%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL755_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 : n003.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 0.17s 1.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 2 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 5 con; 0-5 aty)
% Number of variables : 10 ( 10 !; 0 ?; 10 :)
% 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,
one_one:
!>[X0: $tType] : 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,
abs: dB > dB ).
tff(func_def_4,type,
var: nat > dB ).
tff(func_def_5,type,
dB_case:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,X0)) * fun(dB,X0) * dB ) > X0 ) ).
tff(func_def_6,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_7,type,
lift: ( dB * nat ) > dB ).
tff(func_def_8,type,
liftn: ( nat * dB * nat ) > dB ).
tff(func_def_9,type,
subst: ( dB * dB * nat ) > dB ).
tff(func_def_10,type,
substn: ( dB * dB * nat ) > dB ).
tff(func_def_11,type,
suc: nat > nat ).
tff(func_def_12,type,
nat_case:
!>[X0: $tType] : ( ( X0 * fun(nat,X0) * nat ) > X0 ) ).
tff(func_def_13,type,
nat_rec:
!>[X0: $tType] : ( ( X0 * fun(nat,fun(X0,X0)) * nat ) > X0 ) ).
tff(func_def_14,type,
semiri532925092at_aux:
!>[X0: $tType] : ( ( fun(X0,X0) * nat * X0 ) > X0 ) ).
tff(func_def_15,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_16,type,
fFalse: bool ).
tff(func_def_17,type,
fTrue: bool ).
tff(func_def_18,type,
ia: nat ).
tff(func_def_19,type,
ja: nat ).
tff(func_def_20,type,
ra: dB ).
tff(func_def_21,type,
sK0: ( nat * nat ) > nat ).
tff(func_def_22,type,
sK1: ( nat * nat ) > nat ).
tff(func_def_23,type,
sK2: ( nat * nat ) > nat ).
tff(func_def_24,type,
sK3: ( nat * nat ) > nat ).
tff(pred_def_1,type,
one:
!>[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,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
ordere236663937imp_le:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
ordere223160158up_add:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
it: dB > $o ).
tff(pred_def_12,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_13,type,
pp: bool > $o ).
tff(f1,axiom,
! [X3: dB] :
( it(X3)
=> it(abs(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_Lambda) ).
tff(f90,axiom,
! [X0: nat] : ( suc(X0) = plus_plus(nat,one_one(nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_Suc__eq__plus1__left) ).
tff(f112,axiom,
! [X0: nat,X1: nat] : it(subst(ra,var(X0),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(f113,conjecture,
it(abs(subst(ra,var(suc(ia)),suc(ja)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
tff(f114,negated_conjecture,
~ it(abs(subst(ra,var(suc(ia)),suc(ja)))),
inference(negated_conjecture,[status(cth)],[f113]) ).
tff(f115,plain,
~ it(abs(subst(ra,var(suc(ia)),suc(ja)))),
inference(flattening,[],[f114]) ).
tff(f116,plain,
! [X0: dB] :
( it(X0)
=> it(abs(X0)) ),
inference(rectify,[],[f1]) ).
tff(f118,plain,
! [X0: dB] :
( it(abs(X0))
| ~ it(X0) ),
inference(ennf_transformation,[],[f116]) ).
tff(f177,plain,
! [X0: nat,X1: nat] : it(subst(ra,var(X0),X1)),
inference(cnf_transformation,[],[f112]) ).
tff(f178,plain,
~ it(abs(subst(ra,var(suc(ia)),suc(ja)))),
inference(cnf_transformation,[],[f115]) ).
tff(f180,plain,
! [X0: dB] :
( it(abs(X0))
| ~ it(X0) ),
inference(cnf_transformation,[],[f118]) ).
tff(f232,plain,
! [X0: nat] : ( suc(X0) = plus_plus(nat,one_one(nat),X0) ),
inference(cnf_transformation,[],[f90]) ).
tff(f261,plain,
~ it(abs(subst(ra,var(plus_plus(nat,one_one(nat),ia)),plus_plus(nat,one_one(nat),ja)))),
inference(definition_unfolding,[],[f178,f232,f232]) ).
tff(f312,plain,
~ it(subst(ra,var(plus_plus(nat,one_one(nat),ia)),plus_plus(nat,one_one(nat),ja))),
inference(resolution,[],[f180,f261]) ).
tff(f313,plain,
$false,
inference(resolution,[],[f177,f312]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL755_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n003.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 16:46:26 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.17/1.50 % (770459)Detected formulas, will run a generic FOF schedule.
% 0.17/1.50 % (770465)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=3045541794:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.17/1.50 % (770468)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=512776802:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.17/1.50 % (770466)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=2447173852:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.17/1.50 % (770469)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=431462530:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.17/1.50 % (770467)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1878218998:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.17/1.50 % (770470)dis-21_1_sil=8000:lcm=predicate:random_seed=2111627612: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)
% 0.17/1.50 % (770464)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=2220109499:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.17/1.50 % (770467)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/1.50 % (770468)First to succeed.
% 0.17/1.50 % (770467)Also succeeded, but the first one will report.
% 0.17/1.50 % (770466)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/1.50 % (770468)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-770459"
% 0.17/1.50 % (770469)Also succeeded, but the first one will report.
% 0.17/1.50 % (770470)Also succeeded, but the first one will report.
% 0.17/1.50 % Exception at run slice level
% 0.17/1.50 User error: GNN currently only supports monomorphic FOL.
% 0.17/1.50 % (770468)Refutation found. Thanks to Tanya!
% 0.17/1.50 % SZS status Theorem for theBenchmark
% 0.17/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (770468)------------------------------
% 0.17/1.50 % (770468)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (770468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (770468)CaDiCaL version: 2.1.3
% 0.17/1.50 % (770468)Termination reason: Refutation
% 0.17/1.50 % (770468)Time elapsed: 0.004 s
% 0.17/1.50 % (770468)Peak memory usage: 88 MB
% 0.17/1.50 % (770468)Instructions burned: 4 (million)
% 0.17/1.50 % (770468)------------------------------
% 0.17/1.50 % (770468)------------------------------
% 0.17/1.50 % (770459)Success in time 0.445 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------