%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET002^3 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 08:23:30 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 177 ( 38 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 286 ( 7 ~; 2 |; 0 &; 255 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 34 usr; 5 con; 0-4 aty)
% ( 12 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 87 ( 75 ^; 12 !; 0 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
mrel: mworld > mworld > $o ).
thf(func_def_1,type,
mactual: mworld ).
thf(func_def_2,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_4,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_5,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
qmltpeq: $i > $i > mworld > $o ).
thf(func_def_14,type,
member: $i > $i > mworld > $o ).
thf(func_def_15,type,
subset: $i > $i > mworld > $o ).
thf(func_def_16,type,
union: $i > $i > $i ).
thf(func_def_17,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_19,type,
vNOT: $o > $o ).
thf(func_def_20,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
vAND: $o > $o > $o ).
thf(func_def_22,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
vOR: $o > $o > $o ).
thf(func_def_24,type,
vIMP: $o > $o > $o ).
thf(func_def_25,type,
vIFF: $o > $o > $o ).
thf(func_def_26,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_30,type,
sK0: mworld > mworld ).
thf(func_def_32,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
sK2: $i > $i > $i ).
thf(func_def_35,type,
sK3: $i > $i > $i ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(f5,axiom,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def) ).
thf(f10,axiom,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_di_def) ).
thf(f21,axiom,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mimplies @ ( subset @ X0 @ X1 ) @ ( qmltpeq @ ( union @ X0 @ X1 ) @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_union) ).
thf(f26,axiom,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] : ( subset @ X0 @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(f28,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] : ( qmltpeq @ ( union @ X0 @ X0 ) @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idempotency_of_union) ).
thf(f29,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] : ( qmltpeq @ ( union @ X0 @ X0 ) @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
thf(f30,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f37,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f38,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f47,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f10]) ).
thf(f48,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f69,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mimplies @ ( subset @ X0 @ X1 ) @ ( qmltpeq @ ( union @ X0 @ X1 ) @ X1 ) ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f70,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mimplies @ ( subset @ Y0 @ Y1 ) @ ( qmltpeq @ ( union @ Y0 @ Y1 ) @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f79,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] : ( subset @ X0 @ X0 ) ) ),
inference(rectify,[],[f26]) ).
thf(f80,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( subset @ Y0 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f79]) ).
thf(f83,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] : ( qmltpeq @ ( union @ X0 @ X0 ) @ X0 ) ) ),
inference(rectify,[],[f29]) ).
thf(f84,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f85,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 ) ) ) ),
inference(flattening,[],[f84]) ).
thf(f87,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f91,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f96,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f107,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mimplies @ ( subset @ Y0 @ Y1 ) @ ( qmltpeq @ ( union @ Y0 @ Y1 ) @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f112,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( subset @ Y0 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f80]) ).
thf(f114,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f85]) ).
thf(f126,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( subset @ Y0 @ Y1 )
@ ( qmltpeq @ ( union @ Y0 @ Y1 ) @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f107,f87,f96,f96,f91]) ).
thf(f131,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] : ( subset @ Y0 @ Y0 ) ) ) ),
inference(definition_unfolding,[],[f112,f87,f96]) ).
thf(f133,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] : ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 ) ) ) ),
inference(definition_unfolding,[],[f114,f87,f96]) ).
thf(f134,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 @ mactual ) ) ),
inference(beta-eta_normalization,[],[f133]) ).
thf(f135,plain,
( $false
= ( ^ [Y0: $i] : ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 @ mactual )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f134]) ).
thf(f136,plain,
( $false
= ( qmltpeq @ ( union @ sK1 @ sK1 ) @ sK1 @ mactual ) ),
inference(beta-eta_normalization,[],[f135]) ).
thf(f155,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( subset @ Y0 @ Y0 @ mactual ) ) ),
inference(beta-eta_normalization,[],[f131]) ).
thf(f156,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( subset @ Y0 @ Y0 @ mactual )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X1: $i] :
( $true
= ( subset @ X1 @ X1 @ mactual ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f202,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 @ mactual )
=> ( qmltpeq @ ( union @ Y0 @ Y1 ) @ Y1 @ mactual ) ) ) ) ),
inference(beta-eta_normalization,[],[f126]) ).
thf(f203,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 @ mactual )
=> ( qmltpeq @ ( union @ Y0 @ Y1 ) @ Y1 @ mactual ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ X1 @ Y0 @ mactual )
=> ( qmltpeq @ ( union @ X1 @ Y0 ) @ Y0 @ mactual ) ) ) ),
inference(beta-eta_normalization,[],[f203]) ).
thf(f205,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ X1 @ Y0 @ mactual )
=> ( qmltpeq @ ( union @ X1 @ Y0 ) @ Y0 @ mactual ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( subset @ X1 @ X2 @ mactual )
=> ( qmltpeq @ ( union @ X1 @ X2 ) @ X2 @ mactual ) ) ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( qmltpeq @ ( union @ X1 @ X2 ) @ X2 @ mactual ) )
| ( $false
= ( subset @ X1 @ X2 @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f206]) ).
thf(f305,plain,
( ( $true = $false )
| ( $false
= ( subset @ sK1 @ sK1 @ mactual ) ) ),
inference(constrained_superposition,[],[f136,f207]) ).
thf(f306,plain,
( $false
= ( subset @ sK1 @ sK1 @ mactual ) ),
inference(trivial_inequality_removal,[],[f305]) ).
thf(f564,plain,
$true = $false,
inference(constrained_superposition,[],[f157,f306]) ).
thf(f569,plain,
$false,
inference(trivial_inequality_removal,[],[f564]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET002^3 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n002.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 13:38:22 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.23 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
% 0.20/0.28 % (1285055)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (1285061)% WARNING: option uhcvi not known.
% 0.20/0.28 % (1285061)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=986061414:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (1285061)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (1285061)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.28 % (1285060)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4030033044_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (1285062)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2853673568:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (1285064)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2669211576:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (1285063)dis+10_1_sil=32000:sp=arity:random_seed=1589491233:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (1285064)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (1285065)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=412647925:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (1285066)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2443815017:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.28 % Exception at run slice level
% 0.20/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.28 % (1285061) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1285055-1285061"...
% 0.20/0.28 % (1285061)...printing done.
% 0.20/0.28 % (1285061)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (1285061)------------------------------
% 0.20/0.28 % (1285061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1285061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1285061)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1285061)Termination reason: Refutation
% 0.20/0.28 % (1285061)Time elapsed: 0.014 s
% 0.20/0.28 % (1285061)Peak memory usage: 12 MB
% 0.20/0.28 % (1285061)Instructions burned: 53 (million)
% 0.20/0.28 % (1285055)Success in time 0.046 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------