%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN024^2 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:19:53 AM UTC 2026
% Result : Theorem 0.23s 0.31s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 37 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 288 ( 117 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 375 ( 58 ~; 35 |; 45 &; 220 @)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 93 ( 0 sgn 88 !; 5 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
s: $i > $i ).
thf(func_def_2,type,
ite: $o > $i > $i > $i ).
thf(func_def_3,type,
h: $i > $i ).
thf(func_def_7,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_8,type,
vNOT: $o > $o ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
( ( ! [X3: $i] :
( ( ite @ ( X3 = zero ) @ ( s @ zero ) @ zero )
= ( h @ X3 ) )
& ! [X3: $i] :
( ( s @ X3 )
!= X3 )
& ! [X3: $i] :
( ( s @ X3 )
!= zero )
& ! [X1: $i,X0: $o,X2: $i] :
( ~ X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X2 ) )
& ! [X2: $i,X0: $o,X1: $i] :
( X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X1 ) ) )
=> ? [X4: $i > $i] :
( ( ( X4 @ ( s @ zero ) )
= zero )
& ( ( X4 @ zero )
= ( s @ zero ) )
& ( ( X4 @ ( s @ ( s @ zero ) ) )
= zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n10) ).
thf(f2,negated_conjecture,
~ ( ( ! [X3: $i] :
( ( ite @ ( X3 = zero ) @ ( s @ zero ) @ zero )
= ( h @ X3 ) )
& ! [X3: $i] :
( ( s @ X3 )
!= X3 )
& ! [X3: $i] :
( ( s @ X3 )
!= zero )
& ! [X1: $i,X0: $o,X2: $i] :
( ~ X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X2 ) )
& ! [X2: $i,X0: $o,X1: $i] :
( X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X1 ) ) )
=> ? [X4: $i > $i] :
( ( ( X4 @ ( s @ zero ) )
= zero )
& ( ( X4 @ zero )
= ( s @ zero ) )
& ( ( X4 @ ( s @ ( s @ zero ) ) )
= zero ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: $i] :
( ( ite @ ( zero = X0 ) @ ( s @ zero ) @ zero )
= ( h @ X0 ) )
& ! [X1: $i] :
( ( s @ X1 )
!= X1 )
& ! [X2: $i] :
( zero
!= ( s @ X2 ) )
& ! [X3: $i,X4: $o,X5: $i] :
( ~ X4
=> ( ( ite @ X4 @ X3 @ X5 )
= X5 ) )
& ! [X6: $i,X7: $o,X8: $i] :
( X7
=> ( ( ite @ X7 @ X8 @ X6 )
= X8 ) ) )
=> ? [X9: $i > $i] :
( ( zero
= ( X9 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( X9 @ zero ) )
& ( zero
= ( X9 @ ( s @ ( s @ zero ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] :
( ( h @ X0 )
= ( ite @ ( zero = X0 ) @ ( s @ zero ) @ zero ) )
& ! [X1: $i] :
( ( s @ X1 )
!= X1 )
& ! [X2: $i] :
( zero
!= ( s @ X2 ) )
& ! [X3: $i,X4: $o,X5: $i] :
( ( $true != X4 )
=> ( ( ite @ X4 @ X3 @ X5 )
= X5 ) )
& ! [X8: $i,X7: $o,X6: $i] :
( ( $true = X7 )
=> ( ( ite @ X7 @ X8 @ X6 )
= X8 ) ) )
=> ? [X9: $i > $i] :
( ( zero
= ( X9 @ ( s @ zero ) ) )
& ( zero
= ( X9 @ ( s @ ( s @ zero ) ) ) )
& ( ( s @ zero )
= ( X9 @ zero ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ( ( ! [X8: $i,X7: $o,X6: $i] :
( ( $true = X7 )
=> ( ( ite @ X7 @ X8 @ X6 )
= X8 ) )
& ! [X0: $i] :
( ( h @ X0 )
= ( ite @ ( zero = X0 ) @ ( s @ zero ) @ zero ) )
& ! [X2: $i] :
( zero
!= ( s @ X2 ) )
& ! [X1: $i] :
( ( s @ X1 )
!= X1 )
& ! [X3: $i,X5: $i,X4: $o] :
( ( $true != X4 )
=> ( ( ite @ X4 @ X3 @ X5 )
= X5 ) ) )
=> ? [X9: $i > $i] :
( ( zero
= ( X9 @ ( s @ zero ) ) )
