%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN067+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 03:15:06 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 57
% Syntax : Number of formulae : 263 ( 1 unt; 56 def)
% Number of atoms : 1053 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 1355 ( 565 ~; 626 |; 99 &)
% ( 59 <=>; 4 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 59 ( 58 usr; 54 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-1 aty)
% Number of variables : 244 ( 193 !; 51 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X] :
( ( ( big_p(X)
=> ? [Y] :
( big_r(X,Y)
& big_p(Y) ) )
& big_p(a) )
=> ? [Z,W] :
( big_r(W,Z)
& big_r(X,W)
& big_p(Z) ) )
<=> ! [X1] :
( ( ? [Z2,W2] :
( big_r(W2,Z2)
& big_r(X1,W2)
& big_p(Z2) )
| ~ ? [Y1] :
( big_r(X1,Y1)
& big_p(Y1) )
| ~ big_p(a) )
& ( ? [Z1,W1] :
( big_r(W1,Z1)
& big_r(X1,W1)
& big_p(Z1) )
| big_p(X1)
| ~ big_p(a) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ! [X] :
( ( ( big_p(X)
=> ? [Y] :
( big_r(X,Y)
& big_p(Y) ) )
& big_p(a) )
=> ? [Z,W] :
( big_r(W,Z)
& big_r(X,W)
& big_p(Z) ) )
<=> ! [X1] :
( ( ? [Z2,W2] :
( big_r(W2,Z2)
& big_r(X1,W2)
& big_p(Z2) )
| ~ ? [Y1] :
( big_r(X1,Y1)
& big_p(Y1) )
| ~ big_p(a) )
& ( ? [Z1,W1] :
( big_r(W1,Z1)
& big_r(X1,W1)
& big_p(Z1) )
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X] :
( ? [Z,W] :
( big_r(W,Z)
& big_r(X,W)
& big_p(Z) )
| ( ! [Y] :
( ~ big_r(X,Y)
| ~ big_p(Y) )
& big_p(X) )
| ~ big_p(a) )
<~> ! [X1] :
( ( ? [Z2,W2] :
( big_r(W2,Z2)
& big_r(X1,W2)
& big_p(Z2) )
| ! [Y1] :
( ~ big_r(X1,Y1)
| ~ big_p(Y1) )
| ~ big_p(a) )
& ( ? [Z1,W1] :
( big_r(W1,Z1)
& big_r(X1,W1)
& big_p(Z1) )
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [X] :
( sP0_prd(X)
<=> ( ? [Z,W] :
( big_r(W,Z)
& big_r(X,W)
& big_p(Z) )
| ( ! [Y] :
( ~ big_r(X,Y)
| ~ big_p(Y) )
& big_p(X) )
| ~ big_p(a) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,definition,
! [X1] :
( sP1_prd(X1)
<=> ( ? [Z1,W1] :
( big_r(W1,Z1)
& big_r(X1,W1)
& big_p(Z1) )
| big_p(X1)
| ~ big_p(a) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f6,plain,
( ! [X] : sP0_prd(X)
<~> ! [X1] :
( ( ? [Z2,W2] :
( big_r(W2,Z2)
& big_r(X1,W2)
& big_p(Z2) )
| ! [Y1] :
( ~ big_r(X1,Y1)
| ~ big_p(Y1) )
| ~ big_p(a) )
& sP1_prd(X1) ) ),
inference(formula_renaming,[status(thm)],[f3,f5,f4]) ).
fof(f7,plain,
( ( ? [X1] :
( ( ! [Z2,W2] :
( ~ big_r(W2,Z2)
| ~ big_r(X1,W2)
| ~ big_p(Z2) )
& ? [Y1] :
( big_r(X1,Y1)
& big_p(Y1) )
& big_p(a) )
| ~ sP1_prd(X1) )
| ? [X] : ~ sP0_prd(X) )
& ( ! [X1] :
( ( ? [Z2,W2] :
( big_r(W2,Z2)
& big_r(X1,W2)
& big_p(Z2) )
| ! [Y1] :
( ~ big_r(X1,Y1)
| ~ big_p(Y1) )
| ~ big_p(a) )
& sP1_prd(X1) )
| ! [X] : sP0_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
( ( ? [X1] :
( ! [Z2,W2] :
( ~ big_r(W2,Z2)
| ~ big_r(X1,W2)
| ~ big_p(Z2) )
& ? [Y1] :
( big_r(X1,Y1)
& big_p(Y1) )
& big_p(a) )
| ? [X1] : ~ sP1_prd(X1)
| ? [X] : ~ sP0_prd(X) )
& ( ( ! [X1] :
( ? [Z2,W2] :
( big_r(W2,Z2)
& big_r(X1,W2)
& big_p(Z2) )
| ! [Y1] :
( ~ big_r(X1,Y1)
| ~ big_p(Y1) )
| ~ big_p(a) )
& ! [X1] : sP1_prd(X1) )
| ! [X] : sP0_prd(X) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f9,plain,
( ( ( ! [Z2,W2] :
( ~ big_r(W2,Z2)
| ~ big_r(sK4_skl,W2)
| ~ big_p(Z2) )
& big_r(sK4_skl,sK5_skl)
& big_p(sK5_skl)
& big_p(a) )
| ~ sP1_prd(sK3_skl)
| ~ sP0_prd(sK2_skl) )
& ( ( ! [X1] :
( ( big_r(sK1_skl(X1),sK0_skl(X1))
& big_r(X1,sK1_skl(X1))
& big_p(sK0_skl(X1)) )
| ! [Y1] :
( ~ big_r(X1,Y1)
| ~ big_p(Y1) )
| ~ big_p(a) )
& ! [X1] : sP1_prd(X1) )
| ! [X] : sP0_prd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(Z2,sK0_skl(X1)),skolemize(W2,sK1_skl(X1)),skolemize(X,sK2_skl),skolemize(X1,sK3_skl),skolemize(X1,sK4_skl),skolemize(Y1,sK5_skl)],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( sP1_prd(X1)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( big_p(sK0_skl(X2))
