%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM017-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n004.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 12:17:49 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.46s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 23 ( 11 unt; 0 def)
% Number of atoms : 42 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_product) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X3,X4,X1)
| ~ product(X0,X3,X5)
| product(X5,X4,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_associativity1) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| product(X1,X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_commutativity) ).
fof(f5,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| X1 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f9,axiom,
! [X0,X1] :
( ~ divides(X0,X1)
| product(X0,second_divided_by_1st(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divides_implies_product) ).
fof(f10,axiom,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| divides(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_divisible_by_operand) ).
fof(f11,axiom,
! [X2,X0,X1] :
( ~ prime(X0)
| ~ product(X2,X2,X1)
| ~ divides(X0,X1)
| divides(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',primes_lemma1) ).
fof(f12,axiom,
prime(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_prime) ).
fof(f16,negated_conjecture,
! [X0] :
( ~ divides(X0,c)
| ~ divides(X0,b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_no_common_divisor) ).
fof(f19,plain,
! [X0,X1] : divides(X0,multiply(X0,X1)),
inference(resolution,[],[f10,f1]) ).
fof(f22,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(resolution,[],[f4,f1]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,multiply(X0,X2))
| X1 = X2 ),
inference(resolution,[],[f5,f1]) ).
fof(f41,plain,
! [X0,X1] :
( ~ divides(a,X1)
| ~ product(X0,X0,X1)
| divides(a,X0) ),
inference(resolution,[],[f11,f12]) ).
fof(f44,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ product(X3,X0,X4)
| product(X4,X1,multiply(X3,X2)) ),
inference(resolution,[],[f2,f1]) ).
fof(f116,plain,
! [X0,X1] :
( ~ product(X0,X0,multiply(a,X1))
| divides(a,X0) ),
inference(resolution,[],[f41,f19]) ).
fof(f166,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| product(X2,X3,multiply(X0,multiply(X1,X3))) ),
inference(resolution,[],[f44,f1]) ).
fof(f217,plain,
divides(a,a),
inference(resolution,[],[f116,f22]) ).
fof(f222,plain,
product(a,second_divided_by_1st(a,a),a),
inference(resolution,[],[f217,f9]) ).
fof(f318,plain,
! [X0] : product(a,X0,multiply(a,multiply(second_divided_by_1st(a,a),X0))),
inference(resolution,[],[f166,f222]) ).
fof(f2601,plain,
! [X0] : multiply(second_divided_by_1st(a,a),X0) = X0,
inference(resolution,[],[f318,f31]) ).
fof(f2698,plain,
! [X0] : divides(second_divided_by_1st(a,a),X0),
inference(superposition,[],[f19,f2601]) ).
fof(f3541,plain,
~ divides(second_divided_by_1st(a,a),b),
inference(resolution,[],[f2698,f16]) ).
fof(f3542,plain,
$false,
inference(forward_subsumption_resolution,[],[f3541,f2698]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM017-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n004.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 18:39:52 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.39 Running first-order model finding
% 0.14/0.39 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
% 0.14/0.46 % (3807976)Will run a generic schedule for satisfiability detection.
% 0.14/0.46 % (3807986)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=242875050:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.14/0.46 % (3807982)% WARNING: option uhcvi not known.
% 0.14/0.46 % (3807981)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1814592756_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.46 % (3807987)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=445830740:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.14/0.46 % (3807983)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4279991391:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.14/0.46 % (3807984)dis+10_1_sil=32000:sp=arity:random_seed=1846420988:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.46 % (3807985)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=744168962:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.14/0.46 % (3807982)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2335487513:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.14/0.46 % TRYING [1]
% 0.14/0.46 % TRYING [2]
% 0.14/0.46 % TRYING [3]
% 0.14/0.46 % TRYING [4]
% 0.14/0.46 % TRYING [5]
% 0.14/0.46 % (3807986) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3807976-3807986"...
% 0.14/0.46 % (3807986)...printing done.
% 0.14/0.46 % (3807986)Refutation found. Thanks to Tanya!
% 0.14/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.46 % (3807986)------------------------------
% 0.14/0.46 % (3807986)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.46 % (3807986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.46 % (3807986)CaDiCaL version: 2.1.3
% 0.14/0.46 % (3807986)Termination reason: Refutation
% 0.14/0.46 % (3807986)Time elapsed: 0.030 s
% 0.14/0.46 % (3807986)Peak memory usage: 12 MB
% 0.14/0.46 % (3807986)Instructions burned: 89 (million)
% 0.14/0.46 % (3807976)Success in time 0.06 s
% 0.14/0.46 % Vampire exiting
%------------------------------------------------------------------------------