%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO607+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 02:28:26 PM UTC 2026
% Result : Theorem 0.64s 0.95s
% Output : Refutation 2.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 35
% Syntax : Number of formulae : 191 ( 19 unt; 31 def)
% Number of atoms : 607 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 712 ( 296 ~; 338 |; 45 &)
% ( 33 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 37 ( 36 usr; 27 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-1 aty)
% Number of variables : 247 ( 0 sgn 205 !; 42 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X0] :
( g_false_only(a,X0)
& ? [X1] : g_false_only(X0,X1) )
| ? [X0] :
! [X1] : g_true_only(X0,X1)
| ( ? [X0] :
( ( g_both(a,X0)
| ( ? [X1] : g_both(X0,X1)
& ~ ? [X1] : g_false_only(X0,X1) ) )
& ~ g_true_only(a,X0)
& ~ ! [X1] : g_true_only(X0,X1) )
& ~ ? [X0] :
( g_false_only(a,X0)
& ? [X1] : g_false_only(X0,X1) )
& ? [X0] :
( ? [X1] : g_both(X0,X1)
& ~ ? [X1] : g_false_only(X0,X1) )
& ~ ? [X0] :
! [X1] : g_true_only(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nc6) ).
fof(f2,negated_conjecture,
~ ( ? [X0] :
( g_false_only(a,X0)
& ? [X1] : g_false_only(X0,X1) )
| ? [X0] :
! [X1] : g_true_only(X0,X1)
| ( ? [X0] :
( ( g_both(a,X0)
| ( ? [X1] : g_both(X0,X1)
& ~ ? [X1] : g_false_only(X0,X1) ) )
& ~ g_true_only(a,X0)
& ~ ! [X1] : g_true_only(X0,X1) )
& ~ ? [X0] :
( g_false_only(a,X0)
& ? [X1] : g_false_only(X0,X1) )
& ? [X0] :
( ? [X1] : g_both(X0,X1)
& ~ ? [X1] : g_false_only(X0,X1) )
& ~ ? [X0] :
! [X1] : g_true_only(X0,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/sandbox/benchmark/theBenchmark.p',true_only_g) ).
fof(f5,axiom,
! [X0,X1] :
( g_false_only(X0,X1)
<=> ( g_false(X0,X1)
& ~ g_true(X0,X1) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',exhaustion_g) ).
fof(f7,plain,
~ ( ? [X0] :
( g_false_only(a,X0)
& ? [X1] : g_false_only(X0,X1) )
| ? [X2] :
! [X3] : g_true_only(X2,X3)
| ( ? [X4] :
( ( g_both(a,X4)
| ( ? [X5] : g_both(X4,X5)
& ~ ? [X6] : g_false_only(X4,X6) ) )
& ~ g_true_only(a,X4)
& ~ ! [X7] : g_true_only(X4,X7) )
& ~ ? [X8] :
( g_false_only(a,X8)
& ? [X9] : g_false_only(X8,X9) )
& ? [X10] :
( ? [X11] : g_both(X10,X11)
& ~ ? [X12] : g_false_only(X10,X12) )
& ~ ? [X13] :
! [X14] : g_true_only(X13,X14) ) ),
inference(rectify,[],[f2]) ).
fof(f8,plain,
( ! [X0] :
( ~ g_false_only(a,X0)
| ! [X1] : ~ g_false_only(X0,X1) )
& ! [X2] :
? [X3] : ~ g_true_only(X2,X3)
& ( ! [X4] :
( ( ~ g_both(a,X4)
& ( ! [X5] : ~ g_both(X4,X5)
| ? [X6] : g_false_only(X4,X6) ) )
| g_true_only(a,X4)
| ! [X7] : g_true_only(X4,X7) )
| ? [X8] :
( g_false_only(a,X8)
& ? [X9] : g_false_only(X8,X9) )
| ! [X10] :
( ! [X11] : ~ g_both(X10,X11)
| ? [X12] : g_false_only(X10,X12) )
| ? [X13] :
! [X14] : g_true_only(X13,X14) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f9,plain,
( ! [X0] :
( ~ g_false_only(a,X0)
| ! [X1] : ~ g_false_only(X0,X1) )
& ! [X2] : ~ g_true_only(X2,sK0(X2))
& ( ! [X4] :
( ( ~ g_both(a,X4)
& ( ! [X5] : ~ g_both(X4,X5)
| g_false_only(X4,sK1(X4)) ) )
| g_true_only(a,X4)
| ! [X7] : g_true_only(X4,X7) )
| ( g_false_only(a,sK2)
& g_false_only(sK2,sK3) )
| ! [X10] :
( ! [X11] : ~ g_both(X10,X11)
| g_false_only(X10,sK4(X10)) )
| ! [X14] : g_true_only(sK5,X14) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X3,sK0(X2)),skolemize(X6,sK1(X4)),skolemize(X8,sK2),skolemize(X9,sK3),skolemize(X12,sK4(X10)),skolemize(X13,sK5)],[f8]) ).
