%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET741^4 : 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 : n009.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 08:23:28 AM UTC 2026
% Result : Theorem 0.06s 0.25s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 8
% Syntax : Number of formulae : 85 ( 40 unt; 0 typ; 3 def)
% Number of atoms : 419 ( 170 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 609 ( 40 ~; 36 |; 27 &; 435 @)
% ( 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 : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 31 usr; 10 con; 0-4 aty)
% ( 30 !!; 14 ??; 0 @@+; 0 @@-)
% Number of variables : 155 ( 0 sgn 51 !; 10 ?; 155 :)
% 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,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_15,type,
db2:
!>[X0: $tType] : X0 ).
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_28,type,
sK6: $i > $i ).
thf(func_def_29,type,
sK7: $i > $i ).
thf(f2,axiom,
( ( ^ [X0: $i > $i,X1: $i > $i,X2: $i] : ( X1 @ ( X0 @ X2 ) ) )
= fun_composition ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^1.ax',fun_composition) ).
thf(f4,axiom,
( ( ^ [X0: $i > $i] :
! [X2: $i,X1: $i] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) ) )
= fun_injective ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^1.ax',fun_injective) ).
thf(f5,axiom,
( ( ^ [X0: $i > $i] :
! [X1: $i] :
? [X2: $i] :
( X1
= ( X0 @ X2 ) ) )
= fun_surjective ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^1.ax',fun_surjective) ).
thf(f6,axiom,
( ( ^ [X0: $i > $i] :
( ( fun_surjective @ X0 )
& ( fun_injective @ X0 ) ) )
= fun_bijective ),
file('/export/starexec/sandbox2/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_injective @ ( fun_composition @ ( fun_composition @ X0 @ X1 ) @ X2 ) )
& ( fun_surjective @ ( fun_composition @ ( fun_composition @ X1 @ X2 ) @ X0 ) ) )
=> ( fun_bijective @ X2 ) ),
file('/export/starexec/sandbox2/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_injective @ ( fun_composition @ ( fun_composition @ X0 @ X1 ) @ X2 ) )
& ( fun_surjective @ ( fun_composition @ ( fun_composition @ X1 @ X2 ) @ X0 ) ) )
=> ( fun_bijective @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
thf(f15,plain,
( ( ^ [X0: $i > $i] :
! [X1: $i,X2: $i] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) ) )
= fun_injective ),
inference(rectify,[],[f4]) ).
thf(f16,plain,
( fun_injective
= ( ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( Y0 @ Y1 )
= ( Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f19,plain,
( fun_surjective
= ( ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f22,plain,
( fun_composition
= ( ^ [Y0: $i > $i,Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f23,plain,
~ ! [X0: $i > $i,X1: $i > $i,X2: $i > $i] :
( ( ( fun_surjective @ ( fun_composition @ ( fun_composition @ X2 @ X0 ) @ X1 ) )
& ( fun_injective @ ( fun_composition @ ( fun_composition @ X0 @ X1 ) @ X2 ) )
& ( fun_surjective @ ( fun_composition @ ( fun_composition @ X1 @ X2 ) @ X0 ) ) )
=> ( fun_bijective @ X2 ) ),
inference(rectify,[],[f10]) ).
thf(f24,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,[],[f23]) ).
thf(f25,plain,
( ( ^ [X0: $i > $i] :
( ( fun_surjective @ X0 )
& ( fun_injective @ X0 ) ) )
= fun_bijective ),
inference(rectify,[],[f6]) ).
thf(f26,plain,
( fun_bijective
= ( ^ [Y0: $i > $i] :
( ( fun_injective @ Y0 )
& ( fun_surjective @ Y0 ) ) ) ),
inference(fool_elimination,[],[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(ennf_transformation,[],[f24]) ).
thf(f28,plain,
? [X2: $i > $i,X1: $i > $i,X0: $i > $i] :
( ( ( fun_bijective @ X2 )
!= $true )
& ( ( fun_injective @ ( fun_composition @ ( fun_composition @ X0 @ X1 ) @ X2 ) )
= $true )
& ( ( fun_surjective @ ( fun_composition @ ( fun_composition @ X1 @ X2 ) @ X0 ) )
= $true )
& ( ( fun_surjective @ ( fun_composition @ ( fun_composition @ X2 @ X0 ) @ X1 ) )
= $true ) ),
inference(flattening,[],[f27]) ).
