%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO605+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 02:28:25 PM UTC 2026
% Result : Theorem 0.62s 0.96s
% Output : Refutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 30
% Syntax : Number of formulae : 311 ( 15 unt; 25 def)
% Number of atoms : 1438 ( 0 equ)
% Maximal formula atoms : 57 ( 4 avg)
% Number of connectives : 1742 ( 615 ~; 896 |; 207 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 31 ( 30 usr; 25 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 360 ( 0 sgn 289 !; 71 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
? [X1] :
( ( g_true_only(X1,X0)
& ( g_both(X1,X1)
| g_false_only(X1,X1) ) )
| ( g_both(X1,X0)
& ( g_true_only(X1,X1)
| g_false_only(X1,X1) ) )
| ( g_false_only(X1,X0)
& ( g_true_only(X1,X1)
| g_both(X1,X1) ) ) )
| ? [X1] :
! [X0] :
? [X2] :
( ( g_true_only(X2,X0)
& ( g_both(X2,X1)
| g_true_only(X2,X1) ) )
| ( g_both(X2,X0)
& ( g_false_only(X2,X1)
| g_true_only(X2,X1) ) )
| ( g_false_only(X2,X0)
& ( g_false_only(X2,X1)
| g_both(X2,X1) ) ) )
| ( ? [X0] :
( ? [X1] :
( g_both(X1,X0)
& g_both(X1,X1) )
& ~ ? [X1] :
( ( g_true_only(X1,X0)
& ( g_both(X1,X1)
| g_false_only(X1,X1) ) )
| ( g_both(X1,X0)
& ( g_true_only(X1,X1)
| g_false_only(X1,X1) ) )
| ( g_false_only(X1,X0)
& ( g_true_only(X1,X1)
| g_both(X1,X1) ) ) ) )
& ~ ? [X0] :
! [X1] :
( ( g_true_only(X1,X0)
& g_true_only(X1,X1) )
| ( g_false_only(X1,X0)
& g_false_only(X1,X1) ) )
& ? [X1] :
( ? [X0] :
( ? [X2] :
( g_both(X2,X0)
& g_both(X2,X1) )
& ~ ? [X2] :
( ( g_true_only(X2,X0)
& ( g_both(X2,X1)
| g_true_only(X2,X1) ) )
| ( g_both(X2,X0)
& ( g_false_only(X2,X1)
| g_true_only(X2,X1) ) )
| ( g_false_only(X2,X0)
& ( g_false_only(X2,X1)
| g_both(X2,X1) ) ) ) )
& ~ ? [X0] :
! [X2] :
( ( g_true_only(X2,X0)
& g_false_only(X2,X1) )
| ( g_false_only(X2,X0)
& g_true_only(X2,X1) ) ) )
& ~ ? [X1] :
! [X0] :
? [X2] :
( ( g_true_only(X2,X0)
& ( g_both(X2,X1)
| g_true_only(X2,X1) ) )
| ( g_both(X2,X0)
& ( g_false_only(X2,X1)
| g_true_only(X2,X1) ) )
| ( g_false_only(X2,X0)
& ( g_false_only(X2,X1)
| g_both(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nc4) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
? [X1] :
( ( g_true_only(X1,X0)
& ( g_both(X1,X1)
| g_false_only(X1,X1) ) )
| ( g_both(X1,X0)
& ( g_true_only(X1,X1)
| g_false_only(X1,X1) ) )
| ( g_false_only(X1,X0)
& ( g_true_only(X1,X1)
| g_both(X1,X1) ) ) )
| ? [X1] :
! [X0] :
? [X2] :
( ( g_true_only(X2,X0)
& ( g_both(X2,X1)
| g_true_only(X2,X1) ) )
| ( g_both(X2,X0)
& ( g_false_only(X2,X1)
| g_true_only(X2,X1) ) )
| ( g_false_only(X2,X0)
& ( g_false_only(X2,X1)
| g_both(X2,X1) ) ) )
| ( ? [X0] :
( ? [X1] :
( g_both(X1,X0)
& g_both(X1,X1) )
& ~ ? [X1] :
( ( g_true_only(X1,X0)
& ( g_both(X1,X1)
| g_false_only(X1,X1) ) )
| ( g_both(X1,X0)
& ( g_true_only(X1,X1)
| g_false_only(X1,X1) ) )
| ( g_false_only(X1,X0)
& ( g_true_only(X1,X1)
| g_both(X1,X1) ) ) ) )
& ~ ? [X0] :
! [X1] :
( ( g_true_only(X1,X0)
& g_true_only(X1,X1) )
| ( g_false_only(X1,X0)
& g_false_only(X1,X1) ) )
& ? [X1] :
( ? [X0] :
( ? [X2] :
( g_both(X2,X0)
& g_both(X2,X1) )
& ~ ? [X2] :
( ( g_true_only(X2,X0)
& ( g_both(X2,X1)
| g_true_only(X2,X1) ) )
| ( g_both(X2,X0)
& ( g_false_only(X2,X1)
| g_true_only(X2,X1) ) )
| ( g_false_only(X2,X0)
& ( g_false_only(X2,X1)
| g_both(X2,X1) ) ) ) )
& ~ ? [X0] :
! [X2] :
( ( g_true_only(X2,X0)
& g_false_only(X2,X1) )
| ( g_false_only(X2,X0)
& g_true_only(X2,X1) ) ) )
& ~ ? [X1] :
! [X0] :
? [X2] :
( ( g_true_only(X2,X0)
& ( g_both(X2,X1)
| g_true_only(X2,X1) ) )
| ( g_both(X2,X0)
& ( g_false_only(X2,X1)
| g_true_only(X2,X1) ) )
| ( g_false_only(X2,X0)
& ( g_false_only(X2,X1)
| g_both(X2,X1) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
! [X0,X1] :
( g_true_only(X0,X1)
<=> ( g_true(X0,X1)
& ~ g_false(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',true_only_g) ).
fof(f4,axiom,
! [X0,X1] :
( g_both(X0,X1)
<=> ( g_true(X0,X1)
& g_false(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',both_g) ).
fof(f5,axiom,
! [X0,X1] :
( g_false_only(X0,X1)
<=> ( g_false(X0,X1)
& ~ g_true(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false_only_g) ).
fof(f6,axiom,
! [X0,X1] :
( g_true_only(X0,X1)
| g_both(X0,X1)
| g_false_only(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exhaustion_g) ).
fof(f7,plain,
~ ( ! [X0] :
? [X1] :
( ( g_true_only(X1,X0)
& ( g_both(X1,X1)
| g_false_only(X1,X1) ) )
| ( g_both(X1,X0)
& ( g_true_only(X1,X1)
| g_false_only(X1,X1) ) )
| ( g_false_only(X1,X0)
& ( g_true_only(X1,X1)
| g_both(X1,X1) ) ) )
| ? [X2] :
! [X3] :
? [X4] :
( ( g_true_only(X4,X3)
& ( g_both(X4,X2)
| g_true_only(X4,X2) ) )
| ( g_both(X4,X3)
& ( g_false_only(X4,X2)
| g_true_only(X4,X2) ) )
| ( g_false_only(X4,X3)
& ( g_false_only(X4,X2)
| g_both(X4,X2) ) ) )
| ( ? [X5] :
( ? [X6] :
( g_both(X6,X5)
& g_both(X6,X6) )
& ~ ? [X7] :
( ( g_true_only(X7,X5)
& ( g_both(X7,X7)
| g_false_only(X7,X7) ) )
| ( g_both(X7,X5)
& ( g_true_only(X7,X7)
| g_false_only(X7,X7) ) )
| ( g_false_only(X7,X5)
& ( g_true_only(X7,X7)
| g_both(X7,X7) ) ) ) )
& ~ ? [X8] :
! [X9] :
( ( g_true_only(X9,X8)
& g_true_only(X9,X9) )
| ( g_false_only(X9,X8)
& g_false_only(X9,X9) ) )
& ? [X10] :
( ? [X11] :
( ? [X12] :
( g_both(X12,X11)
& g_both(X12,X10) )
& ~ ? [X13] :
( ( g_true_only(X13,X11)
& ( g_both(X13,X10)
| g_true_only(X13,X10) ) )
| ( g_both(X13,X11)
& ( g_false_only(X13,X10)
| g_true_only(X13,X10) ) )
| ( g_false_only(X13,X11)
& ( g_false_only(X13,X10)
| g_both(X13,X10) ) ) ) )
& ~ ? [X14] :
! [X15] :
( ( g_true_only(X15,X14)
& g_false_only(X15,X10) )
| ( g_false_only(X15,X14)
& g_true_only(X15,X10) ) ) )
& ~ ? [X16] :
! [X17] :
? [X18] :
( ( g_true_only(X18,X17)
& ( g_both(X18,X16)
| g_true_only(X18,X16) ) )
| ( g_both(X18,X17)
& ( g_false_only(X18,X16)
| g_true_only(X18,X16) ) )
| ( g_false_only(X18,X17)
& ( g_false_only(X18,X16)
| g_both(X18,X16) ) ) ) ) ),
inference(rectify,[],[f2]) ).
