%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET764^4 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:23:29 AM UTC 2026
% Result : Theorem 0.26s 0.36s
% Output : Refutation 0.26s
% 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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_26,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_27,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_28,type,
vAND: $o > $o > $o ).
thf(func_def_29,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
vNOT: $o > $o ).
thf(func_def_32,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
vIMP: $o > $o > $o ).
thf(func_def_36,type,
vOR: $o > $o > $o ).
thf(func_def_37,type,
sK0: $i > $i ).
thf(f3,axiom,
( ( ^ [X0: $i] : $false )
= emptyset ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SET008^1.ax',fun_inv_image) ).
thf(f23,conjecture,
! [X0: $i > $i] :
( ( fun_inv_image @ X0 @ emptyset )
= emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f24,negated_conjecture,
~ ! [X0: $i > $i] :
( ( fun_inv_image @ X0 @ emptyset )
= emptyset ),
inference(negated_conjecture,[status(cth)],[f23]) ).
thf(f26,plain,
( fun_inv_image
= ( ^ [X0: $i > $i,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X3
= ( X0 @ X2 ) )
& ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f27,plain,
( fun_inv_image
= ( ^ [Y0: $i > $i,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( ( Y0 @ Y2 )
= Y3 ) ) ) ) ),
inference(fool_elimination,[],[f26]) ).
thf(f36,plain,
( emptyset
= ( ^ [Y0: $i] : $false ) ),
inference(fool_elimination,[],[f3]) ).
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(f63,plain,
( emptyset
= ( ^ [Y0: $i] : $false ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f64,plain,
( emptyset
!= ( fun_inv_image @ sK0 @ emptyset ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f79,plain,
( fun_inv_image
= ( ^ [Y0: $i > $i,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( ( Y0 @ Y2 )
= Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f89,plain,
( ( ^ [Y0: $i > $i,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( ( Y0 @ Y2 )
= Y3 ) ) )
@ sK0
@ ^ [Y0: $i] : $false )
!= ( ^ [Y0: $i] : $false ) ),
inference(definition_unfolding,[],[f64,f63,f79,f63]) ).
thf(f90,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( $false
& ( ( sK0 @ Y0 )
= Y1 ) ) ) )
!= ( ^ [Y0: $i] : $false ) ),
inference(beta-eta_normalization,[],[f89]) ).
thf(f91,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : $false ) )
!= ( ^ [Y0: $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,
( ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : $false )
@ sK1 )
= $true )
| ( ( ^ [Y0: $i] : $false
@ sK1 )
= $true ) ),
inference(xor_proxy_clausification,[],[f92]) ).
thf(f97,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] : $false )
= $true )
| ( $false = $true ) ),
inference(beta-eta_normalization,[],[f93]) ).
thf(f98,plain,
( ( ( ^ [Y0: $i] : $false
@ sK2 )
= $true )
| ( $false = $true ) ),
inference(sigma_proxy_clausification,[],[f97]) ).
thf(f99,plain,
( ( ^ [Y0: $i] : $false
@ sK2 )
= $true ),
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
% 0.00/0.03 % Problem : SET764^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 % Computer : n026.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 13:43:43 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.29 Running higher-order theorem proving
% 0.26/0.30 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.26/0.36 % (610518)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.26/0.36 % (610527)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1643219500:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.26/0.36 % (610524)lrs+10_16_si=on:nwc=1.5:random_seed=1041153544:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.26/0.36 % (610525)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3696905066:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.26/0.36 % (610527)Instruction limit reached!
% 0.26/0.36 % (610527)------------------------------
% 0.26/0.36 % (610527)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.36 % (610527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.36 % (610527)CaDiCaL version: 2.1.3
% 0.26/0.36 % (610527)Termination reason: Instruction limit
% 0.26/0.36 % (610527)Termination phase: Saturation
% 0.26/0.36 % (610527)Time elapsed: 0.014 s
% 0.26/0.36 % (610527)Peak memory usage: 12 MB
% 0.26/0.36 % (610527)Instructions burned: 26 (million)
% 0.26/0.36 % (610526)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=1047317117: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)
% 0.26/0.36 % (610528)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3942472013:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.26/0.36 % (610525)Instruction limit reached!
% 0.26/0.36 % (610525)------------------------------
% 0.26/0.36 % (610525)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.36 % (610525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.36 % (610525)CaDiCaL version: 2.1.3
% 0.26/0.36 % (610525)Termination reason: Instruction limit
% 0.26/0.36 % (610525)Termination phase: Property scanning
% 0.26/0.36 % (610525)Time elapsed: 0.003 s
% 0.26/0.36 % (610525)Peak memory usage: 10 MB
% 0.26/0.36 % (610525)Instructions burned: 3 (million)
% 0.26/0.36 % (610528) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-610518-610528"...
% 0.26/0.36 % (610524) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-610518-610524"...
% 0.26/0.36 % (610528)...printing done.
% 0.26/0.36 % (610524)...printing done.
% 0.26/0.36 % (610528)Refutation found. Thanks to Tanya!
% 0.26/0.36 % SZS status Theorem for theBenchmark
% 0.26/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.36 % (610528)------------------------------
% 0.26/0.36 % (610528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.36 % (610528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.36 % (610528)CaDiCaL version: 2.1.3
% 0.26/0.36 % (610528)Termination reason: Refutation
% 0.26/0.36 % (610528)Time elapsed: 0.005 s
% 0.26/0.36 % (610528)Peak memory usage: 12 MB
% 0.26/0.36 % (610528)Instructions burned: 6 (million)
% 0.26/0.36 % (610518)Success in time 0.044 s
% 0.26/0.36 % Vampire exiting
%------------------------------------------------------------------------------