%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET611^5 : 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 : n016.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 08:23:42 AM UTC 2026
% Result : Theorem 0.10s 0.25s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 72 ( 6 unt; 0 typ; 4 def)
% Number of atoms : 366 ( 90 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 360 ( 75 ~; 96 |; 44 &; 136 @)
% ( 8 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 77 ( 18 sgn 18 !; 4 ?; 77 :)
% 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,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_6,type,
vNOT: $o > $o ).
thf(func_def_7,type,
sK0: a > $o ).
thf(func_def_8,type,
sK1: a > $o ).
thf(func_def_10,type,
sK3: 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] :
( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_84_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [X2: a] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= ( ^ [X2: a] : $false ) )
<=> ( ( ^ [X2: a] :
( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= X0 ) ),
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] :
( ~ ( X1 @ X4 )
& ( X0 @ X4 ) ) )
= X0 ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
<=> ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
= X0 ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o] :
( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) )
<~> ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
= X0 ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
!= X0 )
| ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
!= ( ^ [Y0: a] : $false ) ) )
& ( ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
= X0 )
| ( ( ^ [Y0: a] :
( ( X0 @ Y0 )
& ( X1 @ Y0 ) ) )
= ( ^ [Y0: a] : $false ) ) ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f7,plain,
( ( ( sK0
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) )
| ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) )
& ( ( sK0
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) )
| ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f6]) ).
thf(f8,plain,
( ( sK0
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) )
| ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( ( sK0
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) )
| ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,definition,
( spl2_1
<=> ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f14,plain,
( ( ( ^ [Y0: a] : $false )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| spl2_1 ),
inference(avatar_component_clause,[],[f13]) ).
thf(f15,plain,
( ( ( ^ [Y0: a] : $false )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f13]) ).
thf(f17,definition,
( spl2_2
<=> ( sK0
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f18,plain,
( ( sK0
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) )
| spl2_2 ),
inference(avatar_component_clause,[],[f17]) ).
thf(f19,plain,
( ( sK0
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f17]) ).
thf(f20,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f8,f17,f13]) ).
thf(f21,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f9,f17,f13]) ).
thf(f22,plain,
( ( ( ^ [Y0: a] : $false
@ sK3 )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK3 ) )
| spl2_1 ),
inference(negative_extensionality,[],[f14]) ).
thf(f23,plain,
( ( $true
= ( ^ [Y0: a] : $false
@ sK3 ) )
| ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ sK3 ) )
| spl2_1 ),
inference(xor_proxy_clausification,[],[f22]) ).
thf(f27,plain,
( ( $false = $true )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| spl2_1 ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f28,plain,
( ( $false = $true )
| ( $true
= ( sK1 @ sK3 ) )
| spl2_1 ),
inference(and_proxy_clausification,[],[f27]) ).
thf(f29,plain,
( ( $false = $true )
| ( $true
= ( sK0 @ sK3 ) )
| spl2_1 ),
inference(and_proxy_clausification,[],[f27]) ).
thf(f30,plain,
( ( $true
= ( sK0 @ sK3 ) )
| spl2_1 ),
inference(trivial_inequality_removal,[],[f29]) ).
thf(f31,plain,
( ( $true
= ( sK1 @ sK3 ) )
| spl2_1 ),
inference(trivial_inequality_removal,[],[f28]) ).
thf(f32,plain,
( ! [X1: a] :
( ( sK0 @ X1 )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
@ X1 ) )
| ~ spl2_2 ),
inference(argument_congruence,[],[f19]) ).
thf(f34,plain,
( ! [X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
@ X1 ) ) )
| ~ spl2_2 ),
inference(iff_proxy_clausification,[],[f32]) ).
thf(f35,plain,
( ! [X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( ( sK0 @ X1 )
& ~ ( sK1 @ X1 ) ) ) )
| ~ spl2_2 ),
inference(beta-eta_normalization,[],[f34]) ).
thf(f36,plain,
( ! [X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( ~ ( sK1 @ X1 ) ) ) )
| ~ spl2_2 ),
inference(and_proxy_clausification,[],[f35]) ).
thf(f38,plain,
( ! [X1: a] :
( ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl2_2 ),
inference(not_proxy_clausification,[],[f36]) ).
thf(f43,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK3 ) )
| spl2_1
| ~ spl2_2 ),
inference(constrained_superposition,[],[f31,f38]) ).
thf(f44,plain,
( ( $false
= ( sK0 @ sK3 ) )
| spl2_1
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f43]) ).
thf(f46,plain,
( ( $false = $true )
| spl2_1
| ~ spl2_2 ),
inference(constrained_superposition,[],[f44,f30]) ).
thf(f50,plain,
( $false
| spl2_1
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f46]) ).
thf(f51,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_contradiction_clause,[],[f50]) ).
thf(f52,plain,
( ! [X1: a] :
( ( ^ [Y0: a] : $false
@ X1 )
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 ) )
| ~ spl2_1 ),
inference(argument_congruence,[],[f15]) ).
