%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% 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 12:26:19 PM UTC 2026
% Result : Theorem 0.21s 0.47s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 20
% Syntax : Number of formulae : 75 ( 30 unt; 0 typ; 2 def)
% Number of atoms : 131 ( 32 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 108 ( 52 ~; 42 |; 0 &)
% ( 10 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 17 ( 15 usr; 4 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 3 con; 0-4 aty)
% Number of variables : 53 ( 0 sgn 53 !; 0 ?; 53 :)
% 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(func_def_9,type,
sK0: fun(int,bool) > int ).
tff(func_def_10,type,
sK1: fun(int,bool) > nat ).
tff(func_def_11,type,
sK2: fun(int,bool) > int ).
tff(func_def_12,type,
sK3: fun(int,bool) > nat ).
tff(func_def_13,type,
sK4: fun(nat,bool) > nat ).
tff(func_def_14,type,
sK5: fun(nat,bool) > int ).
tff(func_def_15,type,
sK6: fun(nat,bool) > nat ).
tff(func_def_16,type,
sK7: fun(nat,bool) > int ).
tff(func_def_17,type,
sK8: ( int * fun(nat,bool) ) > nat ).
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(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(f22,axiom,
! [X0: nat,X1: nat] :
( ( X1 != X0 )
<=> ( ord_less(nat,X1,X0)
| ord_less(nat,X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_nat__neq__iff) ).
tff(f23,axiom,
! [X0: nat] : ~ ord_less(nat,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_less__not__refl) ).
tff(f28,axiom,
! [X0: $tType] :
( group_add(X0)
=> ! [X1: X0,X2: X0] :
( ( X2 = X1 )
<=> ( minus_minus(X0,X2,X1) = zero_zero(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_eq__iff__diff__eq__0) ).
tff(f33,axiom,
! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_not__less0) ).
tff(f38,axiom,
! [X0: int] :
( ord_less(nat,zero_zero(nat),nat1(X0))
<=> ord_less(int,zero_zero(int),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_zero__less__nat__eq) ).
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(f43,axiom,
ord_less_eq(int,one_one(int),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_tpos) ).
tff(f54,axiom,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,minus_minus(int,X0,one_one(int)))
<=> ord_less(int,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_zle__diff1__eq) ).
tff(f69,axiom,
! [X0: nat] : ( nat1(semiring_1_of_nat(int,X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_nat__int) ).
tff(f84,axiom,
semiring_1_of_nat(int,one_one(nat)) = one_one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_int__1) ).
tff(f85,axiom,
! [X0: int] :
( ord_less_eq(int,one_one(int),X0)
<=> ord_less(int,zero_zero(int),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_int__one__le__iff__zero__less) ).
tff(f86,axiom,
! [X0: int] :
( ord_less_eq(int,X0,zero_zero(int))
=> ( nat1(X0) = zero_zero(nat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_nat__le__0) ).
tff(f95,axiom,
! [X0: int,X1: nat] :
( ord_less(nat,X1,nat1(X0))
<=> ord_less(int,semiring_1_of_nat(int,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_zless__nat__eq__int__zless) ).
tff(f105,axiom,
group_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ogroup__add) ).
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(f121,plain,
~ thesis,
inference(flattening,[],[f118]) ).
tff(f142,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( X2 = X1 )
<=> ( minus_minus(X0,X2,X1) = zero_zero(X0) ) )
| ~ group_add(X0) ),
inference(ennf_transformation,[],[f28]) ).
tff(f177,plain,
! [X0: int] :
( ( nat1(X0) = zero_zero(nat) )
| ~ ord_less_eq(int,X0,zero_zero(int)) ),
inference(ennf_transformation,[],[f86]) ).
tff(f190,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(f191,plain,
! [X0: nat] :
( thesis
| ~ ord_less(nat,zero_zero(nat),X0)
| ( minus_minus(nat,nat1(t),one_one(nat)) != X0 ) ),
inference(flattening,[],[f190]) ).
tff(f192,plain,
ord_less(int,one_one(int),t),
inference(cnf_transformation,[],[f1]) ).
tff(f193,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,zero_zero(nat),minus_minus(nat,X1,X0))
| ~ ord_less(nat,X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
tff(f215,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ord_less(nat,X1,X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f22]) ).
tff(f218,plain,
! [X0: nat] : ~ ord_less(nat,X0,X0),
inference(cnf_transformation,[],[f23]) ).
