%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO104^5 : 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 : n011.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 08:48:58 AM UTC 2026
% Result : Theorem 0.11s 0.28s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 8 unt; 0 typ; 6 def)
% Number of atoms : 344 ( 60 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 279 ( 49 ~; 53 |; 22 &; 144 @)
% ( 10 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 3 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; 12 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 35 !; 9 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
cQ: $i > $i > $o ).
thf(func_def_2,type,
cP: $i > $i > $o ).
thf(f1,conjecture,
( ! [X0: $i] :
( ( cQ @ X0 @ y )
& ( cP @ X0 @ y ) )
<=> ( ! [X0: $i] : ( cQ @ X0 @ y )
& ! [X0: $i] : ( cP @ X0 @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTTTP2129) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] :
( ( cQ @ X0 @ y )
& ( cP @ X0 @ y ) )
<=> ( ! [X0: $i] : ( cQ @ X0 @ y )
& ! [X0: $i] : ( cP @ X0 @ y ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i] :
( ( cQ @ X0 @ y )
& ( cP @ X0 @ y ) )
<=> ( ! [X1: $i] : ( cQ @ X1 @ y )
& ! [X2: $i] : ( cP @ X2 @ y ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
( ( ( cQ @ X0 @ y )
= $true )
& ( ( cP @ X0 @ y )
= $true ) )
<=> ( ! [X1: $i] :
( ( cQ @ X1 @ y )
= $true )
& ! [X2: $i] :
( ( cP @ X2 @ y )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X0: $i] :
( ( ( cQ @ X0 @ y )
= $true )
& ( ( cP @ X0 @ y )
= $true ) )
<~> ( ! [X1: $i] :
( ( cQ @ X1 @ y )
= $true )
& ! [X2: $i] :
( ( cP @ X2 @ y )
= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ? [X1: $i] :
( ( cQ @ X1 @ y )
!= $true )
| ? [X2: $i] :
( ( cP @ X2 @ y )
!= $true )
| ? [X0: $i] :
( ( ( cQ @ X0 @ y )
!= $true )
| ( ( cP @ X0 @ y )
!= $true ) ) )
& ( ( ! [X1: $i] :
( ( cQ @ X1 @ y )
= $true )
& ! [X2: $i] :
( ( cP @ X2 @ y )
= $true ) )
| ! [X0: $i] :
( ( ( cQ @ X0 @ y )
= $true )
& ( ( cP @ X0 @ y )
= $true ) ) ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f7,plain,
( ( ? [X1: $i] :
( ( cQ @ X1 @ y )
!= $true )
| ? [X2: $i] :
( ( cP @ X2 @ y )
!= $true )
| ? [X0: $i] :
( ( ( cQ @ X0 @ y )
!= $true )
| ( ( cP @ X0 @ y )
!= $true ) ) )
& ( ( ! [X1: $i] :
( ( cQ @ X1 @ y )
= $true )
& ! [X2: $i] :
( ( cP @ X2 @ y )
= $true ) )
| ! [X0: $i] :
( ( ( cQ @ X0 @ y )
= $true )
& ( ( cP @ X0 @ y )
= $true ) ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
( ( ? [X0: $i] :
( ( cQ @ X0 @ y )
!= $true )
| ? [X1: $i] :
( $true
!= ( cP @ X1 @ y ) )
| ? [X2: $i] :
( ( $true
!= ( cQ @ X2 @ y ) )
| ( ( cP @ X2 @ y )
!= $true ) ) )
& ( ( ! [X3: $i] :
( $true
= ( cQ @ X3 @ y ) )
& ! [X4: $i] :
( $true
= ( cP @ X4 @ y ) ) )
| ! [X5: $i] :
( ( $true
= ( cQ @ X5 @ y ) )
& ( $true
= ( cP @ X5 @ y ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ( ( $true
!= ( cQ @ sK0 @ y ) )
| ( $true
!= ( cP @ sK1 @ y ) )
| ( $true
!= ( cQ @ sK2 @ y ) )
| ( $true
!= ( cP @ sK2 @ y ) ) )
& ( ( ! [X3: $i] :
( $true
= ( cQ @ X3 @ y ) )
& ! [X4: $i] :
( $true
= ( cP @ X4 @ y ) ) )
| ! [X5: $i] :
( ( $true
= ( cQ @ X5 @ y ) )
& ( $true
= ( cP @ X5 @ y ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f8]) ).
thf(f10,plain,
! [X4: $i,X5: $i] :
( ( $true
= ( cP @ X4 @ y ) )
| ( $true
= ( cP @ X5 @ y ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
! [X3: $i,X5: $i] :
( ( $true
= ( cQ @ X3 @ y ) )
| ( $true
= ( cQ @ X5 @ y ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f14,plain,
( ( $true
!= ( cQ @ sK0 @ y ) )
| ( $true
!= ( cP @ sK1 @ y ) )
| ( $true
!= ( cQ @ sK2 @ y ) )
| ( $true
!= ( cP @ sK2 @ y ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f18,definition,
( spl3_1
<=> ! [X5: $i] :
( $true
= ( cP @ X5 @ y ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f19,plain,
( ! [X5: $i] :
( $true
= ( cP @ X5 @ y ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f18]) ).
thf(f20,plain,
( spl3_1
| spl3_1 ),
inference(avatar_split_clause,[],[f10,f18,f18]) ).
