%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET775+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 : Tue Sep 29 12:41:53 PM UTC 2026
% Result : Theorem 1.21s 1.74s
% Output : Refutation 4.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 4
% Syntax : Number of formulae : 116 ( 6 unt; 1 def)
% Number of atoms : 831 ( 0 equ)
% Maximal formula atoms : 17 ( 7 avg)
% Number of connectives : 1251 ( 536 ~; 575 |; 102 &)
% ( 8 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 10 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 276 ( 240 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) )
& ! [X2,X3] :
( ( member(X2,X0)
& member(X3,X0) )
=> ( apply(X1,X2,X3)
=> apply(X1,X3,X2) ) )
& ! [X2,X3,X4] :
( ( member(X2,X0)
& member(X3,X0)
& member(X4,X0) )
=> ( ( apply(X1,X2,X3)
& apply(X1,X3,X4) )
=> apply(X1,X2,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence) ).
fof(f16,axiom,
! [X0,X1] :
( pre_order(X0,X1)
<=> ( ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) )
& ! [X2,X3,X4] :
( ( member(X2,X1)
& member(X3,X1)
& member(X4,X1) )
=> ( ( apply(X0,X2,X3)
& apply(X0,X3,X4) )
=> apply(X0,X2,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pre_order) ).
fof(f17,conjecture,
! [X0,X1,X2] :
( ( pre_order(X1,X0)
& ! [X3,X4] :
( ( member(X3,X0)
& member(X4,X0) )
=> ( apply(X2,X3,X4)
<=> ( apply(X1,X3,X4)
& apply(X1,X4,X3) ) ) ) )
=> equivalence(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII11) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( ( pre_order(X1,X0)
& ! [X3,X4] :
( ( member(X3,X0)
& member(X4,X0) )
=> ( apply(X2,X3,X4)
<=> ( apply(X1,X3,X4)
& apply(X1,X4,X3) ) ) ) )
=> equivalence(X2,X0) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) )
& ! [X3,X4] :
( ( member(X3,X0)
& member(X4,X0) )
=> ( apply(X1,X3,X4)
=> apply(X1,X4,X3) ) )
& ! [X5,X6,X7] :
( ( member(X5,X0)
& member(X6,X0)
& member(X7,X0) )
=> ( ( apply(X1,X5,X6)
& apply(X1,X6,X7) )
=> apply(X1,X5,X7) ) ) ) ),
inference(rectify,[],[f14]) ).
fof(f20,plain,
! [X0,X1] :
( pre_order(X0,X1)
<=> ( ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) )
& ! [X3,X4,X5] :
( ( member(X3,X1)
& member(X4,X1)
& member(X5,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X4,X5) )
=> apply(X0,X3,X5) ) ) ) ),
inference(rectify,[],[f16]) ).
fof(f21,plain,
! [X0,X1] :
( pre_order(X0,X1)
=> ( ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) )
& ! [X3,X4,X5] :
( ( member(X3,X1)
& member(X4,X1)
& member(X5,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X4,X5) )
=> apply(X0,X3,X5) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) )
& ! [X3,X4] :
( ( member(X3,X0)
& member(X4,X0) )
=> ( apply(X1,X3,X4)
=> apply(X1,X4,X3) ) )
& ! [X5,X6,X7] :
( ( member(X5,X0)
& member(X6,X0)
& member(X7,X0) )
=> ( ( apply(X1,X5,X6)
& apply(X1,X6,X7) )
=> apply(X1,X5,X7) ) ) )
=> equivalence(X1,X0) ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f23,plain,
? [X0,X1,X2] :
( ~ equivalence(X2,X0)
& pre_order(X1,X0)
& ! [X3,X4] :
( ( apply(X2,X3,X4)
<=> ( apply(X1,X3,X4)
& apply(X1,X4,X3) ) )
| ~ member(X3,X0)
| ~ member(X4,X0) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f24,plain,
? [X0,X1,X2] :
( ~ equivalence(X2,X0)
& pre_order(X1,X0)
& ! [X3,X4] :
( ( apply(X2,X3,X4)
<=> ( apply(X1,X3,X4)
& apply(X1,X4,X3) ) )
| ~ member(X3,X0)
| ~ member(X4,X0) ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( equivalence(X1,X0)
| ? [X2] :
( ~ apply(X1,X2,X2)
& member(X2,X0) )
| ? [X3,X4] :
( ~ apply(X1,X4,X3)
& apply(X1,X3,X4)
& member(X3,X0)
& member(X4,X0) )
| ? [X5,X6,X7] :
( ~ apply(X1,X5,X7)
& apply(X1,X5,X6)
& apply(X1,X6,X7)
& member(X5,X0)
& member(X6,X0)
& member(X7,X0) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f26,plain,
! [X0,X1] :
( equivalence(X1,X0)
| ? [X2] :
( ~ apply(X1,X2,X2)
& member(X2,X0) )
| ? [X3,X4] :
( ~ apply(X1,X4,X3)
& apply(X1,X3,X4)
& member(X3,X0)
& member(X4,X0) )
| ? [X5,X6,X7] :
( ~ apply(X1,X5,X7)
& apply(X1,X5,X6)
& apply(X1,X6,X7)
& member(X5,X0)
& member(X6,X0)
& member(X7,X0) ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
& ! [X3,X4,X5] :
( apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X4,X5)
| ~ member(X3,X1)
| ~ member(X4,X1)
| ~ member(X5,X1) ) )
| ~ pre_order(X0,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f28,plain,
! [X0,X1] :
( ( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
& ! [X3,X4,X5] :
( apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X4,X5)
| ~ member(X3,X1)
| ~ member(X4,X1)
| ~ member(X5,X1) ) )
| ~ pre_order(X0,X1) ),
inference(flattening,[],[f27]) ).
fof(f29,definition,
! [X1,X0] :
( ? [X5,X6,X7] :
( ~ apply(X1,X5,X7)
& apply(X1,X5,X6)
& apply(X1,X6,X7)
& member(X5,X0)
& member(X6,X0)
& member(X7,X0) )
| ~ sP0(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f30,plain,
! [X0,X1] :
( equivalence(X1,X0)
| ? [X2] :
( ~ apply(X1,X2,X2)
& member(X2,X0) )
| ? [X3,X4] :
( ~ apply(X1,X4,X3)
& apply(X1,X3,X4)
& member(X3,X0)
& member(X4,X0) )
| sP0(X1,X0) ),
inference(definition_folding,[],[f26,f29]) ).