| ~ big_r(X2,X1)
| ~ big_p(X1)
| ~ big_p(a)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f12,plain,
! [X0,X1,X2] :
( big_r(X2,sK1_skl(X2))
| ~ big_r(X2,X1)
| ~ big_p(X1)
| ~ big_p(a)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f13,plain,
! [X0,X1,X2] :
( big_r(sK1_skl(X2),sK0_skl(X2))
| ~ big_r(X2,X1)
| ~ big_p(X1)
| ~ big_p(a)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f14,plain,
( big_p(a)
| ~ sP1_prd(sK3_skl)
| ~ sP0_prd(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f15,plain,
( big_p(sK5_skl)
| ~ sP1_prd(sK3_skl)
| ~ sP0_prd(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f16,plain,
( big_r(sK4_skl,sK5_skl)
| ~ sP1_prd(sK3_skl)
| ~ sP0_prd(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f17,plain,
! [X0,X1] :
( ~ big_r(X1,X0)
| ~ big_r(sK4_skl,X1)
| ~ big_p(X0)
| ~ sP1_prd(sK3_skl)
| ~ sP0_prd(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f18,definition,
! [X] :
( sP2_prd(X)
<=> ( ! [Y] :
( ~ big_r(X,Y)
| ~ big_p(Y) )
& big_p(X) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f19,plain,
! [X] :
( sP0_prd(X)
<=> ( ? [Z,W] :
( big_r(W,Z)
& big_r(X,W)
& big_p(Z) )
| sP2_prd(X)
| ~ big_p(a) ) ),
inference(formula_renaming,[status(thm)],[f4,f18]) ).
fof(f20,plain,
! [X] :
( ( ( ! [Z,W] :
( ~ big_r(W,Z)
| ~ big_r(X,W)
| ~ big_p(Z) )
& ~ sP2_prd(X)
& big_p(a) )
| sP0_prd(X) )
& ( ? [Z,W] :
( big_r(W,Z)
& big_r(X,W)
& big_p(Z) )
| sP2_prd(X)
| ~ big_p(a)
| ~ sP0_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
( ! [X] :
( ( ! [Z,W] :
( ~ big_r(W,Z)
| ~ big_r(X,W)
| ~ big_p(Z) )
& ~ sP2_prd(X)
& big_p(a) )
| sP0_prd(X) )
& ! [X] :
( ? [Z,W] :
( big_r(W,Z)
& big_r(X,W)
& big_p(Z) )
| sP2_prd(X)
| ~ big_p(a)
| ~ sP0_prd(X) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f22,plain,
( ! [X] :
( ( ! [Z,W] :
( ~ big_r(W,Z)
| ~ big_r(X,W)
| ~ big_p(Z) )
& ~ sP2_prd(X)
& big_p(a) )
| sP0_prd(X) )
& ! [X] :
( ( big_r(sK7_skl(X),sK6_skl(X))
& big_r(X,sK7_skl(X))
& big_p(sK6_skl(X)) )
| sP2_prd(X)
| ~ big_p(a)
| ~ sP0_prd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(Z,sK6_skl(X)),skolemize(W,sK7_skl(X))],[f21]) ).
fof(f23,plain,
! [X0] :
( big_p(sK6_skl(X0))
| sP2_prd(X0)
| ~ big_p(a)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0] :
( big_r(X0,sK7_skl(X0))
| sP2_prd(X0)
| ~ big_p(a)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
! [X0] :
( big_r(sK7_skl(X0),sK6_skl(X0))
| sP2_prd(X0)
| ~ big_p(a)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f26,plain,
! [X0] :
( big_p(a)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f27,plain,
! [X0] :
( ~ sP2_prd(X0)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ big_r(X2,X1)
| ~ big_r(X0,X2)
| ~ big_p(X1)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f29,plain,
! [X1] :
( ( ( ! [Z1,W1] :
( ~ big_r(W1,Z1)
| ~ big_r(X1,W1)
| ~ big_p(Z1) )
& ~ big_p(X1)
& big_p(a) )
| sP1_prd(X1) )
& ( ? [Z1,W1] :
( big_r(W1,Z1)
& big_r(X1,W1)
& big_p(Z1) )
| big_p(X1)
| ~ big_p(a)
| ~ sP1_prd(X1) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f30,plain,
( ! [X1] :
( ( ! [Z1,W1] :
( ~ big_r(W1,Z1)
| ~ big_r(X1,W1)
| ~ big_p(Z1) )
& ~ big_p(X1)
& big_p(a) )
| sP1_prd(X1) )
& ! [X1] :
( ? [Z1,W1] :
( big_r(W1,Z1)
& big_r(X1,W1)
& big_p(Z1) )
| big_p(X1)
| ~ big_p(a)
| ~ sP1_prd(X1) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f31,plain,
( ! [X1] :
( ( ! [Z1,W1] :
( ~ big_r(W1,Z1)
| ~ big_r(X1,W1)
| ~ big_p(Z1) )
& ~ big_p(X1)
& big_p(a) )
| sP1_prd(X1) )
& ! [X1] :
( ( big_r(sK9_skl(X1),sK8_skl(X1))
& big_r(X1,sK9_skl(X1))
& big_p(sK8_skl(X1)) )
| big_p(X1)
| ~ big_p(a)
| ~ sP1_prd(X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(Z1,sK8_skl(X1)),skolemize(W1,sK9_skl(X1))],[f30]) ).
