%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN067+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 02:06:39 PM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 154 ( 6 unt; 9 def)
% Number of atoms : 736 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 959 ( 377 ~; 457 |; 107 &)
% ( 11 <=>; 4 =>; 0 <=; 3 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-1 aty)
% Number of variables : 203 ( 0 sgn 146 !; 57 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
( ( big_p(a)
& ( big_p(X0)
=> ? [X1] :
( big_p(X1)
& big_r(X0,X1) ) ) )
=> ? [X2,X3] :
( big_p(X2)
& big_r(X0,X3)
& big_r(X3,X2) ) )
<=> ! [X4] :
( ( ~ big_p(a)
| big_p(X4)
| ? [X5,X6] :
( big_p(X5)
& big_r(X4,X6)
& big_r(X6,X5) ) )
& ( ~ big_p(a)
| ~ ? [X7] :
( big_p(X7)
& big_r(X4,X7) )
| ? [X8,X9] :
( big_p(X8)
& big_r(X4,X9)
& big_r(X9,X8) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel38) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
( ( big_p(a)
& ( big_p(X0)
=> ? [X1] :
( big_p(X1)
& big_r(X0,X1) ) ) )
=> ? [X2,X3] :
( big_p(X2)
& big_r(X0,X3)
& big_r(X3,X2) ) )
<=> ! [X4] :
( ( ~ big_p(a)
| big_p(X4)
| ? [X5,X6] :
( big_p(X5)
& big_r(X4,X6)
& big_r(X6,X5) ) )
& ( ~ big_p(a)
| ~ ? [X7] :
( big_p(X7)
& big_r(X4,X7) )
| ? [X8,X9] :
( big_p(X8)
& big_r(X4,X9)
& big_r(X9,X8) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X0] :
( ? [X2,X3] :
( big_p(X2)
& big_r(X0,X3)
& big_r(X3,X2) )
| ~ big_p(a)
| ( ! [X1] :
( ~ big_p(X1)
| ~ big_r(X0,X1) )
& big_p(X0) ) )
<~> ! [X4] :
( ( ~ big_p(a)
| big_p(X4)
| ? [X5,X6] :
( big_p(X5)
& big_r(X4,X6)
& big_r(X6,X5) ) )
& ( ~ big_p(a)
| ! [X7] :
( ~ big_p(X7)
| ~ big_r(X4,X7) )
| ? [X8,X9] :
( big_p(X8)
& big_r(X4,X9)
& big_r(X9,X8) ) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ! [X0] :
( ? [X2,X3] :
( big_p(X2)
& big_r(X0,X3)
& big_r(X3,X2) )
| ~ big_p(a)
| ( ! [X1] :
( ~ big_p(X1)
| ~ big_r(X0,X1) )
& big_p(X0) ) )
<~> ! [X4] :
( ( ~ big_p(a)
| big_p(X4)
| ? [X5,X6] :
( big_p(X5)
& big_r(X4,X6)
& big_r(X6,X5) ) )
& ( ~ big_p(a)
| ! [X7] :
( ~ big_p(X7)
| ~ big_r(X4,X7) )
| ? [X8,X9] :
( big_p(X8)
& big_r(X4,X9)
& big_r(X9,X8) ) ) ) ),
inference(flattening,[],[f3]) ).
fof(f5,definition,
! [X4] :
( sP0(X4)
<=> ( ~ big_p(a)
| ! [X7] :
( ~ big_p(X7)
| ~ big_r(X4,X7) )
| ? [X8,X9] :
( big_p(X8)
& big_r(X4,X9)
& big_r(X9,X8) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f6,definition,
( sP1
<=> ! [X0] :
( ? [X2,X3] :
( big_p(X2)
& big_r(X0,X3)
& big_r(X3,X2) )
| ~ big_p(a)
| ( ! [X1] :
( ~ big_p(X1)
| ~ big_r(X0,X1) )
& big_p(X0) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f7,plain,
( sP1
<~> ! [X4] :
( ( ~ big_p(a)
| big_p(X4)
| ? [X5,X6] :
( big_p(X5)
& big_r(X4,X6)
& big_r(X6,X5) ) )
& sP0(X4) ) ),
inference(definition_folding,[],[f4,f6,f5]) ).
