%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN011-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 01:37:11 PM UTC 2026
% Result : Unsatisfiable 40.17s 5.68s
% Output : Proof 40.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 14
% Syntax : Number of formulae : 167 ( 143 unt; 0 def)
% Number of atoms : 199 ( 138 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 88 ( 56 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 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 : 307 ( 28 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t230,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t257,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(orient,[status(thm)],[t230]) ).
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(t190,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t765,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t190]) ).
cnf(f12,axiom,
( less_equal(divide(X,Z),Y)
| ~ less_equal(divide(X,Y),Z) ),
file('/export/starexec/sandbox/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(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(hi2,axiom,
less_equal(divide(X0,X1),X0) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h4,plain,
less_equal(divide(V0,V0),V1) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi2]) ).
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/sandbox/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(h22,plain,
less_equal(V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi9]) ).
cnf(h36,plain,
less_equal(divide(V0,divide(V0,V1)),V1) = true,
inference(hyper_resolution,[status(thm)],[hi12,h22]) ).
cnf(f11,axiom,
( less_equal(X,Z)
| ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/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(h613,plain,
less_equal(divide(V0,divide(V0,divide(V1,V1))),V2) = true,
inference(hyper_resolution,[status(thm)],[hi11,h36,h4]) ).
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(hi6,axiom,
less_equal(X0,identity) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h21,plain,
less_equal(divide(V0,V1),identity) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi2,hi6]) ).
cnf(f13,axiom,
( less_equal(divide(Z,Y),divide(Z,X))
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/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(hi13,axiom,
ifeq(less_equal(X0,X1),true,less_equal(divide(X2,X1),divide(X2,X0)),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h260,plain,
less_equal(divide(V0,identity),divide(V0,divide(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi13,h21]) ).
cnf(hi5,axiom,
ifeq(less_equal(X0,X1),true,ifeq(less_equal(X1,X0),true,X0,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t164,plain,
divide(X1,divide(X1,divide(X2,X2))) = divide(X1,identity),
inference(hyper_resolution,[status(thm)],[hi5,h260,h613]) ).
cnf(t0,plain,
divide(X1,X1) = zero,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t422,plain,
divide(X1,X1) = zero,
inference(orient,[status(thm)],[t0]) ).
cnf(t7324,plain,
divide(X1,divide(X1,zero)) = divide(X1,identity),
inference(step,[status(thm)],[t164,t422]) ).
cnf(t434,plain,
divide(X1,divide(X1,zero)) = divide(X1,identity),
inference(orient,[status(thm)],[t7324]) ).
cnf(h3,plain,
less_equal(divide(V0,V1),divide(V0,divide(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi2]) ).
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(h63,plain,
less_equal(zero,divide(V0,divide(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi4,h3]) ).
cnf(t46,plain,
divide(X1,divide(X1,divide(X2,X2))) = zero,
inference(hyper_resolution,[status(thm)],[hi5,h63,h613]) ).
cnf(t7325,plain,
divide(X1,divide(X1,zero)) = zero,
inference(step,[status(thm)],[t46,t422]) ).
cnf(t7326,plain,
divide(X1,identity) = zero,
inference(step,[status(thm)],[t7325,t434]) ).
cnf(t436,plain,
divide(X1,identity) = zero,
inference(orient,[status(thm)],[t7326]) ).
cnf(t7327,plain,
divide(X1,divide(X1,zero)) = zero,
inference(step,[status(thm)],[t434,t436]) ).
cnf(t437,plain,
divide(X1,divide(X1,zero)) = zero,
inference(orient,[status(thm)],[t7327]) ).
cnf(t767,plain,
true = ifeq(zero,zero,less_equal(X1,divide(X1,zero)),true),
inference(cp,[status(thm)],[t765,t437]) ).
cnf(t32,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t32]) ).
cnf(t7339,plain,
true = less_equal(X1,divide(X1,zero)),
inference(step,[status(thm)],[t767,t256]) ).
cnf(t935,plain,
less_equal(X1,divide(X1,zero)) = true,
inference(orient,[status(thm)],[t7339]) ).
cnf(t936,plain,
divide(X1,zero) = ifeq(true,true,ifeq(less_equal(divide(X1,zero),X1),true,X1,divide(X1,zero)),divide(X1,zero)),
inference(cp,[status(thm)],[t257,t935]) ).
cnf(t7340,plain,
divide(X1,zero) = ifeq(less_equal(divide(X1,zero),X1),true,X1,divide(X1,zero)),
inference(step,[status(thm)],[t936,t256]) ).
cnf(t34,plain,
less_equal(divide(X1,X2),X1) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t672,plain,
less_equal(divide(X1,X2),X1) = true,
inference(orient,[status(thm)],[t34]) ).