fof(f32,plain,
! [X0] :
( big_p(sK8_skl(X0))
| big_p(X0)
| ~ big_p(a)
| ~ sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0] :
( big_r(X0,sK9_skl(X0))
| big_p(X0)
| ~ big_p(a)
| ~ sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
! [X0] :
( big_r(sK9_skl(X0),sK8_skl(X0))
| big_p(X0)
| ~ big_p(a)
| ~ sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f35,plain,
! [X0] :
( big_p(a)
| sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f36,plain,
! [X0] :
( ~ big_p(X0)
| sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ big_r(X2,X1)
| ~ big_r(X0,X2)
| ~ big_p(X1)
| sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f38,plain,
! [X] :
( ( ? [Y] :
( big_r(X,Y)
& big_p(Y) )
| ~ big_p(X)
| sP2_prd(X) )
& ( ( ! [Y] :
( ~ big_r(X,Y)
| ~ big_p(Y) )
& big_p(X) )
| ~ sP2_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f18]) ).
fof(f39,plain,
( ! [X] :
( ? [Y] :
( big_r(X,Y)
& big_p(Y) )
| ~ big_p(X)
| sP2_prd(X) )
& ! [X] :
( ( ! [Y] :
( ~ big_r(X,Y)
| ~ big_p(Y) )
& big_p(X) )
| ~ sP2_prd(X) ) ),
inference(miniscoping,[status(thm)],[f38]) ).
fof(f40,plain,
( ! [X] :
( ( big_r(X,sK10_skl(X))
& big_p(sK10_skl(X)) )
| ~ big_p(X)
| sP2_prd(X) )
& ! [X] :
( ( ! [Y] :
( ~ big_r(X,Y)
| ~ big_p(Y) )
& big_p(X) )
| ~ sP2_prd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(Y,sK10_skl(X))],[f39]) ).
fof(f41,plain,
! [X0] :
( big_p(X0)
| ~ sP2_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( ~ big_r(X0,X1)
| ~ big_p(X1)
| ~ sP2_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f43,plain,
! [X0] :
( big_p(sK10_skl(X0))
| ~ big_p(X0)
| sP2_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f44,plain,
! [X0] :
( big_r(X0,sK10_skl(X0))
| ~ big_p(X0)
| sP2_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f45,definition,
! [X0] :
( sQ0_spl
<=> sP0_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f46,plain,
! [X0] :
( ~ sQ0_spl
| sP0_prd(X0) ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,definition,
! [X1] :
( sQ1_spl
<=> sP1_prd(X1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f49,plain,
! [X0] :
( ~ sQ1_spl
| sP1_prd(X0) ),
inference(component_clause,[status(thm)],[f48]) ).
fof(f51,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f10,f45,f48]) ).
fof(f52,definition,
( sQ2_spl
<=> big_p(a) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f55,definition,
! [X1,X2] :
( sQ3_spl
<=> ( big_p(sK0_skl(X2))
| ~ big_r(X2,X1)
| ~ big_p(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f56,plain,
! [X0,X1] :
( ~ sQ3_spl
| big_p(sK0_skl(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,plain,
( sQ3_spl
| ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f11,f45,f52,f55]) ).
fof(f59,definition,
! [X1,X2] :
( sQ4_spl
<=> ( big_r(X2,sK1_skl(X2))
| ~ big_r(X2,X1)
| ~ big_p(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f60,plain,
! [X0,X1] :
( ~ sQ4_spl
| big_r(X1,sK1_skl(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,plain,
( sQ4_spl
| ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f12,f45,f52,f59]) ).
fof(f63,definition,
! [X1,X2] :
( sQ5_spl
<=> ( big_r(sK1_skl(X2),sK0_skl(X2))
| ~ big_r(X2,X1)
| ~ big_p(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f64,plain,
! [X0,X1] :
( ~ sQ5_spl
| big_r(sK1_skl(X1),sK0_skl(X1))
| ~ big_r(X1,X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,plain,
( sQ5_spl
| ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f13,f45,f52,f63]) ).
fof(f67,definition,
( sQ6_spl
<=> sP0_prd(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ6_spl
| sP0_prd(sK2_skl) ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f69,plain,
( sQ6_spl
| ~ sP0_prd(sK2_skl) ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,definition,
( sQ7_spl
<=> sP1_prd(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( sQ7_spl
| ~ sP1_prd(sK3_skl) ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,plain,
( sQ2_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f14,f67,f70,f52]) ).
fof(f74,definition,
( sQ8_spl
<=> big_p(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( ~ sQ8_spl
| big_p(sK5_skl) ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,plain,
( sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f15,f67,f70,f74]) ).
fof(f78,definition,
( sQ9_spl
<=> big_r(sK4_skl,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f79,plain,
( ~ sQ9_spl
| big_r(sK4_skl,sK5_skl) ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f81,plain,
( sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f16,f67,f70,f78]) ).
fof(f82,definition,
! [X0,X1] :
( sQ10_spl
<=> ( ~ big_r(X1,X0)
| ~ big_r(sK4_skl,X1)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f83,plain,
! [X0,X1] :
( ~ sQ10_spl
| ~ big_r(X1,X0)
| ~ big_r(sK4_skl,X1)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,plain,
( sQ10_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f17,f67,f70,f82]) ).
