%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN723+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 : Thu Sep 24 03:17:10 PM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 69
% Syntax : Number of formulae : 490 ( 1 unt; 68 def)
% Number of atoms : 1618 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 1909 ( 781 ~; 861 |; 78 &)
% ( 186 <=>; 0 =>; 0 <=; 3 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 73 ( 72 usr; 65 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 23 con; 0-1 aty)
% Number of variables : 453 ( 361 !; 92 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X] :
! [Y] :
( p(X)
<=> p(Y) )
<=> ( ( ? [X] : q(X)
<=> ! [Y] : r(Y) )
<=> ( ( ? [X] :
! [Y] :
( q(X)
<=> q(Y) )
<=> ( ? [X] : r(X)
<=> ! [Y] : s(Y) ) )
<=> ( ? [X] :
! [Y] :
( r(X)
<=> r(Y) )
<=> ( ( ? [X] : s(X)
<=> ! [Y] : p(Y) )
<=> ( ? [X] :
! [Y] :
( s(X)
<=> s(Y) )
<=> ( ? [X] : p(X)
<=> ! [Y] : q(Y) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ? [X] :
! [Y] :
( p(X)
<=> p(Y) )
<=> ( ( ? [X] : q(X)
<=> ! [Y] : r(Y) )
<=> ( ( ? [X] :
! [Y] :
( q(X)
<=> q(Y) )
<=> ( ? [X] : r(X)
<=> ! [Y] : s(Y) ) )
<=> ( ? [X] :
! [Y] :
( r(X)
<=> r(Y) )
<=> ( ( ? [X] : s(X)
<=> ! [Y] : p(Y) )
<=> ( ? [X] :
! [Y] :
( s(X)
<=> s(Y) )
<=> ( ? [X] : p(X)
<=> ! [Y] : q(Y) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ? [X] :
! [Y] :
( p(X)
<=> p(Y) )
<~> ( ( ? [X] : q(X)
<=> ! [Y] : r(Y) )
<=> ( ( ? [X] :
! [Y] :
( q(X)
<=> q(Y) )
<=> ( ? [X] : r(X)
<=> ! [Y] : s(Y) ) )
<=> ( ? [X] :
! [Y] :
( r(X)
<=> r(Y) )
<=> ( ( ? [X] : s(X)
<=> ! [Y] : p(Y) )
<=> ( ? [X] :
! [Y] :
( s(X)
<=> s(Y) )
<=> ( ? [X] : p(X)
<=> ! [Y] : q(Y) ) ) ) ) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [X,Y] :
( sP0_prd(Y,X)
<=> ( p(X)
<=> p(Y) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,definition,
( sP1_prd
<=> ( ? [X] : q(X)
<=> ! [Y] : r(Y) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f6,plain,
( ? [X] :
! [Y] : sP0_prd(Y,X)
<~> ( sP1_prd
<=> ( ( ? [X] :
! [Y] :
( q(X)
<=> q(Y) )
<=> ( ? [X] : r(X)
<=> ! [Y] : s(Y) ) )
<=> ( ? [X] :
! [Y] :
( r(X)
<=> r(Y) )
<=> ( ( ? [X] : s(X)
<=> ! [Y] : p(Y) )
<=> ( ? [X] :
! [Y] :
( s(X)
<=> s(Y) )
<=> ( ? [X] : p(X)
<=> ! [Y] : q(Y) ) ) ) ) ) ) ),
inference(formula_renaming,[status(thm)],[f3,f5,f4]) ).
fof(f7,definition,
( sP2_prd
<=> ( ( ? [X] :
! [Y] :
( q(X)
<=> q(Y) )
<=> ( ? [X] : r(X)
<=> ! [Y] : s(Y) ) )
<=> ( ? [X] :
! [Y] :
( r(X)
<=> r(Y) )
<=> ( ( ? [X] : s(X)
<=> ! [Y] : p(Y) )
<=> ( ? [X] :
! [Y] :
( s(X)
<=> s(Y) )
<=> ( ? [X] : p(X)
<=> ! [Y] : q(Y) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f8,plain,
( ? [X] :
! [Y] : sP0_prd(Y,X)
<~> ( sP1_prd
<=> sP2_prd ) ),
inference(formula_renaming,[status(thm)],[f6,f7]) ).
fof(f9,plain,
( ( ( ( sP2_prd
| sP1_prd )
& ( ~ sP2_prd
| ~ sP1_prd ) )
| ! [X] :
? [Y] : ~ sP0_prd(Y,X) )
& ( ( ( ~ sP2_prd
| sP1_prd )
& ( sP2_prd
| ~ sP1_prd ) )
| ? [X] :
! [Y] : sP0_prd(Y,X) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
( ( ( ( sP2_prd
| sP1_prd )
& ( ~ sP2_prd
| ~ sP1_prd ) )
| ! [X] : ~ sP0_prd(sK1_skl(X),X) )
& ( ( ( ~ sP2_prd
| sP1_prd )
& ( sP2_prd
| ~ sP1_prd ) )
| ! [Y] : sP0_prd(Y,sK0_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl(X))],[f9]) ).
fof(f11,plain,
! [X0] :
( sP2_prd
| ~ sP1_prd
| sP0_prd(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f12,plain,
! [X0] :
( ~ sP2_prd
| sP1_prd
| sP0_prd(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f13,plain,
! [X0] :
( ~ sP2_prd
| ~ sP1_prd
| ~ sP0_prd(sK1_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f14,plain,
! [X0] :
( sP2_prd
| sP1_prd
| ~ sP0_prd(sK1_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f15,plain,
! [X,Y] :
( ( ( ( p(Y)
| p(X) )
& ( ~ p(Y)
| ~ p(X) ) )
| sP0_prd(Y,X) )
& ( ( ( ~ p(Y)
| p(X) )
& ( p(Y)
| ~ p(X) ) )
| ~ sP0_prd(Y,X) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f16,plain,
( ! [X,Y] :
( ( ( p(Y)
| p(X) )
& ( ~ p(Y)
| ~ p(X) ) )
| sP0_prd(Y,X) )
& ! [X,Y] :
( ( ( ~ p(Y)
| p(X) )
& ( p(Y)
| ~ p(X) ) )
| ~ sP0_prd(Y,X) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( p(X0)
| ~ p(X1)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ~ p(X0)
| p(X1)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f19,plain,
! [X0,X1] :
( ~ p(X0)
| ~ p(X1)
| sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f20,plain,
! [X0,X1] :
( p(X0)
| p(X1)
| sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f21,plain,
( ( ( ( ! [Y] : r(Y)
| ? [X] : q(X) )
& ( ? [Y] : ~ r(Y)
| ! [X] : ~ q(X) ) )
| sP1_prd )
& ( ( ( ? [Y] : ~ r(Y)
| ? [X] : q(X) )
& ( ! [Y] : r(Y)
| ! [X] : ~ q(X) ) )
| ~ sP1_prd ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f22,plain,
( ( ( ( ! [Y] : r(Y)
| q(sK5_skl) )
& ( ~ r(sK4_skl)
| ! [X] : ~ q(X) ) )
| sP1_prd )
& ( ( ( ~ r(sK3_skl)
| q(sK2_skl) )
& ( ! [Y] : r(Y)
| ! [X] : ~ q(X) ) )
| ~ sP1_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl),skolemize(Y,sK4_skl),skolemize(X,sK5_skl)],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( r(X1)
| ~ q(X0)
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
( ~ r(sK3_skl)
| q(sK2_skl)
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
! [X0] :
( ~ r(sK4_skl)
| ~ q(X0)
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f26,plain,
! [X0] :
( r(X0)
| q(sK5_skl)
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f27,definition,
( sP3_prd
<=> ( ? [X] :
! [Y] :
( q(X)
<=> q(Y) )
<=> ( ? [X] : r(X)
<=> ! [Y] : s(Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f28,plain,
( sP2_prd
<=> ( sP3_prd
<=> ( ? [X] :
! [Y] :
( r(X)
<=> r(Y) )
<=> ( ( ? [X] : s(X)
<=> ! [Y] : p(Y) )
<=> ( ? [X] :
! [Y] :
( s(X)
<=> s(Y) )
<=> ( ? [X] : p(X)
<=> ! [Y] : q(Y) ) ) ) ) ) ),
inference(formula_renaming,[status(thm)],[f7,f27]) ).
fof(f29,definition,
( sP4_prd
<=> ( ? [X] :
! [Y] :
( r(X)
<=> r(Y) )
<=> ( ( ? [X] : s(X)
<=> ! [Y] : p(Y) )
<=> ( ? [X] :
! [Y] :
( s(X)
<=> s(Y) )
<=> ( ? [X] : p(X)
<=> ! [Y] : q(Y) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f30,plain,
( sP2_prd
<=> ( sP3_prd
<=> sP4_prd ) ),
inference(formula_renaming,[status(thm)],[f28,f29]) ).
