%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN018_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 : Tue Sep 29 12:26:56 PM UTC 2026
% Result : ContradictoryAxioms 0.21s 0.52s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 68 ( 33 unt; 0 typ; 2 def)
% Number of atoms : 145 ( 53 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 142 ( 65 ~; 61 |; 6 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 22 ( 20 usr; 3 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-4 aty)
% Number of variables : 28 ( 0 sgn 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(type_def_8,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
bit0: int > int ).
tff(func_def_3,type,
bit1: int > int ).
tff(func_def_4,type,
pls: int ).
tff(func_def_5,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_6,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_7,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_8,type,
fFalse: bool ).
tff(func_def_9,type,
fTrue: bool ).
tff(func_def_10,type,
n: nat ).
tff(func_def_11,type,
tn: nat ).
tff(func_def_12,type,
v: int ).
tff(func_def_13,type,
w: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
power:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
mult_zero:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
zero_neq_one:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
no_zero_divisors:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
ring_11004092258visors:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
ordere236663937imp_le:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_18,type,
pp: bool > $o ).
tff(f1,axiom,
w != zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096w_A_126_061_A0_096) ).
tff(f4,axiom,
! [X0: $tType] :
( ring_11004092258visors(X0)
=> ! [X1: X0] :
( ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X0) )
<=> ( X1 = zero_zero(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_zero__eq__power2) ).
tff(f28,axiom,
~ ord_less(int,pls,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_rel__simps_I2_J) ).
tff(f38,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_Pls__def) ).
tff(f48,axiom,
! [X0: $tType] :
( ( power(X0)
& mult_zero(X0)
& no_zero_divisors(X0)
& zero_neq_one(X0) )
=> ! [X1: nat,X2: X0] :
( ( power_power(X0,X2,X1) = zero_zero(X0) )
<=> ( ( X2 = zero_zero(X0) )
& ( X1 != zero_zero(nat) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_power__eq__0__iff) ).
tff(f51,axiom,
plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))) = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_calculation_I1_J) ).
tff(f63,axiom,
( ( v != zero_zero(int) )
=> ord_less(int,zero_zero(int),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_calculation_I2_J) ).
tff(f74,axiom,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_add__Pls) ).
tff(f76,axiom,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_Bit0__def) ).
tff(f100,axiom,
ring_11004092258visors(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
tff(f103,axiom,
no_zero_divisors(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
tff(f106,axiom,
zero_neq_one(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
tff(f108,axiom,
mult_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
tff(f111,axiom,
power(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
tff(f134,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X0) )
<=> ( X1 = zero_zero(X0) ) )
| ~ ring_11004092258visors(X0) ),
inference(ennf_transformation,[],[f4]) ).
tff(f151,plain,
! [X0: $tType] :
( ! [X1: nat,X2: X0] :
( ( power_power(X0,X2,X1) = zero_zero(X0) )
<=> ( ( X2 = zero_zero(X0) )
& ( X1 != zero_zero(nat) ) ) )
| ~ power(X0)
| ~ mult_zero(X0)
| ~ no_zero_divisors(X0)
| ~ zero_neq_one(X0) ),
inference(ennf_transformation,[],[f48]) ).
tff(f152,plain,
! [X0: $tType] :
( ! [X1: nat,X2: X0] :
( ( power_power(X0,X2,X1) = zero_zero(X0) )
<=> ( ( X2 = zero_zero(X0) )
& ( X1 != zero_zero(nat) ) ) )
| ~ power(X0)
| ~ mult_zero(X0)
| ~ no_zero_divisors(X0)
| ~ zero_neq_one(X0) ),
inference(flattening,[],[f151]) ).
tff(f157,plain,
( ord_less(int,zero_zero(int),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))))
| ( zero_zero(int) = v ) ),
inference(ennf_transformation,[],[f63]) ).
tff(f184,plain,
w != zero_zero(int),
inference(cnf_transformation,[],[f1]) ).
tff(f188,plain,
! [X0: $tType,X1: X0] :
( ~ ring_11004092258visors(X0)
| ( zero_zero(X0) != X1 )
| ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) ) ),
inference(cnf_transformation,[],[f134]) ).
tff(f230,plain,
~ ord_less(int,pls,pls),
inference(cnf_transformation,[],[f28]) ).
tff(f246,plain,
zero_zero(int) = pls,
inference(cnf_transformation,[],[f38]) ).
tff(f262,plain,
! [X0: $tType,X2: X0,X1: nat] :
( ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0)
| ( zero_zero(X0) = X2 )
| ( zero_zero(X0) != power_power(X0,X2,X1) ) ),
inference(cnf_transformation,[],[f152]) ).
tff(f266,plain,
zero_zero(int) = plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))),
inference(cnf_transformation,[],[f51]) ).
tff(f282,plain,
( ( zero_zero(int) = v )
| ord_less(int,zero_zero(int),plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls)))))) ),
inference(cnf_transformation,[],[f157]) ).
tff(f295,plain,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
inference(cnf_transformation,[],[f74]) ).
tff(f297,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f76]) ).
tff(f336,plain,
ring_11004092258visors(int),
inference(cnf_transformation,[],[f100]) ).
tff(f339,plain,
no_zero_divisors(int),
inference(cnf_transformation,[],[f103]) ).
tff(f342,plain,
zero_neq_one(int),
inference(cnf_transformation,[],[f106]) ).
tff(f344,plain,
mult_zero(int),
inference(cnf_transformation,[],[f108]) ).
tff(f347,plain,
power(int),
inference(cnf_transformation,[],[f111]) ).
tff(f366,plain,
! [X0: $tType,X1: X0] :
( ~ ring_11004092258visors(X0)
| ( zero_zero(X0) != X1 )
| ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) ) ),
inference(definition_unfolding,[],[f188,f297]) ).
