%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM942_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 : 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 12:17:40 PM UTC 2026
% Result : Theorem 2.58s 1.25s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 15 unt; 0 typ; 1 def)
% Number of atoms : 27 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 10 ~; 4 |; 0 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 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,
legendre: ( int * int ) > int ).
tff(func_def_9,type,
fFalse: bool ).
tff(func_def_10,type,
fTrue: bool ).
tff(func_def_11,type,
m: 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,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
zprime: int > $o ).
tff(pred_def_9,type,
pp: bool > $o ).
tff(pred_def_10,type,
sQ0_eqProxy:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(f1,axiom,
zprime(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',fact_0_p) ).
tff(f5,axiom,
! [X0: int] :
( zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),X0),one_one(int)))
=> ( legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),X0),one_one(int))) = one_one(int) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_Legendre__1mod4) ).
tff(f40,axiom,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_Bit0__def) ).
tff(f49,axiom,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_Bit1__def) ).
tff(f112,conjecture,
legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) = one_one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f113,negated_conjecture,
( ( ~ legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ) = one_one(int) ),
inference(negated_conjecture,[status(cth)],[f112]) ).
tff(f114,plain,
one_one(int) != legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(flattening,[],[f113]) ).
tff(f118,plain,
! [X0: int] :
( ( legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),X0),one_one(int))) = one_one(int) )
| ~ zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),X0),one_one(int))) ),
inference(ennf_transformation,[],[f5]) ).
tff(f191,plain,
zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(cnf_transformation,[],[f1]) ).
tff(f195,plain,
! [X0: int] :
( ( one_one(int) = legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),X0),one_one(int))) )
| ~ zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),X0),one_one(int))) ),
inference(cnf_transformation,[],[f118]) ).
tff(f238,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f40]) ).
tff(f247,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f49]) ).
tff(f324,plain,
one_one(int) != legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(cnf_transformation,[],[f114]) ).
tff(f325,plain,
zprime(plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int))),
inference(definition_unfolding,[],[f191,f238,f238,f247]) ).
tff(f329,plain,
! [X0: int] :
( ( one_one(int) = legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),X0),one_one(int))) )
| ~ zprime(plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),X0),one_one(int))) ),
inference(definition_unfolding,[],[f195,f238,f238,f247,f238,f238,f247]) ).
tff(f374,plain,
one_one(int) != legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int))),
inference(definition_unfolding,[],[f324,f238,f238,f247]) ).
tff(f397,definition,
! [X0: $tType,X2: X0,X1: X0] :
( sQ0_eqProxy(X0,X1,X2)
<=> ( X1 = X2 ) ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
tff(f401,plain,
! [X0: int] :
( sQ0_eqProxy(int,one_one(int),legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),X0),one_one(int))))
| ~ zprime(plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),X0),one_one(int))) ),
inference(equality_proxy_replacement,[],[f329,f397]) ).
tff(f513,plain,
~ sQ0_eqProxy(int,one_one(int),legendre(number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int)))),
inference(equality_proxy_replacement,[],[f374,f397]) ).
tff(f655,plain,
~ zprime(plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),m),one_one(int))),
inference(resolution,[],[f401,f513]) ).
tff(f656,plain,
$false,
inference(resolution,[],[f655,f325]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM942_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n010.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 21:46:32 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.58/1.25 % (1336728)Detected formulas, will run a generic FOF schedule.
% 2.58/1.25 % (1336739)dis-21_1_sil=8000:lcm=predicate:random_seed=802613320: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)
% 2.58/1.25 % (1336739)First to succeed.
% 2.58/1.25 % (1336739)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1336728"
% 2.58/1.25 % (1336733)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=912678296:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.58/1.25 % (1336737)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1881581193:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.58/1.25 % (1336734)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=623248251:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.58/1.25 % (1336735)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=2512594792:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.58/1.25 % (1336736)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=131092228:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.58/1.25 % (1336738)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3838094266:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.58/1.25 % (1336736)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.58/1.25 % (1336735)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.58/1.25 % (1336737)Also succeeded, but the first one will report.
% 2.58/1.25 % (1336738)Also succeeded, but the first one will report.
% 2.58/1.25 % (1336736)Instruction limit reached!
% 2.58/1.25 % (1336736)------------------------------
% 2.58/1.25 % (1336736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.25 % (1336736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.25 % (1336736)CaDiCaL version: 2.1.3
% 2.58/1.25 % (1336736)Termination reason: Instruction limit
% 2.58/1.25 % (1336736)Termination phase: Saturation
% 2.58/1.25 % (1336736)Time elapsed: 0.062 s
% 2.58/1.25 % (1336736)Peak memory usage: 88 MB
% 2.58/1.25 % (1336736)Instructions burned: 109 (million)
% 2.58/1.25 % (1336739)Refutation found. Thanks to Tanya!
% 2.58/1.25 % SZS status Theorem for theBenchmark
% 2.58/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 2.58/1.26 % (1336739)------------------------------
% 2.58/1.26 % (1336739)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.26 % (1336739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.26 % (1336739)CaDiCaL version: 2.1.3
% 2.58/1.26 % (1336739)Termination reason: Refutation
% 2.58/1.26 % (1336739)Time elapsed: 0.006 s
% 2.58/1.26 % (1336739)Peak memory usage: 88 MB
% 2.58/1.26 % (1336739)Instructions burned: 16 (million)
% 2.58/1.26 % (1336739)------------------------------
% 2.58/1.26 % (1336739)------------------------------
% 2.58/1.26 % (1336728)Success in time 0.3 s
% 2.58/1.26 % Vampire exiting
%------------------------------------------------------------------------------