%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM016-1 : TPTP v9.3.1. Released v1.0.0.
% 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 12:11:34 PM UTC 2026
% Result : Unsatisfiable 0.17s 1.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 48 ( 13 unt; 5 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 102 ( 45 ~; 52 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 21 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ less(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nothing_is_less_than_itself) ).
fof(f3,axiom,
! [X0] : divides(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',everything_divides_itself) ).
fof(f4,axiom,
! [X2,X0,X1] :
( divides(X0,X2)
| ~ divides(X1,X2)
| ~ divides(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_divides) ).
fof(f5,axiom,
! [X0,X1] :
( ~ divides(X0,X1)
| ~ less(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',small_divides_large) ).
fof(f6,axiom,
! [X0] : less(X0,factorial_plus_one(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_prime_is_less_than_the_next_one) ).
fof(f7,axiom,
! [X0,X1] :
( ~ divides(X0,factorial_plus_one(X1))
| less(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divisor_is_smaller) ).
fof(f8,axiom,
! [X0] :
( prime(X0)
| divides(prime_divisor(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',division_by_prime_divisor) ).
fof(f9,axiom,
! [X0] :
( prime(prime_divisor(X0))
| prime(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prime_divsiors) ).
fof(f12,negated_conjecture,
! [X0] :
( ~ prime(X0)
| ~ less(a,X0)
| less(factorial_plus_one(a),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_another_prime) ).
fof(f21,plain,
! [X0] :
( prime(X0)
| ~ less(a,prime_divisor(X0))
| less(factorial_plus_one(a),prime_divisor(X0)) ),
inference(resolution,[],[f9,f12]) ).
fof(f22,plain,
! [X0] :
( less(factorial_plus_one(a),prime_divisor(X0))
| ~ less(a,prime_divisor(X0))
| ~ less(a,X0)
| less(factorial_plus_one(a),X0) ),
inference(resolution,[],[f21,f12]) ).
fof(f25,plain,
! [X0] :
( divides(prime_divisor(X0),X0)
| ~ less(a,X0)
| less(factorial_plus_one(a),X0) ),
inference(resolution,[],[f8,f12]) ).
fof(f27,plain,
! [X0] :
( less(factorial_plus_one(a),X0)
| ~ less(a,X0)
| ~ less(X0,prime_divisor(X0)) ),
inference(resolution,[],[f25,f5]) ).
fof(f33,plain,
! [X2,X0,X1] :
( less(X1,X2)
| ~ divides(X2,X0)
| ~ divides(X0,factorial_plus_one(X1)) ),
inference(resolution,[],[f4,f7]) ).
fof(f34,plain,
( ~ less(a,factorial_plus_one(a))
| ~ less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
inference(resolution,[],[f27,f1]) ).
fof(f38,definition,
( spl0_3
<=> less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f39,plain,
( ~ less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))
| spl0_3 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f41,definition,
( spl0_4
<=> less(a,factorial_plus_one(a)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f42,plain,
( ~ less(a,factorial_plus_one(a))
| spl0_4 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f43,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f34,f41,f38]) ).
fof(f44,plain,
( ~ less(a,prime_divisor(factorial_plus_one(a)))
| ~ less(a,factorial_plus_one(a))
| less(factorial_plus_one(a),factorial_plus_one(a))
| spl0_3 ),
inference(resolution,[],[f39,f22]) ).
fof(f50,definition,
( spl0_6
<=> less(a,prime_divisor(factorial_plus_one(a))) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f51,plain,
( ~ less(a,prime_divisor(factorial_plus_one(a)))
| spl0_6 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f54,definition,
( spl0_7
<=> less(factorial_plus_one(a),factorial_plus_one(a)) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f55,plain,
( less(factorial_plus_one(a),factorial_plus_one(a))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f56,plain,
( spl0_7
| ~ spl0_4
| ~ spl0_6
| spl0_3 ),
inference(avatar_split_clause,[],[f44,f38,f50,f41,f54]) ).
fof(f65,plain,
( ! [X0] :
( ~ divides(prime_divisor(factorial_plus_one(a)),X0)
| ~ divides(X0,factorial_plus_one(a)) )
| spl0_6 ),
inference(resolution,[],[f33,f51]) ).
fof(f77,plain,
( $false
| spl0_4 ),
inference(resolution,[],[f42,f6]) ).
fof(f79,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f77]) ).
fof(f94,plain,
( $false
| ~ spl0_7 ),
inference(resolution,[],[f55,f1]) ).
fof(f95,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f94]) ).
