%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM122_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 : n010.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 09:39:36 AM UTC 2026
% Result : Theorem 0.29s 1.81s
% Output : Refutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 11 ~; 3 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 50 ( 50 usr; 9 con; 0-6 aty)
% Number of variables : 3 ( 3 !; 0 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
list: $tType > $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
atom: $tType ).
tff(type_def_10,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combi:
!>[X0: $tType] : fun(X0,X0) ).
tff(func_def_1,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
sgn_sgn:
!>[X0: $tType] : ( X0 > X0 ) ).
tff(func_def_3,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_4,type,
ring_1_of_int:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_5,type,
insert:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_6,type,
cons:
!>[X0: $tType] : ( ( X0 * list(X0) ) > list(X0) ) ).
tff(func_def_7,type,
nil:
!>[X0: $tType] : list(X0) ).
tff(func_def_8,type,
map:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * list(X0) ) > list(X1) ) ).
tff(func_def_9,type,
member1:
!>[X0: $tType] : fun(list(X0),fun(X0,bool)) ).
tff(func_def_10,type,
set:
!>[X0: $tType] : fun(list(X0),fun(X0,bool)) ).
tff(func_def_11,type,
sublist:
!>[X0: $tType] : ( ( list(X0) * fun(nat,bool) ) > list(X0) ) ).
tff(func_def_12,type,
semiring_1_Nats:
!>[X0: $tType] : fun(X0,bool) ).
tff(func_def_13,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_14,type,
asubst: ( int * list(int) * atom ) > atom ).
tff(func_def_15,type,
dvd: ( int * int * list(int) ) > atom ).
tff(func_def_16,type,
atom_size: atom > nat ).
tff(func_def_17,type,
decr_Z: atom > atom ).
tff(func_def_18,type,
divisor: atom > int ).
tff(func_def_19,type,
hd_coeff: fun(atom,int) ).
tff(func_def_20,type,
hd_coeff1: int > fun(atom,atom) ).
tff(func_def_21,type,
zlcms: list(int) > int ).
tff(func_def_22,type,
qEpres1907640072oeffs1: list(atom) > list(atom) ).
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,
a: atom ).
tff(func_def_27,type,
as: list(atom) ).
tff(func_def_28,type,
b: atom ).
tff(func_def_29,type,
sK0:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_30,type,
sK1:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun(X1,X0) * list(X0) * X0 ) > X1 ) ).
tff(func_def_31,type,
sK2:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * fun(X1,X0) * list(X0) * X0 ) > list(X1) ) ).
tff(func_def_32,type,
sK3:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun(X0,X1) ) > X0 ) ).
tff(func_def_33,type,
sK4:
!>[X0: $tType,X1: $tType] : ( ( list(X1) * X1 * list(X0) * fun(X0,X1) ) > list(X0) ) ).
tff(func_def_34,type,
sK5:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) * list(X1) ) > X1 ) ).
tff(func_def_35,type,
sK6:
!>[X0: $tType] : ( ( fun(X0,X0) * list(X0) ) > X0 ) ).
tff(func_def_36,type,
sK7:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) * list(X1) ) > X1 ) ).
tff(func_def_37,type,
sK8:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * list(X0) ) > list(X1) ) ).
tff(func_def_38,type,
sK9:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * list(X0) ) > X0 ) ).
tff(func_def_39,type,
sK10:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * X0 ) > X1 ) ).
tff(func_def_40,type,
sK11:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * list(X1) * fun(X1,X0) ) > X1 ) ).
tff(func_def_41,type,
sK12: atom ).
tff(func_def_42,type,
sK13: atom ).
tff(func_def_43,type,
sK14: atom ).
tff(func_def_44,type,
sK15:
!>[X0: $tType] : ( list(X0) > 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] : ( list(X0) > list(X0) ) ).
tff(pred_def_1,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
ring_1:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
sgn_if:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
zero_neq_one:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
iszero:
!>[X0: $tType] : ( X0 > $o ) ).
tff(pred_def_11,type,
listMem:
!>[X0: $tType] : ( ( X0 * list(X0) ) > $o ) ).
tff(pred_def_12,type,
list_ex1:
!>[X0: $tType] : ( ( fun(X0,bool) * list(X0) ) > $o ) ).
tff(pred_def_13,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_14,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_15,type,
pp: bool > $o ).
tff(f3,axiom,
! [X0: atom] :
( member(atom,X0,aa(list(atom),fun(atom,bool),set(atom),as))
=> ( aa(atom,int,hd_coeff,X0) != zero_zero(int) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_hd0) ).
tff(f4,axiom,
member(atom,b,aa(list(atom),fun(atom,bool),set(atom),as)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__096b_A_058_Aset_Aas_096) ).
tff(f116,conjecture,
aa(atom,int,hd_coeff,b) != zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f117,negated_conjecture,
( ( ~ aa(atom,int,hd_coeff,b) ) != zero_zero(int) ),
inference(negated_conjecture,[status(cth)],[f116]) ).
tff(f118,plain,
zero_zero(int) = aa(atom,int,hd_coeff,b),
inference(flattening,[],[f117]) ).
