%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET741^4 : 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 : 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 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 8
% Syntax : Number of formulae : 82 ( 39 unt; 0 typ; 3 def)
% Number of atoms : 394 ( 159 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 585 ( 39 ~; 35 |; 24 &; 416 @)
% ( 3 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 31 usr; 10 con; 0-4 aty)
% ( 31 !!; 13 ??; 0 @@+; 0 @@-)
% Number of variables : 149 ( 0 sgn 49 !; 7 ?; 149 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
fun_image: ( $i > $i ) > ( $i > $o ) > $i > $o ).
thf(func_def_2,type,
fun_composition: ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_3,type,
fun_inv_image: ( $i > $i ) > ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
fun_injective: ( $i > $i ) > $o ).
thf(func_def_5,type,
fun_surjective: ( $i > $i ) > $o ).
thf(func_def_6,type,
fun_bijective: ( $i > $i ) > $o ).
thf(func_def_7,type,
fun_decreasing: ( $i > $i ) > ( $i > $i > $o ) > $o ).
thf(func_def_8,type,
fun_increasing: ( $i > $i ) > ( $i > $i > $o ) > $o ).
thf(func_def_9,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_10,type,
vAND: $o > $o > $o ).
thf(func_def_11,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_16,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_17,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_18,type,
vIMP: $o > $o > $o ).
thf(func_def_21,type,
sK0: $i > $i ).
thf(func_def_22,type,
sK1: $i > $i ).
thf(func_def_23,type,
sK2: $i > $i ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(func_def_25,type,
sK3: $i > $i ).
thf(func_def_26,type,
sK4: $i > $i ).
thf(f2,axiom,
( fun_composition
= ( ^ [X0: $i > $i,X1: $i > $i,X2: $i] : ( X1 @ ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^1.ax',fun_composition) ).
thf(f4,axiom,
( fun_injective
= ( ^ [X0: $i > $i] :
! [X1: $i,X2: $i] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^1.ax',fun_injective) ).
thf(f5,axiom,
( fun_surjective
= ( ^ [X0: $i > $i] :
! [X1: $i] :
? [X2: $i] :
( X1
= ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^1.ax',fun_surjective) ).
thf(f6,axiom,
( fun_bijective
= ( ^ [X0: $i > $i] :
( ( fun_surjective @ X0 )
& ( fun_injective @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^1.ax',fun_bijective) ).
thf(f9,conjecture,
! [X0: $i > $i,X1: $i > $i,X2: $i > $i] :
( ( ( fun_surjective @ ( fun_composition @ ( fun_composition @ X2 @ X0 ) @ X1 ) )
& ( fun_surjective @ ( fun_composition @ ( fun_composition @ X1 @ X2 ) @ X0 ) )
& ( fun_injective @ ( fun_composition @ ( fun_composition @ X0 @ X1 ) @ X2 ) ) )
=> ( fun_bijective @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f10,negated_conjecture,
~ ! [X0: $i > $i,X1: $i > $i,X2: $i > $i] :
( ( ( fun_surjective @ ( fun_composition @ ( fun_composition @ X2 @ X0 ) @ X1 ) )
& ( fun_surjective @ ( fun_composition @ ( fun_composition @ X1 @ X2 ) @ X0 ) )
& ( fun_injective @ ( fun_composition @ ( fun_composition @ X0 @ X1 ) @ X2 ) ) )
=> ( fun_bijective @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
thf(f13,plain,
( fun_composition
= ( ^ [Y0: $i > $i,Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f16,plain,
( fun_injective
= ( ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( Y0 @ Y1 )
= ( Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f17,plain,
( fun_surjective
= ( ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f18,plain,
( fun_bijective
= ( ^ [X0: $i > $i] :
( ( fun_surjective @ X0 )
& ( fun_injective @ X0 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f19,plain,
( fun_bijective
= ( ^ [Y0: $i > $i] :
( ( fun_injective @ Y0 )
& ( fun_surjective @ Y0 ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f24,plain,
~ ! [X0: $i > $i,X1: $i > $i,X2: $i > $i] :
( ( ( fun_surjective @ ( fun_composition @ ( fun_composition @ X2 @ X0 ) @ X1 ) )
& ( fun_surjective @ ( fun_composition @ ( fun_composition @ X1 @ X2 ) @ X0 ) )
& ( fun_injective @ ( fun_composition @ ( fun_composition @ X0 @ X1 ) @ X2 ) ) )
=> ( fun_bijective @ X2 ) ),
inference(rectify,[],[f10]) ).
