%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYO606+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 03:42:49 PM UTC 2026
% Result : Theorem 0.10s 0.53s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 60
% Syntax : Number of formulae : 459 ( 1 unt; 51 def)
% Number of atoms : 1742 ( 0 equ)
% Maximal formula atoms : 41 ( 3 avg)
% Number of connectives : 2243 ( 960 ~;1024 |; 200 &)
% ( 59 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 62 ( 61 usr; 45 prp; 0-3 aty)
% Number of functors : 27 ( 27 usr; 6 con; 0-2 aty)
% Number of variables : 793 ( 649 !; 144 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ~ ? [A,B] :
! [C] :
( ( h_false_only(A,C)
& g_both(A,B) )
| ( ( h_false_only(A,C)
| h_both(A,C) )
& g_true_only(A,B) ) )
& ? [A] :
( ~ ? [B] :
! [C] :
( ( h_false_only(A,C)
& g_both(A,B) )
| ( ( h_false_only(A,C)
| h_both(A,C) )
& g_true_only(A,B) ) )
& ? [B] :
( ~ ? [C] :
( h_true_only(A,C)
| g_false_only(A,B) )
& ? [C] :
( h_both(A,C)
& g_both(A,B) ) ) )
& ~ ? [A] :
( ( ! [B] : h_false_only(A,B)
& ~ ? [B] : g_true_only(A,B)
& ? [B] : g_both(A,B) )
| ( ( ! [B] : h_false_only(A,B)
| ( ~ ? [B] : h_true_only(A,B)
& ? [B] : h_both(A,B) ) )
& ? [B] : g_true_only(A,B) ) )
& ? [A] :
( ~ ? [B] : h_true_only(A,B)
& ? [B] : h_both(A,B)
& ~ ? [B] : g_true_only(A,B)
& ? [B] : g_both(A,B) ) )
| ( ? [A,B] :
! [C] :
( ( h_false_only(A,C)
& g_both(A,B) )
| ( ( h_false_only(A,C)
| h_both(A,C) )
& g_true_only(A,B) ) )
& ? [A] :
( ( ! [B] : h_false_only(A,B)
& ~ ? [B] : g_true_only(A,B)
& ? [B] : g_both(A,B) )
| ( ( ! [B] : h_false_only(A,B)
| ( ~ ? [B] : h_true_only(A,B)
& ? [B] : h_both(A,B) ) )
& ? [B] : g_true_only(A,B) ) ) )
| ( ! [A,B] :
? [C] :
( h_true_only(A,C)
| g_false_only(A,B) )
& ! [A] :
( ? [B] : h_true_only(A,B)
| ! [B] : g_false_only(A,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ( ~ ? [A,B] :
! [C] :
( ( h_false_only(A,C)
& g_both(A,B) )
| ( ( h_false_only(A,C)
| h_both(A,C) )
& g_true_only(A,B) ) )
& ? [A] :
( ~ ? [B] :
! [C] :
( ( h_false_only(A,C)
& g_both(A,B) )
| ( ( h_false_only(A,C)
| h_both(A,C) )
& g_true_only(A,B) ) )
& ? [B] :
( ~ ? [C] :
( h_true_only(A,C)
| g_false_only(A,B) )
& ? [C] :
( h_both(A,C)
& g_both(A,B) ) ) )
& ~ ? [A] :
( ( ! [B] : h_false_only(A,B)
& ~ ? [B] : g_true_only(A,B)
& ? [B] : g_both(A,B) )
| ( ( ! [B] : h_false_only(A,B)
| ( ~ ? [B] : h_true_only(A,B)
& ? [B] : h_both(A,B) ) )
& ? [B] : g_true_only(A,B) ) )
& ? [A] :
( ~ ? [B] : h_true_only(A,B)
& ? [B] : h_both(A,B)
& ~ ? [B] : g_true_only(A,B)
& ? [B] : g_both(A,B) ) )
| ( ? [A,B] :
! [C] :
( ( h_false_only(A,C)
& g_both(A,B) )
| ( ( h_false_only(A,C)
| h_both(A,C) )
& g_true_only(A,B) ) )
& ? [A] :
( ( ! [B] : h_false_only(A,B)
& ~ ? [B] : g_true_only(A,B)
& ? [B] : g_both(A,B) )
| ( ( ! [B] : h_false_only(A,B)
| ( ~ ? [B] : h_true_only(A,B)
& ? [B] : h_both(A,B) ) )
& ? [B] : g_true_only(A,B) ) ) )
| ( ! [A,B] :
? [C] :
( h_true_only(A,C)
| g_false_only(A,B) )
& ! [A] :
( ? [B] : h_true_only(A,B)
| ! [B] : g_false_only(A,B) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
! [X_2,X_1] :
( g_true_only(X_2,X_1)
<=> ( ~ g_false(X_2,X_1)
& g_true(X_2,X_1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X_2,X_1] :
( g_both(X_2,X_1)
<=> ( g_false(X_2,X_1)
& g_true(X_2,X_1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X_2,X_1] :
( g_false_only(X_2,X_1)
<=> ( ~ g_true(X_2,X_1)
& g_false(X_2,X_1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X_2,X_1] :
( g_false_only(X_2,X_1)
| g_both(X_2,X_1)
| g_true_only(X_2,X_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X_2,X_1] :
( h_true_only(X_2,X_1)
<=> ( ~ h_false(X_2,X_1)
& h_true(X_2,X_1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X_2,X_1] :
( h_both(X_2,X_1)
<=> ( h_false(X_2,X_1)
& h_true(X_2,X_1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X_2,X_1] :
( h_false_only(X_2,X_1)
<=> ( ~ h_true(X_2,X_1)
& h_false(X_2,X_1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X_2,X_1] :
( h_false_only(X_2,X_1)
| h_both(X_2,X_1)
| h_true_only(X_2,X_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,plain,
( ( ? [A,B] :
! [C] :
( ( h_false_only(A,C)
& g_both(A,B) )
| ( ( h_false_only(A,C)
| h_both(A,C) )
& g_true_only(A,B) ) )
| ! [A] :
( ? [B] :
! [C] :
( ( h_false_only(A,C)
& g_both(A,B) )
| ( ( h_false_only(A,C)
| h_both(A,C) )
& g_true_only(A,B) ) )
| ! [B] :
( ? [C] :
( h_true_only(A,C)
| g_false_only(A,B) )
| ! [C] :
( ~ h_both(A,C)
| ~ g_both(A,B) ) ) )
| ? [A] :
( ( ! [B] : h_false_only(A,B)
& ! [B] : ~ g_true_only(A,B)
& ? [B] : g_both(A,B) )
| ( ( ! [B] : h_false_only(A,B)
| ( ! [B] : ~ h_true_only(A,B)
& ? [B] : h_both(A,B) ) )
& ? [B] : g_true_only(A,B) ) )
| ! [A] :
( ? [B] : h_true_only(A,B)
| ! [B] : ~ h_both(A,B)
| ? [B] : g_true_only(A,B)
| ! [B] : ~ g_both(A,B) ) )
& ( ! [A,B] :
? [C] :
( ( ~ h_false_only(A,C)
| ~ g_both(A,B) )
& ( ( ~ h_false_only(A,C)
& ~ h_both(A,C) )
| ~ g_true_only(A,B) ) )
| ! [A] :
( ( ? [B] : ~ h_false_only(A,B)
| ? [B] : g_true_only(A,B)
| ! [B] : ~ g_both(A,B) )
& ( ( ? [B] : ~ h_false_only(A,B)
& ( ? [B] : h_true_only(A,B)
| ! [B] : ~ h_both(A,B) ) )
| ! [B] : ~ g_true_only(A,B) ) ) )
& ( ? [A,B] :
! [C] :
( ~ h_true_only(A,C)
& ~ g_false_only(A,B) )
| ? [A] :
( ! [B] : ~ h_true_only(A,B)
& ? [B] : ~ g_false_only(A,B) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f12,definition,
! [A] :
( sP0_prd(A)
<=> ( ! [B] : ~ h_true_only(A,B)
& ? [B] : ~ g_false_only(A,B) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f13,definition,
! [A] :
( sP1_prd(A)
<=> ( ( ? [B] : ~ h_false_only(A,B)
| ? [B] : g_true_only(A,B)
| ! [B] : ~ g_both(A,B) )
& ( ( ? [B] : ~ h_false_only(A,B)
& ( ? [B] : h_true_only(A,B)
| ! [B] : ~ h_both(A,B) ) )
| ! [B] : ~ g_true_only(A,B) ) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f14,definition,
! [A] :
( sP2_prd(A)
<=> ( ( ! [B] : h_false_only(A,B)
& ! [B] : ~ g_true_only(A,B)
& ? [B] : g_both(A,B) )
| ( ( ! [B] : h_false_only(A,B)
| ( ! [B] : ~ h_true_only(A,B)
& ? [B] : h_both(A,B) ) )
& ? [B] : g_true_only(A,B) ) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f15,definition,
! [A,B,C] :
( sP3_prd(C,B,A)
<=> ( ( h_false_only(A,C)
& g_both(A,B) )
| ( ( h_false_only(A,C)
| h_both(A,C) )
& g_true_only(A,B) ) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f16,definition,
! [A,B,C] :
( sP4_prd(C,B,A)
<=> ( ( h_false_only(A,C)
| h_both(A,C) )
& g_true_only(A,B) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f17,plain,
( ( ? [A,B] :
! [C] :
( ( h_false_only(A,C)
& g_both(A,B) )
| sP4_prd(C,B,A) )
| ! [A] :
( ? [B] :
! [C] : sP3_prd(C,B,A)
| ! [B] :
( ? [C] :
( h_true_only(A,C)
| g_false_only(A,B) )
| ! [C] :
( ~ h_both(A,C)
| ~ g_both(A,B) ) ) )
| ? [A] : sP2_prd(A)
| ! [A] :
( ? [B] : h_true_only(A,B)
| ! [B] : ~ h_both(A,B)
| ? [B] : g_true_only(A,B)
| ! [B] : ~ g_both(A,B) ) )
& ( ! [A,B] :
? [C] :
( ( ~ h_false_only(A,C)
| ~ g_both(A,B) )
& ( ( ~ h_false_only(A,C)
& ~ h_both(A,C) )
| ~ g_true_only(A,B) ) )
| ! [A] : sP1_prd(A) )
& ( ? [A,B] :
! [C] :
( ~ h_true_only(A,C)
& ~ g_false_only(A,B) )
| ? [A] : sP0_prd(A) ) ),
inference(formula_renaming,[status(thm)],[f11,f16,f15,f14,f13,f12]) ).
