%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO111^5 : 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 : n018.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 08:46:38 AM UTC 2026
% Result : Theorem 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 10 unt; 0 typ; 3 def)
% Number of atoms : 332 ( 86 equ; 0 cnn)
% Maximal formula atoms : 12 ( 9 avg)
% Number of connectives : 335 ( 99 ~; 83 |; 24 &; 121 @)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 16 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 72 !; 38 ?; 110 :)
% 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,
( ( ~ ( ? [X3: $i] : ( cN @ X3 )
| ! [X2: $i] : ( cM @ X2 ) )
| ~ ( ~ ! [X5: $i] : ( cG @ X5 )
| ! [X4: $i] :
~ ( cN @ X4 ) )
| ! [X0: $i] : ( cM @ X0 )
| ? [X1: $i] :
~ ( cG @ X1 ) )
=> ( ! [X0: $i] : ( cM @ X0 )
| ~ ! [X2: $i] :
( ( cM @ X2 )
| ? [X3: $i] : ( cN @ X3 ) )
| ? [X1: $i] :
~ ( cG @ X1 )
| ~ ! [X4: $i] :
( ~ ( cN @ X4 )
| ~ ! [X5: $i] : ( cG @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM80) ).
thf(f2,negated_conjecture,
~ ( ( ~ ( ? [X3: $i] : ( cN @ X3 )
| ! [X2: $i] : ( cM @ X2 ) )
| ~ ( ~ ! [X5: $i] : ( cG @ X5 )
| ! [X4: $i] :
~ ( cN @ X4 ) )
| ! [X0: $i] : ( cM @ X0 )
| ? [X1: $i] :
~ ( cG @ X1 ) )
=> ( ! [X0: $i] : ( cM @ X0 )
| ~ ! [X2: $i] :
( ( cM @ X2 )
| ? [X3: $i] : ( cN @ X3 ) )
| ? [X1: $i] :
~ ( cG @ X1 )
| ~ ! [X4: $i] :
( ~ ( cN @ X4 )
| ~ ! [X5: $i] : ( cG @ X5 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ~ ( ? [X0: $i] : ( cN @ X0 )
| ! [X1: $i] : ( cM @ X1 ) )
| ~ ( ~ ! [X2: $i] : ( cG @ X2 )
| ! [X3: $i] :
~ ( cN @ X3 ) )
| ! [X4: $i] : ( cM @ X4 )
| ? [X5: $i] :
~ ( cG @ X5 ) )
=> ( ! [X6: $i] : ( cM @ X6 )
| ~ ! [X7: $i] :
( ( cM @ X7 )
| ? [X8: $i] : ( cN @ X8 ) )
| ? [X9: $i] :
~ ( cG @ X9 )
| ~ ! [X10: $i] :
( ~ ( cN @ X10 )
| ~ ! [X11: $i] : ( cG @ X11 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ~ ( ! [X1: $i] :
( $true
= ( cM @ X1 ) )
| ? [X0: $i] :
( $true
= ( cN @ X0 ) ) )
| ~ ( ~ ! [X2: $i] :
( $true
= ( cG @ X2 ) )
| ! [X3: $i] :
( ( cN @ X3 )
!= $true ) )
| ! [X4: $i] :
( $true
= ( cM @ X4 ) )
| ? [X5: $i] :
( ( cG @ X5 )
!= $true ) )
=> ( ! [X6: $i] :
( $true
= ( cM @ X6 ) )
| ~ ! [X7: $i] :
( ? [X8: $i] :
( ( cN @ X8 )
= $true )
| ( $true
= ( cM @ X7 ) ) )
| ? [X9: $i] :
( $true
!= ( cG @ X9 ) )
| ~ ! [X10: $i] :
( ( $true
!= ( cN @ X10 ) )
| ~ ! [X11: $i] :
( ( cG @ X11 )
= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ( ( ~ ( ! [X1: $i] :
( $true
= ( cM @ X1 ) )
| ? [X0: $i] :
( $true
= ( cN @ X0 ) ) )
| ~ ( ! [X3: $i] :
( ( cN @ X3 )
!= $true )
| ~ ! [X2: $i] :
( $true