fof(f126,plain,
( ~ divides(factorial_plus_one(a),factorial_plus_one(a))
| ~ less(a,factorial_plus_one(a))
| less(factorial_plus_one(a),factorial_plus_one(a))
| spl0_6 ),
inference(resolution,[],[f65,f25]) ).
fof(f130,definition,
( spl0_11
<=> divides(factorial_plus_one(a),factorial_plus_one(a)) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f131,plain,
( ~ divides(factorial_plus_one(a),factorial_plus_one(a))
| spl0_11 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f132,plain,
( spl0_7
| ~ spl0_4
| ~ spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f126,f50,f130,f41,f54]) ).
fof(f133,plain,
( $false
| spl0_11 ),
inference(resolution,[],[f131,f3]) ).
fof(f135,plain,
spl0_11,
inference(avatar_contradiction_clause,[],[f133]) ).
cnf(s2,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f43]) ).
cnf(s4,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f56]) ).
cnf(s6,plain,
spl0_4,
inference(sat_conversion,[],[f79]) ).
cnf(s8,plain,
~ spl0_7,
inference(sat_conversion,[],[f95]) ).
cnf(s13,plain,
( ~ spl0_4
| spl0_6
| spl0_7
| ~ spl0_11 ),
inference(sat_conversion,[],[f132]) ).
cnf(s14,plain,
spl0_11,
inference(sat_conversion,[],[f135]) ).
cnf(s15,plain,
( ~ spl0_4
| spl0_6
| spl0_7 ),
inference(rat,[],[s13,s14]) ).
cnf(s17,plain,
spl0_6,
inference(rat,[],[s15,s8,s6]) ).
cnf(s20,plain,
spl0_3,
inference(rat,[],[s4,s8,s17,s6]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s2,s6,s20]) ).
fof(f136,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 18:40:34 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.17/1.50 % (3676149)Input is clausal, will run a generic CNF schedule.
% 0.17/1.50 % (3676156)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2927723887:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.17/1.50 % (3676154)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=1807293453:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.17/1.50 % (3676160)dis-21_1_sil=8000:lcm=predicate:random_seed=4056892671:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 0.17/1.50 % (3676158)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2809806779:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.17/1.50 % (3676155)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=560523353:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.17/1.50 % (3676160)First to succeed.
% 0.17/1.50 % (3676160)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3676149"
% 0.17/1.50 % (3676157)lrs+10_1_sil=8000:sp=occurrence:random_seed=177781532:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.17/1.50 % (3676157)Also succeeded, but the first one will report.
% 0.17/1.50 % (3676159)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=225400545:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.17/1.50 % (3676159)Also succeeded, but the first one will report.
% 0.17/1.50 % (3676158)Instruction limit reached!
% 0.17/1.50 % (3676158)------------------------------
% 0.17/1.50 % (3676158)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (3676158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (3676158)CaDiCaL version: 2.1.3
% 0.17/1.50 % (3676158)Termination reason: Instruction limit
% 0.17/1.50 % (3676158)Termination phase: Saturation
% 0.17/1.50 % (3676158)Time elapsed: 0.044 s
% 0.17/1.50 % (3676158)Peak memory usage: 87 MB
% 0.17/1.50 % (3676158)Instructions burned: 116 (million)
% 0.17/1.50 % (3676168)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=129676239:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.17/1.50 % (3676168)Refutation not found, incomplete strategy
% 0.17/1.50 % (3676168)------------------------------
% 0.17/1.50 % (3676168)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (3676168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (3676168)CaDiCaL version: 2.1.3
% 0.17/1.50 % (3676168)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (3676168)Time elapsed: 0.001 s
% 0.17/1.50 % (3676168)Peak memory usage: 87 MB
% 0.17/1.50 % (3676160)Refutation found. Thanks to Tanya!
% 0.17/1.50 % SZS status Unsatisfiable for theBenchmark
% 0.17/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (3676160)------------------------------
% 0.17/1.50 % (3676160)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (3676160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (3676160)CaDiCaL version: 2.1.3
% 0.17/1.50 % (3676160)Termination reason: Refutation
% 0.17/1.50 % (3676160)Time elapsed: 0.004 s
% 0.17/1.50 % (3676160)Peak memory usage: 89 MB
% 0.17/1.50 % (3676160)Instructions burned: 3 (million)
% 0.17/1.50 % (3676160)------------------------------
% 0.17/1.50 % (3676160)------------------------------
% 0.17/1.50 % (3676149)Success in time 0.448 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------