fof(f86,definition,
! [X0] :
( sQ11_spl
<=> ( big_p(sK6_skl(X0))
| sP2_prd(X0)
| ~ sP0_prd(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f87,plain,
! [X0] :
( ~ sQ11_spl
| big_p(sK6_skl(X0))
| sP2_prd(X0)
| ~ sP0_prd(X0) ),
inference(component_clause,[status(thm)],[f86]) ).
fof(f89,plain,
( ~ sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f23,f86,f52]) ).
fof(f90,definition,
! [X0] :
( sQ12_spl
<=> ( big_r(X0,sK7_skl(X0))
| sP2_prd(X0)
| ~ sP0_prd(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f91,plain,
! [X0] :
( ~ sQ12_spl
| big_r(X0,sK7_skl(X0))
| sP2_prd(X0)
| ~ sP0_prd(X0) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,plain,
( ~ sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f24,f90,f52]) ).
fof(f94,definition,
! [X0] :
( sQ13_spl
<=> ( big_r(sK7_skl(X0),sK6_skl(X0))
| sP2_prd(X0)
| ~ sP0_prd(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f95,plain,
! [X0] :
( ~ sQ13_spl
| big_r(sK7_skl(X0),sK6_skl(X0))
| sP2_prd(X0)
| ~ sP0_prd(X0) ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,plain,
( ~ sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f25,f94,f52]) ).
fof(f98,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f26,f45,f52]) ).
fof(f99,definition,
! [X0] :
( sQ14_spl
<=> ( big_p(sK8_skl(X0))
| big_p(X0)
| ~ sP1_prd(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f100,plain,
! [X0] :
( ~ sQ14_spl
| big_p(sK8_skl(X0))
| big_p(X0)
| ~ sP1_prd(X0) ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( ~ sQ2_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f32,f99,f52]) ).
fof(f103,definition,
! [X0] :
( sQ15_spl
<=> ( big_r(X0,sK9_skl(X0))
| big_p(X0)
| ~ sP1_prd(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f104,plain,
! [X0] :
( ~ sQ15_spl
| big_r(X0,sK9_skl(X0))
| big_p(X0)
| ~ sP1_prd(X0) ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( ~ sQ2_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f33,f103,f52]) ).
fof(f107,definition,
! [X0] :
( sQ16_spl
<=> ( big_r(sK9_skl(X0),sK8_skl(X0))
| big_p(X0)
| ~ sP1_prd(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f108,plain,
! [X0] :
( ~ sQ16_spl
| big_r(sK9_skl(X0),sK8_skl(X0))
| big_p(X0)
| ~ sP1_prd(X0) ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,plain,
( ~ sQ2_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f34,f107,f52]) ).
fof(f111,plain,
( sQ2_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f35,f48,f52]) ).
fof(f113,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ0_spl
| big_p(sK6_skl(X0))
| sP2_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f87,f46]) ).
fof(f116,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ0_spl
| big_r(X0,sK7_skl(X0))
| sP2_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f91,f46]) ).
fof(f121,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ0_spl
| big_r(sK7_skl(X0),sK6_skl(X0))
| sP2_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f95,f46]) ).
fof(f122,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ0_spl
| ~ big_r(X1,sK7_skl(X0))
| ~ big_p(sK6_skl(X0))
| sP1_prd(X1)
| sP2_prd(X0) ),
inference(resolution,[status(thm)],[f121,f37]) ).
fof(f123,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ big_r(X1,sK7_skl(X0))
| sP1_prd(X1)
| sP2_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f122,f113]) ).
fof(f124,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sP2_prd(X0)
| sP1_prd(X0)
| sP2_prd(X0) ),
inference(resolution,[status(thm)],[f123,f116]) ).
fof(f125,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sP1_prd(X0)
| sP2_prd(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f124]) ).
fof(f129,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| big_p(X0)
| sP1_prd(X0) ),
inference(resolution,[status(thm)],[f125,f41]) ).
fof(f130,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sP1_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f129,f36]) ).
fof(f133,plain,
( sQ7_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f72,f130]) ).
fof(f135,plain,
( sQ7_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ6_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f69,f46]) ).
fof(f137,plain,
( sQ6_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f136]) ).
fof(f139,plain,
! [X0] :
( ~ sQ10_spl
| ~ big_p(sK4_skl)
| sP2_prd(sK4_skl)
| ~ big_r(sK10_skl(sK4_skl),X0)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f83,f44]) ).
fof(f140,definition,
! [X0] :
( sQ17_spl
<=> ( ~ big_r(sK10_skl(sK4_skl),X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f141,plain,
! [X0] :
( ~ sQ17_spl
| ~ big_r(sK10_skl(sK4_skl),X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f143,definition,
( sQ18_spl
<=> sP2_prd(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f144,plain,
( ~ sQ18_spl
| sP2_prd(sK4_skl) ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,definition,
( sQ19_spl
<=> big_p(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f148,plain,
( sQ19_spl
| ~ big_p(sK4_skl) ),
inference(component_clause,[status(thm)],[f146]) ).
fof(f149,plain,
( ~ sQ10_spl
| ~ sQ19_spl
| sQ18_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f139,f140,f143,f146,f82]) ).
fof(f154,definition,
( sQ21_spl
<=> sP2_prd(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( ~ sQ21_spl
| sP2_prd(sK5_skl) ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f159,plain,
( ~ sQ21_spl
| big_p(sK5_skl) ),
inference(resolution,[status(thm)],[f155,f41]) ).
fof(f162,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ1_spl
| big_r(sK9_skl(X0),sK8_skl(X0))
| big_p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f49]) ).
fof(f163,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ1_spl
| big_p(sK8_skl(X0))
| big_p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f100,f49]) ).
fof(f164,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ1_spl
| big_r(X0,sK9_skl(X0))
| big_p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f104,f49]) ).
