%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM994_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 : n015.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 12:17:46 PM UTC 2026
% Result : Theorem 2.87s 1.27s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 15 unt; 0 typ; 5 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 78 ( 35 ~; 33 |; 2 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 29 ( 28 usr; 6 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 15 ( 0 sgn 15 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(func_def_0,type,
abs_abs:
!>[X0: $tType] : ( X0 > X0 ) ).
tff(func_def_1,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_3,type,
bit0: int > int ).
tff(func_def_4,type,
bit1: int > int ).
tff(func_def_5,type,
pls: int ).
tff(func_def_6,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_7,type,
fFalse: bool ).
tff(func_def_8,type,
fTrue: bool ).
tff(func_def_9,type,
v: int ).
tff(func_def_10,type,
w: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
mult_zero:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
ordered_ring:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
linordered_ring:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
no_zero_divisors:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
ordered_ring_abs:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
ordered_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
ab_semigroup_mult:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
ordere1490568538miring:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
ring_n68954251visors:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
linord581940658strict:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
ordere453448008miring:
!>[X0: $tType] : $o ).
tff(pred_def_18,type,
ordere142940540dd_abs:
!>[X0: $tType] : $o ).
tff(pred_def_19,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_20,type,
pp: bool > $o ).
tff(pred_def_21,type,
sP0: ( int * bool * bool ) > $o ).
tff(pred_def_22,type,
sP1: ( bool * int * bool ) > $o ).
tff(pred_def_23,type,
sQ2_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f12,axiom,
ord_less_eq(int,zero_zero(int),number_number_of(int,bit0(bit1(pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
tff(f45,axiom,
! [X0: $tType] :
( ordere142940540dd_abs(X0)
=> ! [X1: X0] : ord_less_eq(X0,zero_zero(X0),abs_abs(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_abs__ge__zero) ).
tff(f49,axiom,
! [X0: int,X1: int] :
( ord_less_eq(int,zero_zero(int),X1)
=> ( ord_less_eq(int,zero_zero(int),X0)
=> ord_less_eq(int,zero_zero(int),times_times(int,X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
tff(f98,axiom,
ordere142940540dd_abs(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__group__add__abs) ).
tff(f127,conjecture,
( ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,v)))
& ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,w))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f128,negated_conjecture,
~ ( ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,v)))
& ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,w))) ),
inference(negated_conjecture,[status(cth)],[f127]) ).
tff(f151,plain,
! [X0: $tType] :
( ! [X1: X0] : ord_less_eq(X0,zero_zero(X0),abs_abs(X0,X1))
| ~ ordere142940540dd_abs(X0) ),
inference(ennf_transformation,[],[f45]) ).
tff(f153,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,zero_zero(int),times_times(int,X1,X0))
| ~ ord_less_eq(int,zero_zero(int),X0)
| ~ ord_less_eq(int,zero_zero(int),X1) ),
inference(ennf_transformation,[],[f49]) ).
tff(f154,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,zero_zero(int),times_times(int,X1,X0))
| ~ ord_less_eq(int,zero_zero(int),X0)
| ~ ord_less_eq(int,zero_zero(int),X1) ),
inference(flattening,[],[f153]) ).
tff(f205,plain,
( ~ ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,v)))
| ~ ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,w))) ),
inference(ennf_transformation,[],[f128]) ).
tff(f278,plain,
ord_less_eq(int,zero_zero(int),number_number_of(int,bit0(bit1(pls)))),
inference(cnf_transformation,[],[f12]) ).
tff(f324,plain,
! [X0: $tType,X1: X0] :
( ~ ordere142940540dd_abs(X0)
| ord_less_eq(X0,zero_zero(X0),abs_abs(X0,X1)) ),
inference(cnf_transformation,[],[f151]) ).
tff(f329,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,zero_zero(int),times_times(int,X1,X0))
| ~ ord_less_eq(int,zero_zero(int),X0)
| ~ ord_less_eq(int,zero_zero(int),X1) ),
inference(cnf_transformation,[],[f154]) ).
