%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET587^5 : 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 : n026.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 08:23:38 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 58 ( 8 unt; 0 typ; 4 def)
% Number of atoms : 306 ( 82 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 314 ( 83 ~; 79 |; 30 &; 107 @)
% ( 9 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 80 ( 22 sgn 28 !; 8 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vAND: $o > $o > $o ).
thf(func_def_2,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_3,type,
vNOT: $o > $o ).
thf(func_def_4,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_7,type,
sK0: a > $o ).
thf(func_def_8,type,
sK1: a > $o ).
thf(func_def_9,type,
sK2: a ).
thf(func_def_11,type,
sK4: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] :
( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= ( ^ [X2: a] : $false ) )
<=> ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_45_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] :
( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= ( ^ [X2: a] : $false ) )
<=> ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] :
( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= ( ^ [X3: a] : $false ) )
<=> ! [X4: a] :
( ( X0 @ X4 )
=> ( X1 @ X4 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
<=> ! [X4: a] :
( ( ( X0 @ X4 )
= $true )
=> ( ( X1 @ X4 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
<=> ! [X2: a] :
( ( ( X0 @ X2 )
= $true )
=> ( ( X1 @ X2 )
= $true ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
<~> ! [X2: a] :
( ( ( X1 @ X2 )
= $true )
| ( ( X0 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o] :
( ( ? [X2: a] :
( ( ( X1 @ X2 )
!= $true )
& ( ( X0 @ X2 )
= $true ) )
| ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) ) )
& ( ! [X2: a] :
( ( ( X1 @ X2 )
= $true )
| ( ( X0 @ X2 )
!= $true ) )
| ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ) ) ),
inference(nnf_transformation,[],[f6]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o] :
( ( ? [X2: a] :
( ( ( X1 @ X2 )
!= $true )
& ( ( X0 @ X2 )
= $true ) )
| ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) ) )
& ( ! [X3: a] :
( ( $true
= ( X1 @ X3 ) )
| ( $true
!= ( X0 @ X3 ) ) )
| ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ( ( ( $true
!= ( sK1 @ sK2 ) )
& ( $true
= ( sK0 @ sK2 ) ) )
| ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) )
& ( ! [X3: a] :
( ( $true
= ( sK1 @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) ) )
| ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f8]) ).
thf(f10,plain,
! [X3: a] :
( ( $true
= ( sK1 @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) )
| ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( ( $true
!= ( sK1 @ sK2 ) )
| ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,definition,
( spl3_1
<=> ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f17,plain,
( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) )
| spl3_1 ),
inference(avatar_component_clause,[],[f16]) ).
thf(f18,plain,
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f16]) ).
thf(f20,definition,
( spl3_2
<=> ! [X3: a] :
( ( $true
= ( sK1 @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f21,plain,
( ! [X3: a] :
( ( $true
!= ( sK0 @ X3 ) )
| ( $true
= ( sK1 @ X3 ) ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f20]) ).
thf(f22,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f10,f20,f16]) ).
thf(f24,definition,
( spl3_3
<=> ( $true
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f26,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f27,plain,
( ~ spl3_1
| spl3_3 ),
inference(avatar_split_clause,[],[f11,f24,f16]) ).
thf(f29,definition,
( spl3_4
<=> ( $true
= ( sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f31,plain,
( ( $true
!= ( sK1 @ sK2 ) )
| spl3_4 ),
inference(avatar_component_clause,[],[f29]) ).
thf(f32,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f12,f29,f16]) ).
thf(f33,plain,
( ( ( ^ [Y0: a] : $false
@ sK4 )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
@ sK4 ) )
| spl3_1 ),
inference(negative_extensionality,[],[f17]) ).
thf(f34,plain,
( ( $true
= ( ^ [Y0: a] : $false
@ sK4 ) )
| ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
@ sK4 ) )
| spl3_1 ),
inference(xor_proxy_clausification,[],[f33]) ).
thf(f39,plain,
( ( $false = $true )
| ( $true
= ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) )
| spl3_1 ),
inference(beta-eta_normalization,[],[f34]) ).
thf(f40,plain,
( ( $false = $true )
| ( $true
= ( ~ ( sK1 @ sK4 ) ) )
| spl3_1 ),
inference(and_proxy_clausification,[],[f39]) ).
thf(f41,plain,
( ( $false = $true )
| ( $true
= ( sK0 @ sK4 ) )
| spl3_1 ),
inference(and_proxy_clausification,[],[f39]) ).
thf(f42,plain,
( ( $true
= ( sK0 @ sK4 ) )
| spl3_1 ),
inference(trivial_inequality_removal,[],[f41]) ).
