%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO256^5 : 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 : n020.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 08:49:37 AM UTC 2026
% Result : Theorem 0.18s 0.26s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 10 unt; 0 typ; 4 def)
% Number of atoms : 140 ( 20 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 181 ( 45 ~; 47 |; 0 &; 72 @)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 10 con; 0-4 aty)
% ( 10 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 41 ( 0 sgn 24 !; 7 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
vOR: $o > $o > $o ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_5,type,
sK0: $o > $o ).
thf(func_def_6,type,
sK1: a > $o ).
thf(func_def_7,type,
sK2: a > $o ).
thf(func_def_11,type,
sK4: a ).
thf(func_def_12,type,
sK5: a ).
thf(func_def_13,type,
sK6: a ).
thf(f1,conjecture,
! [X0: $o > $o,X1: a > $o,X2: a > $o] :
? [X3: $o] :
( ( X0 @ X3 )
<=> ( X0
@ ! [X4: a] :
( ( X2 @ X4 )
| ( X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM121) ).
thf(f2,negated_conjecture,
~ ! [X0: $o > $o,X1: a > $o,X2: a > $o] :
? [X3: $o] :
( ( X0 @ X3 )
<=> ( X0
@ ! [X4: a] :
( ( X2 @ X4 )
| ( X1 @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: $o > $o,X1: a > $o,X2: a > $o] :
? [X3: $o] :
( ( X0 @ X3 )
<=> ( X0
@ ! [X4: a] :
( ( X2 @ X4 )
| ( X1 @ X4 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: $o > $o,X1: a > $o,X2: a > $o] :
? [X3: $o] :
( ( X0 @ X3 )
= ( X0
@ ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: $o > $o,X1: a > $o,X2: a > $o] :
! [X3: $o] :
( ( X0 @ X3 )
!= ( X0
@ ( !! @ a
@ ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
! [X3: $o] :
( ( sK0 @ X3 )
!= ( sK0
@ ( !! @ a
@ ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f5]) ).
thf(f7,plain,
! [X3: $o] :
( ( sK0 @ X3 )
!= ( sK0
@ ( !! @ a
@ ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f10,plain,
! [X3: $o] :
( ( ( sK0 @ X3 )
= $true )
| ( ( sK0
@ ( !! @ a
@ ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
= $true ) ),
inference(xor_proxy_clausification,[],[f7]) ).
thf(f11,plain,
! [X3: $o] :
( ( ( sK0 @ X3 )
= $false )
| ( ( sK0
@ ( !! @ a
@ ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
= $false ) ),
inference(xor_proxy_clausification,[],[f7]) ).
thf(f13,definition,
( spl3_1
<=> ( ( sK0
@ ( !! @ a
@ ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f15,plain,
( ( ( sK0
@ ( !! @ a
@ ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
= $false )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f13]) ).
thf(f17,definition,
( spl3_2
<=> ! [X3: $o] :
( ( sK0 @ X3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f18,plain,
( ! [X3: $o] :
( ( sK0 @ X3 )
= $false )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f17]) ).
thf(f19,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f11,f17,f13]) ).
thf(f21,definition,
( spl3_3
<=> ( ( sK0
@ ( !! @ a
@ ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f23,plain,
( ( ( sK0
@ ( !! @ a
@ ^ [Y0: a] :
( ( sK1 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
= $true )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f21]) ).
thf(f25,definition,
( spl3_4
<=> ! [X3: $o] :
( ( sK0 @ X3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f26,plain,
( ! [X3: $o] :
( ( sK0 @ X3 )
= $true )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f25]) ).
thf(f27,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f10,f25,f21]) ).
thf(f37,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f23,f18]) ).
thf(f38,plain,
( $false
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f37]) ).
thf(f39,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f38]) ).
thf(f64,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_3 ),
inference(forward_demodulation,[],[f23,f15]) ).
thf(f65,plain,
( $false
| ~ spl3_1
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f64]) ).
thf(f66,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f65]) ).
thf(f70,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_4 ),
inference(forward_demodulation,[],[f26,f18]) ).
thf(f71,plain,
( $false
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f70]) ).
thf(f72,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f71]) ).
thf(f109,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_4 ),
inference(constrained_superposition,[],[f15,f26]) ).
thf(f113,plain,
( $false
| ~ spl3_1
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f109]) ).
thf(f114,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f113]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f19]) ).
cnf(s2,plain,
( spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f27]) ).
cnf(s3,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f39]) ).
cnf(s6,plain,
( ~ spl3_1
| ~ spl3_3 ),
inference(sat_conversion,[],[f66]) ).
cnf(s7,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(sat_conversion,[],[f72]) ).
cnf(s17,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(sat_conversion,[],[f114]) ).
cnf(s18,plain,
~ spl3_2,
inference(rat,[],[s2,s3,s7]) ).
cnf(s19,plain,
spl3_1,
inference(rat,[],[s1,s18]) ).
cnf(s20,plain,
~ spl3_4,
inference(rat,[],[s17,s19]) ).
cnf(s21,plain,
~ spl3_3,
inference(rat,[],[s6,s19]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s2,s20,s21]) ).
thf(f124,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO256^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n020.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 16:42:35 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.18/0.26 % (1284675)Will run a generic schedule for satisfiability detection.
% 0.18/0.26 % (1284687)% WARNING: option uhcvi not known.
% 0.18/0.26 % (1284687)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2012680080:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.26 % (1284687)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.26 % (1284687)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.18/0.26 % (1284687) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1284675-1284687"...
% 0.18/0.26 % (1284687)...printing done.
% 0.18/0.26 % (1284687)Refutation found. Thanks to Tanya!
% 0.18/0.26 % SZS status Theorem for theBenchmark
% 0.18/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.26 % (1284687)------------------------------
% 0.18/0.26 % (1284687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.26 % (1284687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.26 % (1284687)CaDiCaL version: 2.1.3
% 0.18/0.26 % (1284687)Termination reason: Refutation
% 0.18/0.26 % (1284687)Time elapsed: 0.003 s
% 0.18/0.26 % (1284687)Peak memory usage: 13 MB
% 0.18/0.26 % (1284687)Instructions burned: 4 (million)
% 0.18/0.26 % (1284675)Success in time 0.033 s
% 0.18/0.26 % Vampire exiting
%------------------------------------------------------------------------------