%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN002-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 : Fri Sep 25 01:36:56 PM UTC 2026
% Result : Unsatisfiable 6.00s 1.18s
% Output : Proof 6.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 15 unt; 0 def)
% Number of atoms : 23 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 10 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-4 aty)
% Number of variables : 17 ( 5 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( divide(X,Y) = zero
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal1) ).
fof(f0_nnf,plain,
! [X,Y] :
( divide(X,Y) = zero
| ~ less_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( divide(X,Y) = zero
| ~ less_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( divide(X0,X1) = zero
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(less_equal(X0,X1),true,divide(X0,X1),zero) = zero,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f4,axiom,
less_equal(zero,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_smallest) ).
fof(f4_nnf,plain,
! [X] : less_equal(zero,X),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X] : less_equal(zero,X),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
less_equal(zero,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
less_equal(zero,X0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t1,plain,
divide(zero,X1) = zero,
inference(hyper_resolution,[status(thm)],[hi0,hi4]) ).
cnf(t13,plain,
divide(zero,X1) = zero,
inference(orient,[status(thm)],[t1]) ).
cnf(f8,negated_conjecture,
divide(zero,a) != zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_zero_over_a_is_zero) ).
fof(f8_nnf,plain,
divide(zero,a) != zero,
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
divide(zero,a) != zero,
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
divide(zero,a) != zero,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(goal_0,negated_conjecture,
divide(zero,a) != zero,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(g0_0,plain,
zero != zero,
inference(rw,[status(thm)],[goal_0,t13]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN002-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n005.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 16:08:17 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.00/1.18 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.00/1.18 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------