%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW499_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 01:30:41 PM UTC 2026
% Result : Theorem 2.50s 1.07s
% Output : Refutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 10 unt; 0 typ; 1 def)
% Number of atoms : 32 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 29 ( 15 ~; 9 |; 3 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 28 ( 26 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 24 ( 19 !; 5 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
complex: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
int: $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
poly: $tType > $tType ).
tff(type_def_10,type,
real: $tType ).
tff(func_def_0,type,
fundam1563812824_csqrt: complex > complex ).
tff(func_def_1,type,
fundam1280195782_psize:
!>[X0: $tType] : ( poly(X0) > nat ) ).
tff(func_def_2,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_3,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_4,type,
bit0: int > int ).
tff(func_def_5,type,
bit1: int > int ).
tff(func_def_6,type,
pls: int ).
tff(func_def_7,type,
number_number_of:
!>[X0: $tType] : ( int > 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,
n: nat ).
tff(func_def_12,type,
na: nat ).
tff(func_def_13,type,
sK0: nat > nat ).
tff(pred_def_1,type,
comm_ring_1:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
comm_semiring_0:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
idom:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
power:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
mult_zero:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
zero_neq_one:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
no_zero_divisors:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
comm_monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_18,type,
ab_semigroup_mult:
!>[X0: $tType] : $o ).
tff(pred_def_19,type,
ring_n68954251visors:
!>[X0: $tType] : $o ).
tff(pred_def_20,type,
ring_11004092258visors:
!>[X0: $tType] : $o ).
tff(pred_def_21,type,
ab_sem1668676832m_mult:
!>[X0: $tType] : $o ).
tff(pred_def_22,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_23,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_24,type,
even_odd_even:
!>[X0: $tType] : ( X0 > $o ) ).
tff(pred_def_25,type,
pp: bool > $o ).
tff(pred_def_26,type,
sQ1_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f1,axiom,
even_odd_even(nat,na),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_e) ).
tff(f26,axiom,
! [X0: nat] :
( even_odd_even(nat,X0)
<=> ? [X1: nat] : ( X0 = times_times(nat,number_number_of(nat,bit0(bit1(pls))),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_even__mult__two__ex) ).
tff(f192,conjecture,
? [X0: nat] : ( na = times_times(nat,number_number_of(nat,bit0(bit1(pls))),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f193,negated_conjecture,
~ ? [X0: nat] : ( na = times_times(nat,number_number_of(nat,bit0(bit1(pls))),X0) ),
inference(negated_conjecture,[status(cth)],[f192]) ).
tff(f269,plain,
! [X0: nat] : ( na != times_times(nat,number_number_of(nat,bit0(bit1(pls))),X0) ),
inference(ennf_transformation,[],[f193]) ).
tff(f276,plain,
! [X0: nat] :
( ( even_odd_even(nat,X0)
| ! [X1: nat] : ( times_times(nat,number_number_of(nat,bit0(bit1(pls))),X1) != X0 ) )
& ( ? [X1: nat] : ( X0 = times_times(nat,number_number_of(nat,bit0(bit1(pls))),X1) )
| ~ even_odd_even(nat,X0) ) ),
inference(nnf_transformation,[],[f26]) ).
tff(f277,plain,
! [X0: nat] :
( ( even_odd_even(nat,X0)
| ! [X1: nat] : ( times_times(nat,number_number_of(nat,bit0(bit1(pls))),X1) != X0 ) )
& ( ? [X2: nat] : ( times_times(nat,number_number_of(nat,bit0(bit1(pls))),X2) = X0 )
| ~ even_odd_even(nat,X0) ) ),
inference(rectify,[],[f276]) ).
tff(f278,plain,
! [X0: nat] :
( ( even_odd_even(nat,X0)
| ! [X1: nat] : ( times_times(nat,number_number_of(nat,bit0(bit1(pls))),X1) != X0 ) )
& ( ( times_times(nat,number_number_of(nat,bit0(bit1(pls))),sK0(X0)) = X0 )
| ~ even_odd_even(nat,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0))],[f277]) ).
tff(f308,plain,
even_odd_even(nat,na),
inference(cnf_transformation,[],[f1]) ).
tff(f339,plain,
! [X0: nat] :
( ( times_times(nat,number_number_of(nat,bit0(bit1(pls))),sK0(X0)) = X0 )
| ~ even_odd_even(nat,X0) ),
inference(cnf_transformation,[],[f278]) ).
