%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM934_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 12:17:39 PM UTC 2026
% Result : Theorem 3.85s 1.53s
% Output : Refutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 52 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 69 ( 22 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 24 ~; 11 |; 3 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 44 ( 44 !; 0 ?; 44 :)
% 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,
pls: int ).
tff(func_def_6,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_7,type,
fFalse: bool ).
tff(func_def_8,type,
fTrue: bool ).
tff(func_def_9,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,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
zprime: int > $o ).
tff(pred_def_9,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_10,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_11,type,
pp: bool > $o ).
tff(f1,axiom,
ord_less_eq(int,one_one(int),m),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__0961_A_060_061_Am_096) ).
tff(f8,axiom,
! [X0: int,X1: int] : ( times_times(int,bit1(X1),X0) = plus_plus(int,bit0(times_times(int,X1,X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_mult__Bit1) ).
tff(f10,axiom,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit1(X0)) = bit1(plus_plus(int,X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_add__Bit0__Bit1) ).
tff(f24,axiom,
bit0(pls) = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_Bit0__Pls) ).
tff(f31,axiom,
! [X0: int] : ( times_times(int,pls,X0) = pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_mult__Pls) ).
tff(f32,axiom,
! [X0: int,X1: int] : ( times_times(int,bit0(X1),X0) = bit0(times_times(int,X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_mult__Bit0) ).
tff(f49,axiom,
! [X0: int,X1: int] :
( ord_less_eq(int,bit1(X1),bit0(X0))
<=> ord_less(int,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_rel__simps_I33_J) ).
tff(f50,axiom,
! [X0: int,X1: int] :
( ord_less(int,bit0(X1),bit1(X0))
<=> ord_less_eq(int,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_rel__simps_I15_J) ).
tff(f60,axiom,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_number__of__is__id) ).
tff(f65,axiom,
! [X0: int,X1: int] :
( ord_less_eq(int,plus_plus(int,X1,one_one(int)),X0)
<=> ord_less(int,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_add1__zle__eq) ).
tff(f68,axiom,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_add__Pls__right) ).
tff(f69,axiom,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_add__Pls) ).
tff(f87,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_one__is__num__one) ).
tff(f113,conjecture,
ord_less(int,number_number_of(int,bit0(bit1(pls))),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,
~ ord_less(int,number_number_of(int,bit0(bit1(pls))),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,
~ ord_less(int,number_number_of(int,bit0(bit1(pls))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(flattening,[],[f114]) ).
tff(f187,plain,
! [X0: int,X1: int] :
( ( ord_less_eq(int,bit1(X1),bit0(X0))
| ~ ord_less(int,X1,X0) )
& ( ord_less(int,X1,X0)
| ~ ord_less_eq(int,bit1(X1),bit0(X0)) ) ),
inference(nnf_transformation,[],[f49]) ).
tff(f188,plain,
! [X0: int,X1: int] :
( ( ord_less(int,bit0(X1),bit1(X0))
| ~ ord_less_eq(int,X1,X0) )
& ( ord_less_eq(int,X1,X0)
| ~ ord_less(int,bit0(X1),bit1(X0)) ) ),
inference(nnf_transformation,[],[f50]) ).
tff(f202,plain,
! [X0: int,X1: int] :
( ( ord_less_eq(int,plus_plus(int,X1,one_one(int)),X0)
| ~ ord_less(int,X1,X0) )
& ( ord_less(int,X1,X0)
| ~ ord_less_eq(int,plus_plus(int,X1,one_one(int)),X0) ) ),
inference(nnf_transformation,[],[f65]) ).
tff(f211,plain,
ord_less_eq(int,one_one(int),m),
inference(cnf_transformation,[],[f1]) ).
tff(f220,plain,
! [X0: int,X1: int] : ( times_times(int,bit1(X1),X0) = plus_plus(int,bit0(times_times(int,X1,X0)),X0) ),
inference(cnf_transformation,[],[f8]) ).
tff(f222,plain,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit1(X0)) = bit1(plus_plus(int,X1,X0)) ),
inference(cnf_transformation,[],[f10]) ).
tff(f244,plain,
pls = bit0(pls),
inference(cnf_transformation,[],[f24]) ).
tff(f255,plain,
! [X0: int] : ( pls = times_times(int,pls,X0) ),
inference(cnf_transformation,[],[f31]) ).