fof(f31,plain,
? [X0,X1,X2] :
( ~ equivalence(X2,X0)
& pre_order(X1,X0)
& ! [X3,X4] :
( ( ( apply(X2,X3,X4)
| ~ apply(X1,X3,X4)
| ~ apply(X1,X4,X3) )
& ( ( apply(X1,X3,X4)
& apply(X1,X4,X3) )
| ~ apply(X2,X3,X4) ) )
| ~ member(X3,X0)
| ~ member(X4,X0) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f32,plain,
? [X0,X1,X2] :
( ~ equivalence(X2,X0)
& pre_order(X1,X0)
& ! [X3,X4] :
( ( ( apply(X2,X3,X4)
| ~ apply(X1,X3,X4)
| ~ apply(X1,X4,X3) )
& ( ( apply(X1,X3,X4)
& apply(X1,X4,X3) )
| ~ apply(X2,X3,X4) ) )
| ~ member(X3,X0)
| ~ member(X4,X0) ) ),
inference(flattening,[],[f31]) ).
fof(f33,plain,
( ~ equivalence(sK3,sK1)
& pre_order(sK2,sK1)
& ! [X3,X4] :
( ( ( apply(sK3,X3,X4)
| ~ apply(sK2,X3,X4)
| ~ apply(sK2,X4,X3) )
& ( ( apply(sK2,X3,X4)
& apply(sK2,X4,X3) )
| ~ apply(sK3,X3,X4) ) )
| ~ member(X3,sK1)
| ~ member(X4,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f32]) ).
fof(f34,plain,
! [X1,X0] :
( ? [X5,X6,X7] :
( ~ apply(X1,X5,X7)
& apply(X1,X5,X6)
& apply(X1,X6,X7)
& member(X5,X0)
& member(X6,X0)
& member(X7,X0) )
| ~ sP0(X1,X0) ),
inference(nnf_transformation,[],[f29]) ).
fof(f35,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( ~ apply(X0,X2,X4)
& apply(X0,X2,X3)
& apply(X0,X3,X4)
& member(X2,X1)
& member(X3,X1)
& member(X4,X1) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ( ~ apply(X0,sK4(X0,X1),sK6(X0,X1))
& apply(X0,sK4(X0,X1),sK5(X0,X1))
& apply(X0,sK5(X0,X1),sK6(X0,X1))
& member(sK4(X0,X1),X1)
& member(sK5(X0,X1),X1)
& member(sK6(X0,X1),X1) )
| ~ sP0(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X2,sK4(X0,X1)),skolemize(X3,sK5(X0,X1)),skolemize(X4,sK6(X0,X1))],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( equivalence(X1,X0)
| ( ~ apply(X1,sK7(X0,X1),sK7(X0,X1))
& member(sK7(X0,X1),X0) )
| ( ~ apply(X1,sK9(X0,X1),sK8(X0,X1))
& apply(X1,sK8(X0,X1),sK9(X0,X1))
& member(sK8(X0,X1),X0)
& member(sK9(X0,X1),X0) )
| sP0(X1,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X2,sK7(X0,X1)),skolemize(X3,sK8(X0,X1)),skolemize(X4,sK9(X0,X1))],[f30]) ).
fof(f38,plain,
! [X3,X4] :
( apply(sK2,X4,X3)
| ~ apply(sK3,X3,X4)
| ~ member(X3,sK1)
| ~ member(X4,sK1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f39,plain,
! [X3,X4] :
( apply(sK2,X3,X4)
| ~ apply(sK3,X3,X4)
| ~ member(X3,sK1)
| ~ member(X4,sK1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f40,plain,
! [X3,X4] :
( apply(sK3,X3,X4)
| ~ apply(sK2,X3,X4)
| ~ apply(sK2,X4,X3)
| ~ member(X3,sK1)
| ~ member(X4,sK1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f41,plain,
pre_order(sK2,sK1),
inference(cnf_transformation,[],[f33]) ).
fof(f42,plain,
~ equivalence(sK3,sK1),
inference(cnf_transformation,[],[f33]) ).
fof(f43,plain,
! [X0,X1] :
( member(sK6(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f44,plain,
! [X0,X1] :
( member(sK5(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f45,plain,
! [X0,X1] :
( member(sK4(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f46,plain,
! [X0,X1] :
( apply(X0,sK5(X0,X1),sK6(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f47,plain,
! [X0,X1] :
( apply(X0,sK4(X0,X1),sK5(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f48,plain,
! [X0,X1] :
( ~ apply(X0,sK4(X0,X1),sK6(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f49,plain,
! [X0,X1] :
( member(sK9(X0,X1),X0)
| member(sK7(X0,X1),X0)
| equivalence(X1,X0)
| sP0(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f50,plain,
! [X0,X1] :
( member(sK8(X0,X1),X0)
| member(sK7(X0,X1),X0)
| equivalence(X1,X0)
| sP0(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f51,plain,
! [X0,X1] :
( apply(X1,sK8(X0,X1),sK9(X0,X1))
| member(sK7(X0,X1),X0)
| equivalence(X1,X0)
| sP0(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f52,plain,
! [X0,X1] :
( ~ apply(X1,sK9(X0,X1),sK8(X0,X1))
| member(sK7(X0,X1),X0)
| equivalence(X1,X0)
| sP0(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
! [X0,X1] :
( ~ apply(X1,sK7(X0,X1),sK7(X0,X1))
| equivalence(X1,X0)
| member(sK9(X0,X1),X0)
| sP0(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
! [X0,X1] :
( ~ apply(X1,sK7(X0,X1),sK7(X0,X1))
| equivalence(X1,X0)
| member(sK8(X0,X1),X0)
| sP0(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
! [X0,X1] :
( apply(X1,sK8(X0,X1),sK9(X0,X1))
| ~ apply(X1,sK7(X0,X1),sK7(X0,X1))
| equivalence(X1,X0)
| sP0(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f56,plain,
! [X0,X1] :
( ~ apply(X1,sK9(X0,X1),sK8(X0,X1))
| ~ apply(X1,sK7(X0,X1),sK7(X0,X1))
| equivalence(X1,X0)
| sP0(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f57,plain,
! [X3,X0,X1,X4,X5] :
( apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X4,X5)
| ~ member(X3,X1)
| ~ member(X4,X1)
| ~ member(X5,X1)
| ~ pre_order(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f58,plain,
! [X2,X0,X1] :
( apply(X0,X2,X2)
| ~ member(X2,X1)
| ~ pre_order(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f61,plain,
! [X0] :
( ~ apply(sK2,sK6(sK3,X0),sK4(sK3,X0))
| ~ apply(sK2,sK4(sK3,X0),sK6(sK3,X0))
| ~ sP0(sK3,X0)
| ~ member(sK4(sK3,X0),sK1)
| ~ member(sK6(sK3,X0),sK1) ),
inference(resolution,[],[f48,f40]) ).
