%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV396^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 08:39:27 AM UTC 2026
% Result : Theorem 0.09s 0.30s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 67 ( 6 unt; 0 typ; 6 def)
% Number of atoms : 406 ( 82 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 319 ( 65 ~; 93 |; 31 &; 115 @)
% ( 10 <=>; 4 =>; 0 <=; 1 <~>)
% 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 : 17 ( 14 usr; 10 con; 0-4 aty)
% Number of variables : 39 ( 0 sgn 15 !; 2 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cR: $i > $o ).
thf(func_def_1,type,
cS: $i > $o ).
thf(func_def_5,type,
vAND: $o > $o > $o ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
( ! [X0: $i] :
( ( cR @ X0 )
=> ( cS @ X0 ) )
<=> ( ( ^ [X0: $i] :
( ( cS @ X0 )
& ( cR @ X0 ) ) )
= cR ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM31_pme) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] :
( ( cR @ X0 )
=> ( cS @ X0 ) )
<=> ( ( ^ [X0: $i] :
( ( cS @ X0 )
& ( cR @ X0 ) ) )
= cR ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i] :
( ( cR @ X0 )
=> ( cS @ X0 ) )
<=> ( ( ^ [X1: $i] :
( ( cS @ X1 )
& ( cR @ X1 ) ) )
= cR ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
( ( ( cR @ X0 )
= $true )
=> ( ( cS @ X0 )
= $true ) )
<=> ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X0: $i] :
( ( ( cS @ X0 )
= $true )
| ( ( cR @ X0 )
!= $true ) )
<~> ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ( cR
!= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
| ? [X0: $i] :
( ( ( cS @ X0 )
!= $true )
& ( ( cR @ X0 )
= $true ) ) )
& ( ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
| ! [X0: $i] :
( ( ( cS @ X0 )
= $true )
| ( ( cR @ X0 )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f7,plain,
( ( ( cR
!= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
| ? [X0: $i] :
( ( ( cS @ X0 )
!= $true )
& ( ( cR @ X0 )
= $true ) ) )
& ( ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
| ! [X1: $i] :
( ( ( cS @ X1 )
= $true )
| ( ( cR @ X1 )
!= $true ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ( cR
!= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
| ( ( $true
!= ( cS @ sK0 ) )
& ( $true
= ( cR @ sK0 ) ) ) )
& ( ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
| ! [X1: $i] :
( ( ( cS @ X1 )
= $true )
| ( ( cR @ X1 )
!= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f7]) ).
thf(f9,plain,
! [X1: $i] :
( ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
| ( ( cS @ X1 )
= $true )
| ( ( cR @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( ( cR
!= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
| ( $true
= ( cR @ sK0 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( ( cR
!= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
| ( $true
!= ( cS @ sK0 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,definition,
( spl1_1
<=> ! [X1: $i] :
( ( ( cS @ X1 )
= $true )
| ( ( cR @ X1 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f16,plain,
( ! [X1: $i] :
( ( ( cR @ X1 )
!= $true )
| ( ( cS @ X1 )
= $true ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f15]) ).
thf(f18,definition,
( spl1_2
<=> ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f19,plain,
( ( cR
!= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
| spl1_2 ),
inference(avatar_component_clause,[],[f18]) ).
thf(f20,plain,
( ( cR
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) ) ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f18]) ).
thf(f21,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f9,f18,f15]) ).
thf(f23,definition,
( spl1_3
<=> ( $true
= ( cR @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
thf(f25,plain,
( ( $true
= ( cR @ sK0 ) )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f26,plain,
( spl1_3
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f10,f18,f23]) ).
thf(f28,definition,
( spl1_4
<=> ( $true
= ( cS @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
thf(f30,plain,
( ( $true
!= ( cS @ sK0 ) )
| spl1_4 ),
inference(avatar_component_clause,[],[f28]) ).
thf(f31,plain,
( ~ spl1_4
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f11,f18,f28]) ).
thf(f32,plain,
( ! [X1: $i] :
( ( cR @ X1 )
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) )
@ X1 ) )
| ~ spl1_2 ),
inference(argument_congruence,[],[f20]) ).