fof(f165,plain,
( sQ19_spl
| ~ sQ15_spl
| ~ sQ1_spl
| big_r(sK4_skl,sK9_skl(sK4_skl)) ),
inference(resolution,[status(thm)],[f164,f148]) ).
fof(f166,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ sQ0_spl
| ~ big_r(X0,X1)
| ~ big_p(X1)
| big_r(X0,sK7_skl(X0)) ),
inference(resolution,[status(thm)],[f116,f42]) ).
fof(f169,plain,
! [X0] :
( ~ sQ10_spl
| sQ19_spl
| ~ sQ15_spl
| ~ sQ1_spl
| ~ big_r(sK9_skl(sK4_skl),X0)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f165,f83]) ).
fof(f171,plain,
( ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ10_spl
| sQ19_spl
| ~ sQ15_spl
| big_p(sK4_skl)
| ~ big_p(sK8_skl(sK4_skl)) ),
inference(resolution,[status(thm)],[f169,f162]) ).
fof(f173,definition,
( sQ22_spl
<=> big_p(sK8_skl(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ15_spl
| sQ19_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f171,f173,f146,f103,f82,f48,f107]) ).
fof(f180,definition,
( sQ24_spl
<=> sP2_prd(sK9_skl(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( ~ sQ24_spl
| sP2_prd(sK9_skl(sK4_skl)) ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f183,definition,
( sQ25_spl
<=> big_p(sK9_skl(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( sQ25_spl
| ~ big_p(sK9_skl(sK4_skl)) ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f189,plain,
! [X0,X1] :
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ big_r(sK7_skl(sK4_skl),X1)
| ~ big_p(X1)
| ~ big_r(sK4_skl,X0)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f166,f83]) ).
fof(f197,definition,
! [X0] :
( sQ28_spl
<=> ( ~ big_r(sK4_skl,X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f198,plain,
! [X0] :
( ~ sQ28_spl
| ~ big_r(sK4_skl,X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f200,definition,
! [X1] :
( sQ29_spl
<=> ( ~ big_r(sK7_skl(sK4_skl),X1)
| ~ big_p(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f201,plain,
! [X0] :
( ~ sQ29_spl
| ~ big_r(sK7_skl(sK4_skl),X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f200]) ).
fof(f203,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sQ29_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f189,f197,f200,f45,f90,f82]) ).
fof(f204,plain,
! [X0] :
( ~ sQ18_spl
| ~ big_r(sK4_skl,X0)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f144,f42]) ).
fof(f209,plain,
( ~ sQ24_spl
| big_p(sK9_skl(sK4_skl)) ),
inference(resolution,[status(thm)],[f181,f41]) ).
fof(f210,plain,
( ~ sQ24_spl
| sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f209,f185]) ).
fof(f211,plain,
( ~ sQ24_spl
| sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f210]) ).
fof(f223,plain,
( ~ sQ9_spl
| ~ sQ28_spl
| ~ big_p(sK5_skl) ),
inference(resolution,[status(thm)],[f198,f79]) ).
fof(f225,plain,
( ~ sQ28_spl
| ~ big_p(sK4_skl)
| sP2_prd(sK4_skl)
| ~ big_p(sK10_skl(sK4_skl)) ),
inference(resolution,[status(thm)],[f198,f44]) ).
fof(f226,plain,
( ~ sQ9_spl
| ~ sQ28_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f223,f75]) ).
fof(f227,plain,
( ~ sQ9_spl
| ~ sQ28_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f226]) ).
fof(f228,plain,
( ~ sQ9_spl
| ~ sQ18_spl
| ~ big_p(sK5_skl) ),
inference(resolution,[status(thm)],[f204,f79]) ).
fof(f231,plain,
( ~ sQ9_spl
| ~ sQ18_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f228,f75]) ).
fof(f232,plain,
( ~ sQ9_spl
| ~ sQ18_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f231]) ).
fof(f235,plain,
( ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ29_spl
| sP2_prd(sK4_skl)
| ~ big_p(sK6_skl(sK4_skl)) ),
inference(resolution,[status(thm)],[f201,f121]) ).
fof(f238,definition,
( sQ30_spl
<=> big_p(sK6_skl(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f240,plain,
( sQ30_spl
| ~ big_p(sK6_skl(sK4_skl)) ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,plain,
( ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ29_spl
| sQ18_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f235,f238,f143,f200,f45,f94]) ).
fof(f256,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| sQ30_spl
| sP2_prd(sK4_skl) ),
inference(resolution,[status(thm)],[f240,f113]) ).
fof(f259,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| sQ30_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f256,f143,f238,f45,f86]) ).
fof(f260,plain,
( ~ sQ21_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f159,f74,f154]) ).
fof(f261,definition,
( sQ35_spl
<=> big_p(sK10_skl(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f308,plain,
! [X0,X1] :
( sQ6_spl
| ~ big_r(X1,X0)
| ~ big_r(sK2_skl,X1)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f28,f69]) ).
fof(f309,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| big_r(X1,sK7_skl(X1))
| sP2_prd(X1)
| ~ big_r(X2,X0)
| ~ big_r(X1,X2)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f28,f91]) ).
fof(f317,plain,
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ17_spl
| big_p(sK10_skl(sK4_skl))
| ~ big_p(sK9_skl(sK10_skl(sK4_skl))) ),
inference(resolution,[status(thm)],[f141,f164]) ).
fof(f318,plain,
( ~ sQ17_spl
| ~ big_p(sK10_skl(sK4_skl))
| sP2_prd(sK10_skl(sK4_skl))
| ~ big_p(sK10_skl(sK10_skl(sK4_skl))) ),
inference(resolution,[status(thm)],[f141,f44]) ).
