%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN025^2 : 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 : n008.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 08:19:54 AM UTC 2026
% Result : Theorem 0.21s 0.31s
% Output : Refutation 0.21s
% 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 : 271 ( 109 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 379 ( 50 ~; 35 |; 37 &; 240 @)
% ( 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 : 85 ( 0 sgn 80 !; 5 ?; 85 :)
% 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] :
( ( h @ X3 )
= ( ite
@ ( X3
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
& ! [X2: $i,X1: $i,X0: $o] :
( X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X1 ) )
& ! [X3: $i] :
( ( s @ X3 )
!= X3 )
& ! [X1: $i,X2: $i,X0: $o] :
( ~ X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X2 ) ) )
=> ? [X4: $i > $i] :
( ( ( X4 @ zero )
= ( s @ zero ) )
& ( ( X4 @ ( s @ zero ) )
= zero )
& ( ( X4 @ ( s @ ( s @ zero ) ) )
= ( s @ zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n10) ).
thf(f2,negated_conjecture,
~ ( ( ! [X3: $i] :
( ( h @ X3 )
= ( ite
@ ( X3
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
& ! [X2: $i,X1: $i,X0: $o] :
( X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X1 ) )
& ! [X3: $i] :
( ( s @ X3 )
!= X3 )
& ! [X1: $i,X2: $i,X0: $o] :
( ~ X0
=> ( ( ite @ X0 @ X1 @ X2 )
= X2 ) ) )
=> ? [X4: $i > $i] :
( ( ( X4 @ zero )
= ( s @ zero ) )
& ( ( X4 @ ( s @ zero ) )
= zero )
& ( ( X4 @ ( s @ ( s @ zero ) ) )
= ( s @ zero ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: $i] :
( ( h @ X0 )
= ( ite
@ ( ( s @ zero )
= X0 )
@ zero
@ ( s @ zero ) ) )
& ! [X1: $i,X2: $i,X3: $o] :
( X3
=> ( ( ite @ X3 @ X2 @ X1 )
= X2 ) )
& ! [X4: $i] :
( ( s @ X4 )
!= X4 )
& ! [X5: $i,X6: $i,X7: $o] :
( ~ X7
=> ( ( ite @ X7 @ X5 @ X6 )
= X6 ) ) )
=> ? [X8: $i > $i] :
( ( ( s @ zero )
= ( X8 @ zero ) )
& ( zero
= ( X8 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( X8 @ ( s @ ( s @ zero ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] :
( ( h @ X0 )
= ( ite
@ ( ( s @ zero )
= X0 )
@ zero
@ ( s @ zero ) ) )
& ! [X1: $i,X3: $o,X2: $i] :
( ( $true = X3 )
=> ( ( ite @ X3 @ X2 @ X1 )
= X2 ) )
& ! [X4: $i] :
( ( s @ X4 )
!= X4 )
& ! [X5: $i,X6: $i,X7: $o] :
( ( $true != X7 )
=> ( ( ite @ X7 @ X5 @ X6 )
= X6 ) ) )
=> ? [X8: $i > $i] :
( ( zero
= ( X8 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( X8 @ zero ) )
& ( ( s @ zero )
= ( X8 @ ( s @ ( s @ zero ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ( ( ! [X7: $o,X6: $i,X5: $i] :
( ( $true != X7 )
=> ( ( ite @ X7 @ X5 @ X6 )
= X6 ) )
& ! [X1: $i,X3: $o,X2: $i] :
( ( $true = X3 )
=> ( ( ite @ X3 @ X2 @ X1 )
= X2 ) )
& ! [X0: $i] :
( ( h @ X0 )
= ( ite
@ ( ( s @ zero )
= X0 )
@ zero
@ ( s @ zero ) ) )
& ! [X4: $i] :
( ( s @ X4 )
!= X4 ) )
=> ? [X8: $i > $i] :
( ( zero
= ( X8 @ ( s @ zero ) ) )
& ( ( s @ zero )
= ( X8 @ zero ) )
& ( ( s @ zero )
= ( X8 @ ( s @ ( s @ zero ) ) ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ! [X8: $i > $i] :
( ( ( s @ zero )
!= ( X8 @ zero ) )
| ( zero
!= ( X8 @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( X8 @ ( s @ ( s @ zero ) ) ) ) )
& ! [X6: $i,X5: $i,X7: $o] :
( ( ( ite @ X7 @ X5 @ X6 )
= X6 )
| ( $true = X7 ) )
& ! [X2: $i,X1: $i,X3: $o] :
( ( ( ite @ X3 @ X2 @ X1 )
= X2 )
| ( $true != X3 ) )
& ! [X0: $i] :
( ( h @ X0 )
= ( ite
