%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM925+3 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 12:26:09 PM UTC 2026
% Result : Theorem 0.81s 0.63s
% Output : Refutation 0.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 57 ( 33 unt; 2 def)
% Number of atoms : 88 ( 34 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 66 ( 35 ~; 26 |; 0 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0] :
( is_int(X0)
=> is_int(succ(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Int_Osucc) ).
fof(f20,axiom,
! [X0,X1] : is_int(hAPP_nat_int(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint) ).
fof(f29,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
fof(f77,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_rel__simps_I2_J) ).
fof(f96,axiom,
! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_zadd__commute) ).
fof(f127,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Pls__def) ).
fof(f132,axiom,
! [X0] : bit0(X0) = plus_plus_int(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_Bit0__def) ).
fof(f157,axiom,
! [X0] : bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Bit1__def) ).
fof(f260,axiom,
! [X0,X1] :
( is_int(X1)
=> ( X1 != zero_zero_int
=> hAPP_nat_int(power_power_int(X1),X0) != zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_field__power__not__zero) ).
fof(f795,axiom,
! [X0] : nat(number_number_of_int(X0)) = number_number_of_nat(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_766_nat__number__of) ).
fof(f843,axiom,
! [X0] : succ(X0) = plus_plus_int(X0,one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_814_succ__def) ).
fof(f1233,conjecture,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1234,negated_conjecture,
~ ( hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ),
inference(negated_conjecture,[status(cth)],[f1233]) ).
fof(f1241,plain,
zero_zero_int = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(flattening,[],[f1234]) ).
fof(f1254,plain,
! [X0] :
( is_int(succ(X0))
| ~ is_int(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f1336,plain,
! [X0,X1] :
( hAPP_nat_int(power_power_int(X1),X0) != zero_zero_int
| zero_zero_int = X1
| ~ is_int(X1) ),
inference(ennf_transformation,[],[f260]) ).
fof(f1337,plain,
! [X0,X1] :
( hAPP_nat_int(power_power_int(X1),X0) != zero_zero_int
| zero_zero_int = X1
| ~ is_int(X1) ),
inference(flattening,[],[f1336]) ).
fof(f2106,plain,
! [X0] :
( ~ is_int(X0)
| is_int(succ(X0)) ),
inference(cnf_transformation,[],[f1254]) ).
fof(f2112,plain,
! [X0,X1] : is_int(hAPP_nat_int(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f2121,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
inference(cnf_transformation,[],[f29]) ).
fof(f2184,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
inference(cnf_transformation,[],[f77]) ).
fof(f2210,plain,
! [X0,X1] : plus_plus_int(X0,X1) = plus_plus_int(X1,X0),
inference(cnf_transformation,[],[f96]) ).
fof(f2264,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f127]) ).
fof(f2269,plain,
! [X0] : bit0(X0) = plus_plus_int(X0,X0),
inference(cnf_transformation,[],[f132]) ).
fof(f2300,plain,
! [X0] : bit1(X0) = plus_plus_int(plus_plus_int(one_one_int,X0),X0),
inference(cnf_transformation,[],[f157]) ).
fof(f2447,plain,
! [X0,X1] :
( ~ is_int(X1)
| zero_zero_int = X1
| zero_zero_int != hAPP_nat_int(power_power_int(X1),X0) ),
inference(cnf_transformation,[],[f1337]) ).
fof(f3163,plain,
! [X0] : number_number_of_nat(X0) = nat(number_number_of_int(X0)),
inference(cnf_transformation,[],[f795]) ).
fof(f3253,plain,
! [X0] : succ(X0) = plus_plus_int(X0,one_one_int),
inference(cnf_transformation,[],[f843]) ).
fof(f3833,plain,
zero_zero_int = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f1241]) ).
fof(f3837,plain,
! [X0] :
( ~ is_int(X0)
| is_int(plus_plus_int(X0,one_one_int)) ),
inference(definition_unfolding,[],[f2106,f3253]) ).
fof(f3838,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
inference(definition_unfolding,[],[f2121,f2264]) ).
