%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU280+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 02:51:35 PM UTC 2026
% Result : Theorem 4.96s 1.18s
% Output : Proof 4.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 2
% Syntax : Number of formulae : 76 ( 9 unt; 0 def)
% Number of atoms : 236 ( 88 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 242 ( 82 ~; 128 |; 27 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 84 ( 1 sgn 17 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A] :
( ! [B,C,D] :
( ( ordinal(D)
& B = D
& ordinal(C)
& B = C )
=> C = D )
=> ? [B] :
! [C] :
( in(C,B)
<=> ? [D] :
( ordinal(C)
& D = C
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e6_22__wellord2__1) ).
fof(f5_nnf,plain,
! [A] :
( ? [B] :
! [C] :
( ( ! [D] :
( ~ ordinal(C)
| D != C
| ~ in(D,A) )
| in(C,B) )
& ( ? [D] :
( ordinal(C)
& D = C
& in(D,A) )
| ~ in(C,B) ) )
| ? [B,C,D] :
( C != D
& ordinal(D)
& B = D
& ordinal(C)
& B = C ) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,C,D] :
( ( ( ~ ordinal(C)
| D != C
| ~ in(D,A)
| in(C,sk6(A)) )
& ( ( ordinal(C)
& sk7(A,C) = C
& in(sk7(A,C),A) )
| ~ in(C,sk6(A)) ) )
| ( sk4(A) != sk5(A)
& ordinal(sk5(A))
& sk3(A) = sk5(A)
& ordinal(sk4(A))
& sk3(A) = sk4(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4,sk5,sk6,sk7])],[f5_nnf]) ).
cnf(c24,plain,
( ~ ordinal(X2)
| X3 != X2
| ~ in(X3,X0)
| in(X2,sk6(X0))
| sk3(X0) = sk5(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f0,conjecture,
! [A] :
? [B] :
! [C] :
( in(C,B)
<=> ( ordinal(C)
& in(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e6_22__wellord2) ).
fof(f0_neg,negated_conjecture,
~ ! [A] :
? [B] :
! [C] :
( in(C,B)
<=> ( ordinal(C)
& in(C,A) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [A] :
! [B] :
? [C] :
( ( ordinal(C)
& in(C,A)
& ~ in(C,B) )
| ( ( ~ ordinal(C)
| ~ in(C,A) )
& in(C,B) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [B] :
( ( ordinal(sk1(B))
& in(sk1(B),sk0)
& ~ in(sk1(B),B) )
| ( ( ~ ordinal(sk1(B))
| ~ in(sk1(B),sk0) )
& in(sk1(B),B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c1,plain,
( in(sk1(X1),sk0)
| in(sk1(X1),X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p176,plain,
( in(sk1(X1),X1)
| ~ ordinal(X0)
| sk1(X1) != X0
| in(X0,sk6(sk0))
| sk3(sk0) = sk5(sk0) ),
inference(resolution,[status(thm)],[c24,c1]) ).
cnf(p785,plain,
( in(sk1(X0),X0)
| ~ ordinal(sk1(X0))
| in(sk1(X0),sk6(sk0))
| sk3(sk0) = sk5(sk0) ),
inference(equality_resolution,[status(thm)],[p176]) ).
cnf(p786,plain,
( ~ ordinal(sk1(sk6(sk0)))
| in(sk1(sk6(sk0)),sk6(sk0))
| sk3(sk0) = sk5(sk0) ),
inference(factoring,[status(thm)],[p785]) ).
cnf(c15,plain,
( ordinal(X2)
| ~ in(X2,sk6(X0))
| sk3(X0) = sk4(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(c2,plain,
( ordinal(sk1(X1))
| in(sk1(X1),X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p65,plain,
( ordinal(sk1(sk6(X0)))
| ordinal(sk1(sk6(X0)))
| sk3(X0) = sk4(X0) ),
inference(resolution,[status(thm)],[c15,c2]) ).
cnf(p69,plain,
( ordinal(sk1(sk6(X0)))
| sk3(X0) = sk4(X0) ),
inference(factoring,[status(thm)],[p65]) ).
