%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : HEN009-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 10:19:18 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.48s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 11
% Syntax : Number of formulae : 67 ( 51 unt; 0 def)
% Number of atoms : 84 ( 35 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 19 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 41 ( 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ less_equal(X0,X1)
| divide(X0,X1) = zero ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_less_equal1) ).
fof(f2,axiom,
! [X0,X1] :
( divide(X0,X1) != zero
| less_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',quotient_less_equal2) ).
fof(f3,axiom,
! [X0,X1] : less_equal(divide(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',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/Axioms/HEN002-0.ax',quotient_property) ).
fof(f5,axiom,
! [X0] : less_equal(zero,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
fof(f6,axiom,
! [X0,X1] :
( ~ less_equal(X1,X0)
| ~ less_equal(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',less_equal_and_equal) ).
fof(f7,axiom,
! [X0] : less_equal(X0,identity),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',identity_is_largest) ).
fof(f9,axiom,
divide(identity,a) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id_divide_a_is_b) ).
fof(f10,axiom,
divide(identity,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id_divide_b_is_c) ).
fof(f11,axiom,
divide(identity,c) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id_divide_c_is_d) ).
fof(f12,negated_conjecture,
b != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_equals_d) ).
fof(f25,plain,
! [X0] : zero = divide(zero,X0),
inference(resolution,[],[f1,f5]) ).
fof(f26,plain,
! [X0] : zero = divide(X0,identity),
inference(resolution,[],[f1,f7]) ).
fof(f27,plain,
! [X0,X1] : zero = divide(divide(X0,X1),X0),
inference(resolution,[],[f1,f3]) ).
fof(f161,plain,
! [X0,X1] :
( ~ less_equal(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[],[f6,f3]) ).
fof(f162,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f641,plain,
! [X0] : less_equal(divide(b,divide(X0,a)),divide(divide(identity,X0),a)),
inference(superposition,[],[f4,f9]) ).
fof(f649,plain,
! [X0] : less_equal(divide(divide(X0,a),b),divide(divide(X0,identity),a)),
inference(superposition,[],[f4,f9]) ).
fof(f651,plain,
! [X0] : less_equal(divide(divide(X0,b),c),divide(divide(X0,identity),b)),
inference(superposition,[],[f4,f10]) ).
fof(f652,plain,
! [X0] : less_equal(divide(divide(X0,c),d),divide(divide(X0,identity),c)),
inference(superposition,[],[f4,f11]) ).
fof(f675,plain,
! [X0] : less_equal(divide(divide(X0,a),b),divide(zero,a)),
inference(forward_demodulation,[],[f649,f26]) ).
fof(f692,plain,
! [X0] : less_equal(divide(divide(X0,a),b),zero),
inference(forward_demodulation,[],[f675,f25]) ).
fof(f813,plain,
! [X0] : less_equal(divide(divide(X0,c),d),divide(zero,c)),
inference(forward_demodulation,[],[f652,f26]) ).
fof(f814,plain,
! [X0] : less_equal(divide(divide(X0,b),c),divide(zero,b)),
inference(forward_demodulation,[],[f651,f26]) ).
fof(f815,plain,
! [X0] : less_equal(divide(divide(X0,c),d),zero),
inference(forward_demodulation,[],[f813,f25]) ).
fof(f816,plain,
! [X0] : less_equal(divide(divide(X0,b),c),zero),
inference(forward_demodulation,[],[f814,f25]) ).
fof(f817,plain,
! [X0] : zero = divide(divide(X0,a),b),
inference(resolution,[],[f692,f162]) ).
fof(f842,plain,
! [X0] : zero = divide(divide(X0,c),d),
inference(resolution,[],[f815,f162]) ).
fof(f867,plain,
! [X0] : zero = divide(divide(X0,b),c),
inference(resolution,[],[f816,f162]) ).
fof(f898,plain,
! [X0] : less_equal(divide(divide(X0,b),divide(a,b)),zero),
inference(superposition,[],[f4,f817]) ).
fof(f900,plain,
! [X0] :
( zero != zero
| less_equal(divide(X0,a),b) ),
inference(superposition,[],[f2,f817]) ).
fof(f907,plain,
! [X0] : less_equal(divide(X0,a),b),
inference(trivial_inequality_removal,[],[f900]) ).
fof(f921,plain,
! [X0] :
( zero != zero
| less_equal(divide(X0,c),d) ),
inference(superposition,[],[f2,f842]) ).
fof(f928,plain,
! [X0] : less_equal(divide(X0,c),d),
inference(trivial_inequality_removal,[],[f921]) ).
fof(f943,plain,
! [X0] : less_equal(divide(divide(X0,c),divide(b,c)),zero),
inference(superposition,[],[f4,f867]) ).
fof(f947,plain,
! [X0] :
( zero != zero
| less_equal(divide(X0,b),c) ),
inference(superposition,[],[f2,f867]) ).
fof(f954,plain,
! [X0] : less_equal(divide(X0,b),c),
inference(trivial_inequality_removal,[],[f947]) ).
fof(f1011,plain,
less_equal(divide(c,divide(a,b)),zero),
inference(superposition,[],[f898,f10]) ).
fof(f1015,plain,
zero = divide(c,divide(a,b)),
inference(resolution,[],[f1011,f162]) ).
fof(f1020,plain,
( zero != zero
| less_equal(c,divide(a,b)) ),
inference(superposition,[],[f2,f1015]) ).
