%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM816^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 08:19:35 AM UTC 2026
% Result : Theorem 0.10s 0.25s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 22 unt; 0 typ; 2 def)
% Number of atoms : 236 ( 81 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 370 ( 50 ~; 27 |; 19 &; 224 @)
% ( 2 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 6 con; 0-4 aty)
% ( 16 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 72 ( 0 sgn 33 !; 0 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
cS: $i > $i ).
thf(func_def_2,type,
cEVEN1: $i > $o ).
thf(func_def_3,type,
cODD1: $i > $o ).
thf(func_def_5,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
vIMP: $o > $o > $o ).
thf(func_def_7,type,
vAND: $o > $o > $o ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
vNOT: $o > $o ).
thf(func_def_14,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,axiom,
( cEVEN1
= ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( cS @ ( cS @ X2 ) ) ) )
& ( X1 @ c0 ) )
=> ( X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEVEN1_def) ).
thf(f2,axiom,
( cODD1
= ( ^ [X0: $i] :
~ ( cEVEN1 @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cODD1_def) ).
thf(f3,conjecture,
( ( ! [X1: $i,X2: $i] :
( ( ( cS @ X1 )
= ( cS @ X2 ) )
=> ( X1 = X2 ) )
& ! [X0: $i] :
( ( cS @ X0 )
!= c0 ) )
=> ( cODD1 @ ( cS @ c0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM406) ).
thf(f4,negated_conjecture,
~ ( ( ! [X1: $i,X2: $i] :
( ( ( cS @ X1 )
= ( cS @ X2 ) )
=> ( X1 = X2 ) )
& ! [X0: $i] :
( ( cS @ X0 )
!= c0 ) )
=> ( cODD1 @ ( cS @ c0 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( cEVEN1
= ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( cS @ ( cS @ X2 ) ) ) )
& ( X1 @ c0 ) )
=> ( X1 @ X0 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
( cEVEN1
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cS @ ( cS @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( cODD1
= ( ^ [X0: $i] :
~ ( cEVEN1 @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( cODD1
= ( ^ [Y0: $i] :
~ ( cEVEN1 @ Y0 ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ( ( ! [X0: $i,X1: $i] :
( ( ( cS @ X0 )
= ( cS @ X1 ) )
=> ( X0 = X1 ) )
& ! [X2: $i] :
( c0
!= ( cS @ X2 ) ) )
=> ( cODD1 @ ( cS @ c0 ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ( ( ! [X0: $i,X1: $i] :
( ( ( cS @ X0 )
= ( cS @ X1 ) )
=> ( X0 = X1 ) )
& ! [X2: $i] :
( c0
!= ( cS @ X2 ) ) )
=> ( ( cODD1 @ ( cS @ c0 ) )
= $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( ( cODD1 @ ( cS @ c0 ) )
!= $true )
& ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( cS @ X0 )
!= ( cS @ X1 ) ) )
& ! [X2: $i] :
( c0
!= ( cS @ X2 ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f12,plain,
( ( ( cODD1 @ ( cS @ c0 ) )
!= $true )
& ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( cS @ X0 )
!= ( cS @ X1 ) ) )
& ! [X2: $i] :
( c0
!= ( cS @ X2 ) ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( cEVEN1
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cS @ ( cS @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f14,plain,
( cODD1
= ( ^ [Y0: $i] :
~ ( cEVEN1 @ Y0 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
! [X2: $i] :
( c0
!= ( cS @ X2 ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f16,plain,
! [X0: $i,X1: $i] :
( ( ( cS @ X0 )
!= ( cS @ X1 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f17,plain,
( ( cODD1 @ ( cS @ c0 ) )
!= $true ),
inference(cnf_transformation,[],[f12]) ).
thf(f20,plain,
( cODD1
= ( ^ [Y0: $i] :
~ ( ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( Y2 @ c0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cS @ ( cS @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 ) ) ),
inference(definition_unfolding,[],[f14,f13]) ).
thf(f21,plain,
( $true
!= ( ^ [Y0: $i] :
~ ( ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( Y2 @ c0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cS @ ( cS @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
@ ( cS @ c0 ) ) ),
inference(definition_unfolding,[],[f17,f20]) ).
thf(f22,plain,
( $true
!= ( ~ ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ ( cS @ Y1 ) ) ) ) ) )
=> ( Y0 @ ( cS @ c0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f23,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ ( cS @ Y1 ) ) ) ) ) )
=> ( Y0 @ ( cS @ c0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f22]) ).
thf(f24,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ ( cS @ Y1 ) ) ) ) ) )
=> ( Y0 @ ( cS @ c0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f23]) ).
thf(f25,plain,
! [X1: $i > $o] :
( $true
= ( ( ( X1 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ ( cS @ Y0 ) ) ) ) ) )
=> ( X1 @ ( cS @ c0 ) ) ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
! [X1: $i > $o] :
( ( $false
= ( ( X1 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ ( cS @ Y0 ) ) ) ) ) ) )
| ( $true
= ( X1 @ ( cS @ c0 ) ) ) ),
inference(imp_proxy_clausification,[],[f25]) ).
thf(f27,plain,
! [X1: $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ ( cS @ Y0 ) ) ) ) ) )
| ( $true
= ( X1 @ ( cS @ c0 ) ) )
| ( ( X1 @ c0 )
= $false ) ),
inference(and_proxy_clausification,[],[f26]) ).
