%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV420^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 08:39:29 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 290 ( 87 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 541 ( 12 ~; 30 |; 49 &; 378 @)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 115 ( 115 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 46 usr; 4 con; 0-4 aty)
% ( 28 !!; 5 ??; 0 @@+; 0 @@-)
% Number of variables : 157 ( 113 ^; 34 !; 10 ?; 157 :)
% 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,
is_function: ( $i > $o ) > ( $i > $i ) > ( $i > $o ) > $o ).
thf(func_def_16,type,
injection: ( $i > $o ) > ( $i > $i ) > ( $i > $o ) > $o ).
thf(func_def_17,type,
surjection: ( $i > $o ) > ( $i > $i ) > ( $i > $o ) > $o ).
thf(func_def_18,type,
bijection: ( $i > $o ) > ( $i > $i ) > ( $i > $o ) > $o ).
thf(func_def_19,type,
equinumerous: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_20,type,
embedding: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_21,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_26,type,
vOR: $o > $o > $o ).
thf(func_def_27,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_29,type,
vAND: $o > $o > $o ).
thf(func_def_30,type,
vNOT: $o > $o ).
thf(func_def_31,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_32,type,
vIMP: $o > $o > $o ).
thf(func_def_33,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_34,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
sK0: $i > $o ).
thf(func_def_37,type,
sK1: $i > $o ).
thf(func_def_38,type,
sK2: $i > $o ).
thf(func_def_39,type,
sK3: $i > $o ).
thf(func_def_40,type,
sK4: $i > $i ).
thf(func_def_43,type,
sK7: $i > $i ).
thf(func_def_44,type,
sK8: $i > $i ).
thf(func_def_45,type,
sK9: $i > $i ).
thf(func_def_48,type,
sK12: $i > $i ).
thf(func_def_49,type,
sK13: $i > $i ).
thf(func_def_50,type,
sK14: ( $i > $i ) > $i ).
thf(func_def_51,type,
sK15: ( $i > $i ) > $i ).
thf(f6,axiom,
( union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',union) ).
thf(f15,axiom,
( is_function
= ( ^ [X0: $i > $o,X1: $i > $i,X2: $i > $o] :
! [X3: $i] :
( ( X0 @ X3 )
=> ( X2 @ ( X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',is_function) ).
thf(f16,axiom,
( injection
= ( ^ [X0: $i > $o,X1: $i > $i,X2: $i > $o] :
( ( is_function @ X0 @ X1 @ X2 )
=> ! [X3: $i,X4: $i] :
( ( ( ( X1 @ X3 )
= ( X1 @ X4 ) )
& ( X0 @ X4 )
& ( X0 @ X3 ) )
=> ( X3 = X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injection) ).
thf(f20,axiom,
( embedding
= ( ^ [X0: $i > $o,X1: $i > $o] :
? [X2: $i > $i] : ( injection @ X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',embedding) ).
thf(f21,conjecture,
! [X0: $i > $o,X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( ( intersection @ X1 @ X3 )
= emptyset )
& ( equinumerous @ X2 @ X3 )
& ( equinumerous @ X0 @ X1 ) )
=> ( embedding @ ( union @ X0 @ X2 ) @ ( union @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f22,negated_conjecture,
~ ! [X0: $i > $o,X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( ( intersection @ X1 @ X3 )
= emptyset )
& ( equinumerous @ X2 @ X3 )
& ( equinumerous @ X0 @ X1 ) )
=> ( embedding @ ( union @ X0 @ X2 ) @ ( union @ X1 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
thf(f28,plain,
( union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f29,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f45,plain,
( is_function
= ( ^ [X0: $i > $o,X1: $i > $i,X2: $i > $o] :
! [X3: $i] :
( ( X0 @ X3 )
=> ( X2 @ ( X1 @ X3 ) ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f46,plain,
( is_function
= ( ^ [Y0: $i > $o,Y1: $i > $i,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
=> ( Y2 @ ( Y1 @ Y3 ) ) ) ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f47,plain,
( injection
= ( ^ [X0: $i > $o,X1: $i > $i,X2: $i > $o] :
( ( is_function @ X0 @ X1 @ X2 )
=> ! [X3: $i,X4: $i] :
( ( ( ( X1 @ X3 )
= ( X1 @ X4 ) )
& ( X0 @ X4 )
& ( X0 @ X3 ) )
=> ( X3 = X4 ) ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f48,plain,
( injection
= ( ^ [Y0: $i > $o,Y1: $i > $i,Y2: $i > $o] :
( ( is_function @ Y0 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y0 @ Y4 )
& ( Y0 @ Y3 )
& ( ( Y1 @ Y4 )
= ( Y1 @ Y3 ) ) )
=> ( Y4 = Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f55,plain,
( embedding
= ( ^ [X0: $i > $o,X1: $i > $o] :
? [X2: $i > $i] : ( injection @ X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f20]) ).
