%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU152+1 : 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 02:51:07 PM UTC 2026
% Result : Theorem 6.00s 1.21s
% Output : Proof 6.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 13 unt; 0 def)
% Number of atoms : 49 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 21 ~; 11 |; 4 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 34 ( 0 sgn 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f6_nnf,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c8,plain,
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi4,axiom,
ifeq(in(X0,X1),true,subset(singleton(X0),X1),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
fof(f5,conjecture,
! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
fof(f5_neg,negated_conjecture,
~ ! [A,B] :
( in(A,B)
=> set_union2(singleton(A),B) = B ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f5_nnf,plain,
? [A,B] :
( set_union2(singleton(A),B) != B
& in(A,B) ),
inference(nnf_transformation,[status(thm)],[f5_neg]) ).
fof(f5_sk,plain,
( set_union2(singleton(sk0),sk1) != sk1
& in(sk0,sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f5_nnf]) ).
cnf(c5,plain,
in(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi2,negated_conjecture,
in(sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h0,plain,
subset(singleton(sk0),sk1) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi2]) ).
fof(f8,axiom,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f8_nnf,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c10,plain,
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi6,axiom,
ifeq(subset(X0,X1),true,set_union2(X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h2,plain,
set_union2(singleton(sk0),sk1) = sk1,
inference(hyper_resolution,[status(thm)],[hi6,h0]) ).
cnf(c6,plain,
set_union2(singleton(sk0),sk1) != sk1,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi8,negated_conjecture,
ifeq(set_union2(singleton(sk0),sk1),sk1,false,true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi8,h2]) ).
cnf(t35,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
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]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c6]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t35]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU152+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.36 % Computer : n006.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Thu Sep 24 12:57:56 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.00/1.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.00/1.21 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------