thf(f28,plain,
! [X1: $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ ( cS @ Y0 ) ) ) )
@ ( sK0 @ X1 ) ) )
| ( $true
= ( X1 @ ( cS @ c0 ) ) )
| ( ( X1 @ c0 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X1: $i > $o] :
( ( $false
= ( ( X1 @ ( sK0 @ X1 ) )
=> ( X1 @ ( cS @ ( cS @ ( sK0 @ X1 ) ) ) ) ) )
| ( $true
= ( X1 @ ( cS @ c0 ) ) )
| ( ( X1 @ c0 )
= $false ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
! [X1: $i > $o] :
( ( $false
= ( X1 @ ( cS @ ( cS @ ( sK0 @ X1 ) ) ) ) )
| ( $true
= ( X1 @ ( cS @ c0 ) ) )
| ( ( X1 @ c0 )
= $false ) ),
inference(imp_proxy_clausification,[],[f29]) ).
thf(f59,definition,
( spl1_1
<=> ( c0
= ( cS @ c0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f61,plain,
( ( c0
= ( cS @ c0 ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f59]) ).
thf(f179,plain,
( ( ( cS @ c0 )
= ( cS
@ ( cS
@ ( sK0
@ ^ [Y0: $i] :
( Y0
!= ( cS @ c0 ) ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( Y0
!= ( cS @ c0 ) )
@ c0 ) ) ),
inference(leibniz_equality_elimination,[],[f30]) ).
thf(f226,plain,
( ( ( cS @ c0 )
= ( cS
@ ( cS
@ ( sK0
@ ^ [Y0: $i] :
( Y0
!= ( cS @ c0 ) ) ) ) ) )
| ( $false
= ( c0
!= ( cS @ c0 ) ) ) ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f227,plain,
( ( ( cS @ c0 )
= ( cS
@ ( cS
@ ( sK0
@ ^ [Y0: $i] :
( Y0
!= ( cS @ c0 ) ) ) ) ) )
| ( $true
= ( c0
= ( cS @ c0 ) ) ) ),
inference(not_proxy_clausification,[],[f226]) ).
thf(f228,plain,
( ( ( cS @ c0 )
= ( cS
@ ( cS
@ ( sK0
@ ^ [Y0: $i] :
( Y0
!= ( cS @ c0 ) ) ) ) ) )
| ( c0
= ( cS @ c0 ) ) ),
inference(equality_proxy_clausification,[],[f227]) ).
thf(f230,definition,
( spl1_6
<=> ( ( cS @ c0 )
= ( cS
@ ( cS
@ ( sK0
@ ^ [Y0: $i] :
( Y0
!= ( cS @ c0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
thf(f232,plain,
( ( ( cS @ c0 )
= ( cS
@ ( cS
@ ( sK0
@ ^ [Y0: $i] :
( Y0
!= ( cS @ c0 ) ) ) ) ) )
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f230]) ).
thf(f233,plain,
( spl1_1
| spl1_6 ),
inference(avatar_split_clause,[],[f228,f230,f59]) ).
thf(f236,plain,
( ( c0 != c0 )
| ~ spl1_1 ),
inference(constrained_superposition,[],[f15,f61]) ).
thf(f237,plain,
( $false
| ~ spl1_1 ),
inference(trivial_inequality_removal,[],[f236]) ).
thf(f238,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f237]) ).
thf(f305,plain,
( ! [X0: $i] :
( ( ( cS @ X0 )
!= ( cS @ c0 ) )
| ( ( cS
@ ( sK0
@ ^ [Y0: $i] :
( Y0
!= ( cS @ c0 ) ) ) )
= X0 ) )
| ~ spl1_6 ),
inference(constrained_superposition,[],[f16,f232]) ).
thf(f315,plain,
( ( c0
= ( cS
@ ( sK0
@ ^ [Y0: $i] :
( Y0
!= ( cS @ c0 ) ) ) ) )
| ~ spl1_6 ),
inference(equality_resolution,[],[f305]) ).
thf(f319,plain,
( ( c0 != c0 )
| ~ spl1_6 ),
inference(constrained_superposition,[],[f15,f315]) ).
thf(f328,plain,
( $false
| ~ spl1_6 ),
inference(trivial_inequality_removal,[],[f319]) ).
thf(f329,plain,
~ spl1_6,
inference(avatar_contradiction_clause,[],[f328]) ).
cnf(s6,plain,
( spl1_1
| spl1_6 ),
inference(sat_conversion,[],[f233]) ).
cnf(s7,plain,
~ spl1_1,
inference(sat_conversion,[],[f238]) ).
cnf(s9,plain,
~ spl1_6,
inference(sat_conversion,[],[f329]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s6,s9,s7]) ).
thf(f330,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM816^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n011.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 13:02:41 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 Running first-order model finding
% 0.10/0.21 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
% 0.10/0.25 % (56015)Will run a generic schedule for satisfiability detection.
% 0.10/0.25 % (56026)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3812563478:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.25 % (56021)% WARNING: option uhcvi not known.
% 0.10/0.25 % (56026) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-56015-56026"...
% 0.10/0.25 % (56026)...printing done.
% 0.10/0.25 % (56026)Refutation found. Thanks to Tanya!
% 0.10/0.25 % SZS status Theorem for theBenchmark
% 0.10/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.25 % (56026)------------------------------
% 0.10/0.25 % (56026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.25 % (56026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.25 % (56026)CaDiCaL version: 2.1.3
% 0.10/0.25 % (56026)Termination reason: Refutation
% 0.10/0.25 % (56026)Time elapsed: 0.005 s
% 0.10/0.25 % (56026)Peak memory usage: 13 MB
% 0.10/0.25 % (56026)Instructions burned: 14 (million)
% 0.10/0.25 % (56015)Success in time 0.034 s
% 0.10/0.25 % Vampire exiting
%------------------------------------------------------------------------------