%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO057^2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 08:48:50 AM UTC 2026
% Result : Theorem 0.43s 0.31s
% Output : Refutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 7
% Syntax : Number of formulae : 68 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 362 ( 144 equ; 6 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 807 ( 109 ~; 134 |; 0 &; 521 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 180 ( 180 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 46 usr; 4 con; 0-4 aty)
% ( 43 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 297 ( 158 ^; 134 !; 5 ?; 297 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_35,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_36,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vNOT: $o > $o ).
thf(func_def_38,type,
vOR: $o > $o > $o ).
thf(func_def_39,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vIMP: $o > $o > $o ).
thf(func_def_44,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_45,type,
vAND: $o > $o > $o ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
sK0: $i > ( $i > $i > $o ) > ( $i > $o ) > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f11,axiom,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
thf(f16,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,conjecture,
? [X0: $i > $i > $o] :
~ ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mbox @ X0 @ ( mimplies @ ( mbox @ X0 @ X1 ) @ X1 ) ) @ ( mbox @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ? [X0: $i > $i > $o] :
~ ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mbox @ X0 @ ( mimplies @ ( mbox @ X0 @ X1 ) @ X1 ) ) @ ( mbox @ X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f36,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f37,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f38,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f39,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f41,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f47,plain,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f48,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f54,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f55,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f77,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f78,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f77]) ).
thf(f85,plain,
~ ? [X0: $i > $i > $o] :
~ ( mvalid
@ ( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mbox @ X0 @ ( mimplies @ ( mbox @ X0 @ X1 ) @ X1 ) ) @ ( mbox @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f33]) ).
thf(f86,plain,
~ ? [X0: $i > $i > $o] :
( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ X0 @ ( mimplies @ ( mbox @ X0 @ Y0 ) @ Y0 ) ) @ ( mbox @ X0 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f85]) ).
thf(f87,plain,
~ ? [X0: $i > $i > $o] :
( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ X0 @ ( mimplies @ ( mbox @ X0 @ Y0 ) @ Y0 ) ) @ ( mbox @ X0 @ Y0 ) ) ) ) ),
inference(flattening,[],[f86]) ).
thf(f88,plain,
! [X0: $i > $i > $o] :
( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ X0 @ ( mimplies @ ( mbox @ X0 @ Y0 ) @ Y0 ) ) @ ( mbox @ X0 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f87]) ).
thf(f91,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f92,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f94,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f99,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f104,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f116,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f78]) ).
thf(f120,plain,
! [X0: $i > $i > $o] :
( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ X0 @ ( mimplies @ ( mbox @ X0 @ Y0 ) @ Y0 ) ) @ ( mbox @ X0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f124,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f94,f92,f91]) ).
thf(f132,plain,
! [X0: $i > $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ X0
@ ( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
| ( Y4 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ X0
@ Y0 )
@ Y0 ) )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( Y1 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ X0
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f120,f116,f99,f124,f104,f124,f104,f104]) ).
thf(f133,plain,
! [X0: $i > $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X0 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ( Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f132]) ).
thf(f134,plain,
! [X0: $i > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X0 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( X0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ( Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X0 @ Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f133]) ).
thf(f135,plain,
! [X0: $i > $i > $o,X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X0 @ X1 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X0 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
| ( Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X0 @ X1 @ Y1 )
| ( Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f136,plain,
! [X2: $i > $o,X0: $i > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X0 @ X1 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( X0 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
| ( Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X0 @ X1 @ Y1 )
| ( Y0 @ Y1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f135]) ).
thf(f137,plain,
! [X2: $i > $o,X0: $i > $i > $o,X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X0 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X0 @ Y0 @ Y1 )
| ( X2 @ Y1 ) ) )
| ( X2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X0 @ X1 @ Y0 )
| ( X2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
! [X2: $i > $o,X0: $i > $i > $o,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X0 @ X1 @ Y0 )
| ( X2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X0 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X0 @ Y0 @ Y1 )
| ( X2 @ Y1 ) ) )
| ( X2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f137]) ).
thf(f139,plain,
! [X2: $i > $o,X3: $i,X0: $i > $i > $o,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( X0 @ X1 @ Y0 )
| ( X2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X0 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X0 @ Y0 @ Y1 )
| ( X2 @ Y1 ) ) )
| ( X2 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f138]) ).
thf(f140,plain,
! [X2: $i > $o,X3: $i,X0: $i > $i > $o,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( X0 @ X1 @ Y0 )
| ( X2 @ Y0 ) )
@ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X0 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X0 @ Y0 @ Y1 )
| ( X2 @ Y1 ) ) )
| ( X2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f139]) ).
