%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET752^4 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 : 31
% Number of leaves : 12
% Syntax : Number of formulae : 140 ( 26 unt; 0 typ; 9 def)
% Number of atoms : 1087 ( 286 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 933 ( 102 ~; 264 |; 73 &; 453 @)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 51 usr; 16 con; 0-4 aty)
% ( 0 !!; 32 ??; 0 @@+; 0 @@-)
% Number of variables : 139 ( 0 sgn 41 !; 5 ?; 139 :)
% 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 > $o ).
thf(func_def_38,type,
sK1: $i > $o ).
thf(func_def_39,type,
sK2: $i > $i ).
thf(f6,axiom,
( union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',union) ).
thf(f15,axiom,
( fun_image
= ( ^ [X0: $i > $i,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X2
= ( X0 @ X3 ) )
& ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^1.ax',fun_image) ).
thf(f23,conjecture,
! [X0: $i > $o,X1: $i > $o,X2: $i > $i] :
( ( fun_image @ X2 @ ( union @ X0 @ X1 ) )
= ( union @ ( fun_image @ X2 @ X0 ) @ ( fun_image @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f24,negated_conjecture,
~ ! [X0: $i > $o,X1: $i > $o,X2: $i > $i] :
( ( fun_image @ X2 @ ( union @ X0 @ X1 ) )
= ( union @ ( fun_image @ X2 @ X0 ) @ ( fun_image @ X2 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
thf(f30,plain,
( union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f31,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f47,plain,
( fun_image
= ( ^ [X0: $i > $i,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X2
= ( X0 @ X3 ) )
& ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f48,plain,
( fun_image
= ( ^ [Y0: $i > $i,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( ( Y0 @ Y3 )
= Y2 ) ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f60,plain,
? [X0: $i > $o,X1: $i > $o,X2: $i > $i] :
( ( fun_image @ X2 @ ( union @ X0 @ X1 ) )
!= ( union @ ( fun_image @ X2 @ X0 ) @ ( fun_image @ X2 @ X1 ) ) ),
inference(ennf_transformation,[],[f24]) ).
thf(f61,plain,
( ( fun_image @ sK2 @ ( union @ sK0 @ sK1 ) )
!= ( union @ ( fun_image @ sK2 @ sK0 ) @ ( fun_image @ sK2 @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f60]) ).
thf(f67,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f76,plain,
( fun_image
= ( ^ [Y0: $i > $i,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( ( Y0 @ Y3 )
= Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f84,plain,
( ( fun_image @ sK2 @ ( union @ sK0 @ sK1 ) )
!= ( union @ ( fun_image @ sK2 @ sK0 ) @ ( fun_image @ sK2 @ sK1 ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f89,plain,
( ( ^ [Y0: $i > $i,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( ( Y0 @ Y3 )
= Y2 ) ) )
@ sK2
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ sK0
@ sK1 ) )
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $i,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( ( Y0 @ Y3 )
= Y2 ) ) )
@ sK2
@ sK0 )
@ ( ^ [Y0: $i > $i,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
& ( ( Y0 @ Y3 )
= Y2 ) ) )
@ sK2
@ sK1 ) ) ),
inference(definition_unfolding,[],[f84,f76,f67,f67,f76,f76]) ).
thf(f90,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 )
| ( sK1 @ Y1 ) )
& ( ( sK2 @ Y1 )
= Y0 ) ) ) )
!= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
& ( ( sK2 @ Y1 )
= Y0 ) ) )
| ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
& ( ( sK2 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f89]) ).
thf(f98,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 )
| ( sK1 @ Y1 ) )
& ( ( sK2 @ Y1 )
= Y0 ) ) )
@ sK3 )
!= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
& ( ( sK2 @ Y1 )
= Y0 ) ) )
| ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
& ( ( sK2 @ Y1 )
= Y0 ) ) ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f90]) ).