tff(f256,plain,
! [X0: int,X1: int] : ( bit0(times_times(int,X1,X0)) = times_times(int,bit0(X1),X0) ),
inference(cnf_transformation,[],[f32]) ).
tff(f283,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,bit1(X1),bit0(X0))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f187]) ).
tff(f285,plain,
! [X0: int,X1: int] :
( ord_less(int,bit0(X1),bit1(X0))
| ~ ord_less_eq(int,X1,X0) ),
inference(cnf_transformation,[],[f188]) ).
tff(f305,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f60]) ).
tff(f313,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less_eq(int,plus_plus(int,X1,one_one(int)),X0) ),
inference(cnf_transformation,[],[f202]) ).
tff(f319,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f68]) ).
tff(f320,plain,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
inference(cnf_transformation,[],[f69]) ).
tff(f342,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(cnf_transformation,[],[f87]) ).
tff(f373,plain,
~ ord_less(int,number_number_of(int,bit0(bit1(pls))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(cnf_transformation,[],[f115]) ).
tff(f393,plain,
one_one(int) = bit1(pls),
inference(forward_demodulation,[],[f342,f305]) ).
tff(f395,plain,
ord_less_eq(int,bit1(pls),m),
inference(superposition,[],[f211,f393]) ).
tff(f396,plain,
~ ord_less(int,number_number_of(int,bit0(bit1(pls))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),bit1(pls))),
inference(superposition,[],[f373,f393]) ).
tff(f397,plain,
~ ord_less(int,number_number_of(int,bit0(bit1(pls))),plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),bit1(pls))),
inference(forward_demodulation,[],[f396,f305]) ).
tff(f398,plain,
~ ord_less(int,bit0(bit1(pls)),plus_plus(int,times_times(int,bit0(bit0(bit1(pls))),m),bit1(pls))),
inference(forward_demodulation,[],[f397,f305]) ).
tff(f461,plain,
~ ord_less(int,bit0(bit1(pls)),plus_plus(int,bit0(times_times(int,bit0(bit1(pls)),m)),bit1(pls))),
inference(superposition,[],[f398,f256]) ).
tff(f464,plain,
~ ord_less(int,bit0(bit1(pls)),plus_plus(int,bit0(bit0(times_times(int,bit1(pls),m))),bit1(pls))),
inference(forward_demodulation,[],[f461,f256]) ).
tff(f544,plain,
~ ord_less(int,bit0(bit1(pls)),bit1(plus_plus(int,bit0(times_times(int,bit1(pls),m)),pls))),
inference(superposition,[],[f464,f222]) ).
tff(f547,plain,
~ ord_less(int,bit0(bit1(pls)),bit1(bit0(times_times(int,bit1(pls),m)))),
inference(forward_demodulation,[],[f544,f319]) ).
tff(f553,plain,
~ ord_less_eq(int,bit1(pls),bit0(times_times(int,bit1(pls),m))),
inference(resolution,[],[f547,f285]) ).
tff(f561,plain,
~ ord_less(int,pls,times_times(int,bit1(pls),m)),
inference(resolution,[],[f553,f283]) ).
tff(f617,plain,
! [X0: int,X1: int] :
( ~ ord_less_eq(int,plus_plus(int,X1,bit1(pls)),X0)
| ord_less(int,X1,X0) ),
inference(forward_demodulation,[],[f313,f393]) ).
tff(f688,plain,
! [X0: int] :
( ~ ord_less_eq(int,bit1(pls),X0)
| ord_less(int,pls,X0) ),
inference(superposition,[],[f617,f320]) ).
tff(f732,plain,
! [X0: int] : ( times_times(int,bit1(pls),X0) = plus_plus(int,bit0(pls),X0) ),
inference(superposition,[],[f220,f255]) ).
tff(f746,plain,
! [X0: int] : ( plus_plus(int,pls,X0) = times_times(int,bit1(pls),X0) ),
inference(forward_demodulation,[],[f732,f244]) ).
tff(f747,plain,
! [X0: int] : ( times_times(int,bit1(pls),X0) = X0 ),
inference(forward_demodulation,[],[f746,f320]) ).
tff(f1122,plain,
~ ord_less(int,pls,m),
inference(superposition,[],[f561,f747]) ).
tff(f1260,plain,
ord_less(int,pls,m),
inference(resolution,[],[f688,f395]) ).
tff(f1267,plain,
$false,
inference(forward_subsumption_resolution,[],[f1260,f1122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM934_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n010.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 21:45:47 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 3.02/1.33 % (1336159)Detected formulas, will run a generic FOF schedule.