cnf(t7341,plain,
divide(X1,zero) = ifeq(true,true,X1,divide(X1,zero)),
inference(step,[status(thm)],[t7340,t672]) ).
cnf(t7342,plain,
divide(X1,zero) = X1,
inference(step,[status(thm)],[t7341,t256]) ).
cnf(t945,plain,
divide(X1,zero) = X1,
inference(orient,[status(thm)],[t7342]) ).
cnf(t233,plain,
ifeq(less_equal(divide(X1,X2),X3),true,less_equal(divide(X1,X3),X2),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t890,plain,
ifeq(less_equal(divide(X1,X2),X3),true,less_equal(divide(X1,X3),X2),true) = true,
inference(orient,[status(thm)],[t233]) ).
cnf(t232,plain,
ifeq(less_equal(X1,X2),true,less_equal(divide(X3,X2),divide(X3,X1)),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t784,plain,
ifeq(less_equal(X1,X2),true,less_equal(divide(X3,X2),divide(X3,X1)),true) = true,
inference(orient,[status(thm)],[t232]) ).
cnf(t766,plain,
true = ifeq(zero,zero,less_equal(X1,X1),true),
inference(cp,[status(thm)],[t765,t422]) ).
cnf(t7338,plain,
true = less_equal(X1,X1),
inference(step,[status(thm)],[t766,t256]) ).
cnf(t929,plain,
less_equal(X1,X1) = true,
inference(orient,[status(thm)],[t7338]) ).
cnf(t930,plain,
true = ifeq(true,true,less_equal(divide(X1,divide(X1,X2)),X2),true),
inference(cp,[status(thm)],[t890,t929]) ).
cnf(t7353,plain,
true = less_equal(divide(X1,divide(X1,X2)),X2),
inference(step,[status(thm)],[t930,t256]) ).
cnf(t991,plain,
less_equal(divide(X1,divide(X1,X2)),X2) = true,
inference(orient,[status(thm)],[t7353]) ).
cnf(t1002,plain,
true = ifeq(true,true,less_equal(divide(X1,X2),divide(X1,divide(X3,divide(X3,X2)))),true),
inference(cp,[status(thm)],[t784,t991]) ).
cnf(t7398,plain,
true = less_equal(divide(X1,X2),divide(X1,divide(X3,divide(X3,X2)))),
inference(step,[status(thm)],[t1002,t256]) ).
cnf(t1536,plain,
less_equal(divide(X1,X2),divide(X1,divide(X3,divide(X3,X2)))) = true,
inference(orient,[status(thm)],[t7398]) ).
cnf(t1568,plain,
true = ifeq(true,true,less_equal(divide(X1,divide(X1,divide(X2,divide(X2,X3)))),X3),true),
inference(cp,[status(thm)],[t890,t1536]) ).
cnf(t7449,plain,
true = less_equal(divide(X1,divide(X1,divide(X2,divide(X2,X3)))),X3),
inference(step,[status(thm)],[t1568,t256]) ).
cnf(t3242,plain,
less_equal(divide(X1,divide(X1,divide(X2,divide(X2,X3)))),X3) = true,
inference(orient,[status(thm)],[t7449]) ).
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(t191,plain,
ifeq(less_equal(X1,X2),true,divide(X1,X2),zero) = zero,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t650,plain,
ifeq(less_equal(X1,X2),true,divide(X1,X2),zero) = zero,
inference(orient,[status(thm)],[t191]) ).
cnf(t241,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X3),true,less_equal(X1,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t867,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X3),true,less_equal(X1,X3),true),true) = true,
inference(orient,[status(thm)],[t241]) ).
cnf(t881,plain,
true = ifeq(less_equal(X1,divide(X2,X3)),true,ifeq(true,true,less_equal(X1,X2),true),true),
inference(cp,[status(thm)],[t867,t672]) ).
cnf(t7392,plain,
true = ifeq(less_equal(X1,divide(X2,X3)),true,less_equal(X1,X2),true),
inference(step,[status(thm)],[t881,t256]) ).
cnf(t1374,plain,
ifeq(less_equal(X1,divide(X2,X3)),true,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t7392]) ).
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(t234,plain,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t716,plain,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = true,
inference(orient,[status(thm)],[t234]) ).
cnf(t1380,plain,
true = ifeq(true,true,less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(X1,X3)),true),
inference(cp,[status(thm)],[t1374,t716]) ).
cnf(t7438,plain,
true = less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(X1,X3)),
inference(step,[status(thm)],[t1380,t256]) ).
cnf(t2600,plain,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(X1,X3)) = true,
inference(orient,[status(thm)],[t7438]) ).
cnf(t2663,plain,
zero = ifeq(true,true,divide(divide(divide(X1,X2),divide(X3,X2)),divide(X1,X3)),zero),
inference(cp,[status(thm)],[t650,t2600]) ).