fof(f325,definition,
( sQ44_spl
<=> sP2_prd(sK10_skl(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f333,definition,
( sQ46_spl
<=> big_p(sK9_skl(sK10_skl(sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f336,plain,
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ17_spl
| sQ35_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f317,f333,f261,f140,f48,f103]) ).
fof(f337,definition,
( sQ47_spl
<=> big_p(sK10_skl(sK10_skl(sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f339,plain,
( sQ47_spl
| ~ big_p(sK10_skl(sK10_skl(sK4_skl))) ),
inference(component_clause,[status(thm)],[f337]) ).
fof(f340,plain,
( ~ sQ17_spl
| ~ sQ35_spl
| sQ44_spl
| ~ sQ47_spl ),
inference(split_clause,[status(thm)],[f318,f337,f325,f261,f140]) ).
fof(f341,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| sQ6_spl
| sP2_prd(sK2_skl)
| ~ big_r(X2,X1)
| ~ big_r(sK2_skl,X2)
| ~ big_p(X1)
| ~ big_r(sK7_skl(sK2_skl),X0)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f308,f309]) ).
fof(f342,plain,
! [X0,X1] :
( ~ sQ4_spl
| sQ6_spl
| ~ big_r(sK2_skl,X1)
| ~ big_p(X1)
| ~ big_r(sK1_skl(sK2_skl),X0)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f308,f60]) ).
fof(f343,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ1_spl
| sQ6_spl
| big_p(sK2_skl)
| ~ big_r(sK9_skl(sK2_skl),X0)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f308,f164]) ).
fof(f344,plain,
! [X0] :
( sQ6_spl
| ~ big_p(sK2_skl)
| sP2_prd(sK2_skl)
| ~ big_r(sK10_skl(sK2_skl),X0)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f308,f44]) ).
fof(f345,definition,
! [X0] :
( sQ48_spl
<=> ( ~ big_r(sK7_skl(sK2_skl),X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f348,definition,
! [X1,X2] :
( sQ49_spl
<=> ( ~ big_r(X2,X1)
| ~ big_r(sK2_skl,X2)
| ~ big_p(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f351,definition,
( sQ50_spl
<=> sP2_prd(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f352,plain,
( ~ sQ50_spl
| sP2_prd(sK2_skl) ),
inference(component_clause,[status(thm)],[f351]) ).
fof(f354,plain,
( ~ sQ12_spl
| sQ6_spl
| sQ50_spl
| sQ49_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f341,f345,f348,f351,f67,f90]) ).
fof(f355,definition,
! [X0] :
( sQ51_spl
<=> ( ~ big_r(sK1_skl(sK2_skl),X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f356,plain,
! [X0] :
( ~ sQ51_spl
| ~ big_r(sK1_skl(sK2_skl),X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f355]) ).
fof(f358,definition,
! [X1] :
( sQ52_spl
<=> ( ~ big_r(sK2_skl,X1)
| ~ big_p(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f359,plain,
! [X0] :
( ~ sQ52_spl
| ~ big_r(sK2_skl,X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f358]) ).
fof(f361,plain,
( ~ sQ4_spl
| sQ6_spl
| sQ52_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f342,f355,f358,f67,f59]) ).
fof(f362,definition,
! [X0] :
( sQ53_spl
<=> ( ~ big_r(sK9_skl(sK2_skl),X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f363,plain,
! [X0] :
( ~ sQ53_spl
| ~ big_r(sK9_skl(sK2_skl),X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f362]) ).
fof(f365,definition,
( sQ54_spl
<=> big_p(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f368,plain,
( ~ sQ15_spl
| ~ sQ1_spl
| sQ6_spl
| sQ54_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f343,f362,f365,f67,f48,f103]) ).
fof(f369,definition,
! [X0] :
( sQ55_spl
<=> ( ~ big_r(sK10_skl(sK2_skl),X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f372,plain,
( sQ6_spl
| ~ sQ54_spl
| sQ50_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f344,f369,f351,f365,f67]) ).
fof(f373,plain,
( sQ7_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f72,f49]) ).
fof(f374,plain,
( sQ7_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f373]) ).
fof(f375,plain,
( ~ sQ50_spl
| sP0_prd(sK2_skl) ),
inference(resolution,[status(thm)],[f352,f27]) ).
fof(f378,plain,
( ~ sQ50_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f375,f67,f351]) ).
fof(f379,plain,
( ~ sQ12_spl
| ~ sQ6_spl
| big_r(sK2_skl,sK7_skl(sK2_skl))
| sP2_prd(sK2_skl) ),
inference(resolution,[status(thm)],[f68,f91]) ).
fof(f380,definition,
( sQ56_spl
<=> big_r(sK2_skl,sK7_skl(sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f383,plain,
( ~ sQ12_spl
| ~ sQ6_spl
| sQ56_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f379,f351,f380,f67,f90]) ).
fof(f394,plain,
! [X0,X1] :
( ~ sQ12_spl
| ~ sQ52_spl
| sP2_prd(sK2_skl)
| ~ big_r(X1,X0)
| ~ big_r(sK2_skl,X1)
| ~ big_p(X0)
| ~ big_p(sK7_skl(sK2_skl)) ),
inference(resolution,[status(thm)],[f359,f309]) ).
fof(f396,plain,
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ52_spl
| big_p(sK2_skl)
| ~ big_p(sK9_skl(sK2_skl)) ),
inference(resolution,[status(thm)],[f359,f164]) ).
fof(f397,plain,
( ~ sQ52_spl
| ~ big_p(sK2_skl)
| sP2_prd(sK2_skl)
| ~ big_p(sK10_skl(sK2_skl)) ),
inference(resolution,[status(thm)],[f359,f44]) ).
