%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET764^4 : 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 : n015.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 08:23:49 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 94 ( 30 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 70 ( 8 ~; 3 |; 6 &; 45 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 38 usr; 5 con; 0-4 aty)
% ( 0 !!; 8 ??; 0 @@+; 0 @@-)
% Number of variables : 43 ( 38 ^; 2 !; 3 ?; 43 :)
% 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,
fun_image: ( $i > $i ) > ( $i > $o ) > $i > $o ).
thf(func_def_16,type,
fun_composition: ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_17,type,
fun_inv_image: ( $i > $i ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
fun_injective: ( $i > $i ) > $o ).
thf(func_def_19,type,
fun_surjective: ( $i > $i ) > $o ).
thf(func_def_20,type,
fun_bijective: ( $i > $i ) > $o ).
thf(func_def_21,type,
fun_decreasing: ( $i > $i ) > ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
fun_increasing: ( $i > $i ) > ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_28,type,
vOR: $o > $o > $o ).
thf(func_def_29,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_31,type,
vAND: $o > $o > $o ).
thf(func_def_32,type,
vNOT: $o > $o ).
thf(func_def_33,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_34,type,
vIMP: $o > $o > $o ).
thf(func_def_35,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_36,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
sK0: $i > $i ).
thf(f3,axiom,
( emptyset
= ( ^ [X0: $i] : $false ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',emptyset) ).
thf(f17,axiom,
( fun_inv_image
= ( ^ [X0: $i > $i,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X3
= ( X0 @ X2 ) )
& ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^1.ax',fun_inv_image) ).
thf(f23,conjecture,
! [X0: $i > $i] :
( ( fun_inv_image @ X0 @ emptyset )
= emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f24,negated_conjecture,
~ ! [X0: $i > $i] :
( ( fun_inv_image @ X0 @ emptyset )
= emptyset ),
inference(negated_conjecture,[status(cth)],[f23]) ).
thf(f27,plain,
( emptyset
= ( ^ [Y0: $i] : $false ) ),
inference(fool_elimination,[],[f3]) ).
thf(f50,plain,
( fun_inv_image
= ( ^ [X0: $i > $i,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X3
= ( X0 @ X2 ) )
& ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f51,plain,
( fun_inv_image
= ( ^ [Y0: $i > $i,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( ( Y0 @ Y2 )
= Y3 ) ) ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f60,plain,
? [X0: $i > $i] :
( emptyset
!= ( fun_inv_image @ X0 @ emptyset ) ),
inference(ennf_transformation,[],[f24]) ).
thf(f61,plain,
( emptyset
!= ( fun_inv_image @ sK0 @ emptyset ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f60]) ).
thf(f64,plain,
( emptyset
= ( ^ [Y0: $i] : $false ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f78,plain,
( fun_inv_image
= ( ^ [Y0: $i > $i,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( ( Y0 @ Y2 )
= Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f84,plain,
( emptyset
!= ( fun_inv_image @ sK0 @ emptyset ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f89,plain,
( ( ^ [Y0: $i] : $false )
!= ( ^ [Y0: $i > $i,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( ( Y0 @ Y2 )
= Y3 ) ) )
@ sK0
@ ^ [Y0: $i] : $false ) ),
inference(definition_unfolding,[],[f84,f64,f78,f64]) ).
thf(f90,plain,
( ( ^ [Y0: $i] : $false )
!= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( $false
& ( ( sK0 @ Y0 )
= Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f89]) ).
thf(f91,plain,
( ( ^ [Y0: $i] : $false )
!= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : $false ) ) ),
inference(boolean_simplification,[],[f90]) ).
thf(f92,plain,
( ( ^ [Y0: $i] : $false
@ sK1 )
!= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : $false )
@ sK1 ) ),
inference(negative_extensionality,[],[f91]) ).
thf(f93,plain,
( ( $true
= ( ^ [Y0: $i] : $false
@ sK1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : $false )
@ sK1 ) ) ),
inference(xor_proxy_clausification,[],[f92]) ).
thf(f97,plain,
( ( $false = $true )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] : $false ) ) ),
inference(beta-eta_normalization,[],[f93]) ).
thf(f98,plain,
( ( $false = $true )
| ( $true
= ( ^ [Y0: $i] : $false
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f97]) ).
thf(f99,plain,
( $true
= ( ^ [Y0: $i] : $false
@ sK2 ) ),
inference(trivial_inequality_removal,[],[f98]) ).
thf(f100,plain,
$false = $true,
inference(beta-eta_normalization,[],[f99]) ).
thf(f101,plain,
$false,
inference(trivial_inequality_removal,[],[f100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET764^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n015.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 13:44:18 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 Running first-order model finding
% 0.07/0.21 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
% 0.07/0.25 % (3543723)Will run a generic schedule for satisfiability detection.
% 0.07/0.25 % (3543731)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1082504433_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.25 % (3543733)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=967170037:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.25 % (3543735)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=381397931:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.25 % (3543734)dis+10_1_sil=32000:sp=arity:random_seed=2630399872:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.25 % (3543736)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=83571478:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.25 % (3543737)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=899628161:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.25 % (3543735)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.25 % Exception at run slice level
% 0.07/0.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.07/0.25 % (3543732)% WARNING: option uhcvi not known.
% 0.07/0.25 % (3543735) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3543723-3543735"...
% 0.07/0.25 % (3543734) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3543723-3543734"...
% 0.07/0.25 % (3543736) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3543723-3543736"...
% 0.07/0.25 % (3543733) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3543723-3543733"...
% 0.07/0.25 % (3543737) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3543723-3543737"...
% 0.07/0.25 % (3543732)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1425531475:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.25 % (3543735)...printing done.
% 0.07/0.25 % (3543734)...printing done.
% 0.07/0.25 % (3543733)...printing done.
% 0.07/0.25 % (3543736)...printing done.
% 0.07/0.25 % (3543737)...printing done.
% 0.07/0.25 % (3543732)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.25 % (3543734)Refutation found. Thanks to Tanya!
% 0.07/0.25 % SZS status Theorem for theBenchmark
% 0.07/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.25 % (3543734)------------------------------
% 0.07/0.25 % (3543734)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.25 % (3543734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.25 % (3543734)CaDiCaL version: 2.1.3
% 0.07/0.25 % (3543734)Termination reason: Refutation
% 0.07/0.25 % (3543734)Time elapsed: 0.003 s
% 0.07/0.25 % (3543734)Peak memory usage: 12 MB
% 0.07/0.25 % (3543734)Instructions burned: 5 (million)
% 0.07/0.25 % (3543723)Success in time 0.037 s
% 0.07/0.25 % Vampire exiting
%------------------------------------------------------------------------------