thf(f43,plain,
( ( $false = $true )
| ( $false
= ( sK1 @ sK4 ) )
| spl3_1 ),
inference(not_proxy_clausification,[],[f40]) ).
thf(f44,plain,
( ( $false
= ( sK1 @ sK4 ) )
| spl3_1 ),
inference(trivial_inequality_removal,[],[f43]) ).
thf(f54,plain,
( ( $true != $true )
| ( $true
= ( sK1 @ sK4 ) )
| spl3_1
| ~ spl3_2 ),
inference(constrained_superposition,[],[f21,f42]) ).
thf(f55,plain,
( ( $true
= ( sK1 @ sK4 ) )
| spl3_1
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f54]) ).
thf(f56,plain,
( ( $false = $true )
| spl3_1
| ~ spl3_2 ),
inference(forward_demodulation,[],[f55,f44]) ).
thf(f57,plain,
( $false
| spl3_1
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f56]) ).
thf(f58,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_contradiction_clause,[],[f57]) ).
thf(f65,plain,
( ! [X1: a] :
( ( ^ [Y0: a] : $false
@ X1 )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
@ X1 ) )
| ~ spl3_1 ),
inference(argument_congruence,[],[f18]) ).
thf(f66,plain,
( ! [X1: a] :
( ( $true
= ( ^ [Y0: a] : $false
@ X1 ) )
| ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
@ X1 ) ) )
| ~ spl3_1 ),
inference(iff_proxy_clausification,[],[f65]) ).
thf(f72,plain,
( ! [X1: a] :
( ( $false = $true )
| ( $false
= ( ( sK0 @ X1 )
& ~ ( sK1 @ X1 ) ) ) )
| ~ spl3_1 ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f73,plain,
( ! [X1: a] :
( ( $false = $true )
| ( $false
= ( ~ ( sK1 @ X1 ) ) )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl3_1 ),
inference(and_proxy_clausification,[],[f72]) ).
thf(f74,plain,
( ! [X1: a] :
( ( $false = $true )
| ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl3_1 ),
inference(not_proxy_clausification,[],[f73]) ).
thf(f75,plain,
( ! [X1: a] :
( ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f74]) ).
thf(f81,plain,
( ( $true != $true )
| ( $false
= ( sK0 @ sK2 ) )
| ~ spl3_1
| spl3_4 ),
inference(constrained_superposition,[],[f31,f75]) ).
thf(f82,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ~ spl3_1
| spl3_4 ),
inference(trivial_inequality_removal,[],[f81]) ).
thf(f86,plain,
( ( $false = $true )
| ~ spl3_1
| ~ spl3_3
| spl3_4 ),
inference(constrained_superposition,[],[f82,f26]) ).
thf(f90,plain,
( $false
| ~ spl3_1
| ~ spl3_3
| spl3_4 ),
inference(trivial_inequality_removal,[],[f86]) ).
thf(f91,plain,
( ~ spl3_1
| ~ spl3_3
| spl3_4 ),
inference(avatar_contradiction_clause,[],[f90]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s2,plain,
( ~ spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f27]) ).
cnf(s3,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(sat_conversion,[],[f32]) ).
cnf(s4,plain,
( spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f58]) ).
cnf(s7,plain,
( ~ spl3_1
| ~ spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f91]) ).
cnf(s8,plain,
spl3_1,
inference(rat,[],[s1,s4]) ).
cnf(s9,plain,
~ spl3_4,
inference(rat,[],[s3,s8]) ).
cnf(s10,plain,
spl3_3,
inference(rat,[],[s2,s8]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s7,s9,s8,s10]) ).
thf(f93,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET587^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n026.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 13:40:42 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.23 Running first-order model finding
% 0.07/0.23 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
% 0.19/0.28 % (600782)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (600801)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3732086161:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.28 % (600801) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-600782-600801"...
% 0.19/0.28 % (600797)% WARNING: option uhcvi not known.
% 0.19/0.28 % (600801)...printing done.
% 0.19/0.28 % (600801)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (600801)------------------------------
% 0.19/0.28 % (600801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (600801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (600801)CaDiCaL version: 2.1.3
% 0.19/0.28 % (600801)Termination reason: Refutation
% 0.19/0.28 % (600801)Time elapsed: 0.002 s
% 0.19/0.28 % (600801)Peak memory usage: 12 MB
% 0.19/0.28 % (600801)Instructions burned: 4 (million)
% 0.19/0.28 % (600782)Success in time 0.039 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------