fof(f18,plain,
( ( ? [A,B] :
! [C] :
( ( h_false_only(A,C)
& g_both(A,B) )
| sP4_prd(C,B,A) )
| ! [A] :
( ? [B] :
! [C] : sP3_prd(C,B,A)
| ! [B] :
( ? [C] : h_true_only(A,C)
| g_false_only(A,B)
| ! [C] : ~ h_both(A,C)
| ~ g_both(A,B) ) )
| ? [A] : sP2_prd(A)
| ! [A] :
( ? [B] : h_true_only(A,B)
| ! [B] : ~ h_both(A,B)
| ? [B] : g_true_only(A,B)
| ! [B] : ~ g_both(A,B) ) )
& ( ! [A,B] :
? [C] :
( ( ~ h_false_only(A,C)
| ~ g_both(A,B) )
& ( ( ~ h_false_only(A,C)
& ~ h_both(A,C) )
| ~ g_true_only(A,B) ) )
| ! [A] : sP1_prd(A) )
& ( ? [A] :
( ! [C] : ~ h_true_only(A,C)
& ? [B] : ~ g_false_only(A,B) )
| ? [A] : sP0_prd(A) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f19,plain,
( ( ! [C] :
( ( h_false_only(sK9_skl,C)
& g_both(sK9_skl,sK10_skl) )
| sP4_prd(C,sK10_skl,sK9_skl) )
| ! [A] :
( ! [C] : sP3_prd(C,sK8_skl(A),A)
| ! [B] :
( h_true_only(A,sK7_skl(B,A))
| g_false_only(A,B)
| ! [C] : ~ h_both(A,C)
| ~ g_both(A,B) ) )
| sP2_prd(sK6_skl)
| ! [A] :
( h_true_only(A,sK5_skl(A))
| ! [B] : ~ h_both(A,B)
| g_true_only(A,sK4_skl(A))
| ! [B] : ~ g_both(A,B) ) )
& ( ! [A,B] :
( ( ~ h_false_only(A,sK3_skl(B,A))
| ~ g_both(A,B) )
& ( ( ~ h_false_only(A,sK3_skl(B,A))
& ~ h_both(A,sK3_skl(B,A)) )
| ~ g_true_only(A,B) ) )
| ! [A] : sP1_prd(A) )
& ( ( ! [C] : ~ h_true_only(sK1_skl,C)
& ~ g_false_only(sK1_skl,sK2_skl) )
| sP0_prd(sK0_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl,sK7_skl,sK8_skl,sK9_skl,sK10_skl]),skolemize(A,sK0_skl),skolemize(A,sK1_skl),skolemize(B,sK2_skl),skolemize(C,sK3_skl(B,A)),skolemize(B,sK4_skl(A)),skolemize(B,sK5_skl(A)),skolemize(A,sK6_skl),skolemize(C,sK7_skl(B,A)),skolemize(B,sK8_skl(A)),skolemize(A,sK9_skl),skolemize(B,sK10_skl)],[f18]) ).
fof(f20,plain,
( ~ g_false_only(sK1_skl,sK2_skl)
| sP0_prd(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0] :
( ~ h_true_only(sK1_skl,X0)
| sP0_prd(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ h_both(X1,sK3_skl(X2,X1))
| ~ g_true_only(X1,X2)
| sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ~ h_false_only(X1,sK3_skl(X2,X1))
| ~ g_true_only(X1,X2)
| sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ h_false_only(X1,sK3_skl(X2,X1))
| ~ g_both(X1,X2)
| sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f25,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( g_both(sK9_skl,sK10_skl)
| sP4_prd(X7,sK10_skl,sK9_skl)
| sP3_prd(X6,sK8_skl(X3),X3)
| h_true_only(X3,sK7_skl(X4,X3))
| g_false_only(X3,X4)
| ~ h_both(X3,X5)
| ~ g_both(X3,X4)
| sP2_prd(sK6_skl)
| h_true_only(X0,sK5_skl(X0))
| ~ h_both(X0,X2)
| g_true_only(X0,sK4_skl(X0))
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f26,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( h_false_only(sK9_skl,X7)
| sP4_prd(X7,sK10_skl,sK9_skl)
| sP3_prd(X6,sK8_skl(X3),X3)
| h_true_only(X3,sK7_skl(X4,X3))
| g_false_only(X3,X4)
| ~ h_both(X3,X5)
| ~ g_both(X3,X4)
| sP2_prd(sK6_skl)
| h_true_only(X0,sK5_skl(X0))
| ~ h_both(X0,X2)
| g_true_only(X0,sK4_skl(X0))
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f27,plain,
! [X_2,X_1] :
( ( g_false(X_2,X_1)
| ~ g_true(X_2,X_1)
| g_true_only(X_2,X_1) )
& ( ( ~ g_false(X_2,X_1)
& g_true(X_2,X_1) )
| ~ g_true_only(X_2,X_1) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f28,plain,
( ! [X_2,X_1] :
( g_false(X_2,X_1)
| ~ g_true(X_2,X_1)
| g_true_only(X_2,X_1) )
& ! [X_2,X_1] :
( ( ~ g_false(X_2,X_1)
& g_true(X_2,X_1) )
| ~ g_true_only(X_2,X_1) ) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( g_true(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( ~ g_false(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f32,plain,
! [X_2,X_1] :
( ( ~ g_false(X_2,X_1)
| ~ g_true(X_2,X_1)
| g_both(X_2,X_1) )
& ( ( g_false(X_2,X_1)
& g_true(X_2,X_1) )
| ~ g_both(X_2,X_1) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f33,plain,
( ! [X_2,X_1] :
( ~ g_false(X_2,X_1)
| ~ g_true(X_2,X_1)
| g_both(X_2,X_1) )
& ! [X_2,X_1] :
( ( g_false(X_2,X_1)
& g_true(X_2,X_1) )
| ~ g_both(X_2,X_1) ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( g_true(X0,X1)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( g_false(X0,X1)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f37,plain,
! [X_2,X_1] :
( ( g_true(X_2,X_1)
| ~ g_false(X_2,X_1)
| g_false_only(X_2,X_1) )
& ( ( ~ g_true(X_2,X_1)
& g_false(X_2,X_1) )
| ~ g_false_only(X_2,X_1) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f38,plain,
( ! [X_2,X_1] :
( g_true(X_2,X_1)
| ~ g_false(X_2,X_1)
| g_false_only(X_2,X_1) )
& ! [X_2,X_1] :
( ( ~ g_true(X_2,X_1)
& g_false(X_2,X_1) )
| ~ g_false_only(X_2,X_1) ) ),
inference(miniscoping,[status(thm)],[f37]) ).
fof(f39,plain,
! [X0,X1] :
( g_false(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [X0,X1] :
( ~ g_true(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f42,plain,
! [X0,X1] :
( g_false_only(X0,X1)
| g_both(X0,X1)
| g_true_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f43,plain,
! [X_2,X_1] :
( ( h_false(X_2,X_1)
| ~ h_true(X_2,X_1)
| h_true_only(X_2,X_1) )
& ( ( ~ h_false(X_2,X_1)
& h_true(X_2,X_1) )
| ~ h_true_only(X_2,X_1) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f44,plain,
( ! [X_2,X_1] :
( h_false(X_2,X_1)
| ~ h_true(X_2,X_1)
| h_true_only(X_2,X_1) )
& ! [X_2,X_1] :
( ( ~ h_false(X_2,X_1)
& h_true(X_2,X_1) )
| ~ h_true_only(X_2,X_1) ) ),
inference(miniscoping,[status(thm)],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( h_true(X0,X1)
| ~ h_true_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( ~ h_false(X0,X1)
| ~ h_true_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f48,plain,
! [X_2,X_1] :
( ( ~ h_false(X_2,X_1)
| ~ h_true(X_2,X_1)
| h_both(X_2,X_1) )
& ( ( h_false(X_2,X_1)
& h_true(X_2,X_1) )
| ~ h_both(X_2,X_1) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f49,plain,
( ! [X_2,X_1] :
( ~ h_false(X_2,X_1)
| ~ h_true(X_2,X_1)
| h_both(X_2,X_1) )
& ! [X_2,X_1] :
( ( h_false(X_2,X_1)
& h_true(X_2,X_1) )
| ~ h_both(X_2,X_1) ) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f51,plain,
! [X0,X1] :
( h_false(X0,X1)
| ~ h_both(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
! [X_2,X_1] :
( ( h_true(X_2,X_1)
| ~ h_false(X_2,X_1)
| h_false_only(X_2,X_1) )
& ( ( ~ h_true(X_2,X_1)
& h_false(X_2,X_1) )
| ~ h_false_only(X_2,X_1) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f54,plain,
( ! [X_2,X_1] :
( h_true(X_2,X_1)
| ~ h_false(X_2,X_1)
| h_false_only(X_2,X_1) )
& ! [X_2,X_1] :
( ( ~ h_true(X_2,X_1)
& h_false(X_2,X_1) )
| ~ h_false_only(X_2,X_1) ) ),
inference(miniscoping,[status(thm)],[f53]) ).
fof(f55,plain,
! [X0,X1] :
( h_false(X0,X1)
| ~ h_false_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( ~ h_true(X0,X1)
| ~ h_false_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f58,plain,
! [X0,X1] :
( h_false_only(X0,X1)
| h_both(X0,X1)
| h_true_only(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f59,plain,
! [A] :
( ( ? [B] : h_true_only(A,B)
| ! [B] : g_false_only(A,B)
| sP0_prd(A) )
& ( ( ! [B] : ~ h_true_only(A,B)
& ? [B] : ~ g_false_only(A,B) )
| ~ sP0_prd(A) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f60,plain,
( ! [A] :
( ? [B] : h_true_only(A,B)
| ! [B] : g_false_only(A,B)
| sP0_prd(A) )
& ! [A] :
( ( ! [B] : ~ h_true_only(A,B)
& ? [B] : ~ g_false_only(A,B) )
| ~ sP0_prd(A) ) ),
inference(miniscoping,[status(thm)],[f59]) ).
fof(f61,plain,
( ! [A] :
( h_true_only(A,sK12_skl(A))
| ! [B] : g_false_only(A,B)
| sP0_prd(A) )
& ! [A] :
( ( ! [B] : ~ h_true_only(A,B)
& ~ g_false_only(A,sK11_skl(A)) )
| ~ sP0_prd(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl]),skolemize(B,sK11_skl(A)),skolemize(B,sK12_skl(A))],[f60]) ).
fof(f62,plain,
! [X0] :
( ~ g_false_only(X0,sK11_skl(X0))
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ~ h_true_only(X0,X1)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f64,plain,
! [X0,X1] :
( h_true_only(X0,sK12_skl(X0))
| g_false_only(X0,X1)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f65,definition,
! [A] :
( sP5_prd(A)
<=> ( ( ? [B] : ~ h_false_only(A,B)
& ( ? [B] : h_true_only(A,B)
| ! [B] : ~ h_both(A,B) ) )
| ! [B] : ~ g_true_only(A,B) ) ),
introduced(definition,[new_symbols(definition,[sP5_prd])],[]) ).