fof(f398,definition,
( sQ58_spl
<=> big_p(sK7_skl(sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( ~ sQ12_spl
| ~ sQ52_spl
| sQ50_spl
| sQ49_spl
| ~ sQ58_spl ),
inference(split_clause,[status(thm)],[f394,f398,f348,f351,f358,f90]) ).
fof(f402,definition,
( sQ59_spl
<=> big_p(sK1_skl(sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f404,plain,
( sQ59_spl
| ~ big_p(sK1_skl(sK2_skl)) ),
inference(component_clause,[status(thm)],[f402]) ).
fof(f406,definition,
( sQ60_spl
<=> big_p(sK9_skl(sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f408,plain,
( sQ60_spl
| ~ big_p(sK9_skl(sK2_skl)) ),
inference(component_clause,[status(thm)],[f406]) ).
fof(f409,plain,
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ52_spl
| sQ54_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f396,f406,f365,f358,f48,f103]) ).
fof(f410,definition,
( sQ61_spl
<=> big_p(sK10_skl(sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f412,plain,
( sQ61_spl
| ~ big_p(sK10_skl(sK2_skl)) ),
inference(component_clause,[status(thm)],[f410]) ).
fof(f413,plain,
( ~ sQ52_spl
| ~ sQ54_spl
| sQ50_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f397,f410,f351,f365,f358]) ).
fof(f414,plain,
( sQ61_spl
| ~ big_p(sK2_skl)
| sP2_prd(sK2_skl) ),
inference(resolution,[status(thm)],[f412,f43]) ).
fof(f415,plain,
( sQ61_spl
| ~ sQ54_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f414,f351,f365,f410]) ).
fof(f416,plain,
( sQ47_spl
| ~ big_p(sK10_skl(sK4_skl))
| sP2_prd(sK10_skl(sK4_skl)) ),
inference(resolution,[status(thm)],[f339,f43]) ).
fof(f417,plain,
( sQ47_spl
| ~ sQ35_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f416,f325,f261,f337]) ).
fof(f434,definition,
! [X0] :
( sQ65_spl
<=> ( ~ big_r(sK9_skl(sK4_skl),X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f448,definition,
( sQ67_spl
<=> sP0_prd(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f450,plain,
( sQ67_spl
| ~ sP0_prd(sK4_skl) ),
inference(component_clause,[status(thm)],[f448]) ).
fof(f465,plain,
! [X0,X1] :
( sQ67_spl
| ~ big_r(X1,X0)
| ~ big_r(sK4_skl,X1)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f450,f28]) ).
fof(f466,plain,
( sQ67_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f465,f82,f448]) ).
fof(f477,plain,
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ18_spl
| big_p(sK4_skl)
| ~ big_p(sK9_skl(sK4_skl)) ),
inference(resolution,[status(thm)],[f204,f164]) ).
fof(f484,plain,
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ18_spl
| sQ19_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f477,f183,f146,f143,f48,f103]) ).
fof(f522,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ51_spl
| ~ big_r(sK2_skl,X0)
| ~ big_p(X0)
| ~ big_p(sK0_skl(sK2_skl)) ),
inference(resolution,[status(thm)],[f356,f64]) ).
fof(f526,plain,
( ~ sQ51_spl
| ~ big_p(sK1_skl(sK2_skl))
| sP2_prd(sK1_skl(sK2_skl))
| ~ big_p(sK10_skl(sK1_skl(sK2_skl))) ),
inference(resolution,[status(thm)],[f356,f44]) ).
fof(f527,definition,
( sQ80_spl
<=> big_p(sK0_skl(sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f529,plain,
( sQ80_spl
| ~ big_p(sK0_skl(sK2_skl)) ),
inference(component_clause,[status(thm)],[f527]) ).
fof(f530,plain,
( ~ sQ5_spl
| ~ sQ51_spl
| sQ52_spl
| ~ sQ80_spl ),
inference(split_clause,[status(thm)],[f522,f527,f358,f355,f63]) ).
fof(f537,definition,
( sQ83_spl
<=> sP2_prd(sK1_skl(sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f538,plain,
( ~ sQ83_spl
| sP2_prd(sK1_skl(sK2_skl)) ),
inference(component_clause,[status(thm)],[f537]) ).
fof(f549,definition,
( sQ86_spl
<=> big_p(sK10_skl(sK1_skl(sK2_skl))) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f551,plain,
( sQ86_spl
| ~ big_p(sK10_skl(sK1_skl(sK2_skl))) ),
inference(component_clause,[status(thm)],[f549]) ).
fof(f552,plain,
( ~ sQ51_spl
| ~ sQ59_spl
| sQ83_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f526,f549,f537,f402,f355]) ).
fof(f555,plain,
( ~ sQ83_spl
| big_p(sK1_skl(sK2_skl)) ),
inference(resolution,[status(thm)],[f538,f41]) ).
fof(f556,plain,
! [X0] :
( ~ sQ3_spl
| sQ80_spl
| ~ big_r(sK2_skl,X0)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f529,f56]) ).
fof(f562,plain,
( sQ86_spl
| ~ big_p(sK1_skl(sK2_skl))
| sP2_prd(sK1_skl(sK2_skl)) ),
inference(resolution,[status(thm)],[f551,f43]) ).
fof(f563,plain,
( sQ86_spl
| ~ sQ59_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f562,f537,f402,f549]) ).
fof(f566,plain,
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ3_spl
| sQ80_spl
| big_p(sK2_skl)
| ~ big_p(sK9_skl(sK2_skl)) ),
inference(resolution,[status(thm)],[f556,f164]) ).
