%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET076^1 : 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 : 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 08:23:13 AM UTC 2026
% Result : Theorem 0.35s 0.43s
% Output : Refutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 22 unt; 0 typ; 2 def)
% Number of atoms : 208 ( 64 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 156 ( 22 ~; 21 |; 12 &; 83 @)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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 : 36 ( 32 usr; 8 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 50 ( 0 sgn 14 !; 9 ?; 50 :)
% 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,
vNOT: $o > $o ).
thf(func_def_16,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_17,type,
vAND: $o > $o > $o ).
thf(func_def_18,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_22,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_23,type,
vOR: $o > $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_28,type,
sK0: $i > $o ).
thf(f4,axiom,
( unord_pair
= ( ^ [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',unord_pair) ).
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,
! [X1: $i,X2: $i > $o,X0: $i] :
( ( ( X2 @ X1 )
& ( X2 @ X0 ) )
=> ( subset @ ( unord_pair @ X0 @ X1 ) @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f16,negated_conjecture,
~ ! [X1: $i,X2: $i > $o,X0: $i] :
( ( ( X2 @ X1 )
& ( X2 @ X0 ) )
=> ( subset @ ( unord_pair @ X0 @ X1 ) @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f26,plain,
( unord_pair
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y2 ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f30,plain,
( subset
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f31,plain,
( subset
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f32,plain,
~ ! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( X1 @ X0 )
& ( X1 @ X2 ) )
=> ( subset @ ( unord_pair @ X2 @ X0 ) @ X1 ) ),
inference(rectify,[],[f16]) ).
thf(f33,plain,
~ ! [X2: $i,X0: $i,X1: $i > $o] :
( ( ( ( X1 @ X0 )
= $true )
& ( ( X1 @ X2 )
= $true ) )
=> ( $true
= ( subset @ ( unord_pair @ X2 @ X0 ) @ X1 ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f41,plain,
? [X2: $i,X0: $i,X1: $i > $o] :
( ( $true
!= ( subset @ ( unord_pair @ X2 @ X0 ) @ X1 ) )
& ( ( X1 @ X0 )
= $true )
& ( ( X1 @ X2 )
= $true ) ),
inference(ennf_transformation,[],[f33]) ).
thf(f42,plain,
? [X1: $i > $o,X2: $i,X0: $i] :
( ( ( X1 @ X2 )
= $true )
& ( ( X1 @ X0 )
= $true )
& ( $true
!= ( subset @ ( unord_pair @ X2 @ X0 ) @ X1 ) ) ),
inference(flattening,[],[f41]) ).
thf(f43,plain,
? [X0: $i > $o,X1: $i,X2: $i] :
( ( ( X0 @ X1 )
= $true )
& ( ( X0 @ X2 )
= $true )
& ( $true
!= ( subset @ ( unord_pair @ X1 @ X2 ) @ X0 ) ) ),
inference(rectify,[],[f42]) ).
thf(f44,plain,
( ( $true
= ( sK0 @ sK1 ) )
& ( ( sK0 @ sK2 )
= $true )
& ( $true
!= ( subset @ ( unord_pair @ sK1 @ sK2 ) @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f43]) ).
thf(f45,plain,
( $true
!= ( subset @ ( unord_pair @ sK1 @ sK2 ) @ sK0 ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f46,plain,
( ( sK0 @ sK2 )
= $true ),
inference(cnf_transformation,[],[f44]) ).
thf(f47,plain,
( $true
= ( sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f54,plain,
( unord_pair
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y2 ) ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f60,plain,
( subset
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f65,plain,
( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y2 ) )
@ sK1
@ sK2 )
@ sK0 ) ),
inference(definition_unfolding,[],[f45,f60,f54]) ).
thf(f66,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
| ( sK1 = Y0 ) )
=> ( sK0 @ Y0 ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f65]) ).
thf(f67,plain,
( ( ^ [Y0: $i] :
( ( ( sK2 = Y0 )
| ( sK1 = Y0 ) )
=> ( sK0 @ Y0 ) )
@ sK3 )
= $false ),
inference(sigma_proxy_clausification,[],[f66]) ).
thf(f68,plain,
( $false
= ( ( ( sK2 = sK3 )
| ( sK1 = sK3 ) )
=> ( sK0 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
( $false
= ( sK0 @ sK3 ) ),
inference(imp_proxy_clausification,[],[f68]) ).
thf(f70,plain,
( $true
= ( ( sK2 = sK3 )
| ( sK1 = sK3 ) ) ),
inference(imp_proxy_clausification,[],[f68]) ).
