%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN010-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 : Fri Sep 25 01:37:10 PM UTC 2026
% Result : Unsatisfiable 9.85s 1.76s
% Output : Proof 9.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 14
% Syntax : Number of formulae : 114 ( 98 unt; 0 def)
% Number of atoms : 134 ( 93 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 30 ~; 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 : 9 ( 9 usr; 7 con; 0-4 aty)
% Number of variables : 121 ( 23 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t17,axiom,
sFlat0 = divide(identity,a),
introduced(definition) ).
cnf(t32,plain,
divide(identity,a) = sFlat0,
inference(orient,[status(thm)],[t17]) ).
cnf(t18,axiom,
sFlat1 = divide(identity,divide(identity,a)),
introduced(definition) ).
cnf(t28,plain,
divide(identity,divide(identity,a)) = sFlat1,
inference(orient,[status(thm)],[t18]) ).
cnf(t676,plain,
divide(identity,sFlat0) = sFlat1,
inference(step,[status(thm)],[t28,t32]) ).
cnf(t34,plain,
divide(identity,sFlat0) = sFlat1,
inference(rw,[status(thm)],[t676]) ).
cnf(t139,plain,
divide(identity,sFlat0) = sFlat1,
inference(orient,[status(thm)],[t34]) ).
cnf(t19,axiom,
sFlat2 = divide(divide(identity,a),divide(identity,divide(identity,a))),
introduced(definition) ).
cnf(t24,plain,
divide(divide(identity,a),divide(identity,divide(identity,a))) = sFlat2,
inference(orient,[status(thm)],[t19]) ).
cnf(t675,plain,
divide(divide(identity,a),sFlat1) = sFlat2,
inference(step,[status(thm)],[t24,t28]) ).
cnf(t31,plain,
divide(divide(identity,a),sFlat1) = sFlat2,
inference(rw,[status(thm)],[t675]) ).
cnf(t679,plain,
divide(sFlat0,sFlat1) = sFlat2,
inference(step,[status(thm)],[t31,t32]) ).
cnf(t173,plain,
divide(sFlat0,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t679]) ).
cnf(f5,axiom,
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/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(t11,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t21,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(f1,axiom,
( less_equal(X,Y)
| divide(X,Y) != zero ),
file('/export/starexec/sandbox/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(t9,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t72,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t9]) ).
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(t5,plain,
less_equal(zero,X1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t69,plain,
less_equal(zero,X1) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t71,plain,
zero = ifeq(less_equal(X1,zero),true,ifeq(true,true,X1,zero),zero),
inference(cp,[status(thm)],[t21,t69]) ).
cnf(t6,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t20,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t6]) ).
cnf(t709,plain,
zero = ifeq(less_equal(X1,zero),true,X1,zero),
inference(step,[status(thm)],[t71,t20]) ).
cnf(t387,plain,
ifeq(less_equal(X1,zero),true,X1,zero) = zero,
inference(orient,[status(thm)],[t709]) ).
cnf(f3,axiom,
less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_property) ).
fof(f3_nnf,plain,
! [X,Z,Y] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Z,Y] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t15,plain,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t47,plain,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = true,
inference(orient,[status(thm)],[t15]) ).
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(t10,plain,
ifeq(less_equal(X1,X2),true,divide(X1,X2),zero) = zero,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t132,plain,
ifeq(less_equal(X1,X2),true,divide(X1,X2),zero) = zero,
inference(orient,[status(thm)],[t10]) ).
cnf(f14,axiom,
( less_equal(divide(X,Z),divide(Y,Z))
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/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(t12,plain,
ifeq(less_equal(X1,X2),true,less_equal(divide(X1,X3),divide(X2,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t94,plain,
ifeq(less_equal(X1,X2),true,less_equal(divide(X1,X3),divide(X2,X3)),true) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(t145,plain,
true = ifeq(less_equal(X1,identity),true,less_equal(divide(X1,sFlat0),sFlat1),true),
inference(cp,[status(thm)],[t94,t139]) ).
cnf(f6,axiom,
less_equal(X,identity),
file('/export/starexec/sandbox/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(t37,plain,
less_equal(X1,identity) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t686,plain,
true = ifeq(true,true,less_equal(divide(X1,sFlat0),sFlat1),true),
inference(step,[status(thm)],[t145,t37]) ).
cnf(t687,plain,
true = less_equal(divide(X1,sFlat0),sFlat1),
inference(step,[status(thm)],[t686,t20]) ).
cnf(t238,plain,
less_equal(divide(X1,sFlat0),sFlat1) = true,
inference(orient,[status(thm)],[t687]) ).
cnf(t239,plain,
zero = ifeq(true,true,divide(divide(X1,sFlat0),sFlat1),zero),
inference(cp,[status(thm)],[t132,t238]) ).
cnf(t699,plain,
zero = divide(divide(X1,sFlat0),sFlat1),
inference(step,[status(thm)],[t239,t20]) ).
cnf(t326,plain,
divide(divide(X1,sFlat0),sFlat1) = zero,
inference(orient,[status(thm)],[t699]) ).
cnf(t334,plain,
true = less_equal(divide(divide(X1,sFlat1),divide(sFlat0,sFlat1)),zero),
inference(cp,[status(thm)],[t47,t326]) ).
cnf(t741,plain,
true = less_equal(divide(divide(X1,sFlat1),sFlat2),zero),
inference(step,[status(thm)],[t334,t173]) ).
