%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : HEN004-3 : 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 : n003.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 10:19:13 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 17 unt; 0 def)
% Number of atoms : 42 ( 28 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 16 ~; 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 39 !; 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] :
( less_equal(X0,X1)
| divide(X0,X1) != zero ),
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(X0,X1)
| ~ less_equal(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/HEN002-0.ax',less_equal_and_equal) ).
fof(f8,negated_conjecture,
divide(a,zero) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_x_divide_zero_is_x) ).
fof(f9,plain,
a != divide(a,zero),
inference(reorient_equations,[],[f8]) ).
fof(f10,plain,
! [X0] : zero = divide(zero,X0),
inference(resolution,[],[f1,f5]) ).
fof(f12,plain,
! [X0,X1] : zero = divide(divide(X0,X1),X0),
inference(resolution,[],[f1,f3]) ).
fof(f19,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f22,plain,
! [X0,X1] :
( ~ less_equal(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[],[f6,f3]) ).
fof(f25,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(f29,plain,
! [X0,X1] : less_equal(divide(divide(X0,X1),zero),divide(divide(X0,zero),X1)),
inference(superposition,[],[f4,f10]) ).
fof(f43,plain,
! [X0] :
( zero != divide(X0,zero)
| zero = X0 ),
inference(resolution,[],[f19,f2]) ).
fof(f59,plain,
! [X0,X1] :
( zero != divide(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[],[f22,f2]) ).
fof(f126,plain,
! [X0,X1] :
( ~ less_equal(zero,divide(divide(X0,X0),divide(X1,X0)))
| zero = divide(divide(X0,X0),divide(X1,X0)) ),
inference(superposition,[],[f25,f12]) ).
fof(f145,plain,
! [X0,X1] : zero = divide(divide(X0,X0),divide(X1,X0)),
inference(forward_subsumption_resolution,[],[f126,f5]) ).
fof(f187,plain,
! [X0] : zero = divide(divide(X0,X0),zero),
inference(superposition,[],[f145,f12]) ).
fof(f269,plain,
! [X0] :
( zero != zero
| zero = divide(X0,X0) ),
inference(superposition,[],[f43,f187]) ).
fof(f286,plain,
! [X0] : zero = divide(X0,X0),
inference(trivial_inequality_removal,[],[f269]) ).
fof(f382,plain,
! [X0] : less_equal(divide(divide(X0,divide(X0,zero)),zero),zero),
inference(superposition,[],[f29,f286]) ).
fof(f741,plain,
! [X0] : zero = divide(divide(X0,divide(X0,zero)),zero),
inference(resolution,[],[f382,f19]) ).
fof(f1279,plain,
! [X0] :
( zero != zero
| zero = divide(X0,divide(X0,zero)) ),
inference(superposition,[],[f43,f741]) ).
fof(f1311,plain,
! [X0] : zero = divide(X0,divide(X0,zero)),
inference(trivial_inequality_removal,[],[f1279]) ).
fof(f1535,plain,
! [X0] :
( zero != zero
| divide(X0,zero) = X0 ),
inference(superposition,[],[f59,f1311]) ).
fof(f1584,plain,
! [X0] : divide(X0,zero) = X0,
inference(trivial_inequality_removal,[],[f1535]) ).
fof(f1914,plain,
a != a,
inference(superposition,[],[f9,f1584]) ).
fof(f1915,plain,
$false,
inference(trivial_inequality_removal,[],[f1914]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN004-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n003.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 10:51:30 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 Running first-order model finding
% 0.10/0.40 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
% 0.10/0.45 % (336006)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (336015)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3403617859:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % (336012)% WARNING: option uhcvi not known.
% 0.10/0.45 % (336011)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4090736458_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.45 % (336013)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=123821601:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.45 % (336014)dis+10_1_sil=32000:sp=arity:random_seed=4122733917:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (336016)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=309096046:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.45 % (336017)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1693517154:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.45 % TRYING [1]
% 0.10/0.45 % TRYING [2]
% 0.10/0.45 % TRYING [3]
% 0.10/0.45 % (336012)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2768241923:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.45 % TRYING [4]
% 0.10/0.45 % TRYING [5]
% 0.10/0.45 % (336015) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-336006-336015"...
% 0.10/0.45 % (336015)...printing done.
% 0.10/0.45 % (336015)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (336015)------------------------------
% 0.10/0.45 % (336015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (336015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (336015)CaDiCaL version: 2.1.3
% 0.10/0.45 % (336015)Termination reason: Refutation
% 0.10/0.45 % (336015)Time elapsed: 0.017 s
% 0.10/0.45 % (336015)Peak memory usage: 11 MB
% 0.10/0.45 % (336015)Instructions burned: 54 (million)
% 0.10/0.45 % (336006)Success in time 0.047 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------