fof(f31,plain,
( ( ( ( sP4_prd
| sP3_prd )
& ( ~ sP4_prd
| ~ sP3_prd ) )
| sP2_prd )
& ( ( ( ~ sP4_prd
| sP3_prd )
& ( sP4_prd
| ~ sP3_prd ) )
| ~ sP2_prd ) ),
inference(NNF_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
( sP4_prd
| ~ sP3_prd
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
( ~ sP4_prd
| sP3_prd
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
( ~ sP4_prd
| ~ sP3_prd
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f35,plain,
( sP4_prd
| sP3_prd
| sP2_prd ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f36,definition,
! [X,Y] :
( sP5_prd(Y,X)
<=> ( q(X)
<=> q(Y) ) ),
introduced(definition,[new_symbols(definition,[sP5_prd])],[]) ).
fof(f37,definition,
( sP6_prd
<=> ( ? [X] : r(X)
<=> ! [Y] : s(Y) ) ),
introduced(definition,[new_symbols(definition,[sP6_prd])],[]) ).
fof(f38,plain,
( sP3_prd
<=> ( ? [X] :
! [Y] : sP5_prd(Y,X)
<=> sP6_prd ) ),
inference(formula_renaming,[status(thm)],[f27,f37,f36]) ).
fof(f39,plain,
( ( ( ( sP6_prd
| ? [X] :
! [Y] : sP5_prd(Y,X) )
& ( ~ sP6_prd
| ! [X] :
? [Y] : ~ sP5_prd(Y,X) ) )
| sP3_prd )
& ( ( ( ~ sP6_prd
| ? [X] :
! [Y] : sP5_prd(Y,X) )
& ( sP6_prd
| ! [X] :
? [Y] : ~ sP5_prd(Y,X) ) )
| ~ sP3_prd ) ),
inference(NNF_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
( ( ( ( sP6_prd
| ! [Y] : sP5_prd(Y,sK9_skl) )
& ( ~ sP6_prd
| ! [X] : ~ sP5_prd(sK8_skl(X),X) ) )
| sP3_prd )
& ( ( ( ~ sP6_prd
| ! [Y] : sP5_prd(Y,sK7_skl) )
& ( sP6_prd
| ! [X] : ~ sP5_prd(sK6_skl(X),X) ) )
| ~ sP3_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl,sK8_skl,sK9_skl]),skolemize(Y,sK6_skl(X)),skolemize(X,sK7_skl),skolemize(Y,sK8_skl(X)),skolemize(X,sK9_skl)],[f39]) ).
fof(f41,plain,
! [X0] :
( sP6_prd
| ~ sP5_prd(sK6_skl(X0),X0)
| ~ sP3_prd ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [X0] :
( ~ sP6_prd
| sP5_prd(X0,sK7_skl)
| ~ sP3_prd ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f43,plain,
! [X0] :
( ~ sP6_prd
| ~ sP5_prd(sK8_skl(X0),X0)
| sP3_prd ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f44,plain,
! [X0] :
( sP6_prd
| sP5_prd(X0,sK9_skl)
| sP3_prd ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f45,definition,
! [X,Y] :
( sP7_prd(Y,X)
<=> ( r(X)
<=> r(Y) ) ),
introduced(definition,[new_symbols(definition,[sP7_prd])],[]) ).
fof(f46,definition,
( sP8_prd
<=> ( ( ? [X] : s(X)
<=> ! [Y] : p(Y) )
<=> ( ? [X] :
! [Y] :
( s(X)
<=> s(Y) )
<=> ( ? [X] : p(X)
<=> ! [Y] : q(Y) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8_prd])],[]) ).
fof(f47,plain,
( sP4_prd
<=> ( ? [X] :
! [Y] : sP7_prd(Y,X)
<=> sP8_prd ) ),
inference(formula_renaming,[status(thm)],[f29,f46,f45]) ).
fof(f48,plain,
( ( ( ( sP8_prd
| ? [X] :
! [Y] : sP7_prd(Y,X) )
& ( ~ sP8_prd
| ! [X] :
? [Y] : ~ sP7_prd(Y,X) ) )
| sP4_prd )
& ( ( ( ~ sP8_prd
| ? [X] :
! [Y] : sP7_prd(Y,X) )
& ( sP8_prd
| ! [X] :
? [Y] : ~ sP7_prd(Y,X) ) )
| ~ sP4_prd ) ),
inference(NNF_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
( ( ( ( sP8_prd
| ! [Y] : sP7_prd(Y,sK13_skl) )
& ( ~ sP8_prd
| ! [X] : ~ sP7_prd(sK12_skl(X),X) ) )
| sP4_prd )
& ( ( ( ~ sP8_prd
| ! [Y] : sP7_prd(Y,sK11_skl) )
& ( sP8_prd
| ! [X] : ~ sP7_prd(sK10_skl(X),X) ) )
| ~ sP4_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl,sK13_skl]),skolemize(Y,sK10_skl(X)),skolemize(X,sK11_skl),skolemize(Y,sK12_skl(X)),skolemize(X,sK13_skl)],[f48]) ).
fof(f50,plain,
! [X0] :
( sP8_prd
| ~ sP7_prd(sK10_skl(X0),X0)
| ~ sP4_prd ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0] :
( ~ sP8_prd
| sP7_prd(X0,sK11_skl)
| ~ sP4_prd ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
! [X0] :
( ~ sP8_prd
| ~ sP7_prd(sK12_skl(X0),X0)
| sP4_prd ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
! [X0] :
( sP8_prd
| sP7_prd(X0,sK13_skl)
| sP4_prd ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f54,plain,
! [X,Y] :
( ( ( ( q(Y)
| q(X) )
& ( ~ q(Y)
| ~ q(X) ) )
| sP5_prd(Y,X) )
& ( ( ( ~ q(Y)
| q(X) )
& ( q(Y)
| ~ q(X) ) )
| ~ sP5_prd(Y,X) ) ),
inference(NNF_transformation,[status(thm)],[f36]) ).
fof(f55,plain,
( ! [X,Y] :
( ( ( q(Y)
| q(X) )
& ( ~ q(Y)
| ~ q(X) ) )
| sP5_prd(Y,X) )
& ! [X,Y] :
( ( ( ~ q(Y)
| q(X) )
& ( q(Y)
| ~ q(X) ) )
| ~ sP5_prd(Y,X) ) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( q(X0)
| ~ q(X1)
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( ~ q(X0)
| q(X1)
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f58,plain,
! [X0,X1] :
( ~ q(X0)
| ~ q(X1)
| sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f59,plain,
! [X0,X1] :
( q(X0)
| q(X1)
| sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f60,plain,
( ( ( ( ! [Y] : s(Y)
| ? [X] : r(X) )
& ( ? [Y] : ~ s(Y)
| ! [X] : ~ r(X) ) )
| sP6_prd )
& ( ( ( ? [Y] : ~ s(Y)
| ? [X] : r(X) )
& ( ! [Y] : s(Y)
| ! [X] : ~ r(X) ) )
| ~ sP6_prd ) ),
inference(NNF_transformation,[status(thm)],[f37]) ).
fof(f61,plain,
( ( ( ( ! [Y] : s(Y)
| r(sK17_skl) )
& ( ~ s(sK16_skl)
| ! [X] : ~ r(X) ) )
| sP6_prd )
& ( ( ( ~ s(sK15_skl)
| r(sK14_skl) )
& ( ! [Y] : s(Y)
| ! [X] : ~ r(X) ) )
| ~ sP6_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl,sK17_skl]),skolemize(X,sK14_skl),skolemize(Y,sK15_skl),skolemize(Y,sK16_skl),skolemize(X,sK17_skl)],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( s(X1)
| ~ r(X0)
| ~ sP6_prd ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
( ~ s(sK15_skl)
| r(sK14_skl)
| ~ sP6_prd ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f64,plain,
! [X0] :
( ~ s(sK16_skl)
| ~ r(X0)
| sP6_prd ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f65,plain,
! [X0] :
( s(X0)
| r(sK17_skl)
| sP6_prd ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f66,plain,
! [X,Y] :
( ( ( ( r(Y)
| r(X) )
& ( ~ r(Y)
| ~ r(X) ) )
| sP7_prd(Y,X) )
& ( ( ( ~ r(Y)
| r(X) )
& ( r(Y)
| ~ r(X) ) )
| ~ sP7_prd(Y,X) ) ),
inference(NNF_transformation,[status(thm)],[f45]) ).
fof(f67,plain,
( ! [X,Y] :
( ( ( r(Y)
| r(X) )
& ( ~ r(Y)
| ~ r(X) ) )
| sP7_prd(Y,X) )
& ! [X,Y] :
( ( ( ~ r(Y)
| r(X) )
& ( r(Y)
| ~ r(X) ) )
| ~ sP7_prd(Y,X) ) ),
inference(miniscoping,[status(thm)],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( r(X0)
| ~ r(X1)
| ~ sP7_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ~ r(X0)
| r(X1)
| ~ sP7_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f70,plain,
! [X0,X1] :
( ~ r(X0)
| ~ r(X1)
| sP7_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f71,plain,
! [X0,X1] :
( r(X0)
| r(X1)
| sP7_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f72,definition,
( sP9_prd
<=> ( ? [X] : s(X)
<=> ! [Y] : p(Y) ) ),
introduced(definition,[new_symbols(definition,[sP9_prd])],[]) ).