thf(f25,plain,
~ ! [X0: $i > $i,X1: $i > $i,X2: $i > $i] :
( ( ( ( fun_surjective @ ( fun_composition @ ( fun_composition @ X2 @ X0 ) @ X1 ) )
= $true )
& ( ( fun_surjective @ ( fun_composition @ ( fun_composition @ X1 @ X2 ) @ X0 ) )
= $true )
& ( ( fun_injective @ ( fun_composition @ ( fun_composition @ X0 @ X1 ) @ X2 ) )
= $true ) )
=> ( ( fun_bijective @ X2 )
= $true ) ),
inference(fool_elimination,[],[f24]) ).
thf(f26,plain,
? [X0: $i > $i,X1: $i > $i,X2: $i > $i] :
( ( ( fun_bijective @ X2 )
!= $true )
& ( ( fun_surjective @ ( fun_composition @ ( fun_composition @ X2 @ X0 ) @ X1 ) )
= $true )
& ( ( fun_surjective @ ( fun_composition @ ( fun_composition @ X1 @ X2 ) @ X0 ) )
= $true )
& ( ( fun_injective @ ( fun_composition @ ( fun_composition @ X0 @ X1 ) @ X2 ) )
= $true ) ),
inference(ennf_transformation,[],[f25]) ).
thf(f27,plain,
? [X0: $i > $i,X1: $i > $i,X2: $i > $i] :
( ( ( fun_bijective @ X2 )
!= $true )
& ( ( fun_surjective @ ( fun_composition @ ( fun_composition @ X2 @ X0 ) @ X1 ) )
= $true )
& ( ( fun_surjective @ ( fun_composition @ ( fun_composition @ X1 @ X2 ) @ X0 ) )
= $true )
& ( ( fun_injective @ ( fun_composition @ ( fun_composition @ X0 @ X1 ) @ X2 ) )
= $true ) ),
inference(flattening,[],[f26]) ).
thf(f28,plain,
( ( $true
!= ( fun_bijective @ sK2 ) )
& ( $true
= ( fun_surjective @ ( fun_composition @ ( fun_composition @ sK2 @ sK0 ) @ sK1 ) ) )
& ( $true
= ( fun_surjective @ ( fun_composition @ ( fun_composition @ sK1 @ sK2 ) @ sK0 ) ) )
& ( $true
= ( fun_injective @ ( fun_composition @ ( fun_composition @ sK0 @ sK1 ) @ sK2 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f27]) ).
thf(f30,plain,
( fun_composition
= ( ^ [Y0: $i > $i,Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f32,plain,
( fun_injective
= ( ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( Y0 @ Y1 )
= ( Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f33,plain,
( fun_surjective
= ( ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f34,plain,
( fun_bijective
= ( ^ [Y0: $i > $i] :
( ( fun_injective @ Y0 )
& ( fun_surjective @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f37,plain,
( $true
= ( fun_injective @ ( fun_composition @ ( fun_composition @ sK0 @ sK1 ) @ sK2 ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f39,plain,
( $true
= ( fun_surjective @ ( fun_composition @ ( fun_composition @ sK2 @ sK0 ) @ sK1 ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f40,plain,
( $true
!= ( fun_bijective @ sK2 ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f43,plain,
( fun_bijective
= ( ^ [Y0: $i > $i] :
( ( ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y1 @ Y2 )
= ( Y1 @ Y3 ) )
=> ( Y3 = Y2 ) ) ) )
@ Y0 )
& ( ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
= Y2 ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f34,f32,f33]) ).