fof(f75,plain,
! [X0] :
( ~ apply(sK2,sK9(X0,sK3),sK8(X0,sK3))
| equivalence(sK3,X0)
| sP0(sK3,X0)
| member(sK7(X0,sK3),X0)
| ~ apply(sK2,sK8(X0,sK3),sK9(X0,sK3))
| ~ member(sK9(X0,sK3),sK1)
| ~ member(sK8(X0,sK3),sK1) ),
inference(resolution,[],[f52,f40]) ).
fof(f80,plain,
! [X0] :
( equivalence(sK3,X0)
| member(sK9(X0,sK3),X0)
| sP0(sK3,X0)
| ~ apply(sK2,sK7(X0,sK3),sK7(X0,sK3))
| ~ apply(sK2,sK7(X0,sK3),sK7(X0,sK3))
| ~ member(sK7(X0,sK3),sK1)
| ~ member(sK7(X0,sK3),sK1) ),
inference(resolution,[],[f53,f40]) ).
fof(f82,plain,
! [X0] :
( ~ apply(sK2,sK7(X0,sK3),sK7(X0,sK3))
| member(sK9(X0,sK3),X0)
| sP0(sK3,X0)
| equivalence(sK3,X0)
| ~ member(sK7(X0,sK3),sK1) ),
inference(duplicate_literal_removal,[],[f80]) ).
fof(f87,plain,
! [X0,X1] :
( member(sK9(X0,sK3),X0)
| sP0(sK3,X0)
| equivalence(sK3,X0)
| ~ member(sK7(X0,sK3),sK1)
| ~ member(sK7(X0,sK3),X1)
| ~ pre_order(sK2,X1) ),
inference(resolution,[],[f82,f58]) ).
fof(f92,plain,
! [X0] :
( equivalence(sK3,X0)
| member(sK8(X0,sK3),X0)
| sP0(sK3,X0)
| ~ apply(sK2,sK7(X0,sK3),sK7(X0,sK3))
| ~ apply(sK2,sK7(X0,sK3),sK7(X0,sK3))
| ~ member(sK7(X0,sK3),sK1)
| ~ member(sK7(X0,sK3),sK1) ),
inference(resolution,[],[f54,f40]) ).
fof(f94,plain,
! [X0] :
( ~ apply(sK2,sK7(X0,sK3),sK7(X0,sK3))
| member(sK8(X0,sK3),X0)
| sP0(sK3,X0)
| equivalence(sK3,X0)
| ~ member(sK7(X0,sK3),sK1) ),
inference(duplicate_literal_removal,[],[f92]) ).
fof(f102,plain,
! [X0,X1] :
( member(sK8(X0,sK3),X0)
| sP0(sK3,X0)
| equivalence(sK3,X0)
| ~ member(sK7(X0,sK3),sK1)
| ~ member(sK7(X0,sK3),X1)
| ~ pre_order(sK2,X1) ),
inference(resolution,[],[f94,f58]) ).
fof(f107,plain,
! [X0] :
( ~ apply(sK3,sK7(X0,sK3),sK7(X0,sK3))
| equivalence(sK3,X0)
| sP0(sK3,X0)
| ~ apply(sK2,sK9(X0,sK3),sK8(X0,sK3))
| ~ apply(sK2,sK8(X0,sK3),sK9(X0,sK3))
| ~ member(sK9(X0,sK3),sK1)
| ~ member(sK8(X0,sK3),sK1) ),
inference(resolution,[],[f56,f40]) ).
fof(f115,plain,
! [X2,X0,X1] :
( ~ apply(sK2,sK4(sK3,X0),sK6(sK3,X0))
| ~ apply(sK2,X1,sK4(sK3,X0))
| ~ member(sK6(sK3,X0),X2)
| ~ member(X1,X2)
| ~ member(sK4(sK3,X0),X2)
| ~ pre_order(sK2,X2)
| ~ apply(sK2,sK6(sK3,X0),X1)
| ~ sP0(sK3,X0)
| ~ member(sK4(sK3,X0),sK1)
| ~ member(sK6(sK3,X0),sK1) ),
inference(resolution,[],[f57,f61]) ).
fof(f141,plain,
! [X0] :
( equivalence(sK3,X0)
| sP0(sK3,X0)
| member(sK7(X0,sK3),X0)
| ~ apply(sK2,sK8(X0,sK3),sK9(X0,sK3))
| ~ member(sK9(X0,sK3),sK1)
| ~ member(sK8(X0,sK3),sK1)
| ~ apply(sK3,sK8(X0,sK3),sK9(X0,sK3))
| ~ member(sK8(X0,sK3),sK1)
| ~ member(sK9(X0,sK3),sK1) ),
inference(resolution,[],[f75,f38]) ).
fof(f143,plain,
! [X0] :
( equivalence(sK3,X0)
| sP0(sK3,X0)
| member(sK7(X0,sK3),X0)
| ~ apply(sK2,sK8(X0,sK3),sK9(X0,sK3))
| ~ member(sK9(X0,sK3),sK1)
| ~ member(sK8(X0,sK3),sK1)
| ~ apply(sK3,sK8(X0,sK3),sK9(X0,sK3)) ),
inference(duplicate_literal_removal,[],[f141]) ).
fof(f145,plain,
! [X0] :
( ~ apply(sK2,sK8(X0,sK3),sK9(X0,sK3))
| sP0(sK3,X0)
| member(sK7(X0,sK3),X0)
| equivalence(sK3,X0)
| ~ member(sK9(X0,sK3),sK1)
| ~ member(sK8(X0,sK3),sK1) ),
inference(forward_subsumption_resolution,[],[f143,f51]) ).
fof(f146,plain,
! [X0] :
( sP0(sK3,X0)
| member(sK7(X0,sK3),X0)
| equivalence(sK3,X0)
| ~ member(sK9(X0,sK3),sK1)
| ~ member(sK8(X0,sK3),sK1)
| ~ apply(sK3,sK8(X0,sK3),sK9(X0,sK3))
| ~ member(sK8(X0,sK3),sK1)
| ~ member(sK9(X0,sK3),sK1) ),
inference(resolution,[],[f145,f39]) ).