fof(f73,plain,
( sP8_prd
<=> ( sP9_prd
<=> ( ? [X] :
! [Y] :
( s(X)
<=> s(Y) )
<=> ( ? [X] : p(X)
<=> ! [Y] : q(Y) ) ) ) ),
inference(formula_renaming,[status(thm)],[f46,f72]) ).
fof(f74,definition,
( sP10_prd
<=> ( ? [X] :
! [Y] :
( s(X)
<=> s(Y) )
<=> ( ? [X] : p(X)
<=> ! [Y] : q(Y) ) ) ),
introduced(definition,[new_symbols(definition,[sP10_prd])],[]) ).
fof(f75,plain,
( sP8_prd
<=> ( sP9_prd
<=> sP10_prd ) ),
inference(formula_renaming,[status(thm)],[f73,f74]) ).
fof(f76,plain,
( ( ( ( sP10_prd
| sP9_prd )
& ( ~ sP10_prd
| ~ sP9_prd ) )
| sP8_prd )
& ( ( ( ~ sP10_prd
| sP9_prd )
& ( sP10_prd
| ~ sP9_prd ) )
| ~ sP8_prd ) ),
inference(NNF_transformation,[status(thm)],[f75]) ).
fof(f77,plain,
( sP10_prd
| ~ sP9_prd
| ~ sP8_prd ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
( ~ sP10_prd
| sP9_prd
| ~ sP8_prd ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f79,plain,
( ~ sP10_prd
| ~ sP9_prd
| sP8_prd ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f80,plain,
( sP10_prd
| sP9_prd
| sP8_prd ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f81,plain,
( ( ( ( ! [Y] : p(Y)
| ? [X] : s(X) )
& ( ? [Y] : ~ p(Y)
| ! [X] : ~ s(X) ) )
| sP9_prd )
& ( ( ( ? [Y] : ~ p(Y)
| ? [X] : s(X) )
& ( ! [Y] : p(Y)
| ! [X] : ~ s(X) ) )
| ~ sP9_prd ) ),
inference(NNF_transformation,[status(thm)],[f72]) ).
fof(f82,plain,
( ( ( ( ! [Y] : p(Y)
| s(sK21_skl) )
& ( ~ p(sK20_skl)
| ! [X] : ~ s(X) ) )
| sP9_prd )
& ( ( ( ~ p(sK19_skl)
| s(sK18_skl) )
& ( ! [Y] : p(Y)
| ! [X] : ~ s(X) ) )
| ~ sP9_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl,sK19_skl,sK20_skl,sK21_skl]),skolemize(X,sK18_skl),skolemize(Y,sK19_skl),skolemize(Y,sK20_skl),skolemize(X,sK21_skl)],[f81]) ).
fof(f83,plain,
! [X0,X1] :
( p(X1)
| ~ s(X0)
| ~ sP9_prd ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f84,plain,
( ~ p(sK19_skl)
| s(sK18_skl)
| ~ sP9_prd ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f85,plain,
! [X0] :
( ~ p(sK20_skl)
| ~ s(X0)
| sP9_prd ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f86,plain,
! [X0] :
( p(X0)
| s(sK21_skl)
| sP9_prd ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f87,definition,
! [X,Y] :
( sP11_prd(Y,X)
<=> ( s(X)
<=> s(Y) ) ),
introduced(definition,[new_symbols(definition,[sP11_prd])],[]) ).
fof(f88,definition,
( sP12_prd
<=> ( ? [X] : p(X)
<=> ! [Y] : q(Y) ) ),
introduced(definition,[new_symbols(definition,[sP12_prd])],[]) ).
fof(f89,plain,
( sP10_prd
<=> ( ? [X] :
! [Y] : sP11_prd(Y,X)
<=> sP12_prd ) ),
inference(formula_renaming,[status(thm)],[f74,f88,f87]) ).
fof(f90,plain,
( ( ( ( sP12_prd
| ? [X] :
! [Y] : sP11_prd(Y,X) )
& ( ~ sP12_prd
| ! [X] :
? [Y] : ~ sP11_prd(Y,X) ) )
| sP10_prd )
& ( ( ( ~ sP12_prd
| ? [X] :
! [Y] : sP11_prd(Y,X) )
& ( sP12_prd
| ! [X] :
? [Y] : ~ sP11_prd(Y,X) ) )
| ~ sP10_prd ) ),
inference(NNF_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
( ( ( ( sP12_prd
| ! [Y] : sP11_prd(Y,sK25_skl) )
& ( ~ sP12_prd
| ! [X] : ~ sP11_prd(sK24_skl(X),X) ) )
| sP10_prd )
& ( ( ( ~ sP12_prd
| ! [Y] : sP11_prd(Y,sK23_skl) )
& ( sP12_prd
| ! [X] : ~ sP11_prd(sK22_skl(X),X) ) )
| ~ sP10_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22_skl,sK23_skl,sK24_skl,sK25_skl]),skolemize(Y,sK22_skl(X)),skolemize(X,sK23_skl),skolemize(Y,sK24_skl(X)),skolemize(X,sK25_skl)],[f90]) ).
fof(f92,plain,
! [X0] :
( sP12_prd
| ~ sP11_prd(sK22_skl(X0),X0)
| ~ sP10_prd ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
! [X0] :
( ~ sP12_prd
| sP11_prd(X0,sK23_skl)
| ~ sP10_prd ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f94,plain,
! [X0] :
( ~ sP12_prd
| ~ sP11_prd(sK24_skl(X0),X0)
| sP10_prd ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f95,plain,
! [X0] :
( sP12_prd
| sP11_prd(X0,sK25_skl)
| sP10_prd ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f96,plain,
! [X,Y] :
( ( ( ( s(Y)
| s(X) )
& ( ~ s(Y)
| ~ s(X) ) )
| sP11_prd(Y,X) )
& ( ( ( ~ s(Y)
| s(X) )
& ( s(Y)
| ~ s(X) ) )
| ~ sP11_prd(Y,X) ) ),
inference(NNF_transformation,[status(thm)],[f87]) ).
fof(f97,plain,
( ! [X,Y] :
( ( ( s(Y)
| s(X) )
& ( ~ s(Y)
| ~ s(X) ) )
| sP11_prd(Y,X) )
& ! [X,Y] :
( ( ( ~ s(Y)
| s(X) )
& ( s(Y)
| ~ s(X) ) )
| ~ sP11_prd(Y,X) ) ),
inference(miniscoping,[status(thm)],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( s(X0)
| ~ s(X1)
| ~ sP11_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( ~ s(X0)
| s(X1)
| ~ sP11_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f100,plain,
! [X0,X1] :
( ~ s(X0)
| ~ s(X1)
| sP11_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f101,plain,
! [X0,X1] :
( s(X0)
| s(X1)
| sP11_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f102,plain,
( ( ( ( ! [Y] : q(Y)
| ? [X] : p(X) )
& ( ? [Y] : ~ q(Y)
| ! [X] : ~ p(X) ) )
| sP12_prd )
& ( ( ( ? [Y] : ~ q(Y)
| ? [X] : p(X) )
& ( ! [Y] : q(Y)
| ! [X] : ~ p(X) ) )
| ~ sP12_prd ) ),
inference(NNF_transformation,[status(thm)],[f88]) ).
fof(f103,plain,
( ( ( ( ! [Y] : q(Y)
| p(sK29_skl) )
& ( ~ q(sK28_skl)
| ! [X] : ~ p(X) ) )
| sP12_prd )
& ( ( ( ~ q(sK27_skl)
| p(sK26_skl) )
& ( ! [Y] : q(Y)
| ! [X] : ~ p(X) ) )
| ~ sP12_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26_skl,sK27_skl,sK28_skl,sK29_skl]),skolemize(X,sK26_skl),skolemize(Y,sK27_skl),skolemize(Y,sK28_skl),skolemize(X,sK29_skl)],[f102]) ).
fof(f104,plain,
! [X0,X1] :
( q(X1)
| ~ p(X0)
| ~ sP12_prd ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f105,plain,
( ~ q(sK27_skl)
| p(sK26_skl)
| ~ sP12_prd ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f106,plain,
! [X0] :
( ~ q(sK28_skl)
| ~ p(X0)
| sP12_prd ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f107,plain,
! [X0] :
( q(X0)
| p(sK29_skl)
| sP12_prd ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f108,definition,
! [X0] :
( sQ0_spl
<=> sP0_prd(X0,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f109,plain,
! [X0] :
( ~ sQ0_spl
| sP0_prd(X0,sK0_skl) ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,definition,
( sQ1_spl
<=> sP1_prd ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f114,definition,
( sQ2_spl
<=> sP2_prd ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f117,plain,
( sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f11,f108,f111,f114]) ).
fof(f118,plain,
( ~ sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f12,f108,f111,f114]) ).
