%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUN015_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 : n013.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 12:26:55 PM UTC 2026
% Result : Theorem 0.18s 0.49s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 11 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 29 ( 16 ~; 9 |; 1 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-4 aty)
% Number of variables : 12 ( 12 !; 0 ?; 12 :)
% 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,
v != zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096v_A_126_061_A0_096) ).
tff(f2,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
<=> ( X1 != zero_zero(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_zero__less__power2) ).
tff(f75,axiom,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Bit0__def) ).
tff(f104,axiom,
linordered_idom(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
tff(f127,conjecture,
ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,bit0(bit1(pls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f128,negated_conjecture,
~ ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,bit0(bit1(pls))))),
inference(negated_conjecture,[status(cth)],[f127]) ).
tff(f129,plain,
~ ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,bit0(bit1(pls))))),
inference(flattening,[],[f128]) ).
tff(f132,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
<=> ( X1 != zero_zero(X0) ) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f2]) ).
tff(f183,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
| ( zero_zero(X0) = X1 ) )
& ( ( X1 != zero_zero(X0) )
| ~ ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f132]) ).
tff(f240,plain,
v != zero_zero(int),
inference(cnf_transformation,[],[f1]) ).
tff(f242,plain,
! [X0: $tType,X1: X0] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f183]) ).
tff(f362,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f75]) ).
tff(f408,plain,
linordered_idom(int),
inference(cnf_transformation,[],[f104]) ).
tff(f429,plain,
~ ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,bit0(bit1(pls))))),
inference(cnf_transformation,[],[f129]) ).
tff(f430,plain,
! [X0: $tType,X1: X0] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f242,f362]) ).
tff(f473,plain,
~ ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),
inference(definition_unfolding,[],[f429,f362]) ).
tff(f1288,plain,
( ( v = zero_zero(int) )
| ~ linordered_idom(int) ),
inference(resolution,[],[f430,f473]) ).
tff(f1294,plain,
~ linordered_idom(int),
inference(forward_subsumption_resolution,[],[f1288,f240]) ).
tff(f1295,plain,
$false,
inference(forward_subsumption_resolution,[],[f1294,f408]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN015_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n013.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 21:49:51 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.43 Running first-order model finding
% 0.13/0.43 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
% 0.18/0.49 % (585672)Will run a generic schedule for satisfiability detection.
% 0.18/0.49 % (585680)dis+10_1_sil=32000:sp=arity:random_seed=3348248249:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.49 % (585678)% WARNING: option uhcvi not known.
% 0.18/0.49 % (585677)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3117569623_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.49 % (585678)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1260593633:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.49 % (585681)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2699637307:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.49 % (585679)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1493958988:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.49 % (585682)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4236158112:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.49 % (585683)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=672965430:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.49 % Exception at run slice level
% 0.18/0.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.49 % (585680) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-585672-585680"...
% 0.18/0.49 % (585680)...printing done.
% 0.18/0.49 % (585680)Refutation found. Thanks to Tanya!
% 0.18/0.49 % SZS status Theorem for theBenchmark
% 0.18/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.49 % (585680)------------------------------
% 0.18/0.49 % (585680)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.49 % (585680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.49 % (585680)CaDiCaL version: 2.1.3
% 0.18/0.49 % (585680)Termination reason: Refutation
% 0.18/0.49 % (585680)Time elapsed: 0.014 s
% 0.18/0.49 % (585680)Peak memory usage: 12 MB
% 0.18/0.49 % (585680)Instructions burned: 37 (million)
% 0.18/0.49 % (585672)Success in time 0.054 s
% 0.18/0.49 % Vampire exiting
%------------------------------------------------------------------------------