fof(f150,plain,
! [X0] :
( sP0(sK3,X0)
| member(sK7(X0,sK3),X0)
| equivalence(sK3,X0)
| ~ member(sK9(X0,sK3),sK1)
| ~ member(sK8(X0,sK3),sK1)
| ~ apply(sK3,sK8(X0,sK3),sK9(X0,sK3)) ),
inference(duplicate_literal_removal,[],[f146]) ).
fof(f151,plain,
! [X0] :
( member(sK7(X0,sK3),X0)
| sP0(sK3,X0)
| equivalence(sK3,X0)
| ~ member(sK9(X0,sK3),sK1)
| ~ member(sK8(X0,sK3),sK1) ),
inference(forward_subsumption_resolution,[],[f150,f51]) ).
fof(f152,plain,
! [X0] :
( equivalence(sK3,X0)
| sP0(sK3,X0)
| ~ apply(sK2,sK9(X0,sK3),sK8(X0,sK3))
| ~ apply(sK2,sK8(X0,sK3),sK9(X0,sK3))
| ~ member(sK9(X0,sK3),sK1)
| ~ member(sK8(X0,sK3),sK1)
| ~ apply(sK2,sK7(X0,sK3),sK7(X0,sK3))
| ~ apply(sK2,sK7(X0,sK3),sK7(X0,sK3))
| ~ member(sK7(X0,sK3),sK1)
| ~ member(sK7(X0,sK3),sK1) ),
inference(resolution,[],[f107,f40]) ).
fof(f156,plain,
! [X0] :
( ~ apply(sK2,sK9(X0,sK3),sK8(X0,sK3))
| sP0(sK3,X0)
| equivalence(sK3,X0)
| ~ apply(sK2,sK8(X0,sK3),sK9(X0,sK3))
| ~ member(sK9(X0,sK3),sK1)
| ~ member(sK8(X0,sK3),sK1)
| ~ apply(sK2,sK7(X0,sK3),sK7(X0,sK3))
| ~ member(sK7(X0,sK3),sK1) ),
inference(duplicate_literal_removal,[],[f152]) ).
fof(f255,plain,
! [X0] :
( sP0(sK3,X0)
| equivalence(sK3,X0)
| ~ apply(sK2,sK8(X0,sK3),sK9(X0,sK3))
| ~ member(sK9(X0,sK3),sK1)
| ~ member(sK8(X0,sK3),sK1)
| ~ apply(sK2,sK7(X0,sK3),sK7(X0,sK3))
| ~ member(sK7(X0,sK3),sK1)
| ~ apply(sK3,sK8(X0,sK3),sK9(X0,sK3))
| ~ member(sK8(X0,sK3),sK1)
| ~ member(sK9(X0,sK3),sK1) ),
inference(resolution,[],[f156,f38]) ).
fof(f257,plain,
! [X0] :
( sP0(sK3,X0)
| equivalence(sK3,X0)
| ~ apply(sK2,sK8(X0,sK3),sK9(X0,sK3))
| ~ member(sK9(X0,sK3),sK1)
| ~ member(sK8(X0,sK3),sK1)
| ~ apply(sK2,sK7(X0,sK3),sK7(X0,sK3))
| ~ member(sK7(X0,sK3),sK1)
| ~ apply(sK3,sK8(X0,sK3),sK9(X0,sK3)) ),
inference(duplicate_literal_removal,[],[f255]) ).
fof(f259,plain,
! [X0] :
( ~ apply(sK3,sK8(X0,sK3),sK9(X0,sK3))
| equivalence(sK3,X0)
| ~ member(sK9(X0,sK3),sK1)
| ~ member(sK8(X0,sK3),sK1)
| ~ apply(sK2,sK7(X0,sK3),sK7(X0,sK3))
| ~ member(sK7(X0,sK3),sK1)
| sP0(sK3,X0) ),
inference(forward_subsumption_resolution,[],[f257,f39]) ).
fof(f294,plain,
! [X0] :
( equivalence(sK3,X0)
| ~ member(sK9(X0,sK3),sK1)
| ~ member(sK8(X0,sK3),sK1)
| ~ apply(sK2,sK7(X0,sK3),sK7(X0,sK3))
| ~ member(sK7(X0,sK3),sK1)
| sP0(sK3,X0)
| ~ apply(sK3,sK7(X0,sK3),sK7(X0,sK3))
| equivalence(sK3,X0)
| sP0(sK3,X0) ),
inference(resolution,[],[f259,f55]) ).
fof(f300,plain,
! [X0] :
( ~ apply(sK3,sK7(X0,sK3),sK7(X0,sK3))
| ~ member(sK9(X0,sK3),sK1)
| ~ member(sK8(X0,sK3),sK1)
| ~ apply(sK2,sK7(X0,sK3),sK7(X0,sK3))
| ~ member(sK7(X0,sK3),sK1)
| sP0(sK3,X0)
| equivalence(sK3,X0) ),
inference(duplicate_literal_removal,[],[f294]) ).
fof(f309,plain,
! [X0] :
( ~ member(sK9(X0,sK3),sK1)
| ~ member(sK8(X0,sK3),sK1)
| ~ apply(sK2,sK7(X0,sK3),sK7(X0,sK3))
| ~ member(sK7(X0,sK3),sK1)
| sP0(sK3,X0)
| equivalence(sK3,X0)
| ~ apply(sK2,sK7(X0,sK3),sK7(X0,sK3))
| ~ apply(sK2,sK7(X0,sK3),sK7(X0,sK3))
| ~ member(sK7(X0,sK3),sK1)
| ~ member(sK7(X0,sK3),sK1) ),
inference(resolution,[],[f300,f40]) ).
fof(f313,plain,
! [X0] :
( ~ apply(sK2,sK7(X0,sK3),sK7(X0,sK3))
| ~ member(sK8(X0,sK3),sK1)
| ~ member(sK9(X0,sK3),sK1)
| ~ member(sK7(X0,sK3),sK1)
| sP0(sK3,X0)
| equivalence(sK3,X0) ),
inference(duplicate_literal_removal,[],[f309]) ).
fof(f316,plain,
! [X0,X1] :
( ~ member(sK9(X0,sK3),sK1)
| ~ member(sK8(X0,sK3),sK1)
| ~ member(sK7(X0,sK3),sK1)
| sP0(sK3,X0)
| equivalence(sK3,X0)
| ~ member(sK7(X0,sK3),X1)
| ~ pre_order(sK2,X1) ),
inference(resolution,[],[f313,f58]) ).