thf(f44,plain,
( $true
!= ( ^ [Y0: $i > $i] :
( ( ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y1 @ Y2 )
= ( Y1 @ Y3 ) )
=> ( Y3 = Y2 ) ) ) )
@ Y0 )
& ( ^ [Y1: $i > $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
= Y2 ) ) )
@ Y0 ) )
@ sK2 ) ),
inference(definition_unfolding,[],[f40,f43]) ).
thf(f45,plain,
( $true
= ( ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
= Y1 ) ) )
@ ( ^ [Y0: $i > $i,Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y0 @ Y2 ) )
@ ( ^ [Y0: $i > $i,Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y0 @ Y2 ) )
@ sK2
@ sK0 )
@ sK1 ) ) ),
inference(definition_unfolding,[],[f39,f33,f30,f30]) ).
thf(f47,plain,
( $true
= ( ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( Y0 @ Y1 )
= ( Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) )
@ ( ^ [Y0: $i > $i,Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y0 @ Y2 ) )
@ ( ^ [Y0: $i > $i,Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y0 @ Y2 ) )
@ sK0
@ sK1 )
@ sK2 ) ) ),
inference(definition_unfolding,[],[f37,f32,f30,f30]) ).
thf(f48,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK2 @ ( sK1 @ ( sK0 @ Y0 ) ) )
= ( sK2 @ ( sK1 @ ( sK0 @ Y1 ) ) ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f47]) ).
thf(f49,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK2 @ ( sK1 @ ( sK0 @ Y0 ) ) )
= ( sK2 @ ( sK1 @ ( sK0 @ Y1 ) ) ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f48]) ).
thf(f50,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK2 @ ( sK1 @ ( sK0 @ X1 ) ) )
= ( sK2 @ ( sK1 @ ( sK0 @ Y0 ) ) ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f49]) ).
thf(f51,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( sK2 @ ( sK1 @ ( sK0 @ X1 ) ) )
= ( sK2 @ ( sK1 @ ( sK0 @ Y0 ) ) ) )
=> ( Y0 = X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f50]) ).
thf(f52,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( ( sK2 @ ( sK1 @ ( sK0 @ X1 ) ) )
= ( sK2 @ ( sK1 @ ( sK0 @ X2 ) ) ) )
=> ( X2 = X1 ) ) ),
inference(beta-eta_normalization,[],[f51]) ).
thf(f53,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( sK2 @ ( sK1 @ ( sK0 @ X1 ) ) )
= ( sK2 @ ( sK1 @ ( sK0 @ X2 ) ) ) ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f52]) ).
thf(f54,plain,
! [X2: $i,X1: $i] :
( ( ( sK2 @ ( sK1 @ ( sK0 @ X1 ) ) )
!= ( sK2 @ ( sK1 @ ( sK0 @ X2 ) ) ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(equality_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X2: $i,X1: $i] :
( ( ( sK2 @ ( sK1 @ ( sK0 @ X1 ) ) )
!= ( sK2 @ ( sK1 @ ( sK0 @ X2 ) ) ) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f54]) ).
thf(f62,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK1 @ ( sK0 @ ( sK2 @ Y1 ) ) )
= Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f63,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK1 @ ( sK0 @ ( sK2 @ Y1 ) ) )
= Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f62]) ).
thf(f64,plain,
! [X1: $i] :
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ ( sK0 @ ( sK2 @ Y0 ) ) )
= X1 ) ) ),
inference(beta-eta_normalization,[],[f63]) ).
thf(f65,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK1 @ ( sK0 @ ( sK2 @ Y0 ) ) )
= X1 )
@ ( sK4 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f64]) ).
thf(f66,plain,
! [X1: $i] :
( $true
= ( ( sK1 @ ( sK0 @ ( sK2 @ ( sK4 @ X1 ) ) ) )
= X1 ) ),
inference(beta-eta_normalization,[],[f65]) ).
thf(f67,plain,
! [X1: $i] :
( ( sK1 @ ( sK0 @ ( sK2 @ ( sK4 @ X1 ) ) ) )
= X1 ),
inference(equality_proxy_clausification,[],[f66]) ).