thf(f141,plain,
! [X2: $i > $o,X3: $i,X0: $i > $i > $o,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( X0 @ X1 @ Y0 )
| ( X2 @ Y0 ) )
@ X3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( X0 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( X0 @ Y0 @ Y1 )
| ( X2 @ Y1 ) ) )
| ( X2 @ Y0 ) )
@ ( sK0 @ X1 @ X0 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f140]) ).
thf(f142,plain,
! [X2: $i > $o,X3: $i,X0: $i > $i > $o,X1: $i] :
( ( $true
= ( ~ ( X0 @ X1 @ X3 )
| ( X2 @ X3 ) ) )
| ( $false
= ( ~ ( X0 @ X1 @ ( sK0 @ X1 @ X0 @ X2 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X0 @ ( sK0 @ X1 @ X0 @ X2 ) @ Y0 )
| ( X2 @ Y0 ) ) )
| ( X2 @ ( sK0 @ X1 @ X0 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
! [X2: $i > $o,X3: $i,X0: $i > $i > $o,X1: $i] :
( ( $true
= ( X2 @ X3 ) )
| ( $false
= ( ~ ( X0 @ X1 @ ( sK0 @ X1 @ X0 @ X2 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X0 @ ( sK0 @ X1 @ X0 @ X2 ) @ Y0 )
| ( X2 @ Y0 ) ) )
| ( X2 @ ( sK0 @ X1 @ X0 @ X2 ) ) ) )
| ( $true
= ( ~ ( X0 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f142]) ).
thf(f144,plain,
! [X2: $i > $o,X3: $i,X0: $i > $i > $o,X1: $i] :
( ( $true
= ( X2 @ X3 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X0 @ ( sK0 @ X1 @ X0 @ X2 ) @ Y0 )
| ( X2 @ Y0 ) ) )
| ( X2 @ ( sK0 @ X1 @ X0 @ X2 ) ) ) )
| ( $true
= ( ~ ( X0 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f145,plain,
! [X2: $i > $o,X3: $i,X0: $i > $i > $o,X1: $i] :
( ( $true
= ( X2 @ X3 ) )
| ( $false
= ( ~ ( X0 @ X1 @ ( sK0 @ X1 @ X0 @ X2 ) ) ) )
| ( $true
= ( ~ ( X0 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f146,plain,
! [X2: $i > $o,X3: $i,X0: $i > $i > $o,X1: $i] :
( ( $true
= ( X2 @ X3 ) )
| ( $true
= ( X0 @ X1 @ ( sK0 @ X1 @ X0 @ X2 ) ) )
| ( $true
= ( ~ ( X0 @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f145]) ).
thf(f147,plain,
! [X2: $i > $o,X3: $i,X0: $i > $i > $o,X1: $i] :
( ( $true
= ( X2 @ X3 ) )
| ( $true
= ( X0 @ X1 @ ( sK0 @ X1 @ X0 @ X2 ) ) )
| ( ( X0 @ X1 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f146]) ).
thf(f149,plain,
! [X2: $i > $o,X3: $i,X0: $i > $i > $o,X1: $i] :
( ( $true
= ( X2 @ X3 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X0 @ ( sK0 @ X1 @ X0 @ X2 ) @ Y0 )
| ( X2 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( X0 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f144]) ).
thf(f150,plain,
! [X2: $i > $o,X3: $i,X0: $i > $i > $o,X1: $i] :
( ( $true
= ( X2 @ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( X0 @ ( sK0 @ X1 @ X0 @ X2 ) @ Y0 )
| ( X2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( X0 @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X2: $i > $o,X3: $i,X0: $i > $i > $o,X1: $i,X4: $i] :
( ( $true
= ( X2 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( X0 @ ( sK0 @ X1 @ X0 @ X2 ) @ Y0 )
| ( X2 @ Y0 ) )
@ X4 ) )
| ( $true
= ( ~ ( X0 @ X1 @ X3 ) ) ) ),
inference(pi_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X2: $i > $o,X3: $i,X0: $i > $i > $o,X1: $i,X4: $i] :
( ( $true
= ( X2 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( X0 @ ( sK0 @ X1 @ X0 @ X2 ) @ Y0 )
| ( X2 @ Y0 ) )
@ X4 ) )
| ( ( X0 @ X1 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X2: $i > $o,X3: $i,X0: $i > $i > $o,X1: $i,X4: $i] :
( ( $true
= ( X2 @ X3 ) )
| ( $true
= ( ~ ( X0 @ ( sK0 @ X1 @ X0 @ X2 ) @ X4 )
| ( X2 @ X4 ) ) )
| ( ( X0 @ X1 @ X3 )
= $false ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,plain,
! [X2: $i > $o,X3: $i,X0: $i > $i > $o,X1: $i,X4: $i] :
( ( $true
= ( X2 @ X3 ) )
| ( $true
= ( X2 @ X4 ) )
| ( ( X0 @ X1 @ X3 )
= $false )
| ( $true
= ( ~ ( X0 @ ( sK0 @ X1 @ X0 @ X2 ) @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X2: $i > $o,X3: $i,X0: $i > $i > $o,X1: $i,X4: $i] :
( ( $true
= ( X2 @ X3 ) )
| ( ( X0 @ X1 @ X3 )
= $false )
| ( $false
= ( X0 @ ( sK0 @ X1 @ X0 @ X2 ) @ X4 ) )
| ( $true
= ( X2 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f283,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( X2 @ X3 ) )
| ( $true
= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 )
@ X1
@ ( sK0 @ X1
@ ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 )
@ X2 ) ) )
| ( $false
= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 )
@ X1
@ X3 ) ) ),
inference(primitive_instantiation,[],[f147]) ).