fof(f66,plain,
! [A] :
( sP1_prd(A)
<=> ( ( ? [B] : ~ h_false_only(A,B)
| ? [B] : g_true_only(A,B)
| ! [B] : ~ g_both(A,B) )
& sP5_prd(A) ) ),
inference(formula_renaming,[status(thm)],[f13,f65]) ).
fof(f67,plain,
! [A] :
( ( ( ! [B] : h_false_only(A,B)
& ! [B] : ~ g_true_only(A,B)
& ? [B] : g_both(A,B) )
| ~ sP5_prd(A)
| sP1_prd(A) )
& ( ( ( ? [B] : ~ h_false_only(A,B)
| ? [B] : g_true_only(A,B)
| ! [B] : ~ g_both(A,B) )
& sP5_prd(A) )
| ~ sP1_prd(A) ) ),
inference(NNF_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
( ! [A] :
( ( ! [B] : h_false_only(A,B)
& ! [B] : ~ g_true_only(A,B)
& ? [B] : g_both(A,B) )
| ~ sP5_prd(A)
| sP1_prd(A) )
& ! [A] :
( ( ( ? [B] : ~ h_false_only(A,B)
| ? [B] : g_true_only(A,B)
| ! [B] : ~ g_both(A,B) )
& sP5_prd(A) )
| ~ sP1_prd(A) ) ),
inference(miniscoping,[status(thm)],[f67]) ).
fof(f69,plain,
( ! [A] :
( ( ! [B] : h_false_only(A,B)
& ! [B] : ~ g_true_only(A,B)
& g_both(A,sK15_skl(A)) )
| ~ sP5_prd(A)
| sP1_prd(A) )
& ! [A] :
( ( ( ~ h_false_only(A,sK14_skl(A))
| g_true_only(A,sK13_skl(A))
| ! [B] : ~ g_both(A,B) )
& sP5_prd(A) )
| ~ sP1_prd(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl,sK15_skl]),skolemize(B,sK13_skl(A)),skolemize(B,sK14_skl(A)),skolemize(B,sK15_skl(A))],[f68]) ).
fof(f70,plain,
! [X0] :
( sP5_prd(X0)
| ~ sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ~ h_false_only(X0,sK14_skl(X0))
| g_true_only(X0,sK13_skl(X0))
| ~ g_both(X0,X1)
| ~ sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f72,plain,
! [X0] :
( g_both(X0,sK15_skl(X0))
| ~ sP5_prd(X0)
| sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f73,plain,
! [X0,X1] :
( ~ g_true_only(X0,X1)
| ~ sP5_prd(X0)
| sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f74,plain,
! [X0,X1] :
( h_false_only(X0,X1)
| ~ sP5_prd(X0)
| sP1_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f75,definition,
! [A] :
( sP6_prd(A)
<=> ( ( ! [B] : h_false_only(A,B)
| ( ! [B] : ~ h_true_only(A,B)
& ? [B] : h_both(A,B) ) )
& ? [B] : g_true_only(A,B) ) ),
introduced(definition,[new_symbols(definition,[sP6_prd])],[]) ).
fof(f76,plain,
! [A] :
( sP2_prd(A)
<=> ( ( ! [B] : h_false_only(A,B)
& ! [B] : ~ g_true_only(A,B)
& ? [B] : g_both(A,B) )
| sP6_prd(A) ) ),
inference(formula_renaming,[status(thm)],[f14,f75]) ).
fof(f77,plain,
! [A] :
( ( ( ( ? [B] : ~ h_false_only(A,B)
| ? [B] : g_true_only(A,B)
| ! [B] : ~ g_both(A,B) )
& ~ sP6_prd(A) )
| sP2_prd(A) )
& ( ( ! [B] : h_false_only(A,B)
& ! [B] : ~ g_true_only(A,B)
& ? [B] : g_both(A,B) )
| sP6_prd(A)
| ~ sP2_prd(A) ) ),
inference(NNF_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
( ! [A] :
( ( ( ? [B] : ~ h_false_only(A,B)
| ? [B] : g_true_only(A,B)
| ! [B] : ~ g_both(A,B) )
& ~ sP6_prd(A) )
| sP2_prd(A) )
& ! [A] :
( ( ! [B] : h_false_only(A,B)
& ! [B] : ~ g_true_only(A,B)
& ? [B] : g_both(A,B) )
| sP6_prd(A)
| ~ sP2_prd(A) ) ),
inference(miniscoping,[status(thm)],[f77]) ).
fof(f79,plain,
( ! [A] :
( ( ( ~ h_false_only(A,sK18_skl(A))
| g_true_only(A,sK17_skl(A))
| ! [B] : ~ g_both(A,B) )
& ~ sP6_prd(A) )
| sP2_prd(A) )
& ! [A] :
( ( ! [B] : h_false_only(A,B)
& ! [B] : ~ g_true_only(A,B)
& g_both(A,sK16_skl(A)) )
| sP6_prd(A)
| ~ sP2_prd(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl,sK17_skl,sK18_skl]),skolemize(B,sK16_skl(A)),skolemize(B,sK17_skl(A)),skolemize(B,sK18_skl(A))],[f78]) ).
fof(f80,plain,
! [X0] :
( g_both(X0,sK16_skl(X0))
| sP6_prd(X0)
| ~ sP2_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( ~ g_true_only(X0,X1)
| sP6_prd(X0)
| ~ sP2_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f82,plain,
! [X0,X1] :
( h_false_only(X0,X1)
| sP6_prd(X0)
| ~ sP2_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f83,plain,
! [X0] :
( ~ sP6_prd(X0)
| sP2_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f84,plain,
! [X0,X1] :
( ~ h_false_only(X0,sK18_skl(X0))
| g_true_only(X0,sK17_skl(X0))
| ~ g_both(X0,X1)
| sP2_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f85,plain,
! [A,B,C] :
( ( ( ( ~ h_false_only(A,C)
| ~ g_both(A,B) )
& ( ( ~ h_false_only(A,C)
& ~ h_both(A,C) )
| ~ g_true_only(A,B) ) )
| sP3_prd(C,B,A) )
& ( ( h_false_only(A,C)
& g_both(A,B) )
| ( ( h_false_only(A,C)
| h_both(A,C) )
& g_true_only(A,B) )
| ~ sP3_prd(C,B,A) ) ),
inference(NNF_transformation,[status(thm)],[f15]) ).
fof(f86,plain,
( ! [A,B,C] :
( ( ( ~ h_false_only(A,C)
| ~ g_both(A,B) )
& ( ( ~ h_false_only(A,C)
& ~ h_both(A,C) )
| ~ g_true_only(A,B) ) )
| sP3_prd(C,B,A) )
& ! [A,B,C] :
( ( h_false_only(A,C)
& g_both(A,B) )
| ( ( h_false_only(A,C)
| h_both(A,C) )
& g_true_only(A,B) )
| ~ sP3_prd(C,B,A) ) ),
inference(miniscoping,[status(thm)],[f85]) ).
fof(f88,plain,
! [X0,X1,X2] :
( h_false_only(X2,X0)
| g_true_only(X2,X1)
| ~ sP3_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f94,plain,
! [A,B,C] :
( ( ( ~ h_false_only(A,C)
& ~ h_both(A,C) )
| ~ g_true_only(A,B)
| sP4_prd(C,B,A) )
& ( ( ( h_false_only(A,C)
| h_both(A,C) )
& g_true_only(A,B) )
| ~ sP4_prd(C,B,A) ) ),
inference(NNF_transformation,[status(thm)],[f16]) ).
fof(f95,plain,
( ! [A,B,C] :
( ( ~ h_false_only(A,C)
& ~ h_both(A,C) )
| ~ g_true_only(A,B)
| sP4_prd(C,B,A) )
& ! [A,B,C] :
( ( ( h_false_only(A,C)
| h_both(A,C) )
& g_true_only(A,B) )
| ~ sP4_prd(C,B,A) ) ),
inference(miniscoping,[status(thm)],[f94]) ).
fof(f96,plain,
! [X0,X1,X2] :
( g_true_only(X2,X1)
| ~ sP4_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f97,plain,
! [X0,X1,X2] :
( h_false_only(X2,X0)
| h_both(X2,X0)
| ~ sP4_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f100,plain,
! [A] :
( ( ( ( ! [B] : h_false_only(A,B)
| ( ! [B] : ~ h_true_only(A,B)
& ? [B] : h_both(A,B) ) )
& ? [B] : g_true_only(A,B) )
| sP5_prd(A) )
& ( ( ? [B] : ~ h_false_only(A,B)
& ( ? [B] : h_true_only(A,B)
| ! [B] : ~ h_both(A,B) ) )
| ! [B] : ~ g_true_only(A,B)
| ~ sP5_prd(A) ) ),
inference(NNF_transformation,[status(thm)],[f65]) ).
fof(f101,plain,
( ! [A] :
( ( ( ! [B] : h_false_only(A,B)
| ( ! [B] : ~ h_true_only(A,B)
& ? [B] : h_both(A,B) ) )
& ? [B] : g_true_only(A,B) )
| sP5_prd(A) )
& ! [A] :
( ( ? [B] : ~ h_false_only(A,B)
& ( ? [B] : h_true_only(A,B)
| ! [B] : ~ h_both(A,B) ) )
| ! [B] : ~ g_true_only(A,B)
| ~ sP5_prd(A) ) ),
inference(miniscoping,[status(thm)],[f100]) ).
fof(f102,plain,
( ! [A] :
( ( ( ! [B] : h_false_only(A,B)
| ( ! [B] : ~ h_true_only(A,B)
& h_both(A,sK22_skl(A)) ) )
& g_true_only(A,sK21_skl(A)) )
| sP5_prd(A) )
& ! [A] :
( ( ~ h_false_only(A,sK20_skl(A))
& ( h_true_only(A,sK19_skl(A))
| ! [B] : ~ h_both(A,B) ) )
| ! [B] : ~ g_true_only(A,B)
| ~ sP5_prd(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl,sK20_skl,sK21_skl,sK22_skl]),skolemize(B,sK19_skl(A)),skolemize(B,sK20_skl(A)),skolemize(B,sK21_skl(A)),skolemize(B,sK22_skl(A))],[f101]) ).
fof(f103,plain,
! [X0,X1,X2] :
( h_true_only(X0,sK19_skl(X0))
| ~ h_both(X0,X2)
| ~ g_true_only(X0,X1)
| ~ sP5_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
! [X0,X1] :
( ~ h_false_only(X0,sK20_skl(X0))
| ~ g_true_only(X0,X1)
| ~ sP5_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f105,plain,
! [X0] :
( g_true_only(X0,sK21_skl(X0))
| sP5_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f107,plain,
! [X0,X1,X2] :
( h_false_only(X0,X2)
| ~ h_true_only(X0,X1)
| sP5_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f108,plain,
! [A] :
( ( ( ? [B] : ~ h_false_only(A,B)
& ( ? [B] : h_true_only(A,B)
| ! [B] : ~ h_both(A,B) ) )
| ! [B] : ~ g_true_only(A,B)
| sP6_prd(A) )
& ( ( ( ! [B] : h_false_only(A,B)
| ( ! [B] : ~ h_true_only(A,B)
& ? [B] : h_both(A,B) ) )
& ? [B] : g_true_only(A,B) )
| ~ sP6_prd(A) ) ),
inference(NNF_transformation,[status(thm)],[f75]) ).