fof(f10,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(f11,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,[],[f10]) ).
fof(f12,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(f13,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,[],[f12]) ).
fof(f16,plain,
! [X10,X11,X7,X14,X4,X5] :
( ~ g_both(X4,X5)
| g_false_only(X4,sK1(X4))
| g_true_only(a,X4)
| g_true_only(X4,X7)
| g_false_only(sK2,sK3)
| ~ g_both(X10,X11)
| g_false_only(X10,sK4(X10))
| g_true_only(sK5,X14) ),
inference(cnf_transformation,[],[f9]) ).
fof(f17,plain,
! [X10,X11,X7,X14,X4,X5] :
( ~ g_both(X4,X5)
| g_false_only(X4,sK1(X4))
| g_true_only(a,X4)
| g_true_only(X4,X7)
| g_false_only(a,sK2)
| ~ g_both(X10,X11)
| g_false_only(X10,sK4(X10))
| g_true_only(sK5,X14) ),
inference(cnf_transformation,[],[f9]) ).
fof(f19,plain,
! [X10,X11,X7,X14,X4] :
( ~ g_both(a,X4)
| g_true_only(a,X4)
| g_true_only(X4,X7)
| g_false_only(a,sK2)
| ~ g_both(X10,X11)
| g_false_only(X10,sK4(X10))
| g_true_only(sK5,X14) ),
inference(cnf_transformation,[],[f9]) ).
fof(f20,plain,
! [X2] : ~ g_true_only(X2,sK0(X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f21,plain,
! [X0,X1] :
( ~ g_false_only(a,X0)
| ~ g_false_only(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f22,plain,
! [X0,X1] :
( g_both(X0,X1)
| g_true_only(X0,X1)
| g_false_only(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f24,plain,
! [X0,X1] :
( ~ g_false_only(X0,X1)
| g_false(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f26,plain,
! [X0,X1] :
( ~ g_false(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f32,plain,
! [X14] :
( g_true_only(sK5,X14)
| sP6 ),
inference(cnf_transformation,[],[f32_D]) ).
fof(f32_D,definition,
( ! [X14] : g_true_only(sK5,X14)
<=> ~ sP6 ),
introduced(definition,[new_symbols(definition,[sP6])],[general_splitting_component_introduction]) ).
fof(f33,plain,
! [X10,X11,X7,X4] :
( ~ g_both(a,X4)
| g_true_only(a,X4)
| g_true_only(X4,X7)
| g_false_only(a,sK2)
| ~ g_both(X10,X11)
| g_false_only(X10,sK4(X10))
| ~ sP6 ),
inference(general_splitting,[],[f19,f32_D]) ).
fof(f34,plain,
! [X10,X11] :
( g_false_only(X10,sK4(X10))
| ~ g_both(X10,X11)
| sP7(X11) ),
inference(cnf_transformation,[],[f34_D]) ).
fof(f34_D,definition,
! [X11] :
( ! [X10] :
( g_false_only(X10,sK4(X10))
| ~ g_both(X10,X11) )
<=> ~ sP7(X11) ),
introduced(definition,[new_symbols(definition,[sP7])],[general_splitting_component_introduction]) ).
fof(f35,plain,
! [X11,X7,X4] :
( ~ g_both(a,X4)
| g_true_only(a,X4)
| g_true_only(X4,X7)
| g_false_only(a,sK2)
| ~ sP6
| ~ sP7(X11) ),
inference(general_splitting,[],[f33,f34_D]) ).
fof(f36,plain,
! [X11] :
( ~ sP7(X11)
| sP8 ),
inference(cnf_transformation,[],[f36_D]) ).
fof(f36_D,definition,
( ! [X11] : ~ sP7(X11)
<=> ~ sP8 ),
introduced(definition,[new_symbols(definition,[sP8])],[general_splitting_component_introduction]) ).
fof(f37,plain,
! [X7,X4] :
( ~ g_both(a,X4)
| g_true_only(a,X4)
| g_true_only(X4,X7)
| g_false_only(a,sK2)
| ~ sP6
| ~ sP8 ),
inference(general_splitting,[],[f35,f36_D]) ).
fof(f44,plain,
! [X14] :
( g_true_only(sK5,X14)
| sP12 ),
inference(cnf_transformation,[],[f44_D]) ).
fof(f44_D,definition,
( ! [X14] : g_true_only(sK5,X14)
<=> ~ sP12 ),
introduced(definition,[new_symbols(definition,[sP12])],[general_splitting_component_introduction]) ).
fof(f45,plain,
! [X10,X11,X7,X4,X5] :
( ~ g_both(X4,X5)
| g_false_only(X4,sK1(X4))
| g_true_only(a,X4)
| g_true_only(X4,X7)
| g_false_only(a,sK2)
| ~ g_both(X10,X11)
| g_false_only(X10,sK4(X10))
| ~ sP12 ),
inference(general_splitting,[],[f17,f44_D]) ).
fof(f46,plain,
! [X10,X11] :
( g_false_only(X10,sK4(X10))
| ~ g_both(X10,X11)
| sP13(X11) ),
inference(cnf_transformation,[],[f46_D]) ).
