%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM694^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 08:18:35 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 19 unt; 0 typ; 3 def)
% Number of atoms : 92 ( 22 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 87 ( 18 ~; 10 |; 0 &; 54 @)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 14 !; 0 ?; 14 :)
% 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,
lessis: nat > nat > $o ).
thf(func_def_2,type,
n_1: nat ).
thf(func_def_3,type,
moreis: nat > nat > $o ).
thf(func_def_7,type,
sF0: $o ).
thf(f1,axiom,
! [X1: nat,X0: nat] :
( ( moreis @ X0 @ X1 )
=> ( lessis @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz13) ).
thf(f2,axiom,
! [X0: nat] : ( moreis @ X0 @ n_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz24) ).
thf(f3,conjecture,
lessis @ n_1 @ x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz24a) ).
thf(f4,negated_conjecture,
~ ( lessis @ n_1 @ x ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ( lessis @ n_1 @ x ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
( ( lessis @ n_1 @ x )
!= $true ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: nat,X1: nat] :
( ( moreis @ X1 @ X0 )
=> ( lessis @ X0 @ X1 ) ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
! [X1: nat,X0: nat] :
( ( ( moreis @ X1 @ X0 )
= $true )
=> ( $true
= ( lessis @ X0 @ X1 ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: nat] : ( moreis @ X0 @ n_1 ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
! [X0: nat] :
( ( moreis @ X0 @ n_1 )
= $true ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( lessis @ n_1 @ x )
!= $true ),
inference(flattening,[],[f6]) ).
thf(f12,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( lessis @ X0 @ X1 ) )
| ( ( moreis @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f13,plain,
! [X0: nat,X1: nat] :
( ( $true
= ( lessis @ X0 @ X1 ) )
| ( ( moreis @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f14,plain,
! [X0: nat] :
( ( moreis @ X0 @ n_1 )
= $true ),
inference(cnf_transformation,[],[f10]) ).
thf(f15,plain,
( ( lessis @ n_1 @ x )
!= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f18,definition,
( sF0
= ( lessis @ n_1 @ x ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f19,plain,
( ( lessis @ n_1 @ x )
= sF0 ),
inference(reorient_equations,[],[f18]) ).
thf(f20,plain,
$true != sF0,
inference(definition_folding,[],[f15,f19]) ).
thf(f22,plain,
( ( ( lessis @ n_1 @ x )
= $false )
| ( $true = sF0 ) ),
inference(iff_proxy_clausification,[],[f19]) ).
thf(f24,definition,
( spl1_1
<=> ( ( lessis @ n_1 @ x )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f26,plain,
( ( ( lessis @ n_1 @ x )
= $false )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f28,definition,
( spl1_2
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f31,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f22,f28,f24]) ).
thf(f41,plain,
~ spl1_2,
inference(avatar_split_clause,[],[f20,f28]) ).
thf(f56,plain,
( ( $true = $false )
| ( ( moreis @ x @ n_1 )
!= $true )
| ~ spl1_1 ),
inference(constrained_superposition,[],[f13,f26]) ).
thf(f59,plain,
( ( ( moreis @ x @ n_1 )
!= $true )
| ~ spl1_1 ),
inference(trivial_inequality_removal,[],[f56]) ).
thf(f62,plain,
( $false
| ~ spl1_1 ),
inference(forward_subsumption_resolution,[],[f59,f14]) ).
thf(f63,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f62]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f31]) ).
cnf(s3,plain,
~ spl1_2,
inference(sat_conversion,[],[f41]) ).
cnf(s5,plain,
~ spl1_1,
inference(sat_conversion,[],[f63]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
thf(f64,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM694^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n015.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 12:44:12 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.28 % (3463001)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (3463012)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.28 % (3463012)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.28 % (3463012)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=853306191:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.28 % (3463012) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3463001-3463012"...
% 0.21/0.28 % (3463012)...printing done.
% 0.21/0.28 % (3463012)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (3463012)------------------------------
% 0.21/0.28 % (3463012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (3463012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (3463012)CaDiCaL version: 2.1.3
% 0.21/0.28 % (3463012)Termination reason: Refutation
% 0.21/0.28 % (3463012)Time elapsed: 0.002 s
% 0.21/0.28 % (3463012)Peak memory usage: 13 MB
% 0.21/0.28 % (3463012)Instructions burned: 2 (million)
% 0.21/0.28 % (3463001)Success in time 0.03 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------