%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN009-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 01:37:09 PM UTC 2026
% Result : Unsatisfiable 8.49s 1.69s
% Output : Proof 8.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 10
% Syntax : Number of formulae : 85 ( 69 unt; 0 def)
% Number of atoms : 105 ( 68 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 49 ( 29 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 95 ( 18 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t16,axiom,
sFlat0 = divide(identity,a),
introduced(definition) ).
cnf(t27,plain,
divide(identity,a) = sFlat0,
inference(orient,[status(thm)],[t16]) ).
cnf(t17,axiom,
sFlat1 = divide(identity,divide(identity,a)),
introduced(definition) ).
cnf(t25,plain,
divide(identity,divide(identity,a)) = sFlat1,
inference(orient,[status(thm)],[t17]) ).
cnf(t594,plain,
divide(identity,sFlat0) = sFlat1,
inference(step,[status(thm)],[t25,t27]) ).
cnf(t28,plain,
divide(identity,sFlat0) = sFlat1,
inference(rw,[status(thm)],[t594]) ).
cnf(t134,plain,
divide(identity,sFlat0) = sFlat1,
inference(orient,[status(thm)],[t28]) ).
cnf(t18,axiom,
sFlat2 = divide(identity,divide(identity,divide(identity,a))),
introduced(definition) ).
cnf(t24,plain,
divide(identity,divide(identity,divide(identity,a))) = sFlat2,
inference(orient,[status(thm)],[t18]) ).
cnf(t593,plain,
divide(identity,sFlat1) = sFlat2,
inference(step,[status(thm)],[t24,t25]) ).
cnf(t26,plain,
divide(identity,sFlat1) = sFlat2,
inference(rw,[status(thm)],[t593]) ).
cnf(t122,plain,
divide(identity,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t26]) ).
cnf(f5,axiom,
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_equal_and_equal) ).
fof(f5_nnf,plain,
! [X,Y] :
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] :
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t10,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t20,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(f13,axiom,
( less_equal(divide(Z,Y),divide(Z,X))
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide2) ).
fof(f13_nnf,plain,
! [X,Y,Z] :
( less_equal(divide(Z,Y),divide(Z,X))
| ~ less_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y,Z] :
( less_equal(divide(Z,Y),divide(Z,X))
| ~ less_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( less_equal(divide(X2,X1),divide(X2,X0))
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t12,plain,
ifeq(less_equal(X1,X2),true,less_equal(divide(X3,X2),divide(X3,X1)),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t68,plain,
ifeq(less_equal(X1,X2),true,less_equal(divide(X3,X2),divide(X3,X1)),true) = true,
inference(orient,[status(thm)],[t12]) ).
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(t13,plain,
ifeq(less_equal(divide(X1,X2),X3),true,less_equal(divide(X1,X3),X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t108,plain,
ifeq(less_equal(divide(X1,X2),X3),true,less_equal(divide(X1,X3),X2),true) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(f14,axiom,
( less_equal(divide(X,Z),divide(Y,Z))
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_divide3) ).
fof(f14_nnf,plain,
! [X,Y,Z] :
( less_equal(divide(X,Z),divide(Y,Z))
| ~ less_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X,Y,Z] :
( less_equal(divide(X,Z),divide(Y,Z))
| ~ less_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( less_equal(divide(X0,X2),divide(X1,X2))
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t11,plain,
ifeq(less_equal(X1,X2),true,less_equal(divide(X1,X3),divide(X2,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t81,plain,
ifeq(less_equal(X1,X2),true,less_equal(divide(X1,X3),divide(X2,X3)),true) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t92,plain,
true = ifeq(less_equal(X1,identity),true,less_equal(divide(X1,a),sFlat0),true),
inference(cp,[status(thm)],[t81,t27]) ).
cnf(f6,axiom,
less_equal(X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_is_largest) ).
fof(f6_nnf,plain,
! [X] : less_equal(X,identity),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X] : less_equal(X,identity),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
less_equal(X0,identity),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t4,plain,
less_equal(X1,identity) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t30,plain,
less_equal(X1,identity) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t596,plain,
true = ifeq(true,true,less_equal(divide(X1,a),sFlat0),true),
inference(step,[status(thm)],[t92,t30]) ).
cnf(t6,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t19,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t6]) ).
cnf(t597,plain,
true = less_equal(divide(X1,a),sFlat0),
inference(step,[status(thm)],[t596,t19]) ).
cnf(t158,plain,
less_equal(divide(X1,a),sFlat0) = true,
inference(orient,[status(thm)],[t597]) ).
cnf(t163,plain,
true = ifeq(true,true,less_equal(divide(X1,sFlat0),a),true),
inference(cp,[status(thm)],[t108,t158]) ).
