%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL756_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 : n013.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 11:56:28 AM UTC 2026
% Result : Theorem 2.68s 1.38s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 2
% Syntax : Number of formulae : 7 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 7 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 36 ( 36 usr; 5 con; 0-5 aty)
% Number of variables : 4 ( 4 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
dB: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(type_def_8,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
var: nat > dB ).
tff(func_def_2,type,
dB_case:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,X0)) * fun(dB,X0) * dB ) > X0 ) ).
tff(func_def_3,type,
dB_rec:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,fun(X0,fun(X0,X0)))) * fun(dB,fun(X0,X0)) * dB ) > X0 ) ).
tff(func_def_4,type,
lift: ( dB * nat ) > dB ).
tff(func_def_5,type,
liftn: ( nat * dB * nat ) > dB ).
tff(func_def_6,type,
subst: ( dB * dB * nat ) > dB ).
tff(func_def_7,type,
suc: nat > nat ).
tff(func_def_8,type,
semiri532925092at_aux:
!>[X0: $tType] : ( ( fun(X0,X0) * nat * X0 ) > X0 ) ).
tff(func_def_9,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_10,type,
fFalse: bool ).
tff(func_def_11,type,
fTrue: bool ).
tff(func_def_12,type,
ia: nat ).
tff(func_def_13,type,
ja: nat ).
tff(func_def_14,type,
ra: dB ).
tff(func_def_15,type,
sK0:
!>[X0: $tType] : ( fun(nat,X0) > nat ) ).
tff(func_def_16,type,
sK1:
!>[X0: $tType] : ( fun(nat,X0) > nat ) ).
tff(func_def_17,type,
sK2: ( nat * nat ) > nat ).
tff(func_def_18,type,
sK3: ( nat * nat ) > nat ).
tff(func_def_19,type,
sK4: fun(nat,fun(nat,bool)) > nat ).
tff(func_def_20,type,
sK5: fun(nat,fun(nat,bool)) > nat ).
tff(func_def_21,type,
sK6: fun(nat,fun(nat,bool)) > nat ).
tff(func_def_22,type,
sK7: fun(nat,fun(nat,bool)) > nat ).
tff(func_def_23,type,
sK8: ( fun(nat,bool) * nat ) > nat ).
tff(func_def_24,type,
sK9: ( fun(nat,bool) * nat ) > nat ).
tff(func_def_25,type,
sK10:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_26,type,
sK11:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_27,type,
sK12:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_28,type,
sK13:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_29,type,
sK14:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_30,type,
sK15:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_31,type,
sK16:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_32,type,
sK17:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_33,type,
sK18: ( nat * nat ) > nat ).
tff(func_def_34,type,
sK19: ( nat * nat ) > nat ).
tff(pred_def_1,type,
ord:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
order:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
preorder:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
dense_linorder:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
ordere236663937imp_le:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
ordere223160158up_add:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
it: dB > $o ).
tff(pred_def_13,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_14,type,
pp: bool > $o ).
tff(f117,axiom,
! [X0: nat,X1: nat] : it(subst(ra,var(X0),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(f118,conjecture,
it(subst(ra,var(suc(ia)),suc(ja))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
tff(f119,negated_conjecture,
~ it(subst(ra,var(suc(ia)),suc(ja))),
inference(negated_conjecture,[status(cth)],[f118]) ).
tff(f123,plain,
~ it(subst(ra,var(suc(ia)),suc(ja))),
inference(flattening,[],[f119]) ).
tff(f413,plain,
! [X0: nat,X1: nat] : it(subst(ra,var(X0),X1)),
inference(cnf_transformation,[],[f117]) ).
tff(f414,plain,
~ it(subst(ra,var(suc(ia)),suc(ja))),
inference(cnf_transformation,[],[f123]) ).
tff(f453,plain,
$false,
inference(resolution,[],[f413,f414]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL756_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 16:44:21 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.68/1.38 % (410255)Detected formulas, will run a generic FOF schedule.
% 2.68/1.38 % (410265)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=148479694:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.38 % (410265)First to succeed.
% 2.68/1.38 % (410265)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-410255"
% 2.68/1.38 % (410261)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=2482062399:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.38 % (410262)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=2678210905:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.38 % (410260)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=2167378002:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.38 % (410266)dis-21_1_sil=8000:lcm=predicate:random_seed=3684925563: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)
% 2.68/1.38 % (410263)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3404248431:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.38 % (410263)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.68/1.38 % (410263)Also succeeded, but the first one will report.
% 2.68/1.38 % (410262)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.68/1.38 % (410266)Also succeeded, but the first one will report.
% 2.68/1.38 % (410264)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2612827024:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.38 % (410264)Also succeeded, but the first one will report.
% 2.68/1.38 % (410265)Refutation found. Thanks to Tanya!
% 2.68/1.38 % SZS status Theorem for theBenchmark
% 2.68/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.39 % (410265)------------------------------
% 2.68/1.39 % (410265)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.39 % (410265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.39 % (410265)CaDiCaL version: 2.1.3
% 2.68/1.39 % (410265)Termination reason: Refutation
% 2.68/1.39 % (410265)Time elapsed: 0.004 s
% 2.68/1.39 % (410265)Peak memory usage: 89 MB
% 2.68/1.39 % (410265)Instructions burned: 9 (million)
% 2.68/1.39 % (410265)------------------------------
% 2.68/1.39 % (410265)------------------------------
% 2.68/1.39 % (410255)Success in time 0.304 s
% 2.68/1.39 % Vampire exiting
%------------------------------------------------------------------------------