fof(f119,definition,
! [X0] :
( sQ3_spl
<=> ~ sP0_prd(sK1_skl(X0),X0) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f120,plain,
! [X0] :
( ~ sQ3_spl
| ~ sP0_prd(sK1_skl(X0),X0) ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f122,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f13,f119,f111,f114]) ).
fof(f123,plain,
( sQ2_spl
| sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f14,f119,f111,f114]) ).
fof(f124,definition,
! [X0] :
( sQ4_spl
<=> ~ q(X0) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f125,plain,
! [X0] :
( ~ sQ4_spl
| ~ q(X0) ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,definition,
! [X1] :
( sQ5_spl
<=> r(X1) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f128,plain,
! [X0] :
( ~ sQ5_spl
| r(X0) ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,plain,
( sQ5_spl
| sQ4_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f23,f111,f124,f127]) ).
fof(f131,definition,
( sQ6_spl
<=> q(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f132,plain,
( ~ sQ6_spl
| q(sK2_skl) ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f134,definition,
( sQ7_spl
<=> r(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( sQ7_spl
| ~ r(sK3_skl) ),
inference(component_clause,[status(thm)],[f134]) ).
fof(f137,plain,
( ~ sQ7_spl
| sQ6_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f24,f111,f131,f134]) ).
fof(f138,definition,
( sQ8_spl
<=> r(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( sQ8_spl
| ~ r(sK4_skl) ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f141,plain,
( ~ sQ8_spl
| sQ4_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f25,f111,f124,f138]) ).
fof(f142,definition,
( sQ9_spl
<=> q(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f143,plain,
( ~ sQ9_spl
| q(sK5_skl) ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f144,plain,
( sQ9_spl
| ~ q(sK5_skl) ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( sQ5_spl
| sQ9_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f26,f111,f142,f127]) ).
fof(f146,definition,
( sQ10_spl
<=> sP3_prd ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f149,definition,
( sQ11_spl
<=> sP4_prd ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f152,plain,
( sQ11_spl
| ~ sQ10_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f32,f114,f146,f149]) ).
fof(f153,plain,
( ~ sQ11_spl
| sQ10_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f33,f114,f146,f149]) ).
fof(f154,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f34,f114,f146,f149]) ).
fof(f155,plain,
( sQ11_spl
| sQ10_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f35,f114,f146,f149]) ).
fof(f156,definition,
! [X0] :
( sQ12_spl
<=> ~ sP5_prd(sK6_skl(X0),X0) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f157,plain,
! [X0] :
( ~ sQ12_spl
| ~ sP5_prd(sK6_skl(X0),X0) ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,definition,
( sQ13_spl
<=> sP6_prd ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( sQ13_spl
| sQ12_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f41,f146,f156,f159]) ).
fof(f163,definition,
! [X0] :
( sQ14_spl
<=> sP5_prd(X0,sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f164,plain,
! [X0] :
( ~ sQ14_spl
| sP5_prd(X0,sK7_skl) ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,plain,
( ~ sQ13_spl
| sQ14_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f42,f146,f163,f159]) ).
fof(f167,definition,
! [X0] :
( sQ15_spl
<=> ~ sP5_prd(sK8_skl(X0),X0) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f168,plain,
! [X0] :
( ~ sQ15_spl
| ~ sP5_prd(sK8_skl(X0),X0) ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f170,plain,
( ~ sQ13_spl
| sQ15_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f43,f146,f167,f159]) ).
fof(f171,definition,
! [X0] :
( sQ16_spl
<=> sP5_prd(X0,sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f172,plain,
! [X0] :
( ~ sQ16_spl
| sP5_prd(X0,sK9_skl) ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,plain,
( sQ13_spl
| sQ16_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f44,f146,f171,f159]) ).
fof(f175,definition,
! [X0] :
( sQ17_spl
<=> ~ sP7_prd(sK10_skl(X0),X0) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f176,plain,
! [X0] :
( ~ sQ17_spl
| ~ sP7_prd(sK10_skl(X0),X0) ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,definition,
( sQ18_spl
<=> sP8_prd ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( sQ18_spl
| sQ17_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f50,f149,f175,f178]) ).
fof(f182,definition,
! [X0] :
( sQ19_spl
<=> sP7_prd(X0,sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f183,plain,
! [X0] :
( ~ sQ19_spl
| sP7_prd(X0,sK11_skl) ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,plain,
( ~ sQ18_spl
| sQ19_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f51,f149,f182,f178]) ).
fof(f186,definition,
! [X0] :
( sQ20_spl
<=> ~ sP7_prd(sK12_skl(X0),X0) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f187,plain,
! [X0] :
( ~ sQ20_spl
| ~ sP7_prd(sK12_skl(X0),X0) ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,plain,
( ~ sQ18_spl
| sQ20_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f52,f149,f186,f178]) ).
fof(f190,definition,
! [X0] :
( sQ21_spl
<=> sP7_prd(X0,sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f191,plain,
! [X0] :
( ~ sQ21_spl
| sP7_prd(X0,sK13_skl) ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f193,plain,
( sQ18_spl
| sQ21_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f53,f149,f190,f178]) ).
fof(f194,definition,
! [X0] :
( sQ22_spl
<=> ~ r(X0) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f195,plain,
! [X0] :
( ~ sQ22_spl
| ~ r(X0) ),
inference(component_clause,[status(thm)],[f194]) ).
fof(f197,definition,
! [X1] :
( sQ23_spl
<=> s(X1) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f198,plain,
! [X0] :
( ~ sQ23_spl
| s(X0) ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f200,plain,
( sQ23_spl
| sQ22_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f62,f159,f194,f197]) ).
fof(f201,definition,
( sQ24_spl
<=> r(sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f202,plain,
( ~ sQ24_spl
| r(sK14_skl) ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f204,definition,
( sQ25_spl
<=> s(sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( sQ25_spl
| ~ s(sK15_skl) ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f207,plain,
( ~ sQ25_spl
| sQ24_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f63,f159,f201,f204]) ).
fof(f208,definition,
( sQ26_spl
<=> s(sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f210,plain,
( sQ26_spl
| ~ s(sK16_skl) ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,plain,
( ~ sQ26_spl
| sQ22_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f64,f159,f194,f208]) ).
fof(f212,definition,
( sQ27_spl
<=> r(sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( ~ sQ27_spl
| r(sK17_skl) ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f214,plain,
( sQ27_spl
| ~ r(sK17_skl) ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f215,plain,
( sQ23_spl
| sQ27_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f65,f159,f212,f197]) ).
fof(f216,definition,
( sQ28_spl
<=> sP9_prd ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f219,definition,
( sQ29_spl
<=> sP10_prd ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f222,plain,
( sQ29_spl
| ~ sQ28_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f77,f178,f216,f219]) ).
fof(f223,plain,
( ~ sQ29_spl
| sQ28_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f78,f178,f216,f219]) ).
fof(f224,plain,
( ~ sQ29_spl
| ~ sQ28_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f79,f178,f216,f219]) ).
fof(f225,plain,
( sQ29_spl
| sQ28_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f80,f178,f216,f219]) ).
fof(f226,definition,
! [X0] :
( sQ30_spl
<=> ~ s(X0) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f227,plain,
! [X0] :
( ~ sQ30_spl
| ~ s(X0) ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f229,definition,
! [X1] :
( sQ31_spl
<=> p(X1) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f230,plain,
! [X0] :
( ~ sQ31_spl
| p(X0) ),
inference(component_clause,[status(thm)],[f229]) ).
fof(f232,plain,
( sQ31_spl
| sQ30_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f83,f216,f226,f229]) ).
fof(f233,definition,
( sQ32_spl
<=> s(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f234,plain,
( ~ sQ32_spl
| s(sK18_skl) ),
inference(component_clause,[status(thm)],[f233]) ).
fof(f235,plain,
( sQ32_spl
| ~ s(sK18_skl) ),
inference(component_clause,[status(thm)],[f233]) ).
fof(f236,definition,
( sQ33_spl
<=> p(sK19_skl) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f238,plain,
( sQ33_spl
| ~ p(sK19_skl) ),
inference(component_clause,[status(thm)],[f236]) ).
fof(f239,plain,
( ~ sQ33_spl
| sQ32_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f84,f216,f233,f236]) ).
fof(f240,definition,
( sQ34_spl
<=> p(sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f242,plain,
( sQ34_spl
| ~ p(sK20_skl) ),
inference(component_clause,[status(thm)],[f240]) ).
fof(f243,plain,
( ~ sQ34_spl
| sQ30_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f85,f216,f226,f240]) ).
fof(f244,definition,
( sQ35_spl
<=> s(sK21_skl) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f245,plain,
( ~ sQ35_spl
| s(sK21_skl) ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f246,plain,
( sQ35_spl
| ~ s(sK21_skl) ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,plain,
( sQ31_spl
| sQ35_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f86,f216,f244,f229]) ).
fof(f248,definition,
! [X0] :
( sQ36_spl
<=> ~ sP11_prd(sK22_skl(X0),X0) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f249,plain,
! [X0] :
( ~ sQ36_spl
| ~ sP11_prd(sK22_skl(X0),X0) ),
inference(component_clause,[status(thm)],[f248]) ).
