%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN915^4 : 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 : 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 08:41:44 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 65 ( 17 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 39 ( 7 ~; 0 |; 0 &; 28 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 32 usr; 4 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 20 ( 18 ^; 2 !; 0 ?; 20 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_22,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_27,type,
vOR: $o > $o > $o ).
thf(func_def_28,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_29,type,
vNOT: $o > $o ).
thf(func_def_30,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
vAND: $o > $o > $o ).
thf(func_def_32,type,
vIMP: $o > $o > $o ).
thf(f8,axiom,
( iatom
= ( ^ [X0: $i > $o] : X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iatom) ).
thf(f10,axiom,
( itrue
= ( ^ [X0: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',itrue) ).
thf(f18,axiom,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,conjecture,
ivalid @ ( iatom @ itrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',truth) ).
thf(f23,negated_conjecture,
~ ( ivalid @ ( iatom @ itrue ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
thf(f24,plain,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f25,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f24]) ).
thf(f29,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f38,plain,
( itrue
= ( ^ [Y0: $i] : $true ) ),
inference(fool_elimination,[],[f10]) ).
thf(f44,plain,
~ ( ivalid @ ( iatom @ itrue ) ),
inference(rectify,[],[f23]) ).
thf(f45,plain,
( ( ivalid @ ( iatom @ itrue ) )
!= $true ),
inference(fool_elimination,[],[f44]) ).
thf(f56,plain,
( ( ivalid @ ( iatom @ itrue ) )
!= $true ),
inference(flattening,[],[f45]) ).
thf(f67,plain,
( itrue
= ( ^ [Y0: $i] : $true ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f70,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f79,plain,
( ( ivalid @ ( iatom @ itrue ) )
!= $true ),
inference(cnf_transformation,[],[f56]) ).
thf(f80,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f93,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ ^ [Y0: $i] : $true ) ) ),
inference(definition_unfolding,[],[f79,f80,f70,f67]) ).
thf(f94,plain,
( ( !! @ $i
@ ^ [Y0: $i] : $true )
!= $true ),
inference(beta-eta_normalization,[],[f93]) ).
thf(f95,plain,
( $false
= ( ^ [Y0: $i] : $true
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f94]) ).
thf(f96,plain,
$false = $true,
inference(beta-eta_normalization,[],[f95]) ).
thf(f97,plain,
$false,
inference(trivial_inequality_removal,[],[f96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN915^4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n005.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 16:19:16 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.23 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
% 0.21/0.28 % (1865350)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (1865355)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3964789663:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (1865355) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1865350-1865355"...
% 0.21/0.28 % (1865355)...printing done.
% 0.21/0.28 % (1865355)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (1865355)------------------------------
% 0.21/0.28 % (1865355)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (1865355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (1865355)CaDiCaL version: 2.1.3
% 0.21/0.28 % (1865355)Termination reason: Refutation
% 0.21/0.28 % (1865355)Time elapsed: 0.002 s
% 0.21/0.28 % (1865355)Peak memory usage: 12 MB
% 0.21/0.28 % (1865355)Instructions burned: 4 (million)
% 0.21/0.28 % (1865350)Success in time 0.041 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------