%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM014-1 : 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 : n018.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 2.56s 1.21s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 12 ( 7 unt; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 21 ( 10 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(X0,X0,square(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',square) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| divides(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divides) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( ~ product(X1,X2,X3)
| ~ prime(X0)
| ~ divides(X0,X3)
| divides(X0,X1)
| divides(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',remainder) ).
fof(f5,axiom,
prime(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_prime) ).
fof(f6,axiom,
product(a,square(c),square(b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_equals_b_squared_by_c_squared) ).
fof(f7,negated_conjecture,
~ divides(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_divides_b) ).
fof(f9,plain,
divides(a,square(b)),
inference(resolution,[],[f3,f6]) ).
fof(f11,plain,
! [X0,X1] :
( ~ prime(X0)
| ~ divides(X0,square(X1))
| divides(X0,X1)
| divides(X0,X1) ),
inference(resolution,[],[f4,f1]) ).
fof(f14,plain,
! [X0,X1] :
( ~ divides(X0,square(X1))
| ~ prime(X0)
| divides(X0,X1) ),
inference(duplicate_literal_removal,[],[f11]) ).
fof(f18,plain,
( ~ prime(a)
| divides(a,b) ),
inference(resolution,[],[f14,f9]) ).
fof(f28,plain,
divides(a,b),
inference(forward_subsumption_resolution,[],[f18,f5]) ).
fof(f29,plain,
$false,
inference(forward_subsumption_resolution,[],[f28,f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM014-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 18:41:39 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 2.56/1.21 % (2662340)Input is clausal, will run a generic CNF schedule.
% 2.56/1.21 % (2662349)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=77489226:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.56/1.21 % (2662349)First to succeed.
% 2.56/1.21 % (2662349)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2662340"
% 2.56/1.21 % (2662348)lrs+10_1_sil=8000:sp=occurrence:random_seed=1103448466:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.56/1.21 % (2662346)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=710916025:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.56/1.21 % (2662345)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=3187044927:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.56/1.21 % (2662347)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1374741475:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.56/1.21 % (2662348)Also succeeded, but the first one will report.
% 2.56/1.21 % (2662351)dis-21_1_sil=8000:lcm=predicate:random_seed=2673569003: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)
% 2.56/1.21 % (2662350)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3006791244:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.56/1.21 % (2662351)Also succeeded, but the first one will report.
% 2.56/1.21 % (2662350)Also succeeded, but the first one will report.
% 2.56/1.21 % (2662349)Refutation found. Thanks to Tanya!
% 2.56/1.21 % SZS status Unsatisfiable for theBenchmark
% 2.56/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.21 % (2662349)------------------------------
% 2.56/1.21 % (2662349)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.21 % (2662349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.21 % (2662349)CaDiCaL version: 2.1.3
% 2.56/1.21 % (2662349)Termination reason: Refutation
% 2.56/1.21 % (2662349)Time elapsed: 0.001 s
% 2.56/1.21 % (2662349)Peak memory usage: 88 MB
% 2.56/1.21 % (2662349)Instructions burned: 1 (million)
% 2.56/1.21 % (2662349)------------------------------
% 2.56/1.21 % (2662349)------------------------------
% 2.56/1.21 % (2662340)Success in time 0.287 s
% 2.56/1.21 % Vampire exiting
%------------------------------------------------------------------------------