fof(f8,plain,
( ( sP1
| ? [X0] :
( ! [X2,X3] :
( ~ big_p(X2)
| ~ big_r(X0,X3)
| ~ big_r(X3,X2) )
& big_p(a)
& ( ? [X1] :
( big_p(X1)
& big_r(X0,X1) )
| ~ big_p(X0) ) ) )
& ( ! [X0] :
( ? [X2,X3] :
( big_p(X2)
& big_r(X0,X3)
& big_r(X3,X2) )
| ~ big_p(a)
| ( ! [X1] :
( ~ big_p(X1)
| ~ big_r(X0,X1) )
& big_p(X0) ) )
| ~ sP1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f9,plain,
( ( sP1
| ? [X0] :
( ! [X1,X2] :
( ~ big_p(X1)
| ~ big_r(X0,X2)
| ~ big_r(X2,X1) )
& big_p(a)
& ( ? [X3] :
( big_p(X3)
& big_r(X0,X3) )
| ~ big_p(X0) ) ) )
& ( ! [X4] :
( ? [X5,X6] :
( big_p(X5)
& big_r(X4,X6)
& big_r(X6,X5) )
| ~ big_p(a)
| ( ! [X7] :
( ~ big_p(X7)
| ~ big_r(X4,X7) )
& big_p(X4) ) )
| ~ sP1 ) ),
inference(rectify,[],[f8]) ).
fof(f10,plain,
( ( sP1
| ( ! [X1,X2] :
( ~ big_p(X1)
| ~ big_r(sK2,X2)
| ~ big_r(X2,X1) )
& big_p(a)
& ( ( big_p(sK3)
& big_r(sK2,sK3) )
| ~ big_p(sK2) ) ) )
& ( ! [X4] :
( ( big_p(sK4(X4))
& big_r(X4,sK5(X4))
& big_r(sK5(X4),sK4(X4)) )
| ~ big_p(a)
| ( ! [X7] :
( ~ big_p(X7)
| ~ big_r(X4,X7) )
& big_p(X4) ) )
| ~ sP1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X3,sK3),skolemize(X5,sK4(X4)),skolemize(X6,sK5(X4))],[f9]) ).
fof(f11,plain,
! [X4] :
( ( sP0(X4)
| ( big_p(a)
& ? [X7] :
( big_p(X7)
& big_r(X4,X7) )
& ! [X8,X9] :
( ~ big_p(X8)
| ~ big_r(X4,X9)
| ~ big_r(X9,X8) ) ) )
& ( ~ big_p(a)
| ! [X7] :
( ~ big_p(X7)
| ~ big_r(X4,X7) )
| ? [X8,X9] :
( big_p(X8)
& big_r(X4,X9)
& big_r(X9,X8) )
| ~ sP0(X4) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f12,plain,
! [X4] :
( ( sP0(X4)
| ( big_p(a)
& ? [X7] :
( big_p(X7)
& big_r(X4,X7) )
& ! [X8,X9] :
( ~ big_p(X8)
| ~ big_r(X4,X9)
| ~ big_r(X9,X8) ) ) )
& ( ~ big_p(a)
| ! [X7] :
( ~ big_p(X7)
| ~ big_r(X4,X7) )
| ? [X8,X9] :
( big_p(X8)
& big_r(X4,X9)
& big_r(X9,X8) )
| ~ sP0(X4) ) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0] :
( ( sP0(X0)
| ( big_p(a)
& ? [X1] :
( big_p(X1)
& big_r(X0,X1) )
& ! [X2,X3] :
( ~ big_p(X2)
| ~ big_r(X0,X3)
| ~ big_r(X3,X2) ) ) )
& ( ~ big_p(a)
| ! [X4] :
( ~ big_p(X4)
| ~ big_r(X0,X4) )
| ? [X5,X6] :
( big_p(X5)
& big_r(X0,X6)
& big_r(X6,X5) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f12]) ).
fof(f14,plain,
! [X0] :
( ( sP0(X0)
| ( big_p(a)
& big_p(sK6(X0))
& big_r(X0,sK6(X0))
& ! [X2,X3] :
( ~ big_p(X2)
| ~ big_r(X0,X3)
| ~ big_r(X3,X2) ) ) )
& ( ~ big_p(a)
| ! [X4] :
( ~ big_p(X4)
| ~ big_r(X0,X4) )
| ( big_p(sK7(X0))
& big_r(X0,sK8(X0))
& big_r(sK8(X0),sK7(X0)) )
| ~ sP0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X1,sK6(X0)),skolemize(X5,sK7(X0)),skolemize(X6,sK8(X0))],[f13]) ).
