%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWV432^2 : 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 : n005.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 08:40:06 AM UTC 2026
% Result : Theorem 0.08s 0.28s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 12
% Syntax : Number of formulae : 100 ( 71 unt; 0 typ; 0 def)
% Number of atoms : 726 ( 154 equ; 0 cnn)
% Maximal formula atoms : 15 ( 7 avg)
% Number of connectives : 966 ( 61 ~; 113 |; 0 &; 683 @)
% ( 0 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 161 ( 161 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 50 usr; 6 con; 0-4 aty)
% ( 52 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 282 ( 231 ^; 51 !; 0 ?; 282 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
individuals: $tType ).
thf(func_def_1,type,
prop_a: $i > $o ).
thf(func_def_2,type,
prop_b: $i > $o ).
thf(func_def_3,type,
prop_c: $i > $o ).
thf(func_def_4,type,
mfalse: $i > $o ).
thf(func_def_5,type,
mtrue: $i > $o ).
thf(func_def_6,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mall: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_17,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_18,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_20,type,
rel: $i > $i > $o ).
thf(func_def_21,type,
icl_atom: ( $i > $o ) > $i > $o ).
thf(func_def_22,type,
icl_princ: ( $i > $o ) > $i > $o ).
thf(func_def_23,type,
icl_and: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_24,type,
icl_or: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_25,type,
icl_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_26,type,
icl_true: $i > $o ).
thf(func_def_27,type,
icl_false: $i > $o ).
thf(func_def_28,type,
icl_says: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_29,type,
iclval: ( $i > $o ) > $o ).
thf(func_def_30,type,
icl_impl_princ: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_31,type,
a: $i > $o ).
thf(func_def_32,type,
b: $i > $o ).
thf(func_def_35,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_36,type,
vNOT: $o > $o ).
thf(func_def_37,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vOR: $o > $o > $o ).
thf(func_def_40,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vAND: $o > $o > $o ).
thf(func_def_42,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_43,type,
vIMP: $o > $o > $o ).
thf(func_def_44,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
sK3: $i > ( $i > $o ) > $i ).
thf(func_def_50,type,
sK4: $i > ( $i > $o ) > $i ).
thf(func_def_52,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_53,type,
sK6: ( $i > $o ) > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( mimpl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f8,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f17,axiom,
( icl_princ
= ( ^ [X0: $i > $o] : X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_princ) ).
thf(f20,axiom,
( icl_impl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ rel @ ( mimpl @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_impl) ).
thf(f23,axiom,
( icl_says
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ rel @ ( mor @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_says) ).
thf(f24,axiom,
( iclval
= ( ^ [X0: $i > $o] : ( mvalid @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_s4_valid) ).
thf(f25,axiom,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^1.ax',refl_axiom) ).
thf(f27,axiom,
( icl_impl_princ
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ rel @ ( mimpl @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^2.ax',icl_impl_princ) ).
thf(f28,conjecture,
iclval @ ( icl_impl @ ( icl_says @ ( icl_princ @ b ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',handoff) ).
thf(f29,negated_conjecture,
~ ( iclval @ ( icl_impl @ ( icl_says @ ( icl_princ @ b ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
thf(f32,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f33,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f34,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f35,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f38,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f40,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f41,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f48,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f49,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f57,plain,
( icl_princ
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f17]) ).
thf(f60,plain,
( icl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f61,plain,
( icl_says
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mor @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f62,plain,
( iclval
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f63,plain,
! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) ),
inference(rectify,[],[f25]) ).
thf(f64,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) )
= $true ),
inference(fool_elimination,[],[f63]) ).
thf(f67,plain,
( icl_impl_princ
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f68,plain,
~ ( iclval @ ( icl_impl @ ( icl_says @ ( icl_princ @ b ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ) ),
inference(rectify,[],[f29]) ).
thf(f69,plain,
( ( iclval @ ( icl_impl @ ( icl_says @ ( icl_princ @ b ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ) )
!= $true ),
inference(fool_elimination,[],[f68]) ).
thf(f70,plain,
( ( iclval @ ( icl_impl @ ( icl_says @ ( icl_princ @ b ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ) )
!= $true ),
inference(flattening,[],[f69]) ).