tff(f120,plain,
! [X0: atom] :
( ( aa(atom,int,hd_coeff,X0) != zero_zero(int) )
| ~ member(atom,X0,aa(list(atom),fun(atom,bool),set(atom),as)) ),
inference(ennf_transformation,[],[f3]) ).
tff(f162,plain,
zero_zero(int) = aa(atom,int,hd_coeff,b),
inference(cnf_transformation,[],[f118]) ).
tff(f163,plain,
! [X0: atom] :
( ( zero_zero(int) != aa(atom,int,hd_coeff,X0) )
| ~ member(atom,X0,aa(list(atom),fun(atom,bool),set(atom),as)) ),
inference(cnf_transformation,[],[f120]) ).
tff(f166,plain,
member(atom,b,aa(list(atom),fun(atom,bool),set(atom),as)),
inference(cnf_transformation,[],[f4]) ).
tff(f262,plain,
( ( zero_zero(int) != zero_zero(int) )
| ~ member(atom,b,aa(list(atom),fun(atom,bool),set(atom),as)) ),
inference(superposition,[],[f163,f162]) ).
tff(f263,plain,
~ member(atom,b,aa(list(atom),fun(atom,bool),set(atom),as)),
inference(trivial_inequality_removal,[],[f262]) ).
tff(f264,plain,
$false,
inference(forward_subsumption_resolution,[],[f263,f166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COM122_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.25 % Computer : n010.cluster.edu
% 0.12/0.25 % Model : x86_64 x86_64
% 0.12/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.25 % Memory : 8046.5625MB
% 0.12/0.25 % OS : Linux 6.8.0-71-generic
% 0.12/0.25 % CPULimit : 300
% 0.12/0.25 % WCLimit : 300
% 0.12/0.25 % DateTime : Mon Sep 28 21:55:18 UTC 2026
% 0.12/0.25 % CPUTime :
% 0.12/0.25 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.30 Running first-order theorem proving
% 0.27/0.30 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
% 0.29/1.81 % (2400348)Detected formulas, will run a generic FOF schedule.
% 0.29/1.81 % (2400365)dis-21_1_sil=8000:lcm=predicate:random_seed=2818188996: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)
% 0.29/1.81 % (2400360)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=3525630258:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.29/1.81 % (2400365)Instruction limit reached!
% 0.29/1.81 % (2400365)------------------------------
% 0.29/1.81 % (2400365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.29/1.81 % (2400365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/1.81 % (2400365)CaDiCaL version: 2.1.3
% 0.29/1.81 % (2400365)Termination reason: Instruction limit
% 0.29/1.81 % (2400365)Termination phase: Saturation
% 0.29/1.81 % (2400365)Time elapsed: 0.070 s
% 0.29/1.81 % (2400365)Peak memory usage: 91 MB
% 0.29/1.81 % (2400365)Instructions burned: 132 (million)
% 0.29/1.81 % (2400359)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=2491498444:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.29/1.81 % (2400363)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2835188243:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.29/1.81 % (2400361)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=1549441469:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.29/1.81 % (2400364)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4105985171:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.29/1.81 % (2400362)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3186815952:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.29/1.81 % (2400362)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.29/1.81 % (2400362)Refutation not found, incomplete strategy
% 0.29/1.81 % (2400362)------------------------------
% 0.29/1.81 % (2400362)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.29/1.81 % (2400362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/1.81 % (2400362)CaDiCaL version: 2.1.3
% 0.29/1.81 % (2400362)Termination reason: Refutation not found, incomplete strategy
% 0.29/1.81 % (2400362)Time elapsed: 0.002 s
% 0.29/1.81 % (2400362)Peak memory usage: 88 MB
% 0.29/1.81 % (2400362)Instructions burned: 1 (million)
% 0.29/1.81 % (2400361)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.29/1.81 % (2400363)First to succeed.
% 0.29/1.81 % (2400363)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2400348"
% 0.29/1.81 % (2400364)Also succeeded, but the first one will report.
% 0.29/1.81 % (2400373)lrs+10_1_sil=8000:sp=occurrence:random_seed=894370457:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.29/1.81 % (2400373)Also succeeded, but the first one will report.
% 0.29/1.81 % (2400362)------------------------------
% 0.29/1.81 % (2400362)------------------------------
% 0.29/1.81 % (2400363)Refutation found. Thanks to Tanya!
% 0.29/1.81 % SZS status Theorem for theBenchmark
% 0.29/1.81 % SZS output start Proof for theBenchmark
% See solution above
% 0.29/1.81 % (2400363)------------------------------
% 0.29/1.81 % (2400363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.29/1.81 % (2400363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/1.81 % (2400363)CaDiCaL version: 2.1.3
% 0.29/1.81 % (2400363)Termination reason: Refutation
% 0.29/1.81 % (2400363)Time elapsed: 0.010 s
% 0.29/1.81 % (2400363)Peak memory usage: 88 MB
% 0.29/1.81 % (2400363)Instructions burned: 8 (million)
% 0.29/1.81 % (2400363)------------------------------
% 0.29/1.81 % (2400363)------------------------------
% 0.29/1.81 % (2400348)Success in time 0.69 s
% 0.29/1.81 % Vampire exiting
%------------------------------------------------------------------------------