%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET606^3 : 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 : n007.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 08:23:20 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of formulae : 54 ( 25 unt; 0 typ; 2 def)
% Number of atoms : 349 ( 72 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 281 ( 46 ~; 36 |; 41 &; 156 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 5 con; 0-4 aty)
% Number of variables : 49 ( 0 sgn 4 !; 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,
vAND: $o > $o > $o ).
thf(func_def_16,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vNOT: $o > $o ).
thf(func_def_19,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_21,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_22,type,
vOR: $o > $o > $o ).
thf(func_def_23,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_24,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_25,type,
vIMP: $o > $o > $o ).
thf(func_def_28,type,
sK0: $i > $o ).
thf(func_def_29,type,
sK1: $i > $o ).
thf(f8,axiom,
( intersection
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',intersection) ).
thf(f9,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= setminus ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',setminus) ).
thf(f15,conjecture,
! [X1: $i > $o,X0: $i > $o] :
( ( setminus @ X0 @ ( intersection @ X0 @ X1 ) )
= ( setminus @ X0 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f16,negated_conjecture,
~ ! [X1: $i > $o,X0: $i > $o] :
( ( setminus @ X0 @ ( intersection @ X0 @ X1 ) )
= ( setminus @ X0 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f17,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= setminus ),
inference(rectify,[],[f9]) ).
thf(f18,plain,
( setminus
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f36,plain,
( intersection
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f37,plain,
( intersection
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f39,plain,
? [X1: $i > $o,X0: $i > $o] :
( ( setminus @ X0 @ ( intersection @ X0 @ X1 ) )
!= ( setminus @ X0 @ X1 ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f40,plain,
? [X0: $i > $o,X1: $i > $o] :
( ( setminus @ X1 @ ( intersection @ X1 @ X0 ) )
!= ( setminus @ X1 @ X0 ) ),
inference(rectify,[],[f39]) ).
thf(f41,plain,
( ( setminus @ sK1 @ ( intersection @ sK1 @ sK0 ) )
!= ( setminus @ sK1 @ sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f40]) ).
thf(f43,plain,
( setminus
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f44,plain,
( intersection
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f49,plain,
( ( setminus @ sK1 @ ( intersection @ sK1 @ sK0 ) )
!= ( setminus @ sK1 @ sK0 ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f60,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
@ sK1
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ sK1
@ sK0 ) )
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
@ sK1
@ sK0 ) ),
inference(definition_unfolding,[],[f49,f43,f44,f43]) ).
thf(f61,plain,
( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ~ ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) ) )
!= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f60]) ).
thf(f62,plain,
( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ~ ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
@ sK2 )
!= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
@ sK2 ) ),
inference(negative_extensionality,[],[f61]) ).
thf(f63,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
@ sK2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ~ ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f62]) ).
thf(f64,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ~ ( ( sK1 @ Y0 )
& ( sK0 @ Y0 ) ) )
@ sK2 ) ) ),
inference(xor_proxy_clausification,[],[f62]) ).
thf(f65,plain,
( ( $false
= ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) )
| ( $false
= ( ( sK1 @ sK2 )
& ~ ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
( ( $false
= ( ~ ( sK0 @ sK2 ) ) )
| ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( ( sK1 @ sK2 )
& ~ ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) ) ) ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f67,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $false
= ( ( sK1 @ sK2 )
& ~ ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) ) )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f66]) ).
thf(f68,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( $false
= ( ~ ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) ) ) ),
inference(and_proxy_clausification,[],[f67]) ).
thf(f69,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $false
= ( sK1 @ sK2 ) )
| ( $true
= ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f68]) ).
thf(f70,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $false
= ( sK1 @ sK2 ) )
| ( $true
= ( sK0 @ sK2 ) )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f69]) ).
thf(f73,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(duplicate_literal_removal,[],[f70]) ).
thf(f74,plain,
( ( $true
= ( ( sK1 @ sK2 )
& ~ ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) ) )
| ( $true
= ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f63]) ).
