%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET096^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 08:23:35 AM UTC 2026
% Result : Theorem 0.09s 0.16s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 59 ( 32 unt; 0 typ; 2 def)
% Number of atoms : 265 ( 82 equ; 1 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 151 ( 28 ~; 22 |; 6 &; 77 @)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 32 usr; 9 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 49 ( 6 sgn 14 !; 4 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > ( $i > $o ) > $o ).
thf(func_def_2,type,
is_a: $i > ( $i > $o ) > $o ).
thf(func_def_3,type,
emptyset: $i > $o ).
thf(func_def_4,type,
unord_pair: $i > $i > $i > $o ).
thf(func_def_5,type,
singleton: $i > $i > $o ).
thf(func_def_6,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
complement: ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
disjoint: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_12,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_13,type,
meets: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_14,type,
misses: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_15,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_20,type,
vOR: $o > $o > $o ).
thf(func_def_21,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_23,type,
vAND: $o > $o > $o ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(func_def_25,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vIMP: $o > $o > $o ).
thf(func_def_27,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_28,type,
sK0: $i > $o ).
thf(f3,axiom,
( emptyset
= ( ^ [X0: $i] : $false ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',emptyset) ).
thf(f5,axiom,
( singleton
= ( ^ [X0: $i,X1: $i] : ( X1 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',singleton) ).
thf(f12,axiom,
( subset
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',subset) ).
thf(f15,conjecture,
! [X0: $i > $o,X1: $i] :
( ( subset @ X0 @ ( singleton @ X1 ) )
=> ( ( X0
= ( singleton @ X1 ) )
| ( X0 = emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f16,negated_conjecture,
~ ! [X0: $i > $o,X1: $i] :
( ( subset @ X0 @ ( singleton @ X1 ) )
=> ( ( X0
= ( singleton @ X1 ) )
| ( X0 = emptyset ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f19,plain,
( emptyset
= ( ^ [Y0: $i] : $false ) ),
inference(fool_elimination,[],[f3]) ).
thf(f21,plain,
( singleton
= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f33,plain,
( subset
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f34,plain,
( subset
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f39,plain,
~ ! [X0: $i > $o,X1: $i] :
( ( subset @ X0 @ ( singleton @ X1 ) )
=> ( ( X0
= ( singleton @ X1 ) )
| ( X0 = emptyset ) ) ),
inference(rectify,[],[f16]) ).
thf(f40,plain,
~ ! [X0: $i > $o,X1: $i] :
( ( ( subset @ X0 @ ( singleton @ X1 ) )
= $true )
=> ( ( ( singleton @ X1 )
= X0 )
| ( emptyset = X0 ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
? [X0: $i > $o,X1: $i] :
( ( ( singleton @ X1 )
!= X0 )
& ( emptyset != X0 )
& ( ( subset @ X0 @ ( singleton @ X1 ) )
= $true ) ),
inference(ennf_transformation,[],[f40]) ).
thf(f42,plain,
? [X0: $i > $o,X1: $i] :
( ( ( singleton @ X1 )
!= X0 )
& ( emptyset != X0 )
& ( ( subset @ X0 @ ( singleton @ X1 ) )
= $true ) ),
inference(flattening,[],[f41]) ).
thf(f43,plain,
( ( sK0
!= ( singleton @ sK1 ) )
& ( emptyset != sK0 )
& ( $true
= ( subset @ sK0 @ ( singleton @ sK1 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f42]) ).
thf(f46,plain,
( emptyset
= ( ^ [Y0: $i] : $false ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f48,plain,
( singleton
= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f55,plain,
( subset
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f58,plain,
( $true
= ( subset @ sK0 @ ( singleton @ sK1 ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f59,plain,
emptyset != sK0,
inference(cnf_transformation,[],[f43]) ).
thf(f60,plain,
( sK0
!= ( singleton @ sK1 ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f64,plain,
( sK0
!= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 )
@ sK1 ) ),
inference(definition_unfolding,[],[f60,f48]) ).
thf(f65,plain,
( ( ^ [Y0: $i] : $false )
!= sK0 ),
inference(definition_unfolding,[],[f59,f46]) ).
thf(f66,plain,
( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
@ sK0
@ ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 )
@ sK1 ) ) ),
inference(definition_unfolding,[],[f58,f55,f48]) ).
thf(f67,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK1 = Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f68,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK1 = Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f67]) ).
thf(f69,plain,
! [X1: $i] :
( $true
= ( ( sK0 @ X1 )
=> ( sK1 = X1 ) ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f70,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( sK1 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( sK1 = X1 ) ),
inference(equality_proxy_clausification,[],[f70]) ).
