%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV435^3 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:39:59 AM UTC 2026
% Result : Theorem 0.24s 0.30s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 59 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 225 ( 57 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 186 ( 7 ~; 14 |; 0 &; 142 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 57 ( 57 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 43 usr; 5 con; 0-4 aty)
% ( 12 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 97 ( 89 ^; 8 !; 0 ?; 97 :)
% 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,
a: $i > $o ).
thf(func_def_31,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_33,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_34,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_39,type,
vAND: $o > $o > $o ).
thf(func_def_40,type,
vNOT: $o > $o ).
thf(func_def_41,type,
vOR: $o > $o > $o ).
thf(func_def_42,type,
vIMP: $o > $o > $o ).
thf(func_def_43,type,
db3:
!>[X0: $tType] : X0 ).
thf(f1,axiom,
( ( ^ [X0: $i] : $false )
= mfalse ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mfalse) ).
thf(f2,axiom,
( mtrue
= ( ^ [X0: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mtrue) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f8,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
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,
( ( ^ [X0: $i > $o] : X0 )
= icl_princ ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_princ) ).
thf(f21,axiom,
icl_true = mtrue,
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_true) ).
thf(f22,axiom,
icl_false = mfalse,
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_false) ).
thf(f23,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ rel @ ( mor @ X0 @ X1 ) ) )
= icl_says ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_says) ).
thf(f24,axiom,
( ( ^ [X0: $i > $o] : ( mvalid @ X0 ) )
= iclval ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV008^0.ax',icl_s4_valid) ).
thf(f25,axiom,
( ( icl_princ @ a )
= icl_true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(f26,conjecture,
iclval @ ( icl_says @ ( icl_princ @ a ) @ icl_false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',untrust) ).
thf(f27,negated_conjecture,
~ ( iclval @ ( icl_says @ ( icl_princ @ a ) @ icl_false ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
thf(f33,plain,
( mfalse
= ( ^ [Y0: $i] : $false ) ),
inference(fool_elimination,[],[f1]) ).
thf(f34,plain,
( icl_says
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mor @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f36,plain,
( icl_princ
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f17]) ).
thf(f46,plain,
~ ( iclval @ ( icl_says @ ( icl_princ @ a ) @ icl_false ) ),
inference(rectify,[],[f27]) ).
thf(f47,plain,
( ( iclval @ ( icl_says @ ( icl_princ @ a ) @ icl_false ) )
!= $true ),
inference(fool_elimination,[],[f46]) ).
thf(f48,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f49,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f50,plain,
( iclval
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f51,plain,
( mtrue
= ( ^ [Y0: $i] : $true ) ),
inference(fool_elimination,[],[f2]) ).
thf(f52,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f8]) ).
thf(f53,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f52]) ).
thf(f54,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f55,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f63,plain,
( ( iclval @ ( icl_says @ ( icl_princ @ a ) @ icl_false ) )
!= $true ),
inference(flattening,[],[f47]) ).
thf(f68,plain,
( iclval
= ( ^ [Y0: $i > $o] : ( mvalid @ Y0 ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f69,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f74,plain,
( icl_true
= ( icl_princ @ a ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f75,plain,
mfalse = icl_false,
inference(cnf_transformation,[],[f22]) ).
thf(f76,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f77,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f78,plain,
( mtrue
= ( ^ [Y0: $i] : $true ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f80,plain,
mtrue = icl_true,
inference(cnf_transformation,[],[f21]) ).
thf(f81,plain,
( icl_says
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ rel @ ( mor @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f83,plain,
( ( iclval @ ( icl_says @ ( icl_princ @ a ) @ icl_false ) )
!= $true ),
inference(cnf_transformation,[],[f63]) ).
thf(f87,plain,
( mfalse
= ( ^ [Y0: $i] : $false ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f88,plain,
( icl_princ
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f98,plain,
( icl_true
= ( ^ [Y0: $i > $o] : Y0
@ a ) ),
inference(definition_unfolding,[],[f74,f88]) ).
thf(f99,plain,
( icl_false
= ( ^ [Y0: $i] : $false ) ),
inference(definition_unfolding,[],[f75,f87]) ).
thf(f100,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] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f81,f69,f76]) ).
thf(f101,plain,
( iclval
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ Y0 ) ) ),
inference(definition_unfolding,[],[f68,f77]) ).
thf(f102,plain,
( ( ^ [Y0: $i > $o] : Y0
@ a )
= ( ^ [Y0: $i] : $true ) ),
inference(definition_unfolding,[],[f80,f78,f98]) ).
thf(f103,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] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ Y0
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ^ [Y0: $i] : $false ) ) ),
inference(definition_unfolding,[],[f83,f101,f100,f88,f99]) ).
thf(f104,plain,
( a
= ( ^ [Y0: $i] : $true ) ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f105,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( $false
| ( a @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f103]) ).
thf(f106,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( $false
| ( a @ Y1 ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f105]) ).
thf(f107,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ sK0 @ Y0 )
=> ( $false
| ( a @ Y0 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f106]) ).
thf(f108,plain,
( $false
= ( ^ [Y0: $i] :
( ( rel @ sK0 @ Y0 )
=> ( $false
| ( a @ Y0 ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f107]) ).
thf(f109,plain,
( ( ( rel @ sK0 @ sK1 )
=> ( $false
| ( a @ sK1 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f108]) ).
thf(f110,plain,
( ( $false
| ( a @ sK1 ) )
= $false ),
inference(imp_proxy_clausification,[],[f109]) ).
thf(f112,plain,
( $false
= ( a @ sK1 ) ),
inference(or_proxy_clausification,[],[f110]) ).
thf(f114,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : $true
@ X1 )
= ( a @ X1 ) ),
inference(argument_congruence,[],[f104]) ).
thf(f116,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] : $true
@ X1 )
= $false )
| ( $true
= ( a @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f114]) ).
thf(f117,plain,
! [X1: $i] :
( ( $true = $false )
| ( $true
= ( a @ X1 ) ) ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,plain,
! [X1: $i] :
( $true
= ( a @ X1 ) ),
inference(trivial_inequality_removal,[],[f117]) ).
thf(f120,plain,
$true = $false,
inference(constrained_superposition,[],[f118,f112]) ).
thf(f122,plain,
$false,
inference(trivial_inequality_removal,[],[f120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV435^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n004.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 16:03:37 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.24/0.30 % (1480143)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.30 % (1480158)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2326023916:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.30 % (1480158) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1480143-1480158"...
% 0.24/0.30 % (1480158)...printing done.
% 0.24/0.30 % (1480158)Refutation found. Thanks to Tanya!
% 0.24/0.30 % SZS status Theorem for theBenchmark
% 0.24/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.30 % (1480158)------------------------------
% 0.24/0.30 % (1480158)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.30 % (1480158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.30 % (1480158)CaDiCaL version: 2.1.3
% 0.24/0.30 % (1480158)Termination reason: Refutation
% 0.24/0.30 % (1480158)Time elapsed: 0.003 s
% 0.24/0.30 % (1480158)Peak memory usage: 12 MB
% 0.24/0.30 % (1480158)Instructions burned: 6 (million)
% 0.24/0.30 % (1480143)Success in time 0.037 s
% 0.24/0.30 % Vampire exiting
%------------------------------------------------------------------------------