cnf(t627,plain,
less_equal(divide(divide(X1,sFlat1),sFlat2),zero) = true,
inference(orient,[status(thm)],[t741]) ).
cnf(f15,axiom,
divide(identity,divide(identity,divide(identity,X))) = divide(identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_inversion_equals_three) ).
fof(f15_nnf,plain,
! [X] : divide(identity,divide(identity,divide(identity,X))) = divide(identity,X),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X] : divide(identity,divide(identity,divide(identity,X))) = divide(identity,X),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
divide(identity,divide(identity,divide(identity,X0))) = divide(identity,X0),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t8,plain,
divide(identity,divide(identity,divide(identity,X1))) = divide(identity,X1),
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t25,plain,
divide(identity,divide(identity,divide(identity,X1))) = divide(identity,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t33,plain,
divide(identity,a) = divide(identity,divide(identity,sFlat0)),
inference(cp,[status(thm)],[t25,t32]) ).
cnf(t681,plain,
sFlat0 = divide(identity,divide(identity,sFlat0)),
inference(step,[status(thm)],[t33,t32]) ).
cnf(t682,plain,
sFlat0 = divide(identity,sFlat1),
inference(step,[status(thm)],[t681,t139]) ).
cnf(t205,plain,
divide(identity,sFlat1) = sFlat0,
inference(orient,[status(thm)],[t682]) ).
cnf(t628,plain,
true = less_equal(divide(sFlat0,sFlat2),zero),
inference(cp,[status(thm)],[t627,t205]) ).
cnf(t640,plain,
less_equal(divide(sFlat0,sFlat2),zero) = true,
inference(orient,[status(thm)],[t628]) ).
cnf(t641,plain,
zero = ifeq(true,true,divide(sFlat0,sFlat2),zero),
inference(cp,[status(thm)],[t387,t640]) ).
cnf(t742,plain,
zero = divide(sFlat0,sFlat2),
inference(step,[status(thm)],[t641,t20]) ).
cnf(t652,plain,
divide(sFlat0,sFlat2) = zero,
inference(orient,[status(thm)],[t742]) ).
cnf(t654,plain,
true = ifeq(zero,zero,less_equal(sFlat0,sFlat2),true),
inference(cp,[status(thm)],[t72,t652]) ).
cnf(t743,plain,
true = less_equal(sFlat0,sFlat2),
inference(step,[status(thm)],[t654,t20]) ).
cnf(t661,plain,
less_equal(sFlat0,sFlat2) = true,
inference(orient,[status(thm)],[t743]) ).
cnf(t662,plain,
sFlat2 = ifeq(true,true,ifeq(less_equal(sFlat2,sFlat0),true,sFlat0,sFlat2),sFlat2),
inference(cp,[status(thm)],[t21,t661]) ).
cnf(t748,plain,
sFlat2 = ifeq(less_equal(sFlat2,sFlat0),true,sFlat0,sFlat2),
inference(step,[status(thm)],[t662,t20]) ).
cnf(f2,axiom,
less_equal(divide(X,Y),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).
fof(f2_nnf,plain,
! [X,Y] : less_equal(divide(X,Y),X),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] : less_equal(divide(X,Y),X),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t7,plain,
less_equal(divide(X1,X2),X1) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t40,plain,
less_equal(divide(X1,X2),X1) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t174,plain,
true = less_equal(sFlat2,sFlat0),
inference(cp,[status(thm)],[t40,t173]) ).
cnf(t186,plain,
less_equal(sFlat2,sFlat0) = true,
inference(orient,[status(thm)],[t174]) ).
cnf(t749,plain,
sFlat2 = ifeq(true,true,sFlat0,sFlat2),
inference(step,[status(thm)],[t748,t186]) ).
cnf(t750,plain,
sFlat2 = sFlat0,
inference(step,[status(thm)],[t749,t20]) ).
cnf(t670,plain,
sFlat2 = sFlat0,
inference(orient,[status(thm)],[t750]) ).
cnf(t751,plain,
divide(sFlat0,sFlat1) = sFlat0,
inference(step,[status(thm)],[t173,t670]) ).
cnf(t671,plain,
divide(sFlat0,sFlat1) = sFlat0,
inference(orient,[status(thm)],[t751]) ).
cnf(f16,negated_conjecture,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_of_inversion) ).
fof(f16_nnf,plain,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
divide(divide(identity,a),divide(identity,divide(identity,a))) != divide(identity,a),
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(g0_0,plain,
divide(sFlat0,divide(identity,divide(identity,a))) != divide(identity,a),
inference(rw,[status(thm)],[goal_0,t32]) ).
cnf(g0_1,plain,
divide(sFlat0,divide(identity,sFlat0)) != divide(identity,a),
inference(rw,[status(thm)],[g0_0,t32]) ).
cnf(g0_2,plain,
divide(sFlat0,sFlat1) != divide(identity,a),
inference(rw,[status(thm)],[g0_1,t139]) ).
cnf(g0_3,plain,
sFlat0 != divide(identity,a),
inference(rw,[status(thm)],[g0_2,t671]) ).
cnf(g0_4,plain,
sFlat0 != sFlat0,
inference(rw,[status(thm)],[g0_3,t32]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN010-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 16:14:21 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 9.85/1.76 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.85/1.76 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------