tff(f225,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ~ group_add(X0)
| ( zero_zero(X0) = minus_minus(X0,X2,X1) )
| ( X1 != X2 ) ),
inference(cnf_transformation,[],[f142]) ).
tff(f231,plain,
! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)),
inference(cnf_transformation,[],[f33]) ).
tff(f236,plain,
! [X0: int] :
( ord_less(nat,zero_zero(nat),nat1(X0))
| ~ ord_less(int,zero_zero(int),X0) ),
inference(cnf_transformation,[],[f38]) ).
tff(f242,plain,
one_one(nat) = nat1(one_one(int)),
inference(cnf_transformation,[],[f41]) ).
tff(f245,plain,
ord_less_eq(int,one_one(int),t),
inference(cnf_transformation,[],[f43]) ).
tff(f262,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,minus_minus(int,X0,one_one(int)))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f54]) ).
tff(f286,plain,
! [X0: nat] : ( nat1(semiring_1_of_nat(int,X0)) = X0 ),
inference(cnf_transformation,[],[f69]) ).
tff(f321,plain,
one_one(int) = semiring_1_of_nat(int,one_one(nat)),
inference(cnf_transformation,[],[f84]) ).
tff(f323,plain,
! [X0: int] :
( ~ ord_less_eq(int,one_one(int),X0)
| ord_less(int,zero_zero(int),X0) ),
inference(cnf_transformation,[],[f85]) ).
tff(f324,plain,
! [X0: int] :
( ~ ord_less_eq(int,X0,zero_zero(int))
| ( zero_zero(nat) = nat1(X0) ) ),
inference(cnf_transformation,[],[f177]) ).
tff(f339,plain,
! [X0: int,X1: nat] :
( ~ ord_less(int,semiring_1_of_nat(int,X1),X0)
| ord_less(nat,X1,nat1(X0)) ),
inference(cnf_transformation,[],[f95]) ).
tff(f340,plain,
! [X0: int,X1: nat] :
( ord_less(int,semiring_1_of_nat(int,X1),X0)
| ~ ord_less(nat,X1,nat1(X0)) ),
inference(cnf_transformation,[],[f95]) ).
tff(f353,plain,
group_add(int),
inference(cnf_transformation,[],[f105]) ).
tff(f364,plain,
! [X0: nat] :
( ( minus_minus(nat,nat1(t),one_one(nat)) != X0 )
| ~ ord_less(nat,zero_zero(nat),X0)
| thesis ),
inference(cnf_transformation,[],[f191]) ).
tff(f365,plain,
~ thesis,
inference(cnf_transformation,[],[f121]) ).
tff(f374,plain,
! [X0: $tType,X2: X0] :
( ~ group_add(X0)
| ( zero_zero(X0) = minus_minus(X0,X2,X2) ) ),
inference(equality_resolution,[],[f225]) ).
tff(f398,plain,
( ~ ord_less(nat,zero_zero(nat),minus_minus(nat,nat1(t),one_one(nat)))
| thesis ),
inference(equality_resolution,[],[f364]) ).
tff(f399,plain,
~ ord_less(nat,zero_zero(nat),minus_minus(nat,nat1(t),one_one(nat))),
inference(forward_subsumption_resolution,[],[f398,f365]) ).
tff(f434,plain,
! [X0: int] : ( zero_zero(int) = minus_minus(int,X0,X0) ),
inference(resolution,[],[f374,f353]) ).
tff(f447,plain,
ord_less(int,zero_zero(int),t),
inference(resolution,[],[f323,f245]) ).
tff(f576,plain,
~ ord_less(nat,one_one(nat),nat1(t)),
inference(resolution,[],[f193,f399]) ).
tff(f584,plain,
( ord_less(nat,nat1(t),one_one(nat))
| ( one_one(nat) = nat1(t) ) ),
inference(resolution,[],[f576,f215]) ).
tff(f587,definition,
( spl9_3
<=> ( one_one(nat) = nat1(t) ) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
tff(f589,plain,
( ( one_one(nat) = nat1(t) )
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f587]) ).
tff(f591,definition,
( spl9_4
<=> ord_less(nat,nat1(t),one_one(nat)) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
tff(f593,plain,
( ord_less(nat,nat1(t),one_one(nat))
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f591]) ).
tff(f595,plain,
( spl9_3
| spl9_4 ),
inference(avatar_split_clause,[],[f584,f591,f587]) ).
tff(f603,plain,
( ( one_one(int) = semiring_1_of_nat(int,nat1(t)) )
| ~ spl9_3 ),
inference(superposition,[],[f321,f589]) ).
