%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN006-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 01:37:01 PM UTC 2026
% Result : Unsatisfiable 24.96s 3.92s
% Output : Proof 24.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 16
% Syntax : Number of formulae : 120 ( 96 unt; 0 def)
% Number of atoms : 168 ( 66 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 102 ( 54 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-4 aty)
% Number of variables : 176 ( 28 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f13,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(f13_nnf,plain,
! [X,Y,Z] :
( less_equal(X,Z)
| ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y,Z] :
( less_equal(X,Z)
| ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( less_equal(X0,X2)
| ~ less_equal(X1,X2)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t253,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)],[c13]) ).
cnf(t684,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X3),true,less_equal(X1,X3),true),true) = true,
inference(orient,[status(thm)],[t253]) ).
cnf(f2,axiom,
( less_equal(Z,X)
| ~ quotient(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divisor_existence) ).
fof(f2_nnf,plain,
! [X,Y,Z] :
( less_equal(Z,X)
| ~ quotient(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Z] :
( less_equal(Z,X)
| ~ quotient(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( less_equal(X2,X0)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t248,plain,
ifeq(quotient(X1,X2,X3),true,less_equal(X3,X1),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t544,plain,
ifeq(quotient(X1,X2,X3),true,less_equal(X3,X1),true) = true,
inference(orient,[status(thm)],[t248]) ).
cnf(f7,axiom,
quotient(X,Y,divide(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure) ).
fof(f7_nnf,plain,
! [X,Y] : quotient(X,Y,divide(X,Y)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] : quotient(X,Y,divide(X,Y)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t113,plain,
quotient(X1,X2,divide(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t378,plain,
quotient(X1,X2,divide(X1,X2)) = true,
inference(orient,[status(thm)],[t113]) ).
cnf(t545,plain,
true = ifeq(true,true,less_equal(divide(X1,X2),X1),true),
inference(cp,[status(thm)],[t544,t378]) ).
cnf(t105,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t105]) ).
cnf(t2397,plain,
true = less_equal(divide(X1,X2),X1),
inference(step,[status(thm)],[t545,t256]) ).
cnf(t757,plain,
less_equal(divide(X1,X2),X1) = true,
inference(orient,[status(thm)],[t2397]) ).
cnf(t764,plain,
true = ifeq(less_equal(X1,divide(X2,X3)),true,ifeq(true,true,less_equal(X1,X2),true),true),
inference(cp,[status(thm)],[t684,t757]) ).
cnf(t2582,plain,
true = ifeq(less_equal(X1,divide(X2,X3)),true,less_equal(X1,X2),true),
inference(step,[status(thm)],[t764,t256]) ).
cnf(t2296,plain,
ifeq(less_equal(X1,divide(X2,X3)),true,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t2582]) ).
cnf(f1,axiom,
( less_equal(X,Y)
| ~ quotient(X,Y,zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_quotient) ).
fof(f1_nnf,plain,
! [X,Y] :
( less_equal(X,Y)
| ~ quotient(X,Y,zero) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( less_equal(X,Y)
| ~ quotient(X,Y,zero) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( less_equal(X0,X1)
| ~ quotient(X0,X1,zero) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t249,plain,
ifeq(quotient(X1,X2,zero),true,less_equal(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t653,plain,
ifeq(quotient(X1,X2,zero),true,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t249]) ).
cnf(f0,axiom,
( quotient(X,Y,zero)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal) ).
fof(f0_nnf,plain,
! [X,Y] :
( quotient(X,Y,zero)
| ~ less_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( quotient(X,Y,zero)
| ~ less_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(less_equal(X0,X1),true,quotient(X0,X1,zero),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f15,hypothesis,
less_equal(xQy,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQyLEz) ).
fof(f15_nnf,plain,
less_equal(xQy,z),
inference(nnf_transformation,[status(thm)],[f15]) ).
cnf(c15,plain,
less_equal(xQy,z),
inference(cnf_transformation,[status(esa)],[f15_nnf]) ).
cnf(hi15,axiom,
less_equal(xQy,z) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(h19,plain,
quotient(xQy,z,zero) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi15]) ).
cnf(f3,axiom,
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_property) ).
fof(f3_nnf,plain,
! [X,Y,V1,Z,V2,V3,V4,V5] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y,V1,Z,V2,V3,V4,V5] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( less_equal(X6,X7)
| ~ quotient(X2,X3,X7)
| ~ quotient(X5,X4,X6)
| ~ quotient(X0,X3,X5)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X1,X3,X4),true,ifeq(quotient(X0,X3,X5),true,ifeq(quotient(X5,X4,X6),true,ifeq(quotient(X2,X3,X7),true,less_equal(X6,X7),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f12,axiom,
quotient(X,zero,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
fof(f12_nnf,plain,
! [X] : quotient(X,zero,X),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X] : quotient(X,zero,X),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
quotient(X0,zero,X0),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi12,axiom,
quotient(X0,zero,X0) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(f10,axiom,
quotient(zero,X,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
fof(f10_nnf,plain,
! [X] : quotient(zero,X,zero),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X] : quotient(zero,X,zero),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
quotient(zero,X0,zero),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
quotient(zero,X0,zero) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(hi7,axiom,
quotient(X0,X1,divide(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h364,plain,
less_equal(divide(xQy,z),zero) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi12,hi10,hi7,hi12,h19]) ).
cnf(hi13,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)],[c13]) ).
