%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM692^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 08:18:34 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 75 ( 26 unt; 0 typ; 6 def)
% Number of atoms : 269 ( 64 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 360 ( 56 ~; 48 |; 0 &; 238 @)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 17 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 52 !; 0 ?; 52 :)
% 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,
u: nat ).
thf(func_def_4,type,
lessis: nat > nat > $o ).
thf(func_def_6,type,
ts: nat > nat > nat ).
thf(func_def_7,type,
moreis: nat > nat > $o ).
thf(f1,axiom,
lessis @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
thf(f2,axiom,
lessis @ z @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k) ).
thf(f3,axiom,
! [X0: nat,X1: nat] :
( ( moreis @ X0 @ X1 )
=> ( lessis @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz13) ).
thf(f4,axiom,
! [X1: nat,X2: nat,X0: nat,X3: nat] :
( ( moreis @ X0 @ X1 )
=> ( ( moreis @ X2 @ X3 )
=> ( moreis @ ( ts @ X0 @ X2 ) @ ( ts @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz23) ).
thf(f5,axiom,
! [X0: nat,X1: nat] :
( ( lessis @ X0 @ X1 )
=> ( moreis @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz14) ).
thf(f6,conjecture,
lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz23a) ).
thf(f7,negated_conjecture,
~ ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
~ ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) )
!= $true ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
! [X0: nat,X1: nat] :
( ( moreis @ X0 @ X1 )
=> ( lessis @ X1 @ X0 ) ),
inference(rectify,[],[f3]) ).
thf(f11,plain,
! [X1: nat,X0: nat] :
( ( ( moreis @ X0 @ X1 )
= $true )
=> ( ( lessis @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
lessis @ z @ u,
inference(rectify,[],[f2]) ).
thf(f13,plain,
( ( lessis @ z @ u )
= $true ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
! [X0: nat,X1: nat] :
( ( lessis @ X0 @ X1 )
=> ( moreis @ X1 @ X0 ) ),
inference(rectify,[],[f5]) ).
thf(f15,plain,
! [X0: nat,X1: nat] :
( ( ( lessis @ X0 @ X1 )
= $true )
=> ( ( moreis @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
lessis @ x @ y,
inference(rectify,[],[f1]) ).
thf(f17,plain,
( ( lessis @ x @ y )
= $true ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( moreis @ X2 @ X0 )
=> ( ( moreis @ X1 @ X3 )
=> ( moreis @ ( ts @ X2 @ X1 ) @ ( ts @ X0 @ X3 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f19,plain,
! [X2: nat,X3: nat,X1: nat,X0: nat] :
( ( $true
= ( moreis @ X2 @ X0 ) )
=> ( ( $true
= ( moreis @ X1 @ X3 ) )
=> ( $true
= ( moreis @ ( ts @ X2 @ X1 ) @ ( ts @ X0 @ X3 ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) )
!= $true ),
inference(flattening,[],[f9]) ).
thf(f21,plain,
! [X1: nat,X0: nat] :
( ( ( lessis @ X1 @ X0 )
= $true )
| ( ( moreis @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f22,plain,
! [X1: nat,X0: nat] :
( ( ( moreis @ X1 @ X0 )
= $true )
| ( ( lessis @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f15]) ).
thf(f23,plain,
! [X2: nat,X3: nat,X1: nat,X0: nat] :
( ( $true
= ( moreis @ ( ts @ X2 @ X1 ) @ ( ts @ X0 @ X3 ) ) )
| ( $true
!= ( moreis @ X1 @ X3 ) )
| ( $true
!= ( moreis @ X2 @ X0 ) ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f24,plain,
! [X3: nat,X0: nat,X2: nat,X1: nat] :
( ( $true
!= ( moreis @ X1 @ X3 ) )
| ( $true
= ( moreis @ ( ts @ X2 @ X1 ) @ ( ts @ X0 @ X3 ) ) )
| ( $true
!= ( moreis @ X2 @ X0 ) ) ),
inference(flattening,[],[f23]) ).
thf(f25,plain,
! [X0: nat,X1: nat] :
( ( ( moreis @ X0 @ X1 )
= $true )
| ( ( lessis @ X1 @ X0 )
!= $true ) ),
inference(rectify,[],[f22]) ).
thf(f26,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true
!= ( moreis @ X3 @ X0 ) )
| ( $true
= ( moreis @ ( ts @ X2 @ X3 ) @ ( ts @ X1 @ X0 ) ) )
| ( $true
!= ( moreis @ X2 @ X1 ) ) ),
inference(rectify,[],[f24]) ).
thf(f27,plain,
! [X0: nat,X1: nat] :
( ( ( lessis @ X0 @ X1 )
= $true )
| ( ( moreis @ X1 @ X0 )
!= $true ) ),
inference(rectify,[],[f21]) ).
thf(f28,plain,
( ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) )
!= $true ),
inference(cnf_transformation,[],[f20]) ).
thf(f29,plain,
! [X0: nat,X1: nat] :
( ( ( moreis @ X0 @ X1 )
= $true )
| ( ( lessis @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f30,plain,
( ( lessis @ x @ y )
= $true ),
inference(cnf_transformation,[],[f17]) ).
thf(f31,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true
= ( moreis @ ( ts @ X2 @ X3 ) @ ( ts @ X1 @ X0 ) ) )
| ( $true
!= ( moreis @ X3 @ X0 ) )
| ( $true
!= ( moreis @ X2 @ X1 ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f32,plain,
( ( lessis @ z @ u )
= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f33,plain,
! [X0: nat,X1: nat] :
( ( ( lessis @ X0 @ X1 )
= $true )
| ( ( moreis @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f36,definition,
( spl0_1
<=> ( ( lessis @ x @ y )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f38,plain,
( ( ( lessis @ x @ y )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f39,plain,
spl0_1,
inference(avatar_split_clause,[],[f30,f36]) ).