fof(f109,plain,
( ! [A] :
( ( ? [B] : ~ h_false_only(A,B)
& ( ? [B] : h_true_only(A,B)
| ! [B] : ~ h_both(A,B) ) )
| ! [B] : ~ g_true_only(A,B)
| sP6_prd(A) )
& ! [A] :
( ( ( ! [B] : h_false_only(A,B)
| ( ! [B] : ~ h_true_only(A,B)
& ? [B] : h_both(A,B) ) )
& ? [B] : g_true_only(A,B) )
| ~ sP6_prd(A) ) ),
inference(miniscoping,[status(thm)],[f108]) ).
fof(f110,plain,
( ! [A] :
( ( ~ h_false_only(A,sK26_skl(A))
& ( h_true_only(A,sK25_skl(A))
| ! [B] : ~ h_both(A,B) ) )
| ! [B] : ~ g_true_only(A,B)
| sP6_prd(A) )
& ! [A] :
( ( ( ! [B] : h_false_only(A,B)
| ( ! [B] : ~ h_true_only(A,B)
& h_both(A,sK24_skl(A)) ) )
& g_true_only(A,sK23_skl(A)) )
| ~ sP6_prd(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl,sK24_skl,sK25_skl,sK26_skl]),skolemize(B,sK23_skl(A)),skolemize(B,sK24_skl(A)),skolemize(B,sK25_skl(A)),skolemize(B,sK26_skl(A))],[f109]) ).
fof(f111,plain,
! [X0] :
( g_true_only(X0,sK23_skl(X0))
| ~ sP6_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f112,plain,
! [X0,X1] :
( h_false_only(X0,X1)
| h_both(X0,sK24_skl(X0))
| ~ sP6_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f113,plain,
! [X0,X1,X2] :
( h_false_only(X0,X2)
| ~ h_true_only(X0,X1)
| ~ sP6_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f114,plain,
! [X0,X1,X2] :
( h_true_only(X0,sK25_skl(X0))
| ~ h_both(X0,X2)
| ~ g_true_only(X0,X1)
| sP6_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f115,plain,
! [X0,X1] :
( ~ h_false_only(X0,sK26_skl(X0))
| ~ g_true_only(X0,X1)
| sP6_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f116,definition,
( sQ0_spl
<=> sP0_prd(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f117,plain,
( ~ sQ0_spl
| sP0_prd(sK0_skl) ),
inference(component_clause,[status(thm)],[f116]) ).
fof(f119,definition,
( sQ1_spl
<=> g_false_only(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f121,plain,
( sQ1_spl
| ~ g_false_only(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f122,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f20,f116,f119]) ).
fof(f123,definition,
! [X0] :
( sQ2_spl
<=> ~ h_true_only(sK1_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f124,plain,
! [X0] :
( ~ sQ2_spl
| ~ h_true_only(sK1_skl,X0) ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f126,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f21,f116,f123]) ).
fof(f127,definition,
! [X0] :
( sQ3_spl
<=> sP1_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f128,plain,
! [X0] :
( ~ sQ3_spl
| sP1_prd(X0) ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,definition,
! [X1,X2] :
( sQ4_spl
<=> ( ~ h_both(X1,sK3_skl(X2,X1))
| ~ g_true_only(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f131,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ h_both(X0,sK3_skl(X1,X0))
| ~ g_true_only(X0,X1) ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,plain,
( sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f22,f127,f130]) ).
fof(f134,definition,
! [X1,X2] :
( sQ5_spl
<=> ( ~ h_false_only(X1,sK3_skl(X2,X1))
| ~ g_true_only(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f135,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ h_false_only(X0,sK3_skl(X1,X0))
| ~ g_true_only(X0,X1) ),
inference(component_clause,[status(thm)],[f134]) ).
fof(f137,plain,
( sQ5_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f23,f127,f134]) ).
fof(f138,definition,
! [X1,X2] :
( sQ6_spl
<=> ( ~ h_false_only(X1,sK3_skl(X2,X1))
| ~ g_both(X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f139,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ h_false_only(X0,sK3_skl(X1,X0))
| ~ g_both(X0,X1) ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f141,plain,
( sQ6_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f24,f127,f138]) ).
fof(f142,definition,
! [X0,X1,X2] :
( sQ7_spl
<=> ( h_true_only(X0,sK5_skl(X0))
| ~ h_both(X0,X2)
| g_true_only(X0,sK4_skl(X0))
| ~ g_both(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| h_true_only(X0,sK5_skl(X0))
| ~ h_both(X0,X2)
| g_true_only(X0,sK4_skl(X0))
| ~ g_both(X0,X1) ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,definition,
( sQ8_spl
<=> sP2_prd(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ8_spl
| sP2_prd(sK6_skl) ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,definition,
! [X3,X4,X5,X6] :
( sQ9_spl
<=> ( sP3_prd(X6,sK8_skl(X3),X3)
| h_true_only(X3,sK7_skl(X4,X3))
| g_false_only(X3,X4)
| ~ h_both(X3,X5)
| ~ g_both(X3,X4) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f149,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| sP3_prd(X3,sK8_skl(X0),X0)
| h_true_only(X0,sK7_skl(X1,X0))
| g_false_only(X0,X1)
| ~ h_both(X0,X2)
| ~ g_both(X0,X1) ),
inference(component_clause,[status(thm)],[f148]) ).
fof(f151,definition,
! [X7] :
( sQ10_spl
<=> sP4_prd(X7,sK10_skl,sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f152,plain,
! [X0] :
( ~ sQ10_spl
| sP4_prd(X0,sK10_skl,sK9_skl) ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f154,definition,
( sQ11_spl
<=> g_both(sK9_skl,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( ~ sQ11_spl
| g_both(sK9_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f156,plain,
( sQ11_spl
| ~ g_both(sK9_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,plain,
( sQ11_spl
| sQ10_spl
| sQ9_spl
| sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f25,f142,f145,f148,f151,f154]) ).
fof(f158,definition,
! [X7] :
( sQ12_spl
<=> ( h_false_only(sK9_skl,X7)
| sP4_prd(X7,sK10_skl,sK9_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f159,plain,
! [X0] :
( ~ sQ12_spl
| h_false_only(sK9_skl,X0)
| sP4_prd(X0,sK10_skl,sK9_skl) ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,plain,
( sQ12_spl
| sQ9_spl
| sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f26,f142,f145,f148,f158]) ).
fof(f163,plain,
! [X0] :
( ~ sQ3_spl
| sP5_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f70,f128]) ).
fof(f166,plain,
! [X0,X1,X2] :
( g_false_only(X0,X2)
| sP0_prd(X0)
| h_false_only(X0,X1)
| ~ sP6_prd(X0) ),
inference(resolution,[status(thm)],[f113,f64]) ).
fof(f167,plain,
! [X0] :
( ~ sP0_prd(X0)
| g_both(X0,sK11_skl(X0))
| g_true_only(X0,sK11_skl(X0)) ),
inference(resolution,[status(thm)],[f42,f62]) ).
fof(f169,plain,
! [X0,X1] :
( ~ sP0_prd(X0)
| h_false_only(X0,X1)
| h_both(X0,X1) ),
inference(resolution,[status(thm)],[f58,f63]) ).
fof(f170,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ h_false_only(X0,sK14_skl(X0))
| g_true_only(X0,sK13_skl(X0))
| ~ g_both(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f71,f128]) ).
fof(f171,plain,
! [X0,X1] :
( ~ sQ3_spl
| sP6_prd(X0)
| ~ sP2_prd(X0)
| g_true_only(X0,sK13_skl(X0))
| ~ g_both(X0,X1) ),
inference(resolution,[status(thm)],[f170,f82]) ).
fof(f172,plain,
! [X0,X1] :
( ~ sQ3_spl
| sP6_prd(X0)
| ~ sP2_prd(X0)
| ~ g_both(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f171,f81]) ).
fof(f173,plain,
! [X0] :
( ~ sP6_prd(X0)
| g_true(X0,sK23_skl(X0)) ),
inference(resolution,[status(thm)],[f29,f111]) ).
fof(f179,plain,
! [X0,X1] :
( g_false_only(X0,X1)
| sP0_prd(X0)
| h_true(X0,sK12_skl(X0)) ),
inference(resolution,[status(thm)],[f45,f64]) ).
fof(f182,plain,
! [X0,X1] :
( ~ sP0_prd(X0)
| h_false_only(X0,X1)
| h_false(X0,X1) ),
inference(resolution,[status(thm)],[f51,f169]) ).
fof(f183,plain,
! [X0,X1] :
( sP6_prd(X0)
| ~ sP2_prd(X0)
| h_false(X0,X1) ),
inference(resolution,[status(thm)],[f55,f82]) ).
fof(f186,plain,
! [X0] :
( ~ g_false_only(X0,sK23_skl(X0))
| ~ sP6_prd(X0) ),
inference(resolution,[status(thm)],[f173,f40]) ).
fof(f190,plain,
! [X0,X1] :
( ~ h_true_only(X0,X1)
| sP6_prd(X0)
| ~ sP2_prd(X0) ),
inference(resolution,[status(thm)],[f183,f46]) ).
fof(f199,definition,
( sQ14_spl
<=> sP6_prd(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( ~ sQ14_spl
| sP6_prd(sK0_skl) ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f210,plain,
! [X0] :
( ~ sQ3_spl
| sP6_prd(X0)
| ~ sP2_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f80,f172]) ).
fof(f212,plain,
! [X0,X1] :
( ~ sP0_prd(X0)
| h_false(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f182,f55]) ).
fof(f238,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ h_false_only(X0,sK20_skl(X0))
| ~ g_true_only(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f104,f163]) ).
fof(f243,plain,
! [X0,X1] :
( ~ h_false_only(X0,sK12_skl(X0))
| g_false_only(X0,X1)
| sP0_prd(X0) ),
inference(resolution,[status(thm)],[f179,f56]) ).
fof(f249,plain,
! [X0,X1] :
( ~ sP6_prd(X0)
| sP0_prd(X0)
| h_false_only(X0,X1)
| ~ sP6_prd(X0) ),
inference(resolution,[status(thm)],[f166,f186]) ).
fof(f252,plain,
! [X0,X1] :
( sP0_prd(X0)
| h_false_only(X0,X1)
| ~ sP6_prd(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f249]) ).
fof(f253,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| h_true_only(X0,sK19_skl(X0))
| ~ h_both(X0,X2)
| ~ g_true_only(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f103,f163]) ).