fof(f15,plain,
( ( ? [X4] :
( ( big_p(a)
& ~ big_p(X4)
& ! [X5,X6] :
( ~ big_p(X5)
| ~ big_r(X4,X6)
| ~ big_r(X6,X5) ) )
| ~ sP0(X4) )
| ~ sP1 )
& ( ! [X4] :
( ( ~ big_p(a)
| big_p(X4)
| ? [X5,X6] :
( big_p(X5)
& big_r(X4,X6)
& big_r(X6,X5) ) )
& sP0(X4) )
| sP1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f16,plain,
( ( ? [X0] :
( ( big_p(a)
& ~ big_p(X0)
& ! [X1,X2] :
( ~ big_p(X1)
| ~ big_r(X0,X2)
| ~ big_r(X2,X1) ) )
| ~ sP0(X0) )
| ~ sP1 )
& ( ! [X3] :
( ( ~ big_p(a)
| big_p(X3)
| ? [X4,X5] :
( big_p(X4)
& big_r(X3,X5)
& big_r(X5,X4) ) )
& sP0(X3) )
| sP1 ) ),
inference(rectify,[],[f15]) ).
fof(f17,plain,
( ( ( big_p(a)
& ~ big_p(sK9)
& ! [X1,X2] :
( ~ big_p(X1)
| ~ big_r(sK9,X2)
| ~ big_r(X2,X1) ) )
| ~ sP0(sK9)
| ~ sP1 )
& ( ! [X3] :
( ( ~ big_p(a)
| big_p(X3)
| ( big_p(sK10(X3))
& big_r(X3,sK11(X3))
& big_r(sK11(X3),sK10(X3)) ) )
& sP0(X3) )
| sP1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X0,sK9),skolemize(X4,sK10(X3)),skolemize(X5,sK11(X3))],[f16]) ).
fof(f18,plain,
! [X4] :
( big_r(sK5(X4),sK4(X4))
| ~ big_p(a)
| big_p(X4)
| ~ sP1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f19,plain,
! [X7,X4] :
( big_r(sK5(X4),sK4(X4))
| ~ big_p(a)
| ~ big_p(X7)
| ~ big_r(X4,X7)
| ~ sP1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f20,plain,
! [X4] :
( big_r(X4,sK5(X4))
| ~ big_p(a)
| big_p(X4)
| ~ sP1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f21,plain,
! [X7,X4] :
( big_r(X4,sK5(X4))
| ~ big_p(a)
| ~ big_p(X7)
| ~ big_r(X4,X7)
| ~ sP1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f22,plain,
! [X4] :
( big_p(sK4(X4))
| ~ big_p(a)
| big_p(X4)
| ~ sP1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f23,plain,
! [X7,X4] :
( big_p(sK4(X4))
| ~ big_p(a)
| ~ big_p(X7)
| ~ big_r(X4,X7)
| ~ sP1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f24,plain,
( sP1
| big_r(sK2,sK3)
| ~ big_p(sK2) ),
inference(cnf_transformation,[],[f10]) ).
fof(f25,plain,
( sP1
| big_p(sK3)
| ~ big_p(sK2) ),
inference(cnf_transformation,[],[f10]) ).
fof(f26,plain,
( sP1
| big_p(a) ),
inference(cnf_transformation,[],[f10]) ).
fof(f27,plain,
! [X2,X1] :
( sP1
| ~ big_p(X1)
| ~ big_r(sK2,X2)
| ~ big_r(X2,X1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f28,plain,
! [X0,X4] :
( ~ big_p(a)
| ~ big_p(X4)
| ~ big_r(X0,X4)
| big_r(sK8(X0),sK7(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
! [X0,X4] :
( ~ big_p(a)
| ~ big_p(X4)
| ~ big_r(X0,X4)
| big_r(X0,sK8(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f30,plain,
! [X0,X4] :
( ~ big_p(a)
| ~ big_p(X4)
| ~ big_r(X0,X4)
| big_p(sK7(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f31,plain,
! [X2,X3,X0] :
( ~ big_r(X3,X2)
| ~ big_p(X2)
| ~ big_r(X0,X3)
| sP0(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f32,plain,
! [X0] :
( big_r(X0,sK6(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f33,plain,
! [X0] :
( big_p(sK6(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f34,plain,
! [X0] :
( sP0(X0)
| big_p(a) ),
inference(cnf_transformation,[],[f14]) ).
