%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM977_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 : n002.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 0.19s 1.50s
% Output : Refutation 0.19s
% 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 : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 8 ( 3 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 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,
t: int ).
tff(func_def_14,type,
tn: nat ).
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,
semiring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
zprime: int > $o ).
tff(pred_def_11,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_12,type,
twoSqu1567020053sum2sq: int > $o ).
tff(pred_def_13,type,
pp: bool > $o ).
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)),plus_plus(int,one_one(int),semiring_1_of_nat(int,zero_zero(nat))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_nQ1) ).
tff(f116,conjecture,
~ twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,zero_zero(nat))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f117,negated_conjecture,
~ ~ twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,zero_zero(nat))))),
inference(negated_conjecture,[status(cth)],[f116]) ).
tff(f118,plain,
twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,zero_zero(nat))))),
inference(flattening,[],[f117]) ).
tff(f164,plain,
twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,zero_zero(nat))))),
inference(cnf_transformation,[],[f118]) ).
tff(f255,plain,
~ twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),plus_plus(int,one_one(int),semiring_1_of_nat(int,zero_zero(nat))))),
inference(cnf_transformation,[],[f2]) ).
tff(f701,plain,
$false,
inference(forward_subsumption_resolution,[],[f255,f164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM977_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n002.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 21:51:36 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 0.19/1.50 % (3919647)Detected formulas, will run a generic FOF schedule.
% 0.19/1.50 % (3919755)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=4004219111:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.19/1.50 % (3919755)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/1.50 % (3919753)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=3786530934:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.19/1.50 % (3919754)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=1789180533:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.19/1.50 % (3919758)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3652049360:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.19/1.50 % (3919757)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2847790363:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.19/1.50 % (3919759)dis-21_1_sil=8000:lcm=predicate:random_seed=2822235669: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)
% 0.19/1.50 % (3919757)First to succeed.
% 0.19/1.50 % (3919757)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3919647"
% 0.19/1.50 % (3919758)Also succeeded, but the first one will report.
% 0.19/1.50 % (3919756)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3946757133:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.19/1.50 % (3919756)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/1.50 % (3919756)Also succeeded, but the first one will report.
% 0.19/1.50 % (3919759)Instruction limit reached!
% 0.19/1.50 % (3919759)------------------------------
% 0.19/1.50 % (3919759)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (3919759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (3919759)CaDiCaL version: 2.1.3
% 0.19/1.50 % (3919759)Termination reason: Instruction limit
% 0.19/1.50 % (3919759)Termination phase: Saturation
% 0.19/1.50 % (3919759)Time elapsed: 0.067 s
% 0.19/1.50 % (3919759)Peak memory usage: 89 MB
% 0.19/1.50 % (3919759)Instructions burned: 130 (million)
% 0.19/1.50 % Exception at run slice level
% 0.19/1.50 User error: GNN currently only supports monomorphic FOL.
% 0.19/1.50 % (3919757)Refutation found. Thanks to Tanya!
% 0.19/1.50 % SZS status Theorem for theBenchmark
% 0.19/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.50 % (3919757)------------------------------
% 0.19/1.50 % (3919757)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.50 % (3919757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.50 % (3919757)CaDiCaL version: 2.1.3
% 0.19/1.50 % (3919757)Termination reason: Refutation
% 0.19/1.50 % (3919757)Time elapsed: 0.016 s
% 0.19/1.50 % (3919757)Peak memory usage: 88 MB
% 0.19/1.50 % (3919757)Instructions burned: 22 (million)
% 0.19/1.50 % (3919757)------------------------------
% 0.19/1.50 % (3919757)------------------------------
% 0.19/1.50 % (3919647)Success in time 0.438 s
% 0.19/1.50 % Vampire exiting
%------------------------------------------------------------------------------