%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n002.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 08:23:14 AM UTC 2026
% Result : Theorem 0.07s 0.27s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 60 ( 32 unt; 0 typ; 2 def)
% Number of atoms : 273 ( 85 equ; 1 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 159 ( 30 ~; 22 |; 8 &; 81 @)
% ( 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 : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 32 usr; 9 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 51 ( 6 sgn 14 !; 6 ?; 51 :)
% 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,
vOR: $o > $o > $o ).
thf(func_def_16,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_20,type,
vAND: $o > $o > $o ).
thf(func_def_23,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_24,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_25,type,
vNOT: $o > $o ).
thf(func_def_26,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
vIMP: $o > $o > $o ).
thf(func_def_29,type,
sK1: $i > $o ).
thf(f3,axiom,
( emptyset
= ( ^ [X0: $i] : $false ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',emptyset) ).
thf(f5,axiom,
( ( ^ [X0: $i,X1: $i] : ( X1 = X0 ) )
= singleton ),
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(f22,plain,
~ ! [X0: $i > $o,X1: $i] :
( ( subset @ X0 @ ( singleton @ X1 ) )
=> ( ( X0
= ( singleton @ X1 ) )
| ( X0 = emptyset ) ) ),
inference(rectify,[],[f16]) ).
thf(f23,plain,
~ ! [X0: $i > $o,X1: $i] :
( ( ( subset @ X0 @ ( singleton @ X1 ) )
= $true )
=> ( ( ( singleton @ X1 )
= X0 )
| ( emptyset = X0 ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f32,plain,
( singleton
= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f35,plain,
( emptyset
= ( ^ [Y0: $i] : $false ) ),
inference(fool_elimination,[],[f3]) ).
thf(f39,plain,
( subset
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f40,plain,
( subset
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
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,[],[f23]) ).
thf(f42,plain,
? [X1: $i,X0: $i > $o] :
( ( ( singleton @ X1 )
!= X0 )
& ( emptyset != X0 )
& ( ( subset @ X0 @ ( singleton @ X1 ) )
= $true ) ),
inference(flattening,[],[f41]) ).
thf(f43,plain,
? [X0: $i,X1: $i > $o] :
( ( ( singleton @ X0 )
!= X1 )
& ( emptyset != X1 )
& ( $true
= ( subset @ X1 @ ( singleton @ X0 ) ) ) ),
inference(rectify,[],[f42]) ).
thf(f44,plain,
( ( ( singleton @ sK0 )
!= sK1 )
& ( emptyset != sK1 )
& ( $true
= ( subset @ sK1 @ ( singleton @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f43]) ).
thf(f46,plain,
( emptyset
= ( ^ [Y0: $i] : $false ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f48,plain,
( singleton
= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f56,plain,
( subset
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f59,plain,
( $true
= ( subset @ sK1 @ ( singleton @ sK0 ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f60,plain,
emptyset != sK1,
inference(cnf_transformation,[],[f44]) ).
thf(f61,plain,
( ( singleton @ sK0 )
!= sK1 ),
inference(cnf_transformation,[],[f44]) ).
thf(f65,plain,
( sK1
!= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 )
@ sK0 ) ),
inference(definition_unfolding,[],[f61,f48]) ).
thf(f66,plain,
( ( ^ [Y0: $i] : $false )
!= sK1 ),
inference(definition_unfolding,[],[f60,f46]) ).
thf(f67,plain,
( $true
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
@ sK1
@ ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f59,f56,f48]) ).
thf(f68,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK0 = Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK0 = Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f68]) ).
thf(f70,plain,
! [X1: $i] :
( $true
= ( ( sK1 @ X1 )
=> ( sK0 = X1 ) ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f71,plain,
! [X1: $i] :
( ( $false
= ( sK1 @ X1 ) )
| ( ( sK0 = X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f70]) ).
thf(f72,plain,
! [X1: $i] :
( ( $false
= ( sK1 @ X1 ) )
| ( sK0 = X1 ) ),
inference(equality_proxy_clausification,[],[f71]) ).
thf(f73,plain,
( sK1
!= ( (=) @ sK0 ) ),
inference(beta-eta_normalization,[],[f65]) ).
thf(f74,plain,
( ( sK1 @ sK2 )
!= ( ^ [Y0: $i] : $false
@ sK2 ) ),
inference(negative_extensionality,[],[f66]) ).
