%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM932_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 : 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 12:17:38 PM UTC 2026
% Result : Theorem 3.78s 1.54s
% Output : Refutation 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 43 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 56 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 33 ( 20 ~; 8 |; 2 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 29 ( 29 !; 0 ?; 29 :)
% 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,
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,
fFalse: bool ).
tff(func_def_9,type,
fTrue: bool ).
tff(func_def_10,type,
m: int ).
tff(pred_def_1,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
semiring:
!>[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,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
ordere236663937imp_le:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
zprime: int > $o ).
tff(pred_def_13,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_14,type,
pp: bool > $o ).
tff(f1,axiom,
ord_less_eq(int,m,zero_zero(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096m_A_060_061_A0_096) ).
tff(f11,axiom,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit1(X0)) = bit1(plus_plus(int,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_add__Bit0__Bit1) ).
tff(f14,axiom,
! [X0: int] :
( ord_less_eq(int,bit0(X0),pls)
<=> ord_less_eq(int,X0,pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_rel__simps_I27_J) ).
tff(f27,axiom,
! [X0: int,X1: int] :
( ord_less_eq(int,bit1(X1),bit1(X0))
<=> ord_less_eq(int,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_rel__simps_I34_J) ).
tff(f31,axiom,
! [X0: int,X1: int] : ( times_times(int,bit0(X1),X0) = bit0(times_times(int,X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_mult__Bit0) ).
tff(f44,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Pls__def) ).
tff(f46,axiom,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_number__of__is__id) ).
tff(f53,axiom,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_add__Pls__right) ).
tff(f68,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0] : ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_mult__numeral__1) ).
tff(f71,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_one__is__num__one) ).
tff(f103,axiom,
number_ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
tff(f117,conjecture,
ord_less_eq(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f118,negated_conjecture,
~ ord_less_eq(int,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)],[f117]) ).
tff(f119,plain,
~ ord_less_eq(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)),
inference(flattening,[],[f118]) ).
tff(f158,plain,
! [X0: $tType] :
( ! [X1: X0] : ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f68]) ).
tff(f181,plain,
! [X0: int] :
( ( ord_less_eq(int,bit0(X0),pls)
| ~ ord_less_eq(int,X0,pls) )
& ( ord_less_eq(int,X0,pls)
| ~ ord_less_eq(int,bit0(X0),pls) ) ),
inference(nnf_transformation,[],[f14]) ).
tff(f189,plain,
! [X0: int,X1: int] :
( ( ord_less_eq(int,bit1(X1),bit1(X0))
| ~ ord_less_eq(int,X1,X0) )
& ( ord_less_eq(int,X1,X0)
| ~ ord_less_eq(int,bit1(X1),bit1(X0)) ) ),
inference(nnf_transformation,[],[f27]) ).
tff(f211,plain,
ord_less_eq(int,m,zero_zero(int)),
inference(cnf_transformation,[],[f1]) ).
tff(f223,plain,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit1(X0)) = bit1(plus_plus(int,X1,X0)) ),
inference(cnf_transformation,[],[f11]) ).
tff(f228,plain,
! [X0: int] :
( ord_less_eq(int,bit0(X0),pls)
| ~ ord_less_eq(int,X0,pls) ),
inference(cnf_transformation,[],[f181]) ).
tff(f249,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,bit1(X1),bit1(X0))
| ~ ord_less_eq(int,X1,X0) ),
inference(cnf_transformation,[],[f189]) ).
tff(f254,plain,
! [X0: int,X1: int] : ( bit0(times_times(int,X1,X0)) = times_times(int,bit0(X1),X0) ),
inference(cnf_transformation,[],[f31]) ).
tff(f271,plain,
zero_zero(int) = pls,
inference(cnf_transformation,[],[f44]) ).
tff(f274,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f46]) ).
tff(f283,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f53]) ).
tff(f300,plain,
! [X0: $tType,X1: X0] :
( ~ number_ring(X0)
| ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 ) ),
inference(cnf_transformation,[],[f158]) ).
tff(f303,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(cnf_transformation,[],[f71]) ).
tff(f347,plain,
number_ring(int),
inference(cnf_transformation,[],[f103]) ).
tff(f357,plain,
~ ord_less_eq(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)),
inference(cnf_transformation,[],[f119]) ).
tff(f369,plain,
ord_less_eq(int,m,pls),
inference(forward_demodulation,[],[f211,f271]) ).
tff(f378,plain,
one_one(int) = bit1(pls),
inference(forward_demodulation,[],[f303,f274]) ).
tff(f381,plain,
~ ord_less_eq(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),bit1(pls)),bit1(pls)),
inference(superposition,[],[f357,f378]) ).
tff(f382,plain,
~ ord_less_eq(int,plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),bit1(pls)),bit1(pls)),
inference(forward_demodulation,[],[f381,f274]) ).
tff(f434,plain,
~ ord_less_eq(int,plus_plus(int,bit0(times_times(int,bit0(bit1(pls)),m)),bit1(pls)),bit1(pls)),
inference(superposition,[],[f382,f254]) ).
tff(f437,plain,
~ ord_less_eq(int,plus_plus(int,bit0(bit0(times_times(int,bit1(pls),m))),bit1(pls)),bit1(pls)),
inference(forward_demodulation,[],[f434,f254]) ).
tff(f453,plain,
! [X0: int] : ( times_times(int,number_number_of(int,bit1(pls)),X0) = X0 ),
inference(resolution,[],[f300,f347]) ).
tff(f454,plain,
! [X0: int] : ( times_times(int,bit1(pls),X0) = X0 ),
inference(forward_demodulation,[],[f453,f274]) ).
