%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM290+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 02:18:58 PM UTC 2026
% Result : Theorem 10.60s 1.81s
% Output : Proof 10.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 42 unt; 0 def)
% Number of atoms : 77 ( 24 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 56 ( 30 ~; 17 |; 7 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 36 ( 2 sgn 18 !; 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(hi280,axiom,
ifeq(rdn_translate(X0,rdn_pos(X1)),true,ifeq(rdn_translate(X2,rdn_pos(X3)),true,ifeq(rdn_positive_less(X1,X3),true,less(X0,X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c280]) ).
fof(f0,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn0) ).
fof(f0_nnf,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(hi0,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
fof(f1,axiom,
rdn_translate(n1,rdn_pos(rdnn(n1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn1) ).
fof(f1_nnf,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(hi1,axiom,
rdn_translate(n1,rdn_pos(rdnn(n1))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
fof(f265,axiom,
rdn_positive_less(rdnn(n0),rdnn(n1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn_positive_less01) ).
fof(f265_nnf,plain,
rdn_positive_less(rdnn(n0),rdnn(n1)),
inference(nnf_transformation,[status(thm)],[f265]) ).
cnf(c265,plain,
rdn_positive_less(rdnn(n0),rdnn(n1)),
inference(cnf_transformation,[status(esa)],[f265_nnf]) ).
cnf(hi265,axiom,
rdn_positive_less(rdnn(n0),rdnn(n1)) = true,
inference(equality_encoding,[status(esa)],[c265]) ).
cnf(t2,plain,
less(n0,n1) = true,
inference(hyper_resolution,[status(thm)],[hi280,hi0,hi1,hi265]) ).
cnf(t550,plain,
less(n0,n1) = true,
inference(orient,[status(thm)],[t2]) ).
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(hi2,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
fof(f3,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rdn3) ).
fof(f3_nnf,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(hi3,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
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]) ).
cnf(t5,plain,
less(n2,n3) = true,
inference(hyper_resolution,[status(thm)],[hi280,hi2,hi3,hi267]) ).
cnf(t556,plain,
less(n2,n3) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t21,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t202,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t21]) ).
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]) ).
fof(f401,conjecture,
less(n2,n3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n2_less_n3) ).
fof(f401_neg,negated_conjecture,
~ less(n2,n3),
inference(negated_conjecture,[status(cth)],[f401]) ).
fof(f401_nnf,plain,
~ less(n2,n3),
inference(nnf_transformation,[status(thm)],[f401_neg]) ).
fof(f401_sk,plain,
~ less(n2,n3),
inference(skolemisation,[status(esa)],[f401_nnf]) ).
cnf(c406,plain,
~ less(n2,n3),
inference(cnf_transformation,[status(esa)],[f401_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c283,c284,c406]) ).
cnf(g0_0,plain,
true != ifeq(less(n2,n3),true,false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(less(n2,n3),true,false,less(n0,n1)),
inference(rw,[status(thm)],[g0_0,t550]) ).
cnf(g0_2,plain,
true != ifeq(less(n2,n3),less(n2,n3),false,less(n0,n1)),
inference(rw,[status(thm)],[g0_1,t556]) ).
cnf(g0_3,plain,
true != false,
inference(rw,[status(thm)],[g0_2,t202]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM290+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 03:31:06 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.60/1.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.60/1.81 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------