fof(f8,plain,
( ? [X0] :
! [X1] :
( ( ~ g_true_only(X1,X0)
| ( ~ g_both(X1,X1)
& ~ g_false_only(X1,X1) ) )
& ( ~ g_both(X1,X0)
| ( ~ g_true_only(X1,X1)
& ~ g_false_only(X1,X1) ) )
& ( ~ g_false_only(X1,X0)
| ( ~ g_true_only(X1,X1)
& ~ g_both(X1,X1) ) ) )
& ! [X2] :
? [X3] :
! [X4] :
( ( ~ g_true_only(X4,X3)
| ( ~ g_both(X4,X2)
& ~ g_true_only(X4,X2) ) )
& ( ~ g_both(X4,X3)
| ( ~ g_false_only(X4,X2)
& ~ g_true_only(X4,X2) ) )
& ( ~ g_false_only(X4,X3)
| ( ~ g_false_only(X4,X2)
& ~ g_both(X4,X2) ) ) )
& ( ! [X5] :
( ! [X6] :
( ~ g_both(X6,X5)
| ~ g_both(X6,X6) )
| ? [X7] :
( ( g_true_only(X7,X5)
& ( g_both(X7,X7)
| g_false_only(X7,X7) ) )
| ( g_both(X7,X5)
& ( g_true_only(X7,X7)
| g_false_only(X7,X7) ) )
| ( g_false_only(X7,X5)
& ( g_true_only(X7,X7)
| g_both(X7,X7) ) ) ) )
| ? [X8] :
! [X9] :
( ( g_true_only(X9,X8)
& g_true_only(X9,X9) )
| ( g_false_only(X9,X8)
& g_false_only(X9,X9) ) )
| ! [X10] :
( ! [X11] :
( ! [X12] :
( ~ g_both(X12,X11)
| ~ g_both(X12,X10) )
| ? [X13] :
( ( g_true_only(X13,X11)
& ( g_both(X13,X10)
| g_true_only(X13,X10) ) )
| ( g_both(X13,X11)
& ( g_false_only(X13,X10)
| g_true_only(X13,X10) ) )
| ( g_false_only(X13,X11)
& ( g_false_only(X13,X10)
| g_both(X13,X10) ) ) ) )
| ? [X14] :
! [X15] :
( ( g_true_only(X15,X14)
& g_false_only(X15,X10) )
| ( g_false_only(X15,X14)
& g_true_only(X15,X10) ) ) )
| ? [X16] :
! [X17] :
? [X18] :
( ( g_true_only(X18,X17)
& ( g_both(X18,X16)
| g_true_only(X18,X16) ) )
| ( g_both(X18,X17)
& ( g_false_only(X18,X16)
| g_true_only(X18,X16) ) )
| ( g_false_only(X18,X17)
& ( g_false_only(X18,X16)
| g_both(X18,X16) ) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f9,definition,
! [X10] :
( ! [X11] :
( ! [X12] :
( ~ g_both(X12,X11)
| ~ g_both(X12,X10) )
| ? [X13] :
( ( g_true_only(X13,X11)
& ( g_both(X13,X10)
| g_true_only(X13,X10) ) )
| ( g_both(X13,X11)
& ( g_false_only(X13,X10)
| g_true_only(X13,X10) ) )
| ( g_false_only(X13,X11)
& ( g_false_only(X13,X10)
| g_both(X13,X10) ) ) ) )
| ~ sP0(X10) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f10,definition,
( ? [X16] :
! [X17] :
? [X18] :
( ( g_true_only(X18,X17)
& ( g_both(X18,X16)
| g_true_only(X18,X16) ) )
| ( g_both(X18,X17)
& ( g_false_only(X18,X16)
| g_true_only(X18,X16) ) )
| ( g_false_only(X18,X17)
& ( g_false_only(X18,X16)
| g_both(X18,X16) ) ) )
| ~ sP1 ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f11,definition,
( ! [X5] :
( ! [X6] :
( ~ g_both(X6,X5)
| ~ g_both(X6,X6) )
| ? [X7] :
( ( g_true_only(X7,X5)
& ( g_both(X7,X7)
| g_false_only(X7,X7) ) )
| ( g_both(X7,X5)
& ( g_true_only(X7,X7)
| g_false_only(X7,X7) ) )
| ( g_false_only(X7,X5)
& ( g_true_only(X7,X7)
| g_both(X7,X7) ) ) ) )
| ~ sP2 ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f12,definition,
( ! [X10] :
( sP0(X10)
| ? [X14] :
! [X15] :
( ( g_true_only(X15,X14)
& g_false_only(X15,X10) )
| ( g_false_only(X15,X14)
& g_true_only(X15,X10) ) ) )
| ~ sP3 ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f13,plain,
( ? [X0] :
! [X1] :
( ( ~ g_true_only(X1,X0)
| ( ~ g_both(X1,X1)
& ~ g_false_only(X1,X1) ) )
& ( ~ g_both(X1,X0)
| ( ~ g_true_only(X1,X1)
& ~ g_false_only(X1,X1) ) )
& ( ~ g_false_only(X1,X0)
| ( ~ g_true_only(X1,X1)
& ~ g_both(X1,X1) ) ) )
& ! [X2] :
? [X3] :
! [X4] :
( ( ~ g_true_only(X4,X3)
| ( ~ g_both(X4,X2)
& ~ g_true_only(X4,X2) ) )
& ( ~ g_both(X4,X3)
| ( ~ g_false_only(X4,X2)
& ~ g_true_only(X4,X2) ) )
& ( ~ g_false_only(X4,X3)
| ( ~ g_false_only(X4,X2)
& ~ g_both(X4,X2) ) ) )
& ( sP2
| ? [X8] :
! [X9] :
( ( g_true_only(X9,X8)
& g_true_only(X9,X9) )
| ( g_false_only(X9,X8)
& g_false_only(X9,X9) ) )
| sP3
| sP1 ) ),
inference(definition_folding,[],[f8,f12,f11,f10,f9]) ).
fof(f14,plain,
( ! [X10] :
( sP0(X10)
| ? [X14] :
! [X15] :
( ( g_true_only(X15,X14)
& g_false_only(X15,X10) )
| ( g_false_only(X15,X14)
& g_true_only(X15,X10) ) ) )
| ~ sP3 ),
inference(nnf_transformation,[],[f12]) ).
fof(f15,plain,
( ! [X0] :
( sP0(X0)
| ? [X1] :
! [X2] :
( ( g_true_only(X2,X1)
& g_false_only(X2,X0) )
| ( g_false_only(X2,X1)
& g_true_only(X2,X0) ) ) )
| ~ sP3 ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
( ! [X0] :
( sP0(X0)
| ! [X2] :
( ( g_true_only(X2,sK4(X0))
& g_false_only(X2,X0) )
| ( g_false_only(X2,sK4(X0))
& g_true_only(X2,X0) ) ) )
| ~ sP3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f15]) ).
fof(f17,plain,
( ! [X5] :
( ! [X6] :
( ~ g_both(X6,X5)
| ~ g_both(X6,X6) )
| ? [X7] :
( ( g_true_only(X7,X5)
& ( g_both(X7,X7)
| g_false_only(X7,X7) ) )
| ( g_both(X7,X5)
& ( g_true_only(X7,X7)
| g_false_only(X7,X7) ) )
| ( g_false_only(X7,X5)
& ( g_true_only(X7,X7)
| g_both(X7,X7) ) ) ) )
| ~ sP2 ),
inference(nnf_transformation,[],[f11]) ).
fof(f18,plain,
( ! [X0] :
( ! [X1] :
( ~ g_both(X1,X0)
| ~ g_both(X1,X1) )
| ? [X2] :
( ( g_true_only(X2,X0)
& ( g_both(X2,X2)
| g_false_only(X2,X2) ) )
| ( g_both(X2,X0)
& ( g_true_only(X2,X2)
| g_false_only(X2,X2) ) )
| ( g_false_only(X2,X0)
& ( g_true_only(X2,X2)
| g_both(X2,X2) ) ) ) )
| ~ sP2 ),
inference(rectify,[],[f17]) ).
fof(f19,plain,
( ! [X0] :
( ! [X1] :
( ~ g_both(X1,X0)
| ~ g_both(X1,X1) )
| ( g_true_only(sK5(X0),X0)
& ( g_both(sK5(X0),sK5(X0))
| g_false_only(sK5(X0),sK5(X0)) ) )
| ( g_both(sK5(X0),X0)
& ( g_true_only(sK5(X0),sK5(X0))
| g_false_only(sK5(X0),sK5(X0)) ) )
| ( g_false_only(sK5(X0),X0)
& ( g_true_only(sK5(X0),sK5(X0))
| g_both(sK5(X0),sK5(X0)) ) ) )
| ~ sP2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0))],[f18]) ).
fof(f20,plain,
( ? [X16] :
! [X17] :
? [X18] :
( ( g_true_only(X18,X17)
& ( g_both(X18,X16)
| g_true_only(X18,X16) ) )
| ( g_both(X18,X17)
& ( g_false_only(X18,X16)
| g_true_only(X18,X16) ) )
| ( g_false_only(X18,X17)
& ( g_false_only(X18,X16)
| g_both(X18,X16) ) ) )
| ~ sP1 ),
inference(nnf_transformation,[],[f10]) ).
fof(f21,plain,
( ? [X0] :
! [X1] :
? [X2] :
( ( g_true_only(X2,X1)
& ( g_both(X2,X0)
| g_true_only(X2,X0) ) )
| ( g_both(X2,X1)
& ( g_false_only(X2,X0)
| g_true_only(X2,X0) ) )
| ( g_false_only(X2,X1)
& ( g_false_only(X2,X0)
| g_both(X2,X0) ) ) )
| ~ sP1 ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
( ! [X1] :
( ( g_true_only(sK7(X1),X1)
& ( g_both(sK7(X1),sK6)
| g_true_only(sK7(X1),sK6) ) )
| ( g_both(sK7(X1),X1)
& ( g_false_only(sK7(X1),sK6)
| g_true_only(sK7(X1),sK6) ) )
| ( g_false_only(sK7(X1),X1)
& ( g_false_only(sK7(X1),sK6)
| g_both(sK7(X1),sK6) ) ) )
| ~ sP1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X2,sK7(X1))],[f21]) ).
fof(f23,plain,
! [X10] :
( ! [X11] :
( ! [X12] :
( ~ g_both(X12,X11)
| ~ g_both(X12,X10) )
| ? [X13] :
( ( g_true_only(X13,X11)
& ( g_both(X13,X10)
| g_true_only(X13,X10) ) )
| ( g_both(X13,X11)
& ( g_false_only(X13,X10)
| g_true_only(X13,X10) ) )
| ( g_false_only(X13,X11)
& ( g_false_only(X13,X10)
| g_both(X13,X10) ) ) ) )
| ~ sP0(X10) ),
inference(nnf_transformation,[],[f9]) ).
fof(f24,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ~ g_both(X2,X1)
| ~ g_both(X2,X0) )
| ? [X3] :
( ( g_true_only(X3,X1)
& ( g_both(X3,X0)
| g_true_only(X3,X0) ) )
| ( g_both(X3,X1)
& ( g_false_only(X3,X0)
| g_true_only(X3,X0) ) )
| ( g_false_only(X3,X1)
& ( g_false_only(X3,X0)
| g_both(X3,X0) ) ) ) )
| ~ sP0(X0) ),
inference(rectify,[],[f23]) ).
fof(f25,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ~ g_both(X2,X1)
| ~ g_both(X2,X0) )
| ( g_true_only(sK8(X0,X1),X1)
& ( g_both(sK8(X0,X1),X0)
| g_true_only(sK8(X0,X1),X0) ) )
| ( g_both(sK8(X0,X1),X1)
& ( g_false_only(sK8(X0,X1),X0)
| g_true_only(sK8(X0,X1),X0) ) )
| ( g_false_only(sK8(X0,X1),X1)
& ( g_false_only(sK8(X0,X1),X0)
| g_both(sK8(X0,X1),X0) ) ) )
| ~ sP0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X3,sK8(X0,X1))],[f24]) ).