thf(f99,plain,
( ( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 )
| ( sK1 @ Y1 ) )
& ( ( sK2 @ Y1 )
= Y0 ) ) )
@ sK3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
& ( ( sK2 @ Y1 )
= Y0 ) ) )
| ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
& ( ( sK2 @ Y1 )
= Y0 ) ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f98]) ).
thf(f100,plain,
( ( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 )
| ( sK1 @ Y1 ) )
& ( ( sK2 @ Y1 )
= Y0 ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
& ( ( sK2 @ Y1 )
= Y0 ) ) )
| ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
& ( ( sK2 @ Y1 )
= Y0 ) ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f98]) ).
thf(f101,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK2 @ Y0 )
= sK3 ) ) ) )
| ( $false
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( ( sK2 @ Y0 )
= sK3 ) ) )
| ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( ( sK2 @ Y0 )
= sK3 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f100]) ).
thf(f102,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK2 @ Y0 )
= sK3 ) )
@ X1 ) )
| ( $false
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( ( sK2 @ Y0 )
= sK3 ) ) )
| ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( ( sK2 @ Y0 )
= sK3 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK2 @ Y0 )
= sK3 ) )
@ X1 ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( ( sK2 @ Y0 )
= sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f102]) ).
thf(f104,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK2 @ Y0 )
= sK3 ) )
@ X1 ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( ( sK2 @ Y0 )
= sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f102]) ).
thf(f105,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK2 @ Y0 )
= sK3 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( ( sK2 @ Y0 )
= sK3 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f104]) ).
thf(f106,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( ( sK0 @ X1 )
| ( sK1 @ X1 ) )
& ( ( sK2 @ X1 )
= sK3 ) ) )
| ( $false
= ( ( sK0 @ X2 )
& ( ( sK2 @ X2 )
= sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f105]) ).
thf(f107,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( sK2 @ X1 )
= sK3 ) )
| ( $false
= ( ( sK0 @ X2 )
& ( ( sK2 @ X2 )
= sK3 ) ) )
| ( $false
= ( ( sK0 @ X1 )
| ( sK1 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f106]) ).
thf(f108,plain,
! [X2: $i,X1: $i] :
( ( sK3
!= ( sK2 @ X1 ) )
| ( $false
= ( ( sK0 @ X2 )
& ( ( sK2 @ X2 )
= sK3 ) ) )
| ( $false
= ( ( sK0 @ X1 )
| ( sK1 @ X1 ) ) ) ),
inference(equality_proxy_clausification,[],[f107]) ).
thf(f109,plain,
! [X2: $i,X1: $i] :
( ( sK3
!= ( sK2 @ X1 ) )
| ( $false
= ( ( sK2 @ X2 )
= sK3 ) )
| ( $false
= ( ( sK0 @ X1 )
| ( sK1 @ X1 ) ) )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f108]) ).
thf(f110,plain,
! [X2: $i,X1: $i] :
( ( sK3
!= ( sK2 @ X1 ) )
| ( sK3
!= ( sK2 @ X2 ) )
| ( $false
= ( ( sK0 @ X1 )
| ( sK1 @ X1 ) ) )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(equality_proxy_clausification,[],[f109]) ).
thf(f112,plain,
! [X2: $i,X1: $i] :
( ( sK3
!= ( sK2 @ X1 ) )
| ( sK3
!= ( sK2 @ X2 ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f110]) ).
thf(f113,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK2 @ Y0 )
= sK3 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( ( sK2 @ Y0 )
= sK3 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f103]) ).
thf(f114,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( ( sK0 @ X1 )
| ( sK1 @ X1 ) )
& ( ( sK2 @ X1 )
= sK3 ) ) )
| ( $false
= ( ( sK1 @ X2 )
& ( ( sK2 @ X2 )
= sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f113]) ).
thf(f115,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( sK2 @ X1 )
= sK3 ) )
| ( $false
= ( ( sK1 @ X2 )
& ( ( sK2 @ X2 )
= sK3 ) ) )
| ( $false
= ( ( sK0 @ X1 )
| ( sK1 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f114]) ).