= ( cG @ X2 ) ) )
| ? [X5: $i] :
( ( cG @ X5 )
!= $true )
| ! [X4: $i] :
( $true
= ( cM @ X4 ) ) )
=> ( ? [X9: $i] :
( $true
!= ( cG @ X9 ) )
| ~ ! [X7: $i] :
( ? [X8: $i] :
( ( cN @ X8 )
= $true )
| ( $true
= ( cM @ X7 ) ) )
| ! [X6: $i] :
( $true
= ( cM @ X6 ) )
| ~ ! [X10: $i] :
( ~ ! [X11: $i] :
( ( cG @ X11 )
= $true )
| ( $true
!= ( cN @ X10 ) ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ! [X9: $i] :
( $true
= ( cG @ X9 ) )
& ! [X7: $i] :
( ? [X8: $i] :
( ( cN @ X8 )
= $true )
| ( $true
= ( cM @ X7 ) ) )
& ? [X6: $i] :
( $true
!= ( cM @ X6 ) )
& ! [X10: $i] :
( ( $true
!= ( cN @ X10 ) )
| ? [X11: $i] :
( ( cG @ X11 )
!= $true ) )
& ( ( ? [X3: $i] :
( ( cN @ X3 )
= $true )
& ! [X2: $i] :
( $true
= ( cG @ X2 ) ) )
| ! [X4: $i] :
( $true
= ( cM @ X4 ) )
| ? [X5: $i] :
( ( cG @ X5 )
!= $true )
| ( ? [X1: $i] :
( $true
!= ( cM @ X1 ) )
& ! [X0: $i] :
( $true
!= ( cN @ X0 ) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ( ( ? [X3: $i] :
( ( cN @ X3 )
= $true )
& ! [X2: $i] :
( $true
= ( cG @ X2 ) ) )
| ! [X4: $i] :
( $true
= ( cM @ X4 ) )
| ? [X5: $i] :
( ( cG @ X5 )
!= $true )
| ( ? [X1: $i] :
( $true
!= ( cM @ X1 ) )
& ! [X0: $i] :
( $true
!= ( cN @ X0 ) ) ) )
& ! [X9: $i] :
( $true
= ( cG @ X9 ) )
& ! [X10: $i] :
( ( $true
!= ( cN @ X10 ) )
| ? [X11: $i] :
( ( cG @ X11 )
!= $true ) )
& ! [X7: $i] :
( ? [X8: $i] :
( ( cN @ X8 )
= $true )
| ( $true
= ( cM @ X7 ) ) )
& ? [X6: $i] :
( $true
!= ( cM @ X6 ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
( ( ( ? [X0: $i] :
( $true
= ( cN @ X0 ) )
& ! [X1: $i] :
( ( cG @ X1 )
= $true ) )
| ! [X2: $i] :
( ( cM @ X2 )
= $true )
| ? [X3: $i] :
( $true
!= ( cG @ X3 ) )
| ( ? [X4: $i] :
( $true
!= ( cM @ X4 ) )
& ! [X5: $i] :
( $true
!= ( cN @ X5 ) ) ) )
& ! [X6: $i] :
( $true
= ( cG @ X6 ) )
& ! [X7: $i] :
( ( ( cN @ X7 )
!= $true )
| ? [X8: $i] :
( $true
!= ( cG @ X8 ) ) )
& ! [X9: $i] :
( ? [X10: $i] :
( $true
= ( cN @ X10 ) )
| ( ( cM @ X9 )
= $true ) )
& ? [X11: $i] :
( ( cM @ X11 )
!= $true ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ( ( ( $true
= ( cN @ sK0 ) )
& ! [X1: $i] :
( ( cG @ X1 )
= $true ) )
| ! [X2: $i] :
( ( cM @ X2 )
= $true )
| ( $true
!= ( cG @ sK1 ) )
| ( ( ( cM @ sK2 )
!= $true )
& ! [X5: $i] :
( $true
!= ( cN @ X5 ) ) ) )
& ! [X6: $i] :
( $true
= ( cG @ X6 ) )
& ! [X7: $i] :
( ( ( cN @ X7 )
!= $true )
| ( $true
!= ( cG @ sK3 ) ) )
& ! [X9: $i] :
( ( $true
= ( cN @ sK4 ) )
| ( ( cM @ X9 )
= $true ) )
& ( $true
!= ( cM @ sK5 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X3,sK1),skolemize(X4,sK2),skolemize(X8,sK3),skolemize(X10,sK4),skolemize(X11,sK5)],[f8]) ).
