%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM925_1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 12:26:08 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 59 ( 41 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 51 ( 23 ~; 17 |; 9 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
int: $tType ).
tff(type_def_6,type,
nat: $tType ).
tff(func_def_0,type,
one_one_int: int ).
tff(func_def_1,type,
one_one_nat: nat ).
tff(func_def_2,type,
plus_plus_int: ( int * int ) > int ).
tff(func_def_3,type,
plus_plus_nat: ( nat * nat ) > nat ).
tff(func_def_4,type,
zero_zero_int: int ).
tff(func_def_5,type,
zero_zero_nat: nat ).
tff(func_def_6,type,
bit0: int > int ).
tff(func_def_7,type,
bit1: int > int ).
tff(func_def_8,type,
pls: int ).
tff(func_def_9,type,
number_number_of_int: int > int ).
tff(func_def_10,type,
number_number_of_nat: int > nat ).
tff(func_def_11,type,
semiri1621563631at_int: nat > int ).
tff(func_def_12,type,
semiri984289939at_nat: nat > nat ).
tff(func_def_13,type,
power_power_int: ( int * nat ) > int ).
tff(func_def_14,type,
power_power_nat: ( nat * nat ) > nat ).
tff(func_def_15,type,
n: nat ).
tff(func_def_16,type,
t: int ).
tff(pred_def_1,type,
ord_less_int: ( int * int ) > $o ).
tff(pred_def_2,type,
ord_less_nat: ( nat * nat ) > $o ).
tff(f53,axiom,
! [X0: int,X1: int] : ( plus_plus_int(X0,X1) = plus_plus_int(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_zadd__commute) ).
tff(f66,axiom,
! [X0: int,X1: int] :
( ord_less_int(X0,plus_plus_int(X1,one_one_int))
<=> ( ord_less_int(X0,X1)
| ( X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_zless__add1__eq) ).
tff(f67,axiom,
! [X0: nat] : ~ ord_less_int(semiri1621563631at_int(X0),zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_int__less__0__conv) ).
tff(f79,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Pls__def) ).
tff(f84,axiom,
! [X0: int] : ( bit0(X0) = plus_plus_int(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Bit0__def) ).
tff(f93,axiom,
! [X0: int,X1: int] :
( ( power_power_int(X0,number_number_of_nat(X1)) = zero_zero_int )
<=> ( ( X0 = zero_zero_int )
& ( number_number_of_nat(X1) != zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_power__eq__0__iff__number__of) ).
tff(f100,axiom,
! [X0: int] : ( bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_Bit1__def) ).
tff(f107,conjecture,
power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f108,negated_conjecture,
( ( ~ power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) ) != zero_zero_int ),
inference(negated_conjecture,[status(cth)],[f107]) ).
tff(f109,plain,
zero_zero_int = power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))),
inference(flattening,[],[f108]) ).
tff(f141,plain,
! [X0: int,X1: int] :
( ( ord_less_int(X0,plus_plus_int(X1,one_one_int))
| ( ~ ord_less_int(X0,X1)
& ( X0 != X1 ) ) )
& ( ord_less_int(X0,X1)
| ( X0 = X1 )
| ~ ord_less_int(X0,plus_plus_int(X1,one_one_int)) ) ),
inference(nnf_transformation,[],[f66]) ).
tff(f142,plain,
! [X0: int,X1: int] :
( ( ord_less_int(X0,plus_plus_int(X1,one_one_int))
| ( ~ ord_less_int(X0,X1)
& ( X0 != X1 ) ) )
& ( ord_less_int(X0,X1)
| ( X0 = X1 )
| ~ ord_less_int(X0,plus_plus_int(X1,one_one_int)) ) ),
inference(flattening,[],[f141]) ).
tff(f149,plain,
! [X0: int,X1: int] :
( ( ( power_power_int(X0,number_number_of_nat(X1)) = zero_zero_int )
| ( zero_zero_int != X0 )
| ( zero_zero_nat = number_number_of_nat(X1) ) )
& ( ( ( X0 = zero_zero_int )
& ( number_number_of_nat(X1) != zero_zero_nat ) )
| ( zero_zero_int != power_power_int(X0,number_number_of_nat(X1)) ) ) ),
inference(nnf_transformation,[],[f93]) ).