fof(f46_D,definition,
! [X11] :
( ! [X10] :
( g_false_only(X10,sK4(X10))
| ~ g_both(X10,X11) )
<=> ~ sP13(X11) ),
introduced(definition,[new_symbols(definition,[sP13])],[general_splitting_component_introduction]) ).
fof(f47,plain,
! [X11,X7,X4,X5] :
( ~ g_both(X4,X5)
| g_false_only(X4,sK1(X4))
| g_true_only(a,X4)
| g_true_only(X4,X7)
| g_false_only(a,sK2)
| ~ sP12
| ~ sP13(X11) ),
inference(general_splitting,[],[f45,f46_D]) ).
fof(f48,plain,
! [X11] :
( ~ sP13(X11)
| sP14 ),
inference(cnf_transformation,[],[f48_D]) ).
fof(f48_D,definition,
( ! [X11] : ~ sP13(X11)
<=> ~ sP14 ),
introduced(definition,[new_symbols(definition,[sP14])],[general_splitting_component_introduction]) ).
fof(f49,plain,
! [X7,X4,X5] :
( ~ g_both(X4,X5)
| g_false_only(X4,sK1(X4))
| g_true_only(a,X4)
| g_true_only(X4,X7)
| g_false_only(a,sK2)
| ~ sP12
| ~ sP14 ),
inference(general_splitting,[],[f47,f48_D]) ).
fof(f50,plain,
! [X7,X4] :
( g_true_only(X4,X7)
| sP15(X4) ),
inference(cnf_transformation,[],[f50_D]) ).
fof(f50_D,definition,
! [X4] :
( ! [X7] : g_true_only(X4,X7)
<=> ~ sP15(X4) ),
introduced(definition,[new_symbols(definition,[sP15])],[general_splitting_component_introduction]) ).
fof(f51,plain,
! [X4,X5] :
( ~ g_both(X4,X5)
| g_false_only(X4,sK1(X4))
| g_true_only(a,X4)
| g_false_only(a,sK2)
| ~ sP12
| ~ sP14
| ~ sP15(X4) ),
inference(general_splitting,[],[f49,f50_D]) ).
fof(f52,plain,
! [X14] :
( g_true_only(sK5,X14)
| sP16 ),
inference(cnf_transformation,[],[f52_D]) ).
fof(f52_D,definition,
( ! [X14] : g_true_only(sK5,X14)
<=> ~ sP16 ),
introduced(definition,[new_symbols(definition,[sP16])],[general_splitting_component_introduction]) ).
fof(f53,plain,
! [X10,X11,X7,X4,X5] :
( ~ g_both(X4,X5)
| g_false_only(X4,sK1(X4))
| g_true_only(a,X4)
| g_true_only(X4,X7)
| g_false_only(sK2,sK3)
| ~ g_both(X10,X11)
| g_false_only(X10,sK4(X10))
| ~ sP16 ),
inference(general_splitting,[],[f16,f52_D]) ).
fof(f54,plain,
! [X10,X11] :
( g_false_only(X10,sK4(X10))
| ~ g_both(X10,X11)
| sP17(X11) ),
inference(cnf_transformation,[],[f54_D]) ).
fof(f54_D,definition,
! [X11] :
( ! [X10] :
( g_false_only(X10,sK4(X10))
| ~ g_both(X10,X11) )
<=> ~ sP17(X11) ),
introduced(definition,[new_symbols(definition,[sP17])],[general_splitting_component_introduction]) ).
fof(f55,plain,
! [X11,X7,X4,X5] :
( ~ g_both(X4,X5)
| g_false_only(X4,sK1(X4))
| g_true_only(a,X4)
| g_true_only(X4,X7)
| g_false_only(sK2,sK3)
| ~ sP16
| ~ sP17(X11) ),
inference(general_splitting,[],[f53,f54_D]) ).
fof(f56,plain,
! [X11] :
( ~ sP17(X11)
| sP18 ),
inference(cnf_transformation,[],[f56_D]) ).
fof(f56_D,definition,
( ! [X11] : ~ sP17(X11)
<=> ~ sP18 ),
introduced(definition,[new_symbols(definition,[sP18])],[general_splitting_component_introduction]) ).
fof(f57,plain,
! [X7,X4,X5] :
( ~ g_both(X4,X5)
| g_false_only(X4,sK1(X4))
| g_true_only(a,X4)
| g_true_only(X4,X7)
| g_false_only(sK2,sK3)
| ~ sP16
| ~ sP18 ),
inference(general_splitting,[],[f55,f56_D]) ).
fof(f58,plain,
! [X7,X4] :
( g_true_only(X4,X7)
| sP19(X4) ),
inference(cnf_transformation,[],[f58_D]) ).
fof(f58_D,definition,
! [X4] :
( ! [X7] : g_true_only(X4,X7)
<=> ~ sP19(X4) ),
introduced(definition,[new_symbols(definition,[sP19])],[general_splitting_component_introduction]) ).