thf(f22,definition,
( spl3_2
<=> ! [X5: $i] :
( $true
= ( cQ @ X5 @ y ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f23,plain,
( ! [X5: $i] :
( $true
= ( cQ @ X5 @ y ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f22]) ).
thf(f26,plain,
( spl3_2
| spl3_2 ),
inference(avatar_split_clause,[],[f13,f22,f22]) ).
thf(f28,definition,
( spl3_3
<=> ( $true
= ( cP @ sK2 @ y ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f30,plain,
( ( $true
!= ( cP @ sK2 @ y ) )
| spl3_3 ),
inference(avatar_component_clause,[],[f28]) ).
thf(f32,definition,
( spl3_4
<=> ( $true
= ( cQ @ sK2 @ y ) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f34,plain,
( ( $true
!= ( cQ @ sK2 @ y ) )
| spl3_4 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f36,definition,
( spl3_5
<=> ( $true
= ( cP @ sK1 @ y ) ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
thf(f38,plain,
( ( $true
!= ( cP @ sK1 @ y ) )
| spl3_5 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f40,definition,
( spl3_6
<=> ( $true
= ( cQ @ sK0 @ y ) ) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
thf(f42,plain,
( ( $true
!= ( cQ @ sK0 @ y ) )
| spl3_6 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f43,plain,
( ~ spl3_3
| ~ spl3_4
| ~ spl3_5
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f14,f40,f36,f32,f28]) ).
thf(f44,plain,
( $false
| ~ spl3_1
| spl3_3 ),
inference(forward_subsumption_resolution,[],[f30,f19]) ).
thf(f45,plain,
( ~ spl3_1
| spl3_3 ),
inference(avatar_contradiction_clause,[],[f44]) ).
thf(f46,plain,
( $false
| ~ spl3_2
| spl3_4 ),
inference(forward_subsumption_resolution,[],[f34,f23]) ).
thf(f47,plain,
( ~ spl3_2
| spl3_4 ),
inference(avatar_contradiction_clause,[],[f46]) ).
thf(f48,plain,
( $false
| ~ spl3_1
| spl3_5 ),
inference(forward_subsumption_resolution,[],[f38,f19]) ).
thf(f49,plain,
( ~ spl3_1
| spl3_5 ),
inference(avatar_contradiction_clause,[],[f48]) ).
thf(f50,plain,
( $false
| ~ spl3_2
| spl3_6 ),
inference(forward_subsumption_resolution,[],[f42,f23]) ).
thf(f51,plain,
( ~ spl3_2
| spl3_6 ),
inference(avatar_contradiction_clause,[],[f50]) ).
cnf(s1,plain,
( spl3_1
| spl3_1 ),
inference(sat_conversion,[],[f20]) ).
cnf(s2,plain,
spl3_1,
inference(rat,[],[s1]) ).
cnf(s5,plain,
( spl3_2
| spl3_2 ),
inference(sat_conversion,[],[f26]) ).
cnf(s6,plain,
spl3_2,
inference(rat,[],[s5]) ).
cnf(s7,plain,
( ~ spl3_3
| ~ spl3_4
| ~ spl3_5
| ~ spl3_6 ),
inference(sat_conversion,[],[f43]) ).
cnf(s8,plain,
( ~ spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f45]) ).
cnf(s9,plain,
( ~ spl3_2
| spl3_4 ),
inference(sat_conversion,[],[f47]) ).
cnf(s10,plain,
( ~ spl3_1
| spl3_5 ),
inference(sat_conversion,[],[f49]) ).
cnf(s11,plain,
( ~ spl3_2
| spl3_6 ),
inference(sat_conversion,[],[f51]) ).
cnf(s12,plain,
spl3_6,
inference(rat,[],[s11,s6]) ).
cnf(s13,plain,
spl3_4,
inference(rat,[],[s9,s6]) ).
cnf(s14,plain,
spl3_5,
inference(rat,[],[s10,s2]) ).
cnf(s15,plain,
spl3_3,
inference(rat,[],[s8,s2]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s7,s12,s13,s14,s15]) ).
thf(f52,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO104^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.20 % Computer : n011.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Sep 29 16:34:07 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.23 Running first-order model finding
% 0.11/0.23 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
% 0.11/0.28 % (306449)Will run a generic schedule for satisfiability detection.
% 0.11/0.28 % (306457)dis+10_1_sil=32000:sp=arity:random_seed=1082958200:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.28 % (306457) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-306449-306457"...
% 0.11/0.28 % (306455)% WARNING: option uhcvi not known.
% 0.11/0.28 % (306457)...printing done.
% 0.11/0.28 % (306457)Refutation found. Thanks to Tanya!
% 0.11/0.28 % SZS status Theorem for theBenchmark
% 0.11/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.28 % (306457)------------------------------
% 0.11/0.28 % (306457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.28 % (306457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.28 % (306457)CaDiCaL version: 2.1.3
% 0.11/0.28 % (306457)Termination reason: Refutation
% 0.11/0.28 % (306457)Time elapsed: 0.001 s
% 0.11/0.28 % (306457)Peak memory usage: 12 MB
% 0.11/0.28 % (306457)Instructions burned: 3 (million)
% 0.11/0.28 % (306449)Success in time 0.033 s
% 0.11/0.28 % Vampire exiting
%------------------------------------------------------------------------------