%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN005-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 01:36:59 PM UTC 2026
% Result : Unsatisfiable 25.49s 3.76s
% Output : Proof 25.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 78 ( 58 unt; 0 def)
% Number of atoms : 122 ( 39 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 94 ( 50 ~; 44 |; 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 : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 129 ( 8 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t250,plain,
ifeq(quotient(X1,X2,zero),true,less_equal(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t408,plain,
ifeq(quotient(X1,X2,zero),true,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t250]) ).
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(t88,plain,
quotient(X1,X2,divide(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t298,plain,
quotient(X1,X2,divide(X1,X2)) = true,
inference(orient,[status(thm)],[t88]) ).
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(f14,hypothesis,
less_equal(y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',yLEz) ).
fof(f14_nnf,plain,
less_equal(y,z),
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c14,plain,
less_equal(y,z),
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(hi14,axiom,
less_equal(y,z) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h154,plain,
quotient(y,z,zero) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi14]) ).
cnf(f13,hypothesis,
less_equal(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xLEy) ).
fof(f13_nnf,plain,
less_equal(x,y),
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c13,plain,
less_equal(x,y),
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(hi13,axiom,
less_equal(x,y) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h16,plain,
quotient(x,y,zero) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi13]) ).
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(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/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(h288,plain,
less_equal(divide(divide(x,z),zero),zero) = true,
inference(hyper_resolution,[status(thm)],[hi3,h16,h154,hi7,hi7,hi10]) ).
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(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(t35,plain,
divide(divide(x,z),zero) = zero,
inference(hyper_resolution,[status(thm)],[hi5,hi4,h288]) ).
cnf(f8,axiom,
( Z = W
| ~ quotient(X,Y,W)
| ~ quotient(X,Y,Z) ),
file('/export/starexec/sandbox/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(hi8,axiom,
ifeq(quotient(X0,X1,X2),true,ifeq(quotient(X0,X1,X3),true,X2,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c8]) ).
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(t1,plain,
divide(X1,zero) = X1,
inference(hyper_resolution,[status(thm)],[hi8,hi7,hi12]) ).
cnf(t256,plain,
divide(X1,zero) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t435,plain,
divide(x,z) = zero,
inference(step,[status(thm)],[t35,t256]) ).
cnf(t285,plain,
divide(x,z) = zero,
inference(orient,[status(thm)],[t435]) ).
cnf(t306,plain,
true = quotient(x,z,zero),
inference(cp,[status(thm)],[t298,t285]) ).
cnf(t417,plain,
quotient(x,z,zero) = true,
inference(orient,[status(thm)],[t306]) ).
cnf(t419,plain,
true = ifeq(true,true,less_equal(x,z),true),
inference(cp,[status(thm)],[t408,t417]) ).
cnf(t74,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t257,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t74]) ).
cnf(t440,plain,
true = less_equal(x,z),
inference(step,[status(thm)],[t419,t257]) ).
cnf(t427,plain,
less_equal(x,z) = true,
inference(orient,[status(thm)],[t440]) ).
cnf(f15,negated_conjecture,
~ less_equal(x,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_transitivity_of_less_equal) ).
fof(f15_nnf,plain,
~ less_equal(x,z),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
~ less_equal(x,z),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
~ less_equal(x,z),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(goal_0,negated_conjecture,
less_equal(x,z) != true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t427]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN005-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 16:16:41 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 25.49/3.76 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.49/3.76 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------