fof(f35,plain,
! [X3] :
( sP0(X3)
| sP1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f36,plain,
! [X3] :
( ~ big_p(a)
| big_p(X3)
| big_r(sK11(X3),sK10(X3))
| sP1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f37,plain,
! [X3] :
( ~ big_p(a)
| big_p(X3)
| big_r(X3,sK11(X3))
| sP1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f38,plain,
! [X3] :
( ~ big_p(a)
| big_p(X3)
| big_p(sK10(X3))
| sP1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f39,plain,
! [X2,X1] :
( ~ big_p(X1)
| ~ big_r(sK9,X2)
| ~ big_r(X2,X1)
| ~ sP0(sK9)
| ~ sP1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f40,plain,
( ~ big_p(sK9)
| ~ sP0(sK9)
| ~ sP1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f41,plain,
( big_p(a)
| ~ sP0(sK9)
| ~ sP1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f43,definition,
( spl12_1
<=> sP1 ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f44,plain,
( sP1
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f45,plain,
( ~ sP1
| spl12_1 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f47,definition,
( spl12_2
<=> sP0(sK9) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f48,plain,
( sP0(sK9)
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f49,plain,
( ~ sP0(sK9)
| spl12_2 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f51,definition,
( spl12_3
<=> big_p(sK9) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
fof(f53,plain,
( ~ big_p(sK9)
| spl12_3 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f54,plain,
( ~ spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(avatar_split_clause,[],[f40,f51,f47,f43]) ).
fof(f121,plain,
( ! [X2,X1] :
( ~ big_p(X1)
| ~ big_r(sK9,X2)
| ~ big_r(X2,X1)
| ~ sP0(sK9) )
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f39,f44]) ).
fof(f122,plain,
( big_p(a)
| ~ sP0(sK9)
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f41,f44]) ).
fof(f123,plain,
( ! [X4] :
( big_p(sK4(X4))
| ~ big_p(a)
| big_p(X4) )
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f22,f44]) ).
fof(f124,plain,
( ! [X4] :
( big_r(X4,sK5(X4))
| ~ big_p(a)
| big_p(X4) )
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f20,f44]) ).
fof(f125,plain,
( ! [X4] :
( big_r(sK5(X4),sK4(X4))
| ~ big_p(a)
| big_p(X4) )
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f18,f44]) ).
fof(f126,plain,
( ! [X7,X4] :
( big_p(sK4(X4))
| ~ big_p(a)
| ~ big_p(X7)
| ~ big_r(X4,X7) )
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f23,f44]) ).
fof(f127,plain,
( ! [X7,X4] :
( big_r(X4,sK5(X4))
| ~ big_p(a)
| ~ big_p(X7)
| ~ big_r(X4,X7) )
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f21,f44]) ).
fof(f128,plain,
( ! [X7,X4] :
( big_r(sK5(X4),sK4(X4))
| ~ big_p(a)
| ~ big_p(X7)
| ~ big_r(X4,X7) )
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f19,f44]) ).
fof(f131,plain,
( big_p(a)
| ~ spl12_1
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f122,f48]) ).
fof(f132,plain,
( ! [X4] :
( big_p(sK4(X4))
| big_p(X4) )
| ~ spl12_1
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f123,f131]) ).
fof(f136,plain,
( ! [X4] :
( big_r(X4,sK5(X4))
| big_p(X4) )
| ~ spl12_1
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f124,f131]) ).
fof(f139,plain,
( ! [X2,X1] :
( ~ big_r(sK9,X2)
| ~ big_p(X1)
| ~ big_r(X2,X1) )
| ~ spl12_1
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f121,f48]) ).
fof(f157,plain,
( ! [X0] :
( big_p(sK9)
| ~ big_p(X0)
| ~ big_r(sK5(sK9),X0) )
| ~ spl12_1
| ~ spl12_2 ),
inference(resolution,[],[f136,f139]) ).
fof(f158,plain,
( ! [X0] :
( ~ big_r(sK5(sK9),X0)
| ~ big_p(X0) )
| ~ spl12_1
| ~ spl12_2
| spl12_3 ),
inference(forward_subsumption_resolution,[],[f157,f53]) ).
fof(f172,plain,
( ! [X4] :
( big_r(sK5(X4),sK4(X4))
| big_p(X4) )
| ~ spl12_1
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f125,f131]) ).
fof(f176,plain,
( big_p(sK9)
| ~ big_p(sK4(sK9))
| ~ spl12_1
| ~ spl12_2
| spl12_3 ),
inference(resolution,[],[f172,f158]) ).
fof(f177,plain,
( ~ big_p(sK4(sK9))
| ~ spl12_1
| ~ spl12_2
| spl12_3 ),
inference(forward_subsumption_resolution,[],[f176,f53]) ).
fof(f180,plain,
( big_p(sK9)
| ~ spl12_1
| ~ spl12_2
| spl12_3 ),
inference(resolution,[],[f177,f132]) ).