& ( zero
= ( X9 @ ( s @ ( s @ zero ) ) ) )
& ( ( s @ zero )
= ( X9 @ zero ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ! [X9: $i > $i] :
( ( zero
!= ( X9 @ ( s @ ( s @ zero ) ) ) )
| ( ( s @ zero )
!= ( X9 @ zero ) )
| ( zero
!= ( X9 @ ( s @ zero ) ) ) )
& ! [X8: $i,X7: $o,X6: $i] :
( ( $true != X7 )
| ( ( ite @ X7 @ X8 @ X6 )
= X8 ) )
& ! [X0: $i] :
( ( h @ X0 )
= ( ite @ ( zero = X0 ) @ ( s @ zero ) @ zero ) )
& ! [X2: $i] :
( zero
!= ( s @ X2 ) )
& ! [X1: $i] :
( ( s @ X1 )
!= X1 )
& ! [X4: $o,X5: $i,X3: $i] :
( ( $true = X4 )
| ( ( ite @ X4 @ X3 @ X5 )
= X5 ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ! [X0: $i] :
( ( h @ X0 )
= ( ite @ ( zero = X0 ) @ ( s @ zero ) @ zero ) )
& ! [X8: $i,X7: $o,X6: $i] :
( ( $true != X7 )
| ( ( ite @ X7 @ X8 @ X6 )
= X8 ) )
& ! [X4: $o,X5: $i,X3: $i] :
( ( $true = X4 )
| ( ( ite @ X4 @ X3 @ X5 )
= X5 ) )
& ! [X1: $i] :
( ( s @ X1 )
!= X1 )
& ! [X9: $i > $i] :
( ( zero
!= ( X9 @ ( s @ ( s @ zero ) ) ) )
| ( ( s @ zero )
!= ( X9 @ zero ) )
| ( zero
!= ( X9 @ ( s @ zero ) ) ) )
& ! [X2: $i] :
( zero
!= ( s @ X2 ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
( ! [X0: $i] :
( ( h @ X0 )
= ( ite @ ( zero = X0 ) @ ( s @ zero ) @ zero ) )
& ! [X1: $i,X2: $o,X3: $i] :
( ( $true != X2 )
| ( ( ite @ X2 @ X1 @ X3 )
= X1 ) )
& ! [X4: $o,X5: $i,X6: $i] :
( ( $true = X4 )
| ( ( ite @ X4 @ X6 @ X5 )
= X5 ) )
& ! [X7: $i] :
( ( s @ X7 )
!= X7 )
& ! [X8: $i > $i] :
( ( zero
!= ( X8 @ ( s @ ( s @ zero ) ) ) )
| ( ( s @ zero )
!= ( X8 @ zero ) )
| ( zero
!= ( X8 @ ( s @ zero ) ) ) )
& ! [X9: $i] :
( zero
!= ( s @ X9 ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
! [X9: $i] :
( zero
!= ( s @ X9 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
! [X8: $i > $i] :
( ( zero
!= ( X8 @ ( s @ ( s @ zero ) ) ) )
| ( ( s @ zero )
!= ( X8 @ zero ) )
| ( zero
!= ( X8 @ ( s @ zero ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
! [X6: $i,X4: $o,X5: $i] :
( ( ( ite @ X4 @ X6 @ X5 )
= X5 )
| ( $true = X4 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
! [X2: $o,X3: $i,X1: $i] :
( ( $true != X2 )
| ( ( ite @ X2 @ X1 @ X3 )
= X1 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
! [X0: $i] :
( ( h @ X0 )
= ( ite @ ( zero = X0 ) @ ( s @ zero ) @ zero ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
! [X3: $i,X1: $i] :
( ( ite @ $true @ X1 @ X3 )
= X1 ),
inference(equality_resolution,[],[f13]) ).
thf(f19,plain,
! [X0: $i] :
( ( zero
= ( h @ X0 ) )
| ( $true
= ( zero = X0 ) ) ),
inference(superposition,[],[f12,f14]) ).
thf(f21,plain,
! [X0: $i] :
( ( zero
= ( h @ X0 ) )
| ( zero = X0 ) ),
inference(equality_proxy_clausification,[],[f19]) ).
thf(f50,plain,
( ( zero
= ( s @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( h @ zero ) )
| ( zero
!= ( h @ ( s @ zero ) ) )
| ( zero != zero ) ),
inference(superposition,[],[f10,f21]) ).
thf(f52,plain,
( ( zero
= ( s @ ( s @ zero ) ) )
| ( zero
!= ( h @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( h @ zero ) ) ),
inference(trivial_inequality_removal,[],[f50]) ).
thf(f58,plain,
( ( ( s @ zero )
!= ( h @ zero ) )
| ( zero
!= ( h @ ( s @ zero ) ) ) ),
inference(forward_subsumption_resolution,[],[f52,f9]) ).
