TSTP Solution File: SWW488_5 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SWW488_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:33:15 EDT 2024
% Result : Theorem 0.22s 0.43s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 20 ~; 15 |; 0 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 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 : 31 ( 29 usr; 4 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 4 con; 0-5 aty)
% Number of variables : 16 ( 16 !; 0 ?; 16 :)
% 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,
poly1: $tType > $tType ).
tff(type_def_9,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
fundam296178794t_poly:
!>[X0: $tType] : ( ( poly1(X0) * X0 ) > poly1(X0) ) ).
tff(func_def_1,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_3,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_4,type,
ring_1_Ints:
!>[X0: $tType] : fun(X0,bool) ).
tff(func_def_5,type,
coeff:
!>[X0: $tType] : ( poly1(X0) > fun(nat,X0) ) ).
tff(func_def_6,type,
monom:
!>[X0: $tType] : ( ( X0 * nat ) > poly1(X0) ) ).
tff(func_def_7,type,
order:
!>[X0: $tType] : ( ( X0 * poly1(X0) ) > nat ) ).
tff(func_def_8,type,
pcompose:
!>[X0: $tType] : ( ( poly1(X0) * poly1(X0) ) > poly1(X0) ) ).
tff(func_def_9,type,
poly:
!>[X0: $tType] : ( poly1(X0) > fun(X0,X0) ) ).
tff(func_def_10,type,
poly_rec:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(poly1(X1),fun(X0,X0))) * poly1(X1) ) > X0 ) ).
tff(func_def_11,type,
synthetic_div:
!>[X0: $tType] : ( ( poly1(X0) * X0 ) > poly1(X0) ) ).
tff(func_def_12,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_13,type,
fFalse: bool ).
tff(func_def_14,type,
fTrue: bool ).
tff(func_def_15,type,
h: a ).
tff(func_def_16,type,
x: a ).
tff(func_def_17,type,
sK0:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
comm_ring_1:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
cancel1352612707id_add:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
idom:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
ring_1:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
zero_neq_one:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
comm_semiring_0:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
comm_monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_18,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_19,type,
ordere216010020id_add:
!>[X0: $tType] : $o ).
tff(pred_def_20,type,
ordere236663937imp_le:
!>[X0: $tType] : $o ).
tff(pred_def_21,type,
ordere223160158up_add:
!>[X0: $tType] : $o ).
tff(pred_def_22,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
tff(pred_def_23,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_24,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_25,type,
pp: bool > $o ).
tff(pred_def_26,type,
sP1: a > $o ).
tff(f256,plain,
$false,
inference(avatar_sat_refutation,[],[f240,f246,f248,f255]) ).
tff(f255,plain,
( ~ spl2_1
| ~ spl2_3
| spl2_2 ),
inference(avatar_split_clause,[],[f254,f237,f243,f233]) ).
tff(f233,plain,
( spl2_1
<=> comm_semiring_0(a) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
tff(f243,plain,
( spl2_3
<=> sP1(zero_zero(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
tff(f237,plain,
( spl2_2
<=> sP1(aa(a,a,poly(a,zero_zero(poly1(a))),x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
tff(f254,plain,
( ~ sP1(zero_zero(a))
| ~ comm_semiring_0(a)
| spl2_2 ),
inference(superposition,[],[f239,f197]) ).
tff(f197,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = aa(X0,X0,poly(X0,zero_zero(poly1(X0))),X1) )
| ~ comm_semiring_0(X0) ),
inference(cnf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: $tType] :
( ! [X1: X0] : ( zero_zero(X0) = aa(X0,X0,poly(X0,zero_zero(poly1(X0))),X1) )
| ~ comm_semiring_0(X0) ),
inference(ennf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: $tType] :
( comm_semiring_0(X0)
=> ! [X1: X0] : ( zero_zero(X0) = aa(X0,X0,poly(X0,zero_zero(poly1(X0))),X1) ) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X0: $tType] :
( comm_semiring_0(X0)
=> ! [X3: X0] : ( aa(X0,X0,poly(X0,zero_zero(poly1(X0))),X3) = zero_zero(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f239,plain,
( ~ sP1(aa(a,a,poly(a,zero_zero(poly1(a))),x))
| spl2_2 ),
inference(avatar_component_clause,[],[f237]) ).
tff(f248,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f247]) ).
tff(f247,plain,
( $false
| spl2_1 ),
inference(resolution,[],[f235,f194]) ).
tff(f194,plain,
comm_semiring_0(a),
inference(cnf_transformation,[],[f145]) ).
tff(f145,axiom,
comm_semiring_0(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f235,plain,
( ~ comm_semiring_0(a)
| spl2_1 ),
inference(avatar_component_clause,[],[f233]) ).
tff(f246,plain,
( ~ spl2_1
| spl2_3 ),
inference(avatar_split_clause,[],[f241,f243,f233]) ).
tff(f241,plain,
( sP1(zero_zero(a))
| ~ comm_semiring_0(a) ),
inference(superposition,[],[f226,f197]) ).
tff(f226,plain,
sP1(aa(a,a,poly(a,zero_zero(poly1(a))),plus_plus(a,h,x))),
inference(inequality_splitting,[],[f193,f225]) ).
tff(f225,plain,
~ sP1(aa(a,a,poly(a,fundam296178794t_poly(a,zero_zero(poly1(a)),h)),x)),
introduced(inequality_splitting_name_introduction,[new_symbols(naming,[sP1])]) ).
tff(f193,plain,
aa(a,a,poly(a,fundam296178794t_poly(a,zero_zero(poly1(a)),h)),x) != aa(a,a,poly(a,zero_zero(poly1(a))),plus_plus(a,h,x)),
inference(cnf_transformation,[],[f146]) ).
