%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM689^1 : 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 : 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 08:18:33 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 164 ( 39 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 261 ( 23 ~; 14 |; 0 &; 215 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 60 ( 22 ^; 38 !; 0 ?; 60 :)
% 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,
some: ( nat > $o ) > $o ).
thf(func_def_7,type,
diffprop: nat > nat > nat > $o ).
thf(func_def_8,type,
pl: nat > nat > nat ).
thf(func_def_9,type,
moreis: nat > nat > $o ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,axiom,
lessis @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
thf(f2,axiom,
( some
@ ^ [X0: nat] : ( diffprop @ u @ z @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k) ).
thf(f3,axiom,
! [X2: nat,X0: nat,X3: nat,X1: nat] :
( ( moreis @ X0 @ X1 )
=> ( ( some
@ ^ [X4: nat] : ( diffprop @ X2 @ X3 @ X4 ) )
=> ( some
@ ^ [X4: nat] : ( diffprop @ ( pl @ X0 @ X2 ) @ ( pl @ X1 @ X3 ) @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz22a) ).
thf(f4,axiom,
! [X0: nat,X1: nat] :
( ( lessis @ X0 @ X1 )
=> ( moreis @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz14) ).
thf(f5,conjecture,
( some
@ ^ [X0: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz22c) ).
thf(f6,negated_conjecture,
~ ( some
@ ^ [X0: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( moreis @ X1 @ X3 )
=> ( ( some
@ ^ [X4: nat] : ( diffprop @ X0 @ X2 @ X4 ) )
=> ( some
@ ^ [X5: nat] : ( diffprop @ ( pl @ X1 @ X0 ) @ ( pl @ X3 @ X2 ) @ X5 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f8,plain,
! [X0: nat,X2: nat,X3: nat,X1: nat] :
( ( $true
= ( moreis @ X1 @ X3 ) )
=> ( ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X2 @ Y0 ) ) )
=> ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ X1 @ X0 ) @ ( pl @ X3 @ X2 ) @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( some
@ ^ [X0: nat] : ( diffprop @ u @ z @ X0 ) ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ u @ z @ Y0 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: nat,X1: nat] :
( ( lessis @ X0 @ X1 )
=> ( moreis @ X1 @ X0 ) ),
inference(rectify,[],[f4]) ).
thf(f12,plain,
! [X0: nat,X1: nat] :
( ( ( lessis @ X0 @ X1 )
= $true )
=> ( ( moreis @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
~ ( some
@ ^ [X0: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ X0 ) ),
inference(rectify,[],[f6]) ).
thf(f14,plain,
( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ Y0 ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
lessis @ x @ y,
inference(rectify,[],[f1]) ).
thf(f16,plain,
( ( lessis @ x @ y )
= $true ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ Y0 ) ) ),
inference(flattening,[],[f14]) ).
thf(f18,plain,
! [X0: nat,X2: nat,X3: nat,X1: nat] :
( ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ X1 @ X0 ) @ ( pl @ X3 @ X2 ) @ Y0 ) ) )
| ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X2 @ Y0 ) ) )
| ( $true
!= ( moreis @ X1 @ X3 ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f19,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X2 @ Y0 ) ) )
| ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ X1 @ X0 ) @ ( pl @ X3 @ X2 ) @ Y0 ) ) )
| ( $true
!= ( moreis @ X1 @ X3 ) ) ),
inference(flattening,[],[f18]) ).
thf(f20,plain,
! [X0: nat,X1: nat] :
( ( ( moreis @ X1 @ X0 )
= $true )
| ( ( lessis @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f21,plain,
( ( lessis @ x @ y )
= $true ),
inference(cnf_transformation,[],[f16]) ).
thf(f22,plain,
( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ u @ z @ Y0 ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f23,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true
!= ( moreis @ X1 @ X3 ) )
| ( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ X0 @ X2 @ Y0 ) ) )
| ( $true
= ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ X1 @ X0 ) @ ( pl @ X3 @ X2 ) @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f24,plain,
( $true
!= ( some
@ ^ [Y0: nat] : ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) @ Y0 ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f25,plain,
! [X0: nat,X1: nat] :
( ( ( lessis @ X0 @ X1 )
!= $true )
| ( ( moreis @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f27,plain,
( $true
!= ( some @ ( diffprop @ ( pl @ y @ u ) @ ( pl @ x @ z ) ) ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f28,plain,
( ( some @ ( diffprop @ u @ z ) )
= $true ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f29,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ( $true
= ( some @ ( diffprop @ ( pl @ X1 @ X0 ) @ ( pl @ X3 @ X2 ) ) ) )
| ( $true
!= ( moreis @ X1 @ X3 ) )
| ( $true
!= ( some @ ( diffprop @ X0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f30,plain,
( ( $true != $true )
| ( $true
= ( moreis @ y @ x ) ) ),
inference(superposition,[],[f25,f21]) ).
thf(f31,plain,
( $true
= ( moreis @ y @ x ) ),
inference(trivial_inequality_removal,[],[f30]) ).
thf(f32,plain,
( ( ( some @ ( diffprop @ u @ z ) )
!= $true )
| ( $true != $true )
| ( $true
!= ( moreis @ y @ x ) ) ),
inference(superposition,[],[f27,f29]) ).
thf(f33,plain,
( ( $true
!= ( moreis @ y @ x ) )
| ( ( some @ ( diffprop @ u @ z ) )
!= $true ) ),
inference(trivial_inequality_removal,[],[f32]) ).
thf(f34,plain,
( ( some @ ( diffprop @ u @ z ) )
!= $true ),
inference(forward_subsumption_resolution,[],[f33,f31]) ).
thf(f35,plain,
$false,
inference(forward_subsumption_resolution,[],[f34,f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM689^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n019.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 12:39:33 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.22/0.29 % (697712)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (697723)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.29 % (697723)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
% 0.22/0.29 % (697721)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=254602482:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.29 % (697718)lrs+10_16_si=on:nwc=1.5:random_seed=3114882834:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.29 % (697719)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2345627949:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.29 % (697722)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4160074990:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.29 % (697717)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2113178604:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.29 % (697720)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=3330168962: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)
% 0.22/0.29 % (697723)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=3625992939:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.29 % (697719) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-697712-697719"...
% 0.22/0.29 % (697721) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-697712-697721"...
% 0.22/0.29 % (697717) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-697712-697717"...
% 0.22/0.29 % (697720) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-697712-697720"...
% 0.22/0.29 % (697721)...printing done.
% 0.22/0.29 % (697719)...printing done.
% 0.22/0.29 % (697717)...printing done.
% 0.22/0.29 % (697721)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.29 % (697721)------------------------------
% 0.22/0.29 % (697721)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (697721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (697721)CaDiCaL version: 2.1.3
% 0.22/0.29 % (697721)Termination reason: Refutation
% 0.22/0.29 % (697721)Time elapsed: 0.003 s
% 0.22/0.29 % (697721)Peak memory usage: 12 MB
% 0.22/0.29 % (697721)Instructions burned: 3 (million)
% 0.22/0.29 % (697712)Success in time 0.037 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------