fof(f26,plain,
( ? [X0] :
! [X1] :
( ( ~ g_true_only(X1,X0)
| ( ~ g_both(X1,X1)
& ~ g_false_only(X1,X1) ) )
& ( ~ g_both(X1,X0)
| ( ~ g_true_only(X1,X1)
& ~ g_false_only(X1,X1) ) )
& ( ~ g_false_only(X1,X0)
| ( ~ g_true_only(X1,X1)
& ~ g_both(X1,X1) ) ) )
& ! [X2] :
? [X3] :
! [X4] :
( ( ~ g_true_only(X4,X3)
| ( ~ g_both(X4,X2)
& ~ g_true_only(X4,X2) ) )
& ( ~ g_both(X4,X3)
| ( ~ g_false_only(X4,X2)
& ~ g_true_only(X4,X2) ) )
& ( ~ g_false_only(X4,X3)
| ( ~ g_false_only(X4,X2)
& ~ g_both(X4,X2) ) ) )
& ( sP2
| ? [X5] :
! [X6] :
( ( g_true_only(X6,X5)
& g_true_only(X6,X6) )
| ( g_false_only(X6,X5)
& g_false_only(X6,X6) ) )
| sP3
| sP1 ) ),
inference(rectify,[],[f13]) ).
fof(f27,plain,
( ! [X1] :
( ( ~ g_true_only(X1,sK9)
| ( ~ g_both(X1,X1)
& ~ g_false_only(X1,X1) ) )
& ( ~ g_both(X1,sK9)
| ( ~ g_true_only(X1,X1)
& ~ g_false_only(X1,X1) ) )
& ( ~ g_false_only(X1,sK9)
| ( ~ g_true_only(X1,X1)
& ~ g_both(X1,X1) ) ) )
& ! [X2,X4] :
( ( ~ g_true_only(X4,sK10(X2))
| ( ~ g_both(X4,X2)
& ~ g_true_only(X4,X2) ) )
& ( ~ g_both(X4,sK10(X2))
| ( ~ g_false_only(X4,X2)
& ~ g_true_only(X4,X2) ) )
& ( ~ g_false_only(X4,sK10(X2))
| ( ~ g_false_only(X4,X2)
& ~ g_both(X4,X2) ) ) )
& ( sP2
| ! [X6] :
( ( g_true_only(X6,sK11)
& g_true_only(X6,X6) )
| ( g_false_only(X6,sK11)
& g_false_only(X6,X6) ) )
| sP3
| sP1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X0,sK9),skolemize(X3,sK10(X2)),skolemize(X5,sK11)],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ( g_true_only(X0,X1)
| ~ g_true(X0,X1)
| g_false(X0,X1) )
& ( ( g_true(X0,X1)
& ~ g_false(X0,X1) )
| ~ g_true_only(X0,X1) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f29,plain,
! [X0,X1] :
( ( g_true_only(X0,X1)
| ~ g_true(X0,X1)
| g_false(X0,X1) )
& ( ( g_true(X0,X1)
& ~ g_false(X0,X1) )
| ~ g_true_only(X0,X1) ) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( ( g_both(X0,X1)
| ~ g_true(X0,X1)
| ~ g_false(X0,X1) )
& ( ( g_true(X0,X1)
& g_false(X0,X1) )
| ~ g_both(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f31,plain,
! [X0,X1] :
( ( g_both(X0,X1)
| ~ g_true(X0,X1)
| ~ g_false(X0,X1) )
& ( ( g_true(X0,X1)
& g_false(X0,X1) )
| ~ g_both(X0,X1) ) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ( g_false_only(X0,X1)
| ~ g_false(X0,X1)
| g_true(X0,X1) )
& ( ( g_false(X0,X1)
& ~ g_true(X0,X1) )
| ~ g_false_only(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f33,plain,
! [X0,X1] :
( ( g_false_only(X0,X1)
| ~ g_false(X0,X1)
| g_true(X0,X1) )
& ( ( g_false(X0,X1)
& ~ g_true(X0,X1) )
| ~ g_false_only(X0,X1) ) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X2,X0] :
( g_false_only(X2,X0)
| sP0(X0)
| g_true_only(X2,X0)
| ~ sP3 ),
inference(cnf_transformation,[],[f16]) ).
fof(f41,plain,
! [X0,X1] :
( g_false_only(sK5(X0),sK5(X0))
| ~ g_both(X1,X1)
| g_both(sK5(X0),sK5(X0))
| ~ g_both(X1,X0)
| g_both(sK5(X0),X0)
| g_false_only(sK5(X0),X0)
| ~ sP2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f43,plain,
! [X0,X1] :
( g_false_only(sK5(X0),sK5(X0))
| ~ g_both(X1,X1)
| g_true_only(sK5(X0),X0)
| g_true_only(sK5(X0),sK5(X0))
| ~ g_both(X1,X0)
| g_false_only(sK5(X0),X0)
| ~ sP2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f44,plain,
! [X0,X1] :
( g_both(sK5(X0),sK5(X0))
| ~ g_both(X1,X1)
| g_true_only(sK5(X0),X0)
| g_both(sK5(X0),X0)
| g_true_only(sK5(X0),sK5(X0))
| ~ g_both(X1,X0)
| ~ sP2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f46,plain,
! [X1] :
( g_both(sK7(X1),sK6)
| g_true_only(sK7(X1),sK6)
| g_false_only(sK7(X1),sK6)
| g_true_only(sK7(X1),sK6)
| g_false_only(sK7(X1),sK6)
| g_both(sK7(X1),sK6)
| ~ sP1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f49,plain,
! [X1] :
( g_false_only(sK7(X1),X1)
| g_true_only(sK7(X1),sK6)
| g_both(sK7(X1),X1)
| g_both(sK7(X1),sK6)
| ~ sP1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f51,plain,
! [X1] :
( g_false_only(sK7(X1),sK6)
| g_true_only(sK7(X1),X1)
| g_true_only(sK7(X1),sK6)
| g_false_only(sK7(X1),X1)
| ~ sP1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f52,plain,
! [X1] :
( g_false_only(sK7(X1),sK6)
| g_both(sK7(X1),X1)
| g_true_only(sK7(X1),X1)
| g_both(sK7(X1),sK6)
| ~ sP1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ g_both(X2,X1)
| ~ g_both(X2,X0)
| g_both(sK8(X0,X1),X0)
| g_true_only(sK8(X0,X1),X0)
| g_false_only(sK8(X0,X1),X0)
| g_true_only(sK8(X0,X1),X0)
| g_false_only(sK8(X0,X1),X0)
| g_both(sK8(X0,X1),X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ g_both(X2,X1)
| ~ g_both(X2,X0)
| g_both(sK8(X0,X1),X0)
| g_true_only(sK8(X0,X1),X0)
| g_both(sK8(X0,X1),X1)
| g_false_only(sK8(X0,X1),X0)
| g_both(sK8(X0,X1),X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f57,plain,
! [X2,X0,X1] :
( g_false_only(sK8(X0,X1),X1)
| ~ g_both(X2,X0)
| g_both(sK8(X0,X1),X0)
| g_true_only(sK8(X0,X1),X0)
| g_both(sK8(X0,X1),X1)
| ~ g_both(X2,X1)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f59,plain,
! [X2,X0,X1] :
( g_false_only(sK8(X0,X1),X1)
| ~ g_both(X2,X0)
| g_true_only(sK8(X0,X1),X1)
| g_false_only(sK8(X0,X1),X0)
| g_true_only(sK8(X0,X1),X0)
| ~ g_both(X2,X1)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f60,plain,
! [X2,X0,X1] :
( g_false_only(sK8(X0,X1),X0)
| ~ g_both(X2,X0)
| g_true_only(sK8(X0,X1),X1)
| g_both(sK8(X0,X1),X1)
| ~ g_both(X2,X1)
| g_both(sK8(X0,X1),X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f62,plain,
! [X6] :
( sP2
| g_true_only(X6,X6)
| g_false_only(X6,X6)
| sP3
| sP1 ),
inference(cnf_transformation,[],[f27]) ).
fof(f66,plain,
! [X2,X4] :
( ~ g_false_only(X4,sK10(X2))
| ~ g_both(X4,X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f67,plain,
! [X2,X4] :
( ~ g_false_only(X4,sK10(X2))
| ~ g_false_only(X4,X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f68,plain,
! [X2,X4] :
( ~ g_both(X4,sK10(X2))
| ~ g_true_only(X4,X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f69,plain,
! [X2,X4] :
( ~ g_both(X4,sK10(X2))
| ~ g_false_only(X4,X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f70,plain,
! [X2,X4] :
( ~ g_true_only(X4,sK10(X2))
| ~ g_true_only(X4,X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f71,plain,
! [X2,X4] :
( ~ g_true_only(X4,sK10(X2))
| ~ g_both(X4,X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f72,plain,
! [X1] :
( ~ g_false_only(X1,sK9)
| ~ g_both(X1,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f73,plain,
! [X1] :
( ~ g_false_only(X1,sK9)
| ~ g_true_only(X1,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f74,plain,
! [X1] :
( ~ g_false_only(X1,X1)
| ~ g_both(X1,sK9) ),
inference(cnf_transformation,[],[f27]) ).
fof(f75,plain,
! [X1] :
( ~ g_both(X1,sK9)
| ~ g_true_only(X1,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f76,plain,
! [X1] :
( ~ g_false_only(X1,X1)
| ~ g_true_only(X1,sK9) ),
inference(cnf_transformation,[],[f27]) ).
fof(f77,plain,
! [X1] :
( ~ g_both(X1,X1)
| ~ g_true_only(X1,sK9) ),
inference(cnf_transformation,[],[f27]) ).
fof(f78,plain,
! [X0,X1] :
( g_false_only(X0,X1)
| g_both(X0,X1)
| g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f79,plain,
! [X0,X1] :
( ~ g_false(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f80,plain,
! [X0,X1] :
( ~ g_true_only(X0,X1)
| g_true(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f83,plain,
! [X0,X1] :
( ~ g_both(X0,X1)
| g_true(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f85,plain,
! [X0,X1] :
( ~ g_true(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f86,plain,
! [X0,X1] :
( ~ g_false_only(X0,X1)
| g_false(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f95,plain,
! [X1] :
( g_false_only(sK7(X1),sK6)
| g_true_only(sK7(X1),sK6)
| g_both(sK7(X1),sK6)
| ~ sP1 ),
inference(duplicate_literal_removal,[],[f46]) ).
fof(f97,plain,
! [X2,X0,X1] :
( g_false_only(sK8(X0,X1),X0)
| ~ g_both(X2,X0)
| g_both(sK8(X0,X1),X0)
| g_true_only(sK8(X0,X1),X0)
| g_both(sK8(X0,X1),X1)
| ~ g_both(X2,X1)
| ~ sP0(X0) ),
inference(duplicate_literal_removal,[],[f56]) ).
fof(f99,plain,
! [X2,X0,X1] :
( g_false_only(sK8(X0,X1),X0)
| ~ g_both(X2,X0)
| g_both(sK8(X0,X1),X0)
| g_true_only(sK8(X0,X1),X0)
| ~ g_both(X2,X1)
| ~ sP0(X0) ),
inference(duplicate_literal_removal,[],[f54]) ).