thf(f71,plain,
( ( $true
= ( sK2 = sK3 ) )
| ( ( sK1 = sK3 )
= $true ) ),
inference(or_proxy_clausification,[],[f70]) ).
thf(f72,plain,
( ( sK2 = sK3 )
| ( ( sK1 = sK3 )
= $true ) ),
inference(equality_proxy_clausification,[],[f71]) ).
thf(f73,plain,
( ( sK3 = sK1 )
| ( sK2 = sK3 ) ),
inference(equality_proxy_clausification,[],[f72]) ).
thf(f75,definition,
( spl4_1
<=> ( sK3 = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f77,plain,
( ( sK3 = sK1 )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f75]) ).
thf(f79,definition,
( spl4_2
<=> ( sK2 = sK3 ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f81,plain,
( ( sK2 = sK3 )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f79]) ).
thf(f82,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f73,f79,f75]) ).
thf(f83,plain,
( ( ( sK0 @ sK2 )
= $false )
| ~ spl4_2 ),
inference(constrained_superposition,[],[f69,f81]) ).
thf(f84,plain,
( ( $false = $true )
| ~ spl4_2 ),
inference(forward_demodulation,[],[f83,f46]) ).
thf(f85,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f84]) ).
thf(f86,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f85]) ).
thf(f88,plain,
( ( $false
= ( sK0 @ sK1 ) )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f69,f77]) ).
thf(f89,plain,
( ( $false = $true )
| ~ spl4_1 ),
inference(forward_demodulation,[],[f88,f47]) ).
thf(f90,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f89]) ).
thf(f91,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f90]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f82]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f86]) ).
cnf(s3,plain,
~ spl4_1,
inference(sat_conversion,[],[f91]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f92,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET076^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.28 % Computer : n026.cluster.edu
% 0.12/0.28 % Model : x86_64 x86_64
% 0.12/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.28 % Memory : 8046.5625MB
% 0.12/0.28 % OS : Linux 6.8.0-71-generic
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Sep 29 13:39:27 UTC 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.29/0.34 Running higher-order theorem proving
% 0.29/0.36 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
% 0.35/0.43 % (597246)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.35/0.43 % (597254)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=3699583327: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)
% 0.35/0.43 % (597257)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.35/0.43 % (597257)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
% 0.35/0.43 % (597255)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4058895265:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.35/0.43 % (597253)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1240717612:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.35/0.43 % (597252)lrs+10_16_si=on:nwc=1.5:random_seed=3789931197:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.35/0.43 % (597256)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3005973832:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.35/0.43 % (597251)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1444949948:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.35/0.43 % (597257)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=542472273:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.35/0.43 % (597253)Refutation not found, incomplete strategy
% 0.35/0.43 % (597253)------------------------------
% 0.35/0.43 % (597253)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.43 % (597253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.43 % (597253)CaDiCaL version: 2.1.3
% 0.35/0.43 % (597253)Termination reason: Refutation not found, incomplete strategy
% 0.35/0.43 % (597253)Time elapsed: 0.004 s
% 0.35/0.43 % (597253)Peak memory usage: 12 MB
% 0.35/0.43 % (597253)Instructions burned: 3 (million)
% 0.35/0.43 % (597256) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-597246-597256"...
% 0.35/0.43 % (597251) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-597246-597251"...
% 0.35/0.43 % (597252) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-597246-597252"...
% 0.35/0.43 % (597253)------------------------------
% 0.35/0.43 % (597253)------------------------------
% 0.35/0.43 % (597254) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-597246-597254"...
% 0.35/0.43 % (597257) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-597246-597257"...
% 0.35/0.43 % (597256)...printing done.
% 0.35/0.43 % (597251)...printing done.
% 0.35/0.43 % (597252)...printing done.
% 0.35/0.43 % (597254)...printing done.
% 0.35/0.43 % (597251)Refutation found. Thanks to Tanya!
% 0.35/0.43 % SZS status Theorem for theBenchmark
% 0.35/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.35/0.44 % (597251)------------------------------
% 0.35/0.44 % (597251)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.44 % (597251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.44 % (597251)CaDiCaL version: 2.1.3
% 0.35/0.44 % (597251)Termination reason: Refutation
% 0.35/0.44 % (597251)Time elapsed: 0.006 s
% 0.35/0.44 % (597251)Peak memory usage: 13 MB
% 0.35/0.44 % (597251)Instructions burned: 5 (million)
% 0.35/0.44 % (597246)Success in time 0.058 s
% 0.35/0.44 % Vampire exiting
%------------------------------------------------------------------------------