%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW490_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 3.48s 1.25s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 18 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 3 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 32 ( 32 usr; 3 con; 0-5 aty)
% Number of variables : 8 ( 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
a: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(type_def_8,type,
poly: $tType > $tType ).
tff(type_def_9,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
fundam296178794t_poly:
!>[X0: $tType] : ( ( poly(X0) * X0 ) > poly(X0) ) ).
tff(func_def_1,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_3,type,
if:
!>[X0: $tType] : ( ( bool * X0 * X0 ) > X0 ) ).
tff(func_def_4,type,
suc: nat > nat ).
tff(func_def_5,type,
nat_case:
!>[X0: $tType] : ( ( X0 * fun(nat,X0) ) > fun(nat,X0) ) ).
tff(func_def_6,type,
semiri532925092at_aux:
!>[X0: $tType] : ( ( fun(X0,X0) * nat * X0 ) > X0 ) ).
tff(func_def_7,type,
abs_poly:
!>[X0: $tType] : ( fun(nat,X0) > poly(X0) ) ).
tff(func_def_8,type,
coeff:
!>[X0: $tType] : ( poly(X0) > fun(nat,X0) ) ).
tff(func_def_9,type,
degree:
!>[X0: $tType] : ( poly(X0) > nat ) ).
tff(func_def_10,type,
monom:
!>[X0: $tType] : ( ( X0 * nat ) > poly(X0) ) ).
tff(func_def_11,type,
order:
!>[X0: $tType] : ( ( X0 * poly(X0) ) > nat ) ).
tff(func_def_12,type,
pCons:
!>[X0: $tType] : ( ( X0 * poly(X0) ) > poly(X0) ) ).
tff(func_def_13,type,
pcompose:
!>[X0: $tType] : ( ( poly(X0) * poly(X0) ) > poly(X0) ) ).
tff(func_def_14,type,
poly1:
!>[X0: $tType] : ( poly(X0) > fun(X0,X0) ) ).
tff(func_def_15,type,
poly_rec:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(poly(X1),fun(X0,X0))) * poly(X1) ) > X0 ) ).
tff(func_def_16,type,
smult:
!>[X0: $tType] : ( ( X0 * poly(X0) ) > poly(X0) ) ).
tff(func_def_17,type,
synthetic_div:
!>[X0: $tType] : ( ( poly(X0) * X0 ) > poly(X0) ) ).
tff(func_def_18,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_19,type,
fFalse: bool ).
tff(func_def_20,type,
fTrue: bool ).
tff(func_def_21,type,
fequal:
!>[X0: $tType] : ( ( X0 * X0 ) > bool ) ).
tff(func_def_22,type,
h: a ).
tff(func_def_23,type,
sK0:
!>[X0: $tType] : ( poly(X0) > X0 ) ).
tff(func_def_24,type,
sK1:
!>[X0: $tType] : ( poly(X0) > poly(X0) ) ).
tff(func_def_25,type,
sK2:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_26,type,
sK3: nat > nat ).
tff(func_def_27,type,
sK4: nat > nat ).
tff(func_def_28,type,
sK5:
!>[X0: $tType] : ( ( poly(X0) * poly(X0) ) > nat ) ).
tff(func_def_29,type,
sK6:
!>[X0: $tType] : ( ( poly(X0) * poly(X0) ) > nat ) ).
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,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
comm_semiring_0:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
comm_monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
pp: bool > $o ).
tff(f1,axiom,
! [X0: $tType] :
( comm_semiring_0(X0)
=> ! [X3: X0] : ( fundam296178794t_poly(X0,zero_zero(poly(X0)),X3) = zero_zero(poly(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_offset__poly__0) ).
tff(f134,conjecture,
degree(a,fundam296178794t_poly(a,zero_zero(poly(a)),h)) = degree(a,zero_zero(poly(a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f135,negated_conjecture,
( ( ~ degree(a,fundam296178794t_poly(a,zero_zero(poly(a)),h)) ) = degree(a,zero_zero(poly(a))) ),
inference(negated_conjecture,[status(cth)],[f134]) ).
tff(f136,axiom,
comm_semiring_0(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
tff(f137,plain,
degree(a,fundam296178794t_poly(a,zero_zero(poly(a)),h)) != degree(a,zero_zero(poly(a))),
inference(flattening,[],[f135]) ).