fof(f101,definition,
( spl12_1
<=> sP1 ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f103,plain,
( sP1
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f105,definition,
( spl12_2
<=> sP3 ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f107,plain,
( sP3
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f109,definition,
( spl12_3
<=> ! [X6] :
( g_true_only(X6,X6)
| g_false_only(X6,X6) ) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
fof(f110,plain,
( ! [X6] :
( g_false_only(X6,X6)
| g_true_only(X6,X6) )
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,definition,
( spl12_4
<=> sP2 ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
fof(f114,plain,
( sP2
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f115,plain,
( spl12_1
| spl12_2
| spl12_3
| spl12_4 ),
inference(avatar_split_clause,[],[f62,f112,f109,f105,f101]) ).
fof(f128,plain,
! [X0] :
( ~ g_both(X0,X0)
| g_both(X0,sK9)
| g_true_only(X0,sK9) ),
inference(resolution,[],[f72,f78]) ).
fof(f174,plain,
! [X0] :
( ~ g_both(X0,X0)
| g_both(X0,sK9) ),
inference(forward_subsumption_resolution,[],[f128,f77]) ).
fof(f189,definition,
( spl12_17
<=> g_both(sK5(sK9),sK9) ),
introduced(definition,[new_symbols(definition,[spl12_17])],[avatar_definition]) ).
fof(f190,plain,
( ~ g_both(sK5(sK9),sK9)
| spl12_17 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f191,plain,
( g_both(sK5(sK9),sK9)
| ~ spl12_17 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f196,definition,
( spl12_19
<=> g_both(sK5(sK9),sK5(sK9)) ),
introduced(definition,[new_symbols(definition,[spl12_19])],[avatar_definition]) ).
fof(f197,plain,
( g_both(sK5(sK9),sK5(sK9))
| ~ spl12_19 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f198,plain,
( ~ g_both(sK5(sK9),sK5(sK9))
| spl12_19 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f202,definition,
( spl12_20
<=> ! [X0] : ~ g_both(X0,X0) ),
introduced(definition,[new_symbols(definition,[spl12_20])],[avatar_definition]) ).
fof(f203,plain,
( ! [X0] : ~ g_both(X0,X0)
| ~ spl12_20 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f205,plain,
! [X0] :
( ~ g_true_only(X0,X0)
| g_both(X0,sK9)
| g_true_only(X0,sK9) ),
inference(resolution,[],[f73,f78]) ).
fof(f223,plain,
! [X0] :
( ~ g_true_only(X0,X0)
| g_true_only(X0,sK9) ),
inference(forward_subsumption_resolution,[],[f205,f75]) ).
fof(f237,plain,
! [X0] :
( ~ g_both(X0,sK9)
| g_both(X0,X0)
| g_true_only(X0,X0) ),
inference(resolution,[],[f74,f78]) ).
fof(f244,plain,
! [X0,X1] :
( ~ g_both(sK5(X0),sK9)
| ~ g_both(X1,X1)
| g_true_only(sK5(X0),X0)
| g_true_only(sK5(X0),sK5(X0))
| ~ g_both(X1,X0)
| g_false_only(sK5(X0),X0)
| ~ sP2 ),
inference(resolution,[],[f74,f43]) ).
fof(f251,plain,
! [X0] :
( ~ g_both(X0,sK9)
| g_both(X0,X0) ),
inference(forward_subsumption_resolution,[],[f237,f75]) ).
fof(f257,plain,
( ! [X0] :
( ~ g_both(X0,X0)
| g_true_only(sK5(sK9),sK9)
| g_both(sK5(sK9),sK9)
| g_true_only(sK5(sK9),sK5(sK9))
| ~ g_both(X0,sK9)
| ~ sP2 )
| spl12_19 ),
inference(resolution,[],[f198,f44]) ).
fof(f258,plain,
( ! [X0] :
( ~ g_both(X0,X0)
| g_true_only(sK5(sK9),sK9)
| g_both(sK5(sK9),sK9)
| g_true_only(sK5(sK9),sK5(sK9))
| ~ sP2 )
| spl12_19 ),
inference(forward_subsumption_resolution,[],[f257,f174]) ).
fof(f259,plain,
( ! [X0] :
( ~ g_both(X0,X0)
| g_true_only(sK5(sK9),sK9)
| g_both(sK5(sK9),sK9)
| ~ sP2 )
| spl12_19 ),
inference(forward_subsumption_resolution,[],[f258,f223]) ).
fof(f260,plain,
( ! [X0] :
( ~ g_both(X0,X0)
| g_true_only(sK5(sK9),sK9)
| g_both(sK5(sK9),sK9) )
| ~ spl12_4
| spl12_19 ),
inference(forward_subsumption_resolution,[],[f259,f114]) ).
fof(f262,definition,
( spl12_23
<=> g_true_only(sK5(sK9),sK9) ),
introduced(definition,[new_symbols(definition,[spl12_23])],[avatar_definition]) ).
fof(f263,plain,
( ~ g_true_only(sK5(sK9),sK9)
| spl12_23 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f264,plain,
( g_true_only(sK5(sK9),sK9)
| ~ spl12_23 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f265,plain,
( spl12_17
| spl12_23
| spl12_20
| ~ spl12_4
| spl12_19 ),
inference(avatar_split_clause,[],[f260,f196,f112,f202,f262,f189]) ).
fof(f268,plain,
! [X0] :
( ~ g_true_only(X0,sK9)
| g_both(X0,X0)
| g_true_only(X0,X0) ),
inference(resolution,[],[f76,f78]) ).
fof(f273,plain,
! [X0,X1] :
( ~ g_true_only(sK5(X0),sK9)
| ~ g_both(X1,X1)
| g_both(sK5(X0),sK5(X0))
| ~ g_both(X1,X0)
| g_both(sK5(X0),X0)
| g_false_only(sK5(X0),X0)
| ~ sP2 ),
inference(resolution,[],[f76,f41]) ).
fof(f276,plain,
! [X0] :
( ~ g_true_only(X0,sK9)
| g_true_only(X0,X0) ),
inference(forward_subsumption_resolution,[],[f268,f77]) ).
fof(f279,plain,
! [X0,X1] :
( ~ g_both(X0,X1)
| g_both(X0,sK10(X1))
| g_true_only(X0,sK10(X1)) ),
inference(resolution,[],[f66,f78]) ).
fof(f286,plain,
! [X2,X0,X1] :
( ~ g_both(sK8(X0,sK10(X1)),X1)
| ~ g_both(X2,X0)
| g_true_only(sK8(X0,sK10(X1)),sK10(X1))
| g_false_only(sK8(X0,sK10(X1)),X0)
| g_true_only(sK8(X0,sK10(X1)),X0)
| ~ g_both(X2,sK10(X1))
| ~ sP0(X0) ),
inference(resolution,[],[f66,f59]) ).
fof(f296,plain,
! [X2,X0,X1] :
( ~ g_both(sK8(X0,sK10(X1)),X1)
| ~ g_both(X2,X0)
| g_false_only(sK8(X0,sK10(X1)),X0)
| g_true_only(sK8(X0,sK10(X1)),X0)
| ~ g_both(X2,sK10(X1))
| ~ sP0(X0) ),
inference(forward_subsumption_resolution,[],[f286,f71]) ).
fof(f299,plain,
! [X0,X1] :
( g_both(X0,sK10(X1))
| ~ g_both(X0,X1) ),
inference(forward_subsumption_resolution,[],[f279,f71]) ).
fof(f302,plain,
! [X0,X1] :
( ~ g_false_only(X0,X1)
| g_both(X0,sK10(X1))
| g_true_only(X0,sK10(X1)) ),
inference(resolution,[],[f67,f78]) ).
fof(f305,plain,
! [X0] :
( ~ g_false_only(sK7(sK10(X0)),X0)
| g_true_only(sK7(sK10(X0)),sK6)
| g_both(sK7(sK10(X0)),sK10(X0))
| g_both(sK7(sK10(X0)),sK6)
| ~ sP1 ),
inference(resolution,[],[f67,f49]) ).
fof(f308,plain,
! [X2,X0,X1] :
( ~ g_false_only(sK8(X0,sK10(X1)),X1)
| ~ g_both(X2,X0)
| g_both(sK8(X0,sK10(X1)),X0)
| g_true_only(sK8(X0,sK10(X1)),X0)
| g_both(sK8(X0,sK10(X1)),sK10(X1))
| ~ g_both(X2,sK10(X1))
| ~ sP0(X0) ),
inference(resolution,[],[f67,f57]) ).
fof(f320,plain,
! [X2,X0,X1] :
( ~ g_false_only(sK8(X0,sK10(X1)),X1)
| ~ g_both(X2,X0)
| g_both(sK8(X0,sK10(X1)),X0)
| g_true_only(sK8(X0,sK10(X1)),X0)
| ~ g_both(X2,sK10(X1))
| ~ sP0(X0) ),
inference(forward_subsumption_resolution,[],[f308,f69]) ).
fof(f322,plain,
( ! [X0] :
( ~ g_false_only(sK7(sK10(X0)),X0)
| g_true_only(sK7(sK10(X0)),sK6)
| g_both(sK7(sK10(X0)),sK10(X0))
| g_both(sK7(sK10(X0)),sK6) )
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f305,f103]) ).
fof(f323,plain,
! [X0,X1] :
( g_true_only(X0,sK10(X1))
| ~ g_false_only(X0,X1) ),
inference(forward_subsumption_resolution,[],[f302,f69]) ).
fof(f325,plain,
( ! [X0] :
( ~ g_false_only(sK7(sK10(X0)),X0)
| g_true_only(sK7(sK10(X0)),sK6)
| g_both(sK7(sK10(X0)),sK6) )
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f322,f69]) ).
fof(f326,plain,
! [X0,X1] :
( ~ g_false_only(X0,X1)
| ~ g_both(X0,X1) ),
inference(resolution,[],[f299,f69]) ).
fof(f327,plain,
! [X0,X1] :
( ~ g_both(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(resolution,[],[f299,f68]) ).
fof(f333,plain,
! [X0,X1] :
( ~ g_false_only(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(resolution,[],[f323,f70]) ).
fof(f334,plain,
! [X0] :
( ~ g_false_only(sK10(X0),X0)
| g_true_only(sK10(X0),sK9) ),
inference(resolution,[],[f323,f223]) ).
fof(f339,plain,
! [X0,X1] :
( ~ g_both(X0,X1)
| sP0(X1)
| g_true_only(X0,X1)
| ~ sP3 ),
inference(resolution,[],[f326,f34]) ).
fof(f353,plain,
! [X0] :
( ~ g_both(sK7(X0),sK6)
| g_true_only(sK7(X0),X0)
| g_true_only(sK7(X0),sK6)
| g_false_only(sK7(X0),X0)
| ~ sP1 ),
inference(resolution,[],[f326,f51]) ).