tff(f419,plain,
ordere142940540dd_abs(int),
inference(cnf_transformation,[],[f98]) ).
tff(f448,plain,
( ~ ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,v)))
| ~ ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,w))) ),
inference(cnf_transformation,[],[f205]) ).
tff(f546,definition,
( spl3_1
<=> ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,w))) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
tff(f547,plain,
( ~ ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,w)))
| spl3_1 ),
inference(avatar_component_clause,[],[f546]) ).
tff(f549,definition,
( spl3_2
<=> ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,v))) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f550,plain,
( ~ ord_less_eq(int,zero_zero(int),times_times(int,number_number_of(int,bit0(bit1(pls))),abs_abs(int,v)))
| spl3_2 ),
inference(avatar_component_clause,[],[f549]) ).
tff(f551,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f448,f549,f546]) ).
tff(f560,plain,
! [X0: int] : ord_less_eq(int,zero_zero(int),abs_abs(int,X0)),
inference(resolution,[],[f324,f419]) ).
tff(f821,plain,
( ~ ord_less_eq(int,zero_zero(int),abs_abs(int,w))
| ~ ord_less_eq(int,zero_zero(int),number_number_of(int,bit0(bit1(pls))))
| spl3_1 ),
inference(resolution,[],[f329,f547]) ).
tff(f823,definition,
( spl3_10
<=> ord_less_eq(int,zero_zero(int),number_number_of(int,bit0(bit1(pls)))) ),
introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition]) ).
tff(f824,plain,
( ~ ord_less_eq(int,zero_zero(int),number_number_of(int,bit0(bit1(pls))))
| spl3_10 ),
inference(avatar_component_clause,[],[f823]) ).
tff(f826,definition,
( spl3_11
<=> ord_less_eq(int,zero_zero(int),abs_abs(int,w)) ),
introduced(definition,[new_symbols(definition,[spl3_11])],[avatar_definition]) ).
tff(f827,plain,
( ~ ord_less_eq(int,zero_zero(int),abs_abs(int,w))
| spl3_11 ),
inference(avatar_component_clause,[],[f826]) ).
tff(f828,plain,
( ~ spl3_10
| ~ spl3_11
| spl3_1 ),
inference(avatar_split_clause,[],[f821,f546,f826,f823]) ).
tff(f829,plain,
( $false
| spl3_10 ),
inference(resolution,[],[f824,f278]) ).
tff(f832,plain,
spl3_10,
inference(avatar_contradiction_clause,[],[f829]) ).
tff(f833,plain,
( $false
| spl3_11 ),
inference(resolution,[],[f827,f560]) ).
tff(f834,plain,
spl3_11,
inference(avatar_contradiction_clause,[],[f833]) ).
tff(f835,plain,
( ~ ord_less_eq(int,zero_zero(int),abs_abs(int,v))
| ~ ord_less_eq(int,zero_zero(int),number_number_of(int,bit0(bit1(pls))))
| spl3_2 ),
inference(resolution,[],[f550,f329]) ).
tff(f837,definition,
( spl3_12
<=> ord_less_eq(int,zero_zero(int),abs_abs(int,v)) ),
introduced(definition,[new_symbols(definition,[spl3_12])],[avatar_definition]) ).
tff(f838,plain,
( ~ ord_less_eq(int,zero_zero(int),abs_abs(int,v))
| spl3_12 ),
inference(avatar_component_clause,[],[f837]) ).
tff(f839,plain,
( ~ spl3_10
| ~ spl3_12
| spl3_2 ),
inference(avatar_split_clause,[],[f835,f549,f837,f823]) ).
tff(f840,plain,
( $false
| spl3_12 ),
inference(resolution,[],[f838,f560]) ).
tff(f841,plain,
spl3_12,
inference(avatar_contradiction_clause,[],[f840]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f551]) ).