fof(f4012,plain,
! [X0,X1] :
( ~ is_int(X1)
| pls = X1
| pls != hAPP_nat_int(power_power_int(X1),X0) ),
inference(definition_unfolding,[],[f2447,f2264,f2264]) ).
fof(f4439,plain,
pls = hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),nat(number_number_of_int(plus_plus_int(plus_plus_int(plus_plus_int(one_one_int,pls),pls),plus_plus_int(plus_plus_int(one_one_int,pls),pls))))),
inference(definition_unfolding,[],[f3833,f2264,f3163,f2269,f2300]) ).
fof(f4658,plain,
! [X0] :
( ~ is_int(plus_plus_int(X0,one_one_int))
| is_int(X0) ),
inference(consistent_polarity_flipping,[],[f3837]) ).
fof(f4664,plain,
! [X0,X1] : ~ is_int(hAPP_nat_int(X0,X1)),
inference(consistent_polarity_flipping,[],[f2112]) ).
fof(f4673,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
inference(consistent_polarity_flipping,[],[f3838]) ).
fof(f4692,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
inference(consistent_polarity_flipping,[],[f2184]) ).
fof(f4859,plain,
! [X0,X1] :
( pls != hAPP_nat_int(power_power_int(X1),X0)
| pls = X1
| is_int(X1) ),
inference(consistent_polarity_flipping,[],[f4012]) ).
fof(f6150,plain,
! [X0] :
( ~ is_int(plus_plus_int(one_one_int,X0))
| is_int(X0) ),
inference(superposition,[],[f4658,f2210]) ).
fof(f8845,plain,
( pls != pls
| pls = plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))
| is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) ),
inference(superposition,[],[f4859,f4439]) ).
fof(f8858,plain,
( pls = plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))
| is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) ),
inference(trivial_inequality_removal,[],[f8845]) ).
fof(f8860,definition,
( spl41_32
<=> is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) ),
introduced(definition,[new_symbols(definition,[spl41_32])],[avatar_definition]) ).
fof(f8862,plain,
( is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ spl41_32 ),
inference(avatar_component_clause,[],[f8860]) ).
fof(f8864,definition,
( spl41_33
<=> pls = plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) ),
introduced(definition,[new_symbols(definition,[spl41_33])],[avatar_definition]) ).
fof(f8866,plain,
( pls = plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))
| ~ spl41_33 ),
inference(avatar_component_clause,[],[f8864]) ).
fof(f8872,plain,
( spl41_32
| spl41_33 ),
inference(avatar_split_clause,[],[f8858,f8864,f8860]) ).
fof(f8873,plain,
( is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ spl41_32 ),
inference(resolution,[],[f8862,f6150]) ).
fof(f8876,plain,
( $false
| ~ spl41_32 ),
inference(forward_subsumption_resolution,[],[f8873,f4664]) ).
fof(f8877,plain,
~ spl41_32,
inference(avatar_contradiction_clause,[],[f8876]) ).
fof(f8895,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls))
| ~ spl41_33 ),
inference(superposition,[],[f4673,f8866]) ).
fof(f8913,plain,
( $false
| ~ spl41_33 ),
inference(forward_subsumption_resolution,[],[f8895,f4692]) ).
fof(f8914,plain,
~ spl41_33,
inference(avatar_contradiction_clause,[],[f8913]) ).
cnf(s54,plain,
( spl41_32
| spl41_33 ),
inference(sat_conversion,[],[f8872]) ).
cnf(s55,plain,
~ spl41_32,
inference(sat_conversion,[],[f8877]) ).
cnf(s57,plain,
~ spl41_33,
inference(sat_conversion,[],[f8914]) ).
cnf(s58,plain,
$false,
inference(rat,[],[s54,s57,s55]) ).
fof(f8931,plain,
$false,
inference(avatar_sat_refutation,[],[s58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925+3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n017.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 21:39:23 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.81/0.63 % (2962893)Will run a generic schedule for satisfiability detection.
% 0.81/0.63 % (2962929)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4136690314:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.81/0.63 % (2962924)% WARNING: option uhcvi not known.
