%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM292+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 : n026.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 02:18:58 PM UTC 2026
% Result : Theorem 32.85s 4.69s
% Output : Proof 32.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 60 ( 43 unt; 0 def)
% Number of atoms : 94 ( 34 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 67 ( 33 ~; 23 |; 7 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 82 ( 19 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f280,axiom,
! [X,Y,RDN_X,RDN_Y] :
( ( rdn_positive_less(RDN_X,RDN_Y)
& rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_translate(X,rdn_pos(RDN_X)) )
=> less(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_entry_point_pos_pos) ).
fof(f280_nnf,plain,
! [X,Y,RDN_X,RDN_Y] :
( less(X,Y)
| ~ rdn_positive_less(RDN_X,RDN_Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_pos(RDN_X)) ),
inference(nnf_transformation,[status(thm)],[f280]) ).
fof(f280_sk,plain,
! [X,RDN_X,Y,RDN_Y] :
( less(X,Y)
| ~ rdn_positive_less(RDN_X,RDN_Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_pos(RDN_X)) ),
inference(skolemisation,[status(esa)],[f280_nnf]) ).
cnf(c280,plain,
( less(X0,X1)
| ~ rdn_positive_less(X2,X3)
| ~ rdn_translate(X1,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_pos(X2)) ),
inference(cnf_transformation,[status(esa)],[f280_sk]) ).
cnf(t180,plain,
ifeq(rdn_translate(X1,rdn_pos(X2)),true,ifeq(rdn_translate(X3,rdn_pos(X4)),true,ifeq(rdn_positive_less(X2,X4),true,less(X1,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c280]) ).
cnf(t305,plain,
ifeq(rdn_translate(X1,rdn_pos(X2)),true,ifeq(rdn_translate(X3,rdn_pos(X4)),true,ifeq(rdn_positive_less(X2,X4),true,less(X1,X3),true),true),true) = true,
inference(orient,[status(thm)],[t180]) ).
fof(f278,axiom,
! [X] :
( rdn_non_zero_digit(rdnn(X))
=> rdn_non_zero(rdnn(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_non_zero_by_digit) ).
fof(f278_nnf,plain,
! [X] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) ),
inference(nnf_transformation,[status(thm)],[f278]) ).
fof(f278_sk,plain,
! [X] :
( rdn_non_zero(rdnn(X))
| ~ rdn_non_zero_digit(rdnn(X)) ),
inference(skolemisation,[status(esa)],[f278_nnf]) ).
cnf(c278,plain,
( rdn_non_zero(rdnn(X0))
| ~ rdn_non_zero_digit(rdnn(X0)) ),
inference(cnf_transformation,[status(esa)],[f278_sk]) ).
cnf(hi278,axiom,
ifeq(rdn_non_zero_digit(rdnn(X0)),true,rdn_non_zero(rdnn(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c278]) ).
fof(f256,axiom,
rdn_non_zero_digit(rdnn(n1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_digit1) ).
fof(f256_nnf,plain,
rdn_non_zero_digit(rdnn(n1)),
inference(nnf_transformation,[status(thm)],[f256]) ).
cnf(c256,plain,
rdn_non_zero_digit(rdnn(n1)),
inference(cnf_transformation,[status(esa)],[f256_nnf]) ).
cnf(hi256,axiom,
rdn_non_zero_digit(rdnn(n1)) = true,
inference(equality_encoding,[status(esa)],[c256]) ).
cnf(h16,plain,
rdn_non_zero(rdnn(n1)) = true,
inference(hyper_resolution,[status(thm)],[hi278,hi256]) ).
fof(f277,axiom,
! [D,Db,Ob] :
( rdn_non_zero(Ob)
=> rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_extra_digits_positive_less) ).
fof(f277_nnf,plain,
! [D,Db,Ob] :
( rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob))
| ~ rdn_non_zero(Ob) ),
inference(nnf_transformation,[status(thm)],[f277]) ).
fof(f277_sk,plain,
! [Ob,D,Db] :
( rdn_positive_less(rdnn(D),rdn(rdnn(Db),Ob))
| ~ rdn_non_zero(Ob) ),
inference(skolemisation,[status(esa)],[f277_nnf]) ).
cnf(c277,plain,
( rdn_positive_less(rdnn(X0),rdn(rdnn(X1),X2))
| ~ rdn_non_zero(X2) ),
inference(cnf_transformation,[status(esa)],[f277_sk]) ).
