%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU826^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 08:34:15 AM UTC 2026
% Result : Theorem 0.11s 0.29s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 79 ( 29 unt; 0 typ; 5 def)
% Number of atoms : 601 ( 101 equ; 0 cnn)
% Maximal formula atoms : 13 ( 7 avg)
% Number of connectives : 449 ( 35 ~; 110 |; 26 &; 267 @)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 22 usr; 9 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 56 ( 0 sgn 2 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
seteq: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_2,type,
u: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
n: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
a: $i > $o ).
thf(func_def_5,type,
b: $i > $o ).
thf(func_def_6,type,
c: $i > $o ).
thf(func_def_7,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_8,type,
vIFF: $o > $o > $o ).
thf(func_def_9,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
vOR: $o > $o > $o ).
thf(func_def_14,type,
vAND: $o > $o > $o ).
thf(func_def_17,type,
vNOT: $o > $o ).
thf(f1,axiom,
( seteq
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',seteq) ).
thf(f2,axiom,
( u
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u) ).
thf(f3,axiom,
( n
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).
thf(f4,conjecture,
seteq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f5,negated_conjecture,
~ ( seteq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( seteq
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( seteq
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( u
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
( u
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( n
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f11,plain,
( n
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
~ ( seteq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ) ),
inference(rectify,[],[f5]) ).
thf(f13,plain,
( ( seteq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ) )
!= $true ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
( ( seteq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ) )
!= $true ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
( seteq
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f16,plain,
( u
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f17,plain,
( n
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f18,plain,
( ( seteq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ) )
!= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f21,plain,
( $true
!= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ a
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ b
@ c ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ a
@ b )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ a
@ c ) ) ) ),
inference(definition_unfolding,[],[f18,f15,f16,f17,f17,f16,f16]) ).
thf(f22,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( a @ Y0 )
| ( ( b @ Y0 )
& ( c @ Y0 ) ) )
= ( ( ( a @ Y0 )
| ( b @ Y0 ) )
& ( ( a @ Y0 )
| ( c @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f23,plain,
( $false
= ( ^ [Y0: $i] :
( ( ( a @ Y0 )
| ( ( b @ Y0 )
& ( c @ Y0 ) ) )
= ( ( ( a @ Y0 )
| ( b @ Y0 ) )
& ( ( a @ Y0 )
| ( c @ Y0 ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( $false
= ( ( ( a @ sK0 )
| ( ( b @ sK0 )
& ( c @ sK0 ) ) )
= ( ( ( a @ sK0 )
| ( b @ sK0 ) )
& ( ( a @ sK0 )
| ( c @ sK0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f25,plain,
( ( ( a @ sK0 )
| ( ( b @ sK0 )
& ( c @ sK0 ) ) )
!= ( ( ( a @ sK0 )
| ( b @ sK0 ) )
& ( ( a @ sK0 )
| ( c @ sK0 ) ) ) ),
inference(iff_proxy_clausification,[],[f24]) ).
thf(f26,plain,
( ( $true
= ( ( a @ sK0 )
| ( ( b @ sK0 )
& ( c @ sK0 ) ) ) )
| ( $true
= ( ( ( a @ sK0 )
| ( b @ sK0 ) )
& ( ( a @ sK0 )
| ( c @ sK0 ) ) ) ) ),
inference(xor_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( ( $false
= ( ( a @ sK0 )
| ( ( b @ sK0 )
& ( c @ sK0 ) ) ) )
| ( $false
= ( ( ( a @ sK0 )
| ( b @ sK0 ) )
& ( ( a @ sK0 )
| ( c @ sK0 ) ) ) ) ),
inference(xor_proxy_clausification,[],[f25]) ).
thf(f28,plain,
( ( $false
= ( ( b @ sK0 )
& ( c @ sK0 ) ) )
| ( $false
= ( ( ( a @ sK0 )
| ( b @ sK0 ) )
& ( ( a @ sK0 )
| ( c @ sK0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f27]) ).
thf(f29,plain,
( ( $false
= ( a @ sK0 ) )
| ( $false
= ( ( ( a @ sK0 )
| ( b @ sK0 ) )
& ( ( a @ sK0 )
| ( c @ sK0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f27]) ).
thf(f30,plain,
( ( $false
= ( a @ sK0 ) )
| ( $false
= ( ( a @ sK0 )
| ( c @ sK0 ) ) )
| ( $false
= ( ( a @ sK0 )
| ( b @ sK0 ) ) ) ),
inference(and_proxy_clausification,[],[f29]) ).