thf(f68,plain,
( $true
!= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK2 @ Y0 )
= ( sK2 @ Y1 ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 )
= Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f69,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 )
= Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK2 @ Y0 )
= ( sK2 @ Y1 ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f68]) ).
thf(f70,plain,
( ( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 )
= Y0 ) )
@ sK5 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK2 @ Y0 )
= ( sK2 @ Y1 ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f69]) ).
thf(f71,plain,
( ( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 )
= Y0 ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK2 @ Y0 )
= ( sK2 @ Y1 ) )
=> ( Y1 = Y0 ) ) )
@ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f70]) ).
thf(f72,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
= sK5 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK2 @ sK6 )
= ( sK2 @ Y0 ) )
=> ( Y0 = sK6 ) ) ) ) ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f73,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
= sK5 )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK2 @ sK6 )
= ( sK2 @ Y0 ) )
=> ( Y0 = sK6 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f72]) ).
thf(f74,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
= sK5 )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK2 @ sK6 )
= ( sK2 @ Y0 ) )
=> ( Y0 = sK6 ) )
@ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f73]) ).
thf(f75,plain,
! [X1: $i] :
( ( $false
= ( ( sK2 @ X1 )
= sK5 ) )
| ( $false
= ( ( ( sK2 @ sK6 )
= ( sK2 @ sK7 ) )
=> ( sK7 = sK6 ) ) ) ),
inference(beta-eta_normalization,[],[f74]) ).
thf(f76,plain,
! [X1: $i] :
( ( sK5
!= ( sK2 @ X1 ) )
| ( $false
= ( ( ( sK2 @ sK6 )
= ( sK2 @ sK7 ) )
=> ( sK7 = sK6 ) ) ) ),
inference(equality_proxy_clausification,[],[f75]) ).
thf(f77,plain,
! [X1: $i] :
( ( sK5
!= ( sK2 @ X1 ) )
| ( $false
= ( sK7 = sK6 ) ) ),
inference(imp_proxy_clausification,[],[f76]) ).
thf(f78,plain,
! [X1: $i] :
( ( sK5
!= ( sK2 @ X1 ) )
| ( $true
= ( ( sK2 @ sK6 )
= ( sK2 @ sK7 ) ) ) ),
inference(imp_proxy_clausification,[],[f76]) ).
thf(f79,plain,
! [X1: $i] :
( ( sK5
!= ( sK2 @ X1 ) )
| ( ( sK2 @ sK6 )
= ( sK2 @ sK7 ) ) ),
inference(equality_proxy_clausification,[],[f78]) ).
thf(f80,plain,
! [X1: $i] :
( ( sK5
!= ( sK2 @ X1 ) )
| ( sK6 != sK7 ) ),
inference(equality_proxy_clausification,[],[f77]) ).
thf(f82,definition,
( spl8_1
<=> ( sK6 = sK7 ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f84,plain,
( ( sK6 != sK7 )
| spl8_1 ),
inference(avatar_component_clause,[],[f82]) ).
thf(f86,definition,
( spl8_2
<=> ! [X1: $i] :
( sK5
!= ( sK2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f87,plain,
( ! [X1: $i] :
( sK5
!= ( sK2 @ X1 ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f86]) ).
thf(f88,plain,
( ~ spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f80,f86,f82]) ).
thf(f90,definition,
( spl8_3
<=> ( ( sK2 @ sK6 )
= ( sK2 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
thf(f92,plain,
( ( ( sK2 @ sK6 )
= ( sK2 @ sK7 ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f90]) ).
thf(f93,plain,
( spl8_3
| spl8_2 ),
inference(avatar_split_clause,[],[f79,f86,f90]) ).
thf(f101,plain,
! [X0: $i,X1: $i] :
( ( ( sK2 @ ( sK1 @ ( sK0 @ X1 ) ) )
!= ( sK2 @ X0 ) )
| ( ( sK2 @ ( sK4 @ X0 ) )
= X1 ) ),
inference(constrained_superposition,[],[f55,f67]) ).
thf(f158,plain,
! [X0: $i,X1: $i] :
( ( ( sK2 @ X1 )
!= ( sK2 @ X0 ) )
| ( ( sK2 @ ( sK4 @ X1 ) )
= ( sK2 @ ( sK4 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f101,f67]) ).