fof(f256,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sP0_prd(X0)
| ~ h_both(X0,X2)
| ~ g_true_only(X0,X1) ),
inference(resolution,[status(thm)],[f253,f63]) ).
fof(f262,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| ~ sP0_prd(X0)
| sP3_prd(X3,sK8_skl(X0),X0)
| g_false_only(X0,X1)
| ~ h_both(X0,X2)
| ~ g_both(X0,X1) ),
inference(resolution,[status(thm)],[f149,f63]) ).
fof(f264,plain,
! [X0,X1] :
( g_false_only(X0,X1)
| sP0_prd(X0)
| sP0_prd(X0)
| ~ sP6_prd(X0) ),
inference(resolution,[status(thm)],[f252,f243]) ).
fof(f269,plain,
! [X0,X1] :
( h_false(X0,X1)
| sP0_prd(X0)
| ~ sP6_prd(X0) ),
inference(resolution,[status(thm)],[f252,f55]) ).
fof(f271,plain,
! [X0,X1] :
( g_false_only(X0,X1)
| sP0_prd(X0)
| ~ sP6_prd(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f264]) ).
fof(f272,plain,
! [X0,X1] :
( h_false(X0,X1)
| ~ sP6_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f269,f212]) ).
fof(f274,plain,
! [X0,X1] :
( ~ h_true_only(X0,X1)
| ~ sP6_prd(X0) ),
inference(resolution,[status(thm)],[f272,f46]) ).
fof(f280,plain,
! [X0] :
( ~ sP6_prd(X0)
| sP0_prd(X0)
| ~ sP6_prd(X0) ),
inference(resolution,[status(thm)],[f271,f186]) ).
fof(f283,plain,
! [X0] :
( sP0_prd(X0)
| ~ sP6_prd(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f280]) ).
fof(f289,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| h_false_only(X0,X2)
| ~ sP6_prd(X0)
| ~ sP0_prd(X0)
| ~ g_true_only(X0,X1) ),
inference(resolution,[status(thm)],[f256,f112]) ).
fof(f290,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sP0_prd(X0)
| h_false_only(X0,X2)
| ~ sP0_prd(X0)
| ~ g_true_only(X0,X1) ),
inference(resolution,[status(thm)],[f256,f169]) ).
fof(f291,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| h_false_only(X0,X2)
| ~ sP6_prd(X0)
| ~ g_true_only(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f289,f283]) ).
fof(f292,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| h_false_only(X0,X2)
| ~ sP0_prd(X0)
| ~ g_true_only(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f290]) ).
fof(f308,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sP6_prd(X0)
| h_false_only(X0,X1)
| ~ sP6_prd(X0) ),
inference(resolution,[status(thm)],[f291,f111]) ).
fof(f309,plain,
! [X0,X1] :
( ~ sQ3_spl
| h_false_only(X0,X1)
| ~ sP6_prd(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f308]) ).
fof(f312,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ g_true_only(X0,X1)
| ~ sP6_prd(X0) ),
inference(resolution,[status(thm)],[f309,f238]) ).
fof(f316,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ h_false_only(X0,sK26_skl(X0))
| ~ g_true_only(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f115,f312]) ).
fof(f317,plain,
! [X0] :
( ~ sQ3_spl
| ~ sP6_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f111,f312]) ).
fof(f318,plain,
! [X0] :
( ~ sQ3_spl
| ~ sP2_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f210,f317]) ).
fof(f319,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ h_false_only(X0,sK18_skl(X0))
| g_true_only(X0,sK17_skl(X0))
| ~ g_both(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f84,f318]) ).
fof(f332,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| h_false_only(X0,X3)
| g_true_only(X0,sK8_skl(X0))
| ~ sP0_prd(X0)
| g_false_only(X0,X1)
| ~ h_both(X0,X2)
| ~ g_both(X0,X1) ),
inference(resolution,[status(thm)],[f262,f88]) ).
fof(f334,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| ~ sQ3_spl
| h_false_only(X0,X3)
| ~ sP0_prd(X0)
| g_false_only(X0,X1)
| ~ h_both(X0,X2)
| ~ g_both(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f332,f256]) ).
fof(f337,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| ~ sQ3_spl
| g_false_only(X0,X2)
| g_true_only(X0,X2)
| h_false_only(X0,X3)
| ~ sP0_prd(X0)
| g_false_only(X0,X2)
| ~ h_both(X0,X1) ),
inference(resolution,[status(thm)],[f334,f42]) ).
fof(f340,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| ~ sQ3_spl
| g_true_only(X0,X2)
| h_false_only(X0,X3)
| ~ sP0_prd(X0)
| g_false_only(X0,X2)
| ~ h_both(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f337]) ).
fof(f341,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| ~ sQ3_spl
| h_false_only(X0,X3)
| ~ sP0_prd(X0)
| g_false_only(X0,X2)
| ~ h_both(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f340,f256]) ).
fof(f342,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sP0_prd(X0)
| h_false_only(X0,X3)
| h_false_only(X0,X2)
| ~ sP0_prd(X0)
| g_false_only(X0,X1) ),
inference(resolution,[status(thm)],[f341,f169]) ).
fof(f343,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| ~ sQ3_spl
| h_false_only(X0,X3)
| h_false_only(X0,X2)
| ~ sP0_prd(X0)
| g_false_only(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f342]) ).
fof(f344,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sP0_prd(X0)
| h_false_only(X0,X2)
| h_false_only(X0,X1)
| ~ sP0_prd(X0) ),
inference(resolution,[status(thm)],[f343,f62]) ).
fof(f346,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ sQ3_spl
| h_false_only(X0,X2)
| h_false_only(X0,X1)
| ~ sP0_prd(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f344]) ).
fof(f347,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ9_spl
| g_true_only(X0,sK17_skl(X0))
| ~ g_both(X0,X2)
| h_false_only(X0,X1)
| ~ sP0_prd(X0) ),
inference(resolution,[status(thm)],[f346,f319]) ).
fof(f355,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sQ9_spl
| ~ g_both(X0,X2)
| h_false_only(X0,X1)
| ~ sP0_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f347,f292]) ).
fof(f357,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ9_spl
| ~ sP0_prd(X0)
| g_true_only(X0,sK11_skl(X0))
| h_false_only(X0,X1)
| ~ sP0_prd(X0) ),
inference(resolution,[status(thm)],[f355,f167]) ).
fof(f359,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ9_spl
| g_true_only(X0,sK11_skl(X0))
| h_false_only(X0,X1)
| ~ sP0_prd(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f357]) ).
fof(f360,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ9_spl
| h_false_only(X0,X1)
| ~ sP0_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f359,f292]) ).
fof(f362,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ9_spl
| g_true_only(X0,sK17_skl(X0))
| ~ g_both(X0,X1)
| ~ sP0_prd(X0) ),
inference(resolution,[status(thm)],[f360,f319]) ).
fof(f365,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ9_spl
| ~ g_true_only(X0,X1)
| ~ sP0_prd(X0) ),
inference(resolution,[status(thm)],[f360,f316]) ).
fof(f371,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ9_spl
| ~ sP0_prd(X0)
| g_both(X0,sK11_skl(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f167,f365]) ).
fof(f376,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ9_spl
| ~ sP0_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f371,f377]) ).
fof(f377,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ9_spl
| ~ g_both(X0,X1)
| ~ sP0_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f362,f365]) ).
fof(f383,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ9_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f117,f376]) ).
fof(f384,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f383]) ).
fof(f385,plain,
( ~ sQ8_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f146,f318]) ).
fof(f386,plain,
( ~ sQ8_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f385]) ).
fof(f387,plain,
! [X0] :
( ~ sQ2_spl
| h_false_only(sK1_skl,X0)
| h_both(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f124,f58]) ).
fof(f390,definition,
! [X0] :
( sQ15_spl
<=> ~ g_both(sK1_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f391,plain,
! [X0] :
( ~ sQ15_spl
| ~ g_both(sK1_skl,X0) ),
inference(component_clause,[status(thm)],[f390]) ).
fof(f393,definition,
( sQ16_spl
<=> g_true_only(sK1_skl,sK4_skl(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f394,plain,
( ~ sQ16_spl
| g_true_only(sK1_skl,sK4_skl(sK1_skl)) ),
inference(component_clause,[status(thm)],[f393]) ).
fof(f396,definition,
! [X1] :
( sQ17_spl
<=> ~ h_both(sK1_skl,X1) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f397,plain,
! [X0] :
( ~ sQ17_spl
| ~ h_both(sK1_skl,X0) ),
inference(component_clause,[status(thm)],[f396]) ).
fof(f400,plain,
( sQ1_spl
| g_both(sK1_skl,sK2_skl)
| g_true_only(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f121,f42]) ).
fof(f401,definition,
( sQ18_spl
<=> g_true_only(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f402,plain,
( ~ sQ18_spl
| g_true_only(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f401]) ).
fof(f404,definition,
( sQ19_spl
<=> g_both(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f405,plain,
( ~ sQ19_spl
| g_both(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f404]) ).
fof(f407,plain,
( sQ1_spl
| sQ19_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f400,f401,f404,f119]) ).
fof(f408,plain,
! [X0] :
( ~ sQ15_spl
| g_false_only(sK1_skl,X0)
| g_true_only(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f391,f42]) ).
fof(f409,plain,
( ~ sQ19_spl
| ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f405,f391]) ).
fof(f410,plain,
( ~ sQ19_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f409]) ).
fof(f444,plain,
! [X0] :
( g_true(X0,sK21_skl(X0))
| sP5_prd(X0) ),
inference(resolution,[status(thm)],[f105,f29]) ).
fof(f446,plain,
! [X0] :
( ~ g_false_only(X0,sK21_skl(X0))
| sP5_prd(X0) ),
inference(resolution,[status(thm)],[f444,f40]) ).
fof(f448,plain,
! [X0,X1] :
( ~ h_true_only(X0,X1)
| ~ sP2_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f190,f274]) ).
fof(f457,plain,
( ~ sQ16_spl
| sP6_prd(sK1_skl)
| ~ sP2_prd(sK1_skl) ),
inference(resolution,[status(thm)],[f81,f394]) ).
fof(f458,plain,
( ~ sQ18_spl
| sP6_prd(sK1_skl)
| ~ sP2_prd(sK1_skl) ),
inference(resolution,[status(thm)],[f81,f402]) ).
fof(f461,definition,
( sQ21_spl
<=> sP2_prd(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f462,plain,
( ~ sQ21_spl
| sP2_prd(sK1_skl) ),
inference(component_clause,[status(thm)],[f461]) ).
fof(f463,plain,
( sQ21_spl
| ~ sP2_prd(sK1_skl) ),
inference(component_clause,[status(thm)],[f461]) ).
fof(f464,definition,
( sQ22_spl
<=> sP6_prd(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( ~ sQ22_spl
| sP6_prd(sK1_skl) ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f467,plain,
( ~ sQ16_spl
| sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f457,f461,f464,f393]) ).