tff(f150,plain,
! [X0: int,X1: int] :
( ( ( power_power_int(X0,number_number_of_nat(X1)) = zero_zero_int )
| ( zero_zero_int != X0 )
| ( zero_zero_nat = number_number_of_nat(X1) ) )
& ( ( ( X0 = zero_zero_int )
& ( number_number_of_nat(X1) != zero_zero_nat ) )
| ( zero_zero_int != power_power_int(X0,number_number_of_nat(X1)) ) ) ),
inference(flattening,[],[f149]) ).
tff(f227,plain,
! [X0: int,X1: int] : ( plus_plus_int(X0,X1) = plus_plus_int(X1,X0) ),
inference(cnf_transformation,[],[f53]) ).
tff(f251,plain,
! [X0: int,X1: int] :
( ord_less_int(X0,plus_plus_int(X1,one_one_int))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f142]) ).
tff(f253,plain,
! [X0: nat] : ~ ord_less_int(semiri1621563631at_int(X0),zero_zero_int),
inference(cnf_transformation,[],[f67]) ).
tff(f271,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f79]) ).
tff(f276,plain,
! [X0: int] : ( bit0(X0) = plus_plus_int(X0,X0) ),
inference(cnf_transformation,[],[f84]) ).
tff(f286,plain,
! [X0: int,X1: int] :
( ( zero_zero_int = X0 )
| ( zero_zero_int != power_power_int(X0,number_number_of_nat(X1)) ) ),
inference(cnf_transformation,[],[f150]) ).
tff(f296,plain,
! [X0: int] : ( bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0) ),
inference(cnf_transformation,[],[f100]) ).
tff(f306,plain,
zero_zero_int = power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f109]) ).
tff(f369,plain,
! [X0: nat] : ~ ord_less_int(semiri1621563631at_int(X0),pls),
inference(definition_unfolding,[],[f253,f271]) ).
tff(f395,plain,
! [X0: int,X1: int] :
( ( pls != power_power_int(X0,number_number_of_nat(X1)) )
| ( pls = X0 ) ),
inference(definition_unfolding,[],[f286,f271,f271]) ).
tff(f406,plain,
pls = power_power_int(plus_plus_int(one_one_int,semiri1621563631at_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,[],[f306,f271,f276,f296]) ).
tff(f419,plain,
! [X1: int] : ord_less_int(X1,plus_plus_int(X1,one_one_int)),
inference(equality_resolution,[],[f251]) ).
tff(f444,plain,
! [X0: int] : ord_less_int(X0,plus_plus_int(one_one_int,X0)),
inference(superposition,[],[f419,f227]) ).
tff(f609,plain,
( ( pls != pls )
| ( plus_plus_int(one_one_int,semiri1621563631at_int(n)) = pls ) ),
inference(superposition,[],[f395,f406]) ).
tff(f613,plain,
plus_plus_int(one_one_int,semiri1621563631at_int(n)) = pls,
inference(trivial_inequality_removal,[],[f609]) ).
tff(f619,plain,
ord_less_int(semiri1621563631at_int(n),pls),
inference(superposition,[],[f444,f613]) ).
tff(f620,plain,
$false,
inference(forward_subsumption_resolution,[],[f619,f369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925_1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n004.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 21:42:07 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.17/0.47 % (3901489)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (3901496)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2187798146:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (3901495)% WARNING: option uhcvi not known.
% 0.17/0.47 % (3901494)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=457880861_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (3901495)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2090416771:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (3901497)dis+10_1_sil=32000:sp=arity:random_seed=3564537896:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (3901498)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4118621491:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (3901500)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3560538549:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % (3901499)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3213169206:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (3901497) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3901489-3901497"...
% 0.17/0.47 % (3901495) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3901489-3901495"...
% 0.17/0.47 % (3901497)...printing done.
% 0.17/0.47 % (3901495)...printing done.
% 0.17/0.47 % (3901497)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (3901497)------------------------------
% 0.17/0.47 % (3901497)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (3901497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (3901497)CaDiCaL version: 2.1.3
% 0.17/0.47 % (3901497)Termination reason: Refutation
% 0.17/0.47 % (3901497)Time elapsed: 0.010 s
% 0.17/0.47 % (3901497)Peak memory usage: 12 MB
% 0.17/0.47 % (3901497)Instructions burned: 15 (million)
% 0.17/0.47 % (3901489)Success in time 0.049 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------