fof(f59,plain,
! [X4,X5] :
( ~ g_both(X4,X5)
| g_false_only(X4,sK1(X4))
| g_true_only(a,X4)
| g_false_only(sK2,sK3)
| ~ sP16
| ~ sP18
| ~ sP19(X4) ),
inference(general_splitting,[],[f57,f58_D]) ).
fof(f61,definition,
( spl20_1
<=> sP6 ),
introduced(definition,[new_symbols(definition,[spl20_1])],[avatar_definition]) ).
fof(f65,definition,
( spl20_2
<=> ! [X14] : g_true_only(sK5,X14) ),
introduced(definition,[new_symbols(definition,[spl20_2])],[avatar_definition]) ).
fof(f66,plain,
( ! [X14] : g_true_only(sK5,X14)
| ~ spl20_2 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f67,plain,
( spl20_1
| spl20_2 ),
inference(avatar_split_clause,[],[f32,f65,f61]) ).
fof(f69,definition,
( spl20_3
<=> sP8 ),
introduced(definition,[new_symbols(definition,[spl20_3])],[avatar_definition]) ).
fof(f73,definition,
( spl20_4
<=> ! [X11] : ~ sP7(X11) ),
introduced(definition,[new_symbols(definition,[spl20_4])],[avatar_definition]) ).
fof(f74,plain,
( ! [X11] : ~ sP7(X11)
| ~ spl20_4 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f75,plain,
( spl20_3
| spl20_4 ),
inference(avatar_split_clause,[],[f36,f73,f69]) ).
fof(f77,definition,
( spl20_5
<=> g_false_only(a,sK2) ),
introduced(definition,[new_symbols(definition,[spl20_5])],[avatar_definition]) ).
fof(f79,plain,
( g_false_only(a,sK2)
| ~ spl20_5 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f81,definition,
( spl20_6
<=> ! [X4,X7] :
( ~ g_both(a,X4)
| g_true_only(X4,X7)
| g_true_only(a,X4) ) ),
introduced(definition,[new_symbols(definition,[spl20_6])],[avatar_definition]) ).
fof(f82,plain,
( ! [X7,X4] :
( ~ g_both(a,X4)
| g_true_only(X4,X7)
| g_true_only(a,X4) )
| ~ spl20_6 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f83,plain,
( ~ spl20_3
| ~ spl20_1
| spl20_5
| spl20_6 ),
inference(avatar_split_clause,[],[f37,f81,f77,f61,f69]) ).
fof(f98,definition,
( spl20_10
<=> g_false_only(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl20_10])],[avatar_definition]) ).
fof(f100,plain,
( g_false_only(sK2,sK3)
| ~ spl20_10 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f103,definition,
( spl20_11
<=> sP12 ),
introduced(definition,[new_symbols(definition,[spl20_11])],[avatar_definition]) ).
fof(f106,plain,
( spl20_11
| spl20_2 ),
inference(avatar_split_clause,[],[f44,f65,f103]) ).
fof(f108,definition,
( spl20_12
<=> sP14 ),
introduced(definition,[new_symbols(definition,[spl20_12])],[avatar_definition]) ).
fof(f112,definition,
( spl20_13
<=> ! [X11] : ~ sP13(X11) ),
introduced(definition,[new_symbols(definition,[spl20_13])],[avatar_definition]) ).
fof(f113,plain,
( ! [X11] : ~ sP13(X11)
| ~ spl20_13 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f114,plain,
( spl20_12
| spl20_13 ),
inference(avatar_split_clause,[],[f48,f112,f108]) ).
fof(f116,definition,
( spl20_14
<=> ! [X4,X5] :
( ~ g_both(X4,X5)
| ~ sP15(X4)
| g_true_only(a,X4)
| g_false_only(X4,sK1(X4)) ) ),
introduced(definition,[new_symbols(definition,[spl20_14])],[avatar_definition]) ).
fof(f117,plain,
( ! [X4,X5] :
( ~ g_both(X4,X5)
| ~ sP15(X4)
| g_true_only(a,X4)
| g_false_only(X4,sK1(X4)) )
| ~ spl20_14 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f118,plain,
( ~ spl20_12
| ~ spl20_11
| spl20_5
| spl20_14 ),
inference(avatar_split_clause,[],[f51,f116,f77,f103,f108]) ).
fof(f120,definition,
( spl20_15
<=> sP16 ),
introduced(definition,[new_symbols(definition,[spl20_15])],[avatar_definition]) ).
fof(f123,plain,
( spl20_15
| spl20_2 ),
inference(avatar_split_clause,[],[f52,f65,f120]) ).
fof(f125,definition,
( spl20_16
<=> sP18 ),
introduced(definition,[new_symbols(definition,[spl20_16])],[avatar_definition]) ).
fof(f129,definition,
( spl20_17
<=> ! [X11] : ~ sP17(X11) ),
introduced(definition,[new_symbols(definition,[spl20_17])],[avatar_definition]) ).
