%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n013.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 08:38:34 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 62 ( 6 unt; 0 typ; 5 def)
% Number of atoms : 447 ( 120 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 355 ( 72 ~; 105 |; 29 &; 138 @)
% ( 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 ) )
& ( ( cZ @ X0 )
| ( cX @ X0 ) ) )
<=> ( ( ( cY @ X0 )
& ( cX @ X0 ) )
| ( cZ @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM59_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a] :
( ( ( ( cZ @ X0 )
| ( cY @ X0 ) )
& ( ( cZ @ X0 )
| ( cX @ X0 ) ) )
<=> ( ( ( cY @ X0 )
& ( cX @ X0 ) )
| ( cZ @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a] :
( ( ( ( cZ @ X0 )
| ( cY @ X0 ) )
& ( ( cZ @ X0 )
| ( cX @ X0 ) ) )
<=> ( ( ( cY @ X0 )
& ( cX @ X0 ) )
| ( cZ @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a] :
( ( ( ( ( cZ @ X0 )
= $true )
| ( ( cY @ X0 )
= $true ) )
& ( ( ( cX @ X0 )
= $true )
| ( ( cZ @ X0 )
= $true ) ) )
<=> ( ( ( cZ @ X0 )
= $true )
| ( ( ( cY @ 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 ) ) )
<~> ( ( ( cZ @ X0 )
= $true )
| ( ( ( cY @ X0 )
= $true )
& ( ( cX @ X0 )
= $true ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,definition,
! [X0: a] :
( ( ( sP0 @ X0 )
= $true )
<=> ( ( ( ( cZ @ X0 )
= $true )
| ( ( cY @ X0 )
= $true ) )
& ( ( ( cX @ X0 )
= $true )
| ( ( cZ @ X0 )
= $true ) ) ) ),
introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction]) ).
thf(f7,plain,
? [X0: a] :
( ( ( sP0 @ X0 )
= $true )
<~> ( ( ( cZ @ X0 )
= $true )
| ( ( ( cY @ X0 )
= $true )
& ( ( cX @ X0 )
= $true ) ) ) ),
inference(definition_folding,[],[f5,f6]) ).
thf(f8,plain,
! [X0: a] :
( ( ( ( sP0 @ X0 )
= $true )
| ( ( ( cZ @ X0 )
!= $true )
& ( ( cY @ X0 )
!= $true ) )
| ( ( ( cX @ X0 )
!= $true )
& ( ( cZ @ X0 )
!= $true ) ) )
& ( ( ( ( ( cZ @ X0 )
= $true )
| ( ( cY @ X0 )
= $true ) )
& ( ( ( cX @ X0 )
= $true )
| ( ( cZ @ X0 )
= $true ) ) )
| ( ( sP0 @ X0 )
!= $true ) ) ),
inference(nnf_transformation,[],[f6]) ).
thf(f9,plain,
! [X0: a] :
( ( ( ( sP0 @ X0 )
= $true )
| ( ( ( cZ @ X0 )
!= $true )
& ( ( cY @ X0 )
!= $true ) )
| ( ( ( cX @ X0 )
!= $true )
& ( ( cZ @ X0 )
!= $true ) ) )
& ( ( ( ( ( cZ @ X0 )
= $true )
| ( ( cY @ X0 )
= $true ) )
& ( ( ( cX @ X0 )
= $true )
| ( ( cZ @ X0 )
= $true ) ) )
| ( ( sP0 @ X0 )
!= $true ) ) ),
inference(flattening,[],[f8]) ).
thf(f10,plain,
? [X0: a] :
( ( ( ( ( cZ @ X0 )
!= $true )
& ( ( ( cY @ X0 )
!= $true )
| ( ( cX @ X0 )
!= $true ) ) )
| ( ( sP0 @ X0 )
!= $true ) )
& ( ( ( cZ @ X0 )
= $true )
| ( ( ( cY @ X0 )
= $true )
& ( ( cX @ X0 )
= $true ) )
| ( ( sP0 @ X0 )
= $true ) ) ),
inference(nnf_transformation,[],[f7]) ).
