%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN005-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 01:36:58 PM UTC 2026
% Result : Unsatisfiable 19.91s 3.06s
% Output : Proof 19.91s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t12,axiom,
sFlat0 = less_equal(x,z),
introduced(definition) ).
cnf(t63,plain,
less_equal(x,z) = sFlat0,
inference(orient,[status(thm)],[t12]) ).
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(t8,plain,
ifeq(quotient(X1,X2,zero),true,less_equal(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t24,plain,
ifeq(quotient(X1,X2,zero),true,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t8]) ).
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(t5,plain,
quotient(X1,X2,divide(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t54,plain,
quotient(X1,X2,divide(X1,X2)) = true,
inference(orient,[status(thm)],[t5]) ).
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(t9,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t14,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(orient,[status(thm)],[t9]) ).
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(t3,plain,
less_equal(zero,X1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t33,plain,
less_equal(zero,X1) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t38,plain,
zero = ifeq(less_equal(X1,zero),true,ifeq(true,true,X1,zero),zero),
inference(cp,[status(thm)],[t14,t33]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t13,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t1172,plain,
zero = ifeq(less_equal(X1,zero),true,X1,zero),
inference(step,[status(thm)],[t38,t13]) ).
cnf(t122,plain,
ifeq(less_equal(X1,zero),true,X1,zero) = zero,
inference(orient,[status(thm)],[t1172]) ).
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(t11,plain,
ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X2,X4,X5),true,ifeq(quotient(X1,X4,X6),true,ifeq(quotient(X6,X5,X7),true,ifeq(quotient(X3,X4,X8),true,less_equal(X7,X8),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t18,plain,
ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X2,X4,X5),true,ifeq(quotient(X1,X4,X6),true,ifeq(quotient(X6,X5,X7),true,ifeq(quotient(X3,X4,X8),true,less_equal(X7,X8),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t58,plain,
true = ifeq(true,true,ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X4,X2,X5),true,ifeq(quotient(X5,X3,X6),true,ifeq(quotient(divide(X4,X1),X2,X7),true,less_equal(X6,X7),true),true),true),true),true),
inference(cp,[status(thm)],[t18,t54]) ).
cnf(t1253,plain,
true = ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X4,X2,X5),true,ifeq(quotient(X5,X3,X6),true,ifeq(quotient(divide(X4,X1),X2,X7),true,less_equal(X6,X7),true),true),true),true),
inference(step,[status(thm)],[t58,t13]) ).
cnf(t849,plain,
ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X4,X2,X5),true,ifeq(quotient(X5,X3,X6),true,ifeq(quotient(divide(X4,X1),X2,X7),true,less_equal(X6,X7),true),true),true),true) = true,
inference(orient,[status(thm)],[t1253]) ).
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(t6,plain,
ifeq(less_equal(X1,X2),true,quotient(X1,X2,zero),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t17,plain,
ifeq(less_equal(X1,X2),true,quotient(X1,X2,zero),true) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(f10,hypothesis,
less_equal(y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',yLEz) ).
fof(f10_nnf,plain,
less_equal(y,z),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
less_equal(y,z),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(t2,plain,
less_equal(y,z) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t47,plain,
less_equal(y,z) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t48,plain,
true = ifeq(true,true,quotient(y,z,zero),true),
inference(cp,[status(thm)],[t17,t47]) ).
cnf(t1165,plain,
true = quotient(y,z,zero),
inference(step,[status(thm)],[t48,t13]) ).
cnf(t94,plain,
quotient(y,z,zero) = true,
inference(orient,[status(thm)],[t1165]) ).
cnf(t853,plain,
true = ifeq(true,true,ifeq(quotient(X1,z,X2),true,ifeq(quotient(X2,zero,X3),true,ifeq(quotient(divide(X1,y),z,X4),true,less_equal(X3,X4),true),true),true),true),
inference(cp,[status(thm)],[t849,t94]) ).
cnf(t1273,plain,
true = ifeq(quotient(X1,z,X2),true,ifeq(quotient(X2,zero,X3),true,ifeq(quotient(divide(X1,y),z,X4),true,less_equal(X3,X4),true),true),true),
inference(step,[status(thm)],[t853,t13]) ).
cnf(t959,plain,
ifeq(quotient(X1,z,X2),true,ifeq(quotient(X2,zero,X3),true,ifeq(quotient(divide(X1,y),z,X4),true,less_equal(X3,X4),true),true),true) = true,
inference(orient,[status(thm)],[t1273]) ).
