%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL769_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 12:00:31 PM UTC 2026
% Result : Theorem 0.17s 0.51s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 65 ( 19 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 77 ( 31 ~; 27 |; 18 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 62 ( 62 usr; 9 con; 0-5 aty)
% Number of variables : 47 ( 39 !; 8 ?; 47 :)
% 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,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * 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,
abs: dB > dB ).
tff(func_def_5,type,
app: fun(dB,fun(dB,dB)) ).
tff(func_def_6,type,
var: nat > dB ).
tff(func_def_7,type,
dB_case:
!>[X0: $tType] : ( ( fun(nat,X0) * fun(dB,fun(dB,X0)) * fun(dB,X0) * dB ) > X0 ) ).
tff(func_def_8,type,
append:
!>[X0: $tType] : fun(list(X0),fun(list(X0),list(X0))) ).
tff(func_def_9,type,
butlast:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_10,type,
foldl:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X1,X0)) * X0 * list(X1) ) > X0 ) ).
tff(func_def_11,type,
insert:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_12,type,
last:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_13,type,
cons:
!>[X0: $tType] : fun(X0,fun(list(X0),list(X0))) ).
tff(func_def_14,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_15,type,
list_case:
!>[X0: $tType,X1: $tType] : ( ( X0 * fun(X1,fun(list(X1),X0)) * list(X1) ) > X0 ) ).
tff(func_def_16,type,
maps:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,list(X1)) * list(X0) ) > list(X1) ) ).
tff(func_def_17,type,
rev:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_18,type,
rotate1:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_19,type,
splice:
!>[X0: $tType] : ( ( list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_20,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_21,type,
fFalse: bool ).
tff(func_def_22,type,
fNot: fun(bool,bool) ).
tff(func_def_23,type,
fTrue: bool ).
tff(func_def_24,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_25,type,
fdisj: fun(bool,fun(bool,bool)) ).
tff(func_def_26,type,
fequal:
!>[X0: $tType] : ( X0 > fun(X0,bool) ) ).
tff(func_def_27,type,
i: nat ).
tff(func_def_28,type,
rs: list(dB) ).
tff(func_def_29,type,
sK0:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) ) > X0 ) ).
tff(func_def_30,type,
sK1:
!>[X0: $tType] : ( ( list(X0) * fun(X0,bool) ) > list(X0) ) ).
tff(func_def_31,type,
sK2:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_32,type,
sK3:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_33,type,
sK4:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_34,type,
sK5:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_35,type,
sK6:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_36,type,
sK7:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X1 ) ).
tff(func_def_37,type,
sK8:
!>[X0: $tType,X1: $tType] : ( fun(X0,fun(X1,X0)) > X0 ) ).
tff(func_def_38,type,
sK9: ( list(dB) * dB * dB * dB ) > list(dB) ).
tff(func_def_39,type,
sK10:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_40,type,
sK11:
!>[X0: $tType] : ( fun(list(X0),bool) > list(X0) ) ).
tff(func_def_41,type,
sK12:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_42,type,
sK13:
!>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_43,type,
sK14:
!>[X0: $tType] : ( ( list(X0) * list(X0) * list(X0) * X0 ) > list(X0) ) ).
tff(func_def_44,type,
sK15:
!>[X0: $tType] : ( ( list(X0) * X0 * list(X0) * list(X0) ) > list(X0) ) ).
tff(func_def_45,type,
sK16:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_46,type,
sK17:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_47,type,
sK18:
!>[X0: $tType] : ( fun(list(X0),bool) > X0 ) ).
tff(func_def_48,type,
sK19:
!>[X0: $tType] : ( fun(list(X0),bool) > list(X0) ) ).
tff(func_def_49,type,
sK20:
!>[X0: $tType] : ( list(X0) > list(X0) ) ).
tff(func_def_50,type,
sK21:
!>[X0: $tType] : ( list(X0) > X0 ) ).
tff(func_def_51,type,
sK22:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_52,type,
sK23: dB > dB ).
tff(func_def_53,type,
sK24: dB > dB ).
tff(func_def_54,type,
sK25: dB > dB ).
tff(func_def_55,type,
sK26: dB > nat ).
tff(func_def_56,type,
sK27: dB > list(dB) ).
tff(func_def_57,type,
sK28: dB > dB ).
tff(func_def_58,type,
sK29: dB > nat ).
tff(func_def_59,type,
sK30: dB > dB ).
tff(pred_def_1,type,
list_all:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_2,type,
list_ex1:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_3,type,
listsp:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_4,type,
pp: bool > $o ).
tff(f1,axiom,
! [X4: nat] : pp(aa(dB,bool,it,var(X4))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_Var__IT) ).
tff(f2,axiom,
! [X0: $tType,X1: fun(X0,bool)] : listsp(X0,X1,nil(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_listsp_ONil) ).
tff(f11,axiom,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( listsp(X0,X2,X1)
<=> ( ( X1 = nil(X0) )
| ? [X3: X0,X4: list(X0)] :
( ( X1 = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) )
& pp(aa(X0,bool,X2,X3))
& listsp(X0,X2,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_listsp_Osimps) ).
tff(f117,conjecture,
listsp(dB,it,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f118,negated_conjecture,
~ listsp(dB,it,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB))),
inference(negated_conjecture,[status(cth)],[f117]) ).
tff(f119,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(rectify,[],[f1]) ).
tff(f121,plain,
~ listsp(dB,it,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB))),
inference(flattening,[],[f118]) ).