thf(f75,plain,
( ( $true
= ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) )
| ( $true
= ( ~ ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) ) ) ),
inference(and_proxy_clausification,[],[f74]) ).
thf(f76,plain,
( ( $true
= ( ( sK1 @ sK2 )
& ~ ( sK0 @ sK2 ) ) )
| ( $true
= ( sK1 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f74]) ).
thf(f78,plain,
( ( $true
= ( sK1 @ sK2 ) )
| ( $true
= ( sK1 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f76]) ).
thf(f79,plain,
( $true
= ( sK1 @ sK2 ) ),
inference(duplicate_literal_removal,[],[f78]) ).
thf(f81,plain,
( ( $true
= ( ~ ( sK0 @ sK2 ) ) )
| ( $true
= ( ~ ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) ) ) ),
inference(and_proxy_clausification,[],[f75]) ).
thf(f85,plain,
( ( $true
= ( ~ ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f81]) ).
thf(f86,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( ( sK1 @ sK2 )
& ( sK0 @ sK2 ) ) ) ),
inference(not_proxy_clausification,[],[f85]) ).
thf(f87,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( sK1 @ sK2 ) )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f86]) ).
thf(f88,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(duplicate_literal_removal,[],[f87]) ).
thf(f90,definition,
( spl3_1
<=> ( $true
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f92,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f90]) ).
thf(f94,definition,
( spl3_2
<=> ( $false
= ( sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f96,plain,
( ( $false
= ( sK1 @ sK2 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f94]) ).
thf(f97,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f73,f94,f90]) ).
thf(f98,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK2 ) ) ),
inference(forward_demodulation,[],[f88,f79]) ).
thf(f99,plain,
( $false
= ( sK0 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f98]) ).
thf(f101,plain,
( ( $true = $false )
| ~ spl3_2 ),
inference(constrained_superposition,[],[f96,f79]) ).
thf(f104,plain,
( $false
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f101]) ).
thf(f105,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f104]) ).
thf(f107,plain,
( ( $true = $false )
| ~ spl3_1 ),
inference(forward_demodulation,[],[f92,f99]) ).
thf(f108,plain,
( $false
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f107]) ).
thf(f109,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f108]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f97]) ).
cnf(s3,plain,
~ spl3_2,
inference(sat_conversion,[],[f105]) ).
cnf(s4,plain,
~ spl3_1,
inference(sat_conversion,[],[f109]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s4]) ).
thf(f110,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET606^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n007.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:36:56 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 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
% 0.21/0.29 % (3366702)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (3366720)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (3366720)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
% 0.21/0.29 % (3366714)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2265049406:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (3366715)lrs+10_16_si=on:nwc=1.5:random_seed=3190267767:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (3366717)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=676485578: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)
% 0.21/0.29 % (3366718)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1369038617:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (3366720)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=602088081:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (3366719)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=735136772:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (3366714) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3366702-3366714"...
% 0.21/0.29 % (3366715) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3366702-3366715"...
% 0.21/0.29 % (3366719) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3366702-3366719"...
% 0.21/0.29 % (3366720) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3366702-3366720"...
% 0.21/0.29 % (3366716)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4085685042:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (3366715)...printing done.
% 0.21/0.29 % (3366714)...printing done.
% 0.21/0.29 % (3366719)...printing done.
% 0.21/0.29 % (3366715)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (3366715)------------------------------
% 0.21/0.29 % (3366715)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (3366715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (3366715)CaDiCaL version: 2.1.3
% 0.21/0.29 % (3366715)Termination reason: Refutation
% 0.21/0.29 % (3366715)Time elapsed: 0.005 s
% 0.21/0.29 % (3366715)Peak memory usage: 13 MB
% 0.21/0.29 % (3366715)Instructions burned: 5 (million)
% 0.21/0.29 % (3366702)Success in time 0.046 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------