%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN007-1 : 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 01:37:03 PM UTC 2026
% Result : Unsatisfiable 24.17s 8.79s
% Output : Proof 24.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 12
% Syntax : Number of formulae : 117 ( 97 unt; 0 def)
% Number of atoms : 157 ( 79 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 86 ( 46 ~; 40 |; 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 : 9 ( 9 usr; 7 con; 0-4 aty)
% Number of variables : 145 ( 22 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f2,axiom,
( less_equal(Z,X)
| ~ quotient(X,Y,Z) ),
file('/export/starexec/sandbox2/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(t149,plain,
ifeq(quotient(X1,X2,X3),true,less_equal(X3,X1),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t633,plain,
ifeq(quotient(X1,X2,X3),true,less_equal(X3,X1),true) = true,
inference(orient,[status(thm)],[t149]) ).
cnf(f7,axiom,
quotient(X,Y,divide(X,Y)),
file('/export/starexec/sandbox2/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(t48,plain,
quotient(X1,X2,divide(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t430,plain,
quotient(X1,X2,divide(X1,X2)) = true,
inference(orient,[status(thm)],[t48]) ).
cnf(t634,plain,
true = ifeq(true,true,less_equal(divide(X1,X2),X1),true),
inference(cp,[status(thm)],[t633,t430]) ).
cnf(t47,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t47]) ).
cnf(t1365,plain,
true = less_equal(divide(X1,X2),X1),
inference(step,[status(thm)],[t634,t256]) ).
cnf(t879,plain,
less_equal(divide(X1,X2),X1) = true,
inference(orient,[status(thm)],[t1365]) ).
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(t214,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t259,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(orient,[status(thm)],[t214]) ).
cnf(f1,axiom,
( less_equal(X,Y)
| ~ quotient(X,Y,zero) ),
file('/export/starexec/sandbox2/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(t150,plain,
ifeq(quotient(X1,X2,zero),true,less_equal(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t766,plain,
ifeq(quotient(X1,X2,zero),true,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t150]) ).
cnf(f4,axiom,
less_equal(zero,X),
file('/export/starexec/sandbox2/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(t8,plain,
less_equal(zero,X1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t627,plain,
less_equal(zero,X1) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t629,plain,
zero = ifeq(less_equal(X1,zero),true,ifeq(true,true,X1,zero),zero),
inference(cp,[status(thm)],[t259,t627]) ).
cnf(t1407,plain,
zero = ifeq(less_equal(X1,zero),true,X1,zero),
inference(step,[status(thm)],[t629,t256]) ).
cnf(t1150,plain,
ifeq(less_equal(X1,zero),true,X1,zero) = zero,
inference(orient,[status(thm)],[t1407]) ).
cnf(t628,plain,
X1 = ifeq(true,true,ifeq(less_equal(X1,zero),true,zero,X1),X1),
inference(cp,[status(thm)],[t259,t627]) ).
cnf(t1405,plain,
X1 = ifeq(less_equal(X1,zero),true,zero,X1),
inference(step,[status(thm)],[t628,t256]) ).
cnf(t1143,plain,
ifeq(less_equal(X1,zero),true,zero,X1) = X1,
inference(orient,[status(thm)],[t1405]) ).
cnf(f0,axiom,
( quotient(X,Y,zero)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/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(f9,hypothesis,
less_equal(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xLEy) ).
fof(f9_nnf,plain,
less_equal(x,y),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
less_equal(x,y),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(hi9,axiom,
less_equal(x,y) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h4,plain,
quotient(x,y,zero) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi9]) ).
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/sandbox2/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(f11,hypothesis,
quotient(z,x,zQx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zQx) ).
fof(f11_nnf,plain,
quotient(z,x,zQx),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
quotient(z,x,zQx),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(hi11,axiom,
quotient(z,x,zQx) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(f10,hypothesis,
quotient(z,y,zQy),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zQy) ).
fof(f10_nnf,plain,
quotient(z,y,zQy),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
quotient(z,y,zQy),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(hi10,axiom,
quotient(z,y,zQy) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(hi7,axiom,
quotient(X0,X1,divide(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h114,plain,
less_equal(divide(zQy,zero),divide(zQx,y)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi11,h4,hi10,hi7,hi7]) ).
cnf(h627,plain,
quotient(divide(zQy,zero),divide(zQx,y),zero) = true,
inference(hyper_resolution,[status(thm)],[hi0,h114]) ).
cnf(hi2,axiom,
ifeq(quotient(X0,X1,X2),true,less_equal(X2,X0),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h3,plain,
less_equal(divide(V0,V1),V0) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi7]) ).
cnf(h97,plain,
quotient(divide(V0,V1),V0,zero) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3]) ).
cnf(h606,plain,
less_equal(zero,divide(V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi2,h97]) ).
cnf(h1873,plain,
quotient(zero,divide(V0,V1),zero) = true,
inference(hyper_resolution,[status(thm)],[hi0,h606]) ).
cnf(t115,plain,
less_equal(divide(divide(zQy,divide(zQx,y)),zero),zero) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi7,h1873,hi7,hi7,h627]) ).
cnf(t570,plain,
less_equal(divide(divide(zQy,divide(zQx,y)),zero),zero) = true,
inference(orient,[status(thm)],[t115]) ).
cnf(t1146,plain,
divide(divide(zQy,divide(zQx,y)),zero) = ifeq(true,true,zero,divide(divide(zQy,divide(zQx,y)),zero)),
inference(cp,[status(thm)],[t1143,t570]) ).
