%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM931_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 : n020.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 3.50s 1.48s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 31 ( 15 ~; 10 |; 2 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 3 con; 0-4 aty)
% Number of variables : 17 ( 17 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
archimedean_ceiling:
!>[X0: $tType] : ( X0 > int ) ).
tff(func_def_1,type,
archim2085082626_floor:
!>[X0: $tType] : ( X0 > int ) ).
tff(func_def_2,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_3,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_4,type,
nat_tsub: ( int * int ) > int ).
tff(func_def_5,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_6,type,
fFalse: bool ).
tff(func_def_7,type,
fTrue: bool ).
tff(func_def_8,type,
m: int ).
tff(func_def_9,type,
sK2:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_10,type,
sK3:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_11,type,
sK4:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_12,type,
sK5:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_13,type,
sK6:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_14,type,
sK7:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_15,type,
sK8:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_16,type,
sK9:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_17,type,
sK10:
!>[X0: $tType] : ( X0 > X0 ) ).
tff(func_def_18,type,
sK11:
!>[X0: $tType] : ( X0 > X0 ) ).
tff(func_def_19,type,
sK12:
!>[X0: $tType] : ( X0 > X0 ) ).
tff(func_def_20,type,
sK13:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_21,type,
sK14:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_22,type,
sK15:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_23,type,
sK16:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_24,type,
sK17:
!>[X0: $tType] : ( X0 > X0 ) ).
tff(func_def_25,type,
sK18:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(func_def_26,type,
sK19:
!>[X0: $tType,X1: $tType] : ( fun(X0,X1) > X0 ) ).
tff(pred_def_1,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
ord:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
order:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
preorder:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
zero_neq_one:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
dense_linorder:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
archim1727834104eiling:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_13,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_14,type,
pp: bool > $o ).
tff(pred_def_15,type,
sP0: ( int * bool * bool ) > $o ).
tff(pred_def_16,type,
sP1: ( bool * int * bool ) > $o ).
tff(f1,axiom,
~ ord_less_eq(int,one_one(int),m),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096_126_A1_A_060_061_Am_096) ).
tff(f70,axiom,
! [X0: $tType] :
( linorder(X0)
=> ! [X1: X0,X2: X0] :
( ~ ord_less(X0,X2,X1)
<=> ord_less_eq(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_linorder__not__less) ).
tff(f89,axiom,
! [X0: int] :
( ord_less_eq(int,one_one(int),X0)
<=> ord_less(int,zero_zero(int),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_int__one__le__iff__zero__less) ).
tff(f106,axiom,
linorder(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
tff(f117,conjecture,
ord_less_eq(int,m,zero_zero(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f118,negated_conjecture,
~ ord_less_eq(int,m,zero_zero(int)),
inference(negated_conjecture,[status(cth)],[f117]) ).
tff(f119,plain,
~ ord_less_eq(int,m,zero_zero(int)),
inference(flattening,[],[f118]) ).
tff(f202,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ~ ord_less(X0,X2,X1)
<=> ord_less_eq(X0,X1,X2) )
| ~ linorder(X0) ),
inference(ennf_transformation,[],[f70]) ).
tff(f272,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ~ ord_less(X0,X2,X1)
| ~ ord_less_eq(X0,X1,X2) )
& ( ord_less_eq(X0,X1,X2)
| ord_less(X0,X2,X1) ) )
| ~ linorder(X0) ),
inference(nnf_transformation,[],[f202]) ).
tff(f282,plain,
! [X0: int] :
( ( ord_less_eq(int,one_one(int),X0)
| ~ ord_less(int,zero_zero(int),X0) )
& ( ord_less(int,zero_zero(int),X0)
| ~ ord_less_eq(int,one_one(int),X0) ) ),
inference(nnf_transformation,[],[f89]) ).
tff(f292,plain,
~ ord_less_eq(int,one_one(int),m),
inference(cnf_transformation,[],[f1]) ).
tff(f369,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ~ linorder(X0)
| ord_less(X0,X2,X1)
| ord_less_eq(X0,X1,X2) ),
inference(cnf_transformation,[],[f272]) ).
tff(f399,plain,
! [X0: int] :
( ~ ord_less(int,zero_zero(int),X0)
| ord_less_eq(int,one_one(int),X0) ),
inference(cnf_transformation,[],[f282]) ).
tff(f420,plain,
linorder(int),
inference(cnf_transformation,[],[f106]) ).
tff(f431,plain,
~ ord_less_eq(int,m,zero_zero(int)),
inference(cnf_transformation,[],[f119]) ).
tff(f472,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ord_less(int,X0,X1) ),
inference(resolution,[],[f369,f420]) ).
tff(f475,plain,
ord_less(int,zero_zero(int),m),
inference(resolution,[],[f472,f431]) ).
tff(f504,plain,
ord_less_eq(int,one_one(int),m),
inference(resolution,[],[f399,f475]) ).
tff(f507,plain,
$false,
inference(forward_subsumption_resolution,[],[f504,f292]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM931_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.39 % Computer : n020.cluster.edu
% 0.09/0.39 % Model : x86_64 x86_64
% 0.09/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39 % Memory : 8046.5625MB
% 0.09/0.39 % OS : Linux 6.8.0-71-generic
% 0.09/0.39 % CPULimit : 300
% 0.09/0.39 % WCLimit : 300
% 0.09/0.39 % DateTime : Sun Sep 27 21:46:35 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 3.50/1.48 % (3786326)Detected formulas, will run a generic FOF schedule.