cnf(c31,plain,
( ordinal(X2)
| ~ in(X2,sk6(X0))
| sk4(X0) != sk5(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p294,plain,
( ordinal(X1)
| ~ in(X1,sk6(X0))
| sk3(X0) != sk5(X0)
| ordinal(sk1(sk6(X0))) ),
inference(superposition,[status(thm)],[p69,c31]) ).
cnf(p386,plain,
( ~ in(sk1(sk6(X0)),sk6(X0))
| sk3(X0) != sk5(X0)
| ordinal(sk1(sk6(X0))) ),
inference(factoring,[status(thm)],[p294]) ).
cnf(c23,plain,
( ordinal(X2)
| ~ in(X2,sk6(X0))
| sk3(X0) = sk5(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p162,plain,
( ordinal(sk1(sk6(X0)))
| ordinal(sk1(sk6(X0)))
| sk3(X0) = sk5(X0) ),
inference(resolution,[status(thm)],[c23,c2]) ).
cnf(p168,plain,
( ordinal(sk1(sk6(X0)))
| sk3(X0) = sk5(X0) ),
inference(factoring,[status(thm)],[p162]) ).
cnf(p388,plain,
( ordinal(sk1(sk6(X0)))
| ~ in(sk1(sk6(X0)),sk6(X0))
| ordinal(sk1(sk6(X0))) ),
inference(resolution,[status(thm)],[p386,p168]) ).
cnf(p392,plain,
( ~ in(sk1(sk6(X0)),sk6(X0))
| ordinal(sk1(sk6(X0))) ),
inference(factoring,[status(thm)],[p388]) ).
cnf(p393,plain,
( ordinal(sk1(sk6(X0)))
| ordinal(sk1(sk6(X0))) ),
inference(resolution,[status(thm)],[p392,c2]) ).
cnf(p395,plain,
ordinal(sk1(sk6(X0))),
inference(factoring,[status(thm)],[p393]) ).
cnf(p788,plain,
( in(sk1(sk6(sk0)),sk6(sk0))
| sk3(sk0) = sk5(sk0) ),
inference(resolution,[status(thm)],[p786,p395]) ).
cnf(c22,plain,
( sk7(X0,X2) = X2
| ~ in(X2,sk6(X0))
| sk3(X0) = sk5(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p795,plain,
( sk7(sk0,sk1(sk6(sk0))) = sk1(sk6(sk0))
| sk3(sk0) = sk5(sk0)
| sk3(sk0) = sk5(sk0) ),
inference(resolution,[status(thm)],[p788,c22]) ).
cnf(p862,plain,
( sk7(sk0,sk1(sk6(sk0))) = sk1(sk6(sk0))
| sk3(sk0) = sk5(sk0) ),
inference(factoring,[status(thm)],[p795]) ).
cnf(c21,plain,
( in(sk7(X0,X2),X0)
| ~ in(X2,sk6(X0))
| sk3(X0) = sk5(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p794,plain,
( in(sk7(sk0,sk1(sk6(sk0))),sk0)
| sk3(sk0) = sk5(sk0)
| sk3(sk0) = sk5(sk0) ),
inference(resolution,[status(thm)],[p788,c21]) ).
cnf(p825,plain,
( in(sk7(sk0,sk1(sk6(sk0))),sk0)
| sk3(sk0) = sk5(sk0) ),
inference(factoring,[status(thm)],[p794]) ).
cnf(p863,plain,
( in(sk1(sk6(sk0)),sk0)
| sk3(sk0) = sk5(sk0)
| sk3(sk0) = sk5(sk0) ),
inference(superposition,[status(thm)],[p862,p825]) ).
cnf(p865,plain,
( in(sk1(sk6(sk0)),sk0)
| sk3(sk0) = sk5(sk0) ),
inference(factoring,[status(thm)],[p863]) ).
