%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV397^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 : Wed Sep 30 08:39:27 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 71 ( 6 unt; 0 typ; 5 def)
% Number of atoms : 489 ( 125 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 399 ( 89 ~; 128 |; 29 &; 142 @)
% ( 9 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 12 !; 4 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cZ: a > $o ).
thf(func_def_1,type,
cY: a > $o ).
thf(func_def_2,type,
cX: a > $o ).
thf(func_def_6,type,
sP0: a > $o ).
thf(func_def_7,type,
sK1: a ).
thf(f1,conjecture,
! [X0: a] :
( ( ( cZ @ X0 )
| ( ( cY @ X0 )
& ( cX @ X0 ) ) )
<=> ( ( ( cZ @ X0 )
| ( cY @ X0 ) )
& ( ( cZ @ X0 )
| ( cX @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM59_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a] :
( ( ( cZ @ X0 )
| ( ( cY @ X0 )
& ( cX @ X0 ) ) )
<=> ( ( ( cZ @ X0 )
| ( cY @ X0 ) )
& ( ( cZ @ X0 )
| ( cX @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a] :
( ( ( cZ @ X0 )
| ( ( cY @ X0 )
& ( cX @ X0 ) ) )
<=> ( ( ( cZ @ X0 )
| ( cY @ X0 ) )
& ( ( cZ @ X0 )
| ( cX @ X0 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a] :
( ( ( ( cZ @ X0 )
= $true )
| ( ( ( cY @ X0 )
= $true )
& ( ( cX @ X0 )
= $true ) ) )
<=> ( ( ( ( cZ @ X0 )
= $true )
| ( ( cY @ X0 )
= $true ) )
& ( ( ( cZ @ X0 )
= $true )
| ( ( cX @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a] :
( ( ( ( cZ @ X0 )
= $true )
| ( ( ( cY @ X0 )
= $true )
& ( ( cX @ X0 )
= $true ) ) )
<~> ( ( ( ( cZ @ X0 )
= $true )
| ( ( cY @ X0 )
= $true ) )
& ( ( ( cZ @ X0 )
= $true )
| ( ( cX @ X0 )
= $true ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,definition,
! [X0: a] :
( ( $true
= ( sP0 @ X0 ) )
<=> ( ( ( ( cZ @ X0 )
= $true )
| ( ( cY @ X0 )
= $true ) )
& ( ( ( cZ @ X0 )
= $true )
| ( ( cX @ X0 )
= $true ) ) ) ),
introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction]) ).
thf(f7,plain,
? [X0: a] :
( ( ( ( cZ @ X0 )
= $true )
| ( ( ( cY @ X0 )
= $true )
& ( ( cX @ X0 )
= $true ) ) )
<~> ( $true
= ( sP0 @ X0 ) ) ),
inference(definition_folding,[],[f5,f6]) ).
thf(f8,plain,
! [X0: a] :
( ( ( $true
= ( sP0 @ X0 ) )
| ( ( ( cZ @ X0 )
!= $true )
& ( ( cY @ X0 )
!= $true ) )
| ( ( ( cZ @ X0 )
!= $true )
& ( ( cX @ X0 )
!= $true ) ) )
& ( ( ( ( ( cZ @ X0 )
= $true )
| ( ( cY @ X0 )
= $true ) )
& ( ( ( cZ @ X0 )
= $true )
| ( ( cX @ X0 )
= $true ) ) )
| ( $true
!= ( sP0 @ X0 ) ) ) ),
inference(nnf_transformation,[],[f6]) ).
thf(f9,plain,
! [X0: a] :
( ( ( $true
= ( sP0 @ X0 ) )
| ( ( ( cZ @ X0 )
!= $true )
& ( ( cY @ X0 )
!= $true ) )
| ( ( ( cZ @ X0 )
!= $true )
& ( ( cX @ X0 )
!= $true ) ) )
& ( ( ( ( ( cZ @ X0 )
= $true )
| ( ( cY @ X0 )
= $true ) )
& ( ( ( cZ @ X0 )
= $true )
| ( ( cX @ X0 )
= $true ) ) )
| ( $true
!= ( sP0 @ X0 ) ) ) ),
inference(flattening,[],[f8]) ).
thf(f10,plain,
? [X0: a] :
( ( ( $true
!= ( sP0 @ X0 ) )
| ( ( ( cZ @ X0 )
!= $true )
& ( ( ( cY @ X0 )
!= $true )
| ( ( cX @ X0 )
!= $true ) ) ) )
& ( ( $true
= ( sP0 @ X0 ) )
| ( ( cZ @ X0 )
= $true )
| ( ( ( cY @ X0 )
= $true )
& ( ( cX @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f7]) ).