tff(f138,plain,
! [X0: $tType] :
( comm_semiring_0(X0)
=> ! [X1: X0] : ( zero_zero(poly(X0)) = fundam296178794t_poly(X0,zero_zero(poly(X0)),X1) ) ),
inference(rectify,[],[f1]) ).
tff(f143,plain,
! [X0: $tType] :
( ! [X1: X0] : ( zero_zero(poly(X0)) = fundam296178794t_poly(X0,zero_zero(poly(X0)),X1) )
| ~ comm_semiring_0(X0) ),
inference(ennf_transformation,[],[f138]) ).
tff(f195,plain,
degree(a,fundam296178794t_poly(a,zero_zero(poly(a)),h)) != degree(a,zero_zero(poly(a))),
inference(cnf_transformation,[],[f137]) ).
tff(f196,plain,
comm_semiring_0(a),
inference(cnf_transformation,[],[f136]) ).
tff(f202,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(poly(X0)) = fundam296178794t_poly(X0,zero_zero(poly(X0)),X1) )
| ~ comm_semiring_0(X0) ),
inference(cnf_transformation,[],[f143]) ).
tff(f319,plain,
( ( degree(a,zero_zero(poly(a))) != degree(a,zero_zero(poly(a))) )
| ~ comm_semiring_0(a) ),
inference(superposition,[],[f195,f202]) ).
tff(f320,plain,
~ comm_semiring_0(a),
inference(trivial_inequality_removal,[],[f319]) ).
tff(f321,plain,
$false,
inference(forward_subsumption_resolution,[],[f320,f196]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW490_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n017.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Mon Sep 28 14:10:21 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running first-order theorem proving
% 0.10/0.21 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.48/1.25 % (3575155)Detected formulas, will run a generic FOF schedule.
% 3.48/1.25 % (3575166)dis-21_1_sil=8000:lcm=predicate:random_seed=1320391721: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)
% 3.48/1.25 % (3575164)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=80208638:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.48/1.25 % (3575160)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=3111628904:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.48/1.25 % (3575161)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=365450573:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.48/1.25 % (3575162)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=1318811607:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.48/1.25 % (3575163)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2552327984:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.48/1.25 % (3575164)First to succeed.
% 3.48/1.25 % (3575163)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.48/1.25 % (3575164)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3575155"
% 3.48/1.25 % (3575163)Also succeeded, but the first one will report.
% 3.48/1.25 % (3575162)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.48/1.25 % (3575166)Instruction limit reached!
% 3.48/1.25 % (3575166)------------------------------
% 3.48/1.25 % (3575166)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.25 % (3575166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.25 % (3575166)CaDiCaL version: 2.1.3
% 3.48/1.25 % (3575166)Termination reason: Instruction limit
% 3.48/1.25 % (3575166)Termination phase: Saturation
% 3.48/1.25 % (3575166)Time elapsed: 0.043 s
% 3.48/1.25 % (3575166)Peak memory usage: 90 MB
% 3.48/1.25 % (3575166)Instructions burned: 130 (million)
% 3.48/1.25 % (3575165)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3588474961:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.48/1.25 % (3575165)Also succeeded, but the first one will report.
% 3.48/1.25 % (3575174)lrs+10_1_sil=8000:sp=occurrence:random_seed=2856999796:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.48/1.25 % (3575174)Also succeeded, but the first one will report.
% 3.48/1.25 % (3575164)Refutation found. Thanks to Tanya!
% 3.48/1.25 % SZS status Theorem for theBenchmark
% 3.48/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.25 % (3575164)------------------------------
% 3.48/1.25 % (3575164)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.25 % (3575164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.25 % (3575164)CaDiCaL version: 2.1.3
% 3.48/1.25 % (3575164)Termination reason: Refutation
% 3.48/1.25 % (3575164)Time elapsed: 0.006 s
% 3.48/1.25 % (3575164)Peak memory usage: 88 MB
% 3.48/1.25 % (3575164)Instructions burned: 7 (million)
% 3.48/1.25 % (3575164)------------------------------
% 3.48/1.25 % (3575164)------------------------------
% 3.48/1.25 % (3575155)Success in time 0.411 s
% 3.48/1.25 % Vampire exiting
%------------------------------------------------------------------------------