tff(f146,plain,
aa(a,a,poly(a,fundam296178794t_poly(a,zero_zero(poly1(a)),h)),x) != aa(a,a,poly(a,zero_zero(poly1(a))),plus_plus(a,h,x)),
inference(flattening,[],[f144]) ).
tff(f144,negated_conjecture,
( ~ aa(a,a,poly(a,fundam296178794t_poly(a,zero_zero(poly1(a)),h)),x) = aa(a,a,poly(a,zero_zero(poly1(a))),plus_plus(a,h,x)) ),
inference(negated_conjecture,[],[f143]) ).
tff(f143,conjecture,
aa(a,a,poly(a,fundam296178794t_poly(a,zero_zero(poly1(a)),h)),x) = aa(a,a,poly(a,zero_zero(poly1(a))),plus_plus(a,h,x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f240,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f231,f237,f233]) ).
tff(f231,plain,
( ~ sP1(aa(a,a,poly(a,zero_zero(poly1(a))),x))
| ~ comm_semiring_0(a) ),
inference(superposition,[],[f225,f195]) ).
tff(f195,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(poly1(X0)) = fundam296178794t_poly(X0,zero_zero(poly1(X0)),X1) )
| ~ comm_semiring_0(X0) ),
inference(cnf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: $tType] :
( ! [X1: X0] : ( zero_zero(poly1(X0)) = fundam296178794t_poly(X0,zero_zero(poly1(X0)),X1) )
| ~ comm_semiring_0(X0) ),
inference(ennf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: $tType] :
( comm_semiring_0(X0)
=> ! [X1: X0] : ( zero_zero(poly1(X0)) = fundam296178794t_poly(X0,zero_zero(poly1(X0)),X1) ) ),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
! [X0: $tType] :
( comm_semiring_0(X0)
=> ! [X2: X0] : ( zero_zero(poly1(X0)) = fundam296178794t_poly(X0,zero_zero(poly1(X0)),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW488_5 : TPTP v8.2.0. Released v6.0.0.
% 0.07/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 06:30:24 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.36 This is a TF1_THM_EQU_NAR problem
% 0.12/0.36 Running first-order theorem proving
% 0.12/0.36 Running /export/starexec/sandbox2/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.43 % (23830)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (23834)lrs+10_1:3_drc=off:sil=256000:sp=unary_first:lwlo=on:i=216875:kws=precedence:ins=3:rawr=on:nwc=10.0_0 on theBenchmark for (2999ds/216875Mi)
% 0.22/0.43 % (23830)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (23835)dis+1011_3:1_sil=256000:tgt=ground:sac=on:i=109:sd=1:ss=included_0 on theBenchmark for (2999ds/109Mi)
% 0.22/0.43 % (23830)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (23836)dis+1010_1:1_sil=2000:nwc=3.0:s2a=on:i=132:ins=5:fsr=off:ss=axioms:sd=2:fd=off_0 on theBenchmark for (2999ds/132Mi)
% 0.22/0.43 % (23830)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (23833)lrs+1010_2201:262144_anc=all:drc=encompass:sil=256000:sims=off:sp=frequency:spb=goal_then_units:rp=on:lwlo=on:st=3.0:i=179501:bs=unit_only:nm=6:ins=2:fsd=on:ss=axioms:sgt=16:afr=on:tgt=ground:awrs=decay:awrsf=200:acc=on:ccuc=first_0 on theBenchmark for (2999ds/179501Mi)
% 0.22/0.43 % (23830)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (23837)dis+1010_159245:1048576_to=lpo:sil=2000:etr=on:sp=unary_frequency:spb=goal:rnwc=on:nwc=10.9066:st=2:i=124:sd=1:nm=3:av=off:ss=axioms:rawr=on:drc=encompass:foolp=on:sgt=5:cond=fast:er=filter:erape=on:erml=2:s2a=on_0 on theBenchmark for (2999ds/124Mi)
% 0.22/0.43 % (23830)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (23831)lrs+1011_1:12_anc=none:drc=off:sil=64000:sims=off:sp=unary_first:spb=goal_then_units:lsd=20:rnwc=on:nwc=2.0:i=53554:add=off:awrs=converge:bd=off:uhcvi=on:tgt=ground:afp=300:afq=1.63_0 on theBenchmark for (2999ds/53554Mi)
% 0.22/0.43 % (23830)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (23832)dis+11_1:1_nwc=5.0:s2a=on:i=66616:s2at=3.0:sil=128000:bd=off_0 on theBenchmark for (2999ds/66616Mi)
% 0.22/0.43 % (23836)First to succeed.
% 0.22/0.43 % (23836)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-23830"
% 0.22/0.43 % (23837)Also succeeded, but the first one will report.
% 0.22/0.43 % (23830)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (23836)Refutation found. Thanks to Tanya!
% 0.22/0.43 % SZS status Theorem for theBenchmark
% 0.22/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.43 % (23836)------------------------------
% 0.22/0.43 % (23836)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.22/0.43 % (23836)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.22/0.43 % (23836)Termination reason: Refutation
% 0.22/0.43
% 0.22/0.43 % (23836)Memory used [KB]: 1184
% 0.22/0.43 % (23836)Time elapsed: 0.006 s
% 0.22/0.43 % (23836)Instructions burned: 5 (million)
% 0.22/0.43 % (23836)------------------------------
% 0.22/0.43 % (23836)------------------------------
% 0.22/0.43 % (23830)Success in time 0.057 s
%------------------------------------------------------------------------------