%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : HEN005-6 : 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 : n002.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 10:19:05 AM UTC 2026
% Result : Unsatisfiable 0.14s 1.14s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 23 unt; 0 def)
% Number of atoms : 48 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( divide(X0,X1) = zero
| ~ less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal1) ).
fof(f2,axiom,
! [X0,X1] :
( less_equal(X0,X1)
| divide(X0,X1) != zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal2) ).
fof(f3,axiom,
! [X0,X1] : less_equal(divide(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).
fof(f4,axiom,
! [X2,X0,X1] : less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_property) ).
fof(f5,axiom,
! [X0] : less_equal(zero,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_is_smallest) ).
fof(f6,axiom,
! [X0,X1] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_equal_and_equal) ).
fof(f10,axiom,
! [X0] : divide(zero,X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
fof(f11,plain,
! [X0] : zero = divide(zero,X0),
inference(reorient_equations,[],[f10]) ).
fof(f12,axiom,
less_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_LE_b) ).
fof(f13,axiom,
less_equal(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_LE_c) ).
fof(f14,negated_conjecture,
~ less_equal(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_LE_c) ).
fof(f18,plain,
zero != divide(a,c),
inference(resolution,[],[f2,f14]) ).
fof(f24,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ~ less_equal(X2,X1)
| less_equal(divide(divide(X0,X1),zero),divide(divide(X0,X2),X1)) ),
inference(superposition,[],[f4,f1]) ).
fof(f56,plain,
! [X2,X0,X1] :
( less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(zero,X1))
| ~ less_equal(X0,X2) ),
inference(superposition,[],[f4,f1]) ).
fof(f59,plain,
! [X2,X0,X1] :
( ~ less_equal(divide(X0,X2),X1)
| less_equal(divide(divide(X0,X1),divide(X2,X1)),zero) ),
inference(superposition,[],[f4,f1]) ).
fof(f61,plain,
! [X2,X0,X1] :
( ~ less_equal(X0,X2)
| less_equal(divide(divide(X0,X1),divide(X2,X1)),zero) ),
inference(forward_demodulation,[],[f56,f11]) ).
fof(f75,plain,
! [X0] :
( zero != divide(X0,zero)
| zero = X0 ),
inference(resolution,[],[f24,f2]) ).
fof(f99,plain,
! [X0] : less_equal(divide(divide(a,X0),divide(b,X0)),zero),
inference(resolution,[],[f61,f12]) ).
fof(f120,plain,
! [X0] : less_equal(divide(divide(X0,c),zero),divide(divide(X0,b),c)),
inference(resolution,[],[f52,f13]) ).
fof(f135,plain,
! [X0,X1] : less_equal(divide(divide(X0,X0),divide(X1,X0)),zero),
inference(resolution,[],[f59,f3]) ).
fof(f213,plain,
! [X0] : less_equal(divide(divide(X0,X0),zero),zero),
inference(superposition,[],[f135,f11]) ).
fof(f219,plain,
! [X0] : zero = divide(divide(X0,X0),zero),
inference(resolution,[],[f213,f24]) ).
fof(f236,plain,
! [X0] :
( zero != zero
| zero = divide(X0,X0) ),
inference(superposition,[],[f75,f219]) ).
fof(f250,plain,
! [X0] : zero = divide(X0,X0),
inference(trivial_inequality_removal,[],[f236]) ).
fof(f326,plain,
less_equal(divide(divide(a,b),zero),zero),
inference(superposition,[],[f99,f250]) ).
fof(f415,plain,
zero = divide(divide(a,b),zero),
inference(resolution,[],[f326,f24]) ).
fof(f523,plain,
( zero != zero
| zero = divide(a,b) ),
inference(superposition,[],[f75,f415]) ).
fof(f542,plain,
zero = divide(a,b),
inference(trivial_inequality_removal,[],[f523]) ).
