%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM980_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 12:26:19 PM UTC 2026
% Result : Theorem 0.38s 0.51s
% Output : Refutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 65 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 51 ( 23 ~; 22 |; 0 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-4 aty)
% Number of variables : 38 ( 38 !; 0 ?; 38 :)
% 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,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_3,type,
if:
!>[X0: $tType] : ( ( bool * X0 * X0 ) > X0 ) ).
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,
n: nat ).
tff(func_def_9,type,
t: int ).
tff(func_def_10,type,
tn: nat ).
tff(func_def_11,type,
sK0: int > nat ).
tff(func_def_12,type,
sK1: ( fun(int,bool) * int ) > int ).
tff(func_def_13,type,
sK2: ( nat * nat ) > nat ).
tff(pred_def_1,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
monoid_add:
!>[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,
comm_monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
ordere216010020id_add:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
ordere236663937imp_le:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
ordere223160158up_add:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_18,type,
pp: bool > $o ).
tff(f2,axiom,
ord_less(nat,zero_zero(nat),n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_n0) ).
tff(f64,axiom,
! [X0: nat] :
( ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0))
<=> ord_less(nat,zero_zero(nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_zero__less__int__conv) ).
tff(f67,axiom,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X1: X0] : ( plus_plus(X0,zero_zero(X0),X1) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_add__0) ).
tff(f81,axiom,
! [X0: int,X1: int] :
( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
<=> ( ord_less(int,X1,X0)
| ( X1 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_zless__add1__eq) ).
tff(f96,axiom,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,zero_zero(X0),X3)
=> ( ord_less(X0,X2,X1)
=> ord_less(X0,X2,plus_plus(X0,X3,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_pos__add__strict) ).
tff(f105,axiom,
linordered_semidom(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
tff(f107,axiom,
comm_monoid_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__add) ).
tff(f134,conjecture,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f135,negated_conjecture,
~ ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(negated_conjecture,[status(cth)],[f134]) ).
tff(f136,plain,
~ ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(flattening,[],[f135]) ).
tff(f176,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,zero_zero(X0),X1) = X1 )
| ~ comm_monoid_add(X0) ),
inference(ennf_transformation,[],[f67]) ).
tff(f202,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,X2,plus_plus(X0,X3,X1))
| ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,zero_zero(X0),X3) )
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f96]) ).
tff(f203,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,X2,plus_plus(X0,X3,X1))
| ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,zero_zero(X0),X3) )
| ~ linordered_semidom(X0) ),
inference(flattening,[],[f202]) ).
tff(f207,plain,
ord_less(nat,zero_zero(nat),n),
inference(cnf_transformation,[],[f2]) ).
tff(f292,plain,
! [X0: nat] :
( ~ ord_less(nat,zero_zero(nat),X0)
| ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0)) ),
inference(cnf_transformation,[],[f64]) ).
tff(f296,plain,
! [X0: $tType,X1: X0] :
( ~ comm_monoid_add(X0)
| ( plus_plus(X0,zero_zero(X0),X1) = X1 ) ),
inference(cnf_transformation,[],[f176]) ).
tff(f312,plain,
! [X0: int,X1: int] :
( ( X0 != X1 )
| ord_less(int,X1,plus_plus(int,X0,one_one(int))) ),
inference(cnf_transformation,[],[f81]) ).
tff(f335,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ linordered_semidom(X0)
| ~ ord_less(X0,zero_zero(X0),X3)
| ~ ord_less(X0,X2,X1)
| ord_less(X0,X2,plus_plus(X0,X3,X1)) ),
inference(cnf_transformation,[],[f203]) ).
tff(f344,plain,
linordered_semidom(int),
inference(cnf_transformation,[],[f105]) ).
tff(f346,plain,
comm_monoid_add(int),
inference(cnf_transformation,[],[f107]) ).
tff(f373,plain,
~ ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(cnf_transformation,[],[f136]) ).
tff(f391,plain,
! [X1: int] : ord_less(int,X1,plus_plus(int,X1,one_one(int))),
inference(equality_resolution,[],[f312]) ).
tff(f394,plain,
~ ord_less(nat,zero_zero(nat),n),
inference(consistent_polarity_flipping,[],[f207]) ).