% 0.81/0.63 % (2962923)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=82977935_2999 on theBenchmark for (2999ds/0Mi)
% 0.81/0.63 % (2962924)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3988046808:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.81/0.63 % (2962926)dis+10_1_sil=32000:sp=arity:random_seed=730010857:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.81/0.63 % (2962925)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3142671012:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.81/0.63 % (2962927)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=878503596:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.81/0.63 % (2962930)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1638981097:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.81/0.63 % (2962929)Instruction limit reached!
% 0.81/0.63 % (2962929)------------------------------
% 0.81/0.63 % (2962929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.81/0.63 % (2962929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.63 % (2962929)CaDiCaL version: 2.1.3
% 0.81/0.63 % (2962929)Termination reason: Instruction limit
% 0.81/0.63 % (2962929)Termination phase: Saturation
% 0.81/0.63 % (2962929)Time elapsed: 0.037 s
% 0.81/0.63 % (2962929)Peak memory usage: 14 MB
% 0.81/0.63 % (2962929)Instructions burned: 135 (million)
% 0.81/0.63 % (2962955)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=110098603:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.81/0.63 % (2962926)Instruction limit reached!
% 0.81/0.63 % (2962926)------------------------------
% 0.81/0.63 % (2962926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.81/0.63 % (2962926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.63 % (2962926)CaDiCaL version: 2.1.3
% 0.81/0.63 % (2962926)Termination reason: Instruction limit
% 0.81/0.63 % (2962926)Termination phase: Saturation
% 0.81/0.63 % (2962926)Time elapsed: 0.048 s
% 0.81/0.63 % (2962926)Peak memory usage: 14 MB
% 0.81/0.63 % (2962926)Instructions burned: 104 (million)
% 0.81/0.63 % (2962927)Instruction limit reached!
% 0.81/0.63 % (2962927)------------------------------
% 0.81/0.63 % (2962927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.81/0.63 % (2962927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.63 % (2962927)CaDiCaL version: 2.1.3
% 0.81/0.63 % (2962927)Termination reason: Instruction limit
% 0.81/0.63 % (2962927)Termination phase: Property scanning
% 0.81/0.63 % (2962927)Time elapsed: 0.053 s
% 0.81/0.63 % (2962927)Peak memory usage: 13 MB
% 0.81/0.63 % (2962927)Instructions burned: 118 (million)
% 0.81/0.63 % (2962968)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1085900856:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 0.81/0.63 % (2962971)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2464223032:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.81/0.63 % (2962930)Instruction limit reached!
% 0.81/0.63 % (2962930)------------------------------
% 0.81/0.63 % (2962930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.81/0.63 % (2962930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.63 % (2962930)CaDiCaL version: 2.1.3
% 0.81/0.63 % (2962930)Termination reason: Instruction limit
% 0.81/0.63 % (2962930)Termination phase: Saturation
% 0.81/0.63 % (2962930)Time elapsed: 0.091 s
% 0.81/0.63 % (2962930)Peak memory usage: 15 MB
% 0.81/0.63 % (2962930)Instructions burned: 161 (million)
% 0.81/0.63 % (2962985)ott-21_1_sil=16000:fs=off:random_seed=433373342:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.81/0.63 % (2962924) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2962893-2962924"...
% 0.81/0.63 % (2962924)...printing done.
% 0.81/0.63 % (2962924)Refutation found. Thanks to Tanya!
% 0.81/0.63 % SZS status Theorem for theBenchmark
% 0.81/0.63 % SZS output start Proof for theBenchmark
% See solution above
% 0.81/0.64 % (2962924)------------------------------
% 0.81/0.64 % (2962924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.81/0.64 % (2962924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.81/0.64 % (2962924)CaDiCaL version: 2.1.3
% 0.81/0.64 % (2962924)Termination reason: Refutation
% 0.81/0.64 % (2962924)Time elapsed: 0.124 s
% 0.81/0.64 % (2962924)Peak memory usage: 17 MB
% 0.81/0.64 % (2962924)Instructions burned: 226 (million)
% 0.81/0.64 % (2962893)Success in time 0.201 s
% 0.81/0.64 % Vampire exiting
%------------------------------------------------------------------------------