fof(f251,definition,
( sQ37_spl
<=> sP12_prd ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( sQ37_spl
| sQ36_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f92,f219,f248,f251]) ).
fof(f255,definition,
! [X0] :
( sQ38_spl
<=> sP11_prd(X0,sK23_skl) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f256,plain,
! [X0] :
( ~ sQ38_spl
| sP11_prd(X0,sK23_skl) ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f258,plain,
( ~ sQ37_spl
| sQ38_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f93,f219,f255,f251]) ).
fof(f259,definition,
! [X0] :
( sQ39_spl
<=> ~ sP11_prd(sK24_skl(X0),X0) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f260,plain,
! [X0] :
( ~ sQ39_spl
| ~ sP11_prd(sK24_skl(X0),X0) ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f262,plain,
( ~ sQ37_spl
| sQ39_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f94,f219,f259,f251]) ).
fof(f263,definition,
! [X0] :
( sQ40_spl
<=> sP11_prd(X0,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f264,plain,
! [X0] :
( ~ sQ40_spl
| sP11_prd(X0,sK25_skl) ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f266,plain,
( sQ37_spl
| sQ40_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f95,f219,f263,f251]) ).
fof(f267,definition,
! [X0] :
( sQ41_spl
<=> ~ p(X0) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f268,plain,
! [X0] :
( ~ sQ41_spl
| ~ p(X0) ),
inference(component_clause,[status(thm)],[f267]) ).
fof(f270,definition,
! [X1] :
( sQ42_spl
<=> q(X1) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f271,plain,
! [X0] :
( ~ sQ42_spl
| q(X0) ),
inference(component_clause,[status(thm)],[f270]) ).
fof(f273,plain,
( sQ42_spl
| sQ41_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f104,f251,f267,f270]) ).
fof(f274,definition,
( sQ43_spl
<=> p(sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f275,plain,
( ~ sQ43_spl
| p(sK26_skl) ),
inference(component_clause,[status(thm)],[f274]) ).
fof(f276,plain,
( sQ43_spl
| ~ p(sK26_skl) ),
inference(component_clause,[status(thm)],[f274]) ).
fof(f277,definition,
( sQ44_spl
<=> q(sK27_skl) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f279,plain,
( sQ44_spl
| ~ q(sK27_skl) ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f280,plain,
( ~ sQ44_spl
| sQ43_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f105,f251,f274,f277]) ).
fof(f281,definition,
( sQ45_spl
<=> q(sK28_skl) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f282,plain,
( ~ sQ45_spl
| q(sK28_skl) ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f283,plain,
( sQ45_spl
| ~ q(sK28_skl) ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f284,plain,
( ~ sQ45_spl
| sQ41_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f106,f251,f267,f281]) ).
fof(f285,definition,
( sQ46_spl
<=> p(sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f286,plain,
( ~ sQ46_spl
| p(sK29_skl) ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f287,plain,
( sQ46_spl
| ~ p(sK29_skl) ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f288,plain,
( sQ42_spl
| sQ46_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f107,f251,f285,f270]) ).
fof(f289,plain,
( ~ sQ31_spl
| ~ sQ41_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f230,f268]) ).
fof(f290,plain,
( ~ sQ31_spl
| ~ sQ41_spl ),
inference(contradiction_clause,[status(thm)],[f289]) ).
fof(f291,plain,
( ~ sQ23_spl
| ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f198,f227]) ).
fof(f292,plain,
( ~ sQ23_spl
| ~ sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f291]) ).
fof(f293,plain,
( ~ sQ5_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f128,f195]) ).
fof(f294,plain,
( ~ sQ5_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f293]) ).
fof(f295,plain,
( ~ sQ4_spl
| ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f125,f271]) ).
fof(f296,plain,
( ~ sQ4_spl
| ~ sQ42_spl ),
inference(contradiction_clause,[status(thm)],[f295]) ).
fof(f298,plain,
( ~ sQ46_spl
| ~ sQ41_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f286,f268]) ).
fof(f299,plain,
( ~ sQ46_spl
| ~ sQ41_spl ),
inference(contradiction_clause,[status(thm)],[f298]) ).
fof(f300,plain,
! [X0,X1] :
( ~ sQ42_spl
| ~ q(X1)
| sP5_prd(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f58,f271]) ).
fof(f301,plain,
! [X0,X1] :
( ~ sQ42_spl
| sP5_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f300,f271]) ).
fof(f302,plain,
( sQ45_spl
| ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f283,f271]) ).
fof(f303,plain,
( sQ45_spl
| ~ sQ42_spl ),
inference(contradiction_clause,[status(thm)],[f302]) ).
fof(f304,plain,
! [X0,X1] :
( ~ sQ4_spl
| q(X1)
| sP5_prd(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f59,f125]) ).
fof(f305,plain,
! [X0,X1] :
( ~ sQ4_spl
| sP5_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f304,f125]) ).
fof(f306,plain,
( sQ34_spl
| ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f242,f230]) ).
fof(f307,plain,
( sQ34_spl
| ~ sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f306]) ).
fof(f308,plain,
( ~ sQ32_spl
| ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f234,f227]) ).
fof(f309,plain,
( ~ sQ32_spl
| ~ sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f308]) ).
fof(f310,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ r(X1)
| sP7_prd(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f70,f128]) ).
fof(f311,plain,
! [X0,X1] :
( ~ sQ5_spl
| sP7_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f310,f128]) ).
fof(f312,plain,
( sQ26_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f210,f198]) ).
fof(f313,plain,
( sQ26_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f312]) ).
fof(f314,plain,
( ~ sQ24_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f202,f195]) ).
fof(f315,plain,
( ~ sQ24_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f314]) ).
fof(f316,plain,
( sQ8_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f140,f128]) ).
fof(f317,plain,
( sQ8_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f316]) ).
fof(f318,plain,
( ~ sQ9_spl
| ~ sQ4_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f143,f125]) ).
fof(f319,plain,
( ~ sQ9_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f318]) ).
fof(f320,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| $false ),
inference(resolution,[status(thm)],[f109,f120]) ).
fof(f321,plain,
( ~ sQ3_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f320]) ).
fof(f322,plain,
! [X0] :
( ~ sQ35_spl
| ~ s(X0)
| sP11_prd(X0,sK21_skl) ),
inference(resolution,[status(thm)],[f245,f100]) ).
fof(f323,plain,
! [X0] :
( ~ sQ35_spl
| s(X0)
| ~ sP11_prd(sK21_skl,X0) ),
inference(resolution,[status(thm)],[f245,f99]) ).
fof(f324,plain,
( ~ sQ40_spl
| ~ sQ36_spl
| $false ),
inference(resolution,[status(thm)],[f249,f264]) ).
fof(f326,plain,
( ~ sQ40_spl
| ~ sQ36_spl ),
inference(contradiction_clause,[status(thm)],[f324]) ).
fof(f327,plain,
! [X0,X1] :
( ~ sQ30_spl
| s(X1)
| sP11_prd(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f101,f227]) ).
fof(f328,plain,
! [X0,X1] :
( ~ sQ30_spl
| sP11_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f327,f227]) ).
fof(f329,plain,
( ~ sQ27_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f213,f195]) ).
fof(f330,plain,
( ~ sQ27_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f329]) ).
fof(f331,plain,
! [X0] :
( ~ sQ46_spl
| p(X0)
| ~ sP0_prd(sK29_skl,X0) ),
inference(resolution,[status(thm)],[f18,f286]) ).
fof(f334,plain,
( ~ sQ16_spl
| ~ sQ12_spl
| $false ),
inference(resolution,[status(thm)],[f157,f172]) ).
fof(f335,plain,
( ~ sQ16_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f334]) ).
fof(f336,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f132,f125]) ).
fof(f337,plain,
( ~ sQ6_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f336]) ).
fof(f338,plain,
! [X0,X1] :
( ~ sQ22_spl
| r(X0)
| sP7_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f71,f195]) ).
fof(f340,plain,
( ~ sQ16_spl
| ~ sQ15_spl
| $false ),
inference(resolution,[status(thm)],[f168,f172]) ).
fof(f342,plain,
( ~ sQ16_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f340]) ).
fof(f345,plain,
( ~ sQ21_spl
| ~ sQ20_spl
| $false ),
inference(resolution,[status(thm)],[f187,f191]) ).
fof(f346,plain,
! [X0] :
( ~ sQ22_spl
| ~ sQ20_spl
| r(sK12_skl(X0)) ),
inference(resolution,[status(thm)],[f187,f338]) ).
fof(f347,plain,
( ~ sQ21_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f345]) ).
fof(f348,plain,
( ~ sQ15_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f168,f305]) ).
fof(f349,plain,
( ~ sQ15_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f348]) ).
fof(f350,plain,
( ~ sQ39_spl
| ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f260,f328]) ).
fof(f351,plain,
( ~ sQ39_spl
| ~ sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f350]) ).