thf(f73,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f74,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f76,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f78,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f82,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f87,plain,
( icl_princ
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f90,plain,
( icl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f93,plain,
( icl_says
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mor @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f94,plain,
( iclval
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f95,plain,
! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ rel @ X0 ) @ X0 ) )
= $true ),
inference(cnf_transformation,[],[f64]) ).
thf(f97,plain,
( icl_impl_princ
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f98,plain,
( ( iclval @ ( icl_impl @ ( icl_says @ ( icl_princ @ b ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f70]) ).
thf(f101,plain,
( mimpl
= ( ^ [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,[],[f76,f74,f73]) ).
thf(f106,plain,
( icl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f90,f78,f101]) ).
thf(f109,plain,
( icl_says
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f93,f78,f74]) ).
thf(f110,plain,
( iclval
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 ) ) ),
inference(definition_unfolding,[],[f94,f82]) ).
thf(f111,plain,
( icl_impl_princ
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f97,f78,f101]) ).
thf(f112,plain,
! [X0: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ rel
@ X0 )
@ X0 ) ) ),
inference(definition_unfolding,[],[f95,f82,f101,f78]) ).
thf(f114,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) ) ) ) ),
inference(definition_unfolding,[],[f98,f110,f106,f109,f87,f111,f87,f87,f111,f87,f87]) ).
thf(f115,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( b @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( ~ ( a @ Y3 )
| ( b @ Y3 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ~ ( a @ Y2 )
| ( b @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f114]) ).
thf(f116,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ( b @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( rel @ Y2 @ Y3 )
=> ( ~ ( a @ Y3 )
| ( b @ Y3 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ~ ( a @ Y2 )
| ( b @ Y2 ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f115]) ).
thf(f117,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK0 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( b @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ~ ( a @ Y2 )
| ( b @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( a @ Y1 )
| ( b @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,plain,
( $false
= ( ^ [Y0: $i] :
( ( rel @ sK0 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ( b @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( rel @ Y1 @ Y2 )
=> ( ~ ( a @ Y2 )
| ( b @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( a @ Y1 )
| ( b @ Y1 ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f117]) ).
thf(f119,plain,
( $false
= ( ( rel @ sK0 @ sK1 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
=> ( ( b @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( a @ Y1 )
| ( b @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
=> ( ~ ( a @ Y0 )
| ( b @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
=> ( ( b @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( a @ Y1 )
| ( b @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
=> ( ~ ( a @ Y0 )
| ( b @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f119]) ).
thf(f122,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
=> ( ~ ( a @ Y0 )
| ( b @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f120]) ).
thf(f123,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
=> ( ( b @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( a @ Y1 )
| ( b @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f120]) ).
thf(f124,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
=> ( ( b @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( a @ Y1 )
| ( b @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f123]) ).
thf(f125,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
=> ( ( b @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( ~ ( a @ Y1 )
| ( b @ Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f124]) ).
thf(f126,plain,
! [X1: $i] :
( $true
= ( ( rel @ sK1 @ X1 )
=> ( ( b @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( ~ ( a @ Y0 )
| ( b @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f125]) ).
thf(f127,plain,
! [X1: $i] :
( ( $false
= ( rel @ sK1 @ X1 ) )
| ( $true
= ( ( b @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( ~ ( a @ Y0 )
| ( b @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f126]) ).
thf(f128,plain,
! [X1: $i] :
( ( $false
= ( rel @ sK1 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( ~ ( a @ Y0 )
| ( b @ Y0 ) ) ) ) )
| ( $true
= ( b @ X1 ) ) ),
inference(or_proxy_clausification,[],[f127]) ).
thf(f129,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel @ sK1 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( ~ ( a @ Y0 )
| ( b @ Y0 ) ) )
@ X2 ) )
| ( $true
= ( b @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f128]) ).
thf(f130,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel @ sK1 @ X1 ) )
| ( $true
= ( ( rel @ X1 @ X2 )
=> ( ~ ( a @ X2 )
| ( b @ X2 ) ) ) )
| ( $true
= ( b @ X1 ) ) ),
inference(beta-eta_normalization,[],[f129]) ).