tff(f393,plain,
zero_zero(int) = plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),
inference(definition_unfolding,[],[f266,f297,f297]) ).
tff(f397,plain,
( ( zero_zero(int) = v )
| ord_less(int,zero_zero(int),plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))) ),
inference(definition_unfolding,[],[f282,f297,f297]) ).
tff(f408,plain,
! [X0: $tType] :
( ~ ring_11004092258visors(X0)
| ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) ) ),
inference(equality_resolution,[],[f366]) ).
tff(f442,plain,
! [X0: $tType,X2: X0,X1: nat] :
( ( zero_zero(X0) != power_power(X0,X2,X1) )
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| power(X0)
| ( zero_zero(X0) = X2 )
| ~ zero_neq_one(X0) ),
inference(consistent_polarity_flipping,[],[f262]) ).
tff(f453,plain,
~ power(int),
inference(consistent_polarity_flipping,[],[f347]) ).
tff(f461,definition,
( spl0_1
<=> ord_less(int,zero_zero(int),plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f463,plain,
( ord_less(int,zero_zero(int),plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f461]) ).
tff(f465,definition,
( spl0_2
<=> ( zero_zero(int) = v ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f467,plain,
( ( zero_zero(int) = v )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f465]) ).
tff(f468,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f397,f465,f461]) ).
tff(f471,plain,
( ( pls = v )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f467,f246]) ).
tff(f726,plain,
zero_zero(int) = power_power(int,zero_zero(int),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),
inference(resolution,[],[f408,f336]) ).
tff(f727,plain,
pls = power_power(int,pls,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),
inference(forward_demodulation,[],[f726,f246]) ).
tff(f828,plain,
( ( zero_zero(int) = plus_plus(int,power_power(int,pls,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f393,f471]) ).
tff(f829,plain,
( ( zero_zero(int) = plus_plus(int,pls,power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f828,f727]) ).
tff(f830,plain,
( ( pls = plus_plus(int,pls,power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f829,f246]) ).
tff(f831,plain,
( ( pls = power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) )
| ~ spl0_2 ),
inference(superposition,[],[f830,f295]) ).
tff(f915,plain,
( ( zero_zero(int) != pls )
| ~ no_zero_divisors(int)
| ~ mult_zero(int)
| power(int)
| ( w = zero_zero(int) )
| ~ zero_neq_one(int)
| ~ spl0_2 ),
inference(superposition,[],[f442,f831]) ).
tff(f920,plain,
( ~ no_zero_divisors(int)
| ~ mult_zero(int)
| power(int)
| ( w = zero_zero(int) )
| ~ zero_neq_one(int)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f915,f246]) ).
tff(f925,plain,
( ~ mult_zero(int)
| power(int)
| ( w = zero_zero(int) )
| ~ zero_neq_one(int)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f920,f339]) ).
tff(f929,plain,
( power(int)
| ( w = zero_zero(int) )
| ~ zero_neq_one(int)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f925,f344]) ).
tff(f931,plain,
( ( w = zero_zero(int) )
| ~ zero_neq_one(int)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f929,f453]) ).
tff(f932,plain,
( ~ zero_neq_one(int)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f931,f184]) ).
tff(f933,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f932,f342]) ).
tff(f934,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f933]) ).
tff(f935,plain,
( ord_less(int,pls,plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
| ~ spl0_1 ),
inference(forward_demodulation,[],[f463,f246]) ).
tff(f937,plain,
pls = plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),
inference(forward_demodulation,[],[f393,f246]) ).
tff(f954,plain,
( ord_less(int,pls,pls)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f935,f937]) ).
tff(f955,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f954,f230]) ).
tff(f956,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f955]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f468]) ).
cnf(s5,plain,
~ spl0_2,
inference(sat_conversion,[],[f934]) ).
cnf(s8,plain,
~ spl0_1,
inference(sat_conversion,[],[f956]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s5,s8]) ).
tff(f957,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN018_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.41 % Computer : n014.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sun Sep 27 21:50:46 UTC 2026
% 0.13/0.42 % CPUTime :
% 0.13/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.45 Running first-order model finding
% 0.13/0.46 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.52 % (1205979)Will run a generic schedule for satisfiability detection.
% 0.21/0.52 % (1205985)% WARNING: option uhcvi not known.
% 0.21/0.52 % (1205985)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1843812028:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.52 % (1205986)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=295623720:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.52 % (1205984)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2760901790_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.52 % (1205988)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1571257060:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.52 % (1205989)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1089507404:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.52 % (1205990)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3093119741:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.52 % (1205987)dis+10_1_sil=32000:sp=arity:random_seed=1558390065:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.52 % Exception at run slice level
% 0.21/0.52 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.52 % (1205985) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1205979-1205985"...
% 0.21/0.52 % (1205985)...printing done.
% 0.21/0.52 % (1205985)Refutation found. Thanks to Tanya!
% 0.21/0.52 % SZS status ContradictoryAxioms for theBenchmark
% 0.21/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.52 % (1205985)------------------------------
% 0.21/0.52 % (1205985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.52 % (1205985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.52 % (1205985)CaDiCaL version: 2.1.3
% 0.21/0.52 % (1205985)Termination reason: Refutation
% 0.21/0.52 % (1205985)Time elapsed: 0.024 s
% 0.21/0.52 % (1205985)Peak memory usage: 13 MB
% 0.21/0.52 % (1205985)Instructions burned: 37 (million)
% 0.21/0.52 % (1205979)Success in time 0.051 s
% 0.21/0.52 % Vampire exiting
%------------------------------------------------------------------------------