%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET911+1 : TPTP v9.3.1. Released v3.2.0.
% 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 02:44:16 PM UTC 2026
% Result : Theorem 3.76s 0.91s
% Output : Proof 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 15 unt; 0 def)
% Number of atoms : 39 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 32 ( 20 ~; 6 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 26 ( 0 sgn 16 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A,B] :
( in(A,B)
=> set_intersection2(B,singleton(A)) = singleton(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_zfmisc_1) ).
fof(f6_nnf,plain,
! [A,B] :
( set_intersection2(B,singleton(A)) = singleton(A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B] :
( set_intersection2(B,singleton(A)) = singleton(A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c7,plain,
( set_intersection2(X1,singleton(X0)) = singleton(X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi4,axiom,
ifeq(in(X0,X1),true,set_intersection2(X1,singleton(X0)),singleton(X0)) = singleton(X0),
inference(equality_encoding,[status(esa)],[c7]) ).
fof(f5,conjecture,
! [A,B] :
( in(A,B)
=> set_intersection2(B,singleton(A)) = singleton(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_zfmisc_1) ).
fof(f5_neg,negated_conjecture,
~ ! [A,B] :
( in(A,B)
=> set_intersection2(B,singleton(A)) = singleton(A) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f5_nnf,plain,
? [A,B] :
( set_intersection2(B,singleton(A)) != singleton(A)
& in(A,B) ),
inference(nnf_transformation,[status(thm)],[f5_neg]) ).
fof(f5_sk,plain,
( set_intersection2(sk3,singleton(sk2)) != singleton(sk2)
& in(sk2,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f5_nnf]) ).
cnf(c5,plain,
in(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi3,negated_conjecture,
in(sk2,sk3) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h0,plain,
set_intersection2(sk3,singleton(sk2)) = singleton(sk2),
inference(hyper_resolution,[status(thm)],[hi4,hi3]) ).
cnf(c6,plain,
set_intersection2(sk3,singleton(sk2)) != singleton(sk2),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi7,negated_conjecture,
ifeq(set_intersection2(sk3,singleton(sk2)),singleton(sk2),false,true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi7,h0]) ).
cnf(t16,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f2,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f2_nnf,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f4,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f4_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
~ empty(sk1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f4_nnf]) ).
cnf(c4,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c2,c4,c6]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t16]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET911+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 12:21:58 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.76/0.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.76/0.91 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------