thf(f56,plain,
( embedding
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ?? @ ( $i > $i )
@ ^ [Y2: $i > $i] : ( injection @ Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f57,plain,
~ ! [X0: $i > $o,X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( ( intersection @ X1 @ X3 )
= emptyset )
& ( equinumerous @ X2 @ X3 )
& ( equinumerous @ X0 @ X1 ) )
=> ( embedding @ ( union @ X0 @ X2 ) @ ( union @ X1 @ X3 ) ) ),
inference(rectify,[],[f22]) ).
thf(f58,plain,
~ ! [X0: $i > $o,X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( emptyset
= ( intersection @ X1 @ X3 ) )
& ( ( equinumerous @ X2 @ X3 )
= $true )
& ( ( equinumerous @ X0 @ X1 )
= $true ) )
=> ( ( embedding @ ( union @ X0 @ X2 ) @ ( union @ X1 @ X3 ) )
= $true ) ),
inference(fool_elimination,[],[f57]) ).
thf(f59,plain,
? [X0: $i > $o,X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( embedding @ ( union @ X0 @ X2 ) @ ( union @ X1 @ X3 ) )
!= $true )
& ( emptyset
= ( intersection @ X1 @ X3 ) )
& ( ( equinumerous @ X2 @ X3 )
= $true )
& ( ( equinumerous @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f58]) ).
thf(f60,plain,
? [X0: $i > $o,X1: $i > $o,X2: $i > $o,X3: $i > $o] :
( ( ( embedding @ ( union @ X0 @ X2 ) @ ( union @ X1 @ X3 ) )
!= $true )
& ( emptyset
= ( intersection @ X1 @ X3 ) )
& ( ( equinumerous @ X2 @ X3 )
= $true )
& ( ( equinumerous @ X0 @ X1 )
= $true ) ),
inference(flattening,[],[f59]) ).
thf(f61,plain,
( ( $true
!= ( embedding @ ( union @ sK0 @ sK2 ) @ ( union @ sK1 @ sK3 ) ) )
& ( emptyset
= ( intersection @ sK1 @ sK3 ) )
& ( $true
= ( equinumerous @ sK2 @ sK3 ) )
& ( $true
= ( equinumerous @ sK0 @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f60]) ).
thf(f67,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f76,plain,
( is_function
= ( ^ [Y0: $i > $o,Y1: $i > $i,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 )
=> ( Y2 @ ( Y1 @ Y3 ) ) ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f77,plain,
( injection
= ( ^ [Y0: $i > $o,Y1: $i > $i,Y2: $i > $o] :
( ( is_function @ Y0 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y0 @ Y4 )
& ( Y0 @ Y3 )
& ( ( Y1 @ Y4 )
= ( Y1 @ Y3 ) ) )
=> ( Y4 = Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f81,plain,
( embedding
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ?? @ ( $i > $i )
@ ^ [Y2: $i > $i] : ( injection @ Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f85,plain,
( $true
!= ( embedding @ ( union @ sK0 @ sK2 ) @ ( union @ sK1 @ sK3 ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f89,plain,
( injection
= ( ^ [Y0: $i > $o,Y1: $i > $i,Y2: $i > $o] :
( ( ^ [Y3: $i > $o,Y4: $i > $i,Y5: $i > $o] :
( !! @ $i
@ ^ [Y6: $i] :
( ( Y3 @ Y6 )
=> ( Y5 @ ( Y4 @ Y6 ) ) ) )
@ Y0
@ Y1
@ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y0 @ Y4 )
& ( Y0 @ Y3 )
& ( ( Y1 @ Y4 )
= ( Y1 @ Y3 ) ) )
=> ( Y4 = Y3 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f77,f76]) ).