fof(f364,plain,
! [X0] :
( ~ g_both(sK7(X0),sK6)
| g_true_only(sK7(X0),X0)
| g_false_only(sK7(X0),X0)
| ~ sP1 ),
inference(forward_subsumption_resolution,[],[f353,f327]) ).
fof(f365,plain,
( ! [X0] :
( ~ g_both(sK7(X0),sK6)
| g_true_only(sK7(X0),X0)
| g_false_only(sK7(X0),X0) )
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f364,f103]) ).
fof(f366,plain,
( g_true_only(sK7(sK10(sK6)),sK6)
| g_both(sK7(sK10(sK6)),sK6)
| g_true_only(sK7(sK10(sK6)),sK6)
| g_both(sK7(sK10(sK6)),sK6)
| ~ sP1
| ~ spl12_1 ),
inference(resolution,[],[f325,f95]) ).
fof(f370,plain,
( g_true_only(sK7(sK10(sK6)),sK6)
| g_both(sK7(sK10(sK6)),sK6)
| g_true_only(sK7(sK10(sK6)),sK10(sK6))
| g_true_only(sK7(sK10(sK6)),sK6)
| g_false_only(sK7(sK10(sK6)),sK10(sK6))
| ~ sP1
| ~ spl12_1 ),
inference(resolution,[],[f325,f51]) ).
fof(f377,plain,
( g_true_only(sK7(sK10(sK6)),sK6)
| g_both(sK7(sK10(sK6)),sK6)
| g_true_only(sK7(sK10(sK6)),sK10(sK6))
| g_false_only(sK7(sK10(sK6)),sK10(sK6))
| ~ sP1
| ~ spl12_1 ),
inference(duplicate_literal_removal,[],[f370]) ).
fof(f381,plain,
( g_true_only(sK7(sK10(sK6)),sK6)
| g_both(sK7(sK10(sK6)),sK6)
| ~ sP1
| ~ spl12_1 ),
inference(duplicate_literal_removal,[],[f366]) ).
fof(f383,plain,
( g_true_only(sK7(sK10(sK6)),sK6)
| g_true_only(sK7(sK10(sK6)),sK10(sK6))
| g_false_only(sK7(sK10(sK6)),sK10(sK6))
| ~ sP1
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f377,f365]) ).
fof(f387,plain,
( g_true_only(sK7(sK10(sK6)),sK6)
| g_both(sK7(sK10(sK6)),sK6)
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f381,f103]) ).
fof(f389,plain,
( g_true_only(sK7(sK10(sK6)),sK6)
| g_true_only(sK7(sK10(sK6)),sK10(sK6))
| g_false_only(sK7(sK10(sK6)),sK10(sK6))
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f383,f103]) ).
fof(f391,definition,
( spl12_24
<=> g_true_only(sK7(sK10(sK6)),sK10(sK6)) ),
introduced(definition,[new_symbols(definition,[spl12_24])],[avatar_definition]) ).
fof(f393,plain,
( g_true_only(sK7(sK10(sK6)),sK10(sK6))
| ~ spl12_24 ),
inference(avatar_component_clause,[],[f391]) ).
fof(f395,definition,
( spl12_25
<=> g_both(sK7(sK10(sK6)),sK6) ),
introduced(definition,[new_symbols(definition,[spl12_25])],[avatar_definition]) ).
fof(f397,plain,
( g_both(sK7(sK10(sK6)),sK6)
| ~ spl12_25 ),
inference(avatar_component_clause,[],[f395]) ).
fof(f399,definition,
( spl12_26
<=> g_true_only(sK7(sK10(sK6)),sK6) ),
introduced(definition,[new_symbols(definition,[spl12_26])],[avatar_definition]) ).
fof(f401,plain,
( g_true_only(sK7(sK10(sK6)),sK6)
| ~ spl12_26 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f405,definition,
( spl12_27
<=> g_false_only(sK7(sK10(sK6)),sK10(sK6)) ),
introduced(definition,[new_symbols(definition,[spl12_27])],[avatar_definition]) ).
fof(f407,plain,
( g_false_only(sK7(sK10(sK6)),sK10(sK6))
| ~ spl12_27 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f409,plain,
( spl12_25
| spl12_26
| ~ spl12_1 ),
inference(avatar_split_clause,[],[f387,f101,f399,f395]) ).
fof(f411,definition,
( spl12_28
<=> g_both(sK7(sK10(sK6)),sK10(sK6)) ),
introduced(definition,[new_symbols(definition,[spl12_28])],[avatar_definition]) ).
fof(f413,plain,
( g_both(sK7(sK10(sK6)),sK10(sK6))
| ~ spl12_28 ),
inference(avatar_component_clause,[],[f411]) ).
fof(f415,plain,
( spl12_27
| spl12_24
| spl12_26
| ~ spl12_1 ),
inference(avatar_split_clause,[],[f389,f101,f399,f391,f405]) ).
fof(f427,plain,
! [X0,X1] :
( ~ g_both(X0,X1)
| sP0(X1)
| ~ sP3 ),
inference(forward_subsumption_resolution,[],[f339,f327]) ).
fof(f434,plain,
( ! [X0,X1] :
( ~ g_both(X0,X1)
| sP0(X1) )
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f427,f107]) ).
fof(f460,plain,
! [X0] :
( ~ g_true_only(sK7(X0),sK6)
| g_both(sK7(X0),X0)
| g_true_only(sK7(X0),X0)
| g_both(sK7(X0),sK6)
| ~ sP1 ),
inference(resolution,[],[f333,f52]) ).
fof(f512,plain,
! [X0] :
( g_both(sK10(X0),X0)
| g_true_only(sK10(X0),sK9)
| g_true_only(sK10(X0),X0) ),
inference(resolution,[],[f334,f78]) ).
fof(f524,plain,
! [X2,X0,X1] :
( ~ g_both(X0,X1)
| g_both(sK8(X1,sK10(X1)),X1)
| g_true_only(sK8(X1,sK10(X1)),X1)
| ~ g_both(X0,sK10(X1))
| ~ sP0(X1)
| ~ g_both(X2,X1)
| g_both(sK8(X1,sK10(X1)),X1)
| g_true_only(sK8(X1,sK10(X1)),X1)
| ~ g_both(X2,sK10(X1))
| ~ sP0(X1) ),
inference(resolution,[],[f320,f99]) ).
fof(f525,plain,
! [X2,X0,X1] :
( ~ g_both(X0,X1)
| g_both(sK8(X1,sK10(X1)),X1)
| g_true_only(sK8(X1,sK10(X1)),X1)
| ~ g_both(X0,sK10(X1))
| ~ sP0(X1)
| ~ g_both(X2,X1)
| g_both(sK8(X1,sK10(X1)),X1)
| g_true_only(sK8(X1,sK10(X1)),X1)
| g_both(sK8(X1,sK10(X1)),sK10(X1))
| ~ g_both(X2,sK10(X1))
| ~ sP0(X1) ),
inference(resolution,[],[f320,f97]) ).
fof(f534,plain,
! [X2,X0,X1] :
( ~ g_both(X0,X1)
| g_both(sK8(X1,sK10(X1)),X1)
| g_true_only(sK8(X1,sK10(X1)),X1)
| ~ g_both(X0,sK10(X1))
| ~ sP0(X1)
| ~ g_both(X2,X1)
| g_both(sK8(X1,sK10(X1)),sK10(X1))
| ~ g_both(X2,sK10(X1)) ),
inference(duplicate_literal_removal,[],[f525]) ).
fof(f535,plain,
! [X2,X0,X1] :
( ~ g_both(X0,X1)
| g_both(sK8(X1,sK10(X1)),X1)
| g_true_only(sK8(X1,sK10(X1)),X1)
| ~ g_both(X0,sK10(X1))
| ~ sP0(X1)
| ~ g_both(X2,X1)
| ~ g_both(X2,sK10(X1)) ),
inference(duplicate_literal_removal,[],[f524]) ).
fof(f542,plain,
! [X2,X0,X1] :
( ~ g_both(X0,X1)
| g_both(sK8(X1,sK10(X1)),X1)
| g_true_only(sK8(X1,sK10(X1)),X1)
| ~ sP0(X1)
| ~ g_both(X2,X1)
| g_both(sK8(X1,sK10(X1)),sK10(X1))
| ~ g_both(X2,sK10(X1)) ),
inference(forward_subsumption_resolution,[],[f534,f299]) ).
fof(f543,plain,
! [X2,X0,X1] :
( ~ g_both(X0,X1)
| g_both(sK8(X1,sK10(X1)),X1)
| g_true_only(sK8(X1,sK10(X1)),X1)
| ~ sP0(X1)
| ~ g_both(X2,X1)
| ~ g_both(X2,sK10(X1)) ),
inference(forward_subsumption_resolution,[],[f535,f299]) ).
fof(f549,plain,
! [X2,X0,X1] :
( ~ g_both(X0,X1)
| g_both(sK8(X1,sK10(X1)),X1)
| g_true_only(sK8(X1,sK10(X1)),X1)
| ~ sP0(X1)
| ~ g_both(X2,X1)
| g_both(sK8(X1,sK10(X1)),sK10(X1)) ),
inference(forward_subsumption_resolution,[],[f542,f299]) ).
fof(f550,plain,
( ! [X2,X0,X1] :
( ~ g_both(X0,X1)
| g_both(sK8(X1,sK10(X1)),X1)
| g_true_only(sK8(X1,sK10(X1)),X1)
| ~ g_both(X2,X1)
| ~ g_both(X2,sK10(X1)) )
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f543,f434]) ).
fof(f553,plain,
! [X2,X0,X1] :
( g_both(sK8(X1,sK10(X1)),sK10(X1))
| g_true_only(sK8(X1,sK10(X1)),X1)
| ~ sP0(X1)
| ~ g_both(X2,X1)
| ~ g_both(X0,X1) ),
inference(forward_subsumption_resolution,[],[f549,f299]) ).
fof(f554,plain,
( ! [X2,X0,X1] :
( g_both(sK8(X1,sK10(X1)),X1)
| ~ g_both(X0,X1)
| g_true_only(sK8(X1,sK10(X1)),X1)
| ~ g_both(X2,X1) )
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f550,f299]) ).
fof(f703,plain,
( ! [X0,X1] :
( ~ g_both(X0,sK9)
| g_true_only(sK8(sK9,sK10(sK9)),sK9)
| ~ g_both(X1,sK9)
| g_both(sK8(sK9,sK10(sK9)),sK8(sK9,sK10(sK9))) )
| ~ spl12_2 ),
inference(resolution,[],[f554,f251]) ).
