%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV164^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 08:39:05 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 8 unt; 0 typ; 5 def)
% Number of atoms : 140 ( 33 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 218 ( 59 ~; 40 |; 3 &; 106 @)
% ( 9 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 65 ( 65 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 9 con; 0-4 aty)
% Number of variables : 126 ( 38 sgn 26 !; 24 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
sK0: a > a > $o ).
thf(func_def_7,type,
sK1: ( a > a > a ) > a ).
thf(func_def_8,type,
sK2: a ).
thf(func_def_9,type,
sK3: a ).
thf(f1,conjecture,
! [X0: a > a > $o] :
( ? [X1: a,X2: a] : ( X0 @ X1 @ X2 )
<=> ? [X3: ( a > a > a ) > a] :
( X0
@ ( X3
@ ^ [X1: a,X2: a] : X1 )
@ ( X3
@ ^ [X1: a,X2: a] : X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM185_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o] :
( ? [X1: a,X2: a] : ( X0 @ X1 @ X2 )
<=> ? [X3: ( a > a > a ) > a] :
( X0
@ ( X3
@ ^ [X1: a,X2: a] : X1 )
@ ( X3
@ ^ [X1: a,X2: a] : X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > a > $o] :
( ? [X1: a,X2: a] : ( X0 @ X1 @ X2 )
<=> ? [X3: ( a > a > a ) > a] :
( X0
@ ( X3
@ ^ [X4: a,X5: a] : X4 )
@ ( X3
@ ^ [X6: a,X7: a] : X7 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > a > $o] :
( ? [X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
= $true )
<=> ? [X3: ( a > a > a ) > a] :
( $true
= ( X0
@ ( X3
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X3
@ ^ [Y0: a,Y1: a] : Y1 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > a > $o] :
( ? [X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
= $true )
<~> ? [X3: ( a > a > a ) > a] :
( $true
= ( X0
@ ( X3
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X3
@ ^ [Y0: a,Y1: a] : Y1 ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > a > $o] :
( ( ! [X3: ( a > a > a ) > a] :
( $true
!= ( X0
@ ( X3
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X3
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ! [X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
!= $true ) )
& ( ? [X3: ( a > a > a ) > a] :
( $true
= ( X0
@ ( X3
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X3
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ? [X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
= $true ) ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: a > a > $o] :
( ( ! [X1: ( a > a > a ) > a] :
( $true
!= ( X0
@ ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ! [X2: a,X3: a] :
( $true
!= ( X0 @ X2 @ X3 ) ) )
& ( ? [X4: ( a > a > a ) > a] :
( $true
= ( X0
@ ( X4
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X4
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ? [X5: a,X6: a] :
( $true
= ( X0 @ X5 @ X6 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ! [X1: ( a > a > a ) > a] :
( $true
!= ( sK0
@ ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ! [X2: a,X3: a] :
( $true
!= ( sK0 @ X2 @ X3 ) ) )
& ( ( $true
= ( sK0
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ( $true
= ( sK0 @ sK2 @ sK3 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X4,sK1),skolemize(X5,sK2),skolemize(X6,sK3)],[f7]) ).
thf(f9,plain,
( ( $true
= ( sK0
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ( $true
= ( sK0 @ sK2 @ sK3 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
! [X2: a,X3: a,X1: ( a > a > a ) > a] :
( ( $true
!= ( sK0
@ ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ( $true
!= ( sK0 @ X2 @ X3 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,definition,
( spl4_1
<=> ( $true
= ( sK0 @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f16,plain,
( ( $true
= ( sK0 @ sK2 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f14]) ).
thf(f18,definition,
( spl4_2
<=> ( $true
= ( sK0
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f20,plain,
( ( $true
= ( sK0
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( sK1
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f18]) ).
thf(f21,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f9,f18,f14]) ).
thf(f23,definition,
( spl4_3
<=> ! [X2: a,X3: a] :
( $true
!= ( sK0 @ X2 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f24,plain,
( ! [X2: a,X3: a] :
( $true
!= ( sK0 @ X2 @ X3 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f26,definition,
( spl4_4
<=> ! [X1: ( a > a > a ) > a] :
( $true
!= ( sK0
@ ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f27,plain,
( ! [X1: ( a > a > a ) > a] :
( $true
!= ( sK0
@ ( X1
@ ^ [Y0: a,Y1: a] : Y0 )
@ ( X1
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f28,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f10,f26,f23]) ).
