%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM667^1 : 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 : n015.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 08:19:15 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 62 ( 8 unt; 0 typ; 4 def)
% Number of atoms : 220 ( 71 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 256 ( 76 ~; 44 |; 3 &; 104 @)
% ( 4 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 23 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: nat ).
thf(func_def_1,type,
y: nat ).
thf(func_def_2,type,
z: nat ).
thf(func_def_3,type,
less: nat > nat > $o ).
thf(func_def_7,type,
vNOT: $o > $o ).
thf(f1,axiom,
( ~ ( less @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
thf(f2,axiom,
( ~ ( less @ y @ z )
=> ( y = z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k) ).
thf(f4,axiom,
! [X0: nat,X1: nat,X2: nat] :
( ( ~ ( less @ X0 @ X1 )
=> ( X0 = X1 ) )
=> ( ( less @ X1 @ X2 )
=> ( less @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz16a) ).
thf(f6,conjecture,
( ~ ( less @ x @ z )
=> ( x = z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz17) ).
thf(f7,negated_conjecture,
~ ( ~ ( less @ x @ z )
=> ( x = z ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
( ~ ( less @ x @ y )
=> ( x = y ) ),
inference(rectify,[],[f1]) ).
thf(f9,plain,
( ( ( less @ x @ y )
!= $true )
=> ( x = y ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( ~ ( less @ y @ z )
=> ( y = z ) ),
inference(rectify,[],[f2]) ).
thf(f11,plain,
( ( ( less @ y @ z )
!= $true )
=> ( y = z ) ),
inference(fool_elimination,[],[f10]) ).
thf(f14,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ~ ( less @ X0 @ X1 )
=> ( X0 = X1 ) )
=> ( ( less @ X1 @ X2 )
=> ( less @ X0 @ X2 ) ) ),
inference(rectify,[],[f4]) ).
thf(f15,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( ( less @ X0 @ X1 )
!= $true )
=> ( X0 = X1 ) )
=> ( ( ( less @ X1 @ X2 )
= $true )
=> ( ( less @ X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f18,plain,
~ ( ~ ( less @ x @ z )
=> ( x = z ) ),
inference(rectify,[],[f7]) ).
thf(f19,plain,
~ ( ( ( less @ x @ z )
!= $true )
=> ( x = z ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ( ( less @ x @ y )
!= $true )
=> ( x = y ) ),
inference(flattening,[],[f9]) ).
thf(f21,plain,
( ( ( less @ y @ z )
!= $true )
=> ( y = z ) ),
inference(flattening,[],[f11]) ).
thf(f23,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( ( less @ X0 @ X1 )
!= $true )
=> ( X0 = X1 ) )
=> ( ( ( less @ X1 @ X2 )
= $true )
=> ( ( less @ X0 @ X2 )
= $true ) ) ),
inference(flattening,[],[f15]) ).
thf(f25,plain,
~ ( ( ( less @ x @ z )
!= $true )
=> ( x = z ) ),
inference(flattening,[],[f19]) ).
thf(f26,plain,
( ( x = y )
| ( ( less @ x @ y )
= $true ) ),
inference(ennf_transformation,[],[f20]) ).
thf(f27,plain,
( ( y = z )
| ( ( less @ y @ z )
= $true ) ),
inference(ennf_transformation,[],[f21]) ).
thf(f29,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( less @ X0 @ X2 )
= $true )
| ( ( less @ X1 @ X2 )
!= $true )
| ( ( X0 != X1 )
& ( ( less @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[],[f23]) ).
thf(f30,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( less @ X0 @ X2 )
= $true )
| ( ( less @ X1 @ X2 )
!= $true )
| ( ( X0 != X1 )
& ( ( less @ X0 @ X1 )
!= $true ) ) ),
inference(flattening,[],[f29]) ).
thf(f33,plain,
( ( x != z )
& ( ( less @ x @ z )
!= $true ) ),
inference(ennf_transformation,[],[f25]) ).
thf(f34,plain,
( ( x = y )
| ( ( less @ x @ y )
= $true ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f35,plain,
( ( y = z )
| ( ( less @ y @ z )
= $true ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f37,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( less @ X1 @ X2 )
!= $true )
| ( ( less @ X0 @ X2 )
= $true )
| ( ( less @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f41,plain,
( ( less @ x @ z )
!= $true ),
inference(cnf_transformation,[],[f33]) ).