thf(f93,plain,
( embedding
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ?? @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ^ [Y3: $i > $o,Y4: $i > $i,Y5: $i > $o] :
( ( ^ [Y6: $i > $o,Y7: $i > $i,Y8: $i > $o] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 )
=> ( Y8 @ ( Y7 @ Y9 ) ) ) )
@ Y3
@ Y4
@ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y3 @ Y7 )
& ( Y3 @ Y6 )
& ( ( Y4 @ Y7 )
= ( Y4 @ Y6 ) ) )
=> ( Y7 = Y6 ) ) ) ) )
@ Y0
@ Y2
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f81,f89]) ).
thf(f94,plain,
( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ?? @ ( $i > $i )
@ ^ [Y2: $i > $i] :
( ^ [Y3: $i > $o,Y4: $i > $i,Y5: $i > $o] :
( ( ^ [Y6: $i > $o,Y7: $i > $i,Y8: $i > $o] :
( !! @ $i
@ ^ [Y9: $i] :
( ( Y6 @ Y9 )
=> ( Y8 @ ( Y7 @ Y9 ) ) ) )
@ Y3
@ Y4
@ Y5 )
=> ( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y3 @ Y7 )
& ( Y3 @ Y6 )
& ( ( Y4 @ Y7 )
= ( Y4 @ Y6 ) ) )
=> ( Y7 = Y6 ) ) ) ) )
@ Y0
@ Y2
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ sK0
@ sK2 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ sK1
@ sK3 ) ) ),
inference(definition_unfolding,[],[f85,f93,f67,f67]) ).
thf(f185,plain,
( $true
!= ( ?? @ ( $i > $i )
@ ^ [Y0: $i > $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 )
| ( sK2 @ Y1 ) )
=> ( ( sK1 @ ( Y0 @ Y1 ) )
| ( sK3 @ ( Y0 @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( sK0 @ Y2 )
| ( sK2 @ Y2 ) )
& ( ( sK0 @ Y1 )
| ( sK2 @ Y1 ) )
& ( ( Y0 @ Y2 )
= ( Y0 @ Y1 ) ) )
=> ( Y2 = Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f94]) ).
thf(f186,plain,
! [X1: $i > $i] :
( $false
= ( ^ [Y0: $i > $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 )
| ( sK2 @ Y1 ) )
=> ( ( sK1 @ ( Y0 @ Y1 ) )
| ( sK3 @ ( Y0 @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( sK0 @ Y2 )
| ( sK2 @ Y2 ) )
& ( ( sK0 @ Y1 )
| ( sK2 @ Y1 ) )
& ( ( Y0 @ Y2 )
= ( Y0 @ Y1 ) ) )
=> ( Y2 = Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X1: $i > $i] :
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) )
=> ( ( sK1 @ ( X1 @ Y0 ) )
| ( sK3 @ ( X1 @ Y0 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK0 @ Y1 )
| ( sK2 @ Y1 ) )
& ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) )
& ( ( X1 @ Y1 )
= ( X1 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f188,plain,
! [X1: $i > $i] :
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK0 @ Y1 )
| ( sK2 @ Y1 ) )
& ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) )
& ( ( X1 @ Y1 )
= ( X1 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f187]) ).
thf(f197,plain,
! [X1: $i > $i] :
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK0 @ Y1 )
| ( sK2 @ Y1 ) )
& ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) )
& ( ( X1 @ Y1 )
= ( X1 @ Y0 ) ) )
=> ( Y1 = Y0 ) ) )
@ ( sK14 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f188]) ).
thf(f198,plain,
! [X1: $i > $i] :
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) )
& ( ( sK0 @ ( sK14 @ X1 ) )
| ( sK2 @ ( sK14 @ X1 ) ) )
& ( ( X1 @ Y0 )
= ( X1 @ ( sK14 @ X1 ) ) ) )
=> ( Y0
= ( sK14 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f197]) ).