thf(f116,plain,
! [X2: $i,X1: $i] :
( ( sK3
!= ( sK2 @ X1 ) )
| ( $false
= ( ( sK1 @ X2 )
& ( ( sK2 @ X2 )
= sK3 ) ) )
| ( $false
= ( ( sK0 @ X1 )
| ( sK1 @ X1 ) ) ) ),
inference(equality_proxy_clausification,[],[f115]) ).
thf(f117,plain,
! [X2: $i,X1: $i] :
( ( sK3
!= ( sK2 @ X1 ) )
| ( $false
= ( ( sK2 @ X2 )
= sK3 ) )
| ( $false
= ( ( sK0 @ X1 )
| ( sK1 @ X1 ) ) )
| ( $false
= ( sK1 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f116]) ).
thf(f118,plain,
! [X2: $i,X1: $i] :
( ( sK3
!= ( sK2 @ X1 ) )
| ( sK3
!= ( sK2 @ X2 ) )
| ( $false
= ( ( sK0 @ X1 )
| ( sK1 @ X1 ) ) )
| ( $false
= ( sK1 @ X2 ) ) ),
inference(equality_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X2: $i,X1: $i] :
( ( sK3
!= ( sK2 @ X1 ) )
| ( sK3
!= ( sK2 @ X2 ) )
| ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( sK1 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f118]) ).
thf(f121,plain,
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK2 @ Y0 )
= sK3 ) ) ) )
| ( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( ( sK2 @ Y0 )
= sK3 ) ) )
| ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( ( sK2 @ Y0 )
= sK3 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f99]) ).
thf(f122,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK2 @ Y0 )
= sK3 ) )
@ sK4 ) )
| ( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( ( sK2 @ Y0 )
= sK3 ) ) )
| ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( ( sK2 @ Y0 )
= sK3 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f121]) ).
thf(f123,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK2 @ Y0 )
= sK3 ) )
@ sK4 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( ( sK2 @ Y0 )
= sK3 ) ) ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( ( sK2 @ Y0 )
= sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f122]) ).
thf(f124,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK2 @ Y0 )
= sK3 ) )
@ sK4 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( ( sK2 @ Y0 )
= sK3 ) )
@ sK5 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( ( sK2 @ Y0 )
= sK3 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f123]) ).
thf(f125,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
| ( sK1 @ Y0 ) )
& ( ( sK2 @ Y0 )
= sK3 ) )
@ sK4 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( ( sK2 @ Y0 )
= sK3 ) )
@ sK5 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( ( sK2 @ Y0 )
= sK3 ) )
@ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f124]) ).
thf(f126,plain,
( ( $true
= ( ( ( sK0 @ sK4 )
| ( sK1 @ sK4 ) )
& ( ( sK2 @ sK4 )
= sK3 ) ) )
| ( $true
= ( ( sK1 @ sK5 )
& ( ( sK2 @ sK5 )
= sK3 ) ) )
| ( $true
= ( ( sK0 @ sK6 )
& ( ( sK2 @ sK6 )
= sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f125]) ).
thf(f127,plain,
( ( $true
= ( ( sK2 @ sK4 )
= sK3 ) )
| ( $true
= ( ( sK1 @ sK5 )
& ( ( sK2 @ sK5 )
= sK3 ) ) )
| ( $true
= ( ( sK0 @ sK6 )
& ( ( sK2 @ sK6 )
= sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f126]) ).
thf(f128,plain,
( ( $true
= ( ( sK0 @ sK4 )
| ( sK1 @ sK4 ) ) )
| ( $true
= ( ( sK1 @ sK5 )
& ( ( sK2 @ sK5 )
= sK3 ) ) )
| ( $true
= ( ( sK0 @ sK6 )
& ( ( sK2 @ sK6 )
= sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f126]) ).
thf(f129,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( $true
= ( ( sK1 @ sK5 )
& ( ( sK2 @ sK5 )
= sK3 ) ) )
| ( $true
= ( ( sK0 @ sK6 )
& ( ( sK2 @ sK6 )
= sK3 ) ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(or_proxy_clausification,[],[f128]) ).