thf(f42,plain,
x != z,
inference(cnf_transformation,[],[f33]) ).
thf(f49,definition,
( spl0_1
<=> ( ( less @ y @ z )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f51,plain,
( ( ( less @ y @ z )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f49]) ).
thf(f53,definition,
( spl0_2
<=> ( y = z ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f55,plain,
( ( y = z )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f53]) ).
thf(f56,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f35,f53,f49]) ).
thf(f58,definition,
( spl0_3
<=> ( ( less @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f60,plain,
( ( ( less @ x @ y )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f58]) ).
thf(f62,definition,
( spl0_4
<=> ( x = y ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f64,plain,
( ( x = y )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f65,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f34,f62,f58]) ).
thf(f66,plain,
( ( ( less @ x @ y )
!= $true )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f41,f55]) ).
thf(f67,plain,
( ( x != y )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f42,f55]) ).
thf(f68,plain,
( ~ spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f67,f53,f62]) ).
thf(f69,plain,
( ~ spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f66,f53,f58]) ).
thf(f84,plain,
( ! [X0: nat] :
( ( $true != $true )
| ( $true
= ( less @ X0 @ z ) )
| ( $true
!= ( less @ X0 @ y ) ) )
| ~ spl0_1 ),
inference(constrained_superposition,[],[f37,f51]) ).
thf(f87,plain,
( ! [X0: nat] :
( ( $true
!= ( less @ X0 @ y ) )
| ( $true
= ( less @ X0 @ z ) ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f84]) ).
thf(f92,plain,
( ( $true != $true )
| ( ( less @ x @ z )
= $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(constrained_superposition,[],[f87,f60]) ).
thf(f93,plain,
( ( ( less @ x @ z )
= $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f92]) ).
thf(f95,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f93,f41]) ).
thf(f96,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f95]) ).
thf(f98,plain,
( ( ( less @ x @ z )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(constrained_superposition,[],[f51,f64]) ).
thf(f99,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f98,f41]) ).
thf(f100,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f99]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f56]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f65]) ).
cnf(s3,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f68]) ).
cnf(s4,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f69]) ).
cnf(s5,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f96]) ).
cnf(s6,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f100]) ).
cnf(s7,plain,
~ spl0_2,
inference(rat,[],[s2,s3,s4]) ).
cnf(s8,plain,
spl0_1,
inference(rat,[],[s1,s7]) ).
cnf(s9,plain,
~ spl0_4,
inference(rat,[],[s6,s8]) ).
cnf(s10,plain,
~ spl0_3,
inference(rat,[],[s5,s8]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s2,s9,s10]) ).
thf(f101,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM667^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n015.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 12:36:48 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 Running first-order model finding
% 0.09/0.20 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
% 0.09/0.25 % (3458526)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (3458531)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1703425206_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.25 % Exception at run slice level
% 0.09/0.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.25 % (3458532)% WARNING: option uhcvi not known.
% 0.09/0.25 % (3458532)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1217318154:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.25 % (3458534)dis+10_1_sil=32000:sp=arity:random_seed=2539754533:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.25 % (3458535)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2913638787:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.25 % (3458532)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.25 % (3458536)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3718815666:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.25 % (3458532)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.09/0.25 % (3458535)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.25 % (3458537)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2924192032:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.25 % (3458539)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1628623850:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.09/0.25 % Exception at run slice level
% 0.09/0.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.25 % (3458534) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3458526-3458534"...
% 0.09/0.25 % (3458532) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3458526-3458532"...
% 0.09/0.25 % (3458535) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3458526-3458535"...
% 0.09/0.25 % (3458536) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3458526-3458536"...
% 0.09/0.25 % (3458532)...printing done.
% 0.09/0.25 % (3458534)...printing done.
% 0.09/0.25 % (3458536)...printing done.
% 0.09/0.25 % (3458534)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 % (3458534)------------------------------
% 0.09/0.25 % (3458534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (3458534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (3458534)CaDiCaL version: 2.1.3
% 0.09/0.25 % (3458534)Termination reason: Refutation
% 0.09/0.25 % (3458534)Time elapsed: 0.004 s
% 0.09/0.25 % (3458534)Peak memory usage: 12 MB
% 0.09/0.25 % (3458534)Instructions burned: 4 (million)
% 0.09/0.25 % (3458526)Success in time 0.039 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------