%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL961^11 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 08:14:56 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of formulae : 69 ( 48 unt; 0 typ; 0 def)
% Number of atoms : 422 ( 85 equ; 0 cnn)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 566 ( 27 ~; 28 |; 3 &; 411 @)
% ( 0 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 28 usr; 8 con; 0-4 aty)
% ( 34 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 131 ( 95 ^; 36 !; 0 ?; 131 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
mrel: mworld > mworld > $o ).
thf(func_def_1,type,
mactual: mworld ).
thf(func_def_2,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_4,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_5,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
p: mworld > $o ).
thf(func_def_12,type,
q: mworld > $o ).
thf(func_def_13,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_16,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vOR: $o > $o > $o ).
thf(func_def_18,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
vAND: $o > $o > $o ).
thf(func_def_22,type,
vIMP: $o > $o > $o ).
thf(func_def_23,type,
vIFF: $o > $o > $o ).
thf(func_def_24,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_25,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
sK0: mworld ).
thf(func_def_27,type,
sK1: mworld ).
thf(func_def_28,type,
sK2: mworld ).
thf(func_def_29,type,
sK3: mworld ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(f4,axiom,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor_def) ).
thf(f5,axiom,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def) ).
thf(f9,axiom,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(f10,axiom,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X0 @ X1 )
& ( mrel @ X0 @ X2 ) )
=> ( mrel @ X2 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_euclidean) ).
thf(f11,conjecture,
mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel16) ).
thf(f12,negated_conjecture,
~ ( mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
thf(f13,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f16,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f17,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
inference(rectify,[],[f9]) ).
thf(f19,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f18]) ).
thf(f22,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f23,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f26,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[],[f7]) ).
thf(f27,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f26]) ).
thf(f28,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X0 @ X1 )
& ( mrel @ X0 @ X2 ) )
=> ( mrel @ X2 @ X1 ) ),
inference(rectify,[],[f10]) ).
thf(f29,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( ( mrel @ X0 @ X2 )
= $true )
& ( ( mrel @ X0 @ X1 )
= $true ) )
=> ( ( mrel @ X2 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f28]) ).
thf(f30,plain,
~ ( mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f31,plain,
( ( mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f30]) ).
thf(f34,plain,
( ( mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) )
!= $true ),
inference(flattening,[],[f31]) ).
thf(f35,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X2 @ X1 )
= $true )
| ( ( mrel @ X0 @ X2 )
!= $true )
| ( ( mrel @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f29]) ).
thf(f36,plain,
! [X1: mworld,X0: mworld,X2: mworld] :
( ( ( mrel @ X0 @ X2 )
!= $true )
| ( ( mrel @ X0 @ X1 )
!= $true )
| ( ( mrel @ X2 @ X1 )
= $true ) ),
inference(flattening,[],[f35]) ).
thf(f37,plain,
! [X0: mworld,X1: mworld,X2: mworld] :
( ( ( mrel @ X1 @ X2 )
!= $true )
| ( ( mrel @ X1 @ X0 )
!= $true )
| ( $true
= ( mrel @ X2 @ X0 ) ) ),
inference(rectify,[],[f36]) ).
thf(f38,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f39,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f40,plain,
! [X0: mworld] :
( ( mrel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f19]) ).
thf(f42,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f43,plain,
( ( mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f34]) ).
thf(f44,plain,
! [X2: mworld,X0: mworld,X1: mworld] :
( ( ( mrel @ X1 @ X2 )
!= $true )
| ( ( mrel @ X1 @ X0 )
!= $true )
| ( $true
= ( mrel @ X2 @ X0 ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f47,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f51,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ q )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ p ) ) ) ) ) ),
inference(definition_unfolding,[],[f43,f38,f39,f47,f42,f47,f47,f47,f42,f47,f47]) ).
thf(f52,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) ) )
| ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f51]) ).
thf(f53,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f52]) ).
thf(f54,plain,
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f52]) ).
thf(f55,plain,
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f54]) ).
thf(f56,plain,
( ( ( mrel @ mactual @ sK0 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( q @ Y0 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( q @ Y0 ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f56]) ).
thf(f58,plain,
( $true
= ( mrel @ mactual @ sK0 ) ),
inference(imp_proxy_clausification,[],[f56]) ).
thf(f60,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( p @ Y0 ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f57]) ).
thf(f61,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ sK0 @ Y0 )
=> ( p @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X1: mworld] :
( ( ( mrel @ sK0 @ X1 )
=> ( p @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f63,plain,
! [X1: mworld] :
( ( ( mrel @ sK0 @ X1 )
= $false )
| ( ( p @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f62]) ).