thf(f29,plain,
? [X0: $i > $i,X1: $i > $i,X2: $i > $i] :
( ( $true
!= ( fun_bijective @ X0 ) )
& ( $true
= ( fun_injective @ ( fun_composition @ ( fun_composition @ X2 @ X1 ) @ X0 ) ) )
& ( $true
= ( fun_surjective @ ( fun_composition @ ( fun_composition @ X1 @ X0 ) @ X2 ) ) )
& ( ( fun_surjective @ ( fun_composition @ ( fun_composition @ X0 @ X2 ) @ X1 ) )
= $true ) ),
inference(rectify,[],[f28]) ).
thf(f30,plain,
( ( $true
!= ( fun_bijective @ sK0 ) )
& ( ( fun_injective @ ( fun_composition @ ( fun_composition @ sK2 @ sK1 ) @ sK0 ) )
= $true )
& ( $true
= ( fun_surjective @ ( fun_composition @ ( fun_composition @ sK1 @ sK0 ) @ sK2 ) ) )
& ( $true
= ( fun_surjective @ ( fun_composition @ ( fun_composition @ sK0 @ sK2 ) @ sK1 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f29]) ).
thf(f31,plain,
( fun_composition
= ( ^ [Y0: $i > $i,Y1: $i > $i,Y2: $i] : ( Y1 @ ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f32,plain,
( $true
= ( fun_surjective @ ( fun_composition @ ( fun_composition @ sK0 @ sK2 ) @ sK1 ) ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f34,plain,
( ( fun_injective @ ( fun_composition @ ( fun_composition @ sK2 @ sK1 ) @ sK0 ) )
= $true ),
inference(cnf_transformation,[],[f30]) ).
thf(f35,plain,
( $true
!= ( fun_bijective @ sK0 ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f39,plain,
( fun_bijective
= ( ^ [Y0: $i > $i] :
( ( fun_injective @ Y0 )
& ( fun_surjective @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f41,plain,
( fun_injective
= ( ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( Y0 @ Y1 )
= ( Y0 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f42,plain,
( fun_surjective
= ( ^ [Y0: $i > $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f45,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,[],[f39,f41,f42]) ).
thf(f46,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 ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f35,f45]) ).
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 ) )
@ sK2
@ sK1 )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f34,f41,f31,f31]) ).
thf(f49,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 ) )
@ sK0
@ sK2 )
@ sK1 ) ) ),
inference(definition_unfolding,[],[f32,f42,f31,f31]) ).
thf(f50,plain,
( $true
!= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 )
= ( sK0 @ Y1 ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
= Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f51,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 )
= ( sK0 @ Y1 ) )
=> ( Y1 = Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
= Y0 ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f50]) ).
thf(f52,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 )
= ( sK0 @ Y1 ) )
=> ( Y1 = Y0 ) ) )
@ sK3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
= Y0 ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f51]) ).
thf(f53,plain,
( ( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
= Y0 ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 )
= ( sK0 @ Y1 ) )
=> ( Y1 = Y0 ) ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f52]) ).
thf(f54,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK3 )
= ( sK0 @ Y0 ) )
=> ( Y0 = sK3 ) ) ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
= sK4 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f55,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK3 )
= ( sK0 @ Y0 ) )
=> ( Y0 = sK3 ) )
@ sK5 ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
= sK4 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK3 )
= ( sK0 @ Y0 ) )
=> ( Y0 = sK3 ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
= sK4 )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f55]) ).
thf(f57,plain,
! [X1: $i] :
( ( ( ( ( sK0 @ sK3 )
= ( sK0 @ sK5 ) )
=> ( sK5 = sK3 ) )
= $false )
| ( ( ( sK0 @ X1 )
= sK4 )
= $false ) ),
inference(beta-eta_normalization,[],[f56]) ).
thf(f58,plain,
! [X1: $i] :
( ( ( ( sK0 @ X1 )
= sK4 )
= $false )
| ( $false
= ( sK5 = sK3 ) ) ),
inference(imp_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X1: $i] :
( ( $true
= ( ( sK0 @ sK3 )
= ( sK0 @ sK5 ) ) )
| ( ( ( sK0 @ X1 )
= sK4 )
= $false ) ),
inference(imp_proxy_clausification,[],[f57]) ).
thf(f60,plain,
! [X1: $i] :
( ( ( ( sK0 @ X1 )
= sK4 )
= $false )
| ( ( sK0 @ sK5 )
= ( sK0 @ sK3 ) ) ),
inference(equality_proxy_clausification,[],[f59]) ).
