%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU161+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 4.14s 0.98s
% Output : Proof 4.14s
% 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(f8,axiom,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_zfmisc_1) ).
fof(f8_nnf,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B] :
( set_union2(singleton(A),B) = B
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c9,plain,
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi6,axiom,
ifeq(in(X0,X1),true,set_union2(singleton(X0),X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c9]) ).
fof(f7,conjecture,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
fof(f7_neg,negated_conjecture,
~ ! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f7_nnf,plain,
? [A,B] :
( set_union2(singleton(A),B) != B
& in(A,B) ),
inference(nnf_transformation,[status(thm)],[f7_neg]) ).
fof(f7_sk,plain,
( set_union2(singleton(sk2),sk3) != sk3
& in(sk2,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f7_nnf]) ).
cnf(c7,plain,
in(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi5,negated_conjecture,
in(sk2,sk3) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h0,plain,
set_union2(singleton(sk2),sk3) = sk3,
inference(hyper_resolution,[status(thm)],[hi6,hi5]) ).
cnf(c8,plain,
set_union2(singleton(sk2),sk3) != sk3,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi9,negated_conjecture,
ifeq(set_union2(singleton(sk2),sk3),sk3,false,true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi9,h0]) ).
cnf(t27,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f4,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f4_nnf,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f6,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f6_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
~ empty(sk1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f6_nnf]) ).
cnf(c6,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c4,c6,c8]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t27]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU161+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.06/0.31 % Computer : n012.cluster.edu
% 0.06/0.31 % Model : x86_64 x86_64
% 0.06/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.31 % Memory : 8046.5625MB
% 0.06/0.31 % OS : Linux 6.8.0-71-generic
% 0.06/0.31 % CPULimit : 300
% 0.06/0.31 % WCLimit : 300
% 0.06/0.31 % DateTime : Thu Sep 24 12:59:35 UTC 2026
% 0.06/0.32 % CPUTime :
% 0.06/0.32 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.14/0.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.14/0.98 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------