%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN007-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 01:37:05 PM UTC 2026
% Result : Unsatisfiable 7.26s 1.31s
% Output : Proof 7.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 24 unt; 0 def)
% Number of atoms : 52 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 51 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1,axiom,
( less_equal(X,Y)
| divide(X,Y) != zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal2) ).
fof(f1_nnf,plain,
! [X,Y] :
( less_equal(X,Y)
| divide(X,Y) != zero ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( less_equal(X,Y)
| divide(X,Y) != zero ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( less_equal(X0,X1)
| divide(X0,X1) != zero ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(divide(X0,X1),zero,less_equal(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f9,axiom,
divide(X,X) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
fof(f9_nnf,plain,
! [X] : divide(X,X) = zero,
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X] : divide(X,X) = zero,
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
divide(X0,X0) = zero,
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,axiom,
divide(X0,X0) = zero,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h1,plain,
less_equal(V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi9]) ).
cnf(f12,axiom,
( less_equal(divide(X,Z),Y)
| ~ less_equal(divide(X,Y),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide1) ).
fof(f12_nnf,plain,
! [X,Y,Z] :
( less_equal(divide(X,Z),Y)
| ~ less_equal(divide(X,Y),Z) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y,Z] :
( less_equal(divide(X,Z),Y)
| ~ less_equal(divide(X,Y),Z) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( less_equal(divide(X0,X2),X1)
| ~ less_equal(divide(X0,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi12,axiom,
ifeq(less_equal(divide(X0,X1),X2),true,less_equal(divide(X0,X2),X1),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h3,plain,
less_equal(divide(V0,divide(V0,V1)),V1) = true,
inference(hyper_resolution,[status(thm)],[hi12,h1]) ).
cnf(f11,axiom,
( less_equal(X,Z)
| ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
fof(f11_nnf,plain,
! [X,Y,Z] :
( less_equal(X,Z)
| ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,Z] :
( less_equal(X,Z)
| ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( less_equal(X0,X2)
| ~ less_equal(X1,X2)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,axiom,
ifeq(less_equal(X0,X1),true,ifeq(less_equal(X1,X2),true,less_equal(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(f13,hypothesis,
less_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_LE_b) ).
fof(f13_nnf,plain,
less_equal(a,b),
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c13,plain,
less_equal(a,b),
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(hi13,axiom,
less_equal(a,b) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h40,plain,
less_equal(divide(V0,divide(V0,a)),b) = true,
inference(hyper_resolution,[status(thm)],[hi11,h3,hi13]) ).
cnf(t65,plain,
less_equal(divide(X1,b),divide(X1,a)) = true,
inference(hyper_resolution,[status(thm)],[hi12,h40]) ).
cnf(t436,plain,
less_equal(divide(X1,b),divide(X1,a)) = true,
inference(orient,[status(thm)],[t65]) ).
cnf(f14,negated_conjecture,
~ less_equal(divide(c,b),divide(c,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_divide_b_LE_c_divide_a) ).
fof(f14_nnf,plain,
~ less_equal(divide(c,b),divide(c,a)),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
~ less_equal(divide(c,b),divide(c,a)),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
~ less_equal(divide(c,b),divide(c,a)),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(goal_0,negated_conjecture,
less_equal(divide(c,b),divide(c,a)) != true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t436]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN007-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n016.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 16:18:28 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.26/1.31 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.26/1.31 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------