thf(f41,definition,
( spl0_2
<=> ( ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f43,plain,
( ( ( lessis @ ( ts @ x @ z ) @ ( ts @ y @ u ) )
!= $true )
| spl0_2 ),
inference(avatar_component_clause,[],[f41]) ).
thf(f44,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f28,f41]) ).
thf(f46,definition,
( spl0_3
<=> ( ( lessis @ z @ u )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f48,plain,
( ( ( lessis @ z @ u )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f46]) ).
thf(f49,plain,
spl0_3,
inference(avatar_split_clause,[],[f32,f46]) ).
thf(f50,plain,
( ( $true != $true )
| ( ( moreis @ ( ts @ y @ u ) @ ( ts @ x @ z ) )
!= $true )
| spl0_2 ),
inference(superposition,[],[f43,f33]) ).
thf(f51,plain,
( ( ( moreis @ ( ts @ y @ u ) @ ( ts @ x @ z ) )
!= $true )
| spl0_2 ),
inference(trivial_inequality_removal,[],[f50]) ).
thf(f53,definition,
( spl0_4
<=> ( ( moreis @ ( ts @ y @ u ) @ ( ts @ x @ z ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f55,plain,
( ( ( moreis @ ( ts @ y @ u ) @ ( ts @ x @ z ) )
!= $true )
| spl0_4 ),
inference(avatar_component_clause,[],[f53]) ).
thf(f56,plain,
( ~ spl0_4
| spl0_2 ),
inference(avatar_split_clause,[],[f51,f41,f53]) ).
thf(f57,plain,
( ( $true
!= ( moreis @ u @ z ) )
| ( $true != $true )
| ( ( moreis @ y @ x )
!= $true )
| spl0_4 ),
inference(superposition,[],[f55,f31]) ).
thf(f59,plain,
( ( $true
!= ( moreis @ u @ z ) )
| ( ( moreis @ y @ x )
!= $true )
| spl0_4 ),
inference(trivial_inequality_removal,[],[f57]) ).
thf(f62,definition,
( spl0_5
<=> ( $true
= ( moreis @ u @ z ) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
thf(f64,plain,
( ( $true
!= ( moreis @ u @ z ) )
| spl0_5 ),
inference(avatar_component_clause,[],[f62]) ).
thf(f66,definition,
( spl0_6
<=> ( ( moreis @ y @ x )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
thf(f68,plain,
( ( ( moreis @ y @ x )
!= $true )
| spl0_6 ),
inference(avatar_component_clause,[],[f66]) ).
thf(f69,plain,
( ~ spl0_5
| ~ spl0_6
| spl0_4 ),
inference(avatar_split_clause,[],[f59,f53,f66,f62]) ).
thf(f70,plain,
( ( ( lessis @ z @ u )
!= $true )
| ( $true != $true )
| spl0_5 ),
inference(superposition,[],[f64,f29]) ).
thf(f71,plain,
( ( ( lessis @ z @ u )
!= $true )
| spl0_5 ),
inference(trivial_inequality_removal,[],[f70]) ).
thf(f72,plain,
( $false
| ~ spl0_3
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f71,f48]) ).
thf(f73,plain,
( ~ spl0_3
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f72]) ).
thf(f74,plain,
( ( $true != $true )
| ( ( lessis @ x @ y )
!= $true )
| spl0_6 ),
inference(superposition,[],[f68,f29]) ).
thf(f75,plain,
( ( ( lessis @ x @ y )
!= $true )
| spl0_6 ),
inference(trivial_inequality_removal,[],[f74]) ).
thf(f76,plain,
( $false
| ~ spl0_1
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f75,f38]) ).
thf(f77,plain,
( ~ spl0_1
| spl0_6 ),
inference(avatar_contradiction_clause,[],[f76]) ).
cnf(s1,plain,
spl0_1,
inference(sat_conversion,[],[f39]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f44]) ).
cnf(s3,plain,
spl0_3,
inference(sat_conversion,[],[f49]) ).
cnf(s4,plain,
( spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f56]) ).
cnf(s5,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f69]) ).
cnf(s6,plain,
( ~ spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f73]) ).
cnf(s7,plain,
( ~ spl0_1
| spl0_6 ),
inference(sat_conversion,[],[f77]) ).
cnf(s8,plain,
spl0_5,
inference(rat,[],[s6,s3]) ).
cnf(s9,plain,
~ spl0_4,
inference(rat,[],[s4,s2]) ).
cnf(s10,plain,
~ spl0_6,
inference(rat,[],[s5,s8,s9]) ).
cnf(s11,plain,
~ spl0_1,
inference(rat,[],[s7,s10]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s11]) ).
thf(f78,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM692^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n013.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 12:39:06 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.27 % (2043028)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (2043036)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=77730839:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.27 % (2043036) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2043028-2043036"...
% 0.20/0.27 % (2043036)...printing done.
% 0.20/0.27 % (2043036)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (2043036)------------------------------
% 0.20/0.27 % (2043036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (2043036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (2043036)CaDiCaL version: 2.1.3
% 0.20/0.27 % (2043036)Termination reason: Refutation
% 0.20/0.27 % (2043036)Time elapsed: 0.003 s
% 0.20/0.27 % (2043036)Peak memory usage: 13 MB
% 0.20/0.27 % (2043036)Instructions burned: 5 (million)
% 0.20/0.27 % (2043028)Success in time 0.035 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------