fof(f356,plain,
! [X0] :
( ~ sQ22_spl
| ~ sQ17_spl
| r(sK10_skl(X0)) ),
inference(resolution,[status(thm)],[f176,f338]) ).
fof(f357,plain,
( ~ sQ22_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f356,f195]) ).
fof(f358,plain,
( ~ sQ22_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f357]) ).
fof(f361,plain,
( ~ sQ17_spl
| ~ sQ19_spl
| $false ),
inference(resolution,[status(thm)],[f183,f176]) ).
fof(f362,plain,
( ~ sQ17_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f361]) ).
fof(f363,plain,
( ~ sQ12_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f157,f305]) ).
fof(f364,plain,
( ~ sQ12_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f363]) ).
fof(f366,plain,
( ~ sQ22_spl
| ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f346,f195]) ).
fof(f367,plain,
( ~ sQ22_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f366]) ).
fof(f368,plain,
( ~ sQ35_spl
| ~ sQ30_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f245,f227]) ).
fof(f369,plain,
( ~ sQ35_spl
| ~ sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f368]) ).
fof(f370,plain,
! [X0] :
( ~ sQ9_spl
| q(X0)
| ~ sP5_prd(sK5_skl,X0) ),
inference(resolution,[status(thm)],[f57,f143]) ).
fof(f375,plain,
( ~ sQ38_spl
| ~ sQ36_spl
| $false ),
inference(resolution,[status(thm)],[f249,f256]) ).
fof(f377,plain,
( ~ sQ38_spl
| ~ sQ36_spl ),
inference(contradiction_clause,[status(thm)],[f375]) ).
fof(f380,plain,
! [X0,X1] :
( ~ sQ41_spl
| p(X1)
| sP0_prd(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f20,f268]) ).
fof(f381,plain,
! [X0,X1] :
( ~ sQ41_spl
| sP0_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f380,f268]) ).
fof(f385,plain,
( ~ sQ15_spl
| ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f168,f301]) ).
fof(f386,plain,
( ~ sQ15_spl
| ~ sQ42_spl ),
inference(contradiction_clause,[status(thm)],[f385]) ).
fof(f387,plain,
( ~ sQ12_spl
| ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f157,f301]) ).
fof(f388,plain,
( ~ sQ12_spl
| ~ sQ42_spl ),
inference(contradiction_clause,[status(thm)],[f387]) ).
fof(f392,plain,
( ~ sQ36_spl
| ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f249,f328]) ).
fof(f393,plain,
( ~ sQ36_spl
| ~ sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f392]) ).
fof(f396,plain,
! [X0] :
( ~ sQ35_spl
| ~ sQ23_spl
| sP11_prd(X0,sK21_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f322,f198]) ).
fof(f399,plain,
( sQ25_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f206,f198]) ).
fof(f400,plain,
( sQ25_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f399]) ).
fof(f405,plain,
( ~ sQ40_spl
| ~ sQ39_spl
| $false ),
inference(resolution,[status(thm)],[f260,f264]) ).
fof(f406,plain,
( ~ sQ40_spl
| ~ sQ39_spl ),
inference(contradiction_clause,[status(thm)],[f405]) ).
fof(f408,plain,
! [X0,X1] :
( ~ sQ31_spl
| ~ p(X1)
| sP0_prd(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f19,f230]) ).
fof(f409,plain,
! [X0,X1] :
( ~ sQ31_spl
| sP0_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f408,f230]) ).
fof(f410,plain,
( sQ7_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f136,f128]) ).
fof(f411,plain,
( sQ7_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f410]) ).
fof(f413,plain,
( ~ sQ43_spl
| ~ sQ41_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f275,f268]) ).
fof(f414,plain,
( ~ sQ43_spl
| ~ sQ41_spl ),
inference(contradiction_clause,[status(thm)],[f413]) ).
fof(f415,plain,
( sQ44_spl
| ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f279,f271]) ).
fof(f416,plain,
( sQ44_spl
| ~ sQ42_spl ),
inference(contradiction_clause,[status(thm)],[f415]) ).
fof(f417,plain,
! [X0,X1] :
( ~ sQ23_spl
| ~ s(X0)
| sP11_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f100,f198]) ).
fof(f423,plain,
( ~ sQ35_spl
| ~ sQ23_spl
| ~ sQ39_spl
| $false ),
inference(resolution,[status(thm)],[f260,f396]) ).
fof(f425,plain,
( ~ sQ35_spl
| ~ sQ23_spl
| ~ sQ39_spl ),
inference(contradiction_clause,[status(thm)],[f423]) ).
fof(f426,plain,
( ~ sQ3_spl
| ~ sQ41_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f381]) ).
fof(f427,plain,
( ~ sQ3_spl
| ~ sQ41_spl ),
inference(contradiction_clause,[status(thm)],[f426]) ).
fof(f431,plain,
( sQ33_spl
| ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f238,f230]) ).
fof(f432,plain,
( sQ33_spl
| ~ sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f431]) ).
fof(f433,plain,
! [X0] :
( ~ sQ27_spl
| r(X0)
| ~ sP7_prd(X0,sK17_skl) ),
inference(resolution,[status(thm)],[f68,f213]) ).
fof(f434,plain,
! [X0] :
( ~ sQ27_spl
| ~ r(X0)
| ~ r(sK17_skl)
| r(X0) ),
inference(resolution,[status(thm)],[f433,f70]) ).
fof(f436,definition,
! [X0] :
( sQ47_spl
<=> ( ~ r(X0)
| r(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f439,plain,
( ~ sQ27_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f434,f436,f212]) ).
fof(f448,plain,
! [X0,X1] :
( ~ sQ23_spl
| sP11_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f417,f198]) ).
fof(f449,plain,
( ~ sQ3_spl
| ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f409]) ).
fof(f450,plain,
( ~ sQ3_spl
| ~ sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f449]) ).
fof(f453,plain,
! [X0] :
( ~ sQ27_spl
| r(X0)
| ~ sP7_prd(sK17_skl,X0) ),
inference(resolution,[status(thm)],[f69,f213]) ).
fof(f458,plain,
! [X0] :
( ~ sQ43_spl
| p(X0)
| ~ sP0_prd(sK26_skl,X0) ),
inference(resolution,[status(thm)],[f18,f275]) ).
fof(f461,plain,
( ~ sQ0_spl
| ~ sQ43_spl
| p(sK0_skl) ),
inference(resolution,[status(thm)],[f458,f109]) ).
fof(f465,definition,
! [X0] :
( sQ49_spl
<=> ( p(X0)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f466,plain,
! [X0] :
( ~ sQ49_spl
| p(X0)
| p(X0) ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f472,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ43_spl
| p(X0)
| ~ sP0_prd(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f461,f17]) ).
fof(f473,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ43_spl
| p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f472,f109]) ).
fof(f476,plain,
( sQ34_spl
| ~ sQ0_spl
| ~ sQ43_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f242,f473]) ).
fof(f478,plain,
( sQ34_spl
| ~ sQ0_spl
| ~ sQ43_spl ),
inference(contradiction_clause,[status(thm)],[f476]) ).
fof(f481,plain,
( ~ sQ21_spl
| ~ sQ27_spl
| r(sK13_skl) ),
inference(resolution,[status(thm)],[f453,f191]) ).
fof(f485,plain,
! [X0] :
( ~ sQ21_spl
| ~ sQ27_spl
| r(X0)
| ~ sP7_prd(X0,sK13_skl) ),
inference(resolution,[status(thm)],[f481,f68]) ).
fof(f486,plain,
! [X0] :
( ~ sQ21_spl
| ~ sQ27_spl
| r(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f485,f191]) ).
fof(f487,plain,
( sQ8_spl
| ~ sQ21_spl
| ~ sQ27_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f140,f486]) ).
fof(f488,plain,
( sQ8_spl
| ~ sQ21_spl
| ~ sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f487]) ).
fof(f490,plain,
( ~ sQ17_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f176,f311]) ).
fof(f491,plain,
( ~ sQ17_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f490]) ).
fof(f494,plain,
( ~ sQ0_spl
| ~ sQ46_spl
| p(sK0_skl) ),
inference(resolution,[status(thm)],[f331,f109]) ).
fof(f507,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| $false ),
inference(resolution,[status(thm)],[f168,f164]) ).
fof(f508,plain,
( ~ sQ14_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f507]) ).
fof(f509,plain,
( ~ sQ36_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f249,f448]) ).
fof(f510,plain,
( ~ sQ36_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f509]) ).
fof(f514,plain,
! [X0] :
( ~ sQ9_spl
| q(X0)
| ~ sP5_prd(sK5_skl,X0) ),
inference(resolution,[status(thm)],[f143,f57]) ).
fof(f515,plain,
! [X0] :
( ~ sQ9_spl
| ~ q(X0)
| sP5_prd(X0,sK5_skl) ),
inference(resolution,[status(thm)],[f143,f58]) ).