fof(f130,plain,
( ! [X11] : ~ sP17(X11)
| ~ spl20_17 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f131,plain,
( spl20_16
| spl20_17 ),
inference(avatar_split_clause,[],[f56,f129,f125]) ).
fof(f133,definition,
( spl20_18
<=> ! [X4,X5] :
( ~ g_both(X4,X5)
| ~ sP19(X4)
| g_true_only(a,X4)
| g_false_only(X4,sK1(X4)) ) ),
introduced(definition,[new_symbols(definition,[spl20_18])],[avatar_definition]) ).
fof(f134,plain,
( ! [X4,X5] :
( ~ g_both(X4,X5)
| ~ sP19(X4)
| g_true_only(a,X4)
| g_false_only(X4,sK1(X4)) )
| ~ spl20_18 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f135,plain,
( ~ spl20_16
| ~ spl20_15
| spl20_10
| spl20_18 ),
inference(avatar_split_clause,[],[f59,f133,f98,f120,f125]) ).
fof(f137,plain,
( $false
| ~ spl20_2 ),
inference(resolution,[],[f20,f66]) ).
fof(f138,plain,
~ spl20_2,
inference(avatar_contradiction_clause,[],[f137]) ).
fof(f139,plain,
( g_false(a,sK2)
| ~ spl20_5 ),
inference(resolution,[],[f79,f24]) ).
fof(f142,plain,
( ~ g_true_only(a,sK2)
| ~ spl20_5 ),
inference(resolution,[],[f139,f26]) ).
fof(f154,plain,
! [X0] : sP15(X0),
inference(resolution,[],[f50,f20]) ).
fof(f156,plain,
! [X0] : sP19(X0),
inference(resolution,[],[f58,f20]) ).
fof(f157,plain,
( ! [X0] : ~ g_false_only(sK2,X0)
| ~ spl20_5 ),
inference(resolution,[],[f21,f79]) ).
fof(f171,plain,
! [X0,X1] :
( ~ g_both(a,X0)
| sP7(X0)
| ~ g_false_only(sK4(a),X1) ),
inference(resolution,[],[f34,f21]) ).
fof(f173,definition,
( spl20_23
<=> ! [X1] : ~ g_false_only(sK4(a),X1) ),
introduced(definition,[new_symbols(definition,[spl20_23])],[avatar_definition]) ).
fof(f174,plain,
( ! [X1] : ~ g_false_only(sK4(a),X1)
| ~ spl20_23 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f176,definition,
( spl20_24
<=> ! [X0] :
( ~ g_both(a,X0)
| sP7(X0) ) ),
introduced(definition,[new_symbols(definition,[spl20_24])],[avatar_definition]) ).
fof(f177,plain,
( ! [X0] :
( ~ g_both(a,X0)
| sP7(X0) )
| ~ spl20_24 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f178,plain,
( spl20_23
| spl20_24 ),
inference(avatar_split_clause,[],[f171,f176,f173]) ).
fof(f179,plain,
( $false
| ~ spl20_5
| ~ spl20_10 ),
inference(resolution,[],[f157,f100]) ).
fof(f181,plain,
( ~ spl20_5
| ~ spl20_10 ),
inference(avatar_contradiction_clause,[],[f179]) ).
fof(f194,plain,
( ! [X0] :
( ~ g_both(sK4(a),X0)
| sP7(X0) )
| ~ spl20_23 ),
inference(resolution,[],[f174,f34]) ).
fof(f195,plain,
( ! [X0] : ~ g_both(sK4(a),X0)
| ~ spl20_4
| ~ spl20_23 ),
inference(forward_subsumption_resolution,[],[f194,f74]) ).
fof(f200,plain,
( ! [X0] :
( g_true_only(sK4(a),X0)
| g_false_only(sK4(a),X0) )
| ~ spl20_4
| ~ spl20_23 ),
inference(resolution,[],[f195,f22]) ).
fof(f201,plain,
( ! [X0] : g_true_only(sK4(a),X0)
| ~ spl20_4
| ~ spl20_23 ),
inference(forward_subsumption_resolution,[],[f200,f174]) ).
fof(f206,plain,
( $false
| ~ spl20_4
| ~ spl20_23 ),
inference(resolution,[],[f201,f20]) ).
fof(f207,plain,
( ~ spl20_4
| ~ spl20_23 ),
inference(avatar_contradiction_clause,[],[f206]) ).
fof(f208,plain,
( ! [X0] : ~ g_both(a,X0)
| ~ spl20_4
| ~ spl20_24 ),
inference(forward_subsumption_resolution,[],[f177,f74]) ).
fof(f218,plain,
( ! [X4,X5] :
( g_false_only(X4,sK1(X4))
| g_true_only(a,X4)
| ~ g_both(X4,X5) )
| ~ spl20_18 ),
inference(forward_subsumption_resolution,[],[f134,f156]) ).
fof(f219,plain,
( ! [X0,X1] :
( g_true_only(X0,X1)
| g_true_only(a,X0)
| g_true_only(a,X0)
| g_false_only(a,X0) )
| ~ spl20_6 ),
inference(resolution,[],[f82,f22]) ).