fof(f323,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(sK2,sK6(sK3,X1),X0)
| ~ member(sK6(sK3,X1),X2)
| ~ member(X0,X2)
| ~ member(sK4(sK3,X1),X2)
| ~ pre_order(sK2,X2)
| ~ apply(sK2,X0,sK4(sK3,X1))
| ~ sP0(sK3,X1)
| ~ member(sK4(sK3,X1),sK1)
| ~ member(sK6(sK3,X1),sK1)
| ~ apply(sK2,sK4(sK3,X1),X3)
| ~ apply(sK2,X3,sK6(sK3,X1))
| ~ member(sK4(sK3,X1),X4)
| ~ member(X3,X4)
| ~ member(sK6(sK3,X1),X4)
| ~ pre_order(sK2,X4) ),
inference(resolution,[],[f115,f57]) ).
fof(f326,plain,
! [X0,X1] :
( ~ member(sK8(sK1,sK3),sK1)
| ~ member(sK7(sK1,sK3),sK1)
| sP0(sK3,sK1)
| equivalence(sK3,sK1)
| ~ member(sK7(sK1,sK3),X0)
| ~ pre_order(sK2,X0)
| sP0(sK3,sK1)
| equivalence(sK3,sK1)
| ~ member(sK7(sK1,sK3),sK1)
| ~ member(sK7(sK1,sK3),X1)
| ~ pre_order(sK2,X1) ),
inference(resolution,[],[f316,f87]) ).
fof(f331,plain,
! [X0,X1] :
( ~ member(sK8(sK1,sK3),sK1)
| ~ member(sK7(sK1,sK3),sK1)
| sP0(sK3,sK1)
| equivalence(sK3,sK1)
| ~ member(sK7(sK1,sK3),X0)
| ~ pre_order(sK2,X0)
| ~ member(sK7(sK1,sK3),X1)
| ~ pre_order(sK2,X1) ),
inference(duplicate_literal_removal,[],[f326]) ).
fof(f332,plain,
! [X0,X1] :
( ~ member(sK7(sK1,sK3),sK1)
| sP0(sK3,sK1)
| equivalence(sK3,sK1)
| ~ member(sK7(sK1,sK3),X0)
| ~ pre_order(sK2,X0)
| ~ member(sK7(sK1,sK3),X1)
| ~ pre_order(sK2,X1) ),
inference(forward_subsumption_resolution,[],[f331,f102]) ).
fof(f333,plain,
! [X0,X1] :
( ~ member(sK7(sK1,sK3),sK1)
| sP0(sK3,sK1)
| ~ member(sK7(sK1,sK3),X0)
| ~ pre_order(sK2,X0)
| ~ member(sK7(sK1,sK3),X1)
| ~ pre_order(sK2,X1) ),
inference(forward_subsumption_resolution,[],[f332,f42]) ).
fof(f337,plain,
! [X0] :
( ~ member(sK7(sK1,sK3),sK1)
| sP0(sK3,sK1)
| ~ member(sK7(sK1,sK3),X0)
| ~ pre_order(sK2,X0)
| ~ pre_order(sK2,sK1) ),
inference(factoring,[],[f333]) ).
fof(f340,plain,
! [X0] :
( ~ member(sK7(sK1,sK3),sK1)
| sP0(sK3,sK1)
| ~ member(sK7(sK1,sK3),X0)
| ~ pre_order(sK2,X0) ),
inference(forward_subsumption_resolution,[],[f337,f41]) ).
fof(f350,plain,
( ~ member(sK7(sK1,sK3),sK1)
| sP0(sK3,sK1)
| ~ pre_order(sK2,sK1) ),
inference(factoring,[],[f340]) ).
fof(f353,plain,
( ~ member(sK7(sK1,sK3),sK1)
| sP0(sK3,sK1) ),
inference(forward_subsumption_resolution,[],[f350,f41]) ).
fof(f361,plain,
( sP0(sK3,sK1)
| sP0(sK3,sK1)
| equivalence(sK3,sK1)
| ~ member(sK9(sK1,sK3),sK1)
| ~ member(sK8(sK1,sK3),sK1) ),
inference(resolution,[],[f353,f151]) ).
fof(f362,plain,
( sP0(sK3,sK1)
| equivalence(sK3,sK1)
| ~ member(sK9(sK1,sK3),sK1)
| ~ member(sK8(sK1,sK3),sK1) ),
inference(duplicate_literal_removal,[],[f361]) ).
fof(f364,plain,
( ~ member(sK9(sK1,sK3),sK1)
| sP0(sK3,sK1)
| ~ member(sK8(sK1,sK3),sK1) ),
inference(forward_subsumption_resolution,[],[f362,f42]) ).
fof(f367,plain,
( sP0(sK3,sK1)
| ~ member(sK8(sK1,sK3),sK1)
| member(sK7(sK1,sK3),sK1)
| equivalence(sK3,sK1)
| sP0(sK3,sK1) ),
inference(resolution,[],[f364,f49]) ).
fof(f368,plain,
( sP0(sK3,sK1)
| ~ member(sK8(sK1,sK3),sK1)
| member(sK7(sK1,sK3),sK1)
| equivalence(sK3,sK1) ),
inference(duplicate_literal_removal,[],[f367]) ).
fof(f371,plain,
( sP0(sK3,sK1)
| ~ member(sK8(sK1,sK3),sK1)
| equivalence(sK3,sK1) ),
inference(forward_subsumption_resolution,[],[f368,f353]) ).
fof(f372,plain,
( ~ member(sK8(sK1,sK3),sK1)
| sP0(sK3,sK1) ),
inference(forward_subsumption_resolution,[],[f371,f42]) ).
fof(f382,plain,
( sP0(sK3,sK1)
| member(sK7(sK1,sK3),sK1)
| equivalence(sK3,sK1)
| sP0(sK3,sK1) ),
inference(resolution,[],[f372,f50]) ).
fof(f383,plain,
( sP0(sK3,sK1)
| member(sK7(sK1,sK3),sK1)
| equivalence(sK3,sK1) ),
inference(duplicate_literal_removal,[],[f382]) ).
fof(f386,plain,
( sP0(sK3,sK1)
| equivalence(sK3,sK1) ),
inference(forward_subsumption_resolution,[],[f383,f353]) ).
fof(f387,plain,
sP0(sK3,sK1),
inference(forward_subsumption_resolution,[],[f386,f42]) ).