fof(f710,definition,
( spl12_29
<=> g_both(sK8(sK9,sK10(sK9)),sK8(sK9,sK10(sK9))) ),
introduced(definition,[new_symbols(definition,[spl12_29])],[avatar_definition]) ).
fof(f712,plain,
( g_both(sK8(sK9,sK10(sK9)),sK8(sK9,sK10(sK9)))
| ~ spl12_29 ),
inference(avatar_component_clause,[],[f710]) ).
fof(f714,definition,
( spl12_30
<=> ! [X1] : ~ g_both(X1,sK9) ),
introduced(definition,[new_symbols(definition,[spl12_30])],[avatar_definition]) ).
fof(f715,plain,
( ! [X1] : ~ g_both(X1,sK9)
| ~ spl12_30 ),
inference(avatar_component_clause,[],[f714]) ).
fof(f717,definition,
( spl12_31
<=> g_true_only(sK8(sK9,sK10(sK9)),sK9) ),
introduced(definition,[new_symbols(definition,[spl12_31])],[avatar_definition]) ).
fof(f718,plain,
( ~ g_true_only(sK8(sK9,sK10(sK9)),sK9)
| spl12_31 ),
inference(avatar_component_clause,[],[f717]) ).
fof(f719,plain,
( g_true_only(sK8(sK9,sK10(sK9)),sK9)
| ~ spl12_31 ),
inference(avatar_component_clause,[],[f717]) ).
fof(f720,plain,
( spl12_29
| spl12_30
| spl12_31
| spl12_30
| ~ spl12_2 ),
inference(avatar_split_clause,[],[f703,f105,f714,f717,f714,f710]) ).
fof(f729,plain,
( ! [X0,X1] :
( ~ g_both(sK5(X0),sK9)
| ~ g_both(X1,X1)
| g_true_only(sK5(X0),X0)
| g_true_only(sK5(X0),sK5(X0))
| ~ g_both(X1,X0)
| g_false_only(sK5(X0),X0) )
| ~ spl12_4 ),
inference(forward_subsumption_resolution,[],[f244,f114]) ).
fof(f731,plain,
! [X0,X1] :
( ~ g_true_only(sK5(X0),sK9)
| ~ g_both(X1,X1)
| ~ g_both(X1,X0)
| g_both(sK5(X0),X0)
| g_false_only(sK5(X0),X0)
| ~ sP2 ),
inference(forward_subsumption_resolution,[],[f273,f77]) ).
fof(f744,plain,
( ! [X0,X1] :
( ~ g_both(sK5(X0),sK9)
| ~ g_both(X1,X1)
| g_true_only(sK5(X0),X0)
| ~ g_both(X1,X0)
| g_false_only(sK5(X0),X0) )
| ~ spl12_4 ),
inference(forward_subsumption_resolution,[],[f729,f75]) ).
fof(f745,plain,
( ! [X0,X1] :
( ~ g_true_only(sK5(X0),sK9)
| ~ g_both(X1,X1)
| ~ g_both(X1,X0)
| g_both(sK5(X0),X0)
| g_false_only(sK5(X0),X0) )
| ~ spl12_4 ),
inference(forward_subsumption_resolution,[],[f731,f114]) ).
fof(f750,plain,
( ~ g_true_only(sK5(sK9),sK9)
| ~ spl12_17 ),
inference(resolution,[],[f191,f327]) ).
fof(f752,plain,
( g_true(sK5(sK9),sK9)
| ~ spl12_17 ),
inference(resolution,[],[f191,f83]) ).
fof(f753,plain,
( ~ spl12_23
| ~ spl12_17 ),
inference(avatar_split_clause,[],[f750,f189,f262]) ).
fof(f756,plain,
( g_both(sK5(sK9),sK9)
| ~ spl12_19 ),
inference(resolution,[],[f197,f174]) ).
fof(f761,plain,
( ! [X0] :
( ~ g_both(X0,X0)
| g_true_only(sK5(sK9),sK9)
| ~ g_both(X0,sK9)
| g_false_only(sK5(sK9),sK9) )
| ~ spl12_4
| ~ spl12_17 ),
inference(resolution,[],[f744,f191]) ).
fof(f762,plain,
( ! [X0] :
( ~ g_both(X0,X0)
| g_true_only(sK5(sK9),sK9)
| g_false_only(sK5(sK9),sK9) )
| ~ spl12_4
| ~ spl12_17 ),
inference(forward_subsumption_resolution,[],[f761,f174]) ).
fof(f763,plain,
( ! [X0] :
( ~ g_both(X0,X0)
| g_false_only(sK5(sK9),sK9) )
| ~ spl12_4
| ~ spl12_17
| spl12_23 ),
inference(forward_subsumption_resolution,[],[f762,f263]) ).
fof(f765,definition,
( spl12_33
<=> g_false_only(sK5(sK9),sK9) ),
introduced(definition,[new_symbols(definition,[spl12_33])],[avatar_definition]) ).
fof(f766,plain,
( ~ g_false_only(sK5(sK9),sK9)
| spl12_33 ),
inference(avatar_component_clause,[],[f765]) ).
fof(f767,plain,
( g_false_only(sK5(sK9),sK9)
| ~ spl12_33 ),
inference(avatar_component_clause,[],[f765]) ).
fof(f768,plain,
( spl12_33
| spl12_20
| ~ spl12_4
| ~ spl12_17
| spl12_23 ),
inference(avatar_split_clause,[],[f763,f262,f189,f112,f202,f765]) ).
fof(f772,plain,
( ~ g_false_only(sK5(sK9),sK9)
| ~ spl12_17 ),
inference(resolution,[],[f752,f85]) ).
fof(f790,plain,
( g_false(sK5(sK9),sK9)
| ~ spl12_33 ),
inference(resolution,[],[f767,f86]) ).
fof(f794,plain,
( ~ g_true_only(sK5(sK9),sK9)
| ~ spl12_33 ),
inference(resolution,[],[f790,f79]) ).
fof(f813,plain,
! [X2,X0,X1] :
( g_true_only(sK8(X0,sK10(X0)),X0)
| ~ sP0(X0)
| ~ g_both(X1,X0)
| ~ g_both(X2,X0)
| ~ g_true_only(sK8(X0,sK10(X0)),sK10(X0)) ),
inference(resolution,[],[f553,f327]) ).
fof(f816,plain,
! [X2,X0,X1] :
( ~ g_true_only(sK8(X0,sK10(X0)),sK10(X0))
| ~ g_both(X1,X0)
| ~ g_both(X2,X0)
| ~ sP0(X0) ),
inference(forward_subsumption_resolution,[],[f813,f70]) ).
fof(f911,plain,
( g_true_only(sK10(sK9),sK9)
| g_true_only(sK10(sK9),sK9)
| g_both(sK10(sK9),sK10(sK9)) ),
inference(resolution,[],[f512,f251]) ).
fof(f912,plain,
( g_true_only(sK10(sK9),sK9)
| g_true_only(sK10(sK9),sK9)
| ~ g_true_only(sK10(sK9),sK10(sK9)) ),
inference(resolution,[],[f512,f75]) ).
fof(f915,plain,
( g_true_only(sK10(sK9),sK9)
| ~ g_true_only(sK10(sK9),sK10(sK9)) ),
inference(duplicate_literal_removal,[],[f912]) ).
fof(f916,plain,
( g_true_only(sK10(sK9),sK9)
| g_both(sK10(sK9),sK10(sK9)) ),
inference(duplicate_literal_removal,[],[f911]) ).
fof(f918,plain,
~ g_true_only(sK10(sK9),sK10(sK9)),
inference(forward_subsumption_resolution,[],[f915,f70]) ).
fof(f919,plain,
( g_true_only(sK10(sK9),sK9)
| ~ spl12_20 ),
inference(forward_subsumption_resolution,[],[f916,f203]) ).
fof(f921,plain,
( g_true_only(sK10(sK9),sK10(sK9))
| ~ spl12_20 ),
inference(resolution,[],[f919,f276]) ).
fof(f923,plain,
( $false
| ~ spl12_20 ),
inference(forward_subsumption_resolution,[],[f921,f918]) ).
fof(f924,plain,
~ spl12_20,
inference(avatar_contradiction_clause,[],[f923]) ).
fof(f927,plain,
( $false
| ~ spl12_23
| ~ spl12_33 ),
inference(forward_subsumption_resolution,[],[f794,f264]) ).
fof(f928,plain,
( ~ spl12_23
| ~ spl12_33 ),
inference(avatar_contradiction_clause,[],[f927]) ).
fof(f934,definition,
( spl12_37
<=> g_true_only(sK10(sK9),sK9) ),
introduced(definition,[new_symbols(definition,[spl12_37])],[avatar_definition]) ).
fof(f935,plain,
( ~ g_true_only(sK10(sK9),sK9)
| spl12_37 ),
inference(avatar_component_clause,[],[f934]) ).
fof(f936,plain,
( g_true_only(sK10(sK9),sK9)
| ~ spl12_37 ),
inference(avatar_component_clause,[],[f934]) ).
fof(f939,plain,
( ! [X0] :
( ~ g_both(X0,X0)
| ~ g_both(X0,sK9)
| g_both(sK5(sK9),sK9)
| g_false_only(sK5(sK9),sK9) )
| ~ spl12_4
| ~ spl12_23 ),
inference(resolution,[],[f264,f745]) ).
fof(f942,plain,
( ! [X0] :
( ~ g_both(X0,X0)
| g_both(sK5(sK9),sK9)
| g_false_only(sK5(sK9),sK9) )
| ~ spl12_4
| ~ spl12_23 ),
inference(forward_subsumption_resolution,[],[f939,f174]) ).
fof(f943,plain,
( ! [X0] :
( ~ g_both(X0,X0)
| g_false_only(sK5(sK9),sK9) )
| ~ spl12_4
| spl12_17
| ~ spl12_23 ),
inference(forward_subsumption_resolution,[],[f942,f190]) ).
fof(f944,plain,
( ! [X0] : ~ g_both(X0,X0)
| ~ spl12_4
| spl12_17
| ~ spl12_23
| spl12_33 ),
inference(forward_subsumption_resolution,[],[f943,f766]) ).
fof(f945,plain,
( spl12_20
| ~ spl12_4
| spl12_17
| ~ spl12_23
| spl12_33 ),
inference(avatar_split_clause,[],[f944,f765,f262,f189,f112,f202]) ).
fof(f947,plain,
( $false
| spl12_17
| ~ spl12_19 ),
inference(forward_subsumption_resolution,[],[f756,f190]) ).
fof(f948,plain,
( spl12_17
| ~ spl12_19 ),
inference(avatar_contradiction_clause,[],[f947]) ).
fof(f951,plain,
( ~ spl12_33
| ~ spl12_17 ),
inference(avatar_split_clause,[],[f772,f189,f765]) ).
