%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : HEN006-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 10:19:15 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 25 unt; 0 def)
% Number of atoms : 50 ( 28 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 : 4 ( 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 : 41 ( 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ less_equal(X0,X1)
| divide(X0,X1) = zero ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal1) ).
fof(f2,axiom,
! [X0,X1] :
( less_equal(X0,X1)
| divide(X0,X1) != zero ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_less_equal2) ).
fof(f3,axiom,
! [X0,X1] : less_equal(divide(X0,X1),X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/HEN002-0.ax',quotient_property) ).
fof(f5,axiom,
! [X0] : less_equal(zero,X0),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',zero_is_smallest) ).
fof(f6,axiom,
! [X0,X1] :
( ~ less_equal(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',less_equal_and_equal) ).
fof(f8,axiom,
less_equal(divide(a,b),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_divide_b_LE_d) ).
fof(f9,negated_conjecture,
~ less_equal(divide(a,d),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_divide_d_LE_b) ).
fof(f10,plain,
! [X0] : zero = divide(zero,X0),
inference(resolution,[],[f1,f5]) ).
fof(f12,plain,
zero = divide(divide(a,b),d),
inference(resolution,[],[f1,f8]) ).
fof(f13,plain,
! [X0,X1] : zero = divide(divide(X0,X1),X0),
inference(resolution,[],[f1,f3]) ).
fof(f15,plain,
zero != divide(divide(a,d),b),
inference(resolution,[],[f2,f9]) ).
fof(f22,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f26,plain,
! [X0,X1] :
( ~ less_equal(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[],[f6,f3]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ less_equal(divide(divide(X0,X2),X1),divide(divide(X0,X1),divide(X2,X1)))
| divide(divide(X0,X1),divide(X2,X1)) = divide(divide(X0,X2),X1) ),
inference(resolution,[],[f4,f6]) ).
fof(f42,plain,
! [X0,X1] : less_equal(divide(divide(X0,X1),zero),divide(divide(X0,zero),X1)),
inference(superposition,[],[f4,f10]) ).
fof(f58,plain,
! [X0] :
( zero != divide(X0,zero)
| zero = X0 ),
inference(resolution,[],[f22,f2]) ).
fof(f73,plain,
! [X0,X1] : less_equal(divide(divide(X0,X0),divide(X1,X0)),zero),
inference(superposition,[],[f4,f13]) ).
fof(f76,plain,
! [X2,X0,X1] : less_equal(divide(divide(X0,X1),zero),divide(divide(X0,divide(X1,X2)),X1)),
inference(superposition,[],[f4,f13]) ).
fof(f82,plain,
! [X0,X1] :
( zero != divide(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[],[f26,f2]) ).
fof(f143,plain,
( ~ less_equal(zero,divide(divide(a,d),divide(b,d)))
| zero = divide(divide(a,d),divide(b,d)) ),
inference(superposition,[],[f39,f12]) ).
fof(f167,plain,
zero = divide(divide(a,d),divide(b,d)),
inference(forward_subsumption_resolution,[],[f143,f5]) ).
fof(f255,plain,
! [X0] : less_equal(divide(divide(X0,X0),zero),zero),
inference(superposition,[],[f73,f13]) ).
fof(f258,plain,
! [X0] : zero = divide(divide(X0,X0),zero),
inference(resolution,[],[f255,f22]) ).
fof(f320,plain,
! [X0] :
( zero != zero
| zero = divide(X0,X0) ),
inference(superposition,[],[f58,f258]) ).
fof(f336,plain,
! [X0] : zero = divide(X0,X0),
inference(trivial_inequality_removal,[],[f320]) ).
fof(f645,plain,
! [X0] : less_equal(divide(divide(X0,divide(X0,zero)),zero),zero),
inference(superposition,[],[f42,f336]) ).
fof(f1259,plain,
! [X0] : zero = divide(divide(X0,divide(X0,zero)),zero),
inference(resolution,[],[f645,f22]) ).
fof(f1338,plain,
! [X0] :
( zero != zero
| zero = divide(X0,divide(X0,zero)) ),
inference(superposition,[],[f58,f1259]) ).
fof(f1363,plain,
! [X0] : zero = divide(X0,divide(X0,zero)),
inference(trivial_inequality_removal,[],[f1338]) ).
fof(f1436,plain,
! [X0] :
( zero != zero
| divide(X0,zero) = X0 ),
inference(superposition,[],[f82,f1363]) ).
fof(f1481,plain,
! [X0] : divide(X0,zero) = X0,
inference(trivial_inequality_removal,[],[f1436]) ).
fof(f1798,plain,
less_equal(divide(divide(divide(a,d),b),zero),divide(zero,b)),
inference(superposition,[],[f76,f167]) ).
fof(f1817,plain,
less_equal(divide(divide(divide(a,d),b),zero),zero),
inference(forward_demodulation,[],[f1798,f10]) ).
fof(f1850,plain,
less_equal(divide(divide(a,d),b),zero),
inference(forward_demodulation,[],[f1817,f1481]) ).
fof(f1972,plain,
zero = divide(divide(a,d),b),
inference(resolution,[],[f1850,f22]) ).
fof(f1981,plain,
$false,
inference(forward_subsumption_resolution,[],[f1972,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN006-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n018.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 10:52:59 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.43 Running first-order model finding
% 0.13/0.43 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
% 0.19/0.52 % (2155878)Will run a generic schedule for satisfiability detection.
% 0.19/0.52 % (2155895)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1902894956_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.52 % TRYING [1]
% 0.19/0.52 % TRYING [2]
% 0.19/0.52 % TRYING [3]
% 0.19/0.52 % TRYING [4]
% 0.19/0.52 % (2155896)% WARNING: option uhcvi not known.
% 0.19/0.52 % TRYING [5]
% 0.19/0.52 % (2155896)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=566712509:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.52 % (2155900)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1090671727:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.52 % (2155898)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3923818228:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.52 % (2155899)dis+10_1_sil=32000:sp=arity:random_seed=361825850:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.52 % (2155901)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1487430151:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.52 % (2155902)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2739616020:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.52 % TRYING [6]
% 0.19/0.52 % (2155900) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2155878-2155900"...
% 0.19/0.52 % (2155900)...printing done.
% 0.19/0.52 % TRYING [7]
% 0.19/0.52 % (2155900)Refutation found. Thanks to Tanya!
% 0.19/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52 % (2155900)------------------------------
% 0.19/0.52 % (2155900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.52 % (2155900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.52 % (2155900)CaDiCaL version: 2.1.3
% 0.19/0.52 % (2155900)Termination reason: Refutation
% 0.19/0.52 % (2155900)Time elapsed: 0.033 s
% 0.19/0.52 % (2155900)Peak memory usage: 12 MB
% 0.19/0.52 % (2155900)Instructions burned: 54 (million)
% 0.19/0.52 % (2155878)Success in time 0.079 s
% 0.19/0.52 % Vampire exiting
%------------------------------------------------------------------------------