thf(f11,plain,
? [X0: a] :
( ( ( ( ( cZ @ X0 )
!= $true )
& ( ( ( cY @ X0 )
!= $true )
| ( ( cX @ X0 )
!= $true ) ) )
| ( ( sP0 @ X0 )
!= $true ) )
& ( ( ( cZ @ X0 )
= $true )
| ( ( ( cY @ X0 )
= $true )
& ( ( cX @ X0 )
= $true ) )
| ( ( sP0 @ X0 )
= $true ) ) ),
inference(flattening,[],[f10]) ).
thf(f12,plain,
( ( ( ( ( cZ @ sK1 )
!= $true )
& ( ( $true
!= ( cY @ sK1 ) )
| ( $true
!= ( cX @ sK1 ) ) ) )
| ( $true
!= ( sP0 @ sK1 ) ) )
& ( ( ( cZ @ sK1 )
= $true )
| ( ( $true
= ( cY @ sK1 ) )
& ( $true
= ( cX @ sK1 ) ) )
| ( $true
= ( sP0 @ sK1 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f11]) ).
thf(f13,plain,
! [X0: a] :
( ( ( sP0 @ X0 )
!= $true )
| ( ( cX @ X0 )
= $true )
| ( ( cZ @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f14,plain,
! [X0: a] :
( ( ( sP0 @ X0 )
!= $true )
| ( ( cY @ X0 )
= $true )
| ( ( cZ @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,plain,
! [X0: a] :
( ( ( sP0 @ X0 )
= $true )
| ( ( cX @ X0 )
!= $true )
| ( ( cY @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f17,plain,
! [X0: a] :
( ( ( cZ @ X0 )
!= $true )
| ( ( cZ @ X0 )
!= $true )
| ( ( sP0 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f19,plain,
( ( $true
= ( sP0 @ sK1 ) )
| ( ( cZ @ sK1 )
= $true )
| ( $true
= ( cX @ sK1 ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f20,plain,
( ( $true
= ( sP0 @ sK1 ) )
| ( $true
= ( cY @ sK1 ) )
| ( ( cZ @ sK1 )
= $true ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f21,plain,
( ( $true
!= ( cY @ sK1 ) )
| ( $true
!= ( cX @ sK1 ) )
| ( $true
!= ( sP0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f22,plain,
( ( $true
!= ( sP0 @ sK1 ) )
| ( ( cZ @ sK1 )
!= $true ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f25,plain,
! [X0: a] :
( ( ( cZ @ X0 )
!= $true )
| ( ( sP0 @ X0 )
= $true ) ),
inference(duplicate_literal_removal,[],[f17]) ).
thf(f27,definition,
( spl2_1
<=> ( $true
= ( sP0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f28,plain,
( ( $true
!= ( sP0 @ sK1 ) )
| spl2_1 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f29,plain,
( ( $true
= ( sP0 @ sK1 ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f31,definition,
( spl2_2
<=> ( $true
= ( cX @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f35,definition,
( spl2_3
<=> ( ( cZ @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f36,plain,
( ( ( cZ @ sK1 )
!= $true )
| spl2_3 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f37,plain,
( ( ( cZ @ sK1 )
= $true )
| ~ 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(f39,plain,
( ~ spl2_3
| ~ spl2_1 ),
inference(avatar_split_clause,[],[f22,f27,f35]) ).
thf(f40,plain,
( ( $true
!= ( cY @ sK1 ) )
| ( $true
!= ( cX @ sK1 ) ) ),
inference(forward_subsumption_resolution,[],[f21,f16]) ).
thf(f41,plain,
( ( $true
= ( sP0 @ sK1 ) )
| ( $true
= ( cY @ sK1 ) ) ),
inference(forward_subsumption_resolution,[],[f20,f25]) ).
thf(f43,definition,
( spl2_4
<=> ( $true
= ( cY @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f45,plain,
( ( $true
!= ( cY @ sK1 ) )
| spl2_4 ),
inference(avatar_component_clause,[],[f43]) ).