tff(f472,plain,
~ ord_less_eq(int,bit1(plus_plus(int,bit0(times_times(int,bit1(pls),m)),pls)),bit1(pls)),
inference(superposition,[],[f437,f223]) ).
tff(f476,plain,
~ ord_less_eq(int,bit1(bit0(times_times(int,bit1(pls),m))),bit1(pls)),
inference(forward_demodulation,[],[f472,f283]) ).
tff(f478,plain,
~ ord_less_eq(int,bit1(bit0(m)),bit1(pls)),
inference(forward_demodulation,[],[f476,f454]) ).
tff(f479,plain,
~ ord_less_eq(int,bit0(m),pls),
inference(resolution,[],[f478,f249]) ).
tff(f487,plain,
~ ord_less_eq(int,m,pls),
inference(resolution,[],[f479,f228]) ).
tff(f490,plain,
$false,
inference(forward_subsumption_resolution,[],[f487,f369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM932_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 % Computer : n016.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.42 % CPULimit : 300
% 0.13/0.42 % WCLimit : 300
% 0.13/0.42 % DateTime : Sun Sep 27 21:50:32 UTC 2026
% 0.13/0.42 % CPUTime :
% 0.13/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.45 Running first-order theorem proving
% 0.13/0.45 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
% 2.90/1.34 % (3019529)Detected formulas, will run a generic FOF schedule.
% 2.90/1.34 % (3019534)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=3984322924:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.90/1.34 % (3019540)dis-21_1_sil=8000:lcm=predicate:random_seed=2614762233: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)
% 2.90/1.34 % (3019537)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4265708139:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.90/1.34 % (3019535)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=2236820685:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.90/1.34 % (3019539)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4160074355:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.90/1.34 % (3019536)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=3328391513:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.90/1.34 % (3019538)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2814227120:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.90/1.34 % (3019537)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.90/1.34 % (3019536)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.90/1.34 % (3019537)Refutation not found, incomplete strategy
% 2.90/1.34 % (3019537)------------------------------
% 2.90/1.34 % (3019537)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.34 % (3019537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.34 % (3019537)CaDiCaL version: 2.1.3
% 2.90/1.34 % (3019537)Termination reason: Refutation not found, incomplete strategy
% 2.90/1.34 % (3019537)Time elapsed: 0.004 s
% 2.90/1.34 % (3019537)Peak memory usage: 88 MB
% 2.90/1.34 % (3019537)Instructions burned: 5 (million)
% 2.90/1.34 % (3019539)First to succeed.
% 2.90/1.34 % (3019539)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3019529"
% 2.90/1.34 % (3019540)Instruction limit reached!
% 2.90/1.34 % (3019540)------------------------------
% 2.90/1.34 % (3019540)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.34 % (3019540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.34 % (3019540)CaDiCaL version: 2.1.3
% 2.90/1.34 % (3019540)Termination reason: Instruction limit
% 2.90/1.34 % (3019540)Termination phase: Saturation
% 2.90/1.34 % (3019540)Time elapsed: 0.061 s
% 2.90/1.34 % (3019540)Peak memory usage: 90 MB
% 2.90/1.34 % (3019540)Instructions burned: 129 (million)
% 2.90/1.34 % (3019538)Instruction limit reached!
% 2.90/1.34 % (3019538)------------------------------
% 2.90/1.34 % (3019538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.34 % (3019538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.34 % (3019538)CaDiCaL version: 2.1.3
% 2.90/1.34 % (3019538)Termination reason: Instruction limit
% 2.90/1.34 % (3019538)Termination phase: Saturation
% 2.90/1.34 % (3019538)Time elapsed: 0.066 s
% 2.90/1.34 % (3019538)Peak memory usage: 88 MB
% 2.90/1.34 % (3019538)Instructions burned: 121 (million)
% 2.90/1.34 % (3019534)Aborted by signal SIGSEGV on /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.90/1.34 % (3019534)------------------------------
% 2.90/1.34 % (3019534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.90/1.34 % (3019534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.90/1.34 % (3019534)CaDiCaL version: 2.1.3
% 2.90/1.34 % (3019534)Termination reason: Unknown
% 2.90/1.34 % (3019534)Termination phase: Saturation
% 2.90/1.34 % (3019534)Time elapsed: 0.200 s
% 2.90/1.34 % (3019534)Peak memory usage: 113 MB
% 2.90/1.34 % (3019534)Instructions burned: 541 (million)
% 2.90/1.34 % (3019548)lrs+10_1_sil=8000:sp=occurrence:random_seed=3964281696:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.90/1.34 % (3019549)lrs+10_1_sil=32000:urr=on:br=off:random_seed=545178844:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.78/1.54 % (3019537)------------------------------
% 3.78/1.54 % (3019537)------------------------------
% 3.78/1.54 % (3019539)Refutation found. Thanks to Tanya!
% 3.78/1.54 % SZS status Theorem for theBenchmark
% 3.78/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 3.78/1.54 % (3019539)------------------------------
% 3.78/1.54 % (3019539)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.54 % (3019539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.54 % (3019539)CaDiCaL version: 2.1.3
% 3.78/1.54 % (3019539)Termination reason: Refutation
% 3.78/1.54 % (3019539)Time elapsed: 0.011 s
% 3.78/1.54 % (3019539)Peak memory usage: 89 MB
% 3.78/1.54 % (3019539)Instructions burned: 15 (million)
% 3.78/1.54 % (3019539)------------------------------
% 3.78/1.54 % (3019539)------------------------------
% 3.78/1.54 % (3019529)Success in time 0.446 s
% 3.78/1.54 % Vampire exiting
%------------------------------------------------------------------------------