thf(f32,plain,
( ( $false
= ( a @ sK0 ) )
| ( $false
= ( a @ sK0 ) )
| ( $false
= ( ( a @ sK0 )
| ( b @ sK0 ) ) ) ),
inference(or_proxy_clausification,[],[f30]) ).
thf(f34,plain,
( ( $false
= ( a @ sK0 ) )
| ( $false
= ( a @ sK0 ) )
| ( $false
= ( a @ sK0 ) ) ),
inference(or_proxy_clausification,[],[f32]) ).
thf(f35,plain,
( $false
= ( a @ sK0 ) ),
inference(duplicate_literal_removal,[],[f34]) ).
thf(f40,plain,
( ( $false
= ( c @ sK0 ) )
| ( $false
= ( ( ( a @ sK0 )
| ( b @ sK0 ) )
& ( ( a @ sK0 )
| ( c @ sK0 ) ) ) )
| ( $false
= ( b @ sK0 ) ) ),
inference(and_proxy_clausification,[],[f28]) ).
thf(f41,plain,
( ( $false
= ( c @ sK0 ) )
| ( $false
= ( ( a @ sK0 )
| ( c @ sK0 ) ) )
| ( $false
= ( b @ sK0 ) )
| ( $false
= ( ( a @ sK0 )
| ( b @ sK0 ) ) ) ),
inference(and_proxy_clausification,[],[f40]) ).
thf(f42,plain,
( ( $false
= ( c @ sK0 ) )
| ( $false
= ( c @ sK0 ) )
| ( $false
= ( b @ sK0 ) )
| ( $false
= ( ( a @ sK0 )
| ( b @ sK0 ) ) ) ),
inference(or_proxy_clausification,[],[f41]) ).
thf(f48,plain,
( ( $false
= ( c @ sK0 ) )
| ( $false
= ( c @ sK0 ) )
| ( $false
= ( b @ sK0 ) )
| ( $false
= ( b @ sK0 ) ) ),
inference(or_proxy_clausification,[],[f42]) ).
thf(f51,plain,
( ( $false
= ( c @ sK0 ) )
| ( $false
= ( b @ sK0 ) ) ),
inference(duplicate_literal_removal,[],[f48]) ).
thf(f52,plain,
( ( $true
= ( ( b @ sK0 )
& ( c @ sK0 ) ) )
| ( $true
= ( ( ( a @ sK0 )
| ( b @ sK0 ) )
& ( ( a @ sK0 )
| ( c @ sK0 ) ) ) )
| ( $true
= ( a @ sK0 ) ) ),
inference(or_proxy_clausification,[],[f26]) ).
thf(f53,plain,
( ( $true
= ( c @ sK0 ) )
| ( $true
= ( ( ( a @ sK0 )
| ( b @ sK0 ) )
& ( ( a @ sK0 )
| ( c @ sK0 ) ) ) )
| ( $true
= ( a @ sK0 ) ) ),
inference(and_proxy_clausification,[],[f52]) ).
thf(f54,plain,
( ( $true
= ( b @ sK0 ) )
| ( $true
= ( ( ( a @ sK0 )
| ( b @ sK0 ) )
& ( ( a @ sK0 )
| ( c @ sK0 ) ) ) )
| ( $true
= ( a @ sK0 ) ) ),
inference(and_proxy_clausification,[],[f52]) ).
thf(f56,plain,
( ( $true
= ( b @ sK0 ) )
| ( $true
= ( ( a @ sK0 )
| ( b @ sK0 ) ) )
| ( $true
= ( a @ sK0 ) ) ),
inference(and_proxy_clausification,[],[f54]) ).
thf(f57,plain,
( ( $true
= ( b @ sK0 ) )
| ( $true
= ( b @ sK0 ) )
| ( $true
= ( a @ sK0 ) )
| ( $true
= ( a @ sK0 ) ) ),
inference(or_proxy_clausification,[],[f56]) ).
thf(f58,plain,
( ( $true
= ( b @ sK0 ) )
| ( $true
= ( a @ sK0 ) ) ),
inference(duplicate_literal_removal,[],[f57]) ).
thf(f61,plain,
( ( $true
= ( c @ sK0 ) )
| ( $true
= ( ( a @ sK0 )
| ( c @ sK0 ) ) )
| ( $true
= ( a @ sK0 ) ) ),
inference(and_proxy_clausification,[],[f53]) ).
thf(f65,plain,
( ( $true
= ( c @ sK0 ) )
| ( $true
= ( c @ sK0 ) )
| ( $true
= ( a @ sK0 ) )
| ( $true
= ( a @ sK0 ) ) ),
inference(or_proxy_clausification,[],[f61]) ).
