%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM666^1 : 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 : n016.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 08:18:28 AM UTC 2026
% Result : Theorem 0.10s 0.25s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 188 ( 46 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 227 ( 24 ~; 18 |; 0 &; 176 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 62 ( 24 ^; 38 !; 0 ?; 62 :)
% 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,
some: ( nat > $o ) > $o ).
thf(func_def_4,type,
diffprop: nat > nat > nat > $o ).
thf(func_def_6,type,
moreis: nat > nat > $o ).
thf(func_def_7,type,
lessis: nat > nat > $o ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,axiom,
( some
@ ^ [X0: nat] : ( diffprop @ x @ y @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(f2,axiom,
moreis @ y @ z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).
thf(f3,axiom,
! [X0: nat,X1: nat,X2: nat] :
( ( lessis @ X0 @ X1 )
=> ( ( some
@ ^ [X3: nat] : ( diffprop @ X2 @ X1 @ X3 ) )
=> ( some
@ ^ [X3: nat] : ( diffprop @ X2 @ X0 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz16a) ).
thf(f4,axiom,
! [X0: nat,X1: nat] :
( ( moreis @ X0 @ X1 )
=> ( lessis @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz13) ).
thf(f5,conjecture,
( some
@ ^ [X0: nat] : ( diffprop @ x @ z @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz16d) ).
thf(f6,negated_conjecture,
~ ( some
@ ^ [X0: nat] : ( diffprop @ x @ z @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( some
@ ^ [X0: nat] : ( diffprop @ x @ y @ X0 ) ),
inference(rectify,[],[f1]) ).
thf(f8,plain,
( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ x @ y @ Y0 ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
! [X0: nat,X1: nat] :
( ( moreis @ X0 @ X1 )
=> ( lessis @ X1 @ X0 ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
! [X1: nat,X0: nat] :
( ( ( moreis @ X0 @ X1 )
= $true )
=> ( ( lessis @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( lessis @ X0 @ X1 )
=> ( ( some
@ ^ [X3: nat] : ( diffprop @ X2 @ X1 @ X3 ) )
=> ( some
@ ^ [X4: nat] : ( diffprop @ X2 @ X0 @ X4 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f12,plain,
! [X1: nat,X0: nat,X2: nat] :
( ( ( lessis @ X0 @ X1 )
= $true )
=> ( ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X1 @ Y0 ) ) )
=> ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X0 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
moreis @ y @ z,
inference(rectify,[],[f2]) ).
thf(f14,plain,
( ( moreis @ y @ z )
= $true ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
~ ( some
@ ^ [X0: nat] : ( diffprop @ x @ z @ X0 ) ),
inference(rectify,[],[f6]) ).
thf(f16,plain,
( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ x @ z @ Y0 ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ x @ z @ Y0 ) ) ),
inference(flattening,[],[f16]) ).
thf(f18,plain,
! [X1: nat,X0: nat] :
( ( ( lessis @ X1 @ X0 )
= $true )
| ( ( moreis @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f19,plain,
! [X1: nat,X0: nat,X2: nat] :
( ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X0 @ Y0 ) ) )
| ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X1 @ Y0 ) ) )
| ( ( lessis @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f20,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( lessis @ X0 @ X1 )
!= $true )
| ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X0 @ Y0 ) ) )
| ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X2 @ X1 @ Y0 ) ) ) ),
inference(flattening,[],[f19]) ).
thf(f21,plain,
! [X0: nat,X1: nat] :
( ( ( lessis @ X0 @ X1 )
= $true )
| ( ( moreis @ X1 @ X0 )
!= $true ) ),
inference(rectify,[],[f18]) ).
thf(f22,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( $true
!= ( lessis @ X1 @ X2 ) )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X1 @ Y0 ) )
= $true )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X2 @ Y0 ) )
!= $true ) ),
inference(rectify,[],[f20]) ).
thf(f23,plain,
( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ x @ y @ Y0 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f24,plain,
( ( moreis @ y @ z )
= $true ),
inference(cnf_transformation,[],[f14]) ).
thf(f25,plain,
( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ x @ z @ Y0 ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f26,plain,
! [X0: nat,X1: nat] :
( ( ( moreis @ X1 @ X0 )
!= $true )
| ( ( lessis @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f27,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X2 @ Y0 ) )
!= $true )
| ( $true
!= ( lessis @ X1 @ X2 ) )
| ( ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X1 @ Y0 ) )
= $true ) ),
inference(cnf_transformation,[],[f22]) ).
thf(f30,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( $true
!= ( some @ ( diffprop @ X0 @ X2 ) ) )
| ( $true
!= ( lessis @ X1 @ X2 ) )
| ( ( some @ ( diffprop @ X0 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f31,plain,
( ( some @ ( diffprop @ x @ y ) )
= $true ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f32,plain,
( ( some @ ( diffprop @ x @ z ) )
!= $true ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f33,plain,
( ( $true != $true )
| ( $true
= ( lessis @ z @ y ) ) ),
inference(constrained_superposition,[],[f26,f24]) ).
thf(f34,plain,
( $true
= ( lessis @ z @ y ) ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f35,plain,
! [X0: nat] :
( ( ( some @ ( diffprop @ x @ X0 ) )
= $true )
| ( $true != $true )
| ( $true
!= ( lessis @ X0 @ y ) ) ),
inference(constrained_superposition,[],[f30,f31]) ).
thf(f36,plain,
! [X0: nat] :
( ( $true
!= ( lessis @ X0 @ y ) )
| ( ( some @ ( diffprop @ x @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f35]) ).
thf(f37,plain,
( ( $true != $true )
| ( ( some @ ( diffprop @ x @ z ) )
= $true ) ),
inference(constrained_superposition,[],[f36,f34]) ).
thf(f38,plain,
( ( some @ ( diffprop @ x @ z ) )
= $true ),
inference(trivial_inequality_removal,[],[f37]) ).
thf(f39,plain,
$false,
inference(forward_subsumption_resolution,[],[f38,f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM666^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n016.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 12:39:04 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 Running higher-order theorem proving
% 0.10/0.20 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
% 0.10/0.25 % (284334)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.10/0.25 % (284341)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3865568481:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.10/0.25 % (284341) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-284334-284341"...
% 0.10/0.25 % (284341)...printing done.
% 0.10/0.25 % (284341)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 % (284341)------------------------------
% 0.10/0.25 % (284341)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.25 % (284341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.25 % (284341)CaDiCaL version: 2.1.3
% 0.10/0.25 % (284341)Termination reason: Refutation
% 0.10/0.25 % (284341)Time elapsed: 0.002 s
% 0.10/0.25 % (284341)Peak memory usage: 12 MB
% 0.10/0.25 % (284341)Instructions burned: 3 (million)
% 0.10/0.25 % (284334)Success in time 0.035 s
% 0.10/0.25 % Vampire exiting
%------------------------------------------------------------------------------