fof(f958,plain,
( ! [X0] :
( g_true_only(X0,X0)
| ~ g_both(X0,sK9) )
| ~ spl12_3 ),
inference(resolution,[],[f110,f74]) ).
fof(f969,plain,
( ! [X0] : ~ g_both(X0,sK9)
| ~ spl12_3 ),
inference(forward_subsumption_resolution,[],[f958,f75]) ).
fof(f971,plain,
( spl12_30
| ~ spl12_3 ),
inference(avatar_split_clause,[],[f969,f109,f714]) ).
fof(f974,plain,
( ! [X0] :
( ~ g_true_only(sK7(X0),sK6)
| g_both(sK7(X0),X0)
| g_true_only(sK7(X0),X0)
| g_both(sK7(X0),sK6) )
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f460,f103]) ).
fof(f977,plain,
( ! [X0] :
( ~ g_true_only(sK7(X0),sK6)
| g_both(sK7(X0),X0)
| g_true_only(sK7(X0),X0) )
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f974,f327]) ).
fof(f1244,plain,
( g_both(sK7(sK10(sK6)),sK10(sK6))
| g_true_only(sK7(sK10(sK6)),sK10(sK6))
| ~ spl12_1
| ~ spl12_26 ),
inference(resolution,[],[f977,f401]) ).
fof(f1245,plain,
( spl12_24
| spl12_28
| ~ spl12_1
| ~ spl12_26 ),
inference(avatar_split_clause,[],[f1244,f399,f101,f411,f391]) ).
fof(f1249,plain,
( ~ g_both(sK7(sK10(sK6)),sK6)
| ~ spl12_24 ),
inference(resolution,[],[f393,f71]) ).
fof(f1250,plain,
( ~ g_true_only(sK7(sK10(sK6)),sK6)
| ~ spl12_24 ),
inference(resolution,[],[f393,f70]) ).
fof(f1252,plain,
( $false
| ~ spl12_24
| ~ spl12_26 ),
inference(forward_subsumption_resolution,[],[f1250,f401]) ).
fof(f1253,plain,
( ~ spl12_24
| ~ spl12_26 ),
inference(avatar_contradiction_clause,[],[f1252]) ).
fof(f1254,plain,
( ~ spl12_25
| ~ spl12_24 ),
inference(avatar_split_clause,[],[f1249,f391,f395]) ).
fof(f1267,plain,
( ~ g_true_only(sK7(sK10(sK6)),sK6)
| ~ spl12_28 ),
inference(resolution,[],[f413,f68]) ).
fof(f1271,plain,
( $false
| ~ spl12_26
| ~ spl12_28 ),
inference(forward_subsumption_resolution,[],[f1267,f401]) ).
fof(f1272,plain,
( ~ spl12_26
| ~ spl12_28 ),
inference(avatar_contradiction_clause,[],[f1271]) ).
fof(f1287,plain,
( ~ g_both(sK7(sK10(sK6)),sK6)
| ~ spl12_27 ),
inference(resolution,[],[f407,f66]) ).
fof(f1293,plain,
( $false
| ~ spl12_25
| ~ spl12_27 ),
inference(forward_subsumption_resolution,[],[f1287,f397]) ).
fof(f1294,plain,
( ~ spl12_25
| ~ spl12_27 ),
inference(avatar_contradiction_clause,[],[f1293]) ).
fof(f1299,plain,
( ! [X0,X1] :
( ~ g_both(X0,X1)
| sP0(X1) )
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f427,f107]) ).
fof(f1373,plain,
( g_true_only(sK10(sK9),sK9)
| g_true_only(sK10(sK9),sK9)
| ~ spl12_30 ),
inference(resolution,[],[f715,f512]) ).
fof(f1374,plain,
( g_true_only(sK10(sK9),sK9)
| ~ spl12_30 ),
inference(duplicate_literal_removal,[],[f1373]) ).
fof(f1377,plain,
( $false
| ~ spl12_30
| spl12_37 ),
inference(forward_subsumption_resolution,[],[f1374,f935]) ).
fof(f1378,plain,
( ~ spl12_30
| spl12_37 ),
inference(avatar_contradiction_clause,[],[f1377]) ).
fof(f1602,plain,
( g_both(sK8(sK9,sK10(sK9)),sK9)
| ~ spl12_29 ),
inference(resolution,[],[f712,f174]) ).
fof(f1739,plain,
( ! [X0] :
( ~ g_both(X0,sK9)
| g_false_only(sK8(sK9,sK10(sK9)),sK9)
| g_true_only(sK8(sK9,sK10(sK9)),sK9)
| ~ g_both(X0,sK10(sK9))
| ~ sP0(sK9) )
| ~ spl12_29 ),
inference(resolution,[],[f1602,f296]) ).
fof(f1747,plain,
( g_true(sK8(sK9,sK10(sK9)),sK9)
| ~ spl12_29 ),
inference(resolution,[],[f1602,f83]) ).
fof(f1748,plain,
( ! [X0] :
( ~ g_both(X0,sK9)
| g_false_only(sK8(sK9,sK10(sK9)),sK9)
| g_true_only(sK8(sK9,sK10(sK9)),sK9)
| ~ g_both(X0,sK10(sK9)) )
| ~ spl12_2
| ~ spl12_29 ),
inference(forward_subsumption_resolution,[],[f1739,f1299]) ).
fof(f1749,plain,
( ! [X0] :
( ~ g_both(X0,sK9)
| g_false_only(sK8(sK9,sK10(sK9)),sK9)
| g_true_only(sK8(sK9,sK10(sK9)),sK9) )
| ~ spl12_2
| ~ spl12_29 ),
inference(forward_subsumption_resolution,[],[f1748,f299]) ).
fof(f1750,plain,
( ! [X0] :
( ~ g_both(X0,sK9)
| g_false_only(sK8(sK9,sK10(sK9)),sK9) )
| ~ spl12_2
| ~ spl12_29
| spl12_31 ),
inference(forward_subsumption_resolution,[],[f1749,f718]) ).
fof(f1752,definition,
( spl12_67
<=> g_false_only(sK8(sK9,sK10(sK9)),sK9) ),
introduced(definition,[new_symbols(definition,[spl12_67])],[avatar_definition]) ).
fof(f1753,plain,
( ~ g_false_only(sK8(sK9,sK10(sK9)),sK9)
| spl12_67 ),
inference(avatar_component_clause,[],[f1752]) ).
fof(f1754,plain,
( g_false_only(sK8(sK9,sK10(sK9)),sK9)
| ~ spl12_67 ),
inference(avatar_component_clause,[],[f1752]) ).
fof(f1755,plain,
( spl12_67
| spl12_30
| ~ spl12_2
| ~ spl12_29
| spl12_31 ),
inference(avatar_split_clause,[],[f1750,f717,f710,f105,f714,f1752]) ).
fof(f1922,plain,
( ~ g_false_only(sK8(sK9,sK10(sK9)),sK9)
| ~ spl12_29 ),
inference(resolution,[],[f1747,f85]) ).
fof(f1924,plain,
( $false
| ~ spl12_29
| ~ spl12_67 ),
inference(forward_subsumption_resolution,[],[f1922,f1754]) ).
fof(f1925,plain,
( ~ spl12_29
| ~ spl12_67 ),
inference(avatar_contradiction_clause,[],[f1924]) ).
fof(f1927,plain,
( g_true(sK8(sK9,sK10(sK9)),sK9)
| ~ spl12_31 ),
inference(resolution,[],[f719,f80]) ).
fof(f1928,plain,
( ~ g_false_only(sK8(sK9,sK10(sK9)),sK9)
| ~ spl12_31 ),
inference(resolution,[],[f1927,f85]) ).
fof(f1930,plain,
( ~ spl12_67
| ~ spl12_31 ),
inference(avatar_split_clause,[],[f1928,f717,f1752]) ).
fof(f1934,plain,
( ! [X0] :
( ~ g_both(X0,sK9)
| g_true_only(sK8(sK9,sK10(sK9)),sK10(sK9))
| g_both(sK8(sK9,sK10(sK9)),sK10(sK9))
| ~ g_both(X0,sK10(sK9))
| g_both(sK8(sK9,sK10(sK9)),sK9)
| ~ sP0(sK9) )
| spl12_67 ),
inference(resolution,[],[f1753,f60]) ).
fof(f1937,plain,
( ! [X0] :
( ~ g_both(X0,sK9)
| g_true_only(sK8(sK9,sK10(sK9)),sK10(sK9))
| g_both(sK8(sK9,sK10(sK9)),sK10(sK9))
| g_both(sK8(sK9,sK10(sK9)),sK9)
| ~ sP0(sK9) )
| spl12_67 ),
inference(forward_subsumption_resolution,[],[f1934,f299]) ).
fof(f1939,plain,
( ! [X0] :
( ~ g_both(X0,sK9)
| g_true_only(sK8(sK9,sK10(sK9)),sK10(sK9))
| g_both(sK8(sK9,sK10(sK9)),sK10(sK9))
| ~ sP0(sK9) )
| spl12_67 ),
inference(forward_subsumption_resolution,[],[f1937,f299]) ).
fof(f1940,plain,
( ! [X0] :
( ~ g_both(X0,sK9)
| g_true_only(sK8(sK9,sK10(sK9)),sK10(sK9))
| g_both(sK8(sK9,sK10(sK9)),sK10(sK9)) )
| ~ spl12_2
| spl12_67 ),
inference(forward_subsumption_resolution,[],[f1939,f1299]) ).
fof(f1942,definition,
( spl12_71
<=> g_both(sK8(sK9,sK10(sK9)),sK10(sK9)) ),
introduced(definition,[new_symbols(definition,[spl12_71])],[avatar_definition]) ).
fof(f1944,plain,
( g_both(sK8(sK9,sK10(sK9)),sK10(sK9))
| ~ spl12_71 ),
inference(avatar_component_clause,[],[f1942]) ).
fof(f1946,definition,
( spl12_72
<=> g_true_only(sK8(sK9,sK10(sK9)),sK10(sK9)) ),
introduced(definition,[new_symbols(definition,[spl12_72])],[avatar_definition]) ).
fof(f1948,plain,
( g_true_only(sK8(sK9,sK10(sK9)),sK10(sK9))
| ~ spl12_72 ),
inference(avatar_component_clause,[],[f1946]) ).
fof(f1949,plain,
( spl12_71
| spl12_72
| spl12_30
| ~ spl12_2
| spl12_67 ),
inference(avatar_split_clause,[],[f1940,f1752,f105,f714,f1946,f1942]) ).
fof(f2034,plain,
( ! [X0,X1] :
( ~ g_both(X0,sK9)
| ~ g_both(X1,sK9)
| ~ sP0(sK9) )
| ~ spl12_72 ),
inference(resolution,[],[f1948,f816]) ).