fof(f520,definition,
! [X0] :
( sQ50_spl
<=> ( q(X0)
| q(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f521,plain,
! [X0] :
( ~ sQ50_spl
| q(X0)
| q(X0) ),
inference(component_clause,[status(thm)],[f520]) ).
fof(f524,plain,
( ~ sQ14_spl
| ~ sQ9_spl
| q(sK7_skl) ),
inference(resolution,[status(thm)],[f370,f164]) ).
fof(f527,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ9_spl
| q(X0)
| ~ sP5_prd(X0,sK7_skl) ),
inference(resolution,[status(thm)],[f524,f56]) ).
fof(f530,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ9_spl
| q(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f527,f164]) ).
fof(f532,plain,
( sQ44_spl
| ~ sQ14_spl
| ~ sQ9_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f279,f530]) ).
fof(f534,plain,
( sQ44_spl
| ~ sQ14_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f532]) ).
fof(f545,plain,
( ~ sQ35_spl
| ~ sQ40_spl
| s(sK25_skl) ),
inference(resolution,[status(thm)],[f264,f323]) ).
fof(f547,plain,
! [X0] :
( ~ sQ35_spl
| ~ sQ40_spl
| s(X0)
| ~ sP11_prd(X0,sK25_skl) ),
inference(resolution,[status(thm)],[f545,f98]) ).
fof(f550,plain,
! [X0] :
( ~ sQ35_spl
| ~ sQ40_spl
| s(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f547,f264]) ).
fof(f552,plain,
( sQ25_spl
| ~ sQ35_spl
| ~ sQ40_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f206,f550]) ).
fof(f555,plain,
( sQ25_spl
| ~ sQ35_spl
| ~ sQ40_spl ),
inference(contradiction_clause,[status(thm)],[f552]) ).
fof(f556,plain,
( sQ45_spl
| ~ sQ14_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f283,f530]) ).
fof(f557,plain,
( sQ45_spl
| ~ sQ14_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f556]) ).
fof(f558,plain,
( ~ sQ0_spl
| ~ sQ43_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f473,f229,f274,f108]) ).
fof(f559,plain,
! [X0] :
( ~ sQ32_spl
| s(X0)
| ~ sP11_prd(X0,sK18_skl) ),
inference(resolution,[status(thm)],[f234,f98]) ).
fof(f560,plain,
! [X0] :
( ~ sQ32_spl
| s(X0)
| ~ sP11_prd(sK18_skl,X0) ),
inference(resolution,[status(thm)],[f99,f234]) ).
fof(f561,plain,
! [X0] :
( ~ sQ32_spl
| ~ s(X0)
| ~ s(sK18_skl)
| s(X0) ),
inference(resolution,[status(thm)],[f559,f100]) ).
fof(f563,definition,
! [X0] :
( sQ52_spl
<=> ( ~ s(X0)
| s(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f566,plain,
( ~ sQ32_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f561,f563,f233]) ).
fof(f568,plain,
( ~ sQ38_spl
| ~ sQ32_spl
| s(sK23_skl) ),
inference(resolution,[status(thm)],[f560,f256]) ).
fof(f574,plain,
! [X0] :
( ~ sQ38_spl
| ~ sQ32_spl
| s(X0)
| ~ sP11_prd(X0,sK23_skl) ),
inference(resolution,[status(thm)],[f568,f98]) ).
fof(f575,plain,
! [X0] :
( ~ sQ38_spl
| ~ sQ32_spl
| s(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f574,f256]) ).
fof(f577,plain,
( sQ35_spl
| ~ sQ38_spl
| ~ sQ32_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f246,f575]) ).
fof(f578,plain,
( sQ25_spl
| ~ sQ38_spl
| ~ sQ32_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f206,f575]) ).
fof(f580,plain,
( sQ35_spl
| ~ sQ38_spl
| ~ sQ32_spl ),
inference(contradiction_clause,[status(thm)],[f577]) ).
fof(f586,plain,
! [X0] :
( ~ sQ32_spl
| s(X0)
| ~ sP11_prd(sK18_skl,X0) ),
inference(resolution,[status(thm)],[f234,f99]) ).
fof(f587,plain,
( ~ sQ20_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f187,f311]) ).
fof(f588,plain,
( ~ sQ20_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f587]) ).
fof(f591,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ46_spl
| p(X0)
| ~ sP0_prd(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f494,f18]) ).
fof(f592,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ46_spl
| p(X0)
| ~ sP0_prd(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f494,f17]) ).
fof(f597,plain,
! [X0] :
( ~ sQ46_spl
| ~ p(sK29_skl)
| ~ p(X0)
| p(X0) ),
inference(resolution,[status(thm)],[f331,f19]) ).
fof(f599,definition,
! [X0] :
( sQ53_spl
<=> ( ~ p(X0)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f602,plain,
( ~ sQ46_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f597,f599,f285]) ).
fof(f609,plain,
! [X0] :
( ~ sQ24_spl
| r(X0)
| ~ sP7_prd(sK14_skl,X0) ),
inference(resolution,[status(thm)],[f202,f69]) ).
fof(f611,plain,
! [X0,X1] :
( ~ q(X1)
| q(X0)
| q(X1)
| q(X0) ),
inference(resolution,[status(thm)],[f59,f57]) ).
fof(f612,definition,
! [X1] :
( sQ54_spl
<=> ( ~ q(X1)
| q(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f615,plain,
( sQ54_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f611,f520,f612]) ).
fof(f616,plain,
! [X0] :
( ~ sQ50_spl
| q(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f521]) ).
fof(f618,plain,
( sQ45_spl
| ~ sQ50_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f283,f616]) ).
fof(f620,plain,
( sQ45_spl
| ~ sQ50_spl ),
inference(contradiction_clause,[status(thm)],[f618]) ).
fof(f623,plain,
! [X0] :
( ~ sQ27_spl
| r(X0)
| ~ sP7_prd(sK17_skl,X0) ),
inference(resolution,[status(thm)],[f213,f69]) ).
fof(f625,plain,
! [X0] :
( ~ sQ16_spl
| q(X0)
| ~ q(sK9_skl) ),
inference(resolution,[status(thm)],[f172,f56]) ).
fof(f626,definition,
( sQ55_spl
<=> q(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f628,plain,
( sQ55_spl
| ~ q(sK9_skl) ),
inference(component_clause,[status(thm)],[f626]) ).
fof(f629,plain,
( ~ sQ16_spl
| sQ42_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f625,f626,f270,f171]) ).
fof(f630,plain,
! [X0] :
( ~ sQ9_spl
| q(X0)
| ~ q(sK5_skl)
| ~ q(X0) ),
inference(resolution,[status(thm)],[f515,f56]) ).
fof(f631,plain,
( ~ sQ9_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f630,f612,f142]) ).
fof(f636,plain,
! [X0] :
( ~ sQ45_spl
| q(X0)
| ~ sP5_prd(sK28_skl,X0) ),
inference(resolution,[status(thm)],[f57,f282]) ).
fof(f637,plain,
! [X0] :
( ~ sQ6_spl
| q(X0)
| ~ sP5_prd(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f132,f57]) ).
fof(f644,plain,
! [X0] :
( ~ sQ35_spl
| s(X0)
| ~ sP11_prd(sK21_skl,X0) ),
inference(resolution,[status(thm)],[f99,f245]) ).
fof(f652,plain,
( ~ sQ16_spl
| ~ sQ45_spl
| q(sK9_skl) ),
inference(resolution,[status(thm)],[f636,f172]) ).
fof(f653,plain,
! [X0] :
( ~ sQ45_spl
| ~ q(sK28_skl)
| ~ q(X0)
| q(X0) ),
inference(resolution,[status(thm)],[f636,f58]) ).
fof(f656,plain,
( ~ sQ16_spl
| ~ sQ45_spl
| sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f652,f628]) ).
fof(f657,plain,
( ~ sQ16_spl
| ~ sQ45_spl
| sQ55_spl ),
inference(contradiction_clause,[status(thm)],[f656]) ).
fof(f664,plain,
( ~ sQ16_spl
| ~ sQ6_spl
| q(sK9_skl) ),
inference(resolution,[status(thm)],[f637,f172]) ).
fof(f668,plain,
( ~ sQ16_spl
| ~ sQ6_spl
| sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f664,f628]) ).
fof(f669,plain,
( ~ sQ16_spl
| ~ sQ6_spl
| sQ55_spl ),
inference(contradiction_clause,[status(thm)],[f668]) ).
fof(f672,plain,
( ~ sQ35_spl
| ~ sQ40_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f550,f197,f263,f244]) ).
fof(f700,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ46_spl
| p(sK0_skl)
| p(X0)
| p(X0) ),
inference(resolution,[status(thm)],[f591,f20]) ).
fof(f701,definition,
( sQ57_spl
<=> p(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f705,plain,
( ~ sQ0_spl
| ~ sQ46_spl
| sQ57_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f700,f465,f701,f285,f108]) ).
fof(f706,plain,
! [X0] :
( ~ sQ49_spl
| p(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f466]) ).
fof(f709,plain,
( sQ43_spl
| ~ sQ49_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f276,f706]) ).