thf(f68,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f53]) ).
thf(f69,plain,
( $false
= ( ( mrel @ mactual @ sK2 )
=> ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( q @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f68]) ).
thf(f70,plain,
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( q @ Y0 ) ) )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f69]) ).
thf(f71,plain,
( ( mrel @ mactual @ sK2 )
= $true ),
inference(imp_proxy_clausification,[],[f69]) ).
thf(f72,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f70]) ).
thf(f77,plain,
( ( ^ [Y0: mworld] :
( ( mrel @ sK2 @ Y0 )
=> ( p @ Y0 ) )
@ sK3 )
= $false ),
inference(sigma_proxy_clausification,[],[f72]) ).
thf(f78,plain,
( $false
= ( ( mrel @ sK2 @ sK3 )
=> ( p @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f77]) ).
thf(f79,plain,
( ( p @ sK3 )
= $false ),
inference(imp_proxy_clausification,[],[f78]) ).
thf(f80,plain,
( ( mrel @ sK2 @ sK3 )
= $true ),
inference(imp_proxy_clausification,[],[f78]) ).
thf(f100,plain,
! [X0: mworld] :
( ( ( mrel @ sK0 @ X0 )
= $true )
| ( $true != $true )
| ( ( mrel @ mactual @ X0 )
!= $true ) ),
inference(constrained_superposition,[],[f44,f58]) ).
thf(f102,plain,
! [X0: mworld] :
( ( ( mrel @ sK2 @ X0 )
= $true )
| ( ( mrel @ mactual @ X0 )
!= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f44,f71]) ).
thf(f105,plain,
! [X0: mworld] :
( ( ( mrel @ mactual @ X0 )
!= $true )
| ( ( mrel @ sK2 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f102]) ).
thf(f107,plain,
! [X0: mworld] :
( ( ( mrel @ mactual @ X0 )
!= $true )
| ( ( mrel @ sK0 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f100]) ).
thf(f108,plain,
( ( $true
= ( mrel @ sK2 @ mactual ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f105,f40]) ).
thf(f111,plain,
( $true
= ( mrel @ sK2 @ mactual ) ),
inference(trivial_inequality_removal,[],[f108]) ).
thf(f116,plain,
! [X0: mworld] :
( ( ( mrel @ mactual @ X0 )
= $true )
| ( ( mrel @ sK2 @ X0 )
!= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f44,f111]) ).
thf(f119,plain,
! [X0: mworld] :
( ( ( mrel @ sK2 @ X0 )
!= $true )
| ( ( mrel @ mactual @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f116]) ).
thf(f178,plain,
( ( ( mrel @ mactual @ sK3 )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f119,f80]) ).
thf(f179,plain,
( ( mrel @ mactual @ sK3 )
= $true ),
inference(trivial_inequality_removal,[],[f178]) ).
thf(f183,plain,
( ( $true != $true )
| ( ( mrel @ sK0 @ sK3 )
= $true ) ),
inference(constrained_superposition,[],[f107,f179]) ).
thf(f187,plain,
( ( mrel @ sK0 @ sK3 )
= $true ),
inference(trivial_inequality_removal,[],[f183]) ).
thf(f191,plain,
( ( $true
= ( p @ sK3 ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f63,f187]) ).
thf(f194,plain,
( $true
= ( p @ sK3 ) ),
inference(trivial_inequality_removal,[],[f191]) ).
thf(f197,plain,
$true = $false,
inference(forward_demodulation,[],[f194,f79]) ).
thf(f198,plain,
$false,
inference(trivial_inequality_removal,[],[f197]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL961^11 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 10:58:39 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.21 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
% 0.08/0.25 % (3000349)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.25 % (3000357)lrs+10_16_si=on:nwc=1.5:random_seed=1476481218:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.25 % (3000357) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3000349-3000357"...
% 0.08/0.25 % (3000357)...printing done.
% 0.08/0.25 % (3000357)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.25 % (3000357)------------------------------
% 0.08/0.25 % (3000357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (3000357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (3000357)CaDiCaL version: 2.1.3
% 0.08/0.25 % (3000357)Termination reason: Refutation
% 0.08/0.25 % (3000357)Time elapsed: 0.005 s
% 0.08/0.25 % (3000357)Peak memory usage: 12 MB
% 0.08/0.25 % (3000357)Instructions burned: 19 (million)
% 0.08/0.25 % (3000349)Success in time 0.033 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------