%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV392^5 : 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 : n016.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 08:38:33 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 129 ( 31 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 121 ( 8 ~; 17 |; 15 &; 71 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 31 ( 20 ^; 10 !; 1 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cS: $i > $o ).
thf(func_def_1,type,
cR: $i > $o ).
thf(func_def_3,type,
vOR: $o > $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_6,type,
vAND: $o > $o > $o ).
thf(f1,conjecture,
( ( ( ^ [X1: $i] :
( ( cR @ X1 )
| ( cS @ X1 ) ) )
= ( ^ [X0: $i] :
( ( cR @ X0 )
& ( cS @ X0 ) ) ) )
=> ! [X0: $i] :
( ( cR @ X0 )
=> ( cS @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM38_pme) ).
thf(f2,negated_conjecture,
~ ( ( ( ^ [X1: $i] :
( ( cR @ X1 )
| ( cS @ X1 ) ) )
= ( ^ [X0: $i] :
( ( cR @ X0 )
& ( cS @ X0 ) ) ) )
=> ! [X0: $i] :
( ( cR @ X0 )
=> ( cS @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( ^ [X0: $i] :
( ( cR @ X0 )
| ( cS @ X0 ) ) )
= ( ^ [X1: $i] :
( ( cR @ X1 )
& ( cS @ X1 ) ) ) )
=> ! [X2: $i] :
( ( cR @ X2 )
=> ( cS @ X2 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) )
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
| ( cR @ Y0 ) ) ) )
=> ! [X2: $i] :
( ( $true
= ( cR @ X2 ) )
=> ( $true
= ( cS @ X2 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ( ( ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) )
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
| ( cR @ Y0 ) ) ) )
=> ! [X0: $i] :
( ( ( cR @ X0 )
= $true )
=> ( ( cS @ X0 )
= $true ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
( ? [X0: $i] :
( ( ( cS @ X0 )
!= $true )
& ( ( cR @ X0 )
= $true ) )
& ( ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) )
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
| ( cR @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ( $true
!= ( cS @ sK0 ) )
& ( ( cR @ sK0 )
= $true )
& ( ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) )
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
| ( cR @ Y0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f6]) ).
thf(f8,plain,
( ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) )
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
| ( cR @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( ( cR @ sK0 )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
( $true
!= ( cS @ sK0 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) )
@ X1 )
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
| ( cR @ Y0 ) )
@ X1 ) ),
inference(argument_congruence,[],[f8]) ).
thf(f14,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) )
@ X1 ) )
| ( ( ^ [Y0: $i] :
( ( cS @ Y0 )
| ( cR @ Y0 ) )
@ X1 )
= $false ) ),
inference(iff_proxy_clausification,[],[f13]) ).
thf(f19,plain,
! [X1: $i] :
( ( ( ( cS @ X1 )
& ( cR @ X1 ) )
= $true )
| ( ( ( cS @ X1 )
| ( cR @ X1 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f14]) ).
thf(f21,plain,
! [X1: $i] :
( ( ( cS @ X1 )
= $true )
| ( ( ( cS @ X1 )
| ( cR @ X1 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f19]) ).
thf(f22,plain,
! [X1: $i] :
( ( ( cS @ X1 )
= $true )
| ( ( cR @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f21]) ).
thf(f26,plain,
( ( ( cR @ sK0 )
= $false )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f10,f22]) ).
thf(f27,plain,
( ( cR @ sK0 )
= $false ),
inference(trivial_inequality_removal,[],[f26]) ).
thf(f29,plain,
$true = $false,
inference(constrained_superposition,[],[f9,f27]) ).
thf(f30,plain,
$false,
inference(trivial_inequality_removal,[],[f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV392^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n016.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 15:48:49 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.21 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
% 0.09/0.25 % (509279)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.25 % (509285)lrs+10_16_si=on:nwc=1.5:random_seed=2976332652:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.09/0.25 % (509285) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-509279-509285"...
% 0.09/0.25 % (509285)...printing done.
% 0.09/0.25 % (509285)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.25 % (509285)------------------------------
% 0.09/0.25 % (509285)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (509285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (509285)CaDiCaL version: 2.1.3
% 0.09/0.25 % (509285)Termination reason: Refutation
% 0.09/0.25 % (509285)Time elapsed: 0.001 s
% 0.09/0.25 % (509285)Peak memory usage: 12 MB
% 0.09/0.25 % (509285)Instructions burned: 2 (million)
% 0.09/0.25 % (509279)Success in time 0.031 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------