fof(f567,plain,
( ~ sQ3_spl
| sQ80_spl
| ~ big_p(sK2_skl)
| sP2_prd(sK2_skl)
| ~ big_p(sK10_skl(sK2_skl)) ),
inference(resolution,[status(thm)],[f556,f44]) ).
fof(f570,plain,
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ3_spl
| sQ80_spl
| sQ54_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f566,f406,f365,f527,f55,f48,f103]) ).
fof(f571,plain,
( ~ sQ3_spl
| sQ80_spl
| ~ sQ54_spl
| sQ50_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f567,f410,f351,f365,f527,f55]) ).
fof(f572,plain,
( sQ59_spl
| ~ sQ83_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f404,f555]) ).
fof(f573,plain,
( sQ59_spl
| ~ sQ83_spl ),
inference(contradiction_clause,[status(thm)],[f572]) ).
fof(f591,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sQ10_spl
| ~ big_r(sK4_skl,X1)
| ~ big_p(X1)
| ~ big_r(sK1_skl(sK4_skl),X0)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f83,f60]) ).
fof(f592,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ10_spl
| big_p(sK4_skl)
| ~ big_r(sK9_skl(sK4_skl),X0)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f83,f164]) ).
fof(f595,definition,
! [X0] :
( sQ88_spl
<=> ( ~ big_r(sK1_skl(sK4_skl),X0)
| ~ big_p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f596,plain,
! [X0] :
( ~ sQ88_spl
| ~ big_r(sK1_skl(sK4_skl),X0)
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f595]) ).
fof(f598,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| sQ28_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f591,f595,f197,f82,f59]) ).
fof(f599,plain,
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ10_spl
| sQ19_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f592,f434,f146,f82,f48,f103]) ).
fof(f601,plain,
( ~ sQ28_spl
| ~ sQ19_spl
| sQ18_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f225,f261,f143,f146,f197]) ).
fof(f602,plain,
( ~ sQ3_spl
| sQ80_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f556,f358,f527,f55]) ).
fof(f619,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ88_spl
| ~ big_r(sK4_skl,X0)
| ~ big_p(X0)
| ~ big_p(sK0_skl(sK4_skl)) ),
inference(resolution,[status(thm)],[f596,f64]) ).
fof(f624,definition,
( sQ89_spl
<=> big_p(sK0_skl(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f626,plain,
( sQ89_spl
| ~ big_p(sK0_skl(sK4_skl)) ),
inference(component_clause,[status(thm)],[f624]) ).
fof(f627,plain,
( ~ sQ5_spl
| ~ sQ88_spl
| sQ28_spl
| ~ sQ89_spl ),
inference(split_clause,[status(thm)],[f619,f624,f197,f595,f63]) ).
fof(f653,plain,
( ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ53_spl
| big_p(sK2_skl)
| ~ big_p(sK8_skl(sK2_skl)) ),
inference(resolution,[status(thm)],[f363,f162]) ).
fof(f658,definition,
( sQ96_spl
<=> big_p(sK8_skl(sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f660,plain,
( sQ96_spl
| ~ big_p(sK8_skl(sK2_skl)) ),
inference(component_clause,[status(thm)],[f658]) ).
fof(f661,plain,
( ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ53_spl
| sQ54_spl
| ~ sQ96_spl ),
inference(split_clause,[status(thm)],[f653,f658,f365,f362,f48,f107]) ).
fof(f668,definition,
( sQ99_spl
<=> sP2_prd(sK9_skl(sK2_skl)) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f669,plain,
( ~ sQ99_spl
| sP2_prd(sK9_skl(sK2_skl)) ),
inference(component_clause,[status(thm)],[f668]) ).
fof(f708,plain,
( ~ sQ99_spl
| big_p(sK9_skl(sK2_skl)) ),
inference(resolution,[status(thm)],[f669,f41]) ).
fof(f709,plain,
( ~ sQ99_spl
| sQ60_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f708,f408]) ).
fof(f710,plain,
( ~ sQ99_spl
| sQ60_spl ),
inference(contradiction_clause,[status(thm)],[f709]) ).
fof(f716,plain,
( ~ sQ14_spl
| ~ sQ1_spl
| sQ96_spl
| big_p(sK2_skl) ),
inference(resolution,[status(thm)],[f660,f163]) ).
fof(f733,plain,
! [X0] :
( ~ sQ3_spl
| sQ89_spl
| ~ big_r(sK4_skl,X0)
| ~ big_p(X0) ),
inference(resolution,[status(thm)],[f626,f56]) ).
fof(f734,plain,
( ~ sQ3_spl
| sQ89_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f733,f197,f624,f55]) ).
fof(f735,plain,
( ~ sQ14_spl
| ~ sQ1_spl
| sQ96_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f716,f365,f658,f48,f99]) ).
fof(f736,plain,
$false,
inference(sat_refutation,[status(thm)],[f51,f58,f62,f66,f73,f77,f81,f85,f89,f93,f97,f98,f102,f106,f110,f111,f135,f137,f149,f176,f203,f211,f227,f232,f241,f259,f260,f336,f340,f354,f361,f368,f372,f374,f378,f383,f401,f409,f413,f415,f417,f466,f484,f530,f552,f563,f570,f571,f573,f598,f599,f601,f602,f627,f661,f710,f734,f735]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN067+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 10:41:58 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.42 % Elapsed time: 0.044069 seconds
% 0.09/0.42 % CPU time: 0.191204 seconds
% 0.09/0.42 % Total memory used: 16.557 MB
% 0.09/0.42 % Net memory used: 16.260 MB
%------------------------------------------------------------------------------