thf(f11,plain,
? [X0: a] :
( ( ( $true
!= ( sP0 @ X0 ) )
| ( ( ( cZ @ X0 )
!= $true )
& ( ( ( cY @ X0 )
!= $true )
| ( ( cX @ X0 )
!= $true ) ) ) )
& ( ( $true
= ( sP0 @ X0 ) )
| ( ( cZ @ X0 )
= $true )
| ( ( ( cY @ X0 )
= $true )
& ( ( cX @ X0 )
= $true ) ) ) ),
inference(flattening,[],[f10]) ).
thf(f12,plain,
( ( ( $true
!= ( sP0 @ sK1 ) )
| ( ( $true
!= ( cZ @ sK1 ) )
& ( ( $true
!= ( cY @ sK1 ) )
| ( $true
!= ( cX @ sK1 ) ) ) ) )
& ( ( $true
= ( sP0 @ sK1 ) )
| ( $true
= ( cZ @ sK1 ) )
| ( ( $true
= ( cY @ sK1 ) )
& ( $true
= ( cX @ sK1 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f11]) ).
thf(f13,plain,
! [X0: a] :
( ( $true
!= ( sP0 @ X0 ) )
| ( ( cX @ X0 )
= $true )
| ( ( cZ @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f14,plain,
! [X0: a] :
( ( $true
!= ( sP0 @ X0 ) )
| ( ( cY @ X0 )
= $true )
| ( ( cZ @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,plain,
! [X0: a] :
( ( ( cX @ X0 )
!= $true )
| ( ( cY @ X0 )
!= $true )
| ( $true
= ( sP0 @ X0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f18,plain,
! [X0: a] :
( ( $true
= ( sP0 @ X0 ) )
| ( ( cZ @ X0 )
!= $true )
| ( ( cZ @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f19,plain,
( ( $true
= ( sP0 @ sK1 ) )
| ( $true
= ( cZ @ sK1 ) )
| ( $true
= ( cX @ sK1 ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f20,plain,
( ( $true
= ( sP0 @ sK1 ) )
| ( $true
= ( cZ @ sK1 ) )
| ( $true
= ( cY @ sK1 ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f21,plain,
( ( $true
!= ( sP0 @ sK1 ) )
| ( $true
!= ( cY @ sK1 ) )
| ( $true
!= ( cX @ sK1 ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f22,plain,
( ( $true
!= ( sP0 @ sK1 ) )
| ( $true
!= ( cZ @ sK1 ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f25,plain,
! [X0: a] :
( ( ( cZ @ X0 )
!= $true )
| ( $true
= ( sP0 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f18]) ).
thf(f27,definition,
( spl2_1
<=> ( $true
= ( cX @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f28,plain,
( ( $true
!= ( cX @ sK1 ) )
| spl2_1 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f29,plain,
( ( $true
= ( cX @ sK1 ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f31,definition,
( spl2_2
<=> ( $true
= ( cZ @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f32,plain,
( ( $true
!= ( cZ @ sK1 ) )
| spl2_2 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f33,plain,
( ( $true
= ( cZ @ sK1 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f35,definition,
( spl2_3
<=> ( $true
= ( sP0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f36,plain,
( ( $true
!= ( sP0 @ sK1 ) )
| spl2_3 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f37,plain,
( ( $true
= ( sP0 @ sK1 ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f38,plain,
( spl2_1
| spl2_2
| spl2_3 ),
inference(avatar_split_clause,[],[f19,f35,f31,f27]) ).
thf(f40,definition,
( spl2_4
<=> ( $true
= ( cY @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f41,plain,
( ( $true
!= ( cY @ sK1 ) )
| spl2_4 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f42,plain,
( ( $true
= ( cY @ sK1 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f43,plain,
( spl2_4
| spl2_2
| spl2_3 ),
inference(avatar_split_clause,[],[f20,f35,f31,f40]) ).
thf(f44,plain,
( ~ spl2_1
| ~ spl2_4
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f21,f35,f40,f27]) ).
thf(f45,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f22,f35,f31]) ).
thf(f58,plain,
( ( $true != $true )
| ( $true
= ( sP0 @ sK1 ) )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f25,f33]) ).
thf(f61,plain,
( ( $true
= ( sP0 @ sK1 ) )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f58]) ).
thf(f62,plain,
( $false
| ~ spl2_2
| spl2_3 ),
inference(forward_subsumption_resolution,[],[f61,f36]) ).
thf(f63,plain,
( ~ spl2_2
| spl2_3 ),
inference(avatar_contradiction_clause,[],[f62]) ).
