%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL785_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 : n001.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 11:56:35 AM UTC 2026
% Result : Theorem 5.34s 1.94s
% Output : Refutation 5.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 17 ( 6 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 47 ( 47 usr; 20 con; 0-5 aty)
% Number of variables : 12 ( 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
dB: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
type: $tType ).
tff(type_def_10,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,X1),fun(fun(X2,X0),fun(X2,X1))) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(X0,fun(X1,X2)) > fun(X1,fun(X0,X2)) ) ).
tff(func_def_2,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_3,type,
it: fun(dB,bool) ).
tff(func_def_4,type,
app: fun(dB,fun(dB,dB)) ).
tff(func_def_5,type,
var: nat > dB ).
tff(func_def_6,type,
dB_case:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,X0)) * fun(dB,X0) * dB ) > X0 ) ).
tff(func_def_7,type,
subst: ( dB * dB * nat ) > dB ).
tff(func_def_8,type,
append:
!>[X0: $tType] : fun(list(X0),fun(list(X0),list(X0))) ).
tff(func_def_9,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_10,type,
foldr:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X1)) * list(X0) * X1 ) > X1 ) ).
tff(func_def_11,type,
insert:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_12,type,
cons:
!>[X0: $tType] : fun(X0,fun(list(X0),list(X0))) ).
tff(func_def_13,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_14,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_15,type,
maps:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,list(X1)) * list(X0) ) > list(X1) ) ).
tff(func_def_16,type,
rotate1:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_17,type,
splice:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_18,type,
shift:
!>[X0: $tType] : ( ( fun(nat,X0) * nat * X0 ) > fun(nat,X0) ) ).
tff(func_def_19,type,
fun1: fun(type,fun(type,type)) ).
tff(func_def_20,type,
type_case:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(type,fun(type,X0)) * type ) > X0 ) ).
tff(func_def_21,type,
typing: ( fun(nat,type) * dB ) > fun(type,bool) ).
tff(func_def_22,type,
typings: ( fun(nat,type) * list(dB) ) > fun(list(type),bool) ).
tff(func_def_23,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_24,type,
fFalse: bool ).
tff(func_def_25,type,
fTrue: bool ).
tff(func_def_26,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_27,type,
t: type ).
tff(func_def_28,type,
t_a: type ).
tff(func_def_29,type,
t1: type ).
tff(func_def_30,type,
a: dB ).
tff(func_def_31,type,
as: list(dB) ).
tff(func_def_32,type,
e: fun(nat,type) ).
tff(func_def_33,type,
ea: fun(nat,type) ).
tff(func_def_34,type,
i: nat ).
tff(func_def_35,type,
ia: nat ).
tff(func_def_36,type,
n: nat ).
tff(func_def_37,type,
rs: list(dB) ).
tff(func_def_38,type,
t2: dB ).
tff(func_def_39,type,
u: dB ).
tff(func_def_40,type,
ua: dB ).
tff(func_def_41,type,
sK0: ( list(dB) * dB * dB * dB ) > list(dB) ).
tff(func_def_42,type,
sK1:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_43,type,
sK2:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_44,type,
sK3:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X0 ) ).
tff(pred_def_1,type,
listsp:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_2,type,
pp: bool > $o ).
tff(pred_def_3,type,
sP4: list(dB) > $o ).
tff(pred_def_4,type,
sP5: list(dB) > $o ).
tff(pred_def_5,type,
sP6: list(dB) > $o ).
tff(pred_def_6,type,
sP7: list(dB) > $o ).
tff(f2,axiom,
n = i,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_True) ).
tff(f3,axiom,
rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Cons) ).
tff(f5,axiom,
pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,var(n),rs)),t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_nT) ).
tff(f23,axiom,
! [X0: $tType,X1: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_foldl__Cons) ).
tff(f111,conjecture,
pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a),as)),t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f112,negated_conjecture,
~ pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a),as)),t)),
inference(negated_conjecture,[status(cth)],[f111]) ).
tff(f113,plain,
~ pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a),as)),t)),
inference(flattening,[],[f112]) ).
tff(f131,plain,
~ pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(n)),a),as)),t)),
inference(cnf_transformation,[],[f113]) ).
tff(f157,plain,
! [X1: $tType,X0: $tType,X2: list(X1),X3: X1,X4: X0,X5: fun(X0,fun(X1,X0))] : ( foldl(X0,X1,X5,X4,aa(list(X1),list(X1),aa(X1,fun(list(X1),list(X1)),cons(X1),X3),X2)) = foldl(X0,X1,X5,aa(X1,X0,aa(X0,fun(X1,X0),X5,X4),X3),X2) ),
inference(cnf_transformation,[],[f23]) ).
tff(f160,plain,
pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,var(n),rs)),t)),
inference(cnf_transformation,[],[f5]) ).