fof(f2040,plain,
( ! [X0,X1] :
( ~ g_both(X0,sK9)
| ~ g_both(X1,sK9) )
| ~ spl12_2
| ~ spl12_72 ),
inference(forward_subsumption_resolution,[],[f2034,f1299]) ).
fof(f2041,plain,
( spl12_30
| spl12_30
| ~ spl12_2
| ~ spl12_72 ),
inference(avatar_split_clause,[],[f2040,f1946,f105,f714,f714]) ).
fof(f2046,plain,
( ~ g_true_only(sK8(sK9,sK10(sK9)),sK9)
| ~ spl12_71 ),
inference(resolution,[],[f1944,f68]) ).
fof(f2052,plain,
( $false
| ~ spl12_31
| ~ spl12_71 ),
inference(forward_subsumption_resolution,[],[f2046,f719]) ).
fof(f2053,plain,
( ~ spl12_31
| ~ spl12_71 ),
inference(avatar_contradiction_clause,[],[f2052]) ).
fof(f2084,plain,
( g_true_only(sK10(sK9),sK10(sK9))
| ~ spl12_37 ),
inference(resolution,[],[f936,f276]) ).
fof(f2086,plain,
( $false
| ~ spl12_37 ),
inference(forward_subsumption_resolution,[],[f2084,f918]) ).
fof(f2087,plain,
~ spl12_37,
inference(avatar_contradiction_clause,[],[f2086]) ).
cnf(s1,plain,
( spl12_1
| spl12_2
| spl12_3
| spl12_4 ),
inference(sat_conversion,[],[f115]) ).
cnf(s15,plain,
( ~ spl12_4
| spl12_17
| spl12_19
| spl12_20
| spl12_23 ),
inference(sat_conversion,[],[f265]) ).
cnf(s18,plain,
( ~ spl12_1
| spl12_25
| spl12_26 ),
inference(sat_conversion,[],[f409]) ).
cnf(s20,plain,
( ~ spl12_1
| spl12_24
| spl12_26
| spl12_27 ),
inference(sat_conversion,[],[f415]) ).
cnf(s22,plain,
( spl12_30
| spl12_29
| ~ spl12_2
| spl12_30
| spl12_31 ),
inference(sat_conversion,[],[f720]) ).
cnf(s23,plain,
( ~ spl12_2
| spl12_29
| spl12_30
| spl12_31 ),
inference(rat,[],[s22]) ).
cnf(s26,plain,
( ~ spl12_17
| ~ spl12_23 ),
inference(sat_conversion,[],[f753]) ).
cnf(s28,plain,
( ~ spl12_4
| ~ spl12_17
| spl12_20
| spl12_23
| spl12_33 ),
inference(sat_conversion,[],[f768]) ).
cnf(s36,plain,
~ spl12_20,
inference(sat_conversion,[],[f924]) ).
cnf(s38,plain,
( ~ spl12_23
| ~ spl12_33 ),
inference(sat_conversion,[],[f928]) ).
cnf(s40,plain,
( ~ spl12_4
| spl12_17
| spl12_20
| ~ spl12_23
| spl12_33 ),
inference(sat_conversion,[],[f945]) ).
cnf(s41,plain,
( spl12_17
| ~ spl12_19 ),
inference(sat_conversion,[],[f948]) ).
cnf(s44,plain,
( ~ spl12_17
| ~ spl12_33 ),
inference(sat_conversion,[],[f951]) ).
cnf(s46,plain,
( ~ spl12_3
| spl12_30 ),
inference(sat_conversion,[],[f971]) ).
cnf(s58,plain,
( ~ spl12_1
| spl12_24
| ~ spl12_26
| spl12_28 ),
inference(sat_conversion,[],[f1245]) ).
cnf(s59,plain,
( ~ spl12_24
| ~ spl12_26 ),
inference(sat_conversion,[],[f1253]) ).
cnf(s60,plain,
( ~ spl12_24
| ~ spl12_25 ),
inference(sat_conversion,[],[f1254]) ).
cnf(s61,plain,
( ~ spl12_26
| ~ spl12_28 ),
inference(sat_conversion,[],[f1272]) ).
cnf(s63,plain,
( ~ spl12_25
| ~ spl12_27 ),
inference(sat_conversion,[],[f1294]) ).
cnf(s68,plain,
( ~ spl12_30
| spl12_37 ),
inference(sat_conversion,[],[f1378]) ).
cnf(s96,plain,
( ~ spl12_2
| ~ spl12_29
| spl12_30
| spl12_31
| spl12_67 ),
inference(sat_conversion,[],[f1755]) ).
cnf(s99,plain,
( ~ spl12_29
| ~ spl12_67 ),
inference(sat_conversion,[],[f1925]) ).
cnf(s100,plain,
( ~ spl12_31
| ~ spl12_67 ),
inference(sat_conversion,[],[f1930]) ).
cnf(s101,plain,
( ~ spl12_2
| spl12_30
| spl12_67
| spl12_71
| spl12_72 ),
inference(sat_conversion,[],[f1949]) ).
cnf(s107,plain,
( spl12_30
| ~ spl12_2
| spl12_30
| ~ spl12_72 ),
inference(sat_conversion,[],[f2041]) ).
cnf(s108,plain,
( ~ spl12_2
| spl12_30
| ~ spl12_72 ),
inference(rat,[],[s107]) ).
cnf(s109,plain,
( ~ spl12_31
| ~ spl12_71 ),
inference(sat_conversion,[],[f2053]) ).
cnf(s113,plain,
~ spl12_37,
inference(sat_conversion,[],[f2087]) ).
cnf(s114,plain,
~ spl12_30,
inference(rat,[],[s68,s113]) ).
cnf(s116,plain,
~ spl12_3,
inference(rat,[],[s46,s114]) ).
cnf(s119,plain,
( ~ spl12_4
| ~ spl12_17
| spl12_23
| spl12_33 ),
inference(rat,[],[s28,s36]) ).
cnf(s121,plain,
( ~ spl12_2
| spl12_29
| spl12_31 ),
inference(rat,[],[s23,s114]) ).
cnf(s122,plain,
( ~ spl12_4
| spl12_17
| spl12_19
| spl12_23 ),
inference(rat,[],[s15,s36]) ).
cnf(s125,plain,
( spl12_1
| spl12_2
| spl12_4 ),
inference(rat,[],[s1,s116]) ).
cnf(s126,plain,
( spl12_19
| spl12_17
| ~ spl12_4 ),
inference(rat,[],[s40,s38,s122,s36]) ).
cnf(s127,plain,
( spl12_17
| ~ spl12_4 ),
inference(rat,[],[s126,s41]) ).
cnf(s128,plain,
( ~ spl12_17
| spl12_33
| ~ spl12_4 ),
inference(rat,[],[s26,s119]) ).
cnf(s129,plain,
~ spl12_4,
inference(rat,[],[s128,s44,s127]) ).
cnf(s130,plain,
( ~ spl12_31
| ~ spl12_2 ),
inference(rat,[],[s101,s100,s109,s108,s114]) ).
cnf(s131,plain,
( spl12_31
| ~ spl12_2 ),
inference(rat,[],[s96,s99,s121,s114]) ).
cnf(s132,plain,
~ spl12_2,
inference(rat,[],[s131,s130]) ).
cnf(s133,plain,
spl12_1,
inference(rat,[],[s125,s129,s132]) ).
cnf(s134,plain,
( ~ spl12_26
| spl12_24 ),
inference(rat,[],[s58,s61,s133]) ).
cnf(s135,plain,
spl12_24,
inference(rat,[],[s63,s20,s18,s134,s133]) ).
cnf(s136,plain,
~ spl12_25,
inference(rat,[],[s60,s135]) ).
cnf(s137,plain,
~ spl12_26,
inference(rat,[],[s59,s135]) ).
cnf(s138,plain,
$false,
inference(rat,[],[s18,s133,s136,s137]) ).
fof(f2088,plain,
$false,
inference(avatar_sat_refutation,[],[s138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO605+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n007.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 17:52:25 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running first-order theorem proving
% 0.07/0.20 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.62/0.96 % (2637849)Detected formulas, will run a generic FOF schedule.
% 0.62/0.96 % (2637857)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=869137637:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.62/0.96 % (2637857)First to succeed.
% 0.62/0.96 % (2637857)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2637849"
% 0.62/0.96 % (2637856)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=830130980:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.62/0.96 % (2637854)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2412214262:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.62/0.96 % (2637860)dis-21_1_sil=8000:lcm=predicate:random_seed=1439213247:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.62/0.96 % (2637858)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1404697626:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.62/0.96 % (2637855)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3847702271:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.62/0.96 % (2637859)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3926341199:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.62/0.96 % (2637859)Refutation not found, incomplete strategy
% 0.62/0.96 % (2637859)------------------------------
% 0.62/0.96 % (2637859)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.62/0.96 % (2637859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.96 % (2637859)CaDiCaL version: 2.1.3
% 0.62/0.96 % (2637859)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.96 % (2637859)Time elapsed: 0.005 s
% 0.62/0.96 % (2637859)Peak memory usage: 88 MB
% 0.62/0.96 % (2637859)Instructions burned: 6 (million)
% 0.62/0.96 % (2637858)Also succeeded, but the first one will report.
% 0.62/0.96 % (2637860)Instruction limit reached!
% 0.62/0.96 % (2637860)------------------------------
% 0.62/0.96 % (2637860)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.62/0.96 % (2637860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.96 % (2637860)CaDiCaL version: 2.1.3
% 0.62/0.96 % (2637860)Termination reason: Instruction limit
% 0.62/0.96 % (2637860)Termination phase: Saturation
% 0.62/0.96 % (2637860)Time elapsed: 0.083 s
% 0.62/0.96 % (2637860)Peak memory usage: 89 MB
% 0.62/0.96 % (2637860)Instructions burned: 130 (million)
% 0.62/0.96 % (2637857)Refutation found. Thanks to Tanya!
% 0.62/0.96 % SZS status Theorem for theBenchmark
% 0.62/0.96 % SZS output start Proof for theBenchmark
% See solution above
% 2.83/1.16 % (2637857)------------------------------
% 2.83/1.16 % (2637857)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.16 % (2637857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.16 % (2637857)CaDiCaL version: 2.1.3
% 2.83/1.16 % (2637857)Termination reason: Refutation
% 2.83/1.16 % (2637857)Time elapsed: 0.025 s
% 2.83/1.16 % (2637857)Peak memory usage: 90 MB
% 2.83/1.16 % (2637857)Instructions burned: 71 (million)
% 2.83/1.16 % (2637857)------------------------------
% 2.83/1.16 % (2637857)------------------------------
% 2.83/1.16 % (2637849)Success in time 0.314 s
% 2.83/1.16 % Vampire exiting
%------------------------------------------------------------------------------