thf(f86,plain,
( ( $true != $true )
| ( $true
!= ( cY @ sK1 ) )
| ( $true
= ( sP0 @ sK1 ) )
| ~ spl2_1 ),
inference(constrained_superposition,[],[f15,f29]) ).
thf(f89,plain,
( ( $true
!= ( cY @ sK1 ) )
| ( $true
= ( sP0 @ sK1 ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f86]) ).
thf(f90,plain,
( ( $true
= ( sP0 @ sK1 ) )
| ~ spl2_1
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f89,f42]) ).
thf(f91,plain,
( $false
| ~ spl2_1
| spl2_3
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f90,f36]) ).
thf(f92,plain,
( ~ spl2_1
| spl2_3
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f91]) ).
thf(f93,plain,
( ( $true != $true )
| ( $true
= ( cY @ sK1 ) )
| ( $true
= ( cZ @ sK1 ) )
| ~ spl2_3 ),
inference(constrained_superposition,[],[f14,f37]) ).
thf(f94,plain,
( ( $true != $true )
| ( $true
= ( cX @ sK1 ) )
| ( $true
= ( cZ @ sK1 ) )
| ~ spl2_3 ),
inference(constrained_superposition,[],[f13,f37]) ).
thf(f95,plain,
( ( $true
= ( cX @ sK1 ) )
| ( $true
= ( cZ @ sK1 ) )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f94]) ).
thf(f96,plain,
( ( $true
= ( cY @ sK1 ) )
| ( $true
= ( cZ @ sK1 ) )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f93]) ).
thf(f97,plain,
( ( $true
= ( cZ @ sK1 ) )
| ~ spl2_3
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f96,f41]) ).
thf(f98,plain,
( $false
| spl2_2
| ~ spl2_3
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f97,f32]) ).
thf(f99,plain,
( spl2_2
| ~ spl2_3
| spl2_4 ),
inference(avatar_contradiction_clause,[],[f98]) ).
thf(f100,plain,
( ( $true
= ( cZ @ sK1 ) )
| spl2_1
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f95,f28]) ).
thf(f101,plain,
( $false
| spl2_1
| spl2_2
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f100,f32]) ).
thf(f102,plain,
( spl2_1
| spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f101]) ).
cnf(s1,plain,
( spl2_1
| spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f38]) ).
cnf(s2,plain,
( spl2_2
| spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f43]) ).
cnf(s3,plain,
( ~ spl2_1
| ~ spl2_3
| ~ spl2_4 ),
inference(sat_conversion,[],[f44]) ).
cnf(s4,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f45]) ).
cnf(s5,plain,
( ~ spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f63]) ).
cnf(s6,plain,
( ~ spl2_1
| spl2_3
| ~ spl2_4 ),
inference(sat_conversion,[],[f92]) ).
cnf(s7,plain,
( spl2_2
| ~ spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f99]) ).
cnf(s8,plain,
( spl2_1
| spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f102]) ).
cnf(s9,plain,
( spl2_2
| spl2_1 ),
inference(rat,[],[s1,s8]) ).
cnf(s10,plain,
~ spl2_2,
inference(rat,[],[s4,s5]) ).
cnf(s11,plain,
spl2_1,
inference(rat,[],[s9,s10]) ).
cnf(s12,plain,
spl2_3,
inference(rat,[],[s6,s2,s11,s10]) ).
cnf(s13,plain,
spl2_4,
inference(rat,[],[s7,s10,s12]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s3,s11,s13,s12]) ).
thf(f103,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV397^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n008.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 15:44:54 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.26 % (3321341)Will run a generic schedule for satisfiability detection.
% 0.10/0.26 % (3321351)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1337820646:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.26 % (3321351) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3321341-3321351"...
% 0.10/0.26 % (3321347)% WARNING: option uhcvi not known.
% 0.10/0.26 % (3321351)...printing done.
% 0.10/0.26 % (3321351)Refutation found. Thanks to Tanya!
% 0.10/0.26 % SZS status Theorem for theBenchmark
% 0.10/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.26 % (3321351)------------------------------
% 0.10/0.26 % (3321351)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.26 % (3321351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.26 % (3321351)CaDiCaL version: 2.1.3
% 0.10/0.26 % (3321351)Termination reason: Refutation
% 0.10/0.26 % (3321351)Time elapsed: 0.003 s
% 0.10/0.26 % (3321351)Peak memory usage: 13 MB
% 0.10/0.26 % (3321351)Instructions burned: 5 (million)
% 0.10/0.26 % (3321341)Success in time 0.03 s
% 0.10/0.26 % Vampire exiting
%------------------------------------------------------------------------------