fof(f712,plain,
( sQ43_spl
| ~ sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f709]) ).
fof(f713,plain,
( sQ35_spl
| ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f246,f198]) ).
fof(f714,plain,
( sQ35_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f713]) ).
fof(f715,plain,
( ~ sQ45_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f653,f612,f281]) ).
fof(f717,plain,
( sQ25_spl
| ~ sQ38_spl
| ~ sQ32_spl ),
inference(contradiction_clause,[status(thm)],[f578]) ).
fof(f718,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ46_spl
| p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f592,f109]) ).
fof(f722,plain,
( sQ34_spl
| ~ sQ0_spl
| ~ sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f242,f718]) ).
fof(f723,plain,
( sQ34_spl
| ~ sQ0_spl
| ~ sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f722]) ).
fof(f729,plain,
( ~ sQ38_spl
| ~ sQ35_spl
| s(sK23_skl) ),
inference(resolution,[status(thm)],[f644,f256]) ).
fof(f730,plain,
! [X0] :
( ~ sQ35_spl
| ~ s(sK21_skl)
| ~ s(X0)
| s(X0) ),
inference(resolution,[status(thm)],[f644,f100]) ).
fof(f732,plain,
( ~ sQ35_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f730,f563,f244]) ).
fof(f735,plain,
! [X0] :
( ~ sQ38_spl
| ~ sQ35_spl
| s(X0)
| ~ sP11_prd(X0,sK23_skl) ),
inference(resolution,[status(thm)],[f729,f98]) ).
fof(f736,plain,
! [X0] :
( ~ sQ38_spl
| ~ sQ35_spl
| s(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f735,f256]) ).
fof(f738,plain,
( sQ32_spl
| ~ sQ38_spl
| ~ sQ35_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f235,f736]) ).
fof(f741,plain,
( sQ32_spl
| ~ sQ38_spl
| ~ sQ35_spl ),
inference(contradiction_clause,[status(thm)],[f738]) ).
fof(f763,plain,
( ~ sQ40_spl
| ~ sQ32_spl
| s(sK25_skl) ),
inference(resolution,[status(thm)],[f586,f264]) ).
fof(f768,plain,
! [X0] :
( ~ sQ40_spl
| ~ sQ32_spl
| s(X0)
| ~ sP11_prd(X0,sK25_skl) ),
inference(resolution,[status(thm)],[f763,f98]) ).
fof(f770,plain,
! [X0] :
( ~ sQ40_spl
| ~ sQ32_spl
| s(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f768,f264]) ).
fof(f772,plain,
( sQ35_spl
| ~ sQ40_spl
| ~ sQ32_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f246,f770]) ).
fof(f775,plain,
( sQ35_spl
| ~ sQ40_spl
| ~ sQ32_spl ),
inference(contradiction_clause,[status(thm)],[f772]) ).
fof(f779,plain,
( sQ43_spl
| ~ sQ0_spl
| ~ sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f276,f718]) ).
fof(f780,plain,
( sQ43_spl
| ~ sQ0_spl
| ~ sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f779]) ).
fof(f790,plain,
( ~ sQ19_spl
| ~ sQ27_spl
| r(sK11_skl) ),
inference(resolution,[status(thm)],[f623,f183]) ).
fof(f796,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ27_spl
| r(X0)
| ~ sP7_prd(X0,sK11_skl) ),
inference(resolution,[status(thm)],[f790,f68]) ).
fof(f798,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ27_spl
| r(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f796,f183]) ).
fof(f803,plain,
( ~ sQ38_spl
| ~ sQ32_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f575,f197,f233,f255]) ).
fof(f804,plain,
( ~ sQ38_spl
| ~ sQ35_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f736,f197,f244,f255]) ).
fof(f805,plain,
( ~ sQ21_spl
| ~ sQ27_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f486,f127,f212,f190]) ).
fof(f861,plain,
( ~ sQ16_spl
| ~ sQ9_spl
| q(sK9_skl) ),
inference(resolution,[status(thm)],[f514,f172]) ).
fof(f865,plain,
( ~ sQ16_spl
| ~ sQ9_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f861,f626,f142,f171]) ).
fof(f868,plain,
( ~ sQ19_spl
| ~ sQ27_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f798,f127,f212,f182]) ).
fof(f872,plain,
( sQ32_spl
| ~ sQ23_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f235,f198]) ).
fof(f875,plain,
( sQ32_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f872]) ).
fof(f880,plain,
! [X0] :
( ~ sQ24_spl
| r(X0)
| ~ sP7_prd(sK14_skl,X0) ),
inference(resolution,[status(thm)],[f202,f69]) ).
fof(f890,plain,
( sQ46_spl
| ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f287,f230]) ).
fof(f891,plain,
( sQ46_spl
| ~ sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f890]) ).
fof(f894,plain,
! [X0,X1] :
( ~ p(X1)
| p(X0)
| p(X1)
| p(X0) ),
inference(resolution,[status(thm)],[f20,f18]) ).
fof(f895,plain,
( sQ53_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f894,f465,f599]) ).
fof(f898,plain,
( ~ sQ19_spl
| ~ sQ24_spl
| r(sK11_skl) ),
inference(resolution,[status(thm)],[f609,f183]) ).
fof(f905,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ24_spl
| r(X0)
| ~ sP7_prd(X0,sK11_skl) ),
inference(resolution,[status(thm)],[f898,f68]) ).
fof(f906,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ24_spl
| r(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f905,f183]) ).
fof(f909,plain,
( sQ8_spl
| ~ sQ19_spl
| ~ sQ24_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f140,f906]) ).
fof(f910,plain,
( sQ27_spl
| ~ sQ19_spl
| ~ sQ24_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f214,f906]) ).
fof(f912,plain,
( sQ8_spl
| ~ sQ19_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f909]) ).
fof(f925,plain,
( ~ sQ21_spl
| ~ sQ24_spl
| r(sK13_skl) ),
inference(resolution,[status(thm)],[f880,f191]) ).
fof(f926,plain,
! [X0] :
( ~ sQ24_spl
| ~ r(sK14_skl)
| ~ r(X0)
| r(X0) ),
inference(resolution,[status(thm)],[f880,f70]) ).
fof(f929,plain,
( ~ sQ24_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f926,f436,f201]) ).
fof(f931,plain,
! [X0] :
( ~ sQ21_spl
| ~ sQ24_spl
| r(X0)
| ~ sP7_prd(X0,sK13_skl) ),
inference(resolution,[status(thm)],[f925,f68]) ).
fof(f933,plain,
! [X0] :
( ~ sQ21_spl
| ~ sQ24_spl
| r(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f931,f191]) ).
fof(f936,plain,
( sQ27_spl
| ~ sQ21_spl
| ~ sQ24_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f214,f933]) ).
fof(f939,plain,
( sQ27_spl
| ~ sQ21_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f936]) ).
fof(f940,plain,
( sQ27_spl
| ~ sQ19_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f910]) ).
fof(f945,plain,
( ~ sQ14_spl
| ~ sQ6_spl
| q(sK7_skl) ),
inference(resolution,[status(thm)],[f637,f164]) ).
fof(f951,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ6_spl
| q(X0)
| ~ sP5_prd(X0,sK7_skl) ),
inference(resolution,[status(thm)],[f945,f56]) ).
fof(f952,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ6_spl
| q(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f951,f164]) ).
fof(f955,plain,
( sQ44_spl
| ~ sQ14_spl
| ~ sQ6_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f279,f952]) ).
fof(f956,plain,
( sQ9_spl
| ~ sQ14_spl
| ~ sQ6_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f144,f952]) ).
fof(f958,plain,
( sQ44_spl
| ~ sQ14_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f955]) ).
fof(f959,plain,
( sQ9_spl
| ~ sQ14_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f956]) ).
fof(f960,plain,
$false,
inference(sat_refutation,[status(thm)],[f117,f118,f122,f123,f130,f137,f141,f145,f152,f153,f154,f155,f162,f166,f170,f174,f181,f185,f189,f193,f200,f207,f211,f215,f222,f223,f224,f225,f232,f239,f243,f247,f254,f258,f262,f266,f273,f280,f284,f288,f290,f292,f294,f296,f299,f303,f307,f309,f313,f315,f317,f319,f321,f326,f330,f335,f337,f342,f347,f349,f351,f358,f362,f364,f367,f369,f377,f386,f388,f393,f400,f406,f411,f414,f416,f425,f427,f432,f439,f450,f478,f488,f491,f508,f510,f534,f555,f557,f558,f566,f580,f588,f602,f615,f620,f629,f631,f657,f669,f672,f705,f712,f714,f715,f717,f723,f732,f741,f775,f780,f803,f804,f805,f865,f868,f875,f891,f895,f912,f929,f939,f940,f958,f959]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN723+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.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 : Mon Sep 21 11:14:47 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.063830 seconds
% 0.13/0.43 % CPU time: 0.302318 seconds
% 0.13/0.43 % Total memory used: 16.589 MB
% 0.13/0.43 % Net memory used: 16.383 MB
%------------------------------------------------------------------------------