cnf(c3,plain,
( ~ in(sk1(X1),X1)
| ~ ordinal(sk1(X1))
| ~ in(sk1(X1),sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p866,plain,
( ~ in(sk1(sk6(sk0)),sk6(sk0))
| ~ ordinal(sk1(sk6(sk0)))
| sk3(sk0) = sk5(sk0) ),
inference(resolution,[status(thm)],[p865,c3]) ).
cnf(p871,plain,
( ~ in(sk1(sk6(sk0)),sk6(sk0))
| sk3(sk0) = sk5(sk0) ),
inference(resolution,[status(thm)],[p866,p395]) ).
cnf(p872,plain,
( sk3(sk0) = sk5(sk0)
| sk3(sk0) = sk5(sk0) ),
inference(resolution,[status(thm)],[p871,p788]) ).
cnf(p873,plain,
sk3(sk0) = sk5(sk0),
inference(factoring,[status(thm)],[p872]) ).
cnf(c16,plain,
( ~ ordinal(X2)
| X3 != X2
| ~ in(X3,X0)
| in(X2,sk6(X0))
| sk3(X0) = sk4(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p76,plain,
( in(sk1(X1),X1)
| ~ ordinal(X0)
| sk1(X1) != X0
| in(X0,sk6(sk0))
| sk3(sk0) = sk4(sk0) ),
inference(resolution,[status(thm)],[c16,c1]) ).
cnf(p93,plain,
( in(sk1(X0),X0)
| ~ ordinal(sk1(X0))
| in(sk1(X0),sk6(sk0))
| sk3(sk0) = sk4(sk0) ),
inference(equality_resolution,[status(thm)],[p76]) ).
cnf(p94,plain,
( ~ ordinal(sk1(sk6(sk0)))
| in(sk1(sk6(sk0)),sk6(sk0))
| sk3(sk0) = sk4(sk0) ),
inference(factoring,[status(thm)],[p93]) ).
cnf(p400,plain,
( in(sk1(sk6(sk0)),sk6(sk0))
| sk3(sk0) = sk4(sk0) ),
inference(resolution,[status(thm)],[p395,p94]) ).
cnf(c14,plain,
( sk7(X0,X2) = X2
| ~ in(X2,sk6(X0))
| sk3(X0) = sk4(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p406,plain,
( sk7(sk0,sk1(sk6(sk0))) = sk1(sk6(sk0))
| sk3(sk0) = sk4(sk0)
| sk3(sk0) = sk4(sk0) ),
inference(resolution,[status(thm)],[p400,c14]) ).
cnf(p662,plain,
( sk7(sk0,sk1(sk6(sk0))) = sk1(sk6(sk0))
| sk3(sk0) = sk4(sk0) ),
inference(factoring,[status(thm)],[p406]) ).
cnf(c13,plain,
( in(sk7(X0,X2),X0)
| ~ in(X2,sk6(X0))
| sk3(X0) = sk4(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p405,plain,
( in(sk7(sk0,sk1(sk6(sk0))),sk0)
| sk3(sk0) = sk4(sk0)
| sk3(sk0) = sk4(sk0) ),
inference(resolution,[status(thm)],[p400,c13]) ).
cnf(p467,plain,
( in(sk7(sk0,sk1(sk6(sk0))),sk0)
| sk3(sk0) = sk4(sk0) ),
inference(factoring,[status(thm)],[p405]) ).
cnf(p673,plain,
( in(sk1(sk6(sk0)),sk0)
| sk3(sk0) = sk4(sk0)
| sk3(sk0) = sk4(sk0) ),
inference(superposition,[status(thm)],[p662,p467]) ).
cnf(p675,plain,
( in(sk1(sk6(sk0)),sk0)
| sk3(sk0) = sk4(sk0) ),
inference(factoring,[status(thm)],[p673]) ).
cnf(p676,plain,
( ~ in(sk1(sk6(sk0)),sk6(sk0))
| ~ ordinal(sk1(sk6(sk0)))
| sk3(sk0) = sk4(sk0) ),
inference(resolution,[status(thm)],[p675,c3]) ).
cnf(p687,plain,
( ~ in(sk1(sk6(sk0)),sk6(sk0))
| sk3(sk0) = sk4(sk0) ),
inference(resolution,[status(thm)],[p676,p395]) ).