thf(f53,plain,
( ! [X1: a] :
( ( $true
= ( ^ [Y0: a] : $false
@ X1 ) )
| ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
@ X1 ) ) )
| ~ spl2_1 ),
inference(iff_proxy_clausification,[],[f52]) ).
thf(f58,plain,
( ! [X1: a] :
( ( $false = $true )
| ( $false
= ( ( sK0 @ X1 )
& ( sK1 @ X1 ) ) ) )
| ~ spl2_1 ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f59,plain,
( ! [X1: a] :
( ( $false = $true )
| ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl2_1 ),
inference(and_proxy_clausification,[],[f58]) ).
thf(f60,plain,
( ! [X1: a] :
( ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f59]) ).
thf(f61,plain,
( ( ( sK0 @ sK4 )
!= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
@ sK4 ) )
| spl2_2 ),
inference(negative_extensionality,[],[f18]) ).
thf(f62,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
@ sK4 ) )
| spl2_2 ),
inference(xor_proxy_clausification,[],[f61]) ).
thf(f63,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
@ sK4 ) )
| spl2_2 ),
inference(xor_proxy_clausification,[],[f61]) ).
thf(f64,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ( $false
= ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) )
| spl2_2 ),
inference(beta-eta_normalization,[],[f63]) ).
thf(f65,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ( $false
= ( ~ ( sK1 @ sK4 ) ) )
| ( $false
= ( sK0 @ sK4 ) )
| spl2_2 ),
inference(and_proxy_clausification,[],[f64]) ).
thf(f66,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ( $true
= ( sK1 @ sK4 ) )
| ( $false
= ( sK0 @ sK4 ) )
| spl2_2 ),
inference(not_proxy_clausification,[],[f65]) ).
thf(f67,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ( $true
= ( sK1 @ sK4 ) )
| spl2_2 ),
inference(duplicate_literal_removal,[],[f66]) ).
thf(f68,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( ( sK0 @ sK4 )
& ~ ( sK1 @ sK4 ) ) )
| spl2_2 ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f70,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( sK0 @ sK4 ) )
| spl2_2 ),
inference(and_proxy_clausification,[],[f68]) ).
thf(f71,plain,
( ( $true
= ( sK0 @ sK4 ) )
| spl2_2 ),
inference(duplicate_literal_removal,[],[f70]) ).
thf(f74,definition,
( spl2_3
<=> ( $true
= ( sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f76,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f74]) ).
thf(f78,definition,
( spl2_4
<=> ( $false
= ( sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f80,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f78]) ).
thf(f81,plain,
( spl2_3
| spl2_4
| spl2_2 ),
inference(avatar_split_clause,[],[f67,f17,f78,f74]) ).
thf(f83,plain,
( ( $false = $true )
| spl2_2
| ~ spl2_4 ),
inference(constrained_superposition,[],[f71,f80]) ).
thf(f87,plain,
( $false
| spl2_2
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f83]) ).
thf(f88,plain,
( spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f87]) ).
thf(f90,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK4 ) )
| ~ spl2_1
| ~ spl2_3 ),
inference(constrained_superposition,[],[f60,f76]) ).
thf(f91,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ~ spl2_1
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f90]) ).
thf(f93,plain,
( spl2_4
| ~ spl2_1
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f91,f74,f13,f78]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f20]) ).
cnf(s2,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f21]) ).
cnf(s4,plain,
( spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f51]) ).
cnf(s5,plain,
( spl2_2
| spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f81]) ).
cnf(s7,plain,
( spl2_2
| ~ spl2_4 ),
inference(sat_conversion,[],[f88]) ).
cnf(s8,plain,
( ~ spl2_1
| ~ spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f93]) ).
cnf(s10,plain,
spl2_1,
inference(rat,[],[s1,s4]) ).
cnf(s11,plain,
~ spl2_2,
inference(rat,[],[s2,s10]) ).
cnf(s12,plain,
~ spl2_4,
inference(rat,[],[s7,s11]) ).
cnf(s13,plain,
spl2_3,
inference(rat,[],[s5,s11,s12]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s8,s10,s12,s13]) ).
thf(f94,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET611^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.17 % Computer : n016.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 13:44:04 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 Running first-order model finding
% 0.10/0.21 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
% 0.10/0.25 % (361934)Will run a generic schedule for satisfiability detection.
% 0.10/0.25 % (361958)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2248294979:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.25 % (361958) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-361934-361958"...
% 0.10/0.25 % (361958)...printing done.
% 0.10/0.25 % (361958)Refutation found. Thanks to Tanya!
% 0.10/0.25 % SZS status Theorem for theBenchmark
% 0.10/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.25 % (361958)------------------------------
% 0.10/0.25 % (361958)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.25 % (361958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.25 % (361958)CaDiCaL version: 2.1.3
% 0.10/0.25 % (361958)Termination reason: Refutation
% 0.10/0.25 % (361958)Time elapsed: 0.002 s
% 0.10/0.25 % (361958)Peak memory usage: 12 MB
% 0.10/0.25 % (361958)Instructions burned: 5 (million)
% 0.10/0.25 % (361934)Success in time 0.035 s
% 0.10/0.25 % Vampire exiting
%------------------------------------------------------------------------------