cnf(t7458,plain,
zero = divide(divide(divide(X1,X2),divide(X3,X2)),divide(X1,X3)),
inference(step,[status(thm)],[t2663,t256]) ).
cnf(t4037,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(X1,X3)) = zero,
inference(orient,[status(thm)],[t7458]) ).
cnf(t4166,plain,
true = less_equal(divide(divide(divide(X1,X2),divide(divide(X1,X3),X2)),zero),X3),
inference(cp,[status(thm)],[t3242,t4037]) ).
cnf(t7484,plain,
true = less_equal(divide(divide(X1,X2),divide(divide(X1,X3),X2)),X3),
inference(step,[status(thm)],[t4166,t945]) ).
cnf(t6278,plain,
less_equal(divide(divide(X1,X2),divide(divide(X1,X3),X2)),X3) = true,
inference(orient,[status(thm)],[t7484]) ).
cnf(t1563,plain,
zero = ifeq(true,true,divide(divide(X1,X2),divide(X1,divide(X3,divide(X3,X2)))),zero),
inference(cp,[status(thm)],[t650,t1536]) ).
cnf(t7448,plain,
zero = divide(divide(X1,X2),divide(X1,divide(X3,divide(X3,X2)))),
inference(step,[status(thm)],[t1563,t256]) ).
cnf(t3144,plain,
divide(divide(X1,X2),divide(X1,divide(X3,divide(X3,X2)))) = zero,
inference(orient,[status(thm)],[t7448]) ).
cnf(t4144,plain,
zero = divide(divide(divide(divide(X1,X2),divide(divide(X1,X3),X2)),X3),zero),
inference(cp,[status(thm)],[t3144,t4037]) ).
cnf(t7481,plain,
zero = divide(divide(divide(X1,X2),divide(divide(X1,X3),X2)),X3),
inference(step,[status(thm)],[t4144,t945]) ).
cnf(t6043,plain,
divide(divide(divide(X1,X2),divide(divide(X1,X3),X2)),X3) = zero,
inference(orient,[status(thm)],[t7481]) ).
cnf(t6287,plain,
true = less_equal(divide(divide(divide(X1,X2),X3),zero),divide(divide(X1,X3),X2)),
inference(cp,[status(thm)],[t6278,t6043]) ).
cnf(t7491,plain,
true = less_equal(divide(divide(X1,X2),X3),divide(divide(X1,X3),X2)),
inference(step,[status(thm)],[t6287,t945]) ).
cnf(t6955,plain,
less_equal(divide(divide(X1,X2),X3),divide(divide(X1,X3),X2)) = true,
inference(orient,[status(thm)],[t7491]) ).
cnf(t7016,plain,
divide(divide(X1,X2),X3) = ifeq(true,true,ifeq(less_equal(divide(divide(X1,X2),X3),divide(divide(X1,X3),X2)),true,divide(divide(X1,X3),X2),divide(divide(X1,X2),X3)),divide(divide(X1,X2),X3)),
inference(cp,[status(thm)],[t257,t6955]) ).
cnf(t7493,plain,
divide(divide(X1,X2),X3) = ifeq(less_equal(divide(divide(X1,X2),X3),divide(divide(X1,X3),X2)),true,divide(divide(X1,X3),X2),divide(divide(X1,X2),X3)),
inference(step,[status(thm)],[t7016,t256]) ).
cnf(t7494,plain,
divide(divide(X1,X2),X3) = ifeq(true,true,divide(divide(X1,X3),X2),divide(divide(X1,X2),X3)),
inference(step,[status(thm)],[t7493,t6955]) ).
cnf(t7495,plain,
divide(divide(X1,X2),X3) = divide(divide(X1,X3),X2),
inference(step,[status(thm)],[t7494,t256]) ).
cnf(t7028,plain,
divide(divide(X1,X2),X3) = divide(divide(X1,X3),X2),
inference(orient,[status(thm)],[t7495]) ).
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(t186,plain,
divide(identity,divide(identity,divide(identity,X1))) = divide(identity,X1),
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t634,plain,
divide(identity,divide(identity,divide(identity,X1))) = divide(identity,X1),
inference(orient,[status(thm)],[t186]) ).
cnf(f17,negated_conjecture,
divide(divide(identity,a),divide(identity,divide(identity,b))) != divide(divide(identity,b),divide(identity,divide(identity,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f17_nnf,plain,
divide(divide(identity,a),divide(identity,divide(identity,b))) != divide(divide(identity,b),divide(identity,divide(identity,a))),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
divide(divide(identity,a),divide(identity,divide(identity,b))) != divide(divide(identity,b),divide(identity,divide(identity,a))),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
divide(divide(identity,a),divide(identity,divide(identity,b))) != divide(divide(identity,b),divide(identity,divide(identity,a))),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(goal_0,negated_conjecture,
divide(divide(identity,b),divide(identity,divide(identity,a))) != divide(divide(identity,a),divide(identity,divide(identity,b))),
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(g0_0,plain,
divide(divide(divide(identity,zero),a),divide(identity,divide(identity,b))) != divide(divide(identity,a),divide(identity,divide(identity,b))),
inference(rw,[status(thm)],[goal_0,t945]) ).