thf(f10,plain,
( $true
!= ( cM @ sK5 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
! [X9: $i] :
( ( $true
= ( cN @ sK4 ) )
| ( ( cM @ X9 )
= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
! [X7: $i] :
( ( $true
!= ( cG @ sK3 ) )
| ( ( cN @ X7 )
!= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
! [X6: $i] :
( $true
= ( cG @ X6 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f21,definition,
( spl6_1
<=> ( $true
= ( cN @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f23,plain,
( ( $true
= ( cN @ sK4 ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f21]) ).
thf(f25,definition,
( spl6_2
<=> ! [X9: $i] :
( ( cM @ X9 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f26,plain,
( ! [X9: $i] :
( ( cM @ X9 )
= $true )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f25]) ).
thf(f27,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f11,f25,f21]) ).
thf(f37,definition,
( spl6_5
<=> ! [X5: $i] :
( $true
!= ( cN @ X5 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
thf(f38,plain,
( ! [X5: $i] :
( $true
!= ( cN @ X5 ) )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f40,plain,
! [X7: $i] :
( ( cN @ X7 )
!= $true ),
inference(forward_subsumption_resolution,[],[f12,f13]) ).
thf(f42,plain,
spl6_5,
inference(avatar_split_clause,[],[f40,f37]) ).
thf(f48,plain,
( ( $true != $true )
| ~ spl6_2 ),
inference(constrained_superposition,[],[f10,f26]) ).
thf(f49,plain,
( $false
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f48]) ).
thf(f50,plain,
~ spl6_2,
inference(avatar_contradiction_clause,[],[f49]) ).
thf(f51,plain,
( $false
| ~ spl6_1
| ~ spl6_5 ),
inference(forward_subsumption_resolution,[],[f23,f38]) ).
thf(f52,plain,
( ~ spl6_1
| ~ spl6_5 ),
inference(avatar_contradiction_clause,[],[f51]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f27]) ).
cnf(s3,plain,
spl6_5,
inference(sat_conversion,[],[f42]) ).
cnf(s5,plain,
~ spl6_2,
inference(sat_conversion,[],[f50]) ).
cnf(s6,plain,
( ~ spl6_1
| ~ spl6_5 ),
inference(sat_conversion,[],[f52]) ).
cnf(s8,plain,
~ spl6_1,
inference(rat,[],[s6,s3]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s5,s8]) ).
thf(f53,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO111^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n018.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:36:27 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.22 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
% 0.19/0.26 % (302661)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.26 % (302667)lrs+10_16_si=on:nwc=1.5:random_seed=3129045292:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.26 % (302667) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-302661-302667"...
% 0.19/0.26 % (302667)...printing done.
% 0.19/0.26 % (302667)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Theorem for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.26 % (302667)------------------------------
% 0.19/0.26 % (302667)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.26 % (302667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.26 % (302667)CaDiCaL version: 2.1.3
% 0.19/0.26 % (302667)Termination reason: Refutation
% 0.19/0.26 % (302667)Time elapsed: 0.001 s
% 0.19/0.26 % (302667)Peak memory usage: 13 MB
% 0.19/0.26 % (302667)Instructions burned: 3 (million)
% 0.19/0.26 % (302661)Success in time 0.033 s
% 0.19/0.26 % Vampire exiting
%------------------------------------------------------------------------------