%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM974_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 : n012.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 12:17:43 PM UTC 2026
% Result : Theorem 2.03s 0.89s
% Output : Refutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 15 unt; 0 typ; 1 def)
% Number of atoms : 58 ( 6 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 55 ( 27 ~; 20 |; 2 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 25 ( 23 usr; 2 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 22 ( 22 !; 0 ?; 22 :)
% 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,
minus_minus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_3,type,
nat1: int > nat ).
tff(func_def_4,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
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,
t: int ).
tff(pred_def_1,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
group_add:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
zero_neq_one:
!>[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,
ordered_ab_group_add:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_11,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_12,type,
pp: bool > $o ).
tff(pred_def_14,type,
sP0: nat > $o ).
tff(pred_def_15,type,
sP1: nat > $o ).
tff(pred_def_16,type,
sP2: nat > $o ).
tff(pred_def_17,type,
sP3: nat > $o ).
tff(pred_def_18,type,
sP4: nat > $o ).
tff(pred_def_19,type,
sP5: nat > $o ).
tff(pred_def_20,type,
sP6: nat > $o ).
tff(pred_def_21,type,
sP7: nat > $o ).
tff(pred_def_22,type,
sP8: nat > $o ).
tff(pred_def_23,type,
sP9: nat > $o ).
tff(f1,axiom,
ord_less(int,one_one(int),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_t1) ).
tff(f2,axiom,
! [X0: nat,X1: nat] :
( ord_less(nat,zero_zero(nat),minus_minus(nat,X1,X0))
<=> ord_less(nat,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_zero__less__diff) ).
tff(f41,axiom,
one_one(nat) = nat1(one_one(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_transfer__nat__int__numerals_I2_J) ).
tff(f72,axiom,
ord_less_eq(int,zero_zero(int),one_one(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
tff(f97,axiom,
! [X0: int,X1: int] :
( ord_less_eq(int,zero_zero(int),X1)
=> ( ord_less(nat,nat1(X1),nat1(X0))
<=> ord_less(int,X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_nat__less__eq__zless) ).
tff(f116,axiom,
! [X0: nat] :
( ( X0 = minus_minus(nat,nat1(t),one_one(nat)) )
=> ( ord_less(nat,zero_zero(nat),X0)
=> thesis ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f117,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f118,negated_conjecture,
~ thesis,
inference(negated_conjecture,[status(cth)],[f117]) ).
tff(f119,plain,
~ thesis,
inference(flattening,[],[f118]) ).
tff(f120,plain,
! [X0: nat] :
( thesis
| ~ ord_less(nat,zero_zero(nat),X0)
| ( minus_minus(nat,nat1(t),one_one(nat)) != X0 ) ),
inference(ennf_transformation,[],[f116]) ).
tff(f121,plain,
! [X0: nat] :
( thesis
| ~ ord_less(nat,zero_zero(nat),X0)
| ( minus_minus(nat,nat1(t),one_one(nat)) != X0 ) ),
inference(flattening,[],[f120]) ).
tff(f135,plain,
! [X0: int,X1: int] :
( ( ord_less(nat,nat1(X1),nat1(X0))
<=> ord_less(int,X1,X0) )
| ~ ord_less_eq(int,zero_zero(int),X1) ),
inference(ennf_transformation,[],[f97]) ).
tff(f153,plain,
! [X0: nat,X1: nat] :
( ( ord_less(nat,zero_zero(nat),minus_minus(nat,X1,X0))
| ~ ord_less(nat,X0,X1) )
& ( ord_less(nat,X0,X1)
| ~ ord_less(nat,zero_zero(nat),minus_minus(nat,X1,X0)) ) ),
inference(nnf_transformation,[],[f2]) ).
tff(f157,plain,
! [X0: int,X1: int] :
( ( ( ord_less(nat,nat1(X1),nat1(X0))
| ~ ord_less(int,X1,X0) )
& ( ord_less(int,X1,X0)
| ~ ord_less(nat,nat1(X1),nat1(X0)) ) )
| ~ ord_less_eq(int,zero_zero(int),X1) ),
inference(nnf_transformation,[],[f135]) ).
tff(f176,plain,
! [X0: nat] :
( thesis
| ~ ord_less(nat,zero_zero(nat),X0)
| ( minus_minus(nat,nat1(t),one_one(nat)) != X0 ) ),
inference(cnf_transformation,[],[f121]) ).
tff(f177,plain,
~ thesis,
inference(cnf_transformation,[],[f119]) ).
tff(f188,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,zero_zero(nat),minus_minus(nat,X1,X0))
| ~ ord_less(nat,X0,X1) ),
inference(cnf_transformation,[],[f153]) ).
tff(f193,plain,
ord_less_eq(int,zero_zero(int),one_one(int)),
inference(cnf_transformation,[],[f72]) ).
