%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW486_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 : n009.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 3.68s 1.29s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 18 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 3 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 38 ( 36 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-4 aty)
% Number of variables : 12 ( 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
complex: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
poly1: $tType > $tType ).
tff(type_def_8,type,
real: $tType ).
tff(type_def_9,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_3,type,
pCons:
!>[X0: $tType] : ( ( X0 * poly1(X0) ) > poly1(X0) ) ).
tff(func_def_4,type,
poly:
!>[X0: $tType] : ( poly1(X0) > fun(X0,X0) ) ).
tff(func_def_5,type,
norm_norm:
!>[X0: $tType] : ( X0 > real ) ).
tff(func_def_6,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_7,type,
fFalse: bool ).
tff(func_def_8,type,
fTrue: bool ).
tff(func_def_9,type,
c: complex ).
tff(func_def_10,type,
cs: poly1(complex) ).
tff(func_def_11,type,
m: real ).
tff(func_def_12,type,
r: real ).
tff(func_def_13,type,
z: complex ).
tff(func_def_14,type,
sK0:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_15,type,
sK1: real ).
tff(func_def_16,type,
sK2: real ).
tff(pred_def_1,type,
cancel1352612707id_add:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
idom:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
order:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
mult_zero:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
preorder:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
comm_semiring_0:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
linordered_ring:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
comm_monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
no_zero_divisors:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
ab_semigroup_mult:
!>[X0: $tType] : $o ).
tff(pred_def_18,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_19,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_20,type,
ring_n68954251visors:
!>[X0: $tType] : $o ).
tff(pred_def_21,type,
linord581940658strict:
!>[X0: $tType] : $o ).
tff(pred_def_22,type,
real_normed_vector:
!>[X0: $tType] : $o ).
tff(pred_def_23,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_24,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_25,type,
ordere216010020id_add:
!>[X0: $tType] : $o ).
tff(pred_def_26,type,
real_normed_algebra:
!>[X0: $tType] : $o ).
tff(pred_def_27,type,
ordere779506340up_add:
!>[X0: $tType] : $o ).
tff(pred_def_28,type,
ab_sem1668676832m_mult:
!>[X0: $tType] : $o ).
tff(pred_def_29,type,
linord20386208strict:
!>[X0: $tType] : $o ).
tff(pred_def_30,type,
real_n1866405975lgebra:
!>[X0: $tType] : $o ).
tff(pred_def_31,type,
linord893533164strict:
!>[X0: $tType] : $o ).
tff(pred_def_32,type,
ordere236663937imp_le:
!>[X0: $tType] : $o ).
tff(pred_def_33,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
tff(pred_def_34,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_35,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_36,type,
pp: bool > $o ).
tff(f1,axiom,
ord_less_eq(real,norm_norm(complex,plus_plus(complex,c,times_times(complex,z,aa(complex,complex,poly(complex,cs),z)))),plus_plus(real,norm_norm(complex,c),norm_norm(complex,times_times(complex,z,aa(complex,complex,poly(complex,cs),z))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096cmod_A_Ic_A_L_Az_A_K_Apoly_Acs_Az_J_A_060_061_Acmod_Ac_A_L_Acmod_A_Iz_A_K_Apoly_Acs_Az_J_096) ).
tff(f5,axiom,
! [X0: $tType] :
( comm_semiring_0(X0)
=> ! [X1: X0,X2: poly1(X0),X3: X0] : ( aa(X0,X0,poly(X0,pCons(X0,X3,X2)),X1) = plus_plus(X0,X3,times_times(X0,X1,aa(X0,X0,poly(X0,X2),X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_poly__pCons) ).
tff(f152,axiom,
comm_semiring_0(complex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ocomm__semiring__0) ).
tff(f187,conjecture,
ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,pCons(complex,c,cs)),z)),plus_plus(real,norm_norm(complex,c),norm_norm(complex,times_times(complex,z,aa(complex,complex,poly(complex,cs),z))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f188,negated_conjecture,
~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,pCons(complex,c,cs)),z)),plus_plus(real,norm_norm(complex,c),norm_norm(complex,times_times(complex,z,aa(complex,complex,poly(complex,cs),z))))),
inference(negated_conjecture,[status(cth)],[f187]) ).
tff(f189,plain,
~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,pCons(complex,c,cs)),z)),plus_plus(real,norm_norm(complex,c),norm_norm(complex,times_times(complex,z,aa(complex,complex,poly(complex,cs),z))))),
inference(flattening,[],[f188]) ).
tff(f194,plain,
! [X0: $tType] :
( ! [X1: X0,X2: poly1(X0),X3: X0] : ( aa(X0,X0,poly(X0,pCons(X0,X3,X2)),X1) = plus_plus(X0,X3,times_times(X0,X1,aa(X0,X0,poly(X0,X2),X1))) )
| ~ comm_semiring_0(X0) ),
inference(ennf_transformation,[],[f5]) ).
tff(f213,plain,
~ ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,pCons(complex,c,cs)),z)),plus_plus(real,norm_norm(complex,c),norm_norm(complex,times_times(complex,z,aa(complex,complex,poly(complex,cs),z))))),
inference(cnf_transformation,[],[f189]) ).
