%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM302+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 02:19:00 PM UTC 2026
% Result : Theorem 2.09s 1.60s
% Output : Proof 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 21 unt; 0 def)
% Number of atoms : 52 ( 15 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 46 ( 24 ~; 14 |; 6 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 36 ( 6 sgn 20 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f281,axiom,
! [X,Y,RDN_X,RDN_Y] :
( ( rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_translate(X,rdn_neg(RDN_X)) )
=> less(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_entry_point_neg_pos) ).
fof(f281_nnf,plain,
! [X,Y,RDN_X,RDN_Y] :
( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ),
inference(nnf_transformation,[status(thm)],[f281]) ).
fof(f281_sk,plain,
! [X,RDN_X,Y,RDN_Y] :
( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ),
inference(skolemisation,[status(esa)],[f281_nnf]) ).
cnf(c281,plain,
( less(X0,X1)
| ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_neg(X2)) ),
inference(cnf_transformation,[status(esa)],[f281_sk]) ).
cnf(hi281,axiom,
ifeq(rdn_translate(X0,rdn_neg(X1)),true,ifeq(rdn_translate(X2,rdn_pos(X3)),true,less(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c281]) ).
fof(f129,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('/export/starexec/sandbox/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]) ).
fof(f9,axiom,
rdn_translate(n9,rdn_pos(rdnn(n9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn9) ).
fof(f9_nnf,plain,
rdn_translate(n9,rdn_pos(rdnn(n9))),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
rdn_translate(n9,rdn_pos(rdnn(n9))),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(hi9,axiom,
rdn_translate(n9,rdn_pos(rdnn(n9))) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h200,plain,
less(nn2,n9) = true,
inference(hyper_resolution,[status(thm)],[hi281,hi129,hi9]) ).
fof(f401,conjecture,
? [X] : less(nn2,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nn2_less_something) ).
fof(f401_neg,negated_conjecture,
~ ? [X] : less(nn2,X),
inference(negated_conjecture,[status(cth)],[f401]) ).
fof(f401_nnf,plain,
! [X] : ~ less(nn2,X),
inference(nnf_transformation,[status(thm)],[f401_neg]) ).
fof(f401_sk,plain,
! [X] : ~ less(nn2,X),
inference(skolemisation,[status(esa)],[f401_nnf]) ).
cnf(c406,plain,
~ less(nn2,X0),
inference(cnf_transformation,[status(esa)],[f401_sk]) ).
cnf(hi406,negated_conjecture,
ifeq(less(nn2,X0),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c406]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi406,h200]) ).
cnf(t406,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f283,axiom,
! [X,Y] :
( less(X,Y)
<=> ( Y != X
& ~ less(Y,X) ) ),
file('/export/starexec/sandbox/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(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,c406]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t406]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM302+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n006.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 03:32:26 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.09/1.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.09/1.60 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------