thf(f130,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( $true
= ( ( sK2 @ sK5 )
= sK3 ) )
| ( $true
= ( ( sK0 @ sK6 )
& ( ( sK2 @ sK6 )
= sK3 ) ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f129]) ).
thf(f131,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( ( sK0 @ sK6 )
& ( ( sK2 @ sK6 )
= sK3 ) ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f129]) ).
thf(f132,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( ( sK2 @ sK6 )
= sK3 ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f131]) ).
thf(f133,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK6 ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f131]) ).
thf(f134,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( sK3
= ( sK2 @ sK6 ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(equality_proxy_clausification,[],[f132]) ).
thf(f135,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( sK3
= ( sK2 @ sK5 ) )
| ( $true
= ( ( sK0 @ sK6 )
& ( ( sK2 @ sK6 )
= sK3 ) ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(equality_proxy_clausification,[],[f130]) ).
thf(f136,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( sK3
= ( sK2 @ sK5 ) )
| ( $true
= ( ( sK2 @ sK6 )
= sK3 ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f135]) ).
thf(f137,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( sK3
= ( sK2 @ sK5 ) )
| ( $true
= ( sK0 @ sK6 ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f135]) ).
thf(f138,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( sK3
= ( sK2 @ sK5 ) )
| ( sK3
= ( sK2 @ sK6 ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(equality_proxy_clausification,[],[f136]) ).
thf(f139,plain,
( ( sK3
= ( sK2 @ sK4 ) )
| ( $true
= ( ( sK1 @ sK5 )
& ( ( sK2 @ sK5 )
= sK3 ) ) )
| ( $true
= ( ( sK0 @ sK6 )
& ( ( sK2 @ sK6 )
= sK3 ) ) ) ),
inference(equality_proxy_clausification,[],[f127]) ).
thf(f140,plain,
( ( sK3
= ( sK2 @ sK4 ) )
| ( $true
= ( ( sK2 @ sK5 )
= sK3 ) )
| ( $true
= ( ( sK0 @ sK6 )
& ( ( sK2 @ sK6 )
= sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f139]) ).
thf(f141,plain,
( ( sK3
= ( sK2 @ sK4 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( ( sK0 @ sK6 )
& ( ( sK2 @ sK6 )
= sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f139]) ).
thf(f142,plain,
( ( sK3
= ( sK2 @ sK4 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( ( sK2 @ sK6 )
= sK3 ) ) ),
inference(and_proxy_clausification,[],[f141]) ).
thf(f143,plain,
( ( sK3
= ( sK2 @ sK4 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK6 ) ) ),
inference(and_proxy_clausification,[],[f141]) ).
thf(f144,plain,
( ( sK3
= ( sK2 @ sK4 ) )
| ( $true
= ( sK1 @ sK5 ) )
| ( sK3
= ( sK2 @ sK6 ) ) ),
inference(equality_proxy_clausification,[],[f142]) ).
thf(f145,plain,
( ( sK3
= ( sK2 @ sK4 ) )
| ( sK3
= ( sK2 @ sK5 ) )
| ( $true
= ( ( sK0 @ sK6 )
& ( ( sK2 @ sK6 )
= sK3 ) ) ) ),
inference(equality_proxy_clausification,[],[f140]) ).
thf(f146,plain,
( ( sK3
= ( sK2 @ sK4 ) )
| ( sK3
= ( sK2 @ sK5 ) )
| ( $true
= ( ( sK2 @ sK6 )
= sK3 ) ) ),
inference(and_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( ( sK3
= ( sK2 @ sK4 ) )
| ( sK3
= ( sK2 @ sK5 ) )
| ( $true
= ( sK0 @ sK6 ) ) ),
inference(and_proxy_clausification,[],[f145]) ).
