%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO099^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:46:37 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 10 unt; 0 typ; 4 def)
% Number of atoms : 199 ( 45 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 184 ( 61 ~; 48 |; 9 &; 62 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 36 !; 16 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cG: $i > $o ).
thf(func_def_1,type,
cN: $i > $o ).
thf(func_def_2,type,
cM: $i > $o ).
thf(f1,conjecture,
( ! [X0: $i] : ( cM @ X0 )
| ~ ( ~ ! [X5: $i] : ( cG @ X5 )
| ! [X4: $i] :
~ ( cN @ X4 ) )
| ? [X1: $i] :
~ ( cG @ X1 )
| ~ ( ! [X2: $i] : ( cM @ X2 )
| ? [X3: $i] : ( cN @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM78) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] : ( cM @ X0 )
| ~ ( ~ ! [X5: $i] : ( cG @ X5 )
| ! [X4: $i] :
~ ( cN @ X4 ) )
| ? [X1: $i] :
~ ( cG @ X1 )
| ~ ( ! [X2: $i] : ( cM @ X2 )
| ? [X3: $i] : ( cN @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i] : ( cM @ X0 )
| ~ ( ~ ! [X1: $i] : ( cG @ X1 )
| ! [X2: $i] :
~ ( cN @ X2 ) )
| ? [X3: $i] :
~ ( cG @ X3 )
| ~ ( ! [X4: $i] : ( cM @ X4 )
| ? [X5: $i] : ( cN @ X5 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
( ( cM @ X0 )
= $true )
| ~ ( ~ ! [X1: $i] :
( ( cG @ X1 )
= $true )
| ! [X2: $i] :
( ( cN @ X2 )
!= $true ) )
| ? [X3: $i] :
( $true
!= ( cG @ X3 ) )
| ~ ( ! [X4: $i] :
( ( cM @ X4 )
= $true )
| ? [X5: $i] :
( $true
= ( cN @ X5 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ( ! [X0: $i] :
( ( cM @ X0 )
= $true )
| ? [X3: $i] :
( $true
!= ( cG @ X3 ) )
| ~ ( ! [X4: $i] :
( ( cM @ X4 )
= $true )
| ? [X5: $i] :
( $true
= ( cN @ X5 ) ) )
| ~ ( ~ ! [X1: $i] :
( ( cG @ X1 )
= $true )
| ! [X2: $i] :
( ( cN @ X2 )
!= $true ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ( ! [X4: $i] :
( ( cM @ X4 )
= $true )
| ? [X5: $i] :
( $true
= ( cN @ X5 ) ) )
& ( ? [X1: $i] :
( ( cG @ X1 )
!= $true )
| ! [X2: $i] :
( ( cN @ X2 )
!= $true ) )
& ? [X0: $i] :
( ( cM @ X0 )
!= $true )
& ! [X3: $i] :
( $true
= ( cG @ X3 ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ( ! [X0: $i] :
( ( cM @ X0 )
= $true )
| ? [X1: $i] :
( $true
= ( cN @ X1 ) ) )
& ( ? [X2: $i] :
( $true
!= ( cG @ X2 ) )
| ! [X3: $i] :
( ( cN @ X3 )
!= $true ) )
& ? [X4: $i] :
( ( cM @ X4 )
!= $true )
& ! [X5: $i] :
( ( cG @ X5 )
= $true ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ! [X0: $i] :
( ( cM @ X0 )
= $true )
| ( $true
= ( cN @ sK0 ) ) )
& ( ( $true
!= ( cG @ sK1 ) )
| ! [X3: $i] :
( ( cN @ X3 )
!= $true ) )
& ( $true
!= ( cM @ sK2 ) )
& ! [X5: $i] :
( ( cG @ X5 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X1,sK0),skolemize(X2,sK1),skolemize(X4,sK2)],[f7]) ).
thf(f9,plain,
! [X5: $i] :
( ( cG @ X5 )
= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( $true
!= ( cM @ sK2 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
! [X3: $i] :
( ( $true
!= ( cG @ sK1 ) )
| ( ( cN @ X3 )
!= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
! [X0: $i] :
( ( $true
= ( cN @ sK0 ) )
| ( ( cM @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,definition,
( spl3_1
<=> ! [X3: $i] :
( ( cN @ X3 )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f17,plain,
( ! [X3: $i] :
( ( cN @ X3 )
!= $true )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f16]) ).
thf(f19,definition,
( spl3_2
<=> ( $true
= ( cG @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f21,plain,
( ( $true
!= ( cG @ sK1 ) )
| spl3_2 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f22,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f11,f19,f16]) ).
thf(f24,definition,
( spl3_3
<=> ! [X0: $i] :
( ( cM @ X0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f25,plain,
( ! [X0: $i] :
( ( cM @ X0 )
= $true )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f27,definition,
( spl3_4
<=> ( $true
= ( cN @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f29,plain,
( ( $true
= ( cN @ sK0 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f30,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f12,f27,f24]) ).
thf(f31,plain,
( $false
| spl3_2 ),
inference(forward_subsumption_resolution,[],[f21,f9]) ).
thf(f32,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f31]) ).
thf(f33,plain,
( ( $true != $true )
| ~ spl3_3 ),
inference(constrained_superposition,[],[f10,f25]) ).
thf(f34,plain,
( $false
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f35,plain,
~ spl3_3,
inference(avatar_contradiction_clause,[],[f34]) ).
thf(f36,plain,
( $false
| ~ spl3_1
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f29,f17]) ).
thf(f37,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f36]) ).
cnf(s1,plain,
( spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s2,plain,
( spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f30]) ).
cnf(s3,plain,
spl3_2,
inference(sat_conversion,[],[f32]) ).
cnf(s4,plain,
~ spl3_3,
inference(sat_conversion,[],[f35]) ).
cnf(s5,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(sat_conversion,[],[f37]) ).
cnf(s6,plain,
spl3_4,
inference(rat,[],[s2,s4]) ).
cnf(s7,plain,
~ spl3_1,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s3,s7]) ).
thf(f38,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO099^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n016.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 16:38:35 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.30 % (574349)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (574354)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1548556265:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.30 % (574354) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-574349-574354"...
% 0.21/0.30 % (574354)...printing done.
% 0.21/0.30 % (574354)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (574354)------------------------------
% 0.21/0.30 % (574354)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (574354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (574354)CaDiCaL version: 2.1.3
% 0.21/0.30 % (574354)Termination reason: Refutation
% 0.21/0.30 % (574354)Time elapsed: 0.002 s
% 0.21/0.30 % (574354)Peak memory usage: 13 MB
% 0.21/0.30 % (574354)Instructions burned: 2 (million)
% 0.21/0.30 % (574349)Success in time 0.036 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------