa)],[f49_nnf]) ).
cnf(c124,plain,
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f49_sk]) ).
cnf(p206,plain,
( disjoint(X1,singleton(X0))
| in(X0,X1) ),
inference(resolution,[status(thm)],[c108,c124]) ).
cnf(p537,plain,
( in(X1,X0)
| set_difference(X0,singleton(X1)) = X0 ),
inference(resolution,[status(thm)],[c178,p206]) ).
fof(f81,conjecture,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f81_neg,negated_conjecture,
~ ! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
inference(negated_conjecture,[status(cth)],[f81]) ).
fof(f81_nnf,plain,
? [A,B] :
( ( ~ in(B,A)
& set_difference(A,singleton(B)) != A )
| ( in(B,A)
& set_difference(A,singleton(B)) = A ) ),
inference(nnf_transformation,[status(thm)],[f81_neg]) ).
fof(f81_sk,plain,
( ( ~ in(sk22,sk21)
& set_difference(sk21,singleton(sk22)) != sk21 )
| ( in(sk22,sk21)
& set_difference(sk21,singleton(sk22)) = sk21 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk21,sk22])],[f81_nnf]) ).
cnf(c171,plain,
( set_difference(sk21,singleton(sk22)) != sk21
| in(sk22,sk21) ),
inference(cnf_transformation,[status(esa)],[f81_sk]) ).
cnf(p2102,plain,
( in(sk22,sk21)
| in(sk22,sk21) ),
inference(resolution,[status(thm)],[p537,c171]) ).
cnf(p2104,plain,
in(sk22,sk21),
inference(factoring,[status(thm)],[p2102]) ).
cnf(c170,plain,
( ~ in(sk22,sk21)
| set_difference(sk21,singleton(sk22)) = sk21 ),
inference(cnf_transformation,[status(esa)],[f81_sk]) ).
cnf(p2107,plain,
set_difference(sk21,singleton(sk22)) = sk21,
inference(resolution,[status(thm)],[p2104,c170]) ).
fof(f3,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f3_nnf,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f73,lemma,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(f73_nnf,plain,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(nnf_transformation,[status(thm)],[f73]) ).
fof(f73_sk,plain,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(skolemisation,[status(esa)],[f73_nnf]) ).
cnf(c160,plain,
set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
inference(cnf_transformation,[status(esa)],[f73_sk]) ).
cnf(p492,plain,
set_difference(set_union2(X0,X1),X0) = set_difference(X1,X0),
inference(superposition,[status(thm)],[c3,c160]) ).
fof(f76,lemma,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f76_nnf,plain,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(nnf_transformation,[status(thm)],[f76]) ).
fof(f76_sk,plain,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(skolemisation,[status(esa)],[f76_nnf]) ).
cnf(c163,plain,
set_difference(X0,set_difference(X0,X1)) = set_intersection2(X0,X1),
inference(cnf_transformation,[status(esa)],[f76_sk]) ).
cnf(p773,plain,
set_difference(set_union2(X0,X1),set_difference(X1,X0)) = X0,
inference(superposition,[status(thm)],[p492,c163]) ).
fof(f68,lemma,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f68_nnf,plain,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(nnf_transformation,[status(thm)],[f68]) ).
fof(f68_sk,plain,
! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B),
inference(skolemisation,[status(esa)],[f68_nnf]) ).
cnf(c151,plain,
set_union2(X0,set_difference(X1,X0)) = set_union2(X0,X1),
inference(cnf_transformation,[status(esa)],[f68_sk]) ).
cnf(p495,plain,
set_difference(set_union2(X0,X1),set_difference(X1,X0)) = set_difference(X0,set_difference(X1,X0)),
inference(superposition,[status(thm)],[c151,c160]) ).
cnf(p774,plain,
X0 = set_difference(X0,set_difference(X1,X0)),
inference(demodulation,[status(thm)],[p773,p495]) ).
fof(f58,lemma,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f58_nnf,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f58]) ).
fof(f58_sk,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f58_nnf]) ).
cnf(c133,plain,
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f58_sk]) ).
fof(f64,lemma,
! [A,B] : subset(set_difference(A,B),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(f64_nnf,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(nnf_transformation,[status(thm)],[f64]) ).
fof(f64_sk,plain,
! [A,B] : subset(set_difference(A,B),A),
inference(skolemisation,[status(esa)],[f64_nnf]) ).
cnf(c143,plain,
subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
cnf(p282,plain,
set_intersection2(X0,set_difference(X0,X1)) = set_difference(X0,X1),
inference(resolution,[status(thm)],[c133,c143]) ).
cnf(p781,plain,
set_difference(X0,set_difference(X1,X0)) = X0,
inference(superposition,[status(thm)],[p774,p282]) ).
cnf(c179,plain,
( set_difference(X0,X1) != X0
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f87_sk]) ).
cnf(p787,plain,
disjoint(X0,set_difference(X1,X0)),
inference(resolution,[status(thm)],[p781,c179]) ).
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]) ).
cnf(p789,plain,
~ in(X0,set_difference(X1,singleton(X0))),
inference(resolution,[status(thm)],[p787,c107]) ).
cnf(p2132,plain,
~ in(sk22,sk21),
inference(superposition,[status(thm)],[p2107,p789]) ).
cnf(p2141,plain,
$false,
inference(resolution,[status(thm)],[p2132,p2104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU162+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 12:59:58 UTC 2026
% 0.15/0.37 % CPUTime :
% 0.15/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 61.11/9.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 61.11/9.32 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------