thf(f416,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( X2 @ X3 ) )
| ( $true
= ( X1
= ( sK0 @ X1 @ (=) @ X2 ) ) )
| ( $false
= ( X1 = X3 ) ) ),
inference(beta-eta_normalization,[],[f283]) ).
thf(f417,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( X2 @ X3 ) )
| ( ( sK0 @ X1 @ (=) @ X2 )
= X1 )
| ( $false
= ( X1 = X3 ) ) ),
inference(equality_proxy_clausification,[],[f416]) ).
thf(f418,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( X2 @ X3 ) )
| ( ( sK0 @ X1 @ (=) @ X2 )
= X1 )
| ( X1 != X3 ) ),
inference(equality_proxy_clausification,[],[f417]) ).
thf(f562,plain,
! [X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] : $false
@ X3 ) )
| ( ( sK0 @ X1 @ (=)
@ ^ [Y0: $i] : $false )
= X1 )
| ( X1 != X3 ) ),
inference(primitive_instantiation,[],[f418]) ).
thf(f612,plain,
! [X3: $i,X1: $i] :
( ( $true = $false )
| ( ( sK0 @ X1 @ (=)
@ ^ [Y0: $i] : $false )
= X1 )
| ( X1 != X3 ) ),
inference(beta-eta_normalization,[],[f562]) ).
thf(f613,plain,
! [X3: $i,X1: $i] :
( ( ( sK0 @ X1 @ (=)
@ ^ [Y0: $i] : $false )
= X1 )
| ( X1 != X3 ) ),
inference(trivial_inequality_removal,[],[f612]) ).
thf(f1404,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( X0 = X1 ) )
| ( $true
= ( ^ [Y0: $i] : $false
@ X2 ) )
| ( $false
= ( X0 = X2 ) )
| ( $true
= ( ^ [Y0: $i] : $false
@ X1 ) )
| ( X0 != X3 ) ),
inference(constrained_superposition,[],[f155,f613]) ).
thf(f1681,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( X0 != X1 )
| ( $true
= ( ^ [Y0: $i] : $false
@ X2 ) )
| ( $false
= ( X0 = X2 ) )
| ( $true
= ( ^ [Y0: $i] : $false
@ X1 ) )
| ( X0 != X3 ) ),
inference(equality_proxy_clausification,[],[f1404]) ).
thf(f1682,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( X0 != X1 )
| ( $true
= ( ^ [Y0: $i] : $false
@ X2 ) )
| ( X0 != X2 )
| ( $true
= ( ^ [Y0: $i] : $false
@ X1 ) )
| ( X0 != X3 ) ),
inference(equality_proxy_clausification,[],[f1681]) ).
thf(f1683,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( X0 != X1 )
| ( $true = $false )
| ( X0 != X2 )
| ( $true = $false )
| ( X0 != X3 ) ),
inference(beta-eta_normalization,[],[f1682]) ).
thf(f1684,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( X0 != X1 )
| ( $true = $false )
| ( X0 != X2 )
| ( X0 != X3 ) ),
inference(duplicate_literal_removal,[],[f1683]) ).
thf(f1685,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( X0 != X1 )
| ( X0 != X2 )
| ( X0 != X3 ) ),
inference(trivial_inequality_removal,[],[f1684]) ).
thf(f1686,plain,
$false,
inference(flex-flex_simplification,[],[f1685]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO057^2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n008.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 16:26:25 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.43/0.31 % (3371235)Will run a generic schedule for satisfiability detection.