cnf(g0_1,plain,
divide(divide(divide(identity,zero),divide(a,zero)),divide(identity,divide(identity,b))) != divide(divide(identity,a),divide(identity,divide(identity,b))),
inference(rw,[status(thm)],[g0_0,t945]) ).
cnf(g0_2,plain,
divide(divide(divide(identity,divide(a,zero)),zero),divide(identity,divide(identity,b))) != divide(divide(identity,a),divide(identity,divide(identity,b))),
inference(rw,[status(thm)],[g0_1,t7028]) ).
cnf(g0_3,plain,
divide(divide(divide(identity,divide(a,zero)),divide(identity,divide(identity,b))),zero) != divide(divide(identity,a),divide(identity,divide(identity,b))),
inference(rw,[status(thm)],[g0_2,t7028]) ).
cnf(g0_4,plain,
divide(divide(divide(identity,divide(identity,divide(identity,b))),divide(a,zero)),zero) != divide(divide(identity,a),divide(identity,divide(identity,b))),
inference(rw,[status(thm)],[g0_3,t7028]) ).
cnf(g0_5,plain,
divide(divide(divide(identity,divide(identity,divide(identity,b))),zero),divide(a,zero)) != divide(divide(identity,a),divide(identity,divide(identity,b))),
inference(rw,[status(thm)],[g0_4,t7028]) ).
cnf(g0_6,plain,
divide(divide(divide(identity,divide(identity,divide(identity,b))),zero),a) != divide(divide(identity,a),divide(identity,divide(identity,b))),
inference(rw,[status(thm)],[g0_5,t945]) ).
cnf(g0_7,plain,
divide(divide(divide(identity,b),zero),a) != divide(divide(identity,a),divide(identity,divide(identity,b))),
inference(rw,[status(thm)],[g0_6,t634]) ).
cnf(g0_8,plain,
divide(divide(divide(identity,zero),b),a) != divide(divide(identity,a),divide(identity,divide(identity,b))),
inference(rw,[status(thm)],[g0_7,t7028]) ).
cnf(g0_9,plain,
divide(divide(divide(identity,zero),b),a) != divide(divide(divide(identity,zero),b),divide(identity,divide(identity,a))),
inference(rw,[status(thm)],[g0_8,t945]) ).
cnf(g0_10,plain,
divide(divide(divide(identity,zero),b),a) != divide(divide(divide(identity,zero),b),divide(identity,divide(identity,divide(a,zero)))),
inference(rw,[status(thm)],[g0_9,t945]) ).
cnf(g0_11,plain,
divide(divide(divide(identity,zero),b),a) != divide(divide(divide(identity,b),zero),divide(identity,divide(identity,divide(a,zero)))),
inference(rw,[status(thm)],[g0_10,t7028]) ).
cnf(g0_12,plain,
divide(divide(divide(identity,zero),b),a) != divide(divide(divide(identity,b),divide(identity,divide(identity,divide(a,zero)))),zero),
inference(rw,[status(thm)],[g0_11,t7028]) ).
cnf(g0_13,plain,
divide(divide(divide(identity,zero),b),a) != divide(divide(divide(identity,divide(identity,divide(identity,divide(a,zero)))),b),zero),
inference(rw,[status(thm)],[g0_12,t7028]) ).
cnf(g0_14,plain,
divide(divide(divide(identity,zero),b),a) != divide(divide(divide(identity,divide(identity,divide(identity,divide(a,zero)))),zero),b),
inference(rw,[status(thm)],[g0_13,t7028]) ).
cnf(g0_15,plain,
divide(divide(divide(identity,zero),b),a) != divide(divide(divide(identity,divide(identity,divide(identity,a))),zero),b),
inference(rw,[status(thm)],[g0_14,t945]) ).
cnf(g0_16,plain,
divide(divide(divide(identity,zero),b),a) != divide(divide(divide(identity,a),zero),b),
inference(rw,[status(thm)],[g0_15,t634]) ).
cnf(g0_17,plain,
divide(divide(divide(identity,zero),b),a) != divide(divide(divide(identity,zero),a),b),
inference(rw,[status(thm)],[g0_16,t7028]) ).
cnf(g0_18,plain,
divide(divide(divide(identity,zero),b),a) != divide(divide(divide(identity,zero),b),a),
inference(rw,[status(thm)],[g0_17,t7028]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN011-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 16:18:24 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 40.17/5.68 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 40.17/5.68 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------