tff(f622,plain,
! [X0: int] :
( ord_less_eq(int,X0,zero_zero(int))
| ~ ord_less(int,X0,one_one(int)) ),
inference(superposition,[],[f262,f434]) ).
tff(f627,plain,
( ! [X0: int] :
( ord_less(nat,nat1(t),nat1(X0))
| ~ ord_less(int,one_one(int),X0) )
| ~ spl9_3 ),
inference(superposition,[],[f339,f603]) ).
tff(f649,plain,
( ~ ord_less(int,one_one(int),t)
| ~ spl9_3 ),
inference(resolution,[],[f627,f218]) ).
tff(f657,plain,
( $false
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f649,f192]) ).
tff(f658,plain,
~ spl9_3,
inference(avatar_contradiction_clause,[],[f657]) ).
tff(f734,plain,
! [X0: int] :
( ~ ord_less(int,X0,one_one(int))
| ( zero_zero(nat) = nat1(X0) ) ),
inference(resolution,[],[f622,f324]) ).
tff(f767,plain,
! [X0: nat] :
( ( zero_zero(nat) = nat1(semiring_1_of_nat(int,X0)) )
| ~ ord_less(nat,X0,nat1(one_one(int))) ),
inference(resolution,[],[f734,f340]) ).
tff(f768,plain,
! [X0: nat] :
( ( zero_zero(nat) = X0 )
| ~ ord_less(nat,X0,nat1(one_one(int))) ),
inference(forward_demodulation,[],[f767,f286]) ).
tff(f769,plain,
! [X0: nat] :
( ~ ord_less(nat,X0,one_one(nat))
| ( zero_zero(nat) = X0 ) ),
inference(forward_demodulation,[],[f768,f242]) ).
tff(f779,plain,
( ( zero_zero(nat) = nat1(t) )
| ~ spl9_4 ),
inference(resolution,[],[f769,f593]) ).
tff(f791,plain,
( ord_less(nat,zero_zero(nat),zero_zero(nat))
| ~ ord_less(int,zero_zero(int),t)
| ~ spl9_4 ),
inference(superposition,[],[f236,f779]) ).
tff(f798,plain,
( ~ ord_less(int,zero_zero(int),t)
| ~ spl9_4 ),
inference(forward_subsumption_resolution,[],[f791,f231]) ).
tff(f801,plain,
( $false
| ~ spl9_4 ),
inference(forward_subsumption_resolution,[],[f798,f447]) ).
tff(f802,plain,
~ spl9_4,
inference(avatar_contradiction_clause,[],[f801]) ).
cnf(s3,plain,
( spl9_3
| spl9_4 ),
inference(sat_conversion,[],[f595]) ).
cnf(s4,plain,
~ spl9_3,
inference(sat_conversion,[],[f658]) ).
cnf(s6,plain,
~ spl9_4,
inference(sat_conversion,[],[f802]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s3,s6,s4]) ).
tff(f803,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM974_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 21:49:34 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.21/0.47 % (3789940)Will run a generic schedule for satisfiability detection.
% 0.21/0.47 % (3789950)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2933758887:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.47 % (3789946)% WARNING: option uhcvi not known.
% 0.21/0.47 % (3789945)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4095466023_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.47 % (3789946)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=518333198:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.47 % (3789949)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1251663435:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.47 % (3789947)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2590572152:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.47 % (3789948)dis+10_1_sil=32000:sp=arity:random_seed=3560148385:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.47 % (3789951)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2356505556:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.47 % Exception at run slice level
% 0.21/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.47 % (3789949) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3789940-3789949"...
% 0.21/0.47 % (3789949)...printing done.
% 0.21/0.47 % (3789949)Refutation found. Thanks to Tanya!
% 0.21/0.47 % SZS status Theorem for theBenchmark
% 0.21/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.47 % (3789949)------------------------------
% 0.21/0.47 % (3789949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.47 % (3789949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.47 % (3789949)CaDiCaL version: 2.1.3
% 0.21/0.47 % (3789949)Termination reason: Refutation
% 0.21/0.47 % (3789949)Time elapsed: 0.019 s
% 0.21/0.47 % (3789949)Peak memory usage: 13 MB
% 0.21/0.47 % (3789949)Instructions burned: 27 (million)
% 0.21/0.47 % (3789940)Success in time 0.057 s
% 0.21/0.47 % Vampire exiting
%------------------------------------------------------------------------------