%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN007-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 01:37:04 PM UTC 2026
% Result : Unsatisfiable 6.39s 16.53s
% Output : Proof 6.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 39 unt; 0 def)
% Number of atoms : 91 ( 17 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 78 ( 42 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 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 : 95 ( 3 sgn 38 !; 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(hi2,axiom,
ifeq(quotient(X0,X1,X2),true,less_equal(X2,X0),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
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(hi7,axiom,
quotient(X0,X1,divide(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h30,plain,
less_equal(divide(zQx,y),zQx) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi7]) ).
cnf(f15,hypothesis,
less_equal(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xLEy) ).
fof(f15_nnf,plain,
less_equal(x,y),
inference(nnf_transformation,[status(thm)],[f15]) ).
cnf(c15,plain,
less_equal(x,y),
inference(cnf_transformation,[status(esa)],[f15_nnf]) ).
cnf(hi15,axiom,
less_equal(x,y) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(h27,plain,
less_equal(x,y) = true,
inference(hyper_resolution,[status(thm)],[hi15]) ).
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(h28,plain,
quotient(x,y,zero) = true,
inference(hyper_resolution,[status(thm)],[hi0,h27]) ).
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(f17,hypothesis,
quotient(z,x,zQx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zQx) ).
fof(f17_nnf,plain,
quotient(z,x,zQx),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
quotient(z,x,zQx),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(hi17,axiom,
quotient(z,x,zQx) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(f16,hypothesis,
quotient(z,y,zQy),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zQy) ).
fof(f16_nnf,plain,
quotient(z,y,zQy),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c16,plain,
quotient(z,y,zQy),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(hi16,axiom,
quotient(z,y,zQy) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(f12,axiom,
quotient(X,zero,X),
file('/export/starexec/sandbox2/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(h29,plain,
less_equal(zQy,divide(zQx,y)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi17,h28,hi16,hi12,hi7]) ).
cnf(f13,axiom,
( less_equal(X,Z)
| ~ less_equal(Y,Z)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/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(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(t2,plain,
less_equal(zQy,zQx) = true,
inference(hyper_resolution,[status(thm)],[hi13,h29,h30]) ).
cnf(t155,plain,
less_equal(zQy,zQx) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(f18,negated_conjecture,
~ less_equal(zQy,zQx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_zQyLEzQx) ).
fof(f18_nnf,plain,
~ less_equal(zQy,zQx),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
~ less_equal(zQy,zQx),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
~ less_equal(zQy,zQx),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(goal_0,negated_conjecture,
less_equal(zQy,zQx) != true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t155]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN007-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/15.68 % CPULimit : 300
% 0.08/15.68 % WCLimit : 300
% 0.08/15.68 % DateTime : Wed Sep 23 16:12:59 UTC 2026
% 0.08/15.68 % CPUTime :
% 0.08/15.68 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.39/16.53 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.39/16.53 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------