thf(f64,definition,
( spl0_2
<=> ( ( s @ zero )
= ( h @ zero ) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f66,plain,
( ( ( s @ zero )
!= ( h @ zero ) )
| spl0_2 ),
inference(avatar_component_clause,[],[f64]) ).
thf(f68,definition,
( spl0_3
<=> ( zero
= ( h @ ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f70,plain,
( ( zero
!= ( h @ ( s @ zero ) ) )
| spl0_3 ),
inference(avatar_component_clause,[],[f68]) ).
thf(f73,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f58,f68,f64]) ).
thf(f77,plain,
( ( ( s @ zero )
!= ( ite @ ( zero = zero ) @ ( s @ zero ) @ zero ) )
| spl0_2 ),
inference(superposition,[],[f66,f14]) ).
thf(f78,plain,
( ( ( s @ zero )
!= ( ite @ $true @ ( s @ zero ) @ zero ) )
| spl0_2 ),
inference(boolean_simplification,[],[f77]) ).
thf(f81,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f78,f16]) ).
thf(f82,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f81]) ).
thf(f88,plain,
( ( zero
= ( s @ zero ) )
| ( zero != zero )
| spl0_3 ),
inference(superposition,[],[f70,f21]) ).
thf(f90,plain,
( ( zero
= ( s @ zero ) )
| spl0_3 ),
inference(trivial_inequality_removal,[],[f88]) ).
thf(f97,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f90,f9]) ).
thf(f98,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f97]) ).
cnf(s2,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f73]) ).
cnf(s4,plain,
spl0_2,
inference(sat_conversion,[],[f82]) ).
cnf(s6,plain,
spl0_3,
inference(sat_conversion,[],[f98]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6,s4]) ).
thf(f99,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN024^2 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n018.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 13:08:26 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.26 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
% 0.23/0.31 % (42076)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.31 % (42085)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2989660332:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.31 % (42083)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1746433083:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.31 % (42081)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1524733014:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.31 % (42082)lrs+10_16_si=on:nwc=1.5:random_seed=3704734431:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.31 % (42084)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=976751514: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)
% 0.23/0.31 % (42085)Refutation not found, incomplete strategy
% 0.23/0.31 % (42085)------------------------------
% 0.23/0.31 % (42085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (42085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (42085)CaDiCaL version: 2.1.3
% 0.23/0.31 % (42085)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.31 % (42085)Time elapsed: 0.002 s
% 0.23/0.31 % (42085)Peak memory usage: 12 MB
% 0.23/0.31 % (42085)Instructions burned: 3 (million)
% 0.23/0.31 % (42085)------------------------------
% 0.23/0.31 % (42085)------------------------------
% 0.23/0.31 % (42083)Refutation not found, incomplete strategy
% 0.23/0.31 % (42083)------------------------------
% 0.23/0.31 % (42083)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (42083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (42083)CaDiCaL version: 2.1.3
% 0.23/0.31 % (42083)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.31 % (42083)Time elapsed: 0.002 s
% 0.23/0.31 % (42083)Peak memory usage: 12 MB
% 0.23/0.31 % (42083)Instructions burned: 3 (million)
% 0.23/0.31 % (42081)Refutation not found, incomplete strategy
% 0.23/0.31 % (42081)------------------------------
% 0.23/0.31 % (42081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (42081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (42081)CaDiCaL version: 2.1.3
% 0.23/0.31 % (42081)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.31 % (42081)Time elapsed: 0.003 s
% 0.23/0.31 % (42081)Peak memory usage: 12 MB
% 0.23/0.31 % (42081)Instructions burned: 3 (million)
% 0.23/0.31 % (42083)------------------------------
% 0.23/0.31 % (42083)------------------------------
% 0.23/0.31 % (42081)------------------------------
% 0.23/0.31 % (42081)------------------------------
% 0.23/0.31 % (42084) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-42076-42084"...
% 0.23/0.31 % (42084)...printing done.
% 0.23/0.31 % (42084)Refutation found. Thanks to Tanya!
% 0.23/0.31 % SZS status Theorem for theBenchmark
% 0.23/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.31 % (42084)------------------------------
% 0.23/0.31 % (42084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.31 % (42084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.31 % (42084)CaDiCaL version: 2.1.3
% 0.23/0.31 % (42084)Termination reason: Refutation
% 0.23/0.31 % (42084)Time elapsed: 0.006 s
% 0.23/0.31 % (42084)Peak memory usage: 13 MB
% 0.23/0.31 % (42084)Instructions burned: 7 (million)
% 0.23/0.31 % (42076)Success in time 0.043 s
% 0.23/0.31 % Vampire exiting
%------------------------------------------------------------------------------