thf(f148,plain,
( ( sK3
= ( sK2 @ sK4 ) )
| ( sK3
= ( sK2 @ sK5 ) )
| ( sK3
= ( sK2 @ sK6 ) ) ),
inference(equality_proxy_clausification,[],[f146]) ).
thf(f150,definition,
( spl7_1
<=> ! [X2: $i] :
( ( sK3
!= ( sK2 @ X2 ) )
| ( $false
= ( sK0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
thf(f151,plain,
( ! [X2: $i] :
( ( sK3
!= ( sK2 @ X2 ) )
| ( $false
= ( sK0 @ X2 ) ) )
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f150]) ).
thf(f152,plain,
( spl7_1
| spl7_1 ),
inference(avatar_split_clause,[],[f112,f150,f150]) ).
thf(f154,definition,
( spl7_2
<=> ! [X1: $i] :
( ( sK3
!= ( sK2 @ X1 ) )
| ( $false
= ( sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f155,plain,
( ! [X1: $i] :
( ( sK3
!= ( sK2 @ X1 ) )
| ( $false
= ( sK1 @ X1 ) ) )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f154]) ).
thf(f158,plain,
( spl7_2
| spl7_2 ),
inference(avatar_split_clause,[],[f119,f154,f154]) ).
thf(f160,definition,
( spl7_3
<=> ( $true
= ( sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
thf(f162,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f160]) ).
thf(f164,definition,
( spl7_4
<=> ( $true
= ( sK0 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
thf(f166,plain,
( ( $true
= ( sK0 @ sK6 ) )
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f164]) ).
thf(f168,definition,
( spl7_5
<=> ( $true
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
thf(f170,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f168]) ).
thf(f172,definition,
( spl7_6
<=> ( $true
= ( sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
thf(f174,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f172]) ).
thf(f175,plain,
( spl7_3
| spl7_4
| spl7_5
| spl7_6 ),
inference(avatar_split_clause,[],[f133,f172,f168,f164,f160]) ).
thf(f177,definition,
( spl7_7
<=> ( sK3
= ( sK2 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
thf(f179,plain,
( ( sK3
= ( sK2 @ sK6 ) )
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f177]) ).
thf(f180,plain,
( spl7_3
| spl7_7
| spl7_5
| spl7_6 ),
inference(avatar_split_clause,[],[f134,f172,f168,f177,f160]) ).
thf(f182,definition,
( spl7_8
<=> ( sK3
= ( sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
thf(f184,plain,
( ( sK3
= ( sK2 @ sK5 ) )
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f182]) ).
thf(f185,plain,
( spl7_3
| spl7_4
| spl7_8
| spl7_6 ),
inference(avatar_split_clause,[],[f137,f172,f182,f164,f160]) ).
thf(f186,plain,
( spl7_3
| spl7_7
| spl7_8
| spl7_6 ),
inference(avatar_split_clause,[],[f138,f172,f182,f177,f160]) ).
thf(f188,definition,
( spl7_9
<=> ( sK3
= ( sK2 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_9])],[avatar_definition]) ).
thf(f190,plain,
( ( sK3
= ( sK2 @ sK4 ) )
| ~ spl7_9 ),
inference(avatar_component_clause,[],[f188]) ).
thf(f191,plain,
( spl7_4
| spl7_5
| spl7_9 ),
inference(avatar_split_clause,[],[f143,f188,f168,f164]) ).
thf(f192,plain,
( spl7_7
| spl7_5
| spl7_9 ),
inference(avatar_split_clause,[],[f144,f188,f168,f177]) ).
thf(f193,plain,
( spl7_4
| spl7_8
| spl7_9 ),
inference(avatar_split_clause,[],[f147,f188,f182,f164]) ).
thf(f194,plain,
( spl7_7
| spl7_8
| spl7_9 ),
inference(avatar_split_clause,[],[f148,f188,f182,f177]) ).
thf(f196,plain,
( ( sK3 != sK3 )
| ( $false
= ( sK0 @ sK6 ) )
| ~ spl7_1
| ~ spl7_7 ),
inference(constrained_superposition,[],[f151,f179]) ).