cnf(t960,plain,
true = ifeq(true,true,ifeq(quotient(divide(X1,z),zero,X2),true,ifeq(quotient(divide(X1,y),z,X3),true,less_equal(X2,X3),true),true),true),
inference(cp,[status(thm)],[t959,t54]) ).
cnf(t1275,plain,
true = ifeq(quotient(divide(X1,z),zero,X2),true,ifeq(quotient(divide(X1,y),z,X3),true,less_equal(X2,X3),true),true),
inference(step,[status(thm)],[t960,t13]) ).
cnf(t973,plain,
ifeq(quotient(divide(X1,z),zero,X2),true,ifeq(quotient(divide(X1,y),z,X3),true,less_equal(X2,X3),true),true) = true,
inference(orient,[status(thm)],[t1275]) ).
cnf(t974,plain,
true = ifeq(true,true,ifeq(quotient(divide(X1,y),z,X2),true,less_equal(divide(divide(X1,z),zero),X2),true),true),
inference(cp,[status(thm)],[t973,t54]) ).
cnf(t1276,plain,
true = ifeq(quotient(divide(X1,y),z,X2),true,less_equal(divide(divide(X1,z),zero),X2),true),
inference(step,[status(thm)],[t974,t13]) ).
cnf(t980,plain,
ifeq(quotient(divide(X1,y),z,X2),true,less_equal(divide(divide(X1,z),zero),X2),true) = true,
inference(orient,[status(thm)],[t1276]) ).
cnf(t981,plain,
true = ifeq(true,true,less_equal(divide(divide(X1,z),zero),divide(divide(X1,y),z)),true),
inference(cp,[status(thm)],[t980,t54]) ).
cnf(t1277,plain,
true = less_equal(divide(divide(X1,z),zero),divide(divide(X1,y),z)),
inference(step,[status(thm)],[t981,t13]) ).
cnf(t984,plain,
less_equal(divide(divide(X1,z),zero),divide(divide(X1,y),z)) = true,
inference(orient,[status(thm)],[t1277]) ).
cnf(f8,axiom,
( Z = W
| ~ quotient(X,Y,W)
| ~ quotient(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_defined) ).
fof(f8_nnf,plain,
! [X,Y,Z,W] :
( Z = W
| ~ quotient(X,Y,W)
| ~ quotient(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y,Z,W] :
( Z = W
| ~ quotient(X,Y,W)
| ~ quotient(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( X2 = X3
| ~ quotient(X0,X1,X3)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t10,plain,
ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X1,X2,X4),true,X3,X4),X4) = X4,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t15,plain,
ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X1,X2,X4),true,X3,X4),X4) = X4,
inference(orient,[status(thm)],[t10]) ).
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(t1,plain,
less_equal(x,y) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t40,plain,
less_equal(x,y) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t41,plain,
true = ifeq(true,true,quotient(x,y,zero),true),
inference(cp,[status(thm)],[t17,t40]) ).
cnf(t1164,plain,
true = quotient(x,y,zero),
inference(step,[status(thm)],[t41,t13]) ).
cnf(t86,plain,
quotient(x,y,zero) = true,
inference(orient,[status(thm)],[t1164]) ).
cnf(t87,plain,
X1 = ifeq(true,true,ifeq(quotient(x,y,X1),true,zero,X1),X1),
inference(cp,[status(thm)],[t15,t86]) ).
cnf(t1182,plain,
X1 = ifeq(quotient(x,y,X1),true,zero,X1),
inference(step,[status(thm)],[t87,t13]) ).
cnf(t140,plain,
ifeq(quotient(x,y,X1),true,zero,X1) = X1,
inference(orient,[status(thm)],[t1182]) ).
cnf(t141,plain,
divide(x,y) = ifeq(true,true,zero,divide(x,y)),
inference(cp,[status(thm)],[t140,t54]) ).
cnf(t1183,plain,
divide(x,y) = zero,
inference(step,[status(thm)],[t141,t13]) ).
cnf(t142,plain,
divide(x,y) = zero,
inference(orient,[status(thm)],[t1183]) ).
cnf(t986,plain,
true = less_equal(divide(divide(x,z),zero),divide(zero,z)),
inference(cp,[status(thm)],[t984,t142]) ).
cnf(t37,plain,
X1 = ifeq(true,true,ifeq(less_equal(X1,zero),true,zero,X1),X1),
inference(cp,[status(thm)],[t14,t33]) ).
cnf(t1170,plain,
X1 = ifeq(less_equal(X1,zero),true,zero,X1),
inference(step,[status(thm)],[t37,t13]) ).
cnf(t119,plain,
ifeq(less_equal(X1,zero),true,zero,X1) = X1,
inference(orient,[status(thm)],[t1170]) ).