fof(f608,plain,
less_equal(divide(divide(a,c),zero),divide(zero,c)),
inference(superposition,[],[f120,f542]) ).
fof(f638,plain,
less_equal(divide(divide(a,c),zero),zero),
inference(forward_demodulation,[],[f608,f11]) ).
fof(f1195,plain,
zero = divide(divide(a,c),zero),
inference(resolution,[],[f638,f24]) ).
fof(f1353,plain,
( zero != zero
| zero = divide(a,c) ),
inference(superposition,[],[f75,f1195]) ).
fof(f1389,plain,
zero = divide(a,c),
inference(trivial_inequality_removal,[],[f1353]) ).
fof(f1410,plain,
$false,
inference(forward_subsumption_resolution,[],[f1389,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN005-6 : 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 : n002.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 10:53:27 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 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
% 0.14/1.14 % (3359837)Input is clausal, will run a generic CNF schedule.
% 0.14/1.14 % (3359847)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2457563417:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.14/1.14 % (3359842)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=3016035617:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.14/1.14 % (3359845)lrs+10_1_sil=8000:sp=occurrence:random_seed=3420456742:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.14/1.14 % (3359848)dis-21_1_sil=8000:lcm=predicate:random_seed=2272909711: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)
% 0.14/1.14 % (3359843)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1765732374:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.14/1.14 % (3359846)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1013265698:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.14/1.14 % (3359844)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2066838604:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.14/1.14 % (3359845)Refutation not found, incomplete strategy
% 0.14/1.14 % (3359845)------------------------------
% 0.14/1.14 % (3359845)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.14 % (3359846)Refutation not found, incomplete strategy
% 0.14/1.14 % (3359846)------------------------------
% 0.14/1.14 % (3359846)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.14 % (3359845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.14 % (3359846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.14 % (3359845)CaDiCaL version: 2.1.3
% 0.14/1.14 % (3359845)Termination reason: Refutation not found, incomplete strategy
% 0.14/1.14 % (3359845)Time elapsed: 0.001 s
% 0.14/1.14 % (3359846)CaDiCaL version: 2.1.3
% 0.14/1.14 % (3359845)Peak memory usage: 87 MB
% 0.14/1.14 % (3359846)Termination reason: Refutation not found, incomplete strategy
% 0.14/1.14 % (3359846)Time elapsed: 0.001 s
% 0.14/1.14 % (3359846)Peak memory usage: 87 MB
% 0.14/1.14 % (3359848)Refutation not found, incomplete strategy
% 0.14/1.14 % (3359848)------------------------------
% 0.14/1.14 % (3359848)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.14 % (3359848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.14 % (3359848)CaDiCaL version: 2.1.3
% 0.14/1.14 % (3359848)Termination reason: Refutation not found, incomplete strategy
% 0.14/1.14 % (3359848)Time elapsed: 0.001 s
% 0.14/1.14 % (3359848)Peak memory usage: 88 MB
% 0.14/1.14 % (3359847)First to succeed.
% 0.14/1.14 % (3359847)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3359837"
% 0.14/1.14 % (3359847)Refutation found. Thanks to Tanya!
% 0.14/1.14 % SZS status Unsatisfiable for theBenchmark
% 0.14/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/1.14 % (3359847)------------------------------
% 0.14/1.14 % (3359847)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.14 % (3359847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.14 % (3359847)CaDiCaL version: 2.1.3
% 0.14/1.14 % (3359847)Termination reason: Refutation
% 0.14/1.14 % (3359847)Time elapsed: 0.013 s
% 0.14/1.14 % (3359847)Peak memory usage: 89 MB
% 0.14/1.14 % (3359847)Instructions burned: 38 (million)
% 0.14/1.14 % (3359847)------------------------------
% 0.14/1.14 % (3359847)------------------------------
% 0.14/1.14 % (3359837)Success in time 0.331 s
% 0.14/1.14 % Vampire exiting
%------------------------------------------------------------------------------