thf(f197,plain,
( ( $false
= ( sK0 @ sK6 ) )
| ~ spl7_1
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f196]) ).
thf(f200,plain,
( ( $false = $true )
| ~ spl7_1
| ~ spl7_4
| ~ spl7_7 ),
inference(constrained_superposition,[],[f197,f166]) ).
thf(f204,plain,
( $false
| ~ spl7_1
| ~ spl7_4
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f200]) ).
thf(f205,plain,
( ~ spl7_1
| ~ spl7_4
| ~ spl7_7 ),
inference(avatar_contradiction_clause,[],[f204]) ).
thf(f208,plain,
( ( sK3 != sK3 )
| ( $false
= ( sK1 @ sK4 ) )
| ~ spl7_2
| ~ spl7_9 ),
inference(constrained_superposition,[],[f155,f190]) ).
thf(f209,plain,
( ( sK3 != sK3 )
| ( $false
= ( sK0 @ sK4 ) )
| ~ spl7_1
| ~ spl7_9 ),
inference(constrained_superposition,[],[f151,f190]) ).
thf(f210,plain,
( ( $false
= ( sK0 @ sK4 ) )
| ~ spl7_1
| ~ spl7_9 ),
inference(trivial_inequality_removal,[],[f209]) ).
thf(f211,plain,
( ( $false
= ( sK1 @ sK4 ) )
| ~ spl7_2
| ~ spl7_9 ),
inference(trivial_inequality_removal,[],[f208]) ).
thf(f215,plain,
( ( $false = $true )
| ~ spl7_1
| ~ spl7_3
| ~ spl7_9 ),
inference(constrained_superposition,[],[f210,f162]) ).
thf(f219,plain,
( $false
| ~ spl7_1
| ~ spl7_3
| ~ spl7_9 ),
inference(trivial_inequality_removal,[],[f215]) ).
thf(f220,plain,
( ~ spl7_1
| ~ spl7_3
| ~ spl7_9 ),
inference(avatar_contradiction_clause,[],[f219]) ).
thf(f223,plain,
( ( $false = $true )
| ~ spl7_2
| ~ spl7_6
| ~ spl7_9 ),
inference(forward_demodulation,[],[f174,f211]) ).
thf(f224,plain,
( $false
| ~ spl7_2
| ~ spl7_6
| ~ spl7_9 ),
inference(trivial_inequality_removal,[],[f223]) ).
thf(f225,plain,
( ~ spl7_2
| ~ spl7_6
| ~ spl7_9 ),
inference(avatar_contradiction_clause,[],[f224]) ).
thf(f227,plain,
( ( sK3 != sK3 )
| ( $false
= ( sK1 @ sK5 ) )
| ~ spl7_2
| ~ spl7_8 ),
inference(constrained_superposition,[],[f155,f184]) ).
thf(f230,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ~ spl7_2
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f227]) ).
thf(f236,plain,
( ( $false = $true )
| ~ spl7_2
| ~ spl7_5
| ~ spl7_8 ),
inference(constrained_superposition,[],[f230,f170]) ).
thf(f240,plain,
( $false
| ~ spl7_2
| ~ spl7_5
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f236]) ).
thf(f241,plain,
( ~ spl7_2
| ~ spl7_5
| ~ spl7_8 ),
inference(avatar_contradiction_clause,[],[f240]) ).
cnf(s1,plain,
( spl7_1
| spl7_1 ),
inference(sat_conversion,[],[f152]) ).
cnf(s2,plain,
spl7_1,
inference(rat,[],[s1]) ).
cnf(s5,plain,
( spl7_2
| spl7_2 ),
inference(sat_conversion,[],[f158]) ).
cnf(s6,plain,
spl7_2,
inference(rat,[],[s5]) ).
cnf(s7,plain,
( spl7_3
| spl7_4
| spl7_5
| spl7_6 ),
inference(sat_conversion,[],[f175]) ).
