%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV163+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 : n011.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 03:12:24 PM UTC 2026
% Result : Theorem 60.34s 8.26s
% Output : Proof 60.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 31 unt; 0 def)
% Number of atoms : 95 ( 33 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 83 ( 35 ~; 19 |; 20 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 15 con; 0-4 aty)
% Number of variables : 43 ( 0 sgn 27 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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(f59,axiom,
gt(n0,tptp_minus_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
fof(f59_nnf,plain,
gt(n0,tptp_minus_1),
inference(nnf_transformation,[status(thm)],[f59]) ).
cnf(c267,plain,
gt(n0,tptp_minus_1),
inference(cnf_transformation,[status(esa)],[f59_nnf]) ).
cnf(hi264,axiom,
gt(n0,tptp_minus_1) = trueq,
inference(equality_encoding,[status(esa)],[c267]) ).
cnf(h2188,plain,
leq(tptp_minus_1,n0) = trueq,
inference(hyper_resolution,[status(thm)],[hi8,hi264]) ).
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]) ).
fof(f52,conjecture,
( ( ! [A] :
( ( leq(A,pred(pv10))
& leq(n0,A) )
=> sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 )
& leq(pv10,n135299)
& leq(n0,pv10) )
=> ! [B] :
( ( leq(B,tptp_minus_1)
& leq(n0,B) )
=> a_select3(q,pv10,B) = divide(sqrt(times(minus(a_select3(center,B,n0),a_select2(x,pv10)),minus(a_select3(center,B,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0013) ).
fof(f52_neg,negated_conjecture,
~ ( ( ! [A] :
( ( leq(A,pred(pv10))
& leq(n0,A) )
=> sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1 )
& leq(pv10,n135299)
& leq(n0,pv10) )
=> ! [B] :
( ( leq(B,tptp_minus_1)
& leq(n0,B) )
=> a_select3(q,pv10,B) = divide(sqrt(times(minus(a_select3(center,B,n0),a_select2(x,pv10)),minus(a_select3(center,B,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f52_nnf,plain,
( ? [B] :
( a_select3(q,pv10,B) != divide(sqrt(times(minus(a_select3(center,B,n0),a_select2(x,pv10)),minus(a_select3(center,B,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
& leq(B,tptp_minus_1)
& leq(n0,B) )
& ! [A] :
( sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1
| ~ leq(A,pred(pv10))
| ~ leq(n0,A) )
& leq(pv10,n135299)
& leq(n0,pv10) ),
inference(nnf_transformation,[status(thm)],[f52_neg]) ).
fof(f52_sk,plain,
! [A] :
( a_select3(q,pv10,sk27) != divide(sqrt(times(minus(a_select3(center,sk27,n0),a_select2(x,pv10)),minus(a_select3(center,sk27,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
& leq(sk27,tptp_minus_1)
& leq(n0,sk27)
& ( sum(n0,n4,a_select3(q,A,tptp_sum_index)) = n1
| ~ leq(A,pred(pv10))
| ~ leq(n0,A) )
& leq(pv10,n135299)
& leq(n0,pv10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk27])],[f52_nnf]) ).
cnf(c258,plain,
leq(n0,sk27),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi256,negated_conjecture,
leq(n0,sk27) = trueq,
inference(equality_encoding,[status(esa)],[c258]) ).
cnf(c259,plain,
leq(sk27,tptp_minus_1),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi257,negated_conjecture,
leq(sk27,tptp_minus_1) = trueq,
inference(equality_encoding,[status(esa)],[c259]) ).
cnf(h1731,plain,
leq(n0,tptp_minus_1) = trueq,
inference(hyper_resolution,[status(thm)],[hi3,hi256,hi257]) ).
fof(f83,axiom,
! [X] :
( ( leq(X,n0)
& leq(n0,X) )
=> X = n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_0) ).
fof(f83_nnf,plain,
! [X] :
( X = n0
| ~ leq(X,n0)
| ~ leq(n0,X) ),
inference(nnf_transformation,[status(thm)],[f83]) ).
fof(f83_sk,plain,
! [X] :
( X = n0
| ~ leq(X,n0)
| ~ leq(n0,X) ),
inference(skolemisation,[status(esa)],[f83_nnf]) ).
cnf(c291,plain,
( X0 = n0
| ~ leq(X0,n0)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(esa)],[f83_sk]) ).
cnf(hi288,axiom,
ifeq(leq(n0,X0),trueq,ifeq(leq(X0,n0),trueq,X0,n0),n0) = n0,
inference(equality_encoding,[status(esa)],[c291]) ).
cnf(t0,plain,
tptp_minus_1 = n0,
inference(hyper_resolution,[status(thm)],[hi288,h1731,h2188]) ).
cnf(t1462,plain,
n0 = tptp_minus_1,
inference(orient,[status(thm)],[t0]) ).
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]) ).
cnf(t18,plain,
gt(X1,X1) = false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t1531,plain,
gt(X1,X1) = false,
inference(orient,[status(thm)],[t18]) ).
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,
a_select3(q,pv10,sk27) != divide(sqrt(times(minus(a_select3(center,sk27,n0),a_select2(x,pv10)),minus(a_select3(center,sk27,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(goal_0,negated_conjecture,
trueq != false,
inference(equality_encoding,[status(esa)],[c2,c254,c260]) ).
cnf(g0_0,plain,
trueq != gt(n0,tptp_minus_1),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
trueq != gt(tptp_minus_1,tptp_minus_1),
inference(rw,[status(thm)],[g0_0,t1462]) ).
cnf(g0_2,plain,
trueq != false,
inference(rw,[status(thm)],[g0_1,t1531]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV163+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 18:39:27 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 60.34/8.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 60.34/8.26 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------