%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW492_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 : 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 4.00s 1.42s
% Output : Refutation 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 13 unt; 0 typ; 7 def)
% Number of atoms : 87 ( 37 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 90 ( 46 ~; 29 |; 4 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 28 ( 26 usr; 5 prp; 0-3 aty)
% Number of functors : 27 ( 27 usr; 3 con; 0-5 aty)
% Number of variables : 3 ( 0 sgn 3 !; 0 ?; 3 :)
% 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,
fundam1280195782_psize:
!>[X0: $tType] : ( poly(X0) > nat ) ).
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,
order1:
!>[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,
p: poly(a) ).
tff(func_def_23,type,
sK0: nat > nat ).
tff(func_def_24,type,
sK1: nat > nat ).
tff(pred_def_1,type,
comm_semiring_1:
!>[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,
order:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
semiring_1:
!>[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,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_11,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_12,type,
pp: bool > $o ).
tff(pred_def_13,type,
sP2: poly(a) > $o ).
tff(pred_def_14,type,
sP3: nat > $o ).
tff(pred_def_15,type,
sP4: poly(a) > $o ).
tff(pred_def_16,type,
sP5: poly(a) > $o ).
tff(pred_def_17,type,
sP6: nat > $o ).
tff(pred_def_18,type,
sP7: nat > $o ).
tff(pred_def_19,type,
sP8: nat > $o ).
tff(pred_def_20,type,
sP9: nat > $o ).
tff(pred_def_21,type,
sP10: nat > $o ).
tff(pred_def_22,type,
sP11: nat > $o ).
tff(f9,axiom,
! [X0: nat] : ( suc(X0) != zero_zero(nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_Suc__neq__Zero) ).
tff(f125,conjecture,
~ ( ( ( p != zero_zero(poly(a)) )
=> ( suc(degree(a,p)) = zero_zero(nat) ) )
<=> ( p != zero_zero(poly(a)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f126,negated_conjecture,
~ ~ ( ( ( p != zero_zero(poly(a)) )
=> ( suc(degree(a,p)) = zero_zero(nat) ) )
<=> ( p != zero_zero(poly(a)) ) ),
inference(negated_conjecture,[status(cth)],[f125]) ).
tff(f128,plain,
( ( ( p != zero_zero(poly(a)) )
=> ( suc(degree(a,p)) = zero_zero(nat) ) )
<=> ( p != zero_zero(poly(a)) ) ),
inference(flattening,[],[f126]) ).
tff(f130,plain,
( ( ( suc(degree(a,p)) = zero_zero(nat) )
| ( p = zero_zero(poly(a)) ) )
<=> ( p != zero_zero(poly(a)) ) ),
inference(ennf_transformation,[],[f128]) ).
tff(f140,plain,
( ( ( suc(degree(a,p)) = zero_zero(nat) )
| ( p = zero_zero(poly(a)) )
| ( p = zero_zero(poly(a)) ) )
& ( ( p != zero_zero(poly(a)) )
| ( ( zero_zero(nat) != suc(degree(a,p)) )
& ( p != zero_zero(poly(a)) ) ) ) ),
inference(nnf_transformation,[],[f130]) ).
tff(f141,plain,
( ( ( suc(degree(a,p)) = zero_zero(nat) )
| ( p = zero_zero(poly(a)) )
| ( p = zero_zero(poly(a)) ) )
& ( ( p != zero_zero(poly(a)) )
| ( ( zero_zero(nat) != suc(degree(a,p)) )
& ( p != zero_zero(poly(a)) ) ) ) ),
inference(flattening,[],[f140]) ).
tff(f146,plain,
( ( p != zero_zero(poly(a)) )
| ( p != zero_zero(poly(a)) ) ),
inference(cnf_transformation,[],[f141]) ).
tff(f148,plain,
( ( zero_zero(nat) = suc(degree(a,p)) )
| ( p = zero_zero(poly(a)) )
| ( p = zero_zero(poly(a)) ) ),
inference(cnf_transformation,[],[f141]) ).
tff(f155,plain,
! [X0: nat] : ( zero_zero(nat) != suc(X0) ),
inference(cnf_transformation,[],[f9]) ).
tff(f175,definition,
~ sP4(p),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
tff(f176,definition,
~ sP5(p),
introduced(definition,[new_symbols(definition,[sP5])],[inequality_splitting_name_introduction]) ).
tff(f177,plain,
( sP4(zero_zero(poly(a)))
| sP5(zero_zero(poly(a))) ),
inference(inequality_splitting,[],[f146,f176,f175]) ).
tff(f178,definition,
~ sP6(zero_zero(nat)),
introduced(definition,[new_symbols(definition,[sP6])],[inequality_splitting_name_introduction]) ).
tff(f179,plain,
! [X0: nat] : sP6(suc(X0)),
inference(inequality_splitting,[],[f155,f178]) ).
tff(f194,plain,
( ( zero_zero(nat) = suc(degree(a,p)) )
| ( p = zero_zero(poly(a)) ) ),
inference(duplicate_literal_removal,[],[f148]) ).