thf(f61,plain,
! [X1: $i] :
( ( ( sK0 @ sK5 )
= ( sK0 @ sK3 ) )
| ( sK4
!= ( sK0 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X1: $i] :
( ( $false
= ( sK5 = sK3 ) )
| ( sK4
!= ( sK0 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f58]) ).
thf(f63,plain,
! [X1: $i] :
( ( sK4
!= ( sK0 @ X1 ) )
| ( sK3 != sK5 ) ),
inference(equality_proxy_clausification,[],[f62]) ).
thf(f64,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ ( sK1 @ ( sK2 @ Y0 ) ) )
= ( sK0 @ ( sK1 @ ( sK2 @ Y1 ) ) ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f47]) ).
thf(f65,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ ( sK1 @ ( sK2 @ Y0 ) ) )
= ( sK0 @ ( sK1 @ ( sK2 @ Y1 ) ) ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f64]) ).
thf(f66,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ ( sK1 @ ( sK2 @ X1 ) ) )
= ( sK0 @ ( sK1 @ ( sK2 @ Y0 ) ) ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f65]) ).
thf(f67,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( sK0 @ ( sK1 @ ( sK2 @ X1 ) ) )
= ( sK0 @ ( sK1 @ ( sK2 @ Y0 ) ) ) )
=> ( Y0 = X1 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f66]) ).
thf(f68,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( ( sK0 @ ( sK1 @ ( sK2 @ X1 ) ) )
= ( sK0 @ ( sK1 @ ( sK2 @ X2 ) ) ) )
=> ( X2 = X1 ) ) ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( sK0 @ ( sK1 @ ( sK2 @ X1 ) ) )
= ( sK0 @ ( sK1 @ ( sK2 @ X2 ) ) ) ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f68]) ).
thf(f70,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( X2 = X1 ) )
| ( ( sK0 @ ( sK1 @ ( sK2 @ X1 ) ) )
!= ( sK0 @ ( sK1 @ ( sK2 @ X2 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ ( sK1 @ ( sK2 @ X1 ) ) )
!= ( sK0 @ ( sK1 @ ( sK2 @ X2 ) ) ) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f70]) ).
thf(f78,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK1 @ ( sK2 @ ( sK0 @ Y1 ) ) )
= Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f49]) ).
thf(f79,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK1 @ ( sK2 @ ( sK0 @ Y1 ) ) )
= Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f78]) ).
thf(f80,plain,
! [X1: $i] :
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ ( sK2 @ ( sK0 @ Y0 ) ) )
= X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f79]) ).
thf(f81,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK1 @ ( sK2 @ ( sK0 @ Y0 ) ) )
= X1 )
@ ( sK7 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f80]) ).
thf(f82,plain,
! [X1: $i] :
( ( ( sK1 @ ( sK2 @ ( sK0 @ ( sK7 @ X1 ) ) ) )
= X1 )
= $true ),
inference(beta-eta_normalization,[],[f81]) ).
thf(f83,plain,
! [X1: $i] :
( ( sK1 @ ( sK2 @ ( sK0 @ ( sK7 @ X1 ) ) ) )
= X1 ),
inference(equality_proxy_clausification,[],[f82]) ).
thf(f85,definition,
( spl8_1
<=> ( ( sK0 @ sK5 )
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f86,plain,
( ( ( sK0 @ sK5 )
= ( sK0 @ sK3 ) )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f85]) ).
thf(f88,definition,
( spl8_2
<=> ! [X1: $i] :
( sK4
!= ( sK0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f89,plain,
( ! [X1: $i] :
( sK4
!= ( sK0 @ X1 ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f88]) ).
thf(f90,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f61,f88,f85]) ).
thf(f92,definition,
( spl8_3
<=> ( sK3 = sK5 ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
thf(f93,plain,
( ( sK3 != sK5 )
| spl8_3 ),
inference(avatar_component_clause,[],[f92]) ).
thf(f94,plain,
( ~ spl8_3
| spl8_2 ),
inference(avatar_split_clause,[],[f63,f88,f92]) ).
thf(f96,plain,
! [X0: $i,X1: $i] :
( ( ( sK0 @ ( sK1 @ ( sK2 @ X1 ) ) )
!= ( sK0 @ X0 ) )
| ( ( sK0 @ ( sK7 @ X0 ) )
= X1 ) ),
inference(constrained_superposition,[],[f71,f83]) ).