fof(f468,plain,
( ~ sQ18_spl
| sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f458,f461,f464,f401]) ).
fof(f469,plain,
( ~ sQ22_spl
| sP2_prd(sK1_skl) ),
inference(resolution,[status(thm)],[f465,f83]) ).
fof(f475,plain,
( ~ sQ22_spl
| sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f469,f463]) ).
fof(f476,plain,
( ~ sQ22_spl
| sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f475]) ).
fof(f477,plain,
! [X0,X1] :
( ~ sQ6_spl
| sP6_prd(X0)
| ~ sP2_prd(X0)
| ~ g_both(X0,X1) ),
inference(resolution,[status(thm)],[f139,f82]) ).
fof(f479,plain,
( ~ sQ11_spl
| g_false(sK9_skl,sK10_skl) ),
inference(resolution,[status(thm)],[f155,f35]) ).
fof(f480,plain,
( ~ sQ11_spl
| g_true(sK9_skl,sK10_skl) ),
inference(resolution,[status(thm)],[f155,f34]) ).
fof(f482,plain,
( ~ sQ11_spl
| ~ g_true_only(sK9_skl,sK10_skl) ),
inference(resolution,[status(thm)],[f479,f30]) ).
fof(f489,definition,
( sQ24_spl
<=> g_true_only(sK9_skl,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f490,plain,
( ~ sQ24_spl
| g_true_only(sK9_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f489]) ).
fof(f496,plain,
( ~ sQ10_spl
| g_true_only(sK9_skl,sK10_skl) ),
inference(resolution,[status(thm)],[f152,f96]) ).
fof(f497,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f496,f482]) ).
fof(f498,plain,
( ~ sQ10_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f497]) ).
fof(f501,definition,
( sQ25_spl
<=> sP2_prd(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f502,plain,
( ~ sQ25_spl
| sP2_prd(sK9_skl) ),
inference(component_clause,[status(thm)],[f501]) ).
fof(f503,plain,
( sQ25_spl
| ~ sP2_prd(sK9_skl) ),
inference(component_clause,[status(thm)],[f501]) ).
fof(f504,definition,
( sQ26_spl
<=> sP6_prd(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f505,plain,
( ~ sQ26_spl
| sP6_prd(sK9_skl) ),
inference(component_clause,[status(thm)],[f504]) ).
fof(f508,plain,
( ~ sQ26_spl
| sP2_prd(sK9_skl) ),
inference(resolution,[status(thm)],[f505,f83]) ).
fof(f510,plain,
( ~ sQ26_spl
| sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f508,f503]) ).
fof(f511,plain,
( ~ sQ26_spl
| sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f510]) ).
fof(f512,plain,
( ~ sQ11_spl
| g_false(sK9_skl,sK10_skl) ),
inference(resolution,[status(thm)],[f155,f35]) ).
fof(f518,plain,
( ~ sQ11_spl
| ~ g_false_only(sK9_skl,sK10_skl) ),
inference(resolution,[status(thm)],[f480,f40]) ).
fof(f525,definition,
! [X0] :
( sQ27_spl
<=> h_false_only(sK1_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f526,plain,
! [X0] :
( ~ sQ27_spl
| h_false_only(sK1_skl,X0) ),
inference(component_clause,[status(thm)],[f525]) ).
fof(f533,plain,
! [X0] :
( ~ sQ27_spl
| ~ g_true_only(sK1_skl,X0)
| sP6_prd(sK1_skl) ),
inference(resolution,[status(thm)],[f526,f115]) ).
fof(f534,plain,
! [X0] :
( ~ sQ27_spl
| g_true_only(sK1_skl,sK17_skl(sK1_skl))
| ~ g_both(sK1_skl,X0)
| sP2_prd(sK1_skl) ),
inference(resolution,[status(thm)],[f526,f84]) ).
fof(f535,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ27_spl
| ~ g_both(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f526,f139]) ).
fof(f538,definition,
! [X0] :
( sQ28_spl
<=> ~ g_true_only(sK1_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f539,plain,
! [X0] :
( ~ sQ28_spl
| ~ g_true_only(sK1_skl,X0) ),
inference(component_clause,[status(thm)],[f538]) ).
fof(f541,plain,
( ~ sQ27_spl
| sQ28_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f533,f464,f538,f525]) ).
fof(f542,definition,
( sQ29_spl
<=> g_true_only(sK1_skl,sK17_skl(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f543,plain,
( ~ sQ29_spl
| g_true_only(sK1_skl,sK17_skl(sK1_skl)) ),
inference(component_clause,[status(thm)],[f542]) ).
fof(f545,plain,
( ~ sQ27_spl
| sQ29_spl
| sQ15_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f534,f461,f390,f542,f525]) ).
fof(f546,plain,
( ~ sQ6_spl
| ~ sQ27_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f535,f390,f525,f138]) ).
fof(f547,plain,
! [X0] :
( ~ sQ3_spl
| sP5_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f70,f128]) ).
fof(f552,plain,
( ~ sQ26_spl
| ~ sQ3_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f505,f317]) ).
fof(f553,plain,
( ~ sQ14_spl
| ~ sQ3_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f200,f317]) ).
fof(f554,plain,
( ~ sQ26_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f552]) ).
fof(f558,plain,
( ~ sQ18_spl
| ~ sQ28_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f402,f539]) ).
fof(f559,plain,
( ~ sQ18_spl
| ~ sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f558]) ).
fof(f560,plain,
( ~ sQ14_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f553]) ).
fof(f571,plain,
( ~ sQ25_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f502,f318]) ).
fof(f572,plain,
( ~ sQ25_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f571]) ).
fof(f577,plain,
( ~ sQ15_spl
| ~ sP5_prd(sK1_skl)
| sP1_prd(sK1_skl) ),
inference(resolution,[status(thm)],[f391,f72]) ).
fof(f578,plain,
( ~ sQ15_spl
| sP6_prd(sK1_skl)
| ~ sP2_prd(sK1_skl) ),
inference(resolution,[status(thm)],[f391,f80]) ).
fof(f580,definition,
( sQ30_spl
<=> sP1_prd(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f581,plain,
( ~ sQ30_spl
| sP1_prd(sK1_skl) ),
inference(component_clause,[status(thm)],[f580]) ).
fof(f583,definition,
( sQ31_spl
<=> sP5_prd(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f585,plain,
( sQ31_spl
| ~ sP5_prd(sK1_skl) ),
inference(component_clause,[status(thm)],[f583]) ).
fof(f586,plain,
( ~ sQ15_spl
| ~ sQ31_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f577,f580,f583,f390]) ).
fof(f587,plain,
( ~ sQ15_spl
| sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f578,f461,f464,f390]) ).
fof(f590,plain,
! [X0,X1,X2] :
( g_false_only(X0,X2)
| sP0_prd(X0)
| h_false_only(X0,X1)
| sP5_prd(X0) ),
inference(resolution,[status(thm)],[f107,f64]) ).
fof(f592,plain,
( sQ31_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f585,f547]) ).
fof(f593,plain,
( sQ31_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f592]) ).
fof(f594,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ g_both(X0,X1)
| ~ sP5_prd(X0)
| sP1_prd(X0) ),
inference(resolution,[status(thm)],[f74,f139]) ).
fof(f597,plain,
( ~ sQ30_spl
| sP5_prd(sK1_skl) ),
inference(resolution,[status(thm)],[f70,f581]) ).
fof(f601,plain,
( ~ sQ19_spl
| g_true(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f405,f34]) ).
fof(f609,plain,
! [X0] :
( ~ sQ12_spl
| h_false_only(sK9_skl,X0)
| h_both(sK9_skl,X0)
| h_false_only(sK9_skl,X0) ),
inference(resolution,[status(thm)],[f159,f97]) ).
fof(f610,plain,
! [X0] :
( ~ sQ12_spl
| g_true_only(sK9_skl,sK10_skl)
| h_false_only(sK9_skl,X0) ),
inference(resolution,[status(thm)],[f159,f96]) ).
fof(f611,plain,
! [X0] :
( ~ sQ12_spl
| h_both(sK9_skl,X0)
| h_false_only(sK9_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f609]) ).
fof(f612,definition,
! [X0] :
( sQ33_spl
<=> h_false_only(sK9_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f613,plain,
! [X0] :
( ~ sQ33_spl
| h_false_only(sK9_skl,X0) ),
inference(component_clause,[status(thm)],[f612]) ).
fof(f615,plain,
( ~ sQ12_spl
| sQ24_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f610,f612,f489,f158]) ).
fof(f617,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ33_spl
| ~ g_true_only(sK9_skl,X0) ),
inference(resolution,[status(thm)],[f613,f135]) ).
fof(f618,plain,
! [X0] :
( ~ sQ33_spl
| h_false(sK9_skl,X0) ),
inference(resolution,[status(thm)],[f613,f55]) ).
fof(f621,plain,
! [X0] :
( ~ sQ33_spl
| ~ h_true_only(sK9_skl,X0) ),
inference(resolution,[status(thm)],[f618,f46]) ).
fof(f622,plain,
! [X0] :
( ~ sQ33_spl
| g_false_only(sK9_skl,X0)
| sP0_prd(sK9_skl) ),
inference(resolution,[status(thm)],[f621,f64]) ).
fof(f624,definition,
( sQ34_spl
<=> sP0_prd(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f625,plain,
( ~ sQ34_spl
| sP0_prd(sK9_skl) ),
inference(component_clause,[status(thm)],[f624]) ).
fof(f627,definition,
! [X0] :
( sQ35_spl
<=> g_false_only(sK9_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f628,plain,
! [X0] :
( ~ sQ35_spl
| g_false_only(sK9_skl,X0) ),
inference(component_clause,[status(thm)],[f627]) ).
fof(f630,plain,
( ~ sQ33_spl
| sQ35_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f622,f624,f627,f612]) ).
fof(f635,definition,
! [X0] :
( sQ36_spl
<=> ~ g_true_only(sK9_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f636,plain,
! [X0] :
( ~ sQ36_spl
| ~ g_true_only(sK9_skl,X0) ),
inference(component_clause,[status(thm)],[f635]) ).
fof(f638,definition,
! [X1] :
( sQ37_spl
<=> ~ h_both(sK9_skl,X1) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f639,plain,
! [X0] :
( ~ sQ37_spl
| ~ h_both(sK9_skl,X0) ),
inference(component_clause,[status(thm)],[f638]) ).
fof(f642,plain,
( ~ sQ35_spl
| ~ sP0_prd(sK9_skl) ),
inference(resolution,[status(thm)],[f628,f62]) ).
fof(f643,plain,
! [X0] :
( ~ sQ35_spl
| g_false(sK9_skl,X0) ),
inference(resolution,[status(thm)],[f628,f39]) ).
