%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV067+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 03:12:10 PM UTC 2026
% Result : Theorem 71.09s 9.42s
% Output : Proof 71.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of formulae : 65 ( 51 unt; 0 def)
% Number of atoms : 142 ( 39 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 132 ( 55 ~; 36 |; 33 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 10 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 12 con; 0-4 aty)
% Number of variables : 35 ( 2 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f52,conjecture,
( ( leq(pv63,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n1,pv63)
& leq(n0,pv10) )
=> ( ( gt(a_select3(q,pv10,pv63),pv78)
=> ( leq(pv10,minus(n135300,n1))
& leq(n0,pv10) ) )
& ( ~ gt(a_select3(q,pv10,pv63),pv78)
=> ( leq(pv10,minus(n135300,n1))
& leq(n0,pv10) ) )
& leq(pv63,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv63)
& leq(n0,pv10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_array_0008) ).
fof(f52_neg,negated_conjecture,
~ ( ( leq(pv63,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n1,pv63)
& leq(n0,pv10) )
=> ( ( gt(a_select3(q,pv10,pv63),pv78)
=> ( leq(pv10,minus(n135300,n1))
& leq(n0,pv10) ) )
& ( ~ gt(a_select3(q,pv10,pv63),pv78)
=> ( leq(pv10,minus(n135300,n1))
& leq(n0,pv10) ) )
& leq(pv63,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n0,pv63)
& leq(n0,pv10) ) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f52_nnf,plain,
( ( ( ( ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv10) )
& gt(a_select3(q,pv10,pv63),pv78) )
| ( ( ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv10) )
& ~ gt(a_select3(q,pv10,pv63),pv78) )
| ~ leq(pv63,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv63)
| ~ leq(n0,pv10) )
& leq(pv63,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n1,pv63)
& leq(n0,pv10) ),
inference(nnf_transformation,[status(thm)],[f52_neg]) ).
fof(f52_sk,plain,
( ( ( ( ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv10) )
& gt(a_select3(q,pv10,pv63),pv78) )
| ( ( ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv10) )
& ~ gt(a_select3(q,pv10,pv63),pv78) )
| ~ leq(pv63,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv63)
| ~ leq(n0,pv10) )
& leq(pv63,minus(n5,n1))
& leq(pv10,minus(n135300,n1))
& leq(n1,pv63)
& leq(n0,pv10) ),
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c262,plain,
( ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv10)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv10)
| ~ leq(pv63,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv63)
| ~ leq(n0,pv10) ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(t254,plain,
ifeq(leq(n0,pv10),trueq,ifeq(leq(n0,pv63),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,ifeq(leq(pv63,minus(n5,n1)),trueq,ifeq(leq(n0,pv10),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,ifeq(leq(n0,pv10),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,false,trueq),trueq),trueq),trueq),trueq),trueq),trueq),trueq) = trueq,
inference(equality_encoding,[status(esa)],[c262]) ).
cnf(c255,plain,
leq(n0,pv10),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(t45,plain,
leq(n0,pv10) = trueq,
inference(equality_encoding,[status(esa)],[c255]) ).
cnf(t425,plain,
leq(n0,pv10) = trueq,
inference(orient,[status(thm)],[t45]) ).
cnf(t909,plain,
ifeq(trueq,trueq,ifeq(leq(n0,pv63),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,ifeq(leq(pv63,minus(n5,n1)),trueq,ifeq(leq(n0,pv10),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,ifeq(leq(n0,pv10),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,false,trueq),trueq),trueq),trueq),trueq),trueq),trueq),trueq) = trueq,
inference(step,[status(thm)],[t254,t425]) ).
cnf(t137,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t257,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t137]) ).
cnf(t910,plain,
ifeq(leq(n0,pv63),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,ifeq(leq(pv63,minus(n5,n1)),trueq,ifeq(leq(n0,pv10),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,ifeq(leq(n0,pv10),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,false,trueq),trueq),trueq),trueq),trueq),trueq),trueq) = trueq,
inference(step,[status(thm)],[t909,t257]) ).
fof(f7,axiom,
! [X,Y] :
( gt(Y,X)
=> leq(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt1) ).
fof(f7_nnf,plain,
! [X,Y] :
( leq(X,Y)
| ~ gt(Y,X) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [Y,X] :
( leq(X,Y)
| ~ gt(Y,X) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c9,plain,
( leq(X0,X1)
| ~ gt(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi8,axiom,
ifeq(gt(X0,X1),trueq,leq(X1,X0),trueq) = trueq,
inference(equality_encoding,[status(esa)],[c9]) ).
fof(f66,axiom,
gt(n1,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_0) ).
fof(f66_nnf,plain,
gt(n1,n0),
inference(nnf_transformation,[status(thm)],[f66]) ).
cnf(c276,plain,
gt(n1,n0),
inference(cnf_transformation,[status(esa)],[f66_nnf]) ).
cnf(hi271,axiom,
gt(n1,n0) = trueq,
inference(equality_encoding,[status(esa)],[c276]) ).
cnf(h1624,plain,
leq(n0,n1) = trueq,
inference(hyper_resolution,[status(thm)],[hi8,hi271]) ).
fof(f4,axiom,
! [X,Y,Z] :
( ( leq(Y,Z)
& leq(X,Y) )
=> leq(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_leq) ).
fof(f4_nnf,plain,
! [X,Y,Z] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y,Z] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi3,axiom,
ifeq(leq(X0,X1),trueq,ifeq(leq(X1,X2),trueq,leq(X0,X2),trueq),trueq) = trueq,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(c256,plain,
leq(n1,pv63),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi254,negated_conjecture,
leq(n1,pv63) = trueq,
inference(equality_encoding,[status(esa)],[c256]) ).