cnf(t604,plain,
true = less_equal(divide(X1,sFlat0),a),
inference(step,[status(thm)],[t163,t19]) ).
cnf(t213,plain,
less_equal(divide(X1,sFlat0),a) = true,
inference(orient,[status(thm)],[t604]) ).
cnf(t214,plain,
true = less_equal(sFlat1,a),
inference(cp,[status(thm)],[t213,t134]) ).
cnf(t224,plain,
less_equal(sFlat1,a) = true,
inference(orient,[status(thm)],[t214]) ).
cnf(t233,plain,
true = ifeq(true,true,less_equal(divide(X1,a),divide(X1,sFlat1)),true),
inference(cp,[status(thm)],[t68,t224]) ).
cnf(t647,plain,
true = less_equal(divide(X1,a),divide(X1,sFlat1)),
inference(step,[status(thm)],[t233,t19]) ).
cnf(t566,plain,
less_equal(divide(X1,a),divide(X1,sFlat1)) = true,
inference(orient,[status(thm)],[t647]) ).
cnf(t567,plain,
true = less_equal(sFlat0,divide(identity,sFlat1)),
inference(cp,[status(thm)],[t566,t27]) ).
cnf(t648,plain,
true = less_equal(sFlat0,sFlat2),
inference(step,[status(thm)],[t567,t122]) ).
cnf(t579,plain,
less_equal(sFlat0,sFlat2) = true,
inference(orient,[status(thm)],[t648]) ).
cnf(t582,plain,
sFlat2 = ifeq(true,true,ifeq(less_equal(sFlat2,sFlat0),true,sFlat0,sFlat2),sFlat2),
inference(cp,[status(thm)],[t20,t579]) ).
cnf(t649,plain,
sFlat2 = ifeq(less_equal(sFlat2,sFlat0),true,sFlat0,sFlat2),
inference(step,[status(thm)],[t582,t19]) ).
cnf(t140,plain,
true = ifeq(less_equal(X1,identity),true,less_equal(divide(X1,sFlat0),sFlat1),true),
inference(cp,[status(thm)],[t81,t134]) ).
cnf(t601,plain,
true = ifeq(true,true,less_equal(divide(X1,sFlat0),sFlat1),true),
inference(step,[status(thm)],[t140,t30]) ).
cnf(t602,plain,
true = less_equal(divide(X1,sFlat0),sFlat1),
inference(step,[status(thm)],[t601,t19]) ).
cnf(t191,plain,
less_equal(divide(X1,sFlat0),sFlat1) = true,
inference(orient,[status(thm)],[t602]) ).
cnf(t196,plain,
true = ifeq(true,true,less_equal(divide(X1,sFlat1),sFlat0),true),
inference(cp,[status(thm)],[t108,t191]) ).
cnf(t609,plain,
true = less_equal(divide(X1,sFlat1),sFlat0),
inference(step,[status(thm)],[t196,t19]) ).
cnf(t273,plain,
less_equal(divide(X1,sFlat1),sFlat0) = true,
inference(orient,[status(thm)],[t609]) ).
cnf(t274,plain,
true = less_equal(sFlat2,sFlat0),
inference(cp,[status(thm)],[t273,t122]) ).
cnf(t284,plain,
less_equal(sFlat2,sFlat0) = true,
inference(orient,[status(thm)],[t274]) ).
cnf(t650,plain,
sFlat2 = ifeq(true,true,sFlat0,sFlat2),
inference(step,[status(thm)],[t649,t284]) ).
cnf(t651,plain,
sFlat2 = sFlat0,
inference(step,[status(thm)],[t650,t19]) ).
cnf(t588,plain,
sFlat2 = sFlat0,
inference(orient,[status(thm)],[t651]) ).
cnf(t652,plain,
divide(identity,sFlat1) = sFlat0,
inference(step,[status(thm)],[t122,t588]) ).
cnf(t589,plain,
divide(identity,sFlat1) = sFlat0,
inference(orient,[status(thm)],[t652]) ).
cnf(f15,negated_conjecture,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f15_nnf,plain,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(goal_0,negated_conjecture,
divide(identity,divide(identity,divide(identity,a))) != divide(identity,a),
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(g0_0,plain,
divide(identity,divide(identity,sFlat0)) != divide(identity,a),
inference(rw,[status(thm)],[goal_0,t27]) ).
cnf(g0_1,plain,
divide(identity,sFlat1) != divide(identity,a),
inference(rw,[status(thm)],[g0_0,t134]) ).
cnf(g0_2,plain,
sFlat0 != divide(identity,a),
inference(rw,[status(thm)],[g0_1,t589]) ).
cnf(g0_3,plain,
sFlat0 != sFlat0,
inference(rw,[status(thm)],[g0_2,t27]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n006.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 16:15:35 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.49/1.69 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.49/1.69 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------