%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM299+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 02:18:59 PM UTC 2026
% Result : Theorem 7.52s 6.64s
% Output : Proof 7.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 31 unt; 0 def)
% Number of atoms : 78 ( 20 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 66 ( 32 ~; 23 |; 8 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-4 aty)
% Number of variables : 47 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f274,axiom,
! [X,Y,Z] :
( ( rdn_positive_less(rdnn(Y),rdnn(Z))
& rdn_positive_less(rdnn(X),rdnn(Y)) )
=> rdn_positive_less(rdnn(X),rdnn(Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_positive_less_transitivity) ).
fof(f274_nnf,plain,
! [X,Y,Z] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y)) ),
inference(nnf_transformation,[status(thm)],[f274]) ).
fof(f274_sk,plain,
! [X,Y,Z] :
( rdn_positive_less(rdnn(X),rdnn(Z))
| ~ rdn_positive_less(rdnn(Y),rdnn(Z))
| ~ rdn_positive_less(rdnn(X),rdnn(Y)) ),
inference(skolemisation,[status(esa)],[f274_nnf]) ).
cnf(c274,plain,
( rdn_positive_less(rdnn(X0),rdnn(X2))
| ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_positive_less(rdnn(X0),rdnn(X1)) ),
inference(cnf_transformation,[status(esa)],[f274_sk]) ).
cnf(hi274,axiom,
ifeq(rdn_positive_less(rdnn(X0),rdnn(X1)),true,ifeq(rdn_positive_less(rdnn(X1),rdnn(X2)),true,rdn_positive_less(rdnn(X0),rdnn(X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c274]) ).
fof(f267,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_positive_less23) ).
fof(f267_nnf,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(nnf_transformation,[status(thm)],[f267]) ).
cnf(c267,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(cnf_transformation,[status(esa)],[f267_nnf]) ).
cnf(hi267,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)) = true,
inference(equality_encoding,[status(esa)],[c267]) ).
fof(f268,axiom,
rdn_positive_less(rdnn(n3),rdnn(n4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_positive_less34) ).
fof(f268_nnf,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(nnf_transformation,[status(thm)],[f268]) ).
cnf(c268,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(cnf_transformation,[status(esa)],[f268_nnf]) ).
cnf(hi268,axiom,
rdn_positive_less(rdnn(n3),rdnn(n4)) = true,
inference(equality_encoding,[status(esa)],[c268]) ).
cnf(h988,plain,
rdn_positive_less(rdnn(n2),rdnn(n4)) = true,
inference(hyper_resolution,[status(thm)],[hi274,hi267,hi268]) ).
fof(f282,axiom,
! [X,Y,RDN_X,RDN_Y] :
( ( rdn_positive_less(RDN_Y,RDN_X)
& rdn_translate(Y,rdn_neg(RDN_Y))
& rdn_translate(X,rdn_neg(RDN_X)) )
=> less(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_entry_point_neg_neg) ).
fof(f282_nnf,plain,
! [X,Y,RDN_X,RDN_Y] :
( less(X,Y)
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ),
inference(nnf_transformation,[status(thm)],[f282]) ).
fof(f282_sk,plain,
! [X,RDN_X,Y,RDN_Y] :
( less(X,Y)
| ~ rdn_positive_less(RDN_Y,RDN_X)
| ~ rdn_translate(Y,rdn_neg(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ),
inference(skolemisation,[status(esa)],[f282_nnf]) ).
cnf(c282,plain,
( less(X0,X1)
| ~ rdn_positive_less(X3,X2)
| ~ rdn_translate(X1,rdn_neg(X3))
| ~ rdn_translate(X0,rdn_neg(X2)) ),
inference(cnf_transformation,[status(esa)],[f282_sk]) ).
cnf(hi282,axiom,
ifeq(rdn_translate(X0,rdn_neg(X1)),true,ifeq(rdn_translate(X2,rdn_neg(X3)),true,ifeq(rdn_positive_less(X3,X1),true,less(X0,X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c282]) ).
fof(f131,axiom,
rdn_translate(nn4,rdn_neg(rdnn(n4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdnn4) ).
fof(f131_nnf,plain,
rdn_translate(nn4,rdn_neg(rdnn(n4))),
inference(nnf_transformation,[status(thm)],[f131]) ).
cnf(c131,plain,
rdn_translate(nn4,rdn_neg(rdnn(n4))),
inference(cnf_transformation,[status(esa)],[f131_nnf]) ).
cnf(hi131,axiom,
rdn_translate(nn4,rdn_neg(rdnn(n4))) = true,
inference(equality_encoding,[status(esa)],[c131]) ).
fof(f129,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdnn2) ).
fof(f129_nnf,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(nnf_transformation,[status(thm)],[f129]) ).
cnf(c129,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(cnf_transformation,[status(esa)],[f129_nnf]) ).
cnf(hi129,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))) = true,
inference(equality_encoding,[status(esa)],[c129]) ).
cnf(h2519,plain,
less(nn4,nn2) = true,
inference(hyper_resolution,[status(thm)],[hi282,hi131,hi129,h988]) ).
fof(f283,axiom,
! [X,Y] :
( less(X,Y)
<=> ( Y != X
& ~ less(Y,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_property) ).
fof(f283_nnf,plain,
! [X,Y] :
( ( Y = X
| less(Y,X)
| less(X,Y) )
& ( ( Y != X
& ~ less(Y,X) )
| ~ less(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f283]) ).
fof(f283_sk,plain,
! [X,Y] :
( ( Y = X
| less(Y,X)
| less(X,Y) )
& ( ( Y != X
& ~ less(Y,X) )
| ~ less(X,Y) ) ),
inference(skolemisation,[status(esa)],[f283_nnf]) ).
cnf(c283,plain,
( ~ less(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f283_sk]) ).
cnf(hi405,axiom,
ifeq(less(X0,X1),true,ifeq(less(X1,X0),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c283]) ).
fof(f401,conjecture,
~ less(nn2,nn4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nn2_not_less_nn4) ).
fof(f401_neg,negated_conjecture,
~ ~ less(nn2,nn4),
inference(negated_conjecture,[status(cth)],[f401]) ).
fof(f401_nnf,plain,
less(nn2,nn4),
inference(nnf_transformation,[status(thm)],[f401_neg]) ).
cnf(c406,plain,
less(nn2,nn4),
inference(cnf_transformation,[status(esa)],[f401_nnf]) ).
cnf(hi404,negated_conjecture,
less(nn2,nn4) = true,
inference(equality_encoding,[status(esa)],[c406]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi405,hi404,h2519]) ).
cnf(t467,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(c284,plain,
( X1 != X0
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f283_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c283,c284]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t467]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM299+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.60 % Computer : n019.cluster.edu
% 0.10/5.60 % Model : x86_64 x86_64
% 0.10/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.60 % Memory : 8046.5625MB
% 0.10/5.60 % OS : Linux 6.8.0-71-generic
% 0.10/5.60 % CPULimit : 300
% 0.10/5.60 % WCLimit : 300
% 0.10/5.60 % DateTime : Thu Sep 24 03:32:31 UTC 2026
% 0.10/5.60 % CPUTime :
% 0.10/5.60 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.52/6.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.52/6.64 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------