%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM970_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 : n016.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 12:17:43 PM UTC 2026
% Result : Theorem 3.35s 1.52s
% Output : Refutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 18 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 6 ~; 2 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 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 : 25 ( 23 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-4 aty)
% Number of variables : 8 ( 8 !; 0 ?; 8 :)
% 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,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
bit0: int > int ).
tff(func_def_3,type,
bit1: int > int ).
tff(func_def_4,type,
pls: int ).
tff(func_def_5,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_6,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_7,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_8,type,
fFalse: bool ).
tff(func_def_9,type,
fTrue: bool ).
tff(func_def_10,type,
s: int ).
tff(func_def_11,type,
sK2:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
power:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
ord:
!>[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,
order:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
mult_zero:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
preorder:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
zero_neq_one:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
no_zero_divisors:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_18,type,
ring_11004092258visors:
!>[X0: $tType] : $o ).
tff(pred_def_19,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_20,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_21,type,
pp: bool > $o ).
tff(pred_def_22,type,
sP0: ( int * bool * bool ) > $o ).
tff(pred_def_23,type,
sP1: ( bool * int * bool ) > $o ).
tff(f12,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0] : ord_less_eq(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_zero__le__power2) ).
tff(f34,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_Pls__def) ).
tff(f104,axiom,
linordered_idom(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
tff(f139,conjecture,
ord_less_eq(int,zero_zero(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f140,negated_conjecture,
~ ord_less_eq(int,zero_zero(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),
inference(negated_conjecture,[status(cth)],[f139]) ).
tff(f141,plain,
~ ord_less_eq(int,zero_zero(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),
inference(flattening,[],[f140]) ).
tff(f155,plain,
! [X0: $tType] :
( ! [X1: X0] : ord_less_eq(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f12]) ).
tff(f295,plain,
! [X0: $tType,X1: X0] :
( ~ linordered_idom(X0)
| ord_less_eq(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) ),
inference(cnf_transformation,[],[f155]) ).
tff(f330,plain,
pls = zero_zero(int),
inference(cnf_transformation,[],[f34]) ).
tff(f442,plain,
linordered_idom(int),
inference(cnf_transformation,[],[f104]) ).
tff(f475,plain,
~ ord_less_eq(int,zero_zero(int),power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),
inference(cnf_transformation,[],[f141]) ).
tff(f504,plain,
~ ord_less_eq(int,pls,power_power(int,s,number_number_of(nat,bit0(bit1(pls))))),
inference(superposition,[],[f475,f330]) ).
tff(f704,plain,
! [X0: int] : ord_less_eq(int,zero_zero(int),power_power(int,X0,number_number_of(nat,bit0(bit1(pls))))),
inference(resolution,[],[f295,f442]) ).
tff(f705,plain,
! [X0: int] : ord_less_eq(int,pls,power_power(int,X0,number_number_of(nat,bit0(bit1(pls))))),
inference(forward_demodulation,[],[f704,f330]) ).
tff(f1100,plain,
$false,
inference(resolution,[],[f705,f504]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM970_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n016.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 21:53:32 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 3.35/1.52 % (3024164)Detected formulas, will run a generic FOF schedule.
% 3.35/1.52 % (3024275)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=75840593:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.35/1.52 % (3024275)First to succeed.
% 3.35/1.52 % (3024275)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3024164"
% 3.35/1.52 % (3024273)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2214814743:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.35/1.52 % (3024270)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=3490647655:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.35/1.52 % (3024272)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=4274951829:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.35/1.52 % (3024271)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=1028686829:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.35/1.52 % (3024274)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2517017838:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.35/1.52 % (3024273)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.35/1.52 % (3024272)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.35/1.52 % (3024273)Refutation not found, incomplete strategy
% 3.35/1.52 % (3024273)------------------------------
% 3.35/1.52 % (3024273)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.52 % (3024273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.52 % (3024273)CaDiCaL version: 2.1.3
% 3.35/1.52 % (3024273)Termination reason: Refutation not found, incomplete strategy
% 3.35/1.52 % (3024273)Time elapsed: 0.003 s
% 3.35/1.52 % (3024273)Peak memory usage: 88 MB
% 3.35/1.52 % (3024273)Instructions burned: 3 (million)
% 3.35/1.52 % (3024276)dis-21_1_sil=8000:lcm=predicate:random_seed=2369776280: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)
% 3.35/1.52 % (3024276)Also succeeded, but the first one will report.
% 3.35/1.52 % (3024274)Instruction limit reached!
% 3.35/1.52 % (3024274)------------------------------
% 3.35/1.52 % (3024274)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.52 % (3024274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.52 % (3024274)CaDiCaL version: 2.1.3
% 3.35/1.52 % (3024274)Termination reason: Instruction limit
% 3.35/1.52 % (3024274)Termination phase: Saturation
% 3.35/1.52 % (3024274)Time elapsed: 0.066 s
% 3.35/1.52 % (3024274)Peak memory usage: 87 MB
% 3.35/1.52 % (3024274)Instructions burned: 119 (million)
% 3.35/1.52 % (3024275)Refutation found. Thanks to Tanya!
% 3.35/1.52 % SZS status Theorem for theBenchmark
% 3.35/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 3.35/1.52 % (3024275)------------------------------
% 3.35/1.52 % (3024275)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.52 % (3024275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.52 % (3024275)CaDiCaL version: 2.1.3
% 3.35/1.52 % (3024275)Termination reason: Refutation
% 3.35/1.52 % (3024275)Time elapsed: 0.022 s
% 3.35/1.52 % (3024275)Peak memory usage: 89 MB
% 3.35/1.52 % (3024275)Instructions burned: 66 (million)
% 3.35/1.52 % (3024275)------------------------------
% 3.35/1.52 % (3024275)------------------------------
% 3.35/1.52 % (3024164)Success in time 0.377 s
% 3.35/1.52 % Vampire exiting
%------------------------------------------------------------------------------