@ ( ( s @ zero )
= X0 )
@ zero
@ ( s @ zero ) ) )
& ! [X4: $i] :
( ( s @ X4 )
!= X4 ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ! [X8: $i > $i] :
( ( ( s @ zero )
!= ( X8 @ zero ) )
| ( zero
!= ( X8 @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( X8 @ ( s @ ( s @ zero ) ) ) ) )
& ! [X4: $i] :
( ( s @ X4 )
!= X4 )
& ! [X2: $i,X1: $i,X3: $o] :
( ( ( ite @ X3 @ X2 @ X1 )
= X2 )
| ( $true != X3 ) )
& ! [X6: $i,X5: $i,X7: $o] :
( ( ( ite @ X7 @ X5 @ X6 )
= X6 )
| ( $true = X7 ) )
& ! [X0: $i] :
( ( h @ X0 )
= ( ite
@ ( ( s @ zero )
= X0 )
@ zero
@ ( s @ zero ) ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
( ! [X0: $i > $i] :
( ( ( s @ zero )
!= ( X0 @ zero ) )
| ( zero
!= ( X0 @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( X0 @ ( s @ ( s @ zero ) ) ) ) )
& ! [X1: $i] :
( ( s @ X1 )
!= X1 )
& ! [X2: $i,X3: $i,X4: $o] :
( ( ( ite @ X4 @ X2 @ X3 )
= X2 )
| ( $true != X4 ) )
& ! [X5: $i,X6: $i,X7: $o] :
( ( ( ite @ X7 @ X6 @ X5 )
= X5 )
| ( $true = X7 ) )
& ! [X8: $i] :
( ( h @ X8 )
= ( ite
@ ( ( s @ zero )
= X8 )
@ zero
@ ( s @ zero ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
! [X8: $i] :
( ( h @ X8 )
= ( ite
@ ( ( s @ zero )
= X8 )
@ zero
@ ( s @ zero ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
! [X6: $i,X7: $o,X5: $i] :
( ( ( ite @ X7 @ X6 @ X5 )
= X5 )
| ( $true = X7 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
! [X2: $i,X3: $i,X4: $o] :
( ( ( ite @ X4 @ X2 @ X3 )
= X2 )
| ( $true != X4 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
! [X1: $i] :
( ( s @ X1 )
!= X1 ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
! [X0: $i > $i] :
( ( ( s @ zero )
!= ( X0 @ ( s @ ( s @ zero ) ) ) )
| ( ( s @ zero )
!= ( X0 @ zero ) )
| ( zero
!= ( X0 @ ( s @ zero ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
! [X2: $i,X3: $i] :
( ( ite @ $true @ X2 @ X3 )
= X2 ),
inference(equality_resolution,[],[f11]) ).
thf(f18,plain,
! [X0: $i] :
( ( ( s @ zero )
= ( h @ X0 ) )
| ( $true
= ( ( s @ zero )
= X0 ) ) ),
inference(superposition,[],[f9,f10]) ).
thf(f20,plain,
! [X0: $i] :
( ( ( s @ zero )
= ( h @ X0 ) )
| ( ( s @ zero )
= X0 ) ),
inference(equality_proxy_clausification,[],[f18]) ).
thf(f34,definition,
( spl0_1
<=> ( ( s @ zero )
= ( h @ zero ) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f36,plain,
( ( ( s @ zero )
!= ( h @ zero ) )
| spl0_1 ),
inference(avatar_component_clause,[],[f34]) ).
thf(f38,definition,
( spl0_2
<=> ( zero
= ( h @ ( s @ zero ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f40,plain,
( ( zero
!= ( h @ ( s @ zero ) ) )
| spl0_2 ),
inference(avatar_component_clause,[],[f38]) ).
thf(f57,plain,
( ( ( s @ zero )
= ( s @ ( s @ zero ) ) )
| ( zero
!= ( h @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( s @ zero ) )
| ( ( s @ zero )
!= ( h @ zero ) ) ),
inference(superposition,[],[f13,f20]) ).
thf(f58,plain,
( ( ( s @ zero )
= ( s @ ( s @ zero ) ) )
| ( ( s @ zero )
!= ( h @ zero ) )
| ( zero
!= ( h @ ( s @ zero ) ) ) ),
inference(trivial_inequality_removal,[],[f57]) ).
thf(f59,plain,
( ( ( s @ zero )
!= ( h @ zero ) )
| ( zero
!= ( h @ ( s @ zero ) ) ) ),
inference(forward_subsumption_resolution,[],[f58,f12]) ).
thf(f60,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f59,f38,f34]) ).
thf(f76,plain,
( ( ( s @ zero )
!= ( s @ zero ) )
| ( zero
= ( s @ zero ) )
| spl0_1 ),
inference(superposition,[],[f36,f20]) ).