thf(f199,plain,
! [X1: $i > $i] :
( $false
= ( ^ [Y0: $i] :
( ( ( ( sK0 @ Y0 )
| ( sK2 @ Y0 ) )
& ( ( sK0 @ ( sK14 @ X1 ) )
| ( sK2 @ ( sK14 @ X1 ) ) )
& ( ( X1 @ Y0 )
= ( X1 @ ( sK14 @ X1 ) ) ) )
=> ( Y0
= ( sK14 @ X1 ) ) )
@ ( sK15 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X1: $i > $i] :
( $false
= ( ( ( ( sK0 @ ( sK15 @ X1 ) )
| ( sK2 @ ( sK15 @ X1 ) ) )
& ( ( sK0 @ ( sK14 @ X1 ) )
| ( sK2 @ ( sK14 @ X1 ) ) )
& ( ( X1 @ ( sK15 @ X1 ) )
= ( X1 @ ( sK14 @ X1 ) ) ) )
=> ( ( sK15 @ X1 )
= ( sK14 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f199]) ).
thf(f201,plain,
! [X1: $i > $i] :
( $false
= ( ( sK15 @ X1 )
= ( sK14 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X1: $i > $i] :
( $true
= ( ( ( sK0 @ ( sK15 @ X1 ) )
| ( sK2 @ ( sK15 @ X1 ) ) )
& ( ( sK0 @ ( sK14 @ X1 ) )
| ( sK2 @ ( sK14 @ X1 ) ) )
& ( ( X1 @ ( sK15 @ X1 ) )
= ( X1 @ ( sK14 @ X1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f200]) ).
thf(f203,plain,
! [X1: $i > $i] :
( $true
= ( ( X1 @ ( sK15 @ X1 ) )
= ( X1 @ ( sK14 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f202]) ).
thf(f209,plain,
! [X1: $i > $i] :
( ( X1 @ ( sK14 @ X1 ) )
= ( X1 @ ( sK15 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f203]) ).
thf(f210,plain,
! [X1: $i > $i] :
( ( sK14 @ X1 )
!= ( sK15 @ X1 ) ),
inference(equality_proxy_clausification,[],[f201]) ).
thf(f288,plain,
( ( sK14
@ ^ [Y0: $i] : Y0 )
!= ( ^ [Y0: $i] : Y0
@ ( sK14
@ ^ [Y0: $i] : Y0 ) ) ),
inference(constrained_superposition,[],[f210,f209]) ).
thf(f291,plain,
( ( sK14
@ ^ [Y0: $i] : Y0 )
!= ( sK14
@ ^ [Y0: $i] : Y0 ) ),
inference(beta-eta_normalization,[],[f288]) ).
thf(f292,plain,
$false,
inference(trivial_inequality_removal,[],[f291]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV420^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n013.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 15:46:16 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 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
% 0.19/0.28 % (2276830)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (2276841)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3798555770:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.28 % (2276836)% WARNING: option uhcvi not known.
% 0.19/0.28 % (2276841) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2276830-2276841"...
% 0.19/0.28 % (2276840)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3244777545:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.28 % (2276841)...printing done.
% 0.19/0.28 % (2276835)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1233174429_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.28 % (2276838)dis+10_1_sil=32000:sp=arity:random_seed=2213841754:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.28 % (2276837)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=33686500:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.28 % (2276839)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1825268754:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.28 % (2276836)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3634115965:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.28 % (2276841)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
% 0.19/0.28 % (2276841)------------------------------
% 0.19/0.28 % (2276841)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (2276841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (2276841)CaDiCaL version: 2.1.3
% 0.19/0.28 % (2276841)Termination reason: Refutation
% 0.19/0.28 % (2276841)Time elapsed: 0.006 s
% 0.19/0.28 % (2276841)Peak memory usage: 12 MB
% 0.19/0.28 % (2276841)Instructions burned: 18 (million)
% 0.19/0.28 % (2276830)Success in time 0.042 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------