%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW485_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 : n018.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 01:30:40 PM UTC 2026
% Result : Theorem 0.19s 1.30s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 11 ~; 7 |; 6 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 16 usr; 2 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 5 con; 0-4 aty)
% Number of variables : 17 ( 13 !; 4 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
complex: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(type_def_8,type,
poly1: $tType > $tType ).
tff(type_def_9,type,
real: $tType ).
tff(type_def_10,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_1,type,
order1:
!>[X0: $tType] : ( ( X0 * poly1(X0) ) > nat ) ).
tff(func_def_2,type,
poly:
!>[X0: $tType] : ( poly1(X0) > fun(X0,X0) ) ).
tff(func_def_3,type,
norm_norm:
!>[X0: $tType] : ( X0 > real ) ).
tff(func_def_4,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_5,type,
fFalse: bool ).
tff(func_def_6,type,
fTrue: bool ).
tff(func_def_7,type,
cs: poly1(complex) ).
tff(func_def_8,type,
r: real ).
tff(func_def_9,type,
sK0: real > complex ).
tff(func_def_10,type,
sK1:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_11,type,
sK2:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_12,type,
sK3:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_13,type,
sK4:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_14,type,
sK5:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_15,type,
sK6:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_16,type,
sK7:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_17,type,
sK8:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_18,type,
sK9:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_19,type,
sK10:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_20,type,
sK11:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_21,type,
sK12: real ).
tff(func_def_22,type,
sK13: ( real * real ) > real ).
tff(pred_def_1,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
idom:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
ord:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
order:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
preorder:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
comm_semiring_0:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
dense_linorder:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
real_normed_vector:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_13,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_14,type,
pp: bool > $o ).
tff(pred_def_16,type,
sP14: real > $o ).
tff(f1,axiom,
? [X2: real] :
( ord_less(real,zero_zero(real),X2)
& ! [X3: complex] :
( ord_less_eq(real,norm_norm(complex,X3),r)
=> ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X3)),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_pCons) ).
tff(f140,axiom,
! [X0: real] :
( ! [X1: complex] :
( ord_less_eq(real,norm_norm(complex,X1),r)
=> ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),X0) )
=> thesis ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f141,conjecture,
thesis,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(f142,negated_conjecture,
~ thesis,
inference(negated_conjecture,[status(cth)],[f141]) ).
tff(f143,plain,
~ thesis,
inference(flattening,[],[f142]) ).
tff(f144,plain,
? [X0: real] :
( ord_less(real,zero_zero(real),X0)
& ! [X1: complex] :
( ord_less_eq(real,norm_norm(complex,X1),r)
=> ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),X0) ) ),
inference(rectify,[],[f1]) ).
tff(f145,plain,
! [X0: real] :
( thesis
| ? [X1: complex] :
( ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),X0)
& ord_less_eq(real,norm_norm(complex,X1),r) ) ),
inference(ennf_transformation,[],[f140]) ).
tff(f163,plain,
? [X0: real] :
( ord_less(real,zero_zero(real),X0)
& ! [X1: complex] :
( ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),X0)
| ~ ord_less_eq(real,norm_norm(complex,X1),r) ) ),
inference(ennf_transformation,[],[f144]) ).
tff(f166,plain,
! [X0: real] :
( thesis
| ( ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),sK0(X0))),X0)
& ord_less_eq(real,norm_norm(complex,sK0(X0)),r) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f145]) ).
tff(f176,plain,
( ord_less(real,zero_zero(real),sK12)
& ! [X1: complex] :
( ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),sK12)
| ~ ord_less_eq(real,norm_norm(complex,X1),r) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f163]) ).
tff(f180,plain,
! [X0: real] :
( thesis
| ord_less_eq(real,norm_norm(complex,sK0(X0)),r) ),
inference(cnf_transformation,[],[f166]) ).
tff(f181,plain,
! [X0: real] :
( thesis
| ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),sK0(X0))),X0) ),
inference(cnf_transformation,[],[f166]) ).
tff(f182,plain,
~ thesis,
inference(cnf_transformation,[],[f143]) ).
tff(f204,plain,
! [X1: complex] :
( ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),X1)),sK12)
| ~ ord_less_eq(real,norm_norm(complex,X1),r) ),
inference(cnf_transformation,[],[f176]) ).
tff(f219,plain,
! [X0: real] : ord_less_eq(real,norm_norm(complex,sK0(X0)),r),
inference(forward_subsumption_resolution,[],[f180,f182]) ).
tff(f220,plain,
! [X0: real] : ~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,cs),sK0(X0))),X0),
inference(forward_subsumption_resolution,[],[f181,f182]) ).
tff(f222,plain,
~ ord_less_eq(real,norm_norm(complex,sK0(sK12)),r),
inference(resolution,[],[f220,f204]) ).
tff(f223,plain,
$false,
inference(forward_subsumption_resolution,[],[f222,f219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW485_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n018.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 14:16:25 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running first-order theorem proving
% 0.07/0.23 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
% 0.19/1.30 % (3409755)Detected formulas, will run a generic FOF schedule.
% 0.19/1.30 % (3409766)dis-21_1_sil=8000:lcm=predicate:random_seed=1780319222: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)
% 0.19/1.30 % (3409766)Instruction limit reached!
% 0.19/1.30 % (3409766)------------------------------
% 0.19/1.30 % (3409766)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.30 % (3409766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.30 % (3409766)CaDiCaL version: 2.1.3
% 0.19/1.30 % (3409766)Termination reason: Instruction limit
% 0.19/1.30 % (3409766)Termination phase: Saturation
% 0.19/1.30 % (3409766)Time elapsed: 0.034 s
% 0.19/1.30 % (3409766)Peak memory usage: 89 MB
% 0.19/1.30 % (3409766)Instructions burned: 133 (million)
% 0.19/1.30 % (3409765)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1358852403:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.19/1.30 % (3409764)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3012463583:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.19/1.30 % (3409760)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=2226693440:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.19/1.30 % (3409763)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3250495170:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.19/1.30 % (3409761)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=150990104:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.19/1.30 % (3409762)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=3339532581:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.19/1.30 % (3409763)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/1.30 % (3409763)First to succeed.
% 0.19/1.30 % (3409762)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/1.30 % (3409763)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3409755"
% 0.19/1.30 % (3409764)Also succeeded, but the first one will report.
% 0.19/1.30 % (3409765)Also succeeded, but the first one will report.
% 0.19/1.30 % (3409768)lrs+10_1_sil=8000:sp=occurrence:random_seed=2310971549:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.19/1.30 % (3409768)Also succeeded, but the first one will report.
% 0.19/1.30 % (3409763)Refutation found. Thanks to Tanya!
% 0.19/1.30 % SZS status Theorem for theBenchmark
% 0.19/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.30 % (3409763)------------------------------
% 0.19/1.30 % (3409763)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.30 % (3409763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.30 % (3409763)CaDiCaL version: 2.1.3
% 0.19/1.30 % (3409763)Termination reason: Refutation
% 0.19/1.30 % (3409763)Time elapsed: 0.004 s
% 0.19/1.30 % (3409763)Peak memory usage: 89 MB
% 0.19/1.30 % (3409763)Instructions burned: 5 (million)
% 0.19/1.30 % (3409763)------------------------------
% 0.19/1.30 % (3409763)------------------------------
% 0.19/1.30 % (3409755)Success in time 0.438 s
% 0.19/1.30 % Vampire exiting
%------------------------------------------------------------------------------