thf(f159,plain,
! [X0: $i] :
( ( sK2 @ ( sK4 @ ( sK1 @ ( sK0 @ X0 ) ) ) )
= X0 ),
inference(equality_resolution,[],[f101]) ).
thf(f195,plain,
( ! [X0: $i] : ( sK5 != X0 )
| ~ spl8_2 ),
inference(constrained_superposition,[],[f87,f159]) ).
thf(f196,plain,
( $false
| ~ spl8_2 ),
inference(equality_resolution,[],[f195]) ).
thf(f197,plain,
~ spl8_2,
inference(avatar_contradiction_clause,[],[f196]) ).
thf(f214,plain,
( ! [X0: $i] :
( ( ( sK2 @ sK6 )
!= ( sK2 @ X0 ) )
| ( ( sK2 @ ( sK4 @ X0 ) )
= ( sK2 @ ( sK4 @ sK7 ) ) ) )
| ~ spl8_3 ),
inference(constrained_superposition,[],[f158,f92]) ).
thf(f319,plain,
( ( ( sK2 @ ( sK4 @ sK7 ) )
= ( sK2 @ ( sK4 @ sK6 ) ) )
| ~ spl8_3 ),
inference(equality_resolution,[],[f214]) ).
thf(f443,plain,
( ( sK7
= ( sK1 @ ( sK0 @ ( sK2 @ ( sK4 @ sK6 ) ) ) ) )
| ~ spl8_3 ),
inference(constrained_superposition,[],[f67,f319]) ).
thf(f444,plain,
( ( sK6 = sK7 )
| ~ spl8_3 ),
inference(forward_demodulation,[],[f443,f67]) ).
thf(f445,plain,
( $false
| spl8_1
| ~ spl8_3 ),
inference(forward_subsumption_resolution,[],[f444,f84]) ).
thf(f446,plain,
( spl8_1
| ~ spl8_3 ),
inference(avatar_contradiction_clause,[],[f445]) ).
cnf(s9,plain,
( ~ spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f88]) ).
cnf(s14,plain,
( spl8_2
| spl8_3 ),
inference(sat_conversion,[],[f93]) ).
cnf(s71,plain,
~ spl8_2,
inference(sat_conversion,[],[f197]) ).
cnf(s182,plain,
( spl8_1
| ~ spl8_3 ),
inference(sat_conversion,[],[f446]) ).
cnf(s183,plain,
spl8_3,
inference(rat,[],[s14,s71]) ).
cnf(s184,plain,
spl8_1,
inference(rat,[],[s182,s183]) ).
cnf(s185,plain,
$false,
inference(rat,[],[s9,s71,s184]) ).
thf(f447,plain,
$false,
inference(avatar_sat_refutation,[],[s185]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET741^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n016.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:45:50 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 0.21/0.28 % (366881)Will run a generic schedule for satisfiability detection.
% 0.21/0.28 % (366888)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3922170066:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.28 % (366887)% WARNING: option uhcvi not known.
% 0.21/0.28 % (366890)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4179527271:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.28 % (366886)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2218385954_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.28 % (366887)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2880747271:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.28 % (366889)dis+10_1_sil=32000:sp=arity:random_seed=4000432879:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.28 % (366892)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3900299119:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.28 % (366890)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.28 % (366887)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.28 % Exception at run slice level
% 0.21/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.28 % (366887)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.28 % (366888) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-366881-366888"...
% 0.21/0.28 % (366888)...printing done.
% 0.21/0.28 % (366888)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (366888)------------------------------
% 0.21/0.29 % (366888)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (366888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (366888)CaDiCaL version: 2.1.3
% 0.21/0.29 % (366888)Termination reason: Refutation
% 0.21/0.29 % (366888)Time elapsed: 0.011 s
% 0.21/0.29 % (366888)Peak memory usage: 13 MB
% 0.21/0.29 % (366888)Instructions burned: 33 (million)
% 0.21/0.29 % (366881)Success in time 0.047 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------