%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM027-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 12:17:51 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.45s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 18 ( 9 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X2,X0,X1] :
( ~ less(X2,X0)
| ~ less(X0,X1)
| less(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-1.ax',transitivity_of_less) ).
fof(f13,axiom,
! [X2,X0,X1] :
( equalish(multiply(X0,X2),multiply(X1,X2))
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality_preserved_over_times) ).
fof(f14,axiom,
! [X0,X1] :
( ~ less(X0,X1)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_and_equal) ).
fof(f15,axiom,
! [X0,X1] :
( less(X1,X0)
| less(X0,X1)
| equalish(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',numbers_either_less_or_equal) ).
fof(f16,axiom,
! [X0] : ~ less(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',number_not_less_than_itself) ).
fof(f18,axiom,
! [X2,X0,X1] :
( less(multiply(X0,X2),multiply(X1,X2))
| equalish(X2,n0)
| ~ less(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_lemma) ).
fof(f19,axiom,
~ less(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_not_less_than_a) ).
fof(f20,axiom,
less(multiply(b,c),multiply(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_c_less_than_a_times_c) ).
fof(f21,negated_conjecture,
~ equalish(c,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_is_0) ).
fof(f27,plain,
~ equalish(multiply(b,c),multiply(a,c)),
inference(resolution,[],[f20,f14]) ).
fof(f34,plain,
! [X0] :
( ~ less(multiply(a,c),X0)
| less(multiply(b,c),X0) ),
inference(resolution,[],[f7,f20]) ).
fof(f58,plain,
~ equalish(b,a),
inference(resolution,[],[f13,f27]) ).
fof(f97,plain,
! [X0] :
( less(multiply(b,c),multiply(X0,c))
| equalish(c,n0)
| ~ less(a,X0) ),
inference(resolution,[],[f34,f18]) ).
fof(f101,plain,
! [X0] :
( less(multiply(b,c),multiply(X0,c))
| ~ less(a,X0) ),
inference(forward_subsumption_resolution,[],[f97,f21]) ).
fof(f102,plain,
~ less(a,b),
inference(resolution,[],[f101,f16]) ).
fof(f107,plain,
( less(b,a)
| equalish(b,a) ),
inference(resolution,[],[f102,f15]) ).
fof(f110,plain,
equalish(b,a),
inference(forward_subsumption_resolution,[],[f107,f19]) ).
fof(f111,plain,
$false,
inference(forward_subsumption_resolution,[],[f110,f58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM027-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 18:38:25 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 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
% 0.09/0.45 % (1706747)Will run a generic schedule for satisfiability detection.
% 0.09/0.45 % (1706753)% WARNING: option uhcvi not known.
% 0.09/0.45 % (1706753)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=228587378:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.45 % (1706756)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2272207458:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.45 % (1706752)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=601825403_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.45 % (1706754)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1918149622:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.45 % (1706757)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3885130979:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.45 % (1706755)dis+10_1_sil=32000:sp=arity:random_seed=1985513731:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.45 % (1706758)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1295849190:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.45 % TRYING [1]
% 0.09/0.45 % TRYING [2]
% 0.09/0.45 % TRYING [3]
% 0.09/0.45 % (1706755) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1706747-1706755"...
% 0.09/0.45 % (1706755)...printing done.
% 0.09/0.45 % TRYING [4]
% 0.09/0.45 % (1706755)Refutation found. Thanks to Tanya!
% 0.09/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.45 % (1706755)------------------------------
% 0.09/0.45 % (1706755)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.45 % (1706755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.45 % (1706755)CaDiCaL version: 2.1.3
% 0.09/0.45 % (1706755)Termination reason: Refutation
% 0.09/0.45 % (1706755)Time elapsed: 0.003 s
% 0.09/0.45 % (1706755)Peak memory usage: 11 MB
% 0.09/0.45 % (1706755)Instructions burned: 3 (million)
% 0.09/0.45 % (1706747)Success in time 0.036 s
% 0.09/0.45 % Vampire exiting
%------------------------------------------------------------------------------