tff(f161,plain,
rs = aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as),
inference(cnf_transformation,[],[f3]) ).
tff(f162,plain,
n = i,
inference(cnf_transformation,[],[f2]) ).
tff(f163,plain,
~ pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,var(i)),a),as)),t)),
inference(definition_unfolding,[],[f131,f162]) ).
tff(f164,plain,
pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,var(i),rs)),t)),
inference(definition_unfolding,[],[f160,f162]) ).
tff(f185,plain,
~ pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,var(i),aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),a),as))),t)),
inference(forward_demodulation,[],[f163,f157]) ).
tff(f186,plain,
~ pp(aa(type,bool,typing(shift(type,e,i,t1),foldl(dB,dB,app,var(i),rs)),t)),
inference(forward_demodulation,[],[f185,f161]) ).
tff(f187,plain,
$false,
inference(forward_subsumption_resolution,[],[f186,f164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL785_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.47 % Computer : n001.cluster.edu
% 0.19/0.47 % Model : x86_64 x86_64
% 0.19/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.47 % Memory : 8046.5625MB
% 0.19/0.47 % OS : Linux 6.8.0-71-generic
% 0.19/0.47 % CPULimit : 300
% 0.19/0.47 % WCLimit : 300
% 0.19/0.47 % DateTime : Sun Sep 27 16:55:16 UTC 2026
% 0.22/0.47 % CPUTime :
% 0.22/0.47 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.52 Running first-order theorem proving
% 0.22/0.52 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
% 5.34/1.94 % (3787564)Detected formulas, will run a generic FOF schedule.
% 5.34/1.94 % (3787569)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=1045119704:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.34/1.94 % (3787573)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3160229937:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.34/1.94 % (3787572)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1507896112:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.34/1.94 % (3787570)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=2993517976:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.34/1.94 % (3787571)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=1124148889:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.34/1.94 % (3787572)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.34/1.94 % (3787573)Also succeeded, but the first one will report.
% 5.34/1.94 % (3787572)First to succeed.
% 5.34/1.94 % (3787572)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3787564"
% 5.34/1.94 % (3787571)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.34/1.94 % (3787575)dis-21_1_sil=8000:lcm=predicate:random_seed=562895205: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)
% 5.34/1.94 % (3787574)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1835167756:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.34/1.94 % (3787575)Instruction limit reached!
% 5.34/1.94 % (3787575)------------------------------
% 5.34/1.94 % (3787575)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.34/1.94 % (3787575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.34/1.94 % (3787575)CaDiCaL version: 2.1.3
% 5.34/1.94 % (3787575)Termination reason: Instruction limit
% 5.34/1.94 % (3787575)Termination phase: Saturation
% 5.34/1.94 % (3787575)Time elapsed: 0.119 s
% 5.34/1.94 % (3787575)Peak memory usage: 89 MB
% 5.34/1.94 % (3787575)Instructions burned: 129 (million)
% 5.34/1.94 % (3787574)Instruction limit reached!
% 5.34/1.94 % (3787574)------------------------------
% 5.34/1.94 % (3787574)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.34/1.94 % (3787574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.34/1.94 % (3787574)CaDiCaL version: 2.1.3
% 5.34/1.94 % (3787574)Termination reason: Instruction limit
% 5.34/1.94 % (3787574)Termination phase: Saturation
% 5.34/1.94 % (3787574)Time elapsed: 0.129 s
% 5.34/1.94 % (3787574)Peak memory usage: 89 MB
% 5.34/1.94 % (3787574)Instructions burned: 139 (million)
% 5.34/1.94 % Exception at run slice level
% 5.34/1.94 User error: GNN currently only supports monomorphic FOL.
% 5.34/1.94 % (3787583)lrs+10_1_sil=8000:sp=occurrence:random_seed=2422876784:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 5.34/1.94 % (3787572)Refutation found. Thanks to Tanya!
% 5.34/1.94 % SZS status Theorem for theBenchmark
% 5.34/1.94 % SZS output start Proof for theBenchmark
% See solution above
% 5.34/1.94 % (3787572)------------------------------
% 5.34/1.94 % (3787572)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.34/1.94 % (3787572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.34/1.94 % (3787572)CaDiCaL version: 2.1.3
% 5.34/1.94 % (3787572)Termination reason: Refutation
% 5.34/1.94 % (3787572)Time elapsed: 0.008 s
% 5.34/1.94 % (3787572)Peak memory usage: 89 MB
% 5.34/1.94 % (3787572)Instructions burned: 5 (million)
% 5.34/1.94 % (3787572)------------------------------
% 5.34/1.94 % (3787572)------------------------------
% 5.34/1.94 % (3787564)Success in time 0.648 s
% 5.34/1.94 % Vampire exiting
%------------------------------------------------------------------------------