fof(f644,plain,
( ~ sQ35_spl
| ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f642,f625]) ).
fof(f645,plain,
( ~ sQ35_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f644]) ).
fof(f647,plain,
! [X0] :
( ~ sQ35_spl
| ~ g_true_only(sK9_skl,X0) ),
inference(resolution,[status(thm)],[f643,f30]) ).
fof(f649,plain,
( ~ sQ19_spl
| ~ g_false_only(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f601,f40]) ).
fof(f651,plain,
( ~ sQ24_spl
| ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f490,f636]) ).
fof(f652,plain,
( ~ sQ24_spl
| ~ sQ36_spl ),
inference(contradiction_clause,[status(thm)],[f651]) ).
fof(f653,plain,
( ~ sQ35_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f647,f635,f627]) ).
fof(f655,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ33_spl
| ~ g_both(sK9_skl,X0) ),
inference(resolution,[status(thm)],[f613,f139]) ).
fof(f659,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ h_false_only(X0,sK26_skl(X0))
| ~ g_true_only(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f115,f317]) ).
fof(f660,plain,
! [X0] :
( ~ sQ33_spl
| ~ sQ3_spl
| ~ g_true_only(sK9_skl,X0) ),
inference(resolution,[status(thm)],[f659,f613]) ).
fof(f672,plain,
( ~ sQ24_spl
| g_true(sK9_skl,sK10_skl) ),
inference(resolution,[status(thm)],[f490,f29]) ).
fof(f674,plain,
( ~ sQ24_spl
| ~ g_false_only(sK9_skl,sK10_skl) ),
inference(resolution,[status(thm)],[f672,f40]) ).
fof(f678,plain,
( ~ sQ29_spl
| ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f543,f539]) ).
fof(f679,plain,
( ~ sQ29_spl
| ~ sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f678]) ).
fof(f680,plain,
( ~ sQ22_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f465,f317]) ).
fof(f681,plain,
( ~ sQ22_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f680]) ).
fof(f688,definition,
( sQ38_spl
<=> sP5_prd(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f692,plain,
( ~ sQ33_spl
| ~ sQ3_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f660,f635,f127,f612]) ).
fof(f694,plain,
( ~ sQ5_spl
| ~ sQ33_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f617,f635,f612,f134]) ).
fof(f702,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ h_false_only(X0,sK18_skl(X0))
| g_true_only(X0,sK17_skl(X0))
| ~ g_both(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f318]) ).
fof(f703,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ33_spl
| g_true_only(sK9_skl,sK17_skl(sK9_skl))
| ~ g_both(sK9_skl,X0) ),
inference(resolution,[status(thm)],[f613,f702]) ).
fof(f705,definition,
! [X0] :
( sQ39_spl
<=> ~ g_both(sK9_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f706,plain,
! [X0] :
( ~ sQ39_spl
| ~ g_both(sK9_skl,X0) ),
inference(component_clause,[status(thm)],[f705]) ).
fof(f708,definition,
( sQ40_spl
<=> g_true_only(sK9_skl,sK17_skl(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f709,plain,
( ~ sQ40_spl
| g_true_only(sK9_skl,sK17_skl(sK9_skl)) ),
inference(component_clause,[status(thm)],[f708]) ).
fof(f711,plain,
( ~ sQ3_spl
| ~ sQ33_spl
| sQ40_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f703,f705,f708,f612,f127]) ).
fof(f727,definition,
( sQ41_spl
<=> g_true_only(sK9_skl,sK4_skl(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f728,plain,
( ~ sQ41_spl
| g_true_only(sK9_skl,sK4_skl(sK9_skl)) ),
inference(component_clause,[status(thm)],[f727]) ).
fof(f731,plain,
! [X0] :
( ~ sQ39_spl
| g_false_only(sK9_skl,X0)
| g_true_only(sK9_skl,X0) ),
inference(resolution,[status(thm)],[f706,f42]) ).
fof(f776,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ h_false_only(X0,sK26_skl(X0))
| ~ g_true_only(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f115,f317]) ).
fof(f777,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| h_true_only(X0,sK25_skl(X0))
| ~ h_both(X0,X2)
| ~ g_true_only(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f114,f317]) ).
fof(f780,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ37_spl
| h_false_only(sK9_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f611,f639]) ).
fof(f781,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ37_spl
| ~ g_true_only(sK9_skl,X0) ),
inference(resolution,[status(thm)],[f780,f776]) ).
fof(f786,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ37_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f781,f635,f638,f158,f127]) ).
fof(f794,plain,
( ~ sQ41_spl
| ~ sQ36_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f728,f636]) ).
fof(f795,plain,
( ~ sQ40_spl
| ~ sQ36_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f709,f636]) ).
fof(f796,plain,
( ~ sQ41_spl
| ~ sQ36_spl ),
inference(contradiction_clause,[status(thm)],[f794]) ).
fof(f798,plain,
( ~ sQ34_spl
| ~ sQ3_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f625,f376]) ).
fof(f799,plain,
( ~ sQ34_spl
| ~ sQ3_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f798]) ).
fof(f800,plain,
( ~ sQ19_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f649,f119,f404]) ).
fof(f829,plain,
( ~ sQ39_spl
| ~ sP0_prd(sK9_skl)
| g_true_only(sK9_skl,sK11_skl(sK9_skl)) ),
inference(resolution,[status(thm)],[f731,f62]) ).
fof(f831,definition,
( sQ47_spl
<=> g_true_only(sK9_skl,sK11_skl(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f834,plain,
( ~ sQ39_spl
| ~ sQ34_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f829,f831,f624,f705]) ).
fof(f846,plain,
( ~ sQ15_spl
| ~ sP0_prd(sK1_skl)
| g_true_only(sK1_skl,sK11_skl(sK1_skl)) ),
inference(resolution,[status(thm)],[f408,f62]) ).
fof(f848,definition,
( sQ49_spl
<=> g_true_only(sK1_skl,sK11_skl(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f851,definition,
( sQ50_spl
<=> sP0_prd(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f852,plain,
( ~ sQ50_spl
| sP0_prd(sK1_skl) ),
inference(component_clause,[status(thm)],[f851]) ).
fof(f854,plain,
( ~ sQ15_spl
| ~ sQ50_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f846,f848,f851,f390]) ).
fof(f855,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ h_both(sK1_skl,X1)
| ~ g_true_only(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f124,f777]) ).
fof(f859,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sQ17_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f855,f538,f396,f123,f127]) ).
fof(f871,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ17_spl
| h_false_only(sK1_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f387,f397]) ).
fof(f872,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ17_spl
| ~ g_true_only(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f871,f238]) ).
fof(f875,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ17_spl
| g_true_only(sK1_skl,sK17_skl(sK1_skl))
| ~ g_both(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f871,f702]) ).
fof(f877,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ17_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f872,f538,f396,f123,f127]) ).
fof(f883,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ17_spl
| sQ29_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f875,f390,f542,f396,f123,f127]) ).
fof(f884,plain,
( ~ sQ40_spl
| ~ sQ36_spl ),
inference(contradiction_clause,[status(thm)],[f795]) ).
fof(f891,plain,
! [X0] :
( ~ sQ2_spl
| g_false_only(sK1_skl,X0)
| sP0_prd(sK1_skl) ),
inference(resolution,[status(thm)],[f64,f124]) ).
fof(f895,definition,
! [X0] :
( sQ53_spl
<=> g_false_only(sK1_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f896,plain,
! [X0] :
( ~ sQ53_spl
| g_false_only(sK1_skl,X0) ),
inference(component_clause,[status(thm)],[f895]) ).
fof(f898,plain,
( ~ sQ2_spl
| sQ53_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f891,f851,f895,f123]) ).
fof(f902,plain,
( sQ1_spl
| ~ sQ53_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f121,f896]) ).
fof(f910,plain,
! [X0,X1] :
( g_false_only(X0,X1)
| sP0_prd(X0)
| ~ sP2_prd(X0) ),
inference(resolution,[status(thm)],[f448,f64]) ).
fof(f937,plain,
( ~ sQ18_spl
| ~ sP5_prd(sK1_skl)
| sP1_prd(sK1_skl) ),
inference(resolution,[status(thm)],[f73,f402]) ).
fof(f938,definition,
( sQ55_spl
<=> sP1_prd(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f939,plain,
( ~ sQ55_spl
| sP1_prd(sK9_skl) ),
inference(component_clause,[status(thm)],[f938]) ).
fof(f940,plain,
( sQ55_spl
| ~ sP1_prd(sK9_skl) ),
inference(component_clause,[status(thm)],[f938]) ).
fof(f946,plain,
( ~ sQ18_spl
| ~ sQ31_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f937,f580,f583,f401]) ).
fof(f947,plain,
( sQ31_spl
| ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f585,f597]) ).
fof(f948,plain,
( sQ31_spl
| ~ sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f947]) ).
fof(f953,plain,
( ~ sQ55_spl
| sP5_prd(sK9_skl) ),
inference(resolution,[status(thm)],[f939,f70]) ).
fof(f954,plain,
( ~ sQ55_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f953,f688,f938]) ).
fof(f955,plain,
( ~ sQ6_spl
| ~ sQ33_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f655,f705,f612,f138]) ).
fof(f968,plain,
( ~ sQ36_spl
| ~ sP6_prd(sK9_skl) ),
inference(resolution,[status(thm)],[f111,f636]) ).
fof(f971,plain,
( ~ sQ36_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f968,f504,f635]) ).
fof(f979,plain,
( sQ55_spl
| ~ sQ3_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f940,f128]) ).
fof(f981,plain,
( sQ55_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f979]) ).
fof(f982,plain,
( ~ sQ39_spl
| sP6_prd(sK9_skl)
| ~ sP2_prd(sK9_skl) ),
inference(resolution,[status(thm)],[f80,f706]) ).
fof(f985,plain,
( ~ sQ39_spl
| sQ26_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f982,f501,f504,f705]) ).
fof(f1004,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ h_false_only(X0,sK18_skl(X0))
| g_true_only(X0,sK17_skl(X0))
| ~ g_both(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f318]) ).
fof(f1015,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| h_true_only(X0,sK25_skl(X0))
| ~ h_both(X0,X2)
| ~ g_true_only(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f114,f317]) ).
fof(f1026,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ3_spl
| h_false_only(sK1_skl,X0)
| ~ sP0_prd(sK1_skl) ),
inference(resolution,[status(thm)],[f292,f402]) ).
fof(f1027,plain,
( ~ sQ18_spl
| ~ sQ3_spl
| sQ27_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f1026,f851,f525,f127,f401]) ).
fof(f1044,plain,
( ~ sQ19_spl
| ~ g_false_only(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f601,f40]) ).
fof(f1059,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| ~ sP0_prd(X0)
| ~ h_both(X0,X2)
| g_true_only(X0,sK4_skl(X0))
| ~ g_both(X0,X1) ),
inference(resolution,[status(thm)],[f143,f63]) ).