fof(f826,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(sK6(sK3,X0),X1)
| ~ member(X2,X1)
| ~ member(sK4(sK3,X0),X1)
| ~ pre_order(sK2,X1)
| ~ apply(sK2,X2,sK4(sK3,X0))
| ~ sP0(sK3,X0)
| ~ member(sK4(sK3,X0),sK1)
| ~ member(sK6(sK3,X0),sK1)
| ~ apply(sK2,sK4(sK3,X0),X3)
| ~ apply(sK2,X3,sK6(sK3,X0))
| ~ member(sK4(sK3,X0),X4)
| ~ member(X3,X4)
| ~ member(sK6(sK3,X0),X4)
| ~ pre_order(sK2,X4)
| ~ apply(sK3,X2,sK6(sK3,X0))
| ~ member(X2,sK1)
| ~ member(sK6(sK3,X0),sK1) ),
inference(resolution,[],[f323,f38]) ).
fof(f832,plain,
! [X2,X3,X0,X1,X4] :
( ~ apply(sK3,X2,sK6(sK3,X0))
| ~ member(X2,X1)
| ~ member(sK4(sK3,X0),X1)
| ~ pre_order(sK2,X1)
| ~ apply(sK2,X2,sK4(sK3,X0))
| ~ sP0(sK3,X0)
| ~ member(sK4(sK3,X0),sK1)
| ~ member(sK6(sK3,X0),sK1)
| ~ apply(sK2,sK4(sK3,X0),X3)
| ~ apply(sK2,X3,sK6(sK3,X0))
| ~ member(sK4(sK3,X0),X4)
| ~ member(X3,X4)
| ~ member(sK6(sK3,X0),X4)
| ~ pre_order(sK2,X4)
| ~ member(sK6(sK3,X0),X1)
| ~ member(X2,sK1) ),
inference(duplicate_literal_removal,[],[f826]) ).
fof(f1103,plain,
! [X2,X3,X0,X1] :
( ~ member(sK5(sK3,X0),X1)
| ~ member(sK4(sK3,X0),X1)
| ~ pre_order(sK2,X1)
| ~ apply(sK2,sK5(sK3,X0),sK4(sK3,X0))
| ~ sP0(sK3,X0)
| ~ member(sK4(sK3,X0),sK1)
| ~ member(sK6(sK3,X0),sK1)
| ~ apply(sK2,sK4(sK3,X0),X2)
| ~ apply(sK2,X2,sK6(sK3,X0))
| ~ member(sK4(sK3,X0),X3)
| ~ member(X2,X3)
| ~ member(sK6(sK3,X0),X3)
| ~ pre_order(sK2,X3)
| ~ member(sK6(sK3,X0),X1)
| ~ member(sK5(sK3,X0),sK1)
| ~ sP0(sK3,X0) ),
inference(resolution,[],[f832,f46]) ).
fof(f1109,plain,
! [X2,X3,X0,X1] :
( ~ apply(sK2,sK5(sK3,X0),sK4(sK3,X0))
| ~ member(sK4(sK3,X0),X1)
| ~ pre_order(sK2,X1)
| ~ member(sK5(sK3,X0),X1)
| ~ sP0(sK3,X0)
| ~ member(sK4(sK3,X0),sK1)
| ~ member(sK6(sK3,X0),sK1)
| ~ apply(sK2,sK4(sK3,X0),X2)
| ~ apply(sK2,X2,sK6(sK3,X0))
| ~ member(sK4(sK3,X0),X3)
| ~ member(X2,X3)
| ~ member(sK6(sK3,X0),X3)
| ~ pre_order(sK2,X3)
| ~ member(sK6(sK3,X0),X1)
| ~ member(sK5(sK3,X0),sK1) ),
inference(duplicate_literal_removal,[],[f1103]) ).
fof(f1216,plain,
! [X2,X3,X0,X1] :
( ~ member(sK4(sK3,X0),X1)
| ~ pre_order(sK2,X1)
| ~ member(sK5(sK3,X0),X1)
| ~ sP0(sK3,X0)
| ~ member(sK4(sK3,X0),sK1)
| ~ member(sK6(sK3,X0),sK1)
| ~ apply(sK2,sK4(sK3,X0),X2)
| ~ apply(sK2,X2,sK6(sK3,X0))
| ~ member(sK4(sK3,X0),X3)
| ~ member(X2,X3)
| ~ member(sK6(sK3,X0),X3)
| ~ pre_order(sK2,X3)
| ~ member(sK6(sK3,X0),X1)
| ~ member(sK5(sK3,X0),sK1)
| ~ apply(sK3,sK4(sK3,X0),sK5(sK3,X0))
| ~ member(sK4(sK3,X0),sK1)
| ~ member(sK5(sK3,X0),sK1) ),
inference(resolution,[],[f1109,f38]) ).
fof(f1218,plain,
! [X2,X3,X0,X1] :
( ~ member(sK4(sK3,X0),X1)
| ~ pre_order(sK2,X1)
| ~ member(sK5(sK3,X0),X1)
| ~ sP0(sK3,X0)
| ~ member(sK4(sK3,X0),sK1)
| ~ member(sK6(sK3,X0),sK1)
| ~ apply(sK2,sK4(sK3,X0),X2)
| ~ apply(sK2,X2,sK6(sK3,X0))
| ~ member(sK4(sK3,X0),X3)
| ~ member(X2,X3)
| ~ member(sK6(sK3,X0),X3)
| ~ pre_order(sK2,X3)
| ~ member(sK6(sK3,X0),X1)
| ~ member(sK5(sK3,X0),sK1)
| ~ apply(sK3,sK4(sK3,X0),sK5(sK3,X0)) ),
inference(duplicate_literal_removal,[],[f1216]) ).
fof(f1220,plain,
! [X2,X3,X0,X1] :
( ~ apply(sK2,sK4(sK3,X0),X2)
| ~ pre_order(sK2,X1)
| ~ member(sK5(sK3,X0),X1)
| ~ sP0(sK3,X0)
| ~ member(sK4(sK3,X0),sK1)
| ~ member(sK6(sK3,X0),sK1)
| ~ member(sK4(sK3,X0),X1)
| ~ apply(sK2,X2,sK6(sK3,X0))
| ~ member(sK4(sK3,X0),X3)
| ~ member(X2,X3)
| ~ member(sK6(sK3,X0),X3)
| ~ pre_order(sK2,X3)
| ~ member(sK6(sK3,X0),X1)
| ~ member(sK5(sK3,X0),sK1) ),
inference(forward_subsumption_resolution,[],[f1218,f47]) ).
