%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM925_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 12:26:10 PM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 49 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 85 ( 48 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 70 ( 34 ~; 26 |; 6 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 30 ( 30 !; 0 ?; 30 :)
% 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,
real: $tType ).
tff(func_def_0,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_1,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_3,type,
bit0: int > int ).
tff(func_def_4,type,
bit1: int > int ).
tff(func_def_5,type,
pls: int ).
tff(func_def_6,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_7,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
tff(func_def_8,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_9,type,
fFalse: bool ).
tff(func_def_10,type,
fTrue: bool ).
tff(func_def_11,type,
m1: int ).
tff(func_def_12,type,
n: nat ).
tff(func_def_13,type,
t: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
power:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
mult_zero:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
semiring_0:
!>[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,
ring_11004092258visors:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_16,type,
pp: bool > $o ).
tff(f1,axiom,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).
tff(f27,axiom,
~ ord_less(int,pls,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_rel__simps_I2_J) ).
tff(f40,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_nat__1__add__1) ).
tff(f72,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Pls__def) ).
tff(f73,axiom,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_add__Pls__right) ).
tff(f75,axiom,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Bit0__def) ).
tff(f81,axiom,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_Bit1__def) ).
tff(f98,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/sandbox/benchmark/theBenchmark.p',fact_97_power__eq__0__iff) ).
tff(f102,axiom,
no_zero_divisors(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
tff(f105,axiom,
zero_neq_one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
tff(f108,axiom,
mult_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
tff(f111,axiom,
power(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
tff(f138,conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f139,negated_conjecture,
( ( ~ power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) ) != zero_zero(int) ),
inference(negated_conjecture,[status(cth)],[f138]) ).
tff(f140,plain,
zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))),
inference(flattening,[],[f139]) ).
tff(f190,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,[],[f98]) ).
tff(f191,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,[],[f190]) ).
tff(f192,plain,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(cnf_transformation,[],[f1]) ).
tff(f227,plain,
~ ord_less(int,pls,pls),
inference(cnf_transformation,[],[f27]) ).
tff(f248,plain,
number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,one_one(nat),one_one(nat)),
inference(cnf_transformation,[],[f40]) ).
tff(f298,plain,
zero_zero(int) = pls,
inference(cnf_transformation,[],[f72]) ).
tff(f299,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f73]) ).
tff(f301,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f75]) ).
tff(f307,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f81]) ).
tff(f332,plain,
! [X0: $tType,X2: X0,X1: nat] :
( ~ no_zero_divisors(X0)
| ~ zero_neq_one(X0)
| ~ mult_zero(X0)
| ~ power(X0)
| ( zero_zero(X0) = X2 )
| ( zero_zero(X0) != power_power(X0,X2,X1) ) ),
inference(cnf_transformation,[],[f191]) ).
tff(f337,plain,
no_zero_divisors(int),
inference(cnf_transformation,[],[f102]) ).
tff(f340,plain,
zero_neq_one(int),
inference(cnf_transformation,[],[f105]) ).
tff(f343,plain,
mult_zero(int),
inference(cnf_transformation,[],[f108]) ).
tff(f346,plain,
power(int),
inference(cnf_transformation,[],[f111]) ).
tff(f373,plain,
zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))),
inference(cnf_transformation,[],[f140]) ).
tff(f411,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))),
inference(definition_unfolding,[],[f248,f301,f307]) ).
tff(f446,plain,
zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),
inference(definition_unfolding,[],[f373,f301,f307]) ).
tff(f487,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))),
inference(forward_demodulation,[],[f411,f299]) ).
tff(f496,plain,
ord_less(int,pls,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(forward_demodulation,[],[f192,f298]) ).
tff(f511,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,one_one(int),one_one(int))),
inference(forward_demodulation,[],[f487,f299]) ).
tff(f525,plain,
zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))),
inference(superposition,[],[f446,f299]) ).
tff(f526,plain,
zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),
inference(forward_demodulation,[],[f525,f299]) ).
tff(f528,plain,
zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(nat,one_one(nat),one_one(nat))),
inference(forward_demodulation,[],[f526,f511]) ).
tff(f530,plain,
pls = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(nat,one_one(nat),one_one(nat))),
inference(forward_demodulation,[],[f528,f298]) ).
tff(f1004,plain,
! [X0: int,X1: nat] :
( ~ zero_neq_one(int)
| ~ mult_zero(int)
| ~ power(int)
| ( zero_zero(int) = X0 )
| ( zero_zero(int) != power_power(int,X0,X1) ) ),
inference(resolution,[],[f332,f337]) ).
tff(f1009,plain,
! [X0: int,X1: nat] :
( ~ mult_zero(int)
| ~ power(int)
| ( zero_zero(int) = X0 )
| ( zero_zero(int) != power_power(int,X0,X1) ) ),
inference(forward_subsumption_resolution,[],[f1004,f340]) ).
tff(f1012,plain,
! [X0: int,X1: nat] :
( ~ power(int)
| ( zero_zero(int) = X0 )
| ( zero_zero(int) != power_power(int,X0,X1) ) ),
inference(forward_subsumption_resolution,[],[f1009,f343]) ).
tff(f1015,plain,
! [X0: int,X1: nat] :
( ( zero_zero(int) = X0 )
| ( zero_zero(int) != power_power(int,X0,X1) ) ),
inference(forward_subsumption_resolution,[],[f1012,f346]) ).
tff(f1016,plain,
! [X0: int,X1: nat] :
( ( pls = X0 )
| ( zero_zero(int) != power_power(int,X0,X1) ) ),
inference(forward_demodulation,[],[f1015,f298]) ).
tff(f1017,plain,
! [X0: int,X1: nat] :
( ( pls != power_power(int,X0,X1) )
| ( pls = X0 ) ),
inference(forward_demodulation,[],[f1016,f298]) ).
tff(f1019,plain,
( ( pls != pls )
| ( plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) = pls ) ),
inference(superposition,[],[f1017,f530]) ).
tff(f1021,plain,
plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) = pls,
inference(trivial_inequality_removal,[],[f1019]) ).
tff(f1029,plain,
ord_less(int,pls,pls),
inference(superposition,[],[f496,f1021]) ).
tff(f1047,plain,
$false,
inference(forward_subsumption_resolution,[],[f1029,f227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n001.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 21:48:58 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.48 % (3989410)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (3989419)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1333254040:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (3989416)% WARNING: option uhcvi not known.
% 0.17/0.48 % (3989415)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2779615907_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (3989416)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1208519900:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (3989417)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4288251079:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (3989418)dis+10_1_sil=32000:sp=arity:random_seed=3084688478:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (3989420)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1463401246:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % (3989421)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=254746657:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % Exception at run slice level
% 0.17/0.48 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.48 % (3989419) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3989410-3989419"...
% 0.17/0.48 % (3989419)...printing done.
% 0.17/0.48 % (3989419)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (3989419)------------------------------
% 0.17/0.48 % (3989419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (3989419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (3989419)CaDiCaL version: 2.1.3
% 0.17/0.48 % (3989419)Termination reason: Refutation
% 0.17/0.48 % (3989419)Time elapsed: 0.013 s
% 0.17/0.48 % (3989419)Peak memory usage: 12 MB
% 0.17/0.48 % (3989419)Instructions burned: 39 (million)
% 0.17/0.48 % (3989410)Success in time 0.051 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------