%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN004-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 01:36:57 PM UTC 2026
% Result : Unsatisfiable 11.26s 1.87s
% Output : Proof 11.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 10
% Syntax : Number of formulae : 86 ( 70 unt; 0 def)
% Number of atoms : 122 ( 53 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 78 ( 42 ~; 36 |; 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 : 5 ( 5 usr; 3 con; 0-4 aty)
% Number of variables : 153 ( 17 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t28,plain,
quotient(X1,X2,divide(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t919,plain,
quotient(X1,X2,divide(X1,X2)) = true,
inference(orient,[status(thm)],[t28]) ).
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(t241,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)],[t241]) ).
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(t188,plain,
ifeq(quotient(X1,X2,zero),true,less_equal(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t1056,plain,
ifeq(quotient(X1,X2,zero),true,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t188]) ).
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(t5,plain,
less_equal(zero,X1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t1000,plain,
less_equal(zero,X1) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t1001,plain,
X1 = ifeq(true,true,ifeq(less_equal(X1,zero),true,zero,X1),X1),
inference(cp,[status(thm)],[t259,t1000]) ).
cnf(t24,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t24]) ).
cnf(t1281,plain,
X1 = ifeq(less_equal(X1,zero),true,zero,X1),
inference(step,[status(thm)],[t1001,t256]) ).
cnf(t1122,plain,
ifeq(less_equal(X1,zero),true,zero,X1) = X1,
inference(orient,[status(thm)],[t1281]) ).
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(hi7,axiom,
quotient(X0,X1,divide(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(f10,axiom,
quotient(zero,X,zero),
file('/export/starexec/sandbox2/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(f11,axiom,
quotient(X,X,zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
fof(f11_nnf,plain,
! [X] : quotient(X,X,zero),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X] : quotient(X,X,zero),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
quotient(X0,X0,zero),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,axiom,
quotient(X0,X0,zero) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h52,plain,
less_equal(divide(divide(V0,divide(V0,zero)),zero),zero) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi7,hi10,hi7,hi7,hi11]) ).
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(hi4,axiom,
less_equal(zero,X0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t35,plain,
divide(divide(X1,divide(X1,zero)),zero) = zero,
inference(hyper_resolution,[status(thm)],[hi5,hi4,h52]) ).
cnf(t353,plain,
divide(divide(X1,divide(X1,zero)),zero) = zero,
inference(orient,[status(thm)],[t35]) ).
cnf(t934,plain,
true = quotient(divide(X1,divide(X1,zero)),zero,zero),
inference(cp,[status(thm)],[t919,t353]) ).
cnf(t1186,plain,
quotient(divide(X1,divide(X1,zero)),zero,zero) = true,
inference(orient,[status(thm)],[t934]) ).
cnf(t1188,plain,
true = ifeq(true,true,less_equal(divide(X1,divide(X1,zero)),zero),true),
inference(cp,[status(thm)],[t1056,t1186]) ).
cnf(t1287,plain,
true = less_equal(divide(X1,divide(X1,zero)),zero),
inference(step,[status(thm)],[t1188,t256]) ).
cnf(t1196,plain,
less_equal(divide(X1,divide(X1,zero)),zero) = true,
inference(orient,[status(thm)],[t1287]) ).
cnf(t1197,plain,
divide(X1,divide(X1,zero)) = ifeq(true,true,zero,divide(X1,divide(X1,zero))),
inference(cp,[status(thm)],[t1122,t1196]) ).
cnf(t1288,plain,
divide(X1,divide(X1,zero)) = zero,
inference(step,[status(thm)],[t1197,t256]) ).
cnf(t1203,plain,
divide(X1,divide(X1,zero)) = zero,
inference(orient,[status(thm)],[t1288]) ).
cnf(t1204,plain,
true = quotient(X1,divide(X1,zero),zero),
inference(cp,[status(thm)],[t919,t1203]) ).
cnf(t1224,plain,
quotient(X1,divide(X1,zero),zero) = true,
inference(orient,[status(thm)],[t1204]) ).
cnf(t1229,plain,
true = ifeq(true,true,less_equal(X1,divide(X1,zero)),true),
inference(cp,[status(thm)],[t1056,t1224]) ).
cnf(t1289,plain,
true = less_equal(X1,divide(X1,zero)),
inference(step,[status(thm)],[t1229,t256]) ).
cnf(t1237,plain,
less_equal(X1,divide(X1,zero)) = true,
inference(orient,[status(thm)],[t1289]) ).
cnf(t1244,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)],[t259,t1237]) ).
cnf(t1291,plain,
divide(X1,zero) = ifeq(less_equal(divide(X1,zero),X1),true,X1,divide(X1,zero)),
inference(step,[status(thm)],[t1244,t256]) ).
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(t187,plain,
ifeq(quotient(X1,X2,X3),true,less_equal(X3,X1),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t1003,plain,
ifeq(quotient(X1,X2,X3),true,less_equal(X3,X1),true) = true,
inference(orient,[status(thm)],[t187]) ).
cnf(t1004,plain,
true = ifeq(true,true,less_equal(divide(X1,X2),X1),true),
inference(cp,[status(thm)],[t1003,t919]) ).
cnf(t1273,plain,
true = less_equal(divide(X1,X2),X1),
inference(step,[status(thm)],[t1004,t256]) ).
cnf(t1067,plain,
less_equal(divide(X1,X2),X1) = true,
inference(orient,[status(thm)],[t1273]) ).
cnf(t1292,plain,
divide(X1,zero) = ifeq(true,true,X1,divide(X1,zero)),
inference(step,[status(thm)],[t1291,t1067]) ).
cnf(t1293,plain,
divide(X1,zero) = X1,
inference(step,[status(thm)],[t1292,t256]) ).
cnf(t1254,plain,
divide(X1,zero) = X1,
inference(orient,[status(thm)],[t1293]) ).
cnf(t1255,plain,
true = quotient(X1,zero,X1),
inference(cp,[status(thm)],[t919,t1254]) ).
cnf(t1263,plain,
quotient(X1,zero,X1) = true,
inference(orient,[status(thm)],[t1255]) ).
cnf(f12,negated_conjecture,
~ quotient(x,zero,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_x_divde_zero_is_x) ).
fof(f12_nnf,plain,
~ quotient(x,zero,x),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
~ quotient(x,zero,x),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
~ quotient(x,zero,x),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
quotient(x,zero,x) != true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1263]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : HEN004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Wed Sep 23 16:09:35 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.30 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 11.26/1.87 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.26/1.87 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------