fof(f1230,plain,
! [X2,X3,X0,X1] :
( ~ pre_order(sK2,X0)
| ~ member(sK5(sK3,X1),X0)
| ~ sP0(sK3,X1)
| ~ member(sK4(sK3,X1),sK1)
| ~ member(sK6(sK3,X1),sK1)
| ~ member(sK4(sK3,X1),X0)
| ~ apply(sK2,X2,sK6(sK3,X1))
| ~ member(sK4(sK3,X1),X3)
| ~ member(X2,X3)
| ~ member(sK6(sK3,X1),X3)
| ~ pre_order(sK2,X3)
| ~ member(sK6(sK3,X1),X0)
| ~ member(sK5(sK3,X1),sK1)
| ~ apply(sK3,sK4(sK3,X1),X2)
| ~ member(sK4(sK3,X1),sK1)
| ~ member(X2,sK1) ),
inference(resolution,[],[f1220,f39]) ).
fof(f1236,plain,
! [X2,X3,X0,X1] :
( ~ apply(sK3,sK4(sK3,X1),X2)
| ~ member(sK5(sK3,X1),X0)
| ~ sP0(sK3,X1)
| ~ member(sK4(sK3,X1),sK1)
| ~ member(sK6(sK3,X1),sK1)
| ~ member(sK4(sK3,X1),X0)
| ~ apply(sK2,X2,sK6(sK3,X1))
| ~ member(sK4(sK3,X1),X3)
| ~ member(X2,X3)
| ~ member(sK6(sK3,X1),X3)
| ~ pre_order(sK2,X3)
| ~ member(sK6(sK3,X1),X0)
| ~ member(sK5(sK3,X1),sK1)
| ~ pre_order(sK2,X0)
| ~ member(X2,sK1) ),
inference(duplicate_literal_removal,[],[f1230]) ).
fof(f1271,plain,
! [X2,X0,X1] :
( ~ member(sK5(sK3,X0),X1)
| ~ sP0(sK3,X0)
| ~ member(sK4(sK3,X0),sK1)
| ~ member(sK6(sK3,X0),sK1)
| ~ member(sK4(sK3,X0),X1)
| ~ apply(sK2,sK5(sK3,X0),sK6(sK3,X0))
| ~ member(sK4(sK3,X0),X2)
| ~ member(sK5(sK3,X0),X2)
| ~ member(sK6(sK3,X0),X2)
| ~ pre_order(sK2,X2)
| ~ member(sK6(sK3,X0),X1)
| ~ member(sK5(sK3,X0),sK1)
| ~ pre_order(sK2,X1)
| ~ member(sK5(sK3,X0),sK1)
| ~ sP0(sK3,X0) ),
inference(resolution,[],[f1236,f47]) ).
fof(f1272,plain,
! [X2,X0,X1] :
( ~ apply(sK2,sK5(sK3,X0),sK6(sK3,X0))
| ~ sP0(sK3,X0)
| ~ member(sK4(sK3,X0),sK1)
| ~ member(sK6(sK3,X0),sK1)
| ~ member(sK4(sK3,X0),X1)
| ~ member(sK5(sK3,X0),X1)
| ~ member(sK4(sK3,X0),X2)
| ~ member(sK5(sK3,X0),X2)
| ~ member(sK6(sK3,X0),X2)
| ~ pre_order(sK2,X2)
| ~ member(sK6(sK3,X0),X1)
| ~ member(sK5(sK3,X0),sK1)
| ~ pre_order(sK2,X1) ),
inference(duplicate_literal_removal,[],[f1271]) ).
fof(f1282,plain,
! [X2,X0,X1] :
( ~ sP0(sK3,X0)
| ~ member(sK4(sK3,X0),sK1)
| ~ member(sK6(sK3,X0),sK1)
| ~ member(sK4(sK3,X0),X1)
| ~ member(sK5(sK3,X0),X1)
| ~ member(sK4(sK3,X0),X2)
| ~ member(sK5(sK3,X0),X2)
| ~ member(sK6(sK3,X0),X2)
| ~ pre_order(sK2,X2)
| ~ member(sK6(sK3,X0),X1)
| ~ member(sK5(sK3,X0),sK1)
| ~ pre_order(sK2,X1)
| ~ apply(sK3,sK5(sK3,X0),sK6(sK3,X0))
| ~ member(sK5(sK3,X0),sK1)
| ~ member(sK6(sK3,X0),sK1) ),
inference(resolution,[],[f1272,f39]) ).
fof(f1286,plain,
! [X2,X0,X1] :
( ~ sP0(sK3,X0)
| ~ member(sK4(sK3,X0),sK1)
| ~ member(sK6(sK3,X0),sK1)
| ~ member(sK4(sK3,X0),X1)
| ~ member(sK5(sK3,X0),X1)
| ~ member(sK4(sK3,X0),X2)
| ~ member(sK5(sK3,X0),X2)
| ~ member(sK6(sK3,X0),X2)
| ~ pre_order(sK2,X2)
| ~ member(sK6(sK3,X0),X1)
| ~ member(sK5(sK3,X0),sK1)
| ~ pre_order(sK2,X1)
| ~ apply(sK3,sK5(sK3,X0),sK6(sK3,X0)) ),
inference(duplicate_literal_removal,[],[f1282]) ).
fof(f1287,plain,
! [X2,X0,X1] :
( ~ member(sK6(sK3,X0),sK1)
| ~ member(sK4(sK3,X0),sK1)
| ~ sP0(sK3,X0)
| ~ member(sK4(sK3,X0),X1)
| ~ member(sK5(sK3,X0),X1)
| ~ member(sK4(sK3,X0),X2)
| ~ member(sK5(sK3,X0),X2)
| ~ member(sK6(sK3,X0),X2)
| ~ pre_order(sK2,X2)
| ~ member(sK6(sK3,X0),X1)
| ~ member(sK5(sK3,X0),sK1)
| ~ pre_order(sK2,X1) ),
inference(forward_subsumption_resolution,[],[f1286,f46]) ).
fof(f1295,plain,
! [X0,X1] :
( ~ member(sK6(sK3,X0),sK1)
| ~ member(sK4(sK3,X0),sK1)
| ~ sP0(sK3,X0)
| ~ member(sK4(sK3,X0),sK1)
| ~ member(sK5(sK3,X0),sK1)
| ~ member(sK4(sK3,X0),X1)
| ~ member(sK5(sK3,X0),X1)
| ~ member(sK6(sK3,X0),X1)
| ~ pre_order(sK2,X1)
| ~ member(sK5(sK3,X0),sK1)
| ~ pre_order(sK2,sK1) ),
inference(factoring,[],[f1287]) ).