thf(f29,plain,
( $false
| ~ spl4_2
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f20,f24]) ).
thf(f30,plain,
( ~ spl4_2
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[],[f29]) ).
thf(f31,plain,
( $false
| ~ spl4_1
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f16,f24]) ).
thf(f32,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[],[f31]) ).
thf(f33,plain,
( $false
| ~ spl4_2
| ~ spl4_4 ),
inference(backward_subsumption_resolution,[],[f20,f27]) ).
thf(f34,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f33]) ).
thf(f36,plain,
( ! [X2: ( a > a > a ) > a] :
( ( $true != $true )
| ( sK3
!= ( X2
@ ^ [Y0: a,Y1: a] : Y1 ) ) )
| ~ spl4_1
| ~ spl4_4 ),
inference(constrained_superposition,[],[f27,f16]) ).
thf(f37,plain,
( ! [X2: ( a > a > a ) > a] :
( sK3
!= ( X2
@ ^ [Y0: a,Y1: a] : Y1 ) )
| ~ spl4_1
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f36]) ).
thf(f43,definition,
( spl4_6
<=> ! [X2: ( a > a > a ) > a] :
( sK3
!= ( X2
@ ^ [Y0: a,Y1: a] : Y1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f44,plain,
( ! [X2: ( a > a > a ) > a] :
( sK3
!= ( X2
@ ^ [Y0: a,Y1: a] : Y1 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f43]) ).
thf(f55,plain,
( spl4_6
| ~ spl4_1
| ~ spl4_4 ),
inference(avatar_split_clause,[],[f37,f26,f14,f43]) ).
thf(f57,plain,
( $false
| ~ spl4_6 ),
inference(equality_resolution,[],[f44]) ).
thf(f60,plain,
~ spl4_6,
inference(avatar_contradiction_clause,[],[f57]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f21]) ).
cnf(s2,plain,
( spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f28]) ).
cnf(s3,plain,
( ~ spl4_2
| ~ spl4_3 ),
inference(sat_conversion,[],[f30]) ).
cnf(s4,plain,
( ~ spl4_1
| ~ spl4_3 ),
inference(sat_conversion,[],[f32]) ).
cnf(s5,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(sat_conversion,[],[f34]) ).
cnf(s7,plain,
( ~ spl4_1
| ~ spl4_4
| spl4_6 ),
inference(sat_conversion,[],[f55]) ).
cnf(s9,plain,
~ spl4_6,
inference(sat_conversion,[],[f60]) ).
cnf(s10,plain,
( ~ spl4_1
| ~ spl4_4 ),
inference(rat,[],[s7,s9]) ).
cnf(s12,plain,
~ spl4_2,
inference(rat,[],[s2,s3,s5]) ).
cnf(s13,plain,
spl4_1,
inference(rat,[],[s1,s12]) ).
cnf(s14,plain,
~ spl4_4,
inference(rat,[],[s10,s13]) ).
cnf(s15,plain,
~ spl4_3,
inference(rat,[],[s4,s13]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s2,s14,s15]) ).
thf(f61,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV164^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n014.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
% 0.08/0.17 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 15:17:45 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.25 % (2790933)Will run a generic schedule for satisfiability detection.
% 0.08/0.25 % (2790939)% WARNING: option uhcvi not known.
% 0.08/0.25 % (2790939)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3278412631:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.25 % (2790939)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.25 % (2790939)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.25 % (2790939) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2790933-2790939"...
% 0.08/0.25 % (2790939)...printing done.
% 0.08/0.25 % (2790939)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.25 % (2790939)------------------------------
% 0.08/0.25 % (2790939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (2790939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (2790939)CaDiCaL version: 2.1.3
% 0.08/0.25 % (2790939)Termination reason: Refutation
% 0.08/0.25 % (2790939)Time elapsed: 0.002 s
% 0.08/0.25 % (2790939)Peak memory usage: 13 MB
% 0.08/0.25 % (2790939)Instructions burned: 4 (million)
% 0.08/0.25 % (2790933)Success in time 0.039 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------