cnf(s8,plain,
( spl3_1
| ~ spl3_10
| ~ spl3_11 ),
inference(sat_conversion,[],[f828]) ).
cnf(s9,plain,
spl3_10,
inference(sat_conversion,[],[f832]) ).
cnf(s10,plain,
spl3_11,
inference(sat_conversion,[],[f834]) ).
cnf(s11,plain,
( spl3_2
| ~ spl3_10
| ~ spl3_12 ),
inference(sat_conversion,[],[f839]) ).
cnf(s12,plain,
spl3_12,
inference(sat_conversion,[],[f841]) ).
cnf(s13,plain,
( spl3_2
| ~ spl3_10 ),
inference(rat,[],[s11,s12]) ).
cnf(s14,plain,
spl3_2,
inference(rat,[],[s13,s9]) ).
cnf(s15,plain,
spl3_1,
inference(rat,[],[s8,s10,s9]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s1,s14,s15]) ).
tff(f842,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM994_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 21:53:01 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.87/1.27 % (2041844)Detected formulas, will run a generic FOF schedule.
% 2.87/1.27 % (2041862)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1132401804:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.87/1.27 % (2041863)dis-21_1_sil=8000:lcm=predicate:random_seed=3458825463: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)
% 2.87/1.27 % (2041863)First to succeed.
% 2.87/1.27 % (2041863)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2041844"
% 2.87/1.27 % (2041862)Also succeeded, but the first one will report.
% 2.87/1.27 % (2041861)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=352559038:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.87/1.27 % (2041857)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=2074209911:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.87/1.27 % (2041860)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3925936039:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.87/1.27 % (2041858)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=1450463019:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.87/1.27 % (2041860)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.87/1.27 % (2041860)Refutation not found, incomplete strategy
% 2.87/1.27 % (2041860)------------------------------
% 2.87/1.27 % (2041860)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.87/1.27 % (2041860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.87/1.27 % (2041860)CaDiCaL version: 2.1.3
% 2.87/1.27 % (2041860)Termination reason: Refutation not found, incomplete strategy
% 2.87/1.27 % (2041860)Time elapsed: 0.005 s
% 2.87/1.27 % (2041860)Peak memory usage: 89 MB
% 2.87/1.27 % (2041860)Instructions burned: 3 (million)
% 2.87/1.27 % (2041859)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=3275045062:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.87/1.27 % (2041859)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.87/1.27 % (2041861)Instruction limit reached!
% 2.87/1.27 % (2041861)------------------------------
% 2.87/1.27 % (2041861)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.87/1.27 % (2041861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.87/1.27 % (2041861)CaDiCaL version: 2.1.3
% 2.87/1.27 % (2041861)Termination reason: Instruction limit
% 2.87/1.27 % (2041861)Termination phase: Saturation
% 2.87/1.27 % (2041861)Time elapsed: 0.102 s
% 2.87/1.27 % (2041861)Peak memory usage: 88 MB
% 2.87/1.27 % (2041861)Instructions burned: 120 (million)
% 2.87/1.27 % (2041863)Refutation found. Thanks to Tanya!
% 2.87/1.27 % SZS status Theorem for theBenchmark
% 2.87/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.49 % (2041863)------------------------------
% 3.48/1.49 % (2041863)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.49 % (2041863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.49 % (2041863)CaDiCaL version: 2.1.3
% 3.48/1.49 % (2041863)Termination reason: Refutation
% 3.48/1.49 % (2041863)Time elapsed: 0.011 s
% 3.48/1.49 % (2041863)Peak memory usage: 89 MB
% 3.48/1.49 % (2041863)Instructions burned: 18 (million)
% 3.48/1.49 % (2041863)------------------------------
% 3.48/1.49 % (2041863)------------------------------
% 3.48/1.49 % (2041844)Success in time 0.416 s
% 3.48/1.49 % Vampire exiting
%------------------------------------------------------------------------------