%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV389^5 : 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 : n010.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 0.22s 0.27s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 13 unt; 0 typ; 4 def)
% Number of atoms : 183 ( 37 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 146 ( 32 ~; 26 |; 17 &; 57 @)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 7 con; 0-4 aty)
% Number of variables : 22 ( 0 sgn 9 !; 1 ?; 22 :)
% 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,
vAND: $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(f1,conjecture,
( ( ( ^ [X0: $i] :
( ( cR @ X0 )
& ( cS @ X0 ) ) )
= cR )
=> ! [X0: $i] :
( ( cR @ X0 )
=> ( cS @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM37_pme) ).
thf(f2,negated_conjecture,
~ ( ( ( ^ [X0: $i] :
( ( cR @ X0 )
& ( cS @ X0 ) ) )
= cR )
=> ! [X0: $i] :
( ( cR @ X0 )
=> ( cS @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( ^ [X0: $i] :
( ( cR @ X0 )
& ( cS @ X0 ) ) )
= cR )
=> ! [X1: $i] :
( ( cR @ X1 )
=> ( cS @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( cR
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) ) )
=> ! [X1: $i] :
( ( $true
= ( cR @ X1 ) )
=> ( $true
= ( cS @ X1 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ( ( cR
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) ) )
=> ! [X0: $i] :
( ( ( cR @ X0 )
= $true )
=> ( ( cS @ X0 )
= $true ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
( ( cR
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) ) )
& ? [X0: $i] :
( ( ( cS @ X0 )
!= $true )
& ( ( cR @ X0 )
= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ( cR
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) ) )
& ( $true
!= ( cS @ sK0 ) )
& ( ( cR @ sK0 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f6]) ).
thf(f8,plain,
( ( cR @ sK0 )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( $true
!= ( cS @ sK0 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
( cR
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,definition,
( spl1_1
<=> ( cR
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f15,plain,
( ( cR
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) ) ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f13]) ).
thf(f16,plain,
spl1_1,
inference(avatar_split_clause,[],[f10,f13]) ).
thf(f18,definition,
( spl1_2
<=> ( ( cR @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f20,plain,
( ( ( cR @ sK0 )
= $true )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f18]) ).
thf(f21,plain,
spl1_2,
inference(avatar_split_clause,[],[f8,f18]) ).
thf(f23,definition,
( spl1_3
<=> ( $true
= ( cS @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
thf(f25,plain,
( ( $true
!= ( cS @ sK0 ) )
| spl1_3 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f26,plain,
~ spl1_3,
inference(avatar_split_clause,[],[f9,f23]) ).
thf(f27,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) )
@ X1 )
= ( cR @ X1 ) )
| ~ spl1_1 ),
inference(argument_congruence,[],[f15]) ).
thf(f28,plain,
( ! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( cS @ Y0 )
& ( cR @ Y0 ) )
@ X1 ) )
| ( ( cR @ X1 )
= $false ) )
| ~ spl1_1 ),
inference(iff_proxy_clausification,[],[f27]) ).
thf(f32,plain,
( ! [X1: $i] :
( ( $true
= ( ( cS @ X1 )
& ( cR @ X1 ) ) )
| ( ( cR @ X1 )
= $false ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f34,plain,
( ! [X1: $i] :
( ( $true
= ( cS @ X1 ) )
| ( ( cR @ X1 )
= $false ) )
| ~ spl1_1 ),
inference(and_proxy_clausification,[],[f32]) ).
thf(f35,plain,
( ( ( cR @ sK0 )
= $false )
| ( $true != $true )
| ~ spl1_1
| spl1_3 ),
inference(superposition,[],[f25,f34]) ).
thf(f36,plain,
( ( ( cR @ sK0 )
= $false )
| ~ spl1_1
| spl1_3 ),
inference(trivial_inequality_removal,[],[f35]) ).
thf(f38,definition,
( spl1_4
<=> ( ( cR @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
thf(f40,plain,
( ( ( cR @ sK0 )
= $false )
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f38]) ).
thf(f41,plain,
( spl1_4
| ~ spl1_1
| spl1_3 ),
inference(avatar_split_clause,[],[f36,f23,f13,f38]) ).
thf(f42,plain,
( ( $true = $false )
| ~ spl1_2
| ~ spl1_4 ),
inference(superposition,[],[f40,f20]) ).
thf(f46,plain,
( $false
| ~ spl1_2
| ~ spl1_4 ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f47,plain,
( ~ spl1_2
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f46]) ).
cnf(s1,plain,
spl1_1,
inference(sat_conversion,[],[f16]) ).
cnf(s2,plain,
spl1_2,
inference(sat_conversion,[],[f21]) ).
cnf(s3,plain,
~ spl1_3,
inference(sat_conversion,[],[f26]) ).
cnf(s4,plain,
( ~ spl1_1
| spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f41]) ).
cnf(s6,plain,
( ~ spl1_2
| ~ spl1_4 ),
inference(sat_conversion,[],[f47]) ).
cnf(s7,plain,
~ spl1_4,
inference(rat,[],[s6,s2]) ).
cnf(s8,plain,
~ spl1_1,
inference(rat,[],[s4,s3,s7]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s8]) ).
thf(f48,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV389^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n010.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 15:44:03 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.23 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
% 0.22/0.27 % (3020924)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.27 % (3020932)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1210886433:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.27 % (3020932) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3020924-3020932"...
% 0.22/0.27 % (3020932)...printing done.
% 0.22/0.27 % (3020932)Refutation found. Thanks to Tanya!
% 0.22/0.27 % SZS status Theorem for theBenchmark
% 0.22/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.27 % (3020932)------------------------------
% 0.22/0.27 % (3020932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.27 % (3020932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.27 % (3020932)CaDiCaL version: 2.1.3
% 0.22/0.27 % (3020932)Termination reason: Refutation
% 0.22/0.27 % (3020932)Time elapsed: 0.002 s
% 0.22/0.27 % (3020932)Peak memory usage: 13 MB
% 0.22/0.27 % (3020932)Instructions burned: 2 (million)
% 0.22/0.27 % (3020924)Success in time 0.031 s
% 0.22/0.27 % Vampire exiting
%------------------------------------------------------------------------------