tff(f196,definition,
( spl12_1
<=> sP5(zero_zero(poly(a))) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
tff(f200,definition,
( spl12_2
<=> sP4(zero_zero(poly(a))) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
tff(f202,plain,
( sP4(zero_zero(poly(a)))
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f200]) ).
tff(f203,plain,
( spl12_1
| spl12_2 ),
inference(avatar_split_clause,[],[f177,f200,f196]) ).
tff(f214,definition,
( spl12_5
<=> ( p = zero_zero(poly(a)) ) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
tff(f216,plain,
( ( p = zero_zero(poly(a)) )
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f214]) ).
tff(f218,definition,
( spl12_6
<=> ( zero_zero(nat) = suc(degree(a,p)) ) ),
introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition]) ).
tff(f220,plain,
( ( zero_zero(nat) = suc(degree(a,p)) )
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f218]) ).
tff(f221,plain,
( spl12_5
| spl12_6 ),
inference(avatar_split_clause,[],[f194,f218,f214]) ).
tff(f225,plain,
( ~ sP5(zero_zero(poly(a)))
| ~ spl12_5 ),
inference(superposition,[],[f176,f216]) ).
tff(f226,plain,
( ~ sP4(zero_zero(poly(a)))
| ~ spl12_5 ),
inference(superposition,[],[f175,f216]) ).
tff(f229,plain,
( $false
| ~ spl12_2
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f226,f202]) ).
tff(f230,plain,
( ~ spl12_2
| ~ spl12_5 ),
inference(avatar_contradiction_clause,[],[f229]) ).
tff(f231,plain,
( ~ spl12_1
| ~ spl12_5 ),
inference(avatar_split_clause,[],[f225,f214,f196]) ).
tff(f247,plain,
( sP6(zero_zero(nat))
| ~ spl12_6 ),
inference(superposition,[],[f179,f220]) ).
tff(f263,plain,
( $false
| ~ spl12_6 ),
inference(forward_subsumption_resolution,[],[f247,f178]) ).
tff(f264,plain,
~ spl12_6,
inference(avatar_contradiction_clause,[],[f263]) ).
cnf(s1,plain,
( spl12_1
| spl12_2 ),
inference(sat_conversion,[],[f203]) ).
cnf(s3,plain,
( spl12_5
| spl12_6 ),
inference(sat_conversion,[],[f221]) ).
cnf(s5,plain,
( ~ spl12_2
| ~ spl12_5 ),
inference(sat_conversion,[],[f230]) ).
cnf(s6,plain,
( ~ spl12_1
| ~ spl12_5 ),
inference(sat_conversion,[],[f231]) ).
cnf(s12,plain,
~ spl12_6,
inference(sat_conversion,[],[f264]) ).
cnf(s14,plain,
spl12_5,
inference(rat,[],[s3,s12]) ).
cnf(s15,plain,
~ spl12_1,
inference(rat,[],[s6,s14]) ).
cnf(s16,plain,
~ spl12_2,
inference(rat,[],[s5,s14]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s1,s16,s15]) ).
tff(f275,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW492_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 % Computer : n018.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Mon Sep 28 14:16:55 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.28 Running first-order theorem proving
% 0.26/0.28 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
% 4.00/1.42 % (3410870)Detected formulas, will run a generic FOF schedule.
% 4.00/1.42 % (3410878)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=231202258:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.00/1.42 % (3410878)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.00/1.42 % (3410878)First to succeed.
% 4.00/1.42 % (3410878)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3410870"
% 4.00/1.42 % (3410880)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2770350155:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.00/1.42 % (3410877)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=3261606555:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.00/1.42 % (3410875)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=31460715:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.00/1.42 % (3410879)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3023397524:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.00/1.42 % (3410876)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=123795629:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.00/1.42 % (3410879)Also succeeded, but the first one will report.
% 4.00/1.42 % (3410877)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.00/1.42 % (3410880)Also succeeded, but the first one will report.
% 4.00/1.42 % (3410881)dis-21_1_sil=8000:lcm=predicate:random_seed=2038301266: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)
% 4.00/1.42 % (3410881)Also succeeded, but the first one will report.
% 4.00/1.42 % (3410878)Refutation found. Thanks to Tanya!
% 4.00/1.42 % SZS status Theorem for theBenchmark
% 4.00/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 4.00/1.42 % (3410878)------------------------------
% 4.00/1.42 % (3410878)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.00/1.42 % (3410878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.00/1.42 % (3410878)CaDiCaL version: 2.1.3
% 4.00/1.42 % (3410878)Termination reason: Refutation
% 4.00/1.42 % (3410878)Time elapsed: 0.005 s
% 4.00/1.42 % (3410878)Peak memory usage: 89 MB
% 4.00/1.42 % (3410878)Instructions burned: 4 (million)
% 4.00/1.42 % (3410878)------------------------------
% 4.00/1.42 % (3410878)------------------------------
% 4.00/1.42 % (3410870)Success in time 0.458 s
% 4.00/1.42 % Vampire exiting
%------------------------------------------------------------------------------