thf(f66,plain,
( ( $true
= ( c @ sK0 ) )
| ( $true
= ( a @ sK0 ) ) ),
inference(duplicate_literal_removal,[],[f65]) ).
thf(f68,definition,
( spl1_1
<=> ( $false
= ( b @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f70,plain,
( ( $false
= ( b @ sK0 ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f68]) ).
thf(f72,definition,
( spl1_2
<=> ( $false
= ( c @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f74,plain,
( ( $false
= ( c @ sK0 ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f72]) ).
thf(f75,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f51,f72,f68]) ).
thf(f77,definition,
( spl1_3
<=> ( $true
= ( a @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
thf(f79,plain,
( ( $true
= ( a @ sK0 ) )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f77]) ).
thf(f81,definition,
( spl1_4
<=> ( $true
= ( b @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
thf(f83,plain,
( ( $true
= ( b @ sK0 ) )
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f81]) ).
thf(f84,plain,
( spl1_3
| spl1_4 ),
inference(avatar_split_clause,[],[f58,f81,f77]) ).
thf(f86,definition,
( spl1_5
<=> ( $true
= ( c @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
thf(f88,plain,
( ( $true
= ( c @ sK0 ) )
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f86]) ).
thf(f91,plain,
( spl1_3
| spl1_5 ),
inference(avatar_split_clause,[],[f66,f86,f77]) ).
thf(f92,plain,
( ( $true = $false )
| ~ spl1_3 ),
inference(constrained_superposition,[],[f79,f35]) ).
thf(f96,plain,
( $false
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f92]) ).
thf(f97,plain,
~ spl1_3,
inference(avatar_contradiction_clause,[],[f96]) ).
thf(f100,plain,
( ( $true = $false )
| ~ spl1_2
| ~ spl1_5 ),
inference(constrained_superposition,[],[f74,f88]) ).
thf(f104,plain,
( $false
| ~ spl1_2
| ~ spl1_5 ),
inference(trivial_inequality_removal,[],[f100]) ).
thf(f105,plain,
( ~ spl1_2
| ~ spl1_5 ),
inference(avatar_contradiction_clause,[],[f104]) ).
thf(f106,plain,
( ( $true = $false )
| ~ spl1_1
| ~ spl1_4 ),
inference(constrained_superposition,[],[f70,f83]) ).
thf(f110,plain,
( $false
| ~ spl1_1
| ~ spl1_4 ),
inference(trivial_inequality_removal,[],[f106]) ).
thf(f111,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f110]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f75]) ).
cnf(s2,plain,
( spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f84]) ).
cnf(s5,plain,
( spl1_3
| spl1_5 ),
inference(sat_conversion,[],[f91]) ).
cnf(s7,plain,
~ spl1_3,
inference(sat_conversion,[],[f97]) ).
cnf(s9,plain,
( ~ spl1_2
| ~ spl1_5 ),
inference(sat_conversion,[],[f105]) ).
cnf(s11,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(sat_conversion,[],[f111]) ).
cnf(s12,plain,
spl1_5,
inference(rat,[],[s5,s7]) ).
cnf(s13,plain,
~ spl1_2,
inference(rat,[],[s9,s12]) ).
cnf(s14,plain,
spl1_4,
inference(rat,[],[s2,s7]) ).
cnf(s15,plain,
~ spl1_1,
inference(rat,[],[s11,s14]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s1,s13,s15]) ).
thf(f112,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU826^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.22 % Computer : n019.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 14:35:18 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.26 Running first-order model finding
% 0.11/0.26 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.29 % (869689)Will run a generic schedule for satisfiability detection.
% 0.11/0.29 % (869700)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3987382433:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.11/0.29 % (869700) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-869689-869700"...
% 0.11/0.29 % (869700)...printing done.
% 0.11/0.29 % (869695)% WARNING: option uhcvi not known.
% 0.11/0.29 % (869700)Refutation found. Thanks to Tanya!
% 0.11/0.29 % SZS status Theorem for theBenchmark
% 0.11/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.30 % (869700)------------------------------
% 0.26/0.30 % (869700)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.30 % (869700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.30 % (869700)CaDiCaL version: 2.1.3
% 0.26/0.30 % (869700)Termination reason: Refutation
% 0.26/0.30 % (869700)Time elapsed: 0.004 s
% 0.26/0.30 % (869700)Peak memory usage: 13 MB
% 0.26/0.30 % (869700)Instructions burned: 6 (million)
% 0.26/0.30 % (869689)Success in time 0.027 s
% 0.26/0.30 % Vampire exiting
%------------------------------------------------------------------------------