%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW488_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 : n026.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 3.56s 1.28s
% Output : Refutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 12 unt; 0 typ; 1 def)
% Number of atoms : 32 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 15 ~; 7 |; 0 &)
% ( 0 <=>; 3 =>; 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 : 28 ( 26 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 4 con; 0-5 aty)
% Number of variables : 14 ( 14 !; 0 ?; 14 :)
% 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(f1,axiom,
! [X0: $tType] :
( comm_semiring_0(X0)
=> ! [X2: X0] : ( fundam296178794t_poly(X0,zero_zero(poly1(X0)),X2) = zero_zero(poly1(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_offset__poly__0) ).
tff(f2,axiom,
! [X0: $tType] :
( comm_semiring_0(X0)
=> ! [X1: X0] : ( aa(X0,X0,poly(X0,zero_zero(poly1(X0))),X1) = zero_zero(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_poly__0) ).
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',conj_0) ).
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,[status(cth)],[f143]) ).
tff(f145,axiom,
comm_semiring_0(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
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(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(f149,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(f151,plain,
! [X0: $tType] :
( ! [X1: X0] : ( aa(X0,X0,poly(X0,zero_zero(poly1(X0))),X1) = zero_zero(X0) )
| ~ comm_semiring_0(X0) ),
inference(ennf_transformation,[],[f2]) ).
tff(f155,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(f156,plain,
comm_semiring_0(a),
inference(cnf_transformation,[],[f145]) ).
tff(f157,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(poly1(X0)) = fundam296178794t_poly(X0,zero_zero(poly1(X0)),X1) )
| ~ comm_semiring_0(X0) ),
inference(cnf_transformation,[],[f149]) ).
tff(f159,plain,
! [X0: $tType,X1: X0] :
( ( aa(X0,X0,poly(X0,zero_zero(poly1(X0))),X1) = zero_zero(X0) )
| ~ comm_semiring_0(X0) ),
inference(cnf_transformation,[],[f151]) ).
tff(f163,definition,
~ sP1(aa(a,a,poly(a,fundam296178794t_poly(a,zero_zero(poly1(a)),h)),x)),
introduced(definition,[new_symbols(definition,[sP1])],[inequality_splitting_name_introduction]) ).
tff(f164,plain,
sP1(aa(a,a,poly(a,zero_zero(poly1(a))),plus_plus(a,h,x))),
inference(inequality_splitting,[],[f155,f163]) ).
tff(f165,plain,
( ~ sP1(aa(a,a,poly(a,zero_zero(poly1(a))),x))
| ~ comm_semiring_0(a) ),
inference(superposition,[],[f163,f157]) ).
tff(f166,plain,
~ sP1(aa(a,a,poly(a,zero_zero(poly1(a))),x)),
inference(forward_subsumption_resolution,[],[f165,f156]) ).
tff(f167,plain,
( sP1(zero_zero(a))
| ~ comm_semiring_0(a) ),
inference(superposition,[],[f164,f159]) ).
tff(f168,plain,
sP1(zero_zero(a)),
inference(forward_subsumption_resolution,[],[f167,f156]) ).
tff(f169,plain,
( ~ sP1(zero_zero(a))
| ~ comm_semiring_0(a) ),
inference(superposition,[],[f166,f159]) ).
tff(f170,plain,
~ comm_semiring_0(a),
inference(forward_subsumption_resolution,[],[f169,f168]) ).
tff(f171,plain,
$false,
inference(forward_subsumption_resolution,[],[f170,f156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW488_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n026.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 14:17:27 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running first-order theorem proving
% 0.10/0.23 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
% 3.56/1.28 % (3871270)Detected formulas, will run a generic FOF schedule.
% 3.56/1.28 % (3871328)dis-21_1_sil=8000:lcm=predicate:random_seed=1616853464: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)
% 3.56/1.28 % (3871328)Instruction limit reached!
% 3.56/1.28 % (3871328)------------------------------
% 3.56/1.28 % (3871328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.28 % (3871328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.28 % (3871328)CaDiCaL version: 2.1.3
% 3.56/1.28 % (3871328)Termination reason: Instruction limit
% 3.56/1.28 % (3871328)Termination phase: Saturation
% 3.56/1.28 % (3871328)Time elapsed: 0.043 s
% 3.56/1.28 % (3871328)Peak memory usage: 90 MB
% 3.56/1.28 % (3871328)Instructions burned: 132 (million)
% 3.56/1.28 % (3871327)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=422346749:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.56/1.28 % (3871322)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=1714612066:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.56/1.28 % (3871324)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=4282294214:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.56/1.28 % (3871326)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1851597230:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.56/1.28 % (3871323)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=917132773:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.56/1.28 % (3871325)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2347043349:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.56/1.28 % (3871325)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.56/1.28 % (3871325)First to succeed.
% 3.56/1.28 % (3871325)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3871270"
% 3.56/1.28 % (3871324)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.56/1.28 % (3871326)Also succeeded, but the first one will report.
% 3.56/1.28 % (3871327)Also succeeded, but the first one will report.
% 3.56/1.28 % (3871336)lrs+10_1_sil=8000:sp=occurrence:random_seed=1968292307:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.56/1.28 % (3871336)Also succeeded, but the first one will report.
% 3.56/1.28 % (3871325)Refutation found. Thanks to Tanya!
% 3.56/1.28 % SZS status Theorem for theBenchmark
% 3.56/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.56/1.28 % (3871325)------------------------------
% 3.56/1.28 % (3871325)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.28 % (3871325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.28 % (3871325)CaDiCaL version: 2.1.3
% 3.56/1.28 % (3871325)Termination reason: Refutation
% 3.56/1.28 % (3871325)Time elapsed: 0.003 s
% 3.56/1.28 % (3871325)Peak memory usage: 89 MB
% 3.56/1.28 % (3871325)Instructions burned: 2 (million)
% 3.56/1.28 % (3871325)------------------------------
% 3.56/1.28 % (3871325)------------------------------
% 3.56/1.28 % (3871270)Success in time 0.413 s
% 3.56/1.28 % Vampire exiting
%------------------------------------------------------------------------------