thf(f80,plain,
( ( zero
= ( s @ zero ) )
| spl0_1 ),
inference(trivial_inequality_removal,[],[f76]) ).
thf(f86,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f80,f12]) ).
thf(f87,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f86]) ).
thf(f94,plain,
( ( zero
!= ( ite
@ ( ( s @ zero )
= ( s @ zero ) )
@ zero
@ ( s @ zero ) ) )
| spl0_2 ),
inference(superposition,[],[f40,f9]) ).
thf(f95,plain,
( ( zero
!= ( ite @ $true @ zero @ ( s @ zero ) ) )
| spl0_2 ),
inference(boolean_simplification,[],[f94]) ).
thf(f98,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f95,f15]) ).
thf(f99,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f98]) ).
cnf(s2,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f60]) ).
cnf(s4,plain,
spl0_1,
inference(sat_conversion,[],[f87]) ).
cnf(s8,plain,
spl0_2,
inference(sat_conversion,[],[f99]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s2,s8,s4]) ).
thf(f100,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN025^2 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n008.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:06:54 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
% 0.08/0.25 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
% 0.21/0.31 % (3120586)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.31 % (3120595)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=699141341:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.31 % (3120595)Refutation not found, incomplete strategy
% 0.21/0.31 % (3120595)------------------------------
% 0.21/0.31 % (3120595)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (3120595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (3120595)CaDiCaL version: 2.1.3
% 0.21/0.31 % (3120595)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.31 % (3120595)Time elapsed: 0.002 s
% 0.21/0.31 % (3120595)Peak memory usage: 12 MB
% 0.21/0.31 % (3120595)Instructions burned: 5 (million)
% 0.21/0.31 % (3120595)------------------------------
% 0.21/0.31 % (3120595)------------------------------
% 0.21/0.31 % (3120597)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.31 % (3120597)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
% 0.21/0.31 % (3120593)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1588852143:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.31 % (3120596)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2203895563:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.31 % (3120591)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2986234965:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.31 % (3120592)lrs+10_16_si=on:nwc=1.5:random_seed=2536604080:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.31 % (3120594)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=139291928: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)
% 0.21/0.31 % (3120597)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=1729828500:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.31 % (3120593)Instruction limit reached!
% 0.21/0.31 % (3120593)------------------------------
% 0.21/0.31 % (3120593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (3120593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (3120593)CaDiCaL version: 2.1.3
% 0.21/0.31 % (3120593)Termination reason: Instruction limit
% 0.21/0.31 % (3120593)Termination phase: Saturation
% 0.21/0.31 % (3120593)Time elapsed: 0.003 s
% 0.21/0.31 % (3120593)Peak memory usage: 12 MB
% 0.21/0.31 % (3120593)Instructions burned: 3 (million)
% 0.21/0.31 % (3120591)Refutation not found, incomplete strategy
% 0.21/0.31 % (3120591)------------------------------
% 0.21/0.31 % (3120591)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (3120591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (3120591)CaDiCaL version: 2.1.3
% 0.21/0.31 % (3120591)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.31 % (3120591)Time elapsed: 0.003 s
% 0.21/0.31 % (3120591)Peak memory usage: 12 MB
% 0.21/0.31 % (3120591)Instructions burned: 4 (million)
% 0.21/0.31 % (3120591)------------------------------
% 0.21/0.31 % (3120591)------------------------------
% 0.21/0.31 % (3120599)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3304717789:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.31 % (3120599)Instruction limit reached!
% 0.21/0.31 % (3120599)------------------------------
% 0.21/0.31 % (3120599)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (3120599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (3120594) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3120586-3120594"...
% 0.21/0.31 % (3120599)CaDiCaL version: 2.1.3
% 0.21/0.31 % (3120599)Termination reason: Instruction limit
% 0.21/0.31 % (3120599)Termination phase: Saturation
% 0.21/0.31 % (3120599)Time elapsed: 0.001 s
% 0.21/0.31 % (3120599)Peak memory usage: 12 MB
% 0.21/0.31 % (3120599)Instructions burned: 3 (million)
% 0.21/0.31 % (3120594)...printing done.
% 0.21/0.31 % (3120597) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3120586-3120597"...
% 0.21/0.31 % (3120594)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.31 % (3120594)------------------------------
% 0.21/0.31 % (3120594)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (3120594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (3120594)CaDiCaL version: 2.1.3
% 0.21/0.31 % (3120594)Termination reason: Refutation
% 0.21/0.31 % (3120594)Time elapsed: 0.009 s
% 0.21/0.31 % (3120594)Peak memory usage: 13 MB
% 0.21/0.31 % (3120594)Instructions burned: 8 (million)
% 0.21/0.31 % (3120586)Success in time 0.052 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------