% 3.50/1.48 % (3786334)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=913500275:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.50/1.48 % (3786334)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.50/1.48 % (3786334)Refutation not found, incomplete strategy
% 3.50/1.48 % (3786334)------------------------------
% 3.50/1.48 % (3786334)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.48 % (3786334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.48 % (3786334)CaDiCaL version: 2.1.3
% 3.50/1.48 % (3786334)Termination reason: Refutation not found, incomplete strategy
% 3.50/1.48 % (3786334)Time elapsed: 0.0000 s
% 3.50/1.48 % (3786334)Peak memory usage: 87 MB
% 3.50/1.48 % (3786335)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=338010111:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.50/1.48 % (3786333)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=3680342104:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.50/1.48 % (3786331)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=3710929349:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.50/1.48 % (3786332)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=1873550816:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.50/1.48 % (3786337)dis-21_1_sil=8000:lcm=predicate:random_seed=2995324688: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)
% 3.50/1.48 % (3786336)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1743791618:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.50/1.48 % (3786335)Refutation not found, incomplete strategy
% 3.50/1.48 % (3786335)------------------------------
% 3.50/1.48 % (3786335)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.48 % (3786335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.48 % (3786335)CaDiCaL version: 2.1.3
% 3.50/1.48 % (3786335)Termination reason: Refutation not found, incomplete strategy
% 3.50/1.48 % (3786335)Time elapsed: 0.001 s
% 3.50/1.48 % (3786335)Peak memory usage: 88 MB
% 3.50/1.48 % (3786333)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.50/1.48 % (3786336)First to succeed.
% 3.50/1.48 % (3786336)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3786326"
% 3.50/1.48 % (3786337)Instruction limit reached!
% 3.50/1.48 % (3786337)------------------------------
% 3.50/1.48 % (3786337)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.48 % (3786337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.48 % (3786337)CaDiCaL version: 2.1.3
% 3.50/1.48 % (3786337)Termination reason: Instruction limit
% 3.50/1.48 % (3786337)Termination phase: Saturation
% 3.50/1.48 % (3786337)Time elapsed: 0.058 s
% 3.50/1.48 % (3786337)Peak memory usage: 89 MB
% 3.50/1.48 % (3786337)Instructions burned: 129 (million)
% 3.50/1.48 % (3786334)------------------------------
% 3.50/1.48 % (3786334)------------------------------
% 3.50/1.48 % (3786346)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3416792388:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.50/1.48 % (3786346)Refutation not found, incomplete strategy
% 3.50/1.48 % (3786346)------------------------------
% 3.50/1.48 % (3786346)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.48 % (3786346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.48 % (3786346)CaDiCaL version: 2.1.3
% 3.50/1.48 % (3786346)Termination reason: Refutation not found, incomplete strategy
% 3.50/1.48 % (3786346)Time elapsed: 0.001 s
% 3.50/1.48 % (3786346)Peak memory usage: 88 MB
% 3.50/1.48 % (3786346)Instructions burned: 1 (million)
% 3.50/1.48 % (3786345)lrs+10_1_sil=8000:sp=occurrence:random_seed=3509554317:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.50/1.48 % (3786345)Refutation not found, incomplete strategy
% 3.50/1.48 % (3786345)------------------------------
% 3.50/1.48 % (3786345)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.48 % (3786345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.48 % (3786345)CaDiCaL version: 2.1.3
% 3.50/1.48 % (3786345)Termination reason: Refutation not found, incomplete strategy
% 3.50/1.48 % (3786345)Time elapsed: 0.001 s
% 3.50/1.48 % (3786345)Peak memory usage: 88 MB
% 3.50/1.48 % (3786335)------------------------------
% 3.50/1.48 % (3786335)------------------------------
% 3.50/1.48 % (3786336)Refutation found. Thanks to Tanya!
% 3.50/1.48 % SZS status Theorem for theBenchmark
% 3.50/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.50/1.48 % (3786336)------------------------------
% 3.50/1.48 % (3786336)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.48 % (3786336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.48 % (3786336)CaDiCaL version: 2.1.3
% 3.50/1.48 % (3786336)Termination reason: Refutation
% 3.50/1.48 % (3786336)Time elapsed: 0.008 s
% 3.50/1.48 % (3786336)Peak memory usage: 89 MB
% 3.50/1.48 % (3786336)Instructions burned: 10 (million)
% 3.50/1.48 % (3786336)------------------------------
% 3.50/1.48 % (3786336)------------------------------
% 3.50/1.48 % (3786326)Success in time 0.417 s
% 3.50/1.48 % Vampire exiting
%------------------------------------------------------------------------------