thf(f101,plain,
! [X0: $i,X1: $i] :
( ( ( sK0 @ X0 )
!= ( sK0 @ X1 ) )
| ( ( sK0 @ ( sK7 @ X0 ) )
= ( sK0 @ ( sK7 @ X1 ) ) ) ),
inference(constrained_superposition,[],[f96,f83]) ).
thf(f102,plain,
! [X0: $i] :
( ( sK0 @ ( sK7 @ ( sK1 @ ( sK2 @ X0 ) ) ) )
= X0 ),
inference(equality_resolution,[],[f96]) ).
thf(f110,plain,
( ! [X0: $i] : ( sK4 != X0 )
| ~ spl8_2 ),
inference(constrained_superposition,[],[f89,f102]) ).
thf(f116,plain,
( $false
| ~ spl8_2 ),
inference(equality_resolution,[],[f110]) ).
thf(f117,plain,
~ spl8_2,
inference(avatar_contradiction_clause,[],[f116]) ).
thf(f122,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 )
!= ( sK0 @ sK3 ) )
| ( ( sK0 @ ( sK7 @ X0 ) )
= ( sK0 @ ( sK7 @ sK5 ) ) ) )
| ~ spl8_1 ),
inference(constrained_superposition,[],[f101,f86]) ).
thf(f135,plain,
( ( ( sK0 @ ( sK7 @ sK5 ) )
= ( sK0 @ ( sK7 @ sK3 ) ) )
| ~ spl8_1 ),
inference(equality_resolution,[],[f122]) ).
thf(f155,plain,
( ( ( sK1 @ ( sK2 @ ( sK0 @ ( sK7 @ sK3 ) ) ) )
= sK5 )
| ~ spl8_1 ),
inference(constrained_superposition,[],[f83,f135]) ).
thf(f156,plain,
( ( sK3 = sK5 )
| ~ spl8_1 ),
inference(forward_demodulation,[],[f155,f83]) ).
thf(f157,plain,
( $false
| ~ spl8_1
| spl8_3 ),
inference(forward_subsumption_resolution,[],[f156,f93]) ).
thf(f158,plain,
( ~ spl8_1
| spl8_3 ),
inference(avatar_contradiction_clause,[],[f157]) ).
cnf(s1,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f90]) ).
cnf(s2,plain,
( spl8_2
| ~ spl8_3 ),
inference(sat_conversion,[],[f94]) ).
cnf(s3,plain,
~ spl8_2,
inference(sat_conversion,[],[f117]) ).
cnf(s4,plain,
( ~ spl8_1
| spl8_3 ),
inference(sat_conversion,[],[f158]) ).
cnf(s5,plain,
~ spl8_3,
inference(rat,[],[s2,s3]) ).
cnf(s6,plain,
~ spl8_1,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s3,s6]) ).
thf(f159,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET741^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n009.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 13:41:00 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.20 Running higher-order theorem proving
% 0.06/0.22 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
% 0.06/0.25 % (4005891)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.06/0.25 % (4005901)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1294680545:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.06/0.25 % (4005901) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4005891-4005901"...
% 0.06/0.25 % (4005897)lrs+10_16_si=on:nwc=1.5:random_seed=2486768508:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.06/0.25 % (4005901)...printing done.
% 0.06/0.25 % (4005898)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3943369371:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.06/0.25 % (4005896)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=920358337:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.06/0.25 % (4005900)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2185185632:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.06/0.25 % (4005899)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=782260496: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)
% 0.06/0.25 % (4005901)Refutation found. Thanks to Tanya!
% 0.06/0.25 % SZS status Theorem for theBenchmark
% 0.06/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.26 % (4005901)------------------------------
% 0.35/0.26 % (4005901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.26 % (4005901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.26 % (4005901)CaDiCaL version: 2.1.3
% 0.35/0.26 % (4005901)Termination reason: Refutation
% 0.35/0.26 % (4005901)Time elapsed: 0.006 s
% 0.35/0.26 % (4005901)Peak memory usage: 13 MB
% 0.35/0.26 % (4005901)Instructions burned: 20 (million)
% 0.35/0.26 % (4005891)Success in time 0.032 s
% 0.35/0.26 % Vampire exiting
%------------------------------------------------------------------------------