%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO058^4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 08:46:25 AM UTC 2026
% Result : Theorem 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 83 ( 19 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 57 ( 7 ~; 0 |; 0 &; 44 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 33 usr; 4 con; 0-4 aty)
% ( 6 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 18 ( 15 ^; 3 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
irel: $i > $i > $o ).
thf(func_def_2,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
iatom: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
inot: ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
itrue: $i > $o ).
thf(func_def_10,type,
ifalse: $i > $o ).
thf(func_def_11,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_16,type,
ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
ivalid: ( $i > $o ) > $o ).
thf(func_def_18,type,
isatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
icountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_20,type,
iinvalid: ( $i > $o ) > $o ).
thf(func_def_21,type,
a: $i > $o ).
thf(func_def_24,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_25,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
vAND: $o > $o > $o ).
thf(func_def_29,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
vNOT: $o > $o ).
thf(func_def_32,type,
vOR: $o > $o > $o ).
thf(func_def_33,type,
vIMP: $o > $o > $o ).
thf(f8,axiom,
( iatom
= ( ^ [X0: $i > $o] : X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iatom) ).
thf(f18,axiom,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,axiom,
ivalid @ ( iatom @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).
thf(f23,conjecture,
ivalid @ ( iatom @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f24,negated_conjecture,
~ ( ivalid @ ( iatom @ a ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
thf(f31,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f39,plain,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f40,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f47,plain,
~ ( ivalid @ ( iatom @ a ) ),
inference(rectify,[],[f24]) ).
thf(f48,plain,
( ( ivalid @ ( iatom @ a ) )
!= $true ),
inference(fool_elimination,[],[f47]) ).
thf(f55,plain,
ivalid @ ( iatom @ a ),
inference(rectify,[],[f22]) ).
thf(f56,plain,
( ( ivalid @ ( iatom @ a ) )
= $true ),
inference(fool_elimination,[],[f55]) ).
thf(f59,plain,
( ( ivalid @ ( iatom @ a ) )
!= $true ),
inference(flattening,[],[f48]) ).
thf(f68,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f69,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f71,plain,
( ( ivalid @ ( iatom @ a ) )
!= $true ),
inference(cnf_transformation,[],[f59]) ).
thf(f83,plain,
( ( ivalid @ ( iatom @ a ) )
= $true ),
inference(cnf_transformation,[],[f56]) ).
thf(f97,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a ) )
!= $true ),
inference(definition_unfolding,[],[f71,f69,f68]) ).
thf(f98,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a ) )
= $true ),
inference(definition_unfolding,[],[f83,f69,f68]) ).
thf(f99,plain,
( $true
!= ( !! @ $i @ a ) ),
inference(beta-eta_normalization,[],[f97]) ).
thf(f100,plain,
( ( a @ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f99]) ).
thf(f101,plain,
( $true
= ( !! @ $i @ a ) ),
inference(beta-eta_normalization,[],[f98]) ).
thf(f102,plain,
! [X1: $i] :
( ( a @ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f101]) ).
thf(f104,plain,
$true = $false,
inference(constrained_superposition,[],[f100,f102]) ).
thf(f105,plain,
$false,
inference(trivial_inequality_removal,[],[f104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO058^4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n017.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % 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 16:21:22 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 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
% 0.19/0.26 % (544649)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.26 % (544656)lrs+10_16_si=on:nwc=1.5:random_seed=426323480:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.26 % (544656) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-544649-544656"...
% 0.19/0.26 % (544656)...printing done.
% 0.19/0.26 % (544656)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Theorem for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (544656)------------------------------
% 0.19/0.27 % (544656)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (544656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (544656)CaDiCaL version: 2.1.3
% 0.19/0.27 % (544656)Termination reason: Refutation
% 0.19/0.27 % (544656)Time elapsed: 0.002 s
% 0.19/0.27 % (544656)Peak memory usage: 12 MB
% 0.19/0.27 % (544656)Instructions burned: 4 (million)
% 0.19/0.27 % (544649)Success in time 0.032 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------