cnf(t1415,plain,
divide(divide(zQy,divide(zQx,y)),zero) = zero,
inference(step,[status(thm)],[t1146,t256]) ).
cnf(t1161,plain,
divide(divide(zQy,divide(zQx,y)),zero) = zero,
inference(orient,[status(thm)],[t1415]) ).
cnf(t1162,plain,
true = quotient(divide(zQy,divide(zQx,y)),zero,zero),
inference(cp,[status(thm)],[t430,t1161]) ).
cnf(t1271,plain,
quotient(divide(zQy,divide(zQx,y)),zero,zero) = true,
inference(orient,[status(thm)],[t1162]) ).
cnf(t1273,plain,
true = ifeq(true,true,less_equal(divide(zQy,divide(zQx,y)),zero),true),
inference(cp,[status(thm)],[t766,t1271]) ).
cnf(t1450,plain,
true = less_equal(divide(zQy,divide(zQx,y)),zero),
inference(step,[status(thm)],[t1273,t256]) ).
cnf(t1281,plain,
less_equal(divide(zQy,divide(zQx,y)),zero) = true,
inference(orient,[status(thm)],[t1450]) ).
cnf(t1282,plain,
zero = ifeq(true,true,divide(zQy,divide(zQx,y)),zero),
inference(cp,[status(thm)],[t1150,t1281]) ).
cnf(t1451,plain,
zero = divide(zQy,divide(zQx,y)),
inference(step,[status(thm)],[t1282,t256]) ).
cnf(t1288,plain,
divide(zQy,divide(zQx,y)) = zero,
inference(orient,[status(thm)],[t1451]) ).
cnf(t1289,plain,
true = quotient(zQy,divide(zQx,y),zero),
inference(cp,[status(thm)],[t430,t1288]) ).
cnf(t1292,plain,
quotient(zQy,divide(zQx,y),zero) = true,
inference(orient,[status(thm)],[t1289]) ).
cnf(t1294,plain,
true = ifeq(true,true,less_equal(zQy,divide(zQx,y)),true),
inference(cp,[status(thm)],[t766,t1292]) ).
cnf(t1452,plain,
true = less_equal(zQy,divide(zQx,y)),
inference(step,[status(thm)],[t1294,t256]) ).
cnf(t1302,plain,
less_equal(zQy,divide(zQx,y)) = true,
inference(orient,[status(thm)],[t1452]) ).
cnf(t1304,plain,
divide(zQx,y) = ifeq(true,true,ifeq(less_equal(divide(zQx,y),zQy),true,zQy,divide(zQx,y)),divide(zQx,y)),
inference(cp,[status(thm)],[t259,t1302]) ).
cnf(t1453,plain,
divide(zQx,y) = ifeq(less_equal(divide(zQx,y),zQy),true,zQy,divide(zQx,y)),
inference(step,[status(thm)],[t1304,t256]) ).
cnf(hi4,axiom,
less_equal(zero,X0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h0,plain,
quotient(zero,V0,zero) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi4]) ).
cnf(h20,plain,
less_equal(zQx,z) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi11]) ).
cnf(h134,plain,
quotient(zQx,z,zero) = true,
inference(hyper_resolution,[status(thm)],[hi0,h20]) ).
cnf(h253,plain,
less_equal(divide(divide(zQx,y),zQy),zero) = true,
inference(hyper_resolution,[status(thm)],[hi3,h134,hi10,hi7,hi7,h0]) ).
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(t15,plain,
divide(divide(zQx,y),zQy) = zero,
inference(hyper_resolution,[status(thm)],[hi5,h606,h253]) ).
cnf(t324,plain,
divide(divide(zQx,y),zQy) = zero,
inference(orient,[status(thm)],[t15]) ).
cnf(t476,plain,
true = quotient(divide(zQx,y),zQy,zero),
inference(cp,[status(thm)],[t430,t324]) ).
cnf(t1045,plain,
quotient(divide(zQx,y),zQy,zero) = true,
inference(orient,[status(thm)],[t476]) ).
cnf(t1047,plain,
true = ifeq(true,true,less_equal(divide(zQx,y),zQy),true),
inference(cp,[status(thm)],[t766,t1045]) ).
cnf(t1387,plain,
true = less_equal(divide(zQx,y),zQy),
inference(step,[status(thm)],[t1047,t256]) ).
cnf(t1055,plain,
less_equal(divide(zQx,y),zQy) = true,
inference(orient,[status(thm)],[t1387]) ).
cnf(t1454,plain,
divide(zQx,y) = ifeq(true,true,zQy,divide(zQx,y)),
inference(step,[status(thm)],[t1453,t1055]) ).
cnf(t1455,plain,
divide(zQx,y) = zQy,
inference(step,[status(thm)],[t1454,t256]) ).
cnf(t1307,plain,
divide(zQx,y) = zQy,
inference(orient,[status(thm)],[t1455]) ).
cnf(t1309,plain,
true = less_equal(zQy,zQx),
inference(cp,[status(thm)],[t879,t1307]) ).
cnf(t1312,plain,
less_equal(zQy,zQx) = true,
inference(orient,[status(thm)],[t1309]) ).
cnf(f12,negated_conjecture,
~ less_equal(zQy,zQx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_zQyLEzQx) ).
fof(f12_nnf,plain,
~ less_equal(zQy,zQx),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
~ less_equal(zQy,zQx),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
~ less_equal(zQy,zQx),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
less_equal(zQy,zQx) != true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1312]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/5.36 % Computer : n016.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Wed Sep 23 16:18:01 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.17/8.79 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.17/8.79 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------