tff(f532,plain,
! [X0: nat] : ( na != times_times(nat,number_number_of(nat,bit0(bit1(pls))),X0) ),
inference(cnf_transformation,[],[f269]) ).
tff(f563,definition,
! [X0: $tType,X2: X0,X1: X0] :
( sQ1_eqProxy(X0,X1,X2)
<=> ( X1 = X2 ) ),
introduced(definition,[new_symbols(definition,[sQ1_eqProxy])],[equality_proxy_definition]) ).
tff(f594,plain,
! [X0: nat] :
( sQ1_eqProxy(nat,times_times(nat,number_number_of(nat,bit0(bit1(pls))),sK0(X0)),X0)
| ~ even_odd_even(nat,X0) ),
inference(equality_proxy_replacement,[],[f339,f563]) ).
tff(f667,plain,
! [X0: nat] : ~ sQ1_eqProxy(nat,na,times_times(nat,number_number_of(nat,bit0(bit1(pls))),X0)),
inference(equality_proxy_replacement,[],[f532,f563]) ).
tff(f669,plain,
! [X0: $tType,X2: X0,X1: X0] :
( sQ1_eqProxy(X0,X2,X1)
| ~ sQ1_eqProxy(X0,X1,X2) ),
inference(equality_proxy_axiom,[],[f563]) ).
tff(f692,plain,
! [X0: nat] : ~ sQ1_eqProxy(nat,times_times(nat,number_number_of(nat,bit0(bit1(pls))),X0),na),
inference(resolution,[],[f669,f667]) ).
tff(f774,plain,
~ even_odd_even(nat,na),
inference(resolution,[],[f594,f692]) ).
tff(f775,plain,
$false,
inference(resolution,[],[f774,f308]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW499_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n015.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 14:18:32 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.50/1.07 % (2651409)Detected formulas, will run a generic FOF schedule.
% 2.50/1.07 % (2651420)dis-21_1_sil=8000:lcm=predicate:random_seed=3345310186:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.50/1.07 % (2651420)First to succeed.
% 2.50/1.07 % (2651420)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2651409"
% 2.50/1.07 % (2651414)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2583254878:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.50/1.07 % (2651417)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3005594018:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.50/1.07 % (2651416)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2531006315:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.50/1.07 % (2651415)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1579250560:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.50/1.07 % (2651417)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.50/1.07 % (2651416)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.50/1.07 % (2651419)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1360571646:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.50/1.07 % (2651418)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2431709954:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.50/1.07 % (2651418)Also succeeded, but the first one will report.
% 2.50/1.07 % (2651419)Also succeeded, but the first one will report.
% 2.50/1.07 % (2651417)Instruction limit reached!
% 2.50/1.07 % (2651417)------------------------------
% 2.50/1.07 % (2651417)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.07 % (2651417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.07 % (2651417)CaDiCaL version: 2.1.3
% 2.50/1.07 % (2651417)Termination reason: Instruction limit
% 2.50/1.07 % (2651417)Termination phase: Saturation
% 2.50/1.07 % (2651417)Time elapsed: 0.051 s
% 2.50/1.07 % (2651417)Peak memory usage: 89 MB
% 2.50/1.07 % (2651417)Instructions burned: 109 (million)
% 2.50/1.07 % (2651420)Refutation found. Thanks to Tanya!
% 2.50/1.07 % SZS status Theorem for theBenchmark
% 2.50/1.07 % SZS output start Proof for theBenchmark
% See solution above
% 2.50/1.07 % (2651420)------------------------------
% 2.50/1.07 % (2651420)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.07 % (2651420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.07 % (2651420)CaDiCaL version: 2.1.3
% 2.50/1.07 % (2651420)Termination reason: Refutation
% 2.50/1.07 % (2651420)Time elapsed: 0.005 s
% 2.50/1.07 % (2651420)Peak memory usage: 89 MB
% 2.50/1.07 % (2651420)Instructions burned: 13 (million)
% 2.50/1.07 % (2651420)------------------------------
% 2.50/1.07 % (2651420)------------------------------
% 2.50/1.07 % (2651409)Success in time 0.279 s
% 2.50/1.07 % Vampire exiting
%------------------------------------------------------------------------------