%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET055^12 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 08:23:33 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 130 ( 28 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 162 ( 7 ~; 2 |; 0 &; 135 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 61 usr; 5 con; 0-4 aty)
% ( 6 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 42 ( 37 ^; 5 !; 0 ?; 42 :)
% 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,
eiw_di: $i > mworld > $o ).
thf(func_def_12,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_19,type,
qmltpeq: $i > $i > mworld > $o ).
thf(func_def_20,type,
inductive: $i > mworld > $o ).
thf(func_def_21,type,
disjoint: $i > $i > mworld > $o ).
thf(func_def_22,type,
function: $i > mworld > $o ).
thf(func_def_23,type,
member: $i > $i > mworld > $o ).
thf(func_def_24,type,
subclass: $i > $i > mworld > $o ).
thf(func_def_25,type,
singleton: $i > $i ).
thf(func_def_26,type,
image: $i > $i > $i ).
thf(func_def_27,type,
inverse: $i > $i ).
thf(func_def_28,type,
rotate: $i > $i ).
thf(func_def_29,type,
unordered_pair: $i > $i > $i ).
thf(func_def_30,type,
successor: $i > $i ).
thf(func_def_31,type,
apply: $i > $i > $i ).
thf(func_def_32,type,
power_class: $i > $i ).
thf(func_def_33,type,
range_of: $i > $i ).
thf(func_def_34,type,
union: $i > $i > $i ).
thf(func_def_35,type,
restrict: $i > $i > $i > $i ).
thf(func_def_36,type,
second: $i > $i ).
thf(func_def_37,type,
ordered_pair: $i > $i > $i ).
thf(func_def_38,type,
domain_of: $i > $i ).
thf(func_def_39,type,
sum_class: $i > $i ).
thf(func_def_40,type,
compose: $i > $i > $i ).
thf(func_def_41,type,
intersection: $i > $i > $i ).
thf(func_def_42,type,
cross_product: $i > $i > $i ).
thf(func_def_43,type,
complement: $i > $i ).
thf(func_def_44,type,
flip: $i > $i ).
thf(func_def_45,type,
first: $i > $i ).
thf(func_def_46,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_48,type,
vNOT: $o > $o ).
thf(func_def_49,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vAND: $o > $o > $o ).
thf(func_def_51,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
vOR: $o > $o > $o ).
thf(func_def_53,type,
vIMP: $o > $o > $o ).
thf(func_def_54,type,
vIFF: $o > $o > $o ).
thf(func_def_55,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_56,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_59,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_60,type,
sK0: mworld > $i ).
thf(func_def_63,type,
sK3: $i > $i ).
thf(func_def_64,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_65,type,
sK4: $i > $i > $i ).
thf(func_def_66,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_67,type,
sK5: $i > $i > $i ).
thf(func_def_69,type,
sK7: $i > $i > $i ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f11,axiom,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di_def) ).
thf(f13,axiom,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] : ( qmltpeq @ X0 @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(f96,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] : ( qmltpeq @ X0 @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_0) ).
thf(f97,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] : ( qmltpeq @ X0 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
thf(f98,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f117,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f118,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f117]) ).
thf(f121,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] : ( qmltpeq @ X0 @ X0 ) ) ),
inference(rectify,[],[f13]) ).
thf(f122,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( qmltpeq @ Y0 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f121]) ).
thf(f287,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] : ( qmltpeq @ X0 @ X0 ) ) ),
inference(rectify,[],[f97]) ).
thf(f288,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( qmltpeq @ Y0 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f287]) ).
thf(f289,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( qmltpeq @ Y0 @ Y0 ) ) ) ),
inference(flattening,[],[f288]) ).
thf(f291,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f98]) ).
thf(f301,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f118]) ).
thf(f303,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( qmltpeq @ Y0 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f122]) ).
thf(f386,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( qmltpeq @ Y0 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f289]) ).
thf(f389,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] : ( qmltpeq @ Y0 @ Y0 ) ) ) ),
inference(definition_unfolding,[],[f303,f291,f301]) ).
thf(f472,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] : ( qmltpeq @ Y0 @ Y0 ) ) ) ),
inference(definition_unfolding,[],[f386,f291,f301]) ).
thf(f473,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( qmltpeq @ Y0 @ Y0 @ mactual ) ) ) ),
inference(beta-eta_normalization,[],[f472]) ).
thf(f474,plain,
( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( qmltpeq @ Y0 @ Y0 @ mactual ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f473]) ).
thf(f475,plain,
( $false
= ( ( eiw_di @ sK1 @ mactual )
=> ( qmltpeq @ sK1 @ sK1 @ mactual ) ) ),
inference(beta-eta_normalization,[],[f474]) ).
thf(f476,plain,
( $false
= ( qmltpeq @ sK1 @ sK1 @ mactual ) ),
inference(imp_proxy_clausification,[],[f475]) ).
thf(f477,plain,
( $true
= ( eiw_di @ sK1 @ mactual ) ),
inference(imp_proxy_clausification,[],[f475]) ).
thf(f1345,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( qmltpeq @ Y0 @ Y0 @ mactual ) ) ) ),
inference(beta-eta_normalization,[],[f389]) ).
thf(f1346,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( qmltpeq @ Y0 @ Y0 @ mactual ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1345]) ).
thf(f1347,plain,
! [X1: $i] :
( $true
= ( ( eiw_di @ X1 @ mactual )
=> ( qmltpeq @ X1 @ X1 @ mactual ) ) ),
inference(beta-eta_normalization,[],[f1346]) ).
thf(f1348,plain,
! [X1: $i] :
( ( $true
= ( qmltpeq @ X1 @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(imp_proxy_clausification,[],[f1347]) ).
thf(f1360,plain,
( ( $true = $false )
| ( $false
= ( eiw_di @ sK1 @ mactual ) ) ),
inference(constrained_superposition,[],[f1348,f476]) ).
thf(f1361,plain,
( $false
= ( eiw_di @ sK1 @ mactual ) ),
inference(trivial_inequality_removal,[],[f1360]) ).
thf(f1366,plain,
$true = $false,
inference(constrained_superposition,[],[f477,f1361]) ).
thf(f1367,plain,
$false,
inference(trivial_inequality_removal,[],[f1366]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET055^12 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/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 13:39:23 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.28 % (1288841)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (1288851)% WARNING: option uhcvi not known.
% 0.19/0.28 % (1288851)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3017116887:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.28 % (1288851)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.28 % (1288850)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2935873095_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.28 % (1288852)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1825946574:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.28 % (1288854)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2047699303:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.28 % (1288853)dis+10_1_sil=32000:sp=arity:random_seed=1176331265:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.28 % (1288851)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.28 % (1288855)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4220398711:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.28 % (1288856)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1122266512:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.28 % (1288854)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.28 % Exception at run slice level
% 0.19/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.28 % (1288851) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1288841-1288851"...
% 0.19/0.28 % (1288851)...printing done.
% 0.19/0.28 % (1288851)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.29 % (1288851)------------------------------
% 0.19/0.29 % (1288851)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (1288851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (1288851)CaDiCaL version: 2.1.3
% 0.19/0.29 % (1288851)Termination reason: Refutation
% 0.19/0.29 % (1288851)Time elapsed: 0.032 s
% 0.19/0.29 % (1288851)Peak memory usage: 13 MB
% 0.19/0.29 % (1288851)Instructions burned: 135 (million)
% 0.19/0.29 % (1288841)Success in time 0.061 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------