%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n005.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 08:23:34 AM UTC 2026
% Result : Theorem 0.13s 0.28s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 22 unt; 0 typ; 2 def)
% Number of atoms : 200 ( 61 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 147 ( 21 ~; 21 |; 10 &; 77 @)
% ( 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 : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 32 usr; 8 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 47 ( 0 sgn 14 !; 6 ?; 47 :)
% 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_30,type,
sK2: $i > $o ).
thf(f4,axiom,
( unord_pair
= ( ^ [X0: $i,X1: $i,X2: $i] :
( ( X2 = X1 )
| ( X2 = X0 ) ) ) ),
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,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X1 )
& ( X2 @ X0 ) )
=> ( subset @ ( unord_pair @ X0 @ X1 ) @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f16,negated_conjecture,
~ ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X1 )
& ( X2 @ X0 ) )
=> ( subset @ ( unord_pair @ X0 @ X1 ) @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f20,plain,
( unord_pair
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( Y0 = Y2 )
| ( Y1 = Y2 ) ) ) ),
inference(fool_elimination,[],[f4]) ).
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,X1: $i,X2: $i > $o] :
( ( ( X2 @ X1 )
& ( X2 @ X0 ) )
=> ( subset @ ( unord_pair @ X0 @ X1 ) @ X2 ) ),
inference(rectify,[],[f16]) ).
thf(f40,plain,
~ ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( ( X2 @ X1 )
= $true )
& ( ( X2 @ X0 )
= $true ) )
=> ( ( subset @ ( unord_pair @ X0 @ X1 ) @ X2 )
= $true ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
? [X0: $i,X1: $i,X2: $i > $o] :
( ( ( subset @ ( unord_pair @ X0 @ X1 ) @ X2 )
!= $true )
& ( ( X2 @ X1 )
= $true )
& ( ( X2 @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f40]) ).
thf(f42,plain,
? [X0: $i,X1: $i,X2: $i > $o] :
( ( ( subset @ ( unord_pair @ X0 @ X1 ) @ X2 )
!= $true )
& ( ( X2 @ X1 )
= $true )
& ( ( X2 @ X0 )
= $true ) ),
inference(flattening,[],[f41]) ).
thf(f43,plain,
( ( $true
!= ( subset @ ( unord_pair @ sK0 @ sK1 ) @ sK2 ) )
& ( $true
= ( sK2 @ sK1 ) )
& ( $true
= ( sK2 @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f42]) ).
thf(f47,plain,
( unord_pair
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( Y0 = Y2 )
| ( Y1 = Y2 ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
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
= ( sK2 @ sK0 ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f59,plain,
( $true
= ( sK2 @ sK1 ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f60,plain,
( $true
!= ( subset @ ( unord_pair @ sK0 @ sK1 ) @ sK2 ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f64,plain,
( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( Y0 = Y2 )
| ( Y1 = Y2 ) )
@ sK0
@ sK1 )
@ sK2 ) ),
inference(definition_unfolding,[],[f60,f55,f47]) ).
thf(f65,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 = Y0 )
| ( sK1 = Y0 ) )
=> ( sK2 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
( $false
= ( ^ [Y0: $i] :
( ( ( sK0 = Y0 )
| ( sK1 = Y0 ) )
=> ( sK2 @ Y0 ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f65]) ).
thf(f67,plain,
( $false
= ( ( ( sK0 = sK3 )
| ( sK1 = sK3 ) )
=> ( sK2 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f68,plain,
( $false
= ( sK2 @ sK3 ) ),
inference(imp_proxy_clausification,[],[f67]) ).
thf(f69,plain,
( $true
= ( ( sK0 = sK3 )
| ( sK1 = sK3 ) ) ),
inference(imp_proxy_clausification,[],[f67]) ).
thf(f70,plain,
( ( $true
= ( sK1 = sK3 ) )
| ( $true
= ( sK0 = sK3 ) ) ),
inference(or_proxy_clausification,[],[f69]) ).
thf(f71,plain,
( ( sK1 = sK3 )
| ( $true
= ( sK0 = sK3 ) ) ),
inference(equality_proxy_clausification,[],[f70]) ).