% 3.02/1.33 % (1336170)dis-21_1_sil=8000:lcm=predicate:random_seed=6459391: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)
% 3.02/1.33 % (1336164)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=3587798570:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.02/1.33 % (1336169)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=172163061:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.02/1.33 % (1336165)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=212774302:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.02/1.33 % (1336168)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=779825217:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.02/1.33 % (1336166)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=3951755240:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.02/1.33 % (1336167)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=102611727:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.02/1.33 % (1336170)Instruction limit reached!
% 3.02/1.33 % (1336170)------------------------------
% 3.02/1.33 % (1336170)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.33 % (1336170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.33 % (1336170)CaDiCaL version: 2.1.3
% 3.02/1.33 % (1336170)Termination reason: Instruction limit
% 3.02/1.33 % (1336170)Termination phase: Saturation
% 3.02/1.33 % (1336170)Time elapsed: 0.042 s
% 3.02/1.33 % (1336170)Peak memory usage: 89 MB
% 3.02/1.33 % (1336170)Instructions burned: 131 (million)
% 3.02/1.33 % (1336167)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.02/1.33 % (1336166)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.02/1.33 % (1336169)First to succeed.
% 3.02/1.33 % (1336169)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1336159"
% 3.02/1.33 % (1336167)Instruction limit reached!
% 3.02/1.33 % (1336167)------------------------------
% 3.02/1.33 % (1336167)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.33 % (1336167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.33 % (1336167)CaDiCaL version: 2.1.3
% 3.02/1.33 % (1336167)Termination reason: Instruction limit
% 3.02/1.33 % (1336167)Termination phase: Saturation
% 3.02/1.33 % (1336167)Time elapsed: 0.065 s
% 3.02/1.33 % (1336167)Peak memory usage: 89 MB
% 3.02/1.33 % (1336167)Instructions burned: 110 (million)
% 3.02/1.33 % (1336168)Instruction limit reached!
% 3.02/1.33 % (1336168)------------------------------
% 3.02/1.33 % (1336168)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.33 % (1336168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.33 % (1336168)CaDiCaL version: 2.1.3
% 3.02/1.33 % (1336168)Termination reason: Instruction limit
% 3.02/1.33 % (1336168)Termination phase: Saturation
% 3.02/1.33 % (1336168)Time elapsed: 0.067 s
% 3.02/1.33 % (1336168)Peak memory usage: 88 MB
% 3.02/1.33 % (1336168)Instructions burned: 119 (million)
% 3.02/1.33 % (1336178)lrs+10_1_sil=8000:sp=occurrence:random_seed=1078792785:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.02/1.33 % (1336178)Instruction limit reached!
% 3.02/1.33 % (1336178)------------------------------
% 3.02/1.33 % (1336178)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.33 % (1336178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.33 % (1336178)CaDiCaL version: 2.1.3
% 3.02/1.33 % (1336178)Termination reason: Instruction limit
% 3.02/1.33 % (1336178)Termination phase: Saturation
% 3.02/1.33 % (1336178)Time elapsed: 0.090 s
% 3.02/1.33 % (1336178)Peak memory usage: 90 MB
% 3.02/1.33 % (1336178)Instructions burned: 287 (million)
% 3.02/1.33 % (1336180)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1159585769:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.02/1.33 % (1336179)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3385370194:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.85/1.53 % (1336180)Also succeeded, but the first one will report.
% 3.85/1.53 % (1336179)Also succeeded, but the first one will report.
% 3.85/1.53 % (1336169)Refutation found. Thanks to Tanya!
% 3.85/1.53 % SZS status Theorem for theBenchmark
% 3.85/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 3.85/1.53 % (1336169)------------------------------
% 3.85/1.53 % (1336169)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.53 % (1336169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.53 % (1336169)CaDiCaL version: 2.1.3
% 3.85/1.53 % (1336169)Termination reason: Refutation
% 3.85/1.53 % (1336169)Time elapsed: 0.030 s
% 3.85/1.53 % (1336169)Peak memory usage: 89 MB
% 3.85/1.53 % (1336169)Instructions burned: 44 (million)
% 3.85/1.53 % (1336169)------------------------------
% 3.85/1.53 % (1336169)------------------------------
% 3.85/1.53 % (1336159)Success in time 0.457 s
% 3.85/1.53 % Vampire exiting
%------------------------------------------------------------------------------