%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM972_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 : n012.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 2.39s 0.92s
% Output : Refutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 3 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-3 aty)
% Number of variables : 12 ( 12 !; 0 ?; 12 :)
% 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,
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,
bit0: int > int ).
tff(func_def_4,type,
bit1: int > int ).
tff(func_def_5,type,
min: 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,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_9,type,
legendre: ( int * int ) > int ).
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,
s: int ).
tff(func_def_14,type,
t: int ).
tff(func_def_15,type,
sK0: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
semiring:
!>[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,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
monoid_mult:
!>[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,
zprime: int > $o ).
tff(pred_def_10,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_11,type,
twoSqu1567020053sum2sq: int > $o ).
tff(pred_def_12,type,
pp: bool > $o ).
tff(f1,axiom,
t = one_one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096t_A_061_A1_096) ).
tff(f2,axiom,
twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_qf1pt) ).
tff(f32,axiom,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_number__of__is__id) ).
tff(f47,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0] : ( times_times(X0,X1,number_number_of(X0,bit1(pls))) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_mult__numeral__1__right) ).
tff(f49,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_one__is__num__one) ).
tff(f103,axiom,
number_ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
tff(f113,conjecture,
twoSqu1567020053sum2sq(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f114,negated_conjecture,
~ twoSqu1567020053sum2sq(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(negated_conjecture,[status(cth)],[f113]) ).
tff(f115,plain,
~ twoSqu1567020053sum2sq(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(flattening,[],[f114]) ).
tff(f141,plain,
! [X0: $tType] :
( ! [X1: X0] : ( times_times(X0,X1,number_number_of(X0,bit1(pls))) = X1 )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f47]) ).
tff(f187,plain,
t = one_one(int),
inference(cnf_transformation,[],[f1]) ).
tff(f188,plain,
twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
inference(cnf_transformation,[],[f2]) ).
tff(f223,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f32]) ).
tff(f238,plain,
! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,number_number_of(X0,bit1(pls))) = X1 )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f141]) ).
tff(f240,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(cnf_transformation,[],[f49]) ).
tff(f312,plain,
number_ring(int),
inference(cnf_transformation,[],[f103]) ).
tff(f322,plain,
~ twoSqu1567020053sum2sq(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(cnf_transformation,[],[f115]) ).
tff(f343,plain,
one_one(int) = bit1(pls),
inference(forward_demodulation,[],[f240,f223]) ).
tff(f344,plain,
t = bit1(pls),
inference(forward_demodulation,[],[f343,f187]) ).
tff(f471,plain,
! [X0: $tType,X1: X0] :
( ~ number_ring(X0)
| ( times_times(X0,X1,number_number_of(X0,t)) = X1 ) ),
inference(forward_demodulation,[],[f238,f344]) ).
tff(f473,plain,
! [X0: int] : ( times_times(int,X0,number_number_of(int,t)) = X0 ),
inference(resolution,[],[f471,f312]) ).
tff(f474,plain,
! [X0: int] : ( times_times(int,X0,t) = X0 ),
inference(forward_demodulation,[],[f473,f223]) ).
tff(f747,plain,
twoSqu1567020053sum2sq(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(forward_demodulation,[],[f188,f474]) ).
tff(f748,plain,
$false,
inference(forward_subsumption_resolution,[],[f747,f322]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM972_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 27 21:48:04 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 2.39/0.92 % (2783677)Detected formulas, will run a generic FOF schedule.
% 2.39/0.92 % (2783683)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=1625673331:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.39/0.92 % (2783684)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=2635287005:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.39/0.92 % (2783686)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2012378616:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.39/0.92 % (2783687)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1030526899:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.39/0.92 % (2783685)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3934790855:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.39/0.92 % (2783688)dis-21_1_sil=8000:lcm=predicate:random_seed=1130454015: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)
% 2.39/0.92 % (2783682)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=1719606970:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.39/0.92 % (2783685)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.39/0.92 % (2783684)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.39/0.92 % (2783685)Refutation not found, incomplete strategy
% 2.39/0.92 % (2783685)------------------------------
% 2.39/0.92 % (2783685)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.39/0.92 % (2783685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.92 % (2783685)CaDiCaL version: 2.1.3
% 2.39/0.92 % (2783685)Termination reason: Refutation not found, incomplete strategy
% 2.39/0.92 % (2783685)Time elapsed: 0.002 s
% 2.39/0.92 % (2783685)Peak memory usage: 88 MB
% 2.39/0.92 % (2783685)Instructions burned: 3 (million)
% 2.39/0.92 % (2783688)Refutation not found, incomplete strategy
% 2.39/0.92 % (2783688)------------------------------
% 2.39/0.92 % (2783688)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.39/0.92 % (2783688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.92 % (2783688)CaDiCaL version: 2.1.3
% 2.39/0.92 % (2783688)Termination reason: Refutation not found, incomplete strategy
% 2.39/0.92 % (2783688)Time elapsed: 0.005 s
% 2.39/0.92 % (2783688)Peak memory usage: 88 MB
% 2.39/0.92 % (2783688)Instructions burned: 14 (million)
% 2.39/0.92 % (2783687)First to succeed.
% 2.39/0.92 % (2783687)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2783677"
% 2.39/0.92 % (2783686)Also succeeded, but the first one will report.
% 2.39/0.92 % (2783685)------------------------------
% 2.39/0.92 % (2783685)------------------------------
% 2.39/0.92 % (2783688)------------------------------
% 2.39/0.92 % (2783688)------------------------------
% 2.39/0.92 % (2783687)Refutation found. Thanks to Tanya!
% 2.39/0.92 % SZS status Theorem for theBenchmark
% 2.39/0.92 % SZS output start Proof for theBenchmark
% See solution above
% 2.39/0.92 % (2783687)------------------------------
% 2.39/0.92 % (2783687)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.39/0.92 % (2783687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.39/0.92 % (2783687)CaDiCaL version: 2.1.3
% 2.39/0.92 % (2783687)Termination reason: Refutation
% 2.39/0.92 % (2783687)Time elapsed: 0.010 s
% 2.39/0.92 % (2783687)Peak memory usage: 89 MB
% 2.39/0.92 % (2783687)Instructions burned: 26 (million)
% 2.39/0.92 % (2783687)------------------------------
% 2.39/0.92 % (2783687)------------------------------
% 2.39/0.92 % (2783677)Success in time 0.309 s
% 2.39/0.92 % Vampire exiting
%------------------------------------------------------------------------------