fof(f181,plain,
( $false
| ~ spl12_1
| ~ spl12_2
| spl12_3 ),
inference(forward_subsumption_resolution,[],[f180,f53]) ).
fof(f182,plain,
( ~ spl12_1
| ~ spl12_2
| spl12_3 ),
inference(avatar_contradiction_clause,[],[f181]) ).
fof(f184,definition,
( spl12_15
<=> big_p(a) ),
introduced(definition,[new_symbols(definition,[spl12_15])],[avatar_definition]) ).
fof(f185,plain,
( big_p(a)
| ~ spl12_15 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f186,plain,
( ~ big_p(a)
| spl12_15 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f191,plain,
( ! [X0] : sP0(X0)
| spl12_15 ),
inference(forward_subsumption_resolution,[],[f34,f186]) ).
fof(f192,plain,
( $false
| spl12_2
| spl12_15 ),
inference(resolution,[],[f191,f49]) ).
fof(f193,plain,
( spl12_2
| spl12_15 ),
inference(avatar_contradiction_clause,[],[f192]) ).
fof(f195,definition,
( spl12_17
<=> ! [X0] : sP0(X0) ),
introduced(definition,[new_symbols(definition,[spl12_17])],[avatar_definition]) ).
fof(f196,plain,
( ! [X0] : sP0(X0)
| ~ spl12_17 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f200,plain,
( $false
| spl12_2
| ~ spl12_17 ),
inference(resolution,[],[f196,f49]) ).
fof(f201,plain,
( spl12_2
| ~ spl12_17 ),
inference(avatar_contradiction_clause,[],[f200]) ).
fof(f219,plain,
( ! [X7,X4] :
( ~ big_r(X4,X7)
| ~ big_p(X7)
| big_r(X4,sK5(X4)) )
| ~ spl12_1
| ~ spl12_15 ),
inference(forward_subsumption_resolution,[],[f127,f185]) ).
fof(f230,plain,
( ! [X7,X4] :
( ~ big_r(X4,X7)
| ~ big_p(X7)
| big_r(sK5(X4),sK4(X4)) )
| ~ spl12_1
| ~ spl12_15 ),
inference(forward_subsumption_resolution,[],[f128,f185]) ).
fof(f252,plain,
( ! [X7,X4] :
( ~ big_r(X4,X7)
| ~ big_p(X7)
| big_p(sK4(X4)) )
| ~ spl12_1
| ~ spl12_15 ),
inference(forward_subsumption_resolution,[],[f126,f185]) ).
fof(f254,plain,
( ! [X0] :
( ~ big_p(sK6(X0))
| big_p(sK4(X0))
| sP0(X0) )
| ~ spl12_1
| ~ spl12_15 ),
inference(resolution,[],[f252,f32]) ).
fof(f262,plain,
( ! [X0] :
( big_p(sK4(X0))
| sP0(X0) )
| ~ spl12_1
| ~ spl12_15 ),
inference(forward_subsumption_resolution,[],[f254,f33]) ).
fof(f280,plain,
( ! [X0] :
( ~ big_p(sK6(X0))
| big_r(X0,sK5(X0))
| sP0(X0) )
| ~ spl12_1
| ~ spl12_15 ),
inference(resolution,[],[f219,f32]) ).
fof(f284,plain,
( ! [X0] :
( big_r(X0,sK5(X0))
| sP0(X0) )
| ~ spl12_1
| ~ spl12_15 ),
inference(forward_subsumption_resolution,[],[f280,f33]) ).
fof(f301,plain,
( ! [X0] :
( ~ big_p(sK6(X0))
| big_r(sK5(X0),sK4(X0))
| sP0(X0) )
| ~ spl12_1
| ~ spl12_15 ),
inference(resolution,[],[f230,f32]) ).
fof(f309,plain,
( ! [X0] :
( big_r(sK5(X0),sK4(X0))
| sP0(X0) )
| ~ spl12_1
| ~ spl12_15 ),
inference(forward_subsumption_resolution,[],[f301,f33]) ).
fof(f313,plain,
( ! [X0,X1] :
( sP0(X0)
| ~ big_p(sK4(X0))
| ~ big_r(X1,sK5(X0))
| sP0(X1) )
| ~ spl12_1
| ~ spl12_15 ),
inference(resolution,[],[f309,f31]) ).