% 0.43/0.31 % (3371246)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2437008364:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.43/0.31 % (3371241)% WARNING: option uhcvi not known.
% 0.43/0.31 % (3371241)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3028352695:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.43/0.31 % (3371242)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3081476189:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.43/0.31 % (3371243)dis+10_1_sil=32000:sp=arity:random_seed=1750944475:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.43/0.31 % (3371245)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2952362128:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.43/0.31 % (3371244)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=631717401:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.43/0.31 % (3371241)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.43/0.31 % (3371244)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.43/0.31 % (3371241)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.43/0.31 % (3371240)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3706319311_2999 on theBenchmark for (2999ds/0Mi)
% 0.43/0.31 % Exception at run slice level
% 0.43/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.43/0.31 % (3371264)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1515738372:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.43/0.31 % (3371246)Instruction limit reached!
% 0.43/0.31 % (3371246)------------------------------
% 0.43/0.31 % (3371246)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.43/0.31 % (3371246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.43/0.31 % (3371246)CaDiCaL version: 2.1.3
% 0.43/0.31 % (3371246)Termination reason: Instruction limit
% 0.43/0.31 % (3371246)Termination phase: Saturation
% 0.43/0.31 % (3371246)Time elapsed: 0.040 s
% 0.43/0.31 % (3371246)Peak memory usage: 12 MB
% 0.43/0.31 % (3371246)Instructions burned: 159 (million)
% 0.43/0.31 % Exception at run slice level
% 0.43/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.43/0.31 % (3371272)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=917330298:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.43/0.31 % (3371243)Instruction limit reached!
% 0.43/0.31 % (3371243)------------------------------
% 0.43/0.31 % (3371243)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.43/0.31 % (3371243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.43/0.31 % (3371243)CaDiCaL version: 2.1.3
% 0.43/0.31 % (3371243)Termination reason: Instruction limit
% 0.43/0.31 % (3371243)Termination phase: Saturation
% 0.43/0.31 % (3371243)Time elapsed: 0.049 s
% 0.43/0.31 % (3371243)Peak memory usage: 12 MB
% 0.43/0.31 % (3371243)Instructions burned: 104 (million)
% 0.43/0.31 % (3371244)Instruction limit reached!
% 0.43/0.31 % (3371244)------------------------------
% 0.43/0.31 % (3371244)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.43/0.31 % (3371244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.43/0.31 % (3371244)CaDiCaL version: 2.1.3
% 0.43/0.31 % (3371244)Termination reason: Instruction limit
% 0.43/0.31 % (3371244)Termination phase: Saturation
% 0.43/0.31 % (3371244)Time elapsed: 0.053 s
% 0.43/0.31 % (3371244)Peak memory usage: 12 MB
% 0.43/0.31 % (3371244)Instructions burned: 116 (million)
% 0.43/0.31 % (3371274)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=4209293434:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.43/0.31 % (3371274)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.43/0.31 % (3371274)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.43/0.31 % (3371245)Instruction limit reached!
% 0.43/0.31 % (3371245)------------------------------
% 0.43/0.31 % (3371245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.43/0.31 % (3371245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.43/0.31 % (3371245)CaDiCaL version: 2.1.3
% 0.43/0.31 % (3371245)Termination reason: Instruction limit
% 0.43/0.31 % (3371245)Termination phase: Saturation
% 0.43/0.31 % (3371245)Time elapsed: 0.062 s
% 0.43/0.31 % (3371245)Peak memory usage: 12 MB
% 0.43/0.31 % (3371245)Instructions burned: 133 (million)
% 0.43/0.31 % (3371277)ott-21_1_sil=16000:fs=off:random_seed=2951710993:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.43/0.31 % (3371272) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3371235-3371272"...
% 0.43/0.31 % (3371272)...printing done.
% 0.43/0.31 % (3371272)Refutation found. Thanks to Tanya!
% 0.43/0.31 % SZS status Theorem for theBenchmark
% 0.43/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.43/0.31 % (3371272)------------------------------
% 0.43/0.31 % (3371272)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.43/0.31 % (3371272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.43/0.31 % (3371272)CaDiCaL version: 2.1.3
% 0.43/0.31 % (3371272)Termination reason: Refutation
% 0.43/0.31 % (3371272)Time elapsed: 0.026 s
% 0.43/0.31 % (3371272)Peak memory usage: 12 MB
% 0.43/0.31 % (3371272)Instructions burned: 99 (million)
% 0.43/0.31 % (3371235)Success in time 0.093 s
% 0.43/0.31 % Vampire exiting
%------------------------------------------------------------------------------