tff(f158,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( listsp(X0,X2,X1)
| ( ( nil(X0) != X1 )
& ! [X3: X0,X4: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != X1 )
| ~ pp(aa(X0,bool,X2,X3))
| ~ listsp(X0,X2,X4) ) ) )
& ( ( X1 = nil(X0) )
| ? [X3: X0,X4: list(X0)] :
( ( X1 = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) )
& pp(aa(X0,bool,X2,X3))
& listsp(X0,X2,X4) )
| ~ listsp(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f11]) ).
tff(f159,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( listsp(X0,X2,X1)
| ( ( nil(X0) != X1 )
& ! [X3: X0,X4: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != X1 )
| ~ pp(aa(X0,bool,X2,X3))
| ~ listsp(X0,X2,X4) ) ) )
& ( ( X1 = nil(X0) )
| ? [X3: X0,X4: list(X0)] :
( ( X1 = aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) )
& pp(aa(X0,bool,X2,X3))
& listsp(X0,X2,X4) )
| ~ listsp(X0,X2,X1) ) ),
inference(flattening,[],[f158]) ).
tff(f160,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( listsp(X0,X2,X1)
| ( ( nil(X0) != X1 )
& ! [X3: X0,X4: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != X1 )
| ~ pp(aa(X0,bool,X2,X3))
| ~ listsp(X0,X2,X4) ) ) )
& ( ( X1 = nil(X0) )
| ? [X5: X0,X6: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X5),X6) = X1 )
& pp(aa(X0,bool,X2,X5))
& listsp(X0,X2,X6) )
| ~ listsp(X0,X2,X1) ) ),
inference(rectify,[],[f159]) ).
tff(f161,plain,
! [X0: $tType,X1: list(X0),X2: fun(X0,bool)] :
( ( listsp(X0,X2,X1)
| ( ( nil(X0) != X1 )
& ! [X3: X0,X4: list(X0)] :
( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != X1 )
| ~ pp(aa(X0,bool,X2,X3))
| ~ listsp(X0,X2,X4) ) ) )
& ( ( X1 = nil(X0) )
| ( ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),sK0(X0,X1,X2)),sK1(X0,X1,X2)) = X1 )
& pp(aa(X0,bool,X2,sK0(X0,X1,X2)))
& listsp(X0,X2,sK1(X0,X1,X2)) )
| ~ listsp(X0,X2,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X5,sK0(X0,X1,X2)),skolemize(X6,sK1(X0,X1,X2))],[f160]) ).
tff(f229,plain,
! [X0: nat] : pp(aa(dB,bool,it,var(X0))),
inference(cnf_transformation,[],[f119]) ).
tff(f230,plain,
! [X0: $tType,X1: fun(X0,bool)] : listsp(X0,X1,nil(X0)),
inference(cnf_transformation,[],[f2]) ).
tff(f249,plain,
! [X0: $tType,X2: fun(X0,bool),X3: X0,X1: list(X0),X4: list(X0)] :
( listsp(X0,X2,X1)
| ( aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4) != X1 )
| ~ pp(aa(X0,bool,X2,X3))
| ~ listsp(X0,X2,X4) ),
inference(cnf_transformation,[],[f161]) ).
tff(f430,plain,
~ listsp(dB,it,aa(list(dB),list(dB),aa(dB,fun(list(dB),list(dB)),cons(dB),var(i)),nil(dB))),
inference(cnf_transformation,[],[f121]) ).
tff(f441,plain,
! [X0: $tType,X2: fun(X0,bool),X3: X0,X4: list(X0)] :
( listsp(X0,X2,aa(list(X0),list(X0),aa(X0,fun(list(X0),list(X0)),cons(X0),X3),X4))
| ~ pp(aa(X0,bool,X2,X3))
| ~ listsp(X0,X2,X4) ),
inference(equality_resolution,[],[f249]) ).
tff(f1115,plain,
( ~ pp(aa(dB,bool,it,var(i)))
| ~ listsp(dB,it,nil(dB)) ),
inference(resolution,[],[f441,f430]) ).
tff(f1124,plain,
~ listsp(dB,it,nil(dB)),
inference(forward_subsumption_resolution,[],[f1115,f229]) ).
tff(f1125,plain,
$false,
inference(forward_subsumption_resolution,[],[f1124,f230]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL769_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n014.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 16:46:02 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.41 Running first-order model finding
% 0.13/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.51 % (1005508)Will run a generic schedule for satisfiability detection.
% 0.17/0.51 % (1005514)% WARNING: option uhcvi not known.
% 0.17/0.51 % (1005514)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=424784981:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.51 % (1005513)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1632440290_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.51 % (1005515)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2199582591:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.51 % (1005516)dis+10_1_sil=32000:sp=arity:random_seed=1918517331:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.51 % (1005517)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=380507464:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.51 % (1005519)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3063343607:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.51 % (1005518)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2092481033:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.51 % Exception at run slice level
% 0.17/0.51 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.51 % (1005527)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3666447331:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.17/0.51 % Exception at run slice level
% 0.17/0.51 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.51 % (1005516) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1005508-1005516"...
% 0.17/0.51 % (1005516)...printing done.
% 0.17/0.51 % (1005516)Refutation found. Thanks to Tanya!
% 0.17/0.51 % SZS status Theorem for theBenchmark
% 0.17/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.51 % (1005516)------------------------------
% 0.17/0.51 % (1005516)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.51 % (1005516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.51 % (1005516)CaDiCaL version: 2.1.3
% 0.17/0.51 % (1005516)Termination reason: Refutation
% 0.17/0.51 % (1005516)Time elapsed: 0.046 s
% 0.17/0.51 % (1005516)Peak memory usage: 12 MB
% 0.17/0.51 % (1005516)Instructions burned: 74 (million)
% 0.17/0.51 % (1005508)Success in time 0.094 s
% 0.17/0.51 % Vampire exiting
%------------------------------------------------------------------------------