fof(f314,plain,
( ! [X0,X1] :
( ~ big_r(X1,sK5(X0))
| sP0(X0)
| sP0(X1) )
| ~ spl12_1
| ~ spl12_15 ),
inference(forward_subsumption_resolution,[],[f313,f262]) ).
fof(f326,plain,
( ! [X0] :
( sP0(X0)
| sP0(X0)
| sP0(X0) )
| ~ spl12_1
| ~ spl12_15 ),
inference(resolution,[],[f314,f284]) ).
fof(f331,plain,
( ! [X0] : sP0(X0)
| ~ spl12_1
| ~ spl12_15 ),
inference(duplicate_literal_removal,[],[f326]) ).
fof(f335,plain,
( spl12_17
| ~ spl12_1
| ~ spl12_15 ),
inference(avatar_split_clause,[],[f331,f184,f43,f195]) ).
fof(f337,plain,
( ! [X3] :
( big_p(X3)
| big_p(sK10(X3))
| sP1 )
| ~ spl12_15 ),
inference(forward_subsumption_resolution,[],[f38,f185]) ).
fof(f338,plain,
( ! [X3] :
( big_p(X3)
| big_r(X3,sK11(X3))
| sP1 )
| ~ spl12_15 ),
inference(forward_subsumption_resolution,[],[f37,f185]) ).
fof(f339,plain,
( ! [X3] :
( big_p(X3)
| big_r(sK11(X3),sK10(X3))
| sP1 )
| ~ spl12_15 ),
inference(forward_subsumption_resolution,[],[f36,f185]) ).
fof(f343,plain,
( ! [X3] : sP0(X3)
| spl12_1 ),
inference(forward_subsumption_resolution,[],[f35,f45]) ).
fof(f344,plain,
( spl12_17
| spl12_1 ),
inference(avatar_split_clause,[],[f343,f43,f195]) ).
fof(f346,plain,
( ! [X3] :
( big_p(sK10(X3))
| big_p(X3) )
| spl12_1
| ~ spl12_15 ),
inference(forward_subsumption_resolution,[],[f337,f45]) ).
fof(f347,plain,
( ! [X3] :
( big_r(X3,sK11(X3))
| big_p(X3) )
| spl12_1
| ~ spl12_15 ),
inference(forward_subsumption_resolution,[],[f338,f45]) ).
fof(f353,plain,
( ! [X3] :
( big_r(sK11(X3),sK10(X3))
| big_p(X3) )
| spl12_1
| ~ spl12_15 ),
inference(forward_subsumption_resolution,[],[f339,f45]) ).
fof(f395,plain,
( big_p(sK3)
| ~ big_p(sK2)
| spl12_1 ),
inference(forward_subsumption_resolution,[],[f25,f45]) ).
fof(f397,definition,
( spl12_30
<=> big_p(sK2) ),
introduced(definition,[new_symbols(definition,[spl12_30])],[avatar_definition]) ).
fof(f398,plain,
( big_p(sK2)
| ~ spl12_30 ),
inference(avatar_component_clause,[],[f397]) ).
fof(f399,plain,
( ~ big_p(sK2)
| spl12_30 ),
inference(avatar_component_clause,[],[f397]) ).
fof(f401,definition,
( spl12_31
<=> big_p(sK3) ),
introduced(definition,[new_symbols(definition,[spl12_31])],[avatar_definition]) ).
fof(f403,plain,
( big_p(sK3)
| ~ spl12_31 ),
inference(avatar_component_clause,[],[f401]) ).
fof(f404,plain,
( ~ spl12_30
| spl12_31
| spl12_1 ),
inference(avatar_split_clause,[],[f395,f43,f401,f397]) ).
fof(f405,plain,
( ! [X2,X1] :
( ~ big_r(sK2,X2)
| ~ big_p(X1)
| ~ big_r(X2,X1) )
| spl12_1 ),
inference(forward_subsumption_resolution,[],[f27,f45]) ).
fof(f409,plain,
( ! [X0] :
( ~ big_p(X0)
| ~ big_r(sK11(sK2),X0)
| big_p(sK2) )
| spl12_1
| ~ spl12_15 ),
inference(resolution,[],[f405,f347]) ).
fof(f450,plain,
( big_r(sK2,sK3)
| ~ big_p(sK2)
| spl12_1 ),
inference(forward_subsumption_resolution,[],[f24,f45]) ).
fof(f464,plain,
( big_r(sK2,sK3)
| spl12_1
| ~ spl12_30 ),
inference(forward_subsumption_resolution,[],[f450,f398]) ).
