%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM978_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 : n011.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 12:17:44 PM UTC 2026
% Result : Theorem 5.05s 1.93s
% Output : Refutation 5.05s
% 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 : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 28 ( 27 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-4 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $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,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_3,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_4,type,
bit0: int > int ).
tff(func_def_5,type,
bit1: int > int ).
tff(func_def_6,type,
pls: int ).
tff(func_def_7,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_8,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > 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,
m: int ).
tff(func_def_13,type,
n: nat ).
tff(func_def_14,type,
t: int ).
tff(func_def_15,type,
tn: nat ).
tff(func_def_16,type,
sK0: ( nat * nat ) > nat ).
tff(pred_def_1,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
mult_zero:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
semiring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
comm_monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
ring_n68954251visors:
!>[X0: $tType] : $o ).
tff(pred_def_18,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_19,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_20,type,
ordere216010020id_add:
!>[X0: $tType] : $o ).
tff(pred_def_21,type,
ordere236663937imp_le:
!>[X0: $tType] : $o ).
tff(pred_def_22,type,
ordere223160158up_add:
!>[X0: $tType] : $o ).
tff(pred_def_23,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
tff(pred_def_24,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_25,type,
twoSqu1567020053sum2sq: int > $o ).
tff(pred_def_26,type,
pp: bool > $o ).
tff(pred_def_27,type,
sQ1_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f2,axiom,
ord_less(nat,zero_zero(nat),n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_smaller_I1_J) ).
tff(f140,conjecture,
ord_less(nat,zero_zero(nat),n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f141,negated_conjecture,
~ ord_less(nat,zero_zero(nat),n),
inference(negated_conjecture,[status(cth)],[f140]) ).
tff(f142,plain,
~ ord_less(nat,zero_zero(nat),n),
inference(flattening,[],[f141]) ).
tff(f251,plain,
ord_less(nat,zero_zero(nat),n),
inference(cnf_transformation,[],[f2]) ).
tff(f430,plain,
~ ord_less(nat,zero_zero(nat),n),
inference(cnf_transformation,[],[f142]) ).
tff(f535,plain,
$false,
inference(resolution,[],[f251,f430]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM978_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n011.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sun Sep 27 21:49:00 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 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
% 5.05/1.93 % (2789235)Detected formulas, will run a generic FOF schedule.
% 5.05/1.93 % (2789242)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=1835092128:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.05/1.93 % (2789248)dis-21_1_sil=8000:lcm=predicate:random_seed=4113460908: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)
% 5.05/1.93 % (2789248)First to succeed.
% 5.05/1.93 % (2789248)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2789235"
% 5.05/1.93 % (2789243)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=173226685:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.05/1.93 % (2789245)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=276109414:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.05/1.93 % (2789246)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3624285688:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.05/1.93 % (2789244)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=3186756311:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.05/1.93 % (2789245)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.05/1.93 % (2789246)Also succeeded, but the first one will report.
% 5.05/1.93 % (2789245)Also succeeded, but the first one will report.
% 5.05/1.93 % (2789244)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.05/1.93 % (2789247)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4042628396:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.05/1.93 % (2789247)Also succeeded, but the first one will report.
% 5.05/1.93 % Exception at run slice level
% 5.05/1.93 User error: GNN currently only supports monomorphic FOL.
% 5.05/1.93 % (2789248)Refutation found. Thanks to Tanya!
% 5.05/1.93 % SZS status Theorem for theBenchmark
% 5.05/1.93 % SZS output start Proof for theBenchmark
% See solution above
% 5.05/1.93 % (2789248)------------------------------
% 5.05/1.93 % (2789248)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.05/1.93 % (2789248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.05/1.93 % (2789248)CaDiCaL version: 2.1.3
% 5.05/1.93 % (2789248)Termination reason: Refutation
% 5.05/1.93 % (2789248)Time elapsed: 0.006 s
% 5.05/1.93 % (2789248)Peak memory usage: 89 MB
% 5.05/1.93 % (2789248)Instructions burned: 7 (million)
% 5.05/1.93 % (2789248)------------------------------
% 5.05/1.93 % (2789248)------------------------------
% 5.05/1.93 % (2789235)Success in time 0.587 s
% 5.05/1.93 % Vampire exiting
%------------------------------------------------------------------------------