thf(f72,plain,
( sK0
!= ( (=) @ sK1 ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f73,plain,
( ( ^ [Y0: $i] : $false
@ sK2 )
!= ( sK0 @ sK2 ) ),
inference(negative_extensionality,[],[f65]) ).
thf(f74,plain,
( ( $true
= ( ^ [Y0: $i] : $false
@ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f73]) ).
thf(f77,plain,
( ( $false = $true )
| ( $true
= ( sK0 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f74]) ).
thf(f78,plain,
( $true
= ( sK0 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f77]) ).
thf(f80,plain,
( ( $false = $true )
| ( sK1 = sK2 ) ),
inference(constrained_superposition,[],[f71,f78]) ).
thf(f81,plain,
sK1 = sK2,
inference(trivial_inequality_removal,[],[f80]) ).
thf(f83,plain,
( ( sK0 @ sK3 )
!= ( sK1 = sK3 ) ),
inference(negative_extensionality,[],[f72]) ).
thf(f84,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 = sK3 ) ) ),
inference(xor_proxy_clausification,[],[f83]) ).
thf(f85,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 = sK3 ) ) ),
inference(xor_proxy_clausification,[],[f83]) ).
thf(f86,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( sK1 != sK3 ) ),
inference(equality_proxy_clausification,[],[f85]) ).
thf(f87,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( sK1 = sK3 ) ),
inference(equality_proxy_clausification,[],[f84]) ).
thf(f88,plain,
( $false
= ( sK0 @ sK3 ) ),
inference(forward_subsumption_resolution,[],[f86,f71]) ).
thf(f90,definition,
( spl4_1
<=> ( sK1 = sK3 ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f92,plain,
( ( sK1 = sK3 )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f90]) ).
thf(f94,definition,
( spl4_2
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f96,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f94]) ).
thf(f97,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f87,f94,f90]) ).
thf(f98,plain,
( $true
= ( sK0 @ sK1 ) ),
inference(constrained_superposition,[],[f78,f81]) ).
thf(f110,plain,
( ( $false = $true )
| ~ spl4_2 ),
inference(forward_demodulation,[],[f96,f88]) ).
thf(f111,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f110]) ).
thf(f112,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f111]) ).
thf(f114,plain,
( ( $false
= ( sK0 @ sK1 ) )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f88,f92]) ).
thf(f117,plain,
( ( $false = $true )
| ~ spl4_1 ),
inference(forward_demodulation,[],[f98,f114]) ).
thf(f118,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f117]) ).
thf(f119,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f118]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f97]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f112]) ).
cnf(s3,plain,
~ spl4_1,
inference(sat_conversion,[],[f119]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f120,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET096^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 13:36:34 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.12 Running first-order model finding
% 0.09/0.12 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
% 0.09/0.16 % (107907)Will run a generic schedule for satisfiability detection.
% 0.09/0.16 % (107913)% WARNING: option uhcvi not known.
% 0.09/0.16 % (107912)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1462561567_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.16 % (107915)dis+10_1_sil=32000:sp=arity:random_seed=4075160600:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.16 % (107913)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2442919134:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.16 % (107916)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2624686666:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.16 % (107914)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1848778016:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.16 % (107917)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1289412519:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.16 % (107918)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1761296425:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.16 % (107913)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.16 % (107916)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.16 % Exception at run slice level
% 0.09/0.16 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.16 % (107913)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.09/0.16 % (107915) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-107907-107915"...
% 0.09/0.16 % (107916) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-107907-107916"...
% 0.09/0.16 % (107913) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-107907-107913"...
% 0.09/0.16 % (107918) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-107907-107918"...
% 0.09/0.16 % (107917) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-107907-107917"...
% 0.09/0.16 % (107914) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-107907-107914"...
% 0.09/0.16 % (107913)...printing done.
% 0.09/0.16 % (107915)...printing done.
% 0.09/0.16 % (107916)...printing done.
% 0.09/0.16 % (107918)...printing done.
% 0.09/0.16 % (107917)...printing done.
% 0.09/0.16 % (107914)...printing done.
% 0.09/0.16 % (107915)Refutation found. Thanks to Tanya!
% 0.09/0.16 % SZS status Theorem for theBenchmark
% 0.09/0.16 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.16 % (107915)------------------------------
% 0.09/0.16 % (107915)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.16 % (107915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.16 % (107915)CaDiCaL version: 2.1.3
% 0.09/0.16 % (107915)Termination reason: Refutation
% 0.09/0.16 % (107915)Time elapsed: 0.002 s
% 0.09/0.16 % (107915)Peak memory usage: 12 MB
% 0.09/0.16 % (107915)Instructions burned: 5 (million)
% 0.09/0.16 % (107907)Success in time 0.029 s
% 0.09/0.16 % Vampire exiting
%------------------------------------------------------------------------------