thf(f34,plain,
( ! [X1: $i] :
( ( ( cR @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) )
@ X1 ) ) )
| ~ spl1_2 ),
inference(iff_proxy_clausification,[],[f32]) ).
thf(f35,plain,
( ! [X1: $i] :
( ( ( cR @ X1 )
= $false )
| ( $true
= ( ( cR @ X1 )
& ( cS @ X1 ) ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f34]) ).
thf(f36,plain,
( ! [X1: $i] :
( ( ( cS @ X1 )
= $true )
| ( ( cR @ X1 )
= $false ) )
| ~ spl1_2 ),
inference(and_proxy_clausification,[],[f35]) ).
thf(f40,plain,
( ( $true != $true )
| ( ( cR @ sK0 )
= $false )
| ~ spl1_2
| spl1_4 ),
inference(constrained_superposition,[],[f30,f36]) ).
thf(f41,plain,
( ( ( cR @ sK0 )
= $false )
| ~ spl1_2
| spl1_4 ),
inference(trivial_inequality_removal,[],[f40]) ).
thf(f59,plain,
( ( $true = $false )
| ~ spl1_2
| ~ spl1_3
| spl1_4 ),
inference(constrained_superposition,[],[f41,f25]) ).
thf(f63,plain,
( $false
| ~ spl1_2
| ~ spl1_3
| spl1_4 ),
inference(trivial_inequality_removal,[],[f59]) ).
thf(f64,plain,
( ~ spl1_2
| ~ spl1_3
| spl1_4 ),
inference(avatar_contradiction_clause,[],[f63]) ).
thf(f73,plain,
( ( ( cR @ sK2 )
!= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) )
@ sK2 ) )
| spl1_2 ),
inference(negative_extensionality,[],[f19]) ).
thf(f74,plain,
( ( $true
= ( cR @ sK2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) )
@ sK2 ) )
| spl1_2 ),
inference(xor_proxy_clausification,[],[f73]) ).
thf(f75,plain,
( ( $false
= ( cR @ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( cR @ Y0 )
& ( cS @ Y0 ) )
@ sK2 ) )
| spl1_2 ),
inference(xor_proxy_clausification,[],[f73]) ).
thf(f76,plain,
( ( $false
= ( cR @ sK2 ) )
| ( $false
= ( ( cR @ sK2 )
& ( cS @ sK2 ) ) )
| spl1_2 ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f77,plain,
( ( $false
= ( cR @ sK2 ) )
| ( $false
= ( cS @ sK2 ) )
| ( $false
= ( cR @ sK2 ) )
| spl1_2 ),
inference(and_proxy_clausification,[],[f76]) ).
thf(f78,plain,
( ( $false
= ( cR @ sK2 ) )
| ( $false
= ( cS @ sK2 ) )
| spl1_2 ),
inference(duplicate_literal_removal,[],[f77]) ).
thf(f79,plain,
( ( $true
= ( cR @ sK2 ) )
| ( $true
= ( ( cR @ sK2 )
& ( cS @ sK2 ) ) )
| spl1_2 ),
inference(beta-eta_normalization,[],[f74]) ).
thf(f81,plain,
( ( $true
= ( cR @ sK2 ) )
| ( $true
= ( cR @ sK2 ) )
| spl1_2 ),
inference(and_proxy_clausification,[],[f79]) ).
thf(f82,plain,
( ( $true
= ( cR @ sK2 ) )
| spl1_2 ),
inference(duplicate_literal_removal,[],[f81]) ).
thf(f84,definition,
( spl1_5
<=> ( $false
= ( cS @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
thf(f86,plain,
( ( $false
= ( cS @ sK2 ) )
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f84]) ).
thf(f88,definition,
( spl1_6
<=> ( $false
= ( cR @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
thf(f90,plain,
( ( $false
= ( cR @ sK2 ) )
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f88]) ).
thf(f91,plain,
( spl1_5
| spl1_6
| spl1_2 ),
inference(avatar_split_clause,[],[f78,f18,f88,f84]) ).