thf(f131,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel @ sK1 @ X1 ) )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( $true
= ( b @ X1 ) )
| ( $true
= ( ~ ( a @ X2 )
| ( b @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f130]) ).
thf(f132,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel @ sK1 @ X1 ) )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( $true
= ( b @ X1 ) )
| ( $true
= ( b @ X2 ) )
| ( $true
= ( ~ ( a @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f131]) ).
thf(f133,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel @ sK1 @ X1 ) )
| ( $false
= ( rel @ X1 @ X2 ) )
| ( $true
= ( b @ X1 ) )
| ( $true
= ( b @ X2 ) )
| ( $false
= ( a @ X2 ) ) ),
inference(not_proxy_clausification,[],[f132]) ).
thf(f134,plain,
( $false
= ( ^ [Y0: $i] :
( ( rel @ sK1 @ Y0 )
=> ( ~ ( a @ Y0 )
| ( b @ Y0 ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f122]) ).
thf(f135,plain,
( $false
= ( ( rel @ sK1 @ sK2 )
=> ( ~ ( a @ sK2 )
| ( b @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f134]) ).
thf(f136,plain,
( $false
= ( ~ ( a @ sK2 )
| ( b @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f135]) ).
thf(f137,plain,
( $true
= ( rel @ sK1 @ sK2 ) ),
inference(imp_proxy_clausification,[],[f135]) ).
thf(f138,plain,
( $false
= ( b @ sK2 ) ),
inference(or_proxy_clausification,[],[f136]) ).
thf(f139,plain,
( $false
= ( ~ ( a @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f136]) ).
thf(f140,plain,
( $true
= ( a @ sK2 ) ),
inference(not_proxy_clausification,[],[f139]) ).
thf(f158,plain,
! [X0: $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) )
| ( X0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f112]) ).
thf(f159,plain,
! [X0: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( X0 @ Y1 ) ) )
| ( X0 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X0: $i > $o,X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) )
| ( X0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
=> ( X0 @ Y0 ) )
@ ( sK4 @ X1 @ X0 ) ) ) ),
inference(sigma_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $true )
| ( $false
= ( ( rel @ X1 @ ( sK4 @ X1 @ X0 ) )
=> ( X0 @ ( sK4 @ X1 @ X0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
! [X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK4 @ X1 @ X0 ) ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( rel @ X1 @ ( sK4 @ X1 @ X0 ) ) )
| ( ( X0 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f164]) ).
thf(f300,plain,
! [X0: $i] :
( ( sK4 @ X0
@ ^ [Y0: $i] : ( Y0 != X0 ) )
= X0 ),
inference(leibniz_equality_elimination,[],[f165]) ).
thf(f693,plain,
! [X0: $i,X1: $i > $o] :
( ( $false = $true )
| ( $false
= ( rel @ sK1 @ X0 ) )
| ( $true
= ( b @ X0 ) )
| ( $true
= ( b @ ( sK4 @ X0 @ X1 ) ) )
| ( $false
= ( a @ ( sK4 @ X0 @ X1 ) ) )
| ( $true
= ( X1 @ X0 ) ) ),
inference(constrained_superposition,[],[f133,f166]) ).
thf(f712,plain,
! [X0: $i,X1: $i > $o] :
( ( $false
= ( a @ ( sK4 @ X0 @ X1 ) ) )
| ( $true
= ( b @ X0 ) )
| ( $true
= ( b @ ( sK4 @ X0 @ X1 ) ) )
| ( $false
= ( rel @ sK1 @ X0 ) )
| ( $true
= ( X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f693]) ).
thf(f814,plain,
! [X0: $i] :
( ( $false
= ( a @ X0 ) )
| ( $true
= ( b @ X0 ) )
| ( $true
= ( b @ X0 ) )
| ( $false
= ( rel @ sK1 @ X0 ) )
| ( $true
= ( ^ [Y0: $i] : ( Y0 != X0 )
@ X0 ) ) ),
inference(constrained_superposition,[],[f712,f300]) ).