tff(f197,plain,
one_one(nat) = nat1(one_one(int)),
inference(cnf_transformation,[],[f41]) ).
tff(f201,plain,
! [X0: int,X1: int] :
( ord_less(nat,nat1(X1),nat1(X0))
| ~ ord_less(int,X1,X0)
| ~ ord_less_eq(int,zero_zero(int),X1) ),
inference(cnf_transformation,[],[f157]) ).
tff(f242,plain,
ord_less(int,one_one(int),t),
inference(cnf_transformation,[],[f1]) ).
tff(f258,definition,
~ sP0(minus_minus(nat,nat1(t),one_one(nat))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
tff(f259,plain,
! [X0: nat] :
( thesis
| ~ ord_less(nat,zero_zero(nat),X0)
| sP0(X0) ),
inference(inequality_splitting,[],[f176,f258]) ).
tff(f294,plain,
~ sP0(minus_minus(nat,nat1(t),nat1(one_one(int)))),
inference(forward_demodulation,[],[f258,f197]) ).
tff(f295,plain,
! [X0: nat] :
( ~ ord_less(nat,zero_zero(nat),X0)
| sP0(X0) ),
inference(forward_subsumption_resolution,[],[f259,f177]) ).
tff(f296,plain,
! [X0: nat,X1: nat] :
( sP0(minus_minus(nat,X0,X1))
| ~ ord_less(nat,X1,X0) ),
inference(resolution,[],[f295,f188]) ).
tff(f342,plain,
~ ord_less(nat,nat1(one_one(int)),nat1(t)),
inference(resolution,[],[f296,f294]) ).
tff(f364,plain,
( ~ ord_less(int,one_one(int),t)
| ~ ord_less_eq(int,zero_zero(int),one_one(int)) ),
inference(resolution,[],[f342,f201]) ).
tff(f379,plain,
~ ord_less_eq(int,zero_zero(int),one_one(int)),
inference(forward_subsumption_resolution,[],[f364,f242]) ).
tff(f383,plain,
$false,
inference(forward_subsumption_resolution,[],[f379,f193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM974_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 21:48:20 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 2.03/0.89 % (2784435)Detected formulas, will run a generic FOF schedule.
% 2.03/0.89 % (2784442)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=309933324:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.03/0.89 % (2784442)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.03/0.89 % (2784443)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1826524497:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.03/0.89 % (2784440)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=2960911716:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.03/0.89 % (2784441)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=101727321:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.03/0.89 % (2784444)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1362312982:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.03/0.89 % (2784443)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.03/0.89 % (2784443)First to succeed.
% 2.03/0.89 % (2784443)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2784435"
% 2.03/0.89 % (2784444)Also succeeded, but the first one will report.
% 2.03/0.89 % (2784445)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3940461594:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.03/0.89 % (2784446)dis-21_1_sil=8000:lcm=predicate:random_seed=1689913890: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)
% 2.03/0.89 % (2784445)Also succeeded, but the first one will report.
% 2.03/0.89 % (2784446)Instruction limit reached!
% 2.03/0.89 % (2784446)------------------------------
% 2.03/0.89 % (2784446)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.03/0.89 % (2784446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.89 % (2784446)CaDiCaL version: 2.1.3
% 2.03/0.89 % (2784446)Termination reason: Instruction limit
% 2.03/0.89 % (2784446)Termination phase: Saturation
% 2.03/0.89 % (2784446)Time elapsed: 0.040 s
% 2.03/0.89 % (2784446)Peak memory usage: 90 MB
% 2.03/0.89 % (2784446)Instructions burned: 129 (million)
% 2.03/0.89 % (2784454)lrs+10_1_sil=8000:sp=occurrence:random_seed=2999800054:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.03/0.89 % (2784443)Refutation found. Thanks to Tanya!
% 2.03/0.89 % SZS status Theorem for theBenchmark
% 2.03/0.89 % SZS output start Proof for theBenchmark
% See solution above
% 2.03/0.89 % (2784443)------------------------------
% 2.03/0.89 % (2784443)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.03/0.89 % (2784443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.89 % (2784443)CaDiCaL version: 2.1.3
% 2.03/0.89 % (2784443)Termination reason: Refutation
% 2.03/0.89 % (2784443)Time elapsed: 0.004 s
% 2.03/0.89 % (2784443)Peak memory usage: 88 MB
% 2.03/0.89 % (2784443)Instructions burned: 9 (million)
% 2.03/0.89 % (2784443)------------------------------
% 2.03/0.89 % (2784443)------------------------------
% 2.03/0.89 % (2784435)Success in time 0.267 s
% 2.03/0.89 % Vampire exiting
%------------------------------------------------------------------------------