fof(f482,plain,
( ! [X0,X4] :
( ~ big_p(X4)
| ~ big_r(X0,X4)
| big_p(sK7(X0))
| ~ sP0(X0) )
| ~ spl12_15 ),
inference(forward_subsumption_resolution,[],[f30,f185]) ).
fof(f483,plain,
( ! [X0,X4] :
( ~ big_r(X0,X4)
| ~ big_p(X4)
| big_p(sK7(X0)) )
| ~ spl12_15
| ~ spl12_17 ),
inference(forward_subsumption_resolution,[],[f482,f196]) ).
fof(f491,plain,
( ~ big_p(sK3)
| big_p(sK7(sK2))
| spl12_1
| ~ spl12_15
| ~ spl12_17
| ~ spl12_30 ),
inference(resolution,[],[f483,f464]) ).
fof(f496,plain,
( big_p(sK7(sK2))
| spl12_1
| ~ spl12_15
| ~ spl12_17
| ~ spl12_30
| ~ spl12_31 ),
inference(forward_subsumption_resolution,[],[f491,f403]) ).
fof(f497,plain,
( ! [X0,X4] :
( ~ big_p(X4)
| ~ big_r(X0,X4)
| big_r(X0,sK8(X0))
| ~ sP0(X0) )
| ~ spl12_15 ),
inference(forward_subsumption_resolution,[],[f29,f185]) ).
fof(f498,plain,
( ! [X0,X4] :
( ~ big_r(X0,X4)
| ~ big_p(X4)
| big_r(X0,sK8(X0)) )
| ~ spl12_15
| ~ spl12_17 ),
inference(forward_subsumption_resolution,[],[f497,f196]) ).
fof(f503,plain,
( ~ big_p(sK3)
| big_r(sK2,sK8(sK2))
| spl12_1
| ~ spl12_15
| ~ spl12_17
| ~ spl12_30 ),
inference(resolution,[],[f498,f464]) ).
fof(f508,plain,
( big_r(sK2,sK8(sK2))
| spl12_1
| ~ spl12_15
| ~ spl12_17
| ~ spl12_30
| ~ spl12_31 ),
inference(forward_subsumption_resolution,[],[f503,f403]) ).
fof(f509,plain,
( ! [X0] :
( ~ big_r(sK8(sK2),X0)
| ~ big_p(X0) )
| spl12_1
| ~ spl12_15
| ~ spl12_17
| ~ spl12_30
| ~ spl12_31 ),
inference(resolution,[],[f508,f405]) ).
fof(f537,plain,
( ! [X0,X4] :
( ~ big_p(X4)
| ~ big_r(X0,X4)
| big_r(sK8(X0),sK7(X0))
| ~ sP0(X0) )
| ~ spl12_15 ),
inference(forward_subsumption_resolution,[],[f28,f185]) ).
fof(f538,plain,
( ! [X0,X4] :
( ~ big_r(X0,X4)
| ~ big_p(X4)
| big_r(sK8(X0),sK7(X0)) )
| ~ spl12_15
| ~ spl12_17 ),
inference(forward_subsumption_resolution,[],[f537,f196]) ).
fof(f547,plain,
( ~ big_p(sK3)
| big_r(sK8(sK2),sK7(sK2))
| spl12_1
| ~ spl12_15
| ~ spl12_17
| ~ spl12_30 ),
inference(resolution,[],[f538,f464]) ).
fof(f553,plain,
( big_r(sK8(sK2),sK7(sK2))
| spl12_1
| ~ spl12_15
| ~ spl12_17
| ~ spl12_30
| ~ spl12_31 ),
inference(forward_subsumption_resolution,[],[f547,f403]) ).
fof(f562,plain,
( ~ big_p(sK7(sK2))
| spl12_1
| ~ spl12_15
| ~ spl12_17
| ~ spl12_30
| ~ spl12_31 ),
inference(resolution,[],[f553,f509]) ).
fof(f571,plain,
( big_p(sK7(sK2))
| spl12_1
| ~ spl12_15
| ~ spl12_17
| ~ spl12_30
| ~ spl12_31 ),
inference(global_subsumption,[],[f496]) ).
fof(f580,plain,
( $false
| spl12_1
| ~ spl12_15
| ~ spl12_17
| ~ spl12_30
| ~ spl12_31 ),
inference(global_subsumption,[],[f571,f562]) ).
fof(f581,plain,
( spl12_1
| ~ spl12_15
| ~ spl12_17
| ~ spl12_30
| ~ spl12_31 ),
inference(avatar_contradiction_clause,[],[f580]) ).