thf(f46,plain,
( ~ spl2_4
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f40,f31,f43]) ).
thf(f47,plain,
( spl2_1
| spl2_4 ),
inference(avatar_split_clause,[],[f41,f43,f27]) ).
thf(f48,plain,
( ( $true != $true )
| ( $true
= ( sP0 @ sK1 ) )
| ~ spl2_3 ),
inference(constrained_superposition,[],[f25,f37]) ).
thf(f49,plain,
( ( $true
= ( sP0 @ sK1 ) )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f48]) ).
thf(f50,plain,
( $false
| spl2_1
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f49,f28]) ).
thf(f51,plain,
( spl2_1
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f50]) ).
thf(f52,plain,
( ( $true != $true )
| ( $true
= ( cX @ sK1 ) )
| ( ( cZ @ sK1 )
= $true )
| ~ spl2_1 ),
inference(constrained_superposition,[],[f13,f29]) ).
thf(f53,plain,
( ( $true
= ( cX @ sK1 ) )
| ( ( cZ @ sK1 )
= $true )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f52]) ).
thf(f54,plain,
( ( $true
= ( cX @ sK1 ) )
| ~ spl2_1
| spl2_3 ),
inference(forward_subsumption_resolution,[],[f53,f36]) ).
thf(f55,plain,
( spl2_2
| ~ spl2_1
| spl2_3 ),
inference(avatar_split_clause,[],[f54,f35,f27,f31]) ).
thf(f56,plain,
( ( ( cZ @ sK1 )
= $true )
| ( $true
= ( cY @ sK1 ) )
| ( $true != $true )
| ~ spl2_1 ),
inference(constrained_superposition,[],[f14,f29]) ).
thf(f57,plain,
( ( ( cZ @ sK1 )
= $true )
| ( $true
= ( cY @ sK1 ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f56]) ).
thf(f58,plain,
( ( $true
= ( cY @ sK1 ) )
| ~ spl2_1
| spl2_3 ),
inference(forward_subsumption_resolution,[],[f57,f36]) ).
thf(f59,plain,
( $false
| ~ spl2_1
| spl2_3
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f58,f45]) ).
thf(f60,plain,
( ~ spl2_1
| spl2_3
| spl2_4 ),
inference(avatar_contradiction_clause,[],[f59]) ).
cnf(s1,plain,
( spl2_1
| spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f38]) ).
cnf(s2,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(sat_conversion,[],[f39]) ).
cnf(s3,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(sat_conversion,[],[f46]) ).
cnf(s4,plain,
( spl2_1
| spl2_4 ),
inference(sat_conversion,[],[f47]) ).
cnf(s5,plain,
( spl2_1
| ~ spl2_3 ),
inference(sat_conversion,[],[f51]) ).
cnf(s6,plain,
( ~ spl2_1
| spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f55]) ).
cnf(s7,plain,
( ~ spl2_1
| spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f60]) ).
cnf(s8,plain,
spl2_1,
inference(rat,[],[s3,s1,s4,s5]) ).
cnf(s9,plain,
~ spl2_3,
inference(rat,[],[s2,s8]) ).
cnf(s10,plain,
spl2_4,
inference(rat,[],[s7,s8,s9]) ).
cnf(s11,plain,
spl2_2,
inference(rat,[],[s6,s8,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s3,s10,s11]) ).
thf(f61,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----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 THM
% 0.08/0.19 % Computer : n013.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 15:43:36 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.29 % (2274861)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (2274866)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=750919053:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (2274866) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2274861-2274866"...
% 0.21/0.29 % (2274866)...printing done.
% 0.21/0.29 % (2274866)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (2274866)------------------------------
% 0.21/0.29 % (2274866)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2274866)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2274866)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2274866)Termination reason: Refutation
% 0.21/0.29 % (2274866)Time elapsed: 0.002 s
% 0.21/0.29 % (2274866)Peak memory usage: 13 MB
% 0.21/0.29 % (2274866)Instructions burned: 4 (million)
% 0.21/0.29 % (2274861)Success in time 0.037 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------