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(t7,plain,
ifeq(quotient(X1,X2,X3),true,less_equal(X3,X1),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t21,plain,
ifeq(quotient(X1,X2,X3),true,less_equal(X3,X1),true) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t55,plain,
true = ifeq(true,true,less_equal(divide(X1,X2),X1),true),
inference(cp,[status(thm)],[t21,t54]) ).
cnf(t1166,plain,
true = less_equal(divide(X1,X2),X1),
inference(step,[status(thm)],[t55,t13]) ).
cnf(t102,plain,
less_equal(divide(X1,X2),X1) = true,
inference(orient,[status(thm)],[t1166]) ).
cnf(t120,plain,
divide(zero,X1) = ifeq(true,true,zero,divide(zero,X1)),
inference(cp,[status(thm)],[t119,t102]) ).
cnf(t1171,plain,
divide(zero,X1) = zero,
inference(step,[status(thm)],[t120,t13]) ).
cnf(t121,plain,
divide(zero,X1) = zero,
inference(orient,[status(thm)],[t1171]) ).
cnf(t1278,plain,
true = less_equal(divide(divide(x,z),zero),zero),
inference(step,[status(thm)],[t986,t121]) ).
cnf(t990,plain,
less_equal(divide(divide(x,z),zero),zero) = true,
inference(orient,[status(thm)],[t1278]) ).
cnf(t992,plain,
zero = ifeq(true,true,divide(divide(x,z),zero),zero),
inference(cp,[status(thm)],[t122,t990]) ).
cnf(t1279,plain,
zero = divide(divide(x,z),zero),
inference(step,[status(thm)],[t992,t13]) ).
cnf(t996,plain,
divide(divide(x,z),zero) = zero,
inference(orient,[status(thm)],[t1279]) ).
cnf(t999,plain,
true = quotient(divide(x,z),zero,zero),
inference(cp,[status(thm)],[t54,t996]) ).
cnf(t1001,plain,
quotient(divide(x,z),zero,zero) = true,
inference(orient,[status(thm)],[t999]) ).
cnf(t1003,plain,
true = ifeq(true,true,less_equal(divide(x,z),zero),true),
inference(cp,[status(thm)],[t24,t1001]) ).
cnf(t1280,plain,
true = less_equal(divide(x,z),zero),
inference(step,[status(thm)],[t1003,t13]) ).
cnf(t1013,plain,
less_equal(divide(x,z),zero) = true,
inference(orient,[status(thm)],[t1280]) ).
cnf(t1014,plain,
zero = ifeq(true,true,divide(x,z),zero),
inference(cp,[status(thm)],[t122,t1013]) ).
cnf(t1281,plain,
zero = divide(x,z),
inference(step,[status(thm)],[t1014,t13]) ).
cnf(t1018,plain,
divide(x,z) = zero,
inference(orient,[status(thm)],[t1281]) ).
cnf(t1021,plain,
true = quotient(x,z,zero),
inference(cp,[status(thm)],[t54,t1018]) ).
cnf(t1023,plain,
quotient(x,z,zero) = true,
inference(orient,[status(thm)],[t1021]) ).
cnf(t1025,plain,
true = ifeq(true,true,less_equal(x,z),true),
inference(cp,[status(thm)],[t24,t1023]) ).
cnf(t1285,plain,
true = less_equal(x,z),
inference(step,[status(thm)],[t1025,t13]) ).
cnf(t1286,plain,
true = sFlat0,
inference(step,[status(thm)],[t1285,t63]) ).
cnf(t1036,plain,
true = sFlat0,
inference(orient,[status(thm)],[t1286]) ).
cnf(f11,negated_conjecture,
~ less_equal(x,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_transitivity_of_less_equal) ).
fof(f11_nnf,plain,
~ less_equal(x,z),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
~ less_equal(x,z),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
~ less_equal(x,z),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(goal_0,negated_conjecture,
less_equal(x,z) != true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(g0_0,plain,
sFlat0 != true,
inference(rw,[status(thm)],[goal_0,t63]) ).
cnf(g0_1,plain,
sFlat0 != sFlat0,
inference(rw,[status(thm)],[g0_0,t1036]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN005-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 16:13:34 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 19.91/3.06 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.91/3.06 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------