tff(f442,plain,
! [X0: nat] :
( ~ ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0))
| ord_less(nat,zero_zero(nat),X0) ),
inference(consistent_polarity_flipping,[],[f292]) ).
tff(f445,plain,
! [X0: $tType,X1: X0] :
( comm_monoid_add(X0)
| ( plus_plus(X0,zero_zero(X0),X1) = X1 ) ),
inference(consistent_polarity_flipping,[],[f296]) ).
tff(f460,plain,
! [X1: int] : ~ ord_less(int,X1,plus_plus(int,X1,one_one(int))),
inference(consistent_polarity_flipping,[],[f391]) ).
tff(f476,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ~ ord_less(X0,X2,plus_plus(X0,X3,X1))
| ord_less(X0,zero_zero(X0),X3)
| ord_less(X0,X2,X1)
| linordered_semidom(X0) ),
inference(consistent_polarity_flipping,[],[f335]) ).
tff(f481,plain,
~ linordered_semidom(int),
inference(consistent_polarity_flipping,[],[f344]) ).
tff(f482,plain,
~ comm_monoid_add(int),
inference(consistent_polarity_flipping,[],[f346]) ).
tff(f494,plain,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(consistent_polarity_flipping,[],[f373]) ).
tff(f610,plain,
! [X0: int] : ( plus_plus(int,zero_zero(int),X0) = X0 ),
inference(resolution,[],[f445,f482]) ).
tff(f624,plain,
~ ord_less(int,zero_zero(int),one_one(int)),
inference(superposition,[],[f460,f610]) ).
tff(f1651,plain,
( ord_less(int,zero_zero(int),one_one(int))
| ord_less(int,zero_zero(int),semiring_1_of_nat(int,n))
| linordered_semidom(int) ),
inference(resolution,[],[f476,f494]) ).
tff(f1686,plain,
( ord_less(int,zero_zero(int),semiring_1_of_nat(int,n))
| linordered_semidom(int) ),
inference(forward_subsumption_resolution,[],[f1651,f624]) ).
tff(f1691,plain,
ord_less(int,zero_zero(int),semiring_1_of_nat(int,n)),
inference(forward_subsumption_resolution,[],[f1686,f481]) ).
tff(f1752,plain,
ord_less(nat,zero_zero(nat),n),
inference(resolution,[],[f1691,f442]) ).
tff(f1757,plain,
$false,
inference(forward_subsumption_resolution,[],[f1752,f394]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM980_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n016.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 21:54:02 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/0.42 Running first-order model finding
% 0.15/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.38/0.51 % (3025825)Will run a generic schedule for satisfiability detection.
% 0.38/0.51 % (3025835)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1927795404_2999 on theBenchmark for (2999ds/0Mi)
% 0.38/0.51 % Exception at run slice level
% 0.38/0.51 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.38/0.51 % (3025836)% WARNING: option uhcvi not known.
% 0.38/0.51 % (3025838)dis+10_1_sil=32000:sp=arity:random_seed=3323577244:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.38/0.51 % (3025837)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=717074379:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.38/0.51 % (3025839)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3232241954:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.38/0.51 % (3025840)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1554425614:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.38/0.51 % (3025841)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3640341337:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.38/0.51 % (3025836)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1157923385:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.38/0.51 % (3025848)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=700499877:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.38/0.51 % Exception at run slice level
% 0.38/0.51 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.38/0.51 % (3025859)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2828571128:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.38/0.51 % (3025836) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3025825-3025836"...
% 0.38/0.51 % (3025836)...printing done.
% 0.38/0.51 % (3025836)Refutation found. Thanks to Tanya!
% 0.38/0.51 % SZS status Theorem for theBenchmark
% 0.38/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.38/0.51 % (3025836)------------------------------
% 0.38/0.51 % (3025836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.38/0.51 % (3025836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.38/0.51 % (3025836)CaDiCaL version: 2.1.3
% 0.38/0.51 % (3025836)Termination reason: Refutation
% 0.38/0.51 % (3025836)Time elapsed: 0.036 s
% 0.38/0.51 % (3025836)Peak memory usage: 13 MB
% 0.38/0.51 % (3025836)Instructions burned: 54 (million)
% 0.38/0.51 % (3025825)Success in time 0.079 s
% 0.38/0.51 % Vampire exiting
%------------------------------------------------------------------------------