%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM816^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 08:18:58 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 3
% Syntax : Number of formulae : 37 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 207 ( 79 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 347 ( 38 ~; 18 |; 21 &; 222 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 4 con; 0-4 aty)
% ( 16 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 74 ( 38 ^; 36 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
cS: $i > $i ).
thf(func_def_2,type,
cEVEN1: $i > $o ).
thf(func_def_3,type,
cODD1: $i > $o ).
thf(func_def_7,type,
vNOT: $o > $o ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_11,type,
vIMP: $o > $o > $o ).
thf(func_def_12,type,
vAND: $o > $o > $o ).
thf(func_def_13,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,axiom,
( cEVEN1
= ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( cS @ ( cS @ X2 ) ) ) )
& ( X1 @ c0 ) )
=> ( X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEVEN1_def) ).
thf(f2,axiom,
( cODD1
= ( ^ [X0: $i] :
~ ( cEVEN1 @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cODD1_def) ).
thf(f3,conjecture,
( ( ! [X0: $i] :
( ( cS @ X0 )
!= c0 )
& ! [X1: $i,X2: $i] :
( ( ( cS @ X1 )
= ( cS @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( cODD1 @ ( cS @ c0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM406) ).
thf(f4,negated_conjecture,
~ ( ( ! [X0: $i] :
( ( cS @ X0 )
!= c0 )
& ! [X1: $i,X2: $i] :
( ( ( cS @ X1 )
= ( cS @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( cODD1 @ ( cS @ c0 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ( ( ! [X0: $i] :
( ( cS @ X0 )
!= c0 )
& ! [X1: $i,X2: $i] :
( ( ( cS @ X1 )
= ( cS @ X2 ) )
=> ( X1 = X2 ) ) )
=> ( cODD1 @ ( cS @ c0 ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ( ( ! [X1: $i,X2: $i] :
( ( ( cS @ X2 )
= ( cS @ X1 ) )
=> ( X1 = X2 ) )
& ! [X0: $i] :
( c0
!= ( cS @ X0 ) ) )
=> ( ( cODD1 @ ( cS @ c0 ) )
= $true ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( cODD1
= ( ^ [X0: $i] :
~ ( cEVEN1 @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( cODD1
= ( ^ [Y0: $i] :
~ ( cEVEN1 @ Y0 ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( cEVEN1
= ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( cS @ ( cS @ X2 ) ) ) )
& ( X1 @ c0 ) )
=> ( X1 @ X0 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( cEVEN1
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cS @ ( cS @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
( ( ( cODD1 @ ( cS @ c0 ) )
!= $true )
& ! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ( ( cS @ X2 )
!= ( cS @ X1 ) ) )
& ! [X0: $i] :
( c0
!= ( cS @ X0 ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f12,plain,
( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ( ( cS @ X2 )
!= ( cS @ X1 ) ) )
& ( ( cODD1 @ ( cS @ c0 ) )
!= $true )
& ! [X0: $i] :
( c0
!= ( cS @ X0 ) ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( cS @ X0 )
!= ( cS @ X1 ) ) )
& ( ( cODD1 @ ( cS @ c0 ) )
!= $true )
& ! [X2: $i] :
( c0
!= ( cS @ X2 ) ) ),
inference(rectify,[],[f12]) ).
thf(f14,plain,
! [X2: $i] :
( c0
!= ( cS @ X2 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f15,plain,
( ( cODD1 @ ( cS @ c0 ) )
!= $true ),
inference(cnf_transformation,[],[f13]) ).
thf(f16,plain,
! [X0: $i,X1: $i] :
( ( ( cS @ X0 )
!= ( cS @ X1 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f17,plain,
( cODD1
= ( ^ [Y0: $i] :
~ ( cEVEN1 @ Y0 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f18,plain,
( cEVEN1
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( Y1 @ c0 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( cS @ ( cS @ Y2 ) ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f21,plain,
( cODD1
= ( ^ [Y0: $i] :
~ ( ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( Y2 @ c0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cS @ ( cS @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 ) ) ),
inference(definition_unfolding,[],[f17,f18]) ).
thf(f22,plain,
( $true
!= ( ^ [Y0: $i] :
~ ( ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( Y2 @ c0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( cS @ ( cS @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ Y0 )
@ ( cS @ c0 ) ) ),
inference(definition_unfolding,[],[f15,f21]) ).
thf(f23,plain,
( $true
!= ( ~ ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ ( cS @ Y1 ) ) ) ) ) )
=> ( Y0 @ ( cS @ c0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ ( cS @ Y1 ) ) ) ) ) )
=> ( Y0 @ ( cS @ c0 ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f23]) ).
thf(f25,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ ( cS @ Y1 ) ) ) ) ) )
=> ( Y0 @ ( cS @ c0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f24]) ).
thf(f26,plain,
! [X1: $i > $o] :
( ( ( ( X1 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ ( cS @ Y0 ) ) ) ) ) )
=> ( X1 @ ( cS @ c0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f27,plain,
! [X1: $i > $o] :
( ( ( X1 @ ( cS @ c0 ) )
= $true )
| ( ( ( X1 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ ( cS @ Y0 ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f26]) ).