fof(f220,plain,
( ! [X0,X1] :
( g_true_only(a,X0)
| g_true_only(X0,X1)
| g_false_only(a,X0) )
| ~ spl20_6 ),
inference(duplicate_literal_removal,[],[f219]) ).
fof(f232,definition,
( spl20_28
<=> ! [X0] : ~ g_both(a,X0) ),
introduced(definition,[new_symbols(definition,[spl20_28])],[avatar_definition]) ).
fof(f233,plain,
( ! [X0] : ~ g_both(a,X0)
| ~ spl20_28 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f247,plain,
( ! [X0] :
( g_true_only(sK0(a),X0)
| g_false_only(a,sK0(a)) )
| ~ spl20_6 ),
inference(resolution,[],[f220,f20]) ).
fof(f250,definition,
( spl20_30
<=> g_false_only(a,sK0(a)) ),
introduced(definition,[new_symbols(definition,[spl20_30])],[avatar_definition]) ).
fof(f251,plain,
( ~ g_false_only(a,sK0(a))
| spl20_30 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f252,plain,
( g_false_only(a,sK0(a))
| ~ spl20_30 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f254,definition,
( spl20_31
<=> ! [X0] : g_true_only(sK0(a),X0) ),
introduced(definition,[new_symbols(definition,[spl20_31])],[avatar_definition]) ).
fof(f255,plain,
( ! [X0] : g_true_only(sK0(a),X0)
| ~ spl20_31 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f256,plain,
( spl20_30
| spl20_31
| ~ spl20_6 ),
inference(avatar_split_clause,[],[f247,f81,f254,f250]) ).
fof(f262,plain,
( ! [X0] : ~ g_false_only(sK0(a),X0)
| ~ spl20_30 ),
inference(resolution,[],[f252,f21]) ).
fof(f284,plain,
( ! [X0] :
( ~ g_both(sK2,X0)
| sP17(X0) )
| ~ spl20_5 ),
inference(resolution,[],[f157,f54]) ).
fof(f288,plain,
( ! [X0] :
( g_true_only(a,sK2)
| ~ g_both(sK2,X0) )
| ~ spl20_5
| ~ spl20_18 ),
inference(resolution,[],[f157,f218]) ).
fof(f289,plain,
( ! [X0] : ~ g_both(sK2,X0)
| ~ spl20_5
| ~ spl20_18 ),
inference(forward_subsumption_resolution,[],[f288,f142]) ).
fof(f299,plain,
( ! [X0] :
( g_true_only(sK2,X0)
| g_false_only(sK2,X0) )
| ~ spl20_5
| ~ spl20_18 ),
inference(resolution,[],[f289,f22]) ).
fof(f300,plain,
( ! [X0] : g_true_only(sK2,X0)
| ~ spl20_5
| ~ spl20_18 ),
inference(forward_subsumption_resolution,[],[f299,f157]) ).
fof(f303,plain,
( $false
| ~ spl20_5
| ~ spl20_18 ),
inference(resolution,[],[f300,f20]) ).
fof(f304,plain,
( ~ spl20_5
| ~ spl20_18 ),
inference(avatar_contradiction_clause,[],[f303]) ).
fof(f305,plain,
( ! [X0] :
( sP17(X0)
| g_true_only(sK2,X0)
| g_false_only(sK2,X0) )
| ~ spl20_5 ),
inference(resolution,[],[f284,f22]) ).
fof(f306,plain,
( ! [X0] :
( g_true_only(sK2,X0)
| g_false_only(sK2,X0) )
| ~ spl20_5
| ~ spl20_17 ),
inference(forward_subsumption_resolution,[],[f305,f130]) ).
fof(f307,plain,
( ! [X0] : g_true_only(sK2,X0)
| ~ spl20_5
| ~ spl20_17 ),
inference(forward_subsumption_resolution,[],[f306,f157]) ).
fof(f309,plain,
( $false
| ~ spl20_5
| ~ spl20_17 ),
inference(resolution,[],[f307,f20]) ).
fof(f310,plain,
( ~ spl20_5
| ~ spl20_17 ),
inference(avatar_contradiction_clause,[],[f309]) ).
fof(f311,plain,
( ! [X4,X5] :
( g_false_only(X4,sK1(X4))
| g_true_only(a,X4)
| ~ g_both(X4,X5) )
| ~ spl20_14 ),
inference(forward_subsumption_resolution,[],[f117,f154]) ).
fof(f319,plain,
( ! [X0] :
( g_true_only(a,sK0(a))
| ~ g_both(sK0(a),X0) )
| ~ spl20_14
| ~ spl20_30 ),
inference(resolution,[],[f311,f262]) ).
fof(f350,plain,
( ! [X0] :
( g_true_only(a,X0)
| g_false_only(a,X0) )
| ~ spl20_28 ),
inference(resolution,[],[f233,f22]) ).
fof(f356,plain,
( $false
| ~ spl20_31 ),
inference(resolution,[],[f255,f20]) ).