fof(f592,plain,
( ! [X0] :
( ~ big_r(sK11(sK2),X0)
| ~ big_p(X0) )
| spl12_1
| ~ spl12_15
| spl12_30 ),
inference(forward_subsumption_resolution,[],[f409,f399]) ).
fof(f594,plain,
( ~ big_p(sK10(sK2))
| big_p(sK2)
| spl12_1
| ~ spl12_15
| spl12_30 ),
inference(resolution,[],[f592,f353]) ).
fof(f599,plain,
( big_p(sK2)
| spl12_1
| ~ spl12_15
| spl12_30 ),
inference(forward_subsumption_resolution,[],[f594,f346]) ).
fof(f600,plain,
( $false
| spl12_1
| ~ spl12_15
| spl12_30 ),
inference(forward_subsumption_resolution,[],[f599,f399]) ).
fof(f601,plain,
( spl12_1
| ~ spl12_15
| spl12_30 ),
inference(avatar_contradiction_clause,[],[f600]) ).
fof(f605,plain,
( big_p(a)
| spl12_1 ),
inference(forward_subsumption_resolution,[],[f26,f45]) ).
fof(f613,plain,
( $false
| spl12_1
| spl12_15 ),
inference(forward_subsumption_resolution,[],[f605,f186]) ).
fof(f614,plain,
( spl12_1
| spl12_15 ),
inference(avatar_contradiction_clause,[],[f613]) ).
cnf(s26,plain,
( ~ spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(sat_conversion,[],[f54]) ).
cnf(s169,plain,
( ~ spl12_1
| ~ spl12_2
| spl12_3 ),
inference(sat_conversion,[],[f182]) ).
cnf(s185,plain,
( spl12_2
| spl12_15 ),
inference(sat_conversion,[],[f193]) ).
cnf(s193,plain,
( spl12_2
| ~ spl12_17 ),
inference(sat_conversion,[],[f201]) ).
cnf(s299,plain,
( ~ spl12_1
| ~ spl12_15
| spl12_17 ),
inference(sat_conversion,[],[f335]) ).
cnf(s316,plain,
( spl12_1
| spl12_17 ),
inference(sat_conversion,[],[f344]) ).
cnf(s377,plain,
( spl12_1
| ~ spl12_30
| spl12_31 ),
inference(sat_conversion,[],[f404]) ).
cnf(s497,plain,
( spl12_1
| ~ spl12_15
| ~ spl12_17
| ~ spl12_30
| ~ spl12_31 ),
inference(sat_conversion,[],[f581]) ).
cnf(s519,plain,
( spl12_1
| ~ spl12_15
| spl12_30 ),
inference(sat_conversion,[],[f601]) ).
cnf(s533,plain,
( spl12_1
| spl12_15 ),
inference(sat_conversion,[],[f614]) ).
cnf(s534,plain,
spl12_1,
inference(rat,[],[s497,s377,s519,s316,s533]) ).
cnf(s535,plain,
~ spl12_2,
inference(rat,[],[s26,s169,s534]) ).
cnf(s536,plain,
~ spl12_17,
inference(rat,[],[s193,s535]) ).
cnf(s537,plain,
spl12_15,
inference(rat,[],[s185,s535]) ).
cnf(s540,plain,
$false,
inference(rat,[],[s299,s534,s536,s537]) ).
fof(f615,plain,
$false,
inference(avatar_sat_refutation,[],[s540]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN067+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n005.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 15:27:46 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.27 % (866682)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (866689)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4283824832:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.27 % (866688)% WARNING: option uhcvi not known.
% 0.20/0.27 % (866688)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=813801832:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.27 % (866687)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=533142365_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.27 % (866689) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-866682-866689"...
% 0.20/0.27 % (866690)dis+10_1_sil=32000:sp=arity:random_seed=513116143:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.27 % (866691)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1471749878:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.27 % (866692)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2636221962:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.27 % (866693)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2210694216:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.27 % (866689)...printing done.
% 0.20/0.27 % TRYING [1]
% 0.20/0.27 % TRYING [2]
% 0.20/0.27 % (866689)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (866689)------------------------------
% 0.20/0.27 % (866689)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (866689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (866689)CaDiCaL version: 2.1.3
% 0.20/0.27 % (866689)Termination reason: Refutation
% 0.20/0.27 % (866689)Time elapsed: 0.009 s
% 0.20/0.27 % (866689)Peak memory usage: 12 MB
% 0.20/0.27 % (866689)Instructions burned: 22 (million)
% 0.20/0.27 % (866682)Success in time 0.04 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------