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(h6949,plain,
less_equal(divide(xQy,z),V0) = true,
inference(hyper_resolution,[status(thm)],[hi13,h364,hi4]) ).
cnf(f14,hypothesis,
quotient(x,y,xQy),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQy) ).
fof(f14_nnf,plain,
quotient(x,y,xQy),
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c14,plain,
quotient(x,y,xQy),
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(hi14,axiom,
quotient(x,y,xQy) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(f16,hypothesis,
quotient(x,z,xQz),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQz) ).
fof(f16_nnf,plain,
quotient(x,z,xQz),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c16,plain,
quotient(x,z,xQz),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(hi16,axiom,
quotient(x,z,xQz) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h233,plain,
less_equal(divide(xQz,divide(y,z)),divide(xQy,z)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi14,hi7,hi16,hi7,hi7]) ).
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(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(t189,plain,
divide(xQz,divide(y,z)) = divide(xQy,z),
inference(hyper_resolution,[status(thm)],[hi5,h233,h6949]) ).
cnf(h404,plain,
less_equal(divide(divide(xQy,zero),z),zero) = true,
inference(hyper_resolution,[status(thm)],[hi3,h19,hi12,hi7,hi7,hi12]) ).
cnf(hi2,axiom,
ifeq(quotient(X0,X1,X2),true,less_equal(X2,X0),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h2,plain,
less_equal(divide(V0,V1),V0) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi7]) ).
cnf(f9,axiom,
quotient(X,identity,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',everything_divide_identity_is_zero) ).
fof(f9_nnf,plain,
! [X] : quotient(X,identity,zero),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X] : quotient(X,identity,zero),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
quotient(X0,identity,zero),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,axiom,
quotient(X0,identity,zero) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h33,plain,
less_equal(zero,divide(divide(V0,V1),identity)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi7,hi9,hi9,hi10,hi7]) ).
cnf(h539,plain,
less_equal(zero,divide(V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi13,h33,h2]) ).
cnf(t44,plain,
divide(divide(xQy,zero),z) = zero,
inference(hyper_resolution,[status(thm)],[hi5,h539,h404]) ).
cnf(h199,plain,
less_equal(divide(divide(x,zero),y),xQy) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi14,hi12,hi7,hi7,hi12]) ).
cnf(h184,plain,
less_equal(xQy,divide(divide(x,zero),y)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi7,hi10,hi14,hi12,hi7]) ).
cnf(t40,plain,
divide(divide(x,zero),y) = xQy,
inference(hyper_resolution,[status(thm)],[hi5,h184,h199]) ).
cnf(h200,plain,
less_equal(divide(divide(x,zero),y),divide(xQy,zero)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi14,hi12,hi7,hi7,hi7]) ).
cnf(h185,plain,
less_equal(divide(xQy,zero),divide(divide(x,zero),y)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi7,hi10,hi14,hi7,hi7]) ).
cnf(t176,plain,
divide(divide(x,zero),y) = divide(xQy,zero),
inference(hyper_resolution,[status(thm)],[hi5,h185,h200]) ).
cnf(t292,plain,
divide(divide(x,zero),y) = divide(xQy,zero),
inference(orient,[status(thm)],[t176]) ).
cnf(t2327,plain,
divide(xQy,zero) = xQy,
inference(step,[status(thm)],[t40,t292]) ).
cnf(t293,plain,
divide(xQy,zero) = xQy,
inference(orient,[status(thm)],[t2327]) ).
cnf(t2335,plain,
divide(xQy,z) = zero,
inference(step,[status(thm)],[t44,t293]) ).
cnf(t324,plain,
divide(xQy,z) = zero,
inference(orient,[status(thm)],[t2335]) ).
cnf(t2353,plain,
divide(xQz,divide(y,z)) = zero,
inference(step,[status(thm)],[t189,t324]) ).
cnf(t362,plain,
divide(xQz,divide(y,z)) = zero,
inference(orient,[status(thm)],[t2353]) ).
cnf(t390,plain,
true = quotient(xQz,divide(y,z),zero),
inference(cp,[status(thm)],[t378,t362]) ).
cnf(t850,plain,
quotient(xQz,divide(y,z),zero) = true,
inference(orient,[status(thm)],[t390]) ).
cnf(t852,plain,
true = ifeq(true,true,less_equal(xQz,divide(y,z)),true),
inference(cp,[status(thm)],[t653,t850]) ).
cnf(t2407,plain,
true = less_equal(xQz,divide(y,z)),
inference(step,[status(thm)],[t852,t256]) ).
cnf(t860,plain,
less_equal(xQz,divide(y,z)) = true,
inference(orient,[status(thm)],[t2407]) ).
cnf(t2304,plain,
true = ifeq(true,true,less_equal(xQz,y),true),
inference(cp,[status(thm)],[t2296,t860]) ).
cnf(t2583,plain,
true = less_equal(xQz,y),
inference(step,[status(thm)],[t2304,t256]) ).
cnf(t2305,plain,
less_equal(xQz,y) = true,
inference(orient,[status(thm)],[t2583]) ).
cnf(f17,negated_conjecture,
~ less_equal(xQz,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_xQzLEy) ).
fof(f17_nnf,plain,
~ less_equal(xQz,y),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
~ less_equal(xQz,y),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
~ less_equal(xQz,y),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(goal_0,negated_conjecture,
less_equal(xQz,y) != true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2305]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN006-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 16:11:12 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 24.96/3.92 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.96/3.92 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------