tff(f221,plain,
! [X0: $tType,X2: poly1(X0),X3: X0,X1: X0] :
( ( aa(X0,X0,poly(X0,pCons(X0,X3,X2)),X1) = plus_plus(X0,X3,times_times(X0,X1,aa(X0,X0,poly(X0,X2),X1))) )
| ~ comm_semiring_0(X0) ),
inference(cnf_transformation,[],[f194]) ).
tff(f227,plain,
ord_less_eq(real,norm_norm(complex,plus_plus(complex,c,times_times(complex,z,aa(complex,complex,poly(complex,cs),z)))),plus_plus(real,norm_norm(complex,c),norm_norm(complex,times_times(complex,z,aa(complex,complex,poly(complex,cs),z))))),
inference(cnf_transformation,[],[f1]) ).
tff(f235,plain,
comm_semiring_0(complex),
inference(cnf_transformation,[],[f152]) ).
tff(f314,plain,
( ord_less_eq(real,norm_norm(complex,aa(complex,complex,poly(complex,pCons(complex,c,cs)),z)),plus_plus(real,norm_norm(complex,c),norm_norm(complex,times_times(complex,z,aa(complex,complex,poly(complex,cs),z)))))
| ~ comm_semiring_0(complex) ),
inference(superposition,[],[f227,f221]) ).
tff(f315,plain,
~ comm_semiring_0(complex),
inference(forward_subsumption_resolution,[],[f314,f213]) ).
tff(f316,plain,
$false,
inference(forward_subsumption_resolution,[],[f315,f235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW486_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n009.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 14:14:00 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 3.68/1.29 % (3049560)Detected formulas, will run a generic FOF schedule.
% 3.68/1.29 % (3049571)dis-21_1_sil=8000:lcm=predicate:random_seed=3770252723: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)
% 3.68/1.29 % (3049571)Instruction limit reached!
% 3.68/1.29 % (3049571)------------------------------
% 3.68/1.29 % (3049571)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.29 % (3049571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.29 % (3049571)CaDiCaL version: 2.1.3
% 3.68/1.29 % (3049571)Termination reason: Instruction limit
% 3.68/1.29 % (3049571)Termination phase: Saturation
% 3.68/1.29 % (3049571)Time elapsed: 0.037 s
% 3.68/1.29 % (3049571)Peak memory usage: 89 MB
% 3.68/1.29 % (3049571)Instructions burned: 132 (million)
% 3.68/1.29 % (3049570)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=286633467:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.68/1.29 % (3049566)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=1688949896:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.68/1.29 % (3049568)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1605995536:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.68/1.29 % (3049565)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=348240850:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.68/1.29 % (3049569)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=553203205:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.68/1.29 % (3049567)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=1635529135:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.68/1.29 % (3049568)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.68/1.29 % (3049568)Refutation not found, incomplete strategy
% 3.68/1.29 % (3049568)------------------------------
% 3.68/1.29 % (3049568)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.29 % (3049568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.29 % (3049568)CaDiCaL version: 2.1.3
% 3.68/1.29 % (3049568)Termination reason: Refutation not found, incomplete strategy
% 3.68/1.29 % (3049568)Time elapsed: 0.002 s
% 3.68/1.29 % (3049568)Peak memory usage: 88 MB
% 3.68/1.29 % (3049568)Instructions burned: 1 (million)
% 3.68/1.29 % (3049567)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.68/1.29 % (3049569)First to succeed.
% 3.68/1.29 % (3049569)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3049560"
% 3.68/1.29 % (3049570)Instruction limit reached!
% 3.68/1.29 % (3049570)------------------------------
% 3.68/1.29 % (3049570)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.29 % (3049570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.29 % (3049570)CaDiCaL version: 2.1.3
% 3.68/1.29 % (3049570)Termination reason: Instruction limit
% 3.68/1.29 % (3049570)Termination phase: Saturation
% 3.68/1.29 % (3049570)Time elapsed: 0.091 s
% 3.68/1.29 % (3049570)Peak memory usage: 89 MB
% 3.68/1.29 % (3049570)Instructions burned: 139 (million)
% 3.68/1.29 % (3049579)lrs+10_1_sil=8000:sp=occurrence:random_seed=2005800490:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.68/1.29 % (3049579)Also succeeded, but the first one will report.
% 3.68/1.29 % (3049568)------------------------------
% 3.68/1.29 % (3049568)------------------------------
% 3.68/1.29 % (3049580)lrs+10_1_sil=32000:urr=on:br=off:random_seed=92694045:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.68/1.29 % (3049569)Refutation found. Thanks to Tanya!
% 3.68/1.29 % SZS status Theorem for theBenchmark
% 3.68/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.68/1.29 % (3049569)------------------------------
% 3.68/1.29 % (3049569)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.29 % (3049569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.29 % (3049569)CaDiCaL version: 2.1.3
% 3.68/1.29 % (3049569)Termination reason: Refutation
% 3.68/1.29 % (3049569)Time elapsed: 0.006 s
% 3.68/1.29 % (3049569)Peak memory usage: 88 MB
% 3.68/1.29 % (3049569)Instructions burned: 8 (million)
% 3.68/1.29 % (3049569)------------------------------
% 3.68/1.29 % (3049569)------------------------------
% 3.68/1.29 % (3049560)Success in time 0.439 s
% 3.68/1.29 % Vampire exiting
%------------------------------------------------------------------------------