fof(f357,plain,
~ spl20_31,
inference(avatar_contradiction_clause,[],[f356]) ).
fof(f359,plain,
( g_false_only(a,sK0(a))
| ~ spl20_28 ),
inference(resolution,[],[f350,f20]) ).
fof(f360,plain,
( $false
| ~ spl20_28
| spl20_30 ),
inference(forward_subsumption_resolution,[],[f359,f251]) ).
fof(f361,plain,
( ~ spl20_28
| spl20_30 ),
inference(avatar_contradiction_clause,[],[f360]) ).
fof(f363,plain,
( spl20_28
| ~ spl20_4
| ~ spl20_24 ),
inference(avatar_split_clause,[],[f208,f176,f73,f232]) ).
fof(f364,plain,
( ! [X0] : ~ g_both(sK0(a),X0)
| ~ spl20_14
| ~ spl20_30 ),
inference(forward_subsumption_resolution,[],[f319,f20]) ).
fof(f370,plain,
( ! [X0] :
( ~ g_both(sK0(a),X0)
| sP13(X0) )
| ~ spl20_30 ),
inference(resolution,[],[f262,f46]) ).
fof(f372,plain,
( ! [X0] :
( ~ g_both(sK0(a),X0)
| sP7(X0) )
| ~ spl20_30 ),
inference(resolution,[],[f262,f34]) ).
fof(f386,plain,
( ! [X0] :
( g_true_only(sK0(a),X0)
| g_false_only(sK0(a),X0) )
| ~ spl20_14
| ~ spl20_30 ),
inference(resolution,[],[f364,f22]) ).
fof(f387,plain,
( ! [X0] : g_true_only(sK0(a),X0)
| ~ spl20_14
| ~ spl20_30 ),
inference(forward_subsumption_resolution,[],[f386,f262]) ).
fof(f388,plain,
( spl20_31
| ~ spl20_14
| ~ spl20_30 ),
inference(avatar_split_clause,[],[f387,f250,f116,f254]) ).
fof(f390,plain,
( ! [X0] : ~ g_both(sK0(a),X0)
| ~ spl20_4
| ~ spl20_30 ),
inference(forward_subsumption_resolution,[],[f372,f74]) ).
fof(f392,plain,
( ! [X0] : ~ g_both(sK0(a),X0)
| ~ spl20_13
| ~ spl20_30 ),
inference(forward_subsumption_resolution,[],[f370,f113]) ).
fof(f396,plain,
( ! [X0] :
( g_true_only(sK0(a),X0)
| g_false_only(sK0(a),X0) )
| ~ spl20_4
| ~ spl20_30 ),
inference(resolution,[],[f390,f22]) ).
fof(f397,plain,
( ! [X0] : g_true_only(sK0(a),X0)
| ~ spl20_4
| ~ spl20_30 ),
inference(forward_subsumption_resolution,[],[f396,f262]) ).
fof(f398,plain,
( spl20_31
| ~ spl20_4
| ~ spl20_30 ),
inference(avatar_split_clause,[],[f397,f250,f73,f254]) ).
fof(f402,plain,
( ! [X0] :
( g_true_only(sK0(a),X0)
| g_false_only(sK0(a),X0) )
| ~ spl20_13
| ~ spl20_30 ),
inference(resolution,[],[f392,f22]) ).
fof(f403,plain,
( ! [X0] : g_true_only(sK0(a),X0)
| ~ spl20_13
| ~ spl20_30 ),
inference(forward_subsumption_resolution,[],[f402,f262]) ).
fof(f404,plain,
( spl20_31
| ~ spl20_13
| ~ spl20_30 ),
inference(avatar_split_clause,[],[f403,f250,f112,f254]) ).
cnf(s1,plain,
( spl20_1
| spl20_2 ),
inference(sat_conversion,[],[f67]) ).
cnf(s2,plain,
( spl20_3
| spl20_4 ),
inference(sat_conversion,[],[f75]) ).
cnf(s3,plain,
( ~ spl20_1
| ~ spl20_3
| spl20_5
| spl20_6 ),
inference(sat_conversion,[],[f83]) ).
cnf(s7,plain,
( spl20_2
| spl20_11 ),
inference(sat_conversion,[],[f106]) ).
cnf(s8,plain,
( spl20_12
| spl20_13 ),
inference(sat_conversion,[],[f114]) ).
cnf(s9,plain,
( spl20_5
| ~ spl20_11
| ~ spl20_12
| spl20_14 ),
inference(sat_conversion,[],[f118]) ).
cnf(s10,plain,
( spl20_2
| spl20_15 ),
inference(sat_conversion,[],[f123]) ).
cnf(s11,plain,
( spl20_16
| spl20_17 ),
inference(sat_conversion,[],[f131]) ).
cnf(s12,plain,
( spl20_10
| ~ spl20_15
| ~ spl20_16
| spl20_18 ),
inference(sat_conversion,[],[f135]) ).