cnf(p688,plain,
( sk3(sk0) = sk4(sk0)
| sk3(sk0) = sk4(sk0) ),
inference(resolution,[status(thm)],[p687,p400]) ).
cnf(p689,plain,
sk3(sk0) = sk4(sk0),
inference(factoring,[status(thm)],[p688]) ).
cnf(c32,plain,
( ~ ordinal(X2)
| X3 != X2
| ~ in(X3,X0)
| in(X2,sk6(X0))
| sk4(X0) != sk5(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p696,plain,
( ~ ordinal(X0)
| X1 != X0
| ~ in(X1,sk0)
| in(X0,sk6(sk0))
| sk3(sk0) != sk5(sk0) ),
inference(superposition,[status(thm)],[p689,c32]) ).
cnf(p727,plain,
( ~ ordinal(X0)
| ~ in(X0,sk0)
| in(X0,sk6(sk0))
| sk3(sk0) != sk5(sk0) ),
inference(equality_resolution,[status(thm)],[p696]) ).
cnf(p904,plain,
( ~ ordinal(X0)
| ~ in(X0,sk0)
| in(X0,sk6(sk0)) ),
inference(resolution,[status(thm)],[p873,p727]) ).
cnf(p952,plain,
( in(sk1(X0),X0)
| ~ ordinal(sk1(X0))
| in(sk1(X0),sk6(sk0)) ),
inference(resolution,[status(thm)],[p904,c1]) ).
cnf(p956,plain,
( ~ ordinal(sk1(sk6(sk0)))
| in(sk1(sk6(sk0)),sk6(sk0)) ),
inference(factoring,[status(thm)],[p952]) ).
cnf(p982,plain,
in(sk1(sk6(sk0)),sk6(sk0)),
inference(resolution,[status(thm)],[p956,p395]) ).
cnf(c30,plain,
( sk7(X0,X2) = X2
| ~ in(X2,sk6(X0))
| sk4(X0) != sk5(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p693,plain,
( sk7(sk0,X0) = X0
| ~ in(X0,sk6(sk0))
| sk3(sk0) != sk5(sk0) ),
inference(superposition,[status(thm)],[p689,c30]) ).
cnf(p902,plain,
( sk7(sk0,X0) = X0
| ~ in(X0,sk6(sk0)) ),
inference(resolution,[status(thm)],[p873,p693]) ).
cnf(p991,plain,
sk7(sk0,sk1(sk6(sk0))) = sk1(sk6(sk0)),
inference(resolution,[status(thm)],[p982,p902]) ).
cnf(c29,plain,
( in(sk7(X0,X2),X0)
| ~ in(X2,sk6(X0))
| sk4(X0) != sk5(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p690,plain,
( in(sk7(sk0,X0),sk0)
| ~ in(X0,sk6(sk0))
| sk3(sk0) != sk5(sk0) ),
inference(superposition,[status(thm)],[p689,c29]) ).
cnf(p901,plain,
( in(sk7(sk0,X0),sk0)
| ~ in(X0,sk6(sk0)) ),
inference(resolution,[status(thm)],[p873,p690]) ).
cnf(p990,plain,
in(sk7(sk0,sk1(sk6(sk0))),sk0),
inference(resolution,[status(thm)],[p982,p901]) ).
cnf(p993,plain,
in(sk1(sk6(sk0)),sk0),
inference(demodulation,[status(thm)],[p991,p990]) ).
cnf(p994,plain,
( ~ in(sk1(sk6(sk0)),sk6(sk0))
| ~ ordinal(sk1(sk6(sk0))) ),
inference(resolution,[status(thm)],[p993,c3]) ).
cnf(p1007,plain,
~ in(sk1(sk6(sk0)),sk6(sk0)),
inference(resolution,[status(thm)],[p994,p395]) ).
cnf(p1008,plain,
$false,
inference(resolution,[status(thm)],[p1007,p982]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU280+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 13:33:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.96/1.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.96/1.18 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------