fof(f1296,plain,
! [X0,X1] :
( ~ member(sK6(sK3,X0),sK1)
| ~ member(sK4(sK3,X0),sK1)
| ~ sP0(sK3,X0)
| ~ member(sK5(sK3,X0),sK1)
| ~ member(sK4(sK3,X0),X1)
| ~ member(sK5(sK3,X0),X1)
| ~ member(sK6(sK3,X0),X1)
| ~ pre_order(sK2,X1)
| ~ pre_order(sK2,sK1) ),
inference(duplicate_literal_removal,[],[f1295]) ).
fof(f1299,plain,
! [X0,X1] :
( ~ member(sK6(sK3,X0),sK1)
| ~ member(sK4(sK3,X0),sK1)
| ~ sP0(sK3,X0)
| ~ member(sK5(sK3,X0),sK1)
| ~ member(sK4(sK3,X0),X1)
| ~ member(sK5(sK3,X0),X1)
| ~ member(sK6(sK3,X0),X1)
| ~ pre_order(sK2,X1) ),
inference(forward_subsumption_resolution,[],[f1296,f41]) ).
fof(f1304,plain,
! [X0] :
( ~ member(sK6(sK3,X0),sK1)
| ~ member(sK4(sK3,X0),sK1)
| ~ sP0(sK3,X0)
| ~ member(sK5(sK3,X0),sK1)
| ~ member(sK4(sK3,X0),sK1)
| ~ member(sK5(sK3,X0),sK1)
| ~ pre_order(sK2,sK1) ),
inference(factoring,[],[f1299]) ).
fof(f1305,plain,
! [X0] :
( ~ member(sK6(sK3,X0),sK1)
| ~ member(sK4(sK3,X0),sK1)
| ~ sP0(sK3,X0)
| ~ member(sK5(sK3,X0),sK1)
| ~ pre_order(sK2,sK1) ),
inference(duplicate_literal_removal,[],[f1304]) ).
fof(f1307,plain,
! [X0] :
( ~ member(sK6(sK3,X0),sK1)
| ~ member(sK4(sK3,X0),sK1)
| ~ sP0(sK3,X0)
| ~ member(sK5(sK3,X0),sK1) ),
inference(forward_subsumption_resolution,[],[f1305,f41]) ).
fof(f1315,plain,
( ~ member(sK4(sK3,sK1),sK1)
| ~ sP0(sK3,sK1)
| ~ member(sK5(sK3,sK1),sK1)
| ~ sP0(sK3,sK1) ),
inference(resolution,[],[f1307,f43]) ).
fof(f1316,plain,
( ~ member(sK4(sK3,sK1),sK1)
| ~ sP0(sK3,sK1)
| ~ member(sK5(sK3,sK1),sK1) ),
inference(duplicate_literal_removal,[],[f1315]) ).
fof(f1317,plain,
( ~ sP0(sK3,sK1)
| ~ member(sK5(sK3,sK1),sK1) ),
inference(forward_subsumption_resolution,[],[f1316,f45]) ).
fof(f1318,plain,
~ member(sK5(sK3,sK1),sK1),
inference(forward_subsumption_resolution,[],[f1317,f387]) ).
fof(f1326,plain,
~ sP0(sK3,sK1),
inference(resolution,[],[f1318,f44]) ).
fof(f1327,plain,
$false,
inference(forward_subsumption_resolution,[],[f1326,f387]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET775+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.63 % Computer : n005.cluster.edu
% 0.17/0.63 % Model : x86_64 x86_64
% 0.17/0.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.63 % Memory : 8046.5625MB
% 0.17/0.63 % OS : Linux 6.8.0-71-generic
% 0.17/0.63 % CPULimit : 300
% 0.17/0.63 % WCLimit : 300
% 0.17/0.63 % DateTime : Mon Sep 28 02:45:33 UTC 2026
% 0.17/0.63 % CPUTime :
% 0.21/0.63 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.68 Running first-order theorem proving
% 0.21/0.68 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.21/1.74 % (381985)Detected formulas, will run a generic FOF schedule.
% 1.21/1.74 % (381996)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3915548920:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.21/1.74 % (381996)First to succeed.
% 1.21/1.74 % (381996)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-381985"
% 1.21/1.74 % (381994)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4200864850:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.21/1.74 % (381995)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1501706799:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.21/1.74 % (381992)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2897416210:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.21/1.74 % (381993)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=511626575:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.21/1.74 % (381997)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1779069738:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.21/1.74 % (381995)Also succeeded, but the first one will report.
% 1.21/1.74 % (381998)dis-21_1_sil=8000:lcm=predicate:random_seed=3912550183:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 1.21/1.74 % (381998)Also succeeded, but the first one will report.
% 1.21/1.74 % (381997)Instruction limit reached!
% 1.21/1.74 % (381997)------------------------------
% 1.21/1.74 % (381997)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.21/1.74 % (381997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.21/1.74 % (381997)CaDiCaL version: 2.1.3
% 1.21/1.74 % (381997)Termination reason: Instruction limit
% 1.21/1.74 % (381997)Termination phase: Saturation
% 1.21/1.74 % (381997)Time elapsed: 0.141 s
% 1.21/1.74 % (381997)Peak memory usage: 89 MB
% 1.21/1.74 % (381997)Instructions burned: 139 (million)
% 1.21/1.74 % (381996)Refutation found. Thanks to Tanya!
% 1.21/1.74 % SZS status Theorem for theBenchmark
% 1.21/1.74 % SZS output start Proof for theBenchmark
% See solution above
% 4.37/2.03 % (381996)------------------------------
% 4.37/2.03 % (381996)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.37/2.03 % (381996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.37/2.03 % (381996)CaDiCaL version: 2.1.3
% 4.37/2.03 % (381996)Termination reason: Refutation
% 4.37/2.03 % (381996)Time elapsed: 0.036 s
% 4.37/2.03 % (381996)Peak memory usage: 89 MB
% 4.37/2.03 % (381996)Instructions burned: 104 (million)
% 4.37/2.03 % (381996)------------------------------
% 4.37/2.03 % (381996)------------------------------
% 4.37/2.03 % (381985)Success in time 0.509 s
% 4.37/2.03 % Vampire exiting
%------------------------------------------------------------------------------