cnf(s8,plain,
( spl7_3
| spl7_5
| spl7_6
| spl7_7 ),
inference(sat_conversion,[],[f180]) ).
cnf(s9,plain,
( spl7_3
| spl7_4
| spl7_6
| spl7_8 ),
inference(sat_conversion,[],[f185]) ).
cnf(s10,plain,
( spl7_3
| spl7_6
| spl7_7
| spl7_8 ),
inference(sat_conversion,[],[f186]) ).
cnf(s11,plain,
( spl7_4
| spl7_5
| spl7_9 ),
inference(sat_conversion,[],[f191]) ).
cnf(s12,plain,
( spl7_5
| spl7_7
| spl7_9 ),
inference(sat_conversion,[],[f192]) ).
cnf(s13,plain,
( spl7_4
| spl7_8
| spl7_9 ),
inference(sat_conversion,[],[f193]) ).
cnf(s14,plain,
( spl7_7
| spl7_8
| spl7_9 ),
inference(sat_conversion,[],[f194]) ).
cnf(s16,plain,
( ~ spl7_1
| ~ spl7_4
| ~ spl7_7 ),
inference(sat_conversion,[],[f205]) ).
cnf(s18,plain,
( ~ spl7_1
| ~ spl7_3
| ~ spl7_9 ),
inference(sat_conversion,[],[f220]) ).
cnf(s19,plain,
( ~ spl7_2
| ~ spl7_6
| ~ spl7_9 ),
inference(sat_conversion,[],[f225]) ).
cnf(s21,plain,
( ~ spl7_2
| ~ spl7_5
| ~ spl7_8 ),
inference(sat_conversion,[],[f241]) ).
cnf(s22,plain,
( spl7_5
| spl7_4
| spl7_3 ),
inference(rat,[],[s19,s7,s11,s6]) ).
cnf(s23,plain,
( spl7_4
| spl7_3 ),
inference(rat,[],[s19,s9,s13,s21,s22,s6]) ).
cnf(s24,plain,
( spl7_5
| spl7_3 ),
inference(rat,[],[s19,s8,s12,s16,s23,s6,s2]) ).
cnf(s25,plain,
( spl7_8
| spl7_7
| spl7_3 ),
inference(rat,[],[s19,s14,s10,s6]) ).
cnf(s26,plain,
spl7_3,
inference(rat,[],[s25,s21,s24,s16,s23,s6,s2]) ).
cnf(s27,plain,
~ spl7_9,
inference(rat,[],[s18,s2,s26]) ).
cnf(s28,plain,
spl7_5,
inference(rat,[],[s16,s12,s11,s2,s27]) ).
cnf(s29,plain,
~ spl7_8,
inference(rat,[],[s21,s6,s28]) ).
cnf(s30,plain,
spl7_4,
inference(rat,[],[s13,s27,s29]) ).
cnf(s31,plain,
spl7_7,
inference(rat,[],[s14,s27,s29]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s16,s2,s31,s30]) ).
thf(f243,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET752^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n016.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:45:50 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 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
% 0.07/0.25 % (367136)Will run a generic schedule for satisfiability detection.
% 0.07/0.25 % (367146)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3313837572:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.25 % (367142)% WARNING: option uhcvi not known.
% 0.07/0.25 % (367146) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-367136-367146"...
% 0.07/0.25 % (367146)...printing done.
% 0.07/0.25 % (367146)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 % (367146)------------------------------
% 0.07/0.25 % (367146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.25 % (367146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.25 % (367146)CaDiCaL version: 2.1.3
% 0.07/0.25 % (367146)Termination reason: Refutation
% 0.07/0.25 % (367146)Time elapsed: 0.005 s
% 0.07/0.25 % (367146)Peak memory usage: 13 MB
% 0.07/0.25 % (367146)Instructions burned: 15 (million)
% 0.07/0.25 % (367136)Success in time 0.02 s
% 0.07/0.25 % Vampire exiting
%------------------------------------------------------------------------------