thf(f833,plain,
! [X0: $i] :
( ( $false
= ( a @ X0 ) )
| ( $true
= ( b @ X0 ) )
| ( $false
= ( rel @ sK1 @ X0 ) )
| ( $true
= ( ^ [Y0: $i] : ( Y0 != X0 )
@ X0 ) ) ),
inference(duplicate_literal_removal,[],[f814]) ).
thf(f834,plain,
! [X0: $i] :
( ( $false
= ( a @ X0 ) )
| ( $true
= ( b @ X0 ) )
| ( $false
= ( rel @ sK1 @ X0 ) )
| ( $true
= ( X0 != X0 ) ) ),
inference(beta-eta_normalization,[],[f833]) ).
thf(f835,plain,
! [X0: $i] :
( ( $false
= ( a @ X0 ) )
| ( $true
= ( b @ X0 ) )
| ( $false
= ( rel @ sK1 @ X0 ) )
| ( $false
= ( X0 = X0 ) ) ),
inference(not_proxy_clausification,[],[f834]) ).
thf(f836,plain,
! [X0: $i] :
( ( $false
= ( a @ X0 ) )
| ( $true
= ( b @ X0 ) )
| ( $false
= ( rel @ sK1 @ X0 ) )
| ( X0 != X0 ) ),
inference(equality_proxy_clausification,[],[f835]) ).
thf(f837,plain,
! [X0: $i] :
( ( $false
= ( rel @ sK1 @ X0 ) )
| ( $true
= ( b @ X0 ) )
| ( $false
= ( a @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f836]) ).
thf(f850,plain,
( ( $false = $true )
| ( $true
= ( b @ sK2 ) )
| ( $false
= ( a @ sK2 ) ) ),
inference(constrained_superposition,[],[f137,f837]) ).
thf(f851,plain,
( ( $true
= ( b @ sK2 ) )
| ( $false
= ( a @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f850]) ).
thf(f863,plain,
( ( $false = $true )
| ( $false
= ( a @ sK2 ) ) ),
inference(forward_demodulation,[],[f851,f138]) ).
thf(f864,plain,
( $false
= ( a @ sK2 ) ),
inference(trivial_inequality_removal,[],[f863]) ).
thf(f870,plain,
$false = $true,
inference(constrained_superposition,[],[f140,f864]) ).
thf(f871,plain,
$false,
inference(trivial_inequality_removal,[],[f870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV432^2 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n005.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
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:02:46 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.08/0.28 % (1848750)Will run a generic schedule for satisfiability detection.
% 0.08/0.28 % (1848761)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=644669211:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.28 % (1848756)% WARNING: option uhcvi not known.
% 0.08/0.28 % (1848755)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1184200965_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.28 % (1848757)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3169380485:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.28 % (1848756)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2219237496:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.28 % (1848758)dis+10_1_sil=32000:sp=arity:random_seed=4080339777:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.28 % (1848760)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2499564197:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.28 % (1848756)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.28 % Exception at run slice level
% 0.08/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.28 % (1848756)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.28 % (1848759)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2809062085:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.28 % (1848759)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.28 % (1848768)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3825938857:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.08/0.28 % Exception at run slice level
% 0.08/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.28 % (1848757) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1848750-1848757"...
% 0.08/0.28 % (1848757)...printing done.
% 0.08/0.28 % (1848761)Instruction limit reached!
% 0.08/0.28 % (1848761)------------------------------
% 0.08/0.28 % (1848761)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.28 % (1848761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.28 % (1848757)Refutation found. Thanks to Tanya!
% 0.08/0.28 % SZS status Theorem for theBenchmark
% 0.08/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.28 % (1848757)------------------------------
% 0.08/0.28 % (1848757)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.28 % (1848757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.28 % (1848757)CaDiCaL version: 2.1.3
% 0.08/0.28 % (1848757)Termination reason: Refutation
% 0.08/0.28 % (1848757)Time elapsed: 0.033 s
% 0.08/0.28 % (1848757)Peak memory usage: 12 MB
% 0.08/0.28 % (1848757)Instructions burned: 58 (million)
% 0.08/0.28 % (1848750)Success in time 0.065 s
% 0.08/0.28 % Vampire exiting
%------------------------------------------------------------------------------