fof(f1062,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sP0_prd(X0)
| ~ h_both(X0,X2)
| ~ g_both(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1059,f256]) ).
fof(f1076,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sP0_prd(sK1_skl)
| ~ h_both(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f1062,f405]) ).
fof(f1077,plain,
! [X0,X1] :
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sP0_prd(X0)
| g_true_only(X0,sK11_skl(X0))
| ~ sP0_prd(X0)
| ~ h_both(X0,X1) ),
inference(resolution,[status(thm)],[f1062,f167]) ).
fof(f1079,plain,
( ~ sQ19_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ50_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f1076,f396,f851,f127,f142,f404]) ).
fof(f1080,plain,
! [X0,X1] :
( ~ sQ7_spl
| ~ sQ3_spl
| g_true_only(X0,sK11_skl(X0))
| ~ sP0_prd(X0)
| ~ h_both(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f1077]) ).
fof(f1081,plain,
! [X0,X1] :
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sP0_prd(X0)
| ~ h_both(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1080,f256]) ).
fof(f1084,plain,
! [X0,X1] :
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sP0_prd(X0)
| h_false_only(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f169,f1081]) ).
fof(f1089,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ7_spl
| ~ g_true_only(X0,X1)
| ~ sP0_prd(X0) ),
inference(resolution,[status(thm)],[f1084,f776]) ).
fof(f1091,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ7_spl
| g_true_only(X0,sK17_skl(X0))
| ~ g_both(X0,X1)
| ~ sP0_prd(X0) ),
inference(resolution,[status(thm)],[f1084,f1004]) ).
fof(f1094,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ7_spl
| ~ sP0_prd(X0)
| g_both(X0,sK11_skl(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f167,f1089]) ).
fof(f1100,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ7_spl
| ~ sP0_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f1094,f1101]) ).
fof(f1101,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ7_spl
| ~ g_both(X0,X1)
| ~ sP0_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1091,f1089]) ).
fof(f1108,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f117,f1100]) ).
fof(f1109,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1108]) ).
fof(f1110,plain,
( ~ sQ50_spl
| ~ sQ3_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f852,f376]) ).
fof(f1111,plain,
( ~ sQ50_spl
| ~ sQ3_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f1110]) ).
fof(f1112,plain,
( ~ sQ10_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f496,f489,f151]) ).
fof(f1117,plain,
( ~ sQ11_spl
| ~ sQ39_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f706]) ).
fof(f1118,plain,
( ~ sQ11_spl
| ~ sQ39_spl ),
inference(contradiction_clause,[status(thm)],[f1117]) ).
fof(f1119,plain,
( sQ1_spl
| ~ sQ53_spl ),
inference(contradiction_clause,[status(thm)],[f902]) ).
fof(f1122,plain,
( sQ11_spl
| g_false_only(sK9_skl,sK10_skl)
| g_true_only(sK9_skl,sK10_skl) ),
inference(resolution,[status(thm)],[f156,f42]) ).
fof(f1123,definition,
( sQ58_spl
<=> g_false_only(sK9_skl,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f1124,plain,
( ~ sQ58_spl
| g_false_only(sK9_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f1123]) ).
fof(f1126,plain,
( sQ11_spl
| sQ58_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f1122,f489,f1123,f154]) ).
fof(f1142,plain,
( ~ sQ24_spl
| ~ g_false_only(sK9_skl,sK10_skl) ),
inference(resolution,[status(thm)],[f672,f40]) ).
fof(f1144,plain,
( ~ sQ24_spl
| ~ sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1142,f1124]) ).
fof(f1145,plain,
( ~ sQ24_spl
| ~ sQ58_spl ),
inference(contradiction_clause,[status(thm)],[f1144]) ).
fof(f1146,plain,
! [X0] :
( ~ sQ33_spl
| ~ g_true_only(sK9_skl,X0)
| sP6_prd(sK9_skl) ),
inference(resolution,[status(thm)],[f613,f115]) ).
fof(f1148,plain,
( ~ sQ33_spl
| sQ36_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f1146,f504,f635,f612]) ).
fof(f1154,plain,
( ~ sQ11_spl
| ~ g_true_only(sK9_skl,sK10_skl) ),
inference(resolution,[status(thm)],[f512,f30]) ).
fof(f1269,plain,
( ~ sQ19_spl
| sP0_prd(sK1_skl)
| ~ sP2_prd(sK1_skl) ),
inference(resolution,[status(thm)],[f1044,f910]) ).
fof(f1271,plain,
( ~ sQ19_spl
| sQ50_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1269,f461,f851,f404]) ).
fof(f1283,plain,
! [X0] :
( ~ sQ6_spl
| ~ sP5_prd(X0)
| sP1_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f72,f594]) ).
fof(f1285,plain,
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sP5_prd(sK9_skl)
| sP1_prd(sK9_skl) ),
inference(resolution,[status(thm)],[f594,f155]) ).
fof(f1289,plain,
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ38_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f1285,f938,f688,f138,f154]) ).
fof(f1299,plain,
( ~ sQ24_spl
| sP0_prd(sK9_skl)
| ~ sP2_prd(sK9_skl) ),
inference(resolution,[status(thm)],[f674,f910]) ).
fof(f1301,plain,
( ~ sQ24_spl
| sQ34_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f1299,f501,f624,f489]) ).
fof(f1318,plain,
! [X0] :
( ~ sQ6_spl
| sP6_prd(X0)
| ~ sP2_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f80,f477]) ).
fof(f1319,plain,
( ~ sQ19_spl
| ~ sQ6_spl
| sP6_prd(sK1_skl)
| ~ sP2_prd(sK1_skl) ),
inference(resolution,[status(thm)],[f477,f405]) ).
fof(f1322,plain,
( ~ sQ19_spl
| ~ sQ6_spl
| sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1319,f461,f464,f138,f404]) ).
fof(f1337,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ g_true_only(X0,X1)
| ~ sP0_prd(X0)
| h_false_only(X0,sK3_skl(X1,X0)) ),
inference(resolution,[status(thm)],[f169,f131]) ).
fof(f1341,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ g_true_only(X0,X1)
| ~ sP0_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1337,f135]) ).
fof(f1345,plain,
( ~ sQ24_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sP0_prd(sK9_skl) ),
inference(resolution,[status(thm)],[f1341,f490]) ).
fof(f1346,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| sP5_prd(X0)
| ~ sP0_prd(X0) ),
inference(resolution,[status(thm)],[f1341,f105]) ).
fof(f1347,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sP6_prd(X0)
| ~ sP0_prd(X0) ),
inference(resolution,[status(thm)],[f1341,f111]) ).
fof(f1348,plain,
( ~ sQ24_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f1345,f624,f134,f130,f489]) ).
fof(f1349,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sP6_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1347,f283]) ).
fof(f1351,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sP2_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f1318,f1349]) ).
fof(f1352,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ h_false_only(X0,sK26_skl(X0))
| ~ g_true_only(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f115,f1349]) ).
fof(f1392,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| ~ sQ5_spl
| g_false_only(X0,X2)
| h_false_only(X0,X1)
| sP5_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f590,f1346]) ).
fof(f1394,plain,
! [X0] :
( ~ sQ24_spl
| ~ sQ4_spl
| ~ sQ5_spl
| h_false_only(sK9_skl,X0)
| sP5_prd(sK9_skl) ),
inference(resolution,[status(thm)],[f1392,f674]) ).
fof(f1396,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sQ5_spl
| sP5_prd(X0)
| h_false_only(X0,X1)
| sP5_prd(X0) ),
inference(resolution,[status(thm)],[f1392,f446]) ).
fof(f1400,plain,
( ~ sQ24_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sQ33_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f1394,f688,f612,f134,f130,f489]) ).
fof(f1402,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sQ5_spl
| h_false_only(X0,X1)
| sP5_prd(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1396]) ).
fof(f1403,plain,
( ~ sQ21_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f462,f1351]) ).
fof(f1404,plain,
( ~ sQ21_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f1403]) ).
fof(f1444,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ11_spl
| h_false_only(sK9_skl,X0)
| sP5_prd(sK9_skl) ),
inference(resolution,[status(thm)],[f518,f1392]) ).
fof(f1446,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ11_spl
| sQ33_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f1444,f688,f612,f154,f134,f130]) ).
fof(f1449,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ g_true_only(X0,X1)
| sP5_prd(X0) ),
inference(resolution,[status(thm)],[f1402,f1352]) ).
fof(f1458,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| sP5_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f105,f1449]) ).
fof(f1462,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sP1_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f1283,f1458]) ).
fof(f1463,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f1462,f127,f134,f130,f138]) ).
fof(f1464,plain,
( ~ sQ11_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f1154,f489,f154]) ).
fof(f1489,plain,
! [X0] :
( ~ sQ12_spl
| h_false(sK9_skl,X0)
| h_false_only(sK9_skl,X0) ),
inference(resolution,[status(thm)],[f611,f51]) ).
fof(f1491,plain,
! [X0] :
( ~ sQ12_spl
| h_false(sK9_skl,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1489,f55]) ).
fof(f1493,plain,
! [X0] :
( ~ sQ12_spl
| ~ h_true_only(sK9_skl,X0) ),
inference(resolution,[status(thm)],[f1491,f46]) ).
fof(f1494,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ12_spl
| ~ h_both(sK9_skl,X1)
| ~ g_true_only(sK9_skl,X0) ),
inference(resolution,[status(thm)],[f1493,f1015]) ).
fof(f1496,plain,
! [X0] :
( ~ sQ12_spl
| g_false_only(sK9_skl,X0)
| sP0_prd(sK9_skl) ),
inference(resolution,[status(thm)],[f1493,f64]) ).
fof(f1498,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| sQ37_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f1494,f635,f638,f158,f127]) ).
fof(f1500,plain,
( ~ sQ12_spl
| sQ35_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f1496,f624,f627,f158]) ).
fof(f1501,plain,
$false,
inference(sat_refutation,[status(thm)],[f122,f126,f133,f137,f141,f157,f161,f384,f386,f407,f410,f467,f468,f476,f498,f511,f541,f545,f546,f554,f559,f560,f572,f586,f587,f593,f615,f630,f645,f652,f653,f679,f681,f692,f694,f711,f786,f796,f799,f800,f834,f854,f859,f877,f883,f884,f898,f946,f948,f954,f955,f971,f981,f985,f1027,f1079,f1109,f1111,f1112,f1118,f1119,f1126,f1145,f1148,f1271,f1289,f1301,f1322,f1348,f1400,f1404,f1446,f1463,f1464,f1498,f1500]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO606+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 12:04:18 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.53 % Refutation found
% 0.10/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.54 % Elapsed time: 0.169707 seconds
% 0.10/0.54 % CPU time: 1.137696 seconds
% 0.10/0.54 % Total memory used: 32.472 MB
% 0.10/0.54 % Net memory used: 31.094 MB
%------------------------------------------------------------------------------