thf(f75,plain,
( ( $true
= ( ^ [Y0: $i] : $false
@ sK2 ) )
| ( $true
= ( sK1 @ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f74]) ).
thf(f78,plain,
( ( $true = $false )
| ( $true
= ( sK1 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f79,plain,
( $true
= ( sK1 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f78]) ).
thf(f80,plain,
( ( sK2 = sK0 )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f79,f72]) ).
thf(f82,plain,
sK2 = sK0,
inference(trivial_inequality_removal,[],[f80]) ).
thf(f84,plain,
( $true
= ( sK1 @ sK0 ) ),
inference(constrained_superposition,[],[f79,f82]) ).
thf(f85,plain,
( ( sK0 = sK3 )
!= ( sK1 @ sK3 ) ),
inference(negative_extensionality,[],[f73]) ).
thf(f86,plain,
( ( $true
= ( sK0 = sK3 ) )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f85]) ).
thf(f87,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 = sK3 ) ) ),
inference(xor_proxy_clausification,[],[f85]) ).
thf(f88,plain,
( ( sK3 != sK0 )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(equality_proxy_clausification,[],[f87]) ).
thf(f89,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( sK3 = sK0 ) ),
inference(equality_proxy_clausification,[],[f86]) ).
thf(f90,plain,
( $false
= ( sK1 @ sK3 ) ),
inference(forward_subsumption_resolution,[],[f88,f72]) ).
thf(f92,definition,
( spl4_1
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f94,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f92]) ).
thf(f96,definition,
( spl4_2
<=> ( sK3 = sK0 ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f98,plain,
( ( sK3 = sK0 )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f96]) ).
thf(f99,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f89,f96,f92]) ).
thf(f100,plain,
( ( $false
= ( sK1 @ sK0 ) )
| ~ spl4_2 ),
inference(constrained_superposition,[],[f90,f98]) ).
thf(f101,plain,
( ( $true = $false )
| ~ spl4_2 ),
inference(forward_demodulation,[],[f100,f84]) ).
thf(f102,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f101]) ).
thf(f103,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f102]) ).
thf(f104,plain,
( ( $true = $false )
| ~ spl4_1 ),
inference(forward_demodulation,[],[f94,f90]) ).
thf(f105,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f104]) ).
thf(f106,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f105]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f99]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f103]) ).
cnf(s3,plain,
~ spl4_1,
inference(sat_conversion,[],[f106]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f107,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET096^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n002.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:39:37 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.27 % (1289548)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.07/0.27 % (1289559)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2463263626:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.07/0.27 % (1289557)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2137403106:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.07/0.27 % (1289555)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2614168825:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.07/0.27 % (1289557)Refutation not found, incomplete strategy
% 0.07/0.27 % (1289557)------------------------------
% 0.07/0.27 % (1289557)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.27 % (1289557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.27 % (1289557)CaDiCaL version: 2.1.3
% 0.07/0.27 % (1289557)Termination reason: Refutation not found, incomplete strategy
% 0.07/0.27 % (1289557)Time elapsed: 0.002 s
% 0.07/0.27 % (1289557)Peak memory usage: 12 MB
% 0.07/0.27 % (1289557)Instructions burned: 3 (million)
% 0.07/0.27 % (1289559) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1289548-1289559"...
% 0.07/0.27 % (1289557)------------------------------
% 0.07/0.27 % (1289557)------------------------------
% 0.07/0.27 % (1289555) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1289548-1289555"...
% 0.07/0.27 % (1289558)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1267324048:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.07/0.27 % (1289559)...printing done.
% 0.07/0.27 % (1289555)...printing done.
% 0.07/0.27 % (1289561)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.07/0.27 % (1289561)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.07/0.27 % (1289555)Refutation found. Thanks to Tanya!
% 0.07/0.27 % SZS status Theorem for theBenchmark
% 0.07/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.27 % (1289555)------------------------------
% 0.07/0.27 % (1289555)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.27 % (1289555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.27 % (1289555)CaDiCaL version: 2.1.3
% 0.07/0.27 % (1289555)Termination reason: Refutation
% 0.07/0.27 % (1289555)Time elapsed: 0.004 s
% 0.07/0.27 % (1289555)Peak memory usage: 13 MB
% 0.07/0.27 % (1289555)Instructions burned: 5 (million)
% 0.07/0.27 % (1289548)Success in time 0.048 s
% 0.07/0.27 % Vampire exiting
%------------------------------------------------------------------------------