thf(f95,plain,
( ( $true != $true )
| ( $true
= ( cS @ sK2 ) )
| ~ spl1_1
| spl1_2 ),
inference(constrained_superposition,[],[f16,f82]) ).
thf(f96,plain,
( ( $true
= ( cS @ sK2 ) )
| ~ spl1_1
| spl1_2 ),
inference(trivial_inequality_removal,[],[f95]) ).
thf(f97,plain,
( ( $true = $false )
| ~ spl1_1
| spl1_2
| ~ spl1_5 ),
inference(forward_demodulation,[],[f96,f86]) ).
thf(f98,plain,
( $false
| ~ spl1_1
| spl1_2
| ~ spl1_5 ),
inference(trivial_inequality_removal,[],[f97]) ).
thf(f99,plain,
( ~ spl1_1
| spl1_2
| ~ spl1_5 ),
inference(avatar_contradiction_clause,[],[f98]) ).
thf(f103,plain,
( ( $true = $false )
| spl1_2
| ~ spl1_6 ),
inference(constrained_superposition,[],[f90,f82]) ).
thf(f108,plain,
( $false
| spl1_2
| ~ spl1_6 ),
inference(trivial_inequality_removal,[],[f103]) ).
thf(f109,plain,
( spl1_2
| ~ spl1_6 ),
inference(avatar_contradiction_clause,[],[f108]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f21]) ).
cnf(s2,plain,
( ~ spl1_2
| spl1_3 ),
inference(sat_conversion,[],[f26]) ).
cnf(s3,plain,
( ~ spl1_2
| ~ spl1_4 ),
inference(sat_conversion,[],[f31]) ).
cnf(s5,plain,
( ~ spl1_2
| ~ spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f64]) ).
cnf(s8,plain,
( spl1_2
| spl1_5
| spl1_6 ),
inference(sat_conversion,[],[f91]) ).
cnf(s9,plain,
( ~ spl1_1
| spl1_2
| ~ spl1_5 ),
inference(sat_conversion,[],[f99]) ).
cnf(s11,plain,
( spl1_2
| ~ spl1_6 ),
inference(sat_conversion,[],[f109]) ).
cnf(s12,plain,
~ spl1_2,
inference(rat,[],[s5,s2,s3]) ).
cnf(s13,plain,
~ spl1_6,
inference(rat,[],[s11,s12]) ).
cnf(s14,plain,
spl1_5,
inference(rat,[],[s8,s13,s12]) ).
cnf(s15,plain,
spl1_1,
inference(rat,[],[s1,s12]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s9,s12,s15,s14]) ).
thf(f111,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV396^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 % Computer : n010.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 15:44:34 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.25 Running first-order model finding
% 0.09/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.30 % (3022747)Will run a generic schedule for satisfiability detection.
% 0.09/0.30 % (3022753)% WARNING: option uhcvi not known.
% 0.09/0.30 % (3022753)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4224361506:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.09/0.30 % (3022753)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.30 % (3022753)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.09/0.30 % (3022755)dis+10_1_sil=32000:sp=arity:random_seed=3298622660:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.09/0.30 % (3022753) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3022747-3022753"...
% 0.09/0.30 % (3022755) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3022747-3022755"...
% 0.09/0.30 % (3022754)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2519222570:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.09/0.30 % (3022757)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3718882481:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.09/0.30 % (3022753)...printing done.
% 0.09/0.30 % (3022755)...printing done.
% 0.09/0.30 % (3022757)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.30 % (3022753)Refutation found. Thanks to Tanya!
% 0.09/0.30 % SZS status Theorem for theBenchmark
% 0.09/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.30 % (3022753)------------------------------
% 0.09/0.30 % (3022753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.30 % (3022753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.30 % (3022753)CaDiCaL version: 2.1.3
% 0.09/0.30 % (3022753)Termination reason: Refutation
% 0.09/0.30 % (3022753)Time elapsed: 0.007 s
% 0.09/0.30 % (3022753)Peak memory usage: 13 MB
% 0.09/0.30 % (3022753)Instructions burned: 5 (million)
% 0.09/0.30 % (3022747)Success in time 0.036 s
% 0.09/0.30 % Vampire exiting
%------------------------------------------------------------------------------