cnf(hi277,axiom,
ifeq(rdn_non_zero(X0),true,rdn_positive_less(rdnn(X1),rdn(rdnn(X2),X0)),true) = true,
inference(equality_encoding,[status(esa)],[c277]) ).
cnf(t55,plain,
rdn_positive_less(rdnn(X1),rdn(rdnn(X2),rdnn(n1))) = true,
inference(hyper_resolution,[status(thm)],[hi277,h16]) ).
cnf(t321,plain,
rdn_positive_less(rdnn(X1),rdn(rdnn(X2),rdnn(n1))) = true,
inference(orient,[status(thm)],[t55]) ).
cnf(t324,plain,
true = ifeq(rdn_translate(X1,rdn_pos(rdnn(X2))),true,ifeq(rdn_translate(X3,rdn_pos(rdn(rdnn(X4),rdnn(n1)))),true,ifeq(true,true,less(X1,X3),true),true),true),
inference(cp,[status(thm)],[t305,t321]) ).
cnf(t21,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t182,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t21]) ).
cnf(t3183,plain,
true = ifeq(rdn_translate(X1,rdn_pos(rdnn(X2))),true,ifeq(rdn_translate(X3,rdn_pos(rdn(rdnn(X4),rdnn(n1)))),true,less(X1,X3),true),true),
inference(step,[status(thm)],[t324,t182]) ).
cnf(t2732,plain,
ifeq(rdn_translate(X1,rdn_pos(rdnn(X2))),true,ifeq(rdn_translate(X3,rdn_pos(rdn(rdnn(X4),rdnn(n1)))),true,less(X1,X3),true),true) = true,
inference(orient,[status(thm)],[t3183]) ).
fof(f13,axiom,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn13) ).
fof(f13_nnf,plain,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c13,plain,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))),
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(t64,plain,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t567,plain,
rdn_translate(n13,rdn_pos(rdn(rdnn(n3),rdnn(n1)))) = true,
inference(orient,[status(thm)],[t64]) ).
cnf(t2744,plain,
true = ifeq(rdn_translate(X1,rdn_pos(rdnn(X2))),true,ifeq(true,true,less(X1,n13),true),true),
inference(cp,[status(thm)],[t2732,t567]) ).
cnf(t3186,plain,
true = ifeq(rdn_translate(X1,rdn_pos(rdnn(X2))),true,less(X1,n13),true),
inference(step,[status(thm)],[t2744,t182]) ).
cnf(t2766,plain,
ifeq(rdn_translate(X1,rdn_pos(rdnn(X2))),true,less(X1,n13),true) = true,
inference(orient,[status(thm)],[t3186]) ).
fof(f2,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn2) ).
fof(f2_nnf,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(t35,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t513,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))) = true,
inference(orient,[status(thm)],[t35]) ).
cnf(t2774,plain,
true = ifeq(true,true,less(n2,n13),true),
inference(cp,[status(thm)],[t2766,t513]) ).
cnf(t3187,plain,
true = less(n2,n13),
inference(step,[status(thm)],[t2774,t182]) ).
fof(f401,conjecture,
less(n2,n13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n2_less_n13) ).
fof(f401_neg,negated_conjecture,
~ less(n2,n13),
inference(negated_conjecture,[status(cth)],[f401]) ).
fof(f401_nnf,plain,
~ less(n2,n13),
inference(nnf_transformation,[status(thm)],[f401_neg]) ).
fof(f401_sk,plain,
~ less(n2,n13),
inference(skolemisation,[status(esa)],[f401_nnf]) ).
cnf(c406,plain,
~ less(n2,n13),
inference(cnf_transformation,[status(esa)],[f401_sk]) ).
cnf(t0,plain,
less(n2,n13) = false,
inference(equality_encoding,[status(esa)],[c406]) ).
cnf(t681,plain,
less(n2,n13) = false,
inference(orient,[status(thm)],[t0]) ).
cnf(t3188,plain,
true = false,
inference(step,[status(thm)],[t3187,t681]) ).
cnf(t2779,plain,
false = true,
inference(orient,[status(thm)],[t3188]) ).
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(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,t2779]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM292+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 03:34:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 32.85/4.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.85/4.69 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------