thf(f28,plain,
! [X1: $i > $o] :
( ( ( X1 @ c0 )
= $false )
| ( ( X1 @ ( cS @ c0 ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ ( cS @ Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f27]) ).
thf(f29,plain,
! [X1: $i > $o] :
( ( ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ ( cS @ Y0 ) ) ) )
@ ( sK0 @ X1 ) )
= $false )
| ( ( X1 @ c0 )
= $false )
| ( ( X1 @ ( cS @ c0 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f28]) ).
thf(f30,plain,
! [X1: $i > $o] :
( ( ( X1 @ ( cS @ c0 ) )
= $true )
| ( $false
= ( ( X1 @ ( sK0 @ X1 ) )
=> ( X1 @ ( cS @ ( cS @ ( sK0 @ X1 ) ) ) ) ) )
| ( ( X1 @ c0 )
= $false ) ),
inference(beta-eta_normalization,[],[f29]) ).
thf(f31,plain,
! [X1: $i > $o] :
( ( $false
= ( X1 @ ( cS @ ( cS @ ( sK0 @ X1 ) ) ) ) )
| ( ( X1 @ c0 )
= $false )
| ( ( X1 @ ( cS @ c0 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f30]) ).
thf(f52,plain,
( ( ( cS @ c0 )
= ( cS
@ ( cS
@ ( sK0
@ ^ [Y0: $i] :
( Y0
!= ( cS @ c0 ) ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( Y0
!= ( cS @ c0 ) )
@ c0 ) ) ),
inference(leibniz_equality_elimination,[],[f31]) ).
thf(f61,plain,
( ( ( cS @ c0 )
= ( cS
@ ( cS
@ ( sK0
@ ^ [Y0: $i] :
( Y0
!= ( cS @ c0 ) ) ) ) ) )
| ( ( c0
!= ( cS @ c0 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f62,plain,
( ( ( cS @ c0 )
= ( cS
@ ( cS
@ ( sK0
@ ^ [Y0: $i] :
( Y0
!= ( cS @ c0 ) ) ) ) ) )
| ( ( c0
= ( cS @ c0 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f61]) ).
thf(f63,plain,
( ( c0
= ( cS @ c0 ) )
| ( ( cS @ c0 )
= ( cS
@ ( cS
@ ( sK0
@ ^ [Y0: $i] :
( Y0
!= ( cS @ c0 ) ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f62]) ).
thf(f72,plain,
( ( cS @ c0 )
= ( cS
@ ( cS
@ ( sK0
@ ^ [Y0: $i] :
( Y0
!= ( cS @ c0 ) ) ) ) ) ),
inference(forward_subsumption_resolution,[],[f63,f14]) ).
thf(f99,plain,
! [X0: $i] :
( ( ( cS @ X0 )
!= ( cS @ c0 ) )
| ( ( cS
@ ( sK0
@ ^ [Y0: $i] :
( Y0
!= ( cS @ c0 ) ) ) )
= X0 ) ),
inference(constrained_superposition,[],[f16,f72]) ).
thf(f103,plain,
( c0
= ( cS
@ ( sK0
@ ^ [Y0: $i] :
( Y0
!= ( cS @ c0 ) ) ) ) ),
inference(equality_resolution,[],[f99]) ).
thf(f104,plain,
$false,
inference(forward_subsumption_resolution,[],[f103,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM816^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n019.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % 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 13:02:42 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.21/0.29 % (724060)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (724067)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2470581113:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (724067)Refutation not found, incomplete strategy
% 0.21/0.29 % (724067)------------------------------
% 0.21/0.29 % (724067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (724067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (724067)CaDiCaL version: 2.1.3
% 0.21/0.29 % (724067)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.29 % (724067)Time elapsed: 0.001 s
% 0.21/0.29 % (724067)Peak memory usage: 12 MB
% 0.21/0.29 % (724067)Instructions burned: 1 (million)
% 0.21/0.29 % (724067)------------------------------
% 0.21/0.29 % (724067)------------------------------
% 0.21/0.29 % (724069)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1022751860:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (724065)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1074393360:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (724066)lrs+10_16_si=on:nwc=1.5:random_seed=4164362900:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (724068)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=807748528: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)
% 0.21/0.29 % (724065) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-724060-724065"...
% 0.21/0.29 % (724071)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (724071)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
% 0.21/0.29 % (724073)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1792976315:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.29 % (724065)...printing done.
% 0.21/0.29 % (724066) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-724060-724066"...
% 0.21/0.29 % (724065)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (724065)------------------------------
% 0.21/0.29 % (724065)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (724065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (724065)CaDiCaL version: 2.1.3
% 0.21/0.29 % (724065)Termination reason: Refutation
% 0.21/0.29 % (724065)Time elapsed: 0.005 s
% 0.21/0.29 % (724065)Peak memory usage: 12 MB
% 0.21/0.29 % (724065)Instructions burned: 6 (million)
% 0.21/0.29 % (724060)Success in time 0.038 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------