thf(f72,plain,
( ( sK1 = sK3 )
| ( sK0 = sK3 ) ),
inference(equality_proxy_clausification,[],[f71]) ).
thf(f74,definition,
( spl4_1
<=> ( sK0 = sK3 ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f76,plain,
( ( sK0 = sK3 )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f74]) ).
thf(f78,definition,
( spl4_2
<=> ( sK1 = sK3 ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f80,plain,
( ( sK1 = sK3 )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f78]) ).
thf(f81,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f72,f78,f74]) ).
thf(f82,plain,
( ( $false
= ( sK2 @ sK1 ) )
| ~ spl4_2 ),
inference(constrained_superposition,[],[f68,f80]) ).
thf(f93,plain,
( ( $false = $true )
| ~ spl4_2 ),
inference(constrained_superposition,[],[f82,f59]) ).
thf(f97,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f93]) ).
thf(f98,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f97]) ).
thf(f101,plain,
( ( $false
= ( sK2 @ sK0 ) )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f68,f76]) ).
thf(f103,plain,
( ( $false = $true )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f101,f58]) ).
thf(f107,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f103]) ).
thf(f108,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f107]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f81]) ).
cnf(s3,plain,
~ spl4_2,
inference(sat_conversion,[],[f98]) ).
cnf(s5,plain,
~ spl4_1,
inference(sat_conversion,[],[f108]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
thf(f110,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET076^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.19 % Computer : n005.cluster.edu
% 0.13/0.19 % Model : x86_64 x86_64
% 0.13/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.19 % Memory : 8046.5625MB
% 0.13/0.19 % OS : Linux 6.8.0-71-generic
% 0.13/0.19 % CPULimit : 300
% 0.13/0.19 % WCLimit : 300
% 0.13/0.19 % DateTime : Tue Sep 29 13:36:31 UTC 2026
% 0.13/0.20 % CPUTime :
% 0.13/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.23 Running first-order model finding
% 0.13/0.23 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
% 0.13/0.28 % (1667316)Will run a generic schedule for satisfiability detection.
% 0.13/0.28 % (1667322)% WARNING: option uhcvi not known.
% 0.13/0.28 % (1667324)dis+10_1_sil=32000:sp=arity:random_seed=1825340581:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.28 % (1667321)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1289605028_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/0.28 % (1667325)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1258806543:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.28 % (1667322)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3379050873:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.28 % (1667323)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1597177899:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.28 % (1667325)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.13/0.28 % (1667322)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.13/0.28 % (1667327)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=230765108:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.28 % Exception at run slice level
% 0.13/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.28 % (1667322)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.13/0.28 % (1667324) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1667316-1667324"...
% 0.13/0.28 % (1667325) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1667316-1667325"...
% 0.13/0.28 % (1667322) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1667316-1667322"...
% 0.13/0.28 % (1667323) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1667316-1667323"...
% 0.13/0.28 % (1667326)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2177746315:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.28 % (1667324)...printing done.
% 0.13/0.28 % (1667325)...printing done.
% 0.13/0.28 % (1667322)...printing done.
% 0.13/0.28 % (1667323)...printing done.
% 0.13/0.28 % (1667327) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1667316-1667327"...
% 0.13/0.28 % (1667326) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1667316-1667326"...
% 0.13/0.28 % (1667325)Refutation found. Thanks to Tanya!
% 0.13/0.28 % SZS status Theorem for theBenchmark
% 0.13/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.28 % (1667325)------------------------------
% 0.13/0.28 % (1667325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.28 % (1667325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.28 % (1667325)CaDiCaL version: 2.1.3
% 0.13/0.28 % (1667325)Termination reason: Refutation
% 0.13/0.28 % (1667325)Time elapsed: 0.004 s
% 0.13/0.28 % (1667325)Peak memory usage: 13 MB
% 0.13/0.28 % (1667325)Instructions burned: 5 (million)
% 0.13/0.28 % (1667316)Success in time 0.044 s
% 0.13/0.28 % Vampire exiting
%------------------------------------------------------------------------------