cnf(t46,plain,
leq(n0,pv63) = trueq,
inference(hyper_resolution,[status(thm)],[hi3,h1624,hi254]) ).
cnf(t433,plain,
leq(n0,pv63) = trueq,
inference(orient,[status(thm)],[t46]) ).
cnf(t911,plain,
ifeq(trueq,trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,ifeq(leq(pv63,minus(n5,n1)),trueq,ifeq(leq(n0,pv10),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,ifeq(leq(n0,pv10),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,false,trueq),trueq),trueq),trueq),trueq),trueq),trueq) = trueq,
inference(step,[status(thm)],[t910,t433]) ).
cnf(t912,plain,
ifeq(leq(pv10,minus(n135300,n1)),trueq,ifeq(leq(pv63,minus(n5,n1)),trueq,ifeq(leq(n0,pv10),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,ifeq(leq(n0,pv10),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,false,trueq),trueq),trueq),trueq),trueq),trueq) = trueq,
inference(step,[status(thm)],[t911,t257]) ).
cnf(c257,plain,
leq(pv10,minus(n135300,n1)),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(t149,plain,
leq(pv10,minus(n135300,n1)) = trueq,
inference(equality_encoding,[status(esa)],[c257]) ).
cnf(t466,plain,
leq(pv10,minus(n135300,n1)) = trueq,
inference(orient,[status(thm)],[t149]) ).
cnf(t913,plain,
ifeq(trueq,trueq,ifeq(leq(pv63,minus(n5,n1)),trueq,ifeq(leq(n0,pv10),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,ifeq(leq(n0,pv10),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,false,trueq),trueq),trueq),trueq),trueq),trueq) = trueq,
inference(step,[status(thm)],[t912,t466]) ).
cnf(t914,plain,
ifeq(leq(pv63,minus(n5,n1)),trueq,ifeq(leq(n0,pv10),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,ifeq(leq(n0,pv10),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,false,trueq),trueq),trueq),trueq),trueq) = trueq,
inference(step,[status(thm)],[t913,t257]) ).
cnf(c258,plain,
leq(pv63,minus(n5,n1)),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(t150,plain,
leq(pv63,minus(n5,n1)) = trueq,
inference(equality_encoding,[status(esa)],[c258]) ).
cnf(t481,plain,
leq(pv63,minus(n5,n1)) = trueq,
inference(orient,[status(thm)],[t150]) ).
cnf(t915,plain,
ifeq(trueq,trueq,ifeq(leq(n0,pv10),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,ifeq(leq(n0,pv10),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,false,trueq),trueq),trueq),trueq),trueq) = trueq,
inference(step,[status(thm)],[t914,t481]) ).
cnf(t916,plain,
ifeq(leq(n0,pv10),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,ifeq(leq(n0,pv10),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,false,trueq),trueq),trueq),trueq) = trueq,
inference(step,[status(thm)],[t915,t257]) ).
cnf(t917,plain,
ifeq(trueq,trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,ifeq(leq(n0,pv10),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,false,trueq),trueq),trueq),trueq) = trueq,
inference(step,[status(thm)],[t916,t425]) ).
cnf(t918,plain,
ifeq(leq(pv10,minus(n135300,n1)),trueq,ifeq(leq(n0,pv10),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,false,trueq),trueq),trueq) = trueq,
inference(step,[status(thm)],[t917,t257]) ).
cnf(t919,plain,
ifeq(trueq,trueq,ifeq(leq(n0,pv10),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,false,trueq),trueq),trueq) = trueq,
inference(step,[status(thm)],[t918,t466]) ).
cnf(t920,plain,
ifeq(leq(n0,pv10),trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,false,trueq),trueq) = trueq,
inference(step,[status(thm)],[t919,t257]) ).
cnf(t921,plain,
ifeq(trueq,trueq,ifeq(leq(pv10,minus(n135300,n1)),trueq,false,trueq),trueq) = trueq,
inference(step,[status(thm)],[t920,t425]) ).
cnf(t922,plain,
ifeq(leq(pv10,minus(n135300,n1)),trueq,false,trueq) = trueq,
inference(step,[status(thm)],[t921,t257]) ).
cnf(t923,plain,
ifeq(trueq,trueq,false,trueq) = trueq,
inference(step,[status(thm)],[t922,t466]) ).
cnf(t924,plain,
false = trueq,
inference(step,[status(thm)],[t923,t257]) ).
cnf(t869,plain,
false = trueq,
inference(orient,[status(thm)],[t924]) ).
fof(f2,axiom,
! [X] : ~ gt(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_gt) ).
fof(f2_nnf,plain,
! [X] : ~ gt(X,X),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : ~ gt(X,X),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ gt(X0,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f51,axiom,
def != use,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',defuse) ).
fof(f51_nnf,plain,
def != use,
inference(nnf_transformation,[status(thm)],[f51]) ).
fof(f51_sk,plain,
def != use,
inference(skolemisation,[status(esa)],[f51_nnf]) ).
cnf(c254,plain,
def != use,
inference(cnf_transformation,[status(esa)],[f51_sk]) ).
cnf(c260,plain,
( ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv10)
| ~ gt(a_select3(q,pv10,pv63),pv78)
| ~ leq(pv63,minus(n5,n1))
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(n0,pv63)
| ~ leq(n0,pv10) ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(goal_0,negated_conjecture,
trueq != false,
inference(equality_encoding,[status(esa)],[c2,c254,c260,c262]) ).
cnf(g0_0,plain,
trueq != trueq,
inference(rw,[status(thm)],[goal_0,t869]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV067+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 18:25:50 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 71.09/9.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 71.09/9.42 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------