cnf(s13,plain,
~ spl20_2,
inference(sat_conversion,[],[f138]) ).
cnf(s16,plain,
( spl20_23
| spl20_24 ),
inference(sat_conversion,[],[f178]) ).
cnf(s17,plain,
( ~ spl20_5
| ~ spl20_10 ),
inference(sat_conversion,[],[f181]) ).
cnf(s18,plain,
( ~ spl20_4
| ~ spl20_23 ),
inference(sat_conversion,[],[f207]) ).
cnf(s22,plain,
( ~ spl20_6
| spl20_30
| spl20_31 ),
inference(sat_conversion,[],[f256]) ).
cnf(s25,plain,
( ~ spl20_5
| ~ spl20_18 ),
inference(sat_conversion,[],[f304]) ).
cnf(s26,plain,
( ~ spl20_5
| ~ spl20_17 ),
inference(sat_conversion,[],[f310]) ).
cnf(s32,plain,
~ spl20_31,
inference(sat_conversion,[],[f357]) ).
cnf(s33,plain,
( ~ spl20_28
| spl20_30 ),
inference(sat_conversion,[],[f361]) ).
cnf(s34,plain,
( ~ spl20_4
| ~ spl20_24
| spl20_28 ),
inference(sat_conversion,[],[f363]) ).
cnf(s35,plain,
( ~ spl20_14
| ~ spl20_30
| spl20_31 ),
inference(sat_conversion,[],[f388]) ).
cnf(s36,plain,
( ~ spl20_4
| ~ spl20_30
| spl20_31 ),
inference(sat_conversion,[],[f398]) ).
cnf(s38,plain,
( ~ spl20_13
| ~ spl20_30
| spl20_31 ),
inference(sat_conversion,[],[f404]) ).
cnf(s40,plain,
( ~ spl20_6
| spl20_30 ),
inference(rat,[],[s22,s32]) ).
cnf(s41,plain,
spl20_15,
inference(rat,[],[s10,s13]) ).
cnf(s42,plain,
spl20_11,
inference(rat,[],[s7,s13]) ).
cnf(s44,plain,
spl20_1,
inference(rat,[],[s1,s13]) ).
cnf(s45,plain,
~ spl20_4,
inference(rat,[],[s34,s16,s33,s18,s36,s32]) ).
cnf(s46,plain,
spl20_3,
inference(rat,[],[s2,s45]) ).
cnf(s47,plain,
spl20_5,
inference(rat,[],[s9,s8,s35,s38,s40,s3,s42,s32,s44,s46]) ).
cnf(s48,plain,
~ spl20_17,
inference(rat,[],[s26,s47]) ).
cnf(s49,plain,
~ spl20_18,
inference(rat,[],[s25,s47]) ).
cnf(s50,plain,
~ spl20_10,
inference(rat,[],[s17,s47]) ).
cnf(s51,plain,
spl20_16,
inference(rat,[],[s11,s48]) ).
cnf(s52,plain,
$false,
inference(rat,[],[s12,s51,s41,s49,s50]) ).
fof(f405,plain,
$false,
inference(avatar_sat_refutation,[],[s52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO607+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.19 % Computer : n009.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Mon Sep 28 17:54:45 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running first-order theorem proving
% 0.06/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.64/0.95 % (3296793)Detected formulas, will run a generic FOF schedule.
% 0.64/0.95 % (3296801)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1126134256:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.64/0.95 % (3296801)First to succeed.
% 0.64/0.95 % (3296801)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3296793"
% 0.64/0.95 % (3296799)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=2524057511:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.64/0.95 % (3296798)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=2027122454:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.64/0.95 % (3296800)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=1687069682:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.64/0.95 % (3296803)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3713271404:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.64/0.95 % (3296802)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2492504697:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.64/0.95 % (3296804)dis-21_1_sil=8000:lcm=predicate:random_seed=3773683792: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)
% 0.64/0.95 % (3296803)Also succeeded, but the first one will report.
% 0.64/0.95 % (3296804)Also succeeded, but the first one will report.
% 0.64/0.95 % (3296802)Also succeeded, but the first one will report.
% 0.64/0.95 % (3296801)Refutation found. Thanks to Tanya!
% 0.64/0.95 % SZS status Theorem for theBenchmark
% 0.64/0.95 % SZS output start Proof for theBenchmark
% See solution above
% 2.70/1.15 % (3296801)------------------------------
% 2.70/1.15 % (3296801)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.15 % (3296801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.15 % (3296801)CaDiCaL version: 2.1.3
% 2.70/1.15 % (3296801)Termination reason: Refutation
% 2.70/1.15 % (3296801)Time elapsed: 0.006 s
% 2.70/1.15 % (3296801)Peak memory usage: 89 MB
% 2.70/1.15 % (3296801)Instructions burned: 11 (million)
% 2.70/1.15 % (3296801)------------------------------
% 2.70/1.15 % (3296801)------------------------------
% 2.70/1.15 % (3296793)Success in time 0.289 s
% 2.70/1.15 % Vampire exiting
%------------------------------------------------------------------------------