fof(f1028,plain,
less_equal(c,divide(a,b)),
inference(trivial_inequality_removal,[],[f1020]) ).
fof(f1031,plain,
( ~ less_equal(divide(a,b),c)
| c = divide(a,b) ),
inference(resolution,[],[f1028,f6]) ).
fof(f1033,plain,
c = divide(a,b),
inference(forward_subsumption_resolution,[],[f1031,f954]) ).
fof(f1047,plain,
zero = divide(c,a),
inference(superposition,[],[f27,f1033]) ).
fof(f1216,plain,
less_equal(divide(d,divide(b,c)),zero),
inference(superposition,[],[f943,f11]) ).
fof(f1221,plain,
zero = divide(d,divide(b,c)),
inference(resolution,[],[f1216,f162]) ).
fof(f1226,plain,
( zero != zero
| less_equal(d,divide(b,c)) ),
inference(superposition,[],[f2,f1221]) ).
fof(f1235,plain,
less_equal(d,divide(b,c)),
inference(trivial_inequality_removal,[],[f1226]) ).
fof(f1238,plain,
( ~ less_equal(divide(b,c),d)
| d = divide(b,c) ),
inference(resolution,[],[f1235,f6]) ).
fof(f1240,plain,
d = divide(b,c),
inference(forward_subsumption_resolution,[],[f1238,f928]) ).
fof(f1255,plain,
( ~ less_equal(b,d)
| b = d ),
inference(superposition,[],[f161,f1240]) ).
fof(f1259,plain,
~ less_equal(b,d),
inference(forward_subsumption_resolution,[],[f1255,f12]) ).
fof(f1409,plain,
less_equal(divide(b,divide(c,a)),divide(d,a)),
inference(superposition,[],[f641,f11]) ).
fof(f1414,plain,
less_equal(divide(b,zero),divide(d,a)),
inference(forward_demodulation,[],[f1409,f1047]) ).
fof(f1424,plain,
zero = divide(divide(b,zero),divide(d,a)),
inference(resolution,[],[f1414,f1]) ).
fof(f1477,plain,
less_equal(divide(divide(b,divide(d,a)),divide(zero,divide(d,a))),zero),
inference(superposition,[],[f4,f1424]) ).
fof(f1492,plain,
less_equal(divide(divide(b,divide(d,a)),zero),zero),
inference(forward_demodulation,[],[f1477,f25]) ).
fof(f1496,plain,
zero = divide(divide(b,divide(d,a)),zero),
inference(resolution,[],[f1492,f162]) ).
fof(f1505,plain,
( zero != zero
| less_equal(divide(b,divide(d,a)),zero) ),
inference(superposition,[],[f2,f1496]) ).
fof(f1516,plain,
less_equal(divide(b,divide(d,a)),zero),
inference(trivial_inequality_removal,[],[f1505]) ).
fof(f1519,plain,
zero = divide(b,divide(d,a)),
inference(resolution,[],[f1516,f162]) ).
fof(f1527,plain,
( zero != zero
| less_equal(b,divide(d,a)) ),
inference(superposition,[],[f2,f1519]) ).
fof(f1538,plain,
less_equal(b,divide(d,a)),
inference(trivial_inequality_removal,[],[f1527]) ).
fof(f1541,plain,
( ~ less_equal(divide(d,a),b)
| b = divide(d,a) ),
inference(resolution,[],[f1538,f6]) ).
fof(f1543,plain,
b = divide(d,a),
inference(forward_subsumption_resolution,[],[f1541,f907]) ).
fof(f1556,plain,
less_equal(b,d),
inference(superposition,[],[f3,f1543]) ).
fof(f1571,plain,
$false,
inference(forward_subsumption_resolution,[],[f1556,f1259]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n019.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 10:51:19 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.12/0.48 % (2909029)Will run a generic schedule for satisfiability detection.
% 0.12/0.48 % (2909035)% WARNING: option uhcvi not known.
% 0.12/0.48 % (2909034)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3350683798_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.48 % (2909040)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1485939823:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.48 % (2909037)dis+10_1_sil=32000:sp=arity:random_seed=2705883408:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.48 % (2909036)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2070490137:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.48 % (2909035)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2630786391:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.48 % (2909038)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3101869579:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.48 % (2909039)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=263786302:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.48 % TRYING [1]
% 0.12/0.48 % TRYING [2]
% 0.12/0.48 % TRYING [3]
% 0.12/0.48 % TRYING [4]
% 0.12/0.48 % TRYING [5]
% 0.12/0.48 % (2909036) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2909029-2909036"...
% 0.12/0.48 % TRYING [6]
% 0.12/0.48 % (2909036)...printing done.
% 0.12/0.48 % (2909036)Refutation found. Thanks to Tanya!
% 0.12/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.48 % (2909036)------------------------------
% 0.12/0.48 % (2909036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.48 % (2909036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.48 % (2909036)CaDiCaL version: 2.1.3
% 0.12/0.48 % (2909036)Termination reason: Refutation
% 0.12/0.48 % (2909036)Time elapsed: 0.024 s
% 0.12/0.48 % (2909036)Peak memory usage: 12 MB
% 0.12/0.48 % (2909036)Instructions burned: 36 (million)
% 0.12/0.48 % (2909029)Success in time 0.061 s
% 0.12/0.48 % Vampire exiting
%------------------------------------------------------------------------------