%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : HEN004-4 : 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 : 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 10:19:14 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 18 unt; 0 def)
% Number of atoms : 31 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 7 |; 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 : 27 ( 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( divide(X0,X1) != zero
| less_equal(X0,X1) ),
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(X1,X0)
| ~ less_equal(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/HEN002-0.ax',less_equal_and_equal) ).
fof(f10,axiom,
! [X0] : divide(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
fof(f11,plain,
! [X0] : zero = divide(zero,X0),
inference(reorient_equations,[],[f10]) ).
fof(f12,axiom,
! [X0] : divide(X0,X0) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
fof(f13,plain,
! [X0] : zero = divide(X0,X0),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
divide(a,zero) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_x_divide_zero_is_x) ).
fof(f15,plain,
a != divide(a,zero),
inference(reorient_equations,[],[f14]) ).
fof(f36,plain,
! [X0] :
( ~ less_equal(X0,zero)
| zero = X0 ),
inference(resolution,[],[f6,f5]) ).
fof(f39,plain,
! [X0,X1] :
( ~ less_equal(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[],[f6,f3]) ).
fof(f51,plain,
! [X0,X1] : less_equal(divide(divide(X0,X1),zero),divide(divide(X0,zero),X1)),
inference(superposition,[],[f4,f11]) ).
fof(f161,plain,
! [X0] : less_equal(divide(divide(X0,divide(X0,zero)),zero),zero),
inference(superposition,[],[f51,f13]) ).
fof(f172,plain,
! [X0] : zero = divide(divide(X0,divide(X0,zero)),zero),
inference(resolution,[],[f161,f36]) ).
fof(f285,plain,
! [X0] :
( zero != zero
| less_equal(divide(X0,divide(X0,zero)),zero) ),
inference(superposition,[],[f2,f172]) ).
fof(f301,plain,
! [X0] : less_equal(divide(X0,divide(X0,zero)),zero),
inference(trivial_inequality_removal,[],[f285]) ).
fof(f396,plain,
! [X0] : zero = divide(X0,divide(X0,zero)),
inference(resolution,[],[f301,f36]) ).
fof(f453,plain,
! [X0] :
( zero != zero
| less_equal(X0,divide(X0,zero)) ),
inference(superposition,[],[f2,f396]) ).
fof(f485,plain,
! [X0] : less_equal(X0,divide(X0,zero)),
inference(trivial_inequality_removal,[],[f453]) ).
fof(f500,plain,
! [X0] : divide(X0,zero) = X0,
inference(resolution,[],[f485,f39]) ).
fof(f553,plain,
a != a,
inference(superposition,[],[f15,f500]) ).
fof(f554,plain,
$false,
inference(trivial_inequality_removal,[],[f553]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN004-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 10:47:45 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.16/0.47 % (1233037)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (1233045)dis+10_1_sil=32000:sp=arity:random_seed=554926522:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (1233043)% WARNING: option uhcvi not known.
% 0.16/0.47 % (1233045) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1233037-1233045"...
% 0.16/0.47 % (1233045)...printing done.
% 0.16/0.47 % (1233045)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (1233045)------------------------------
% 0.16/0.47 % (1233045)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (1233045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (1233045)CaDiCaL version: 2.1.3
% 0.16/0.47 % (1233045)Termination reason: Refutation
% 0.16/0.47 % (1233045)Time elapsed: 0.005 s
% 0.16/0.47 % (1233045)Peak memory usage: 11 MB
% 0.16/0.47 % (1233045)Instructions burned: 15 (million)
% 0.16/0.47 % (1233037)Success in time 0.038 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------