%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV164+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 : n005.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 47.22s 6.50s
% Output : Proof 47.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 67 ( 8 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 68 ( 23 ~; 16 |; 21 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 16 con; 0-3 aty)
% Number of variables : 32 ( 0 sgn 24 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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]) ).
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(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,B)),minus(a_select2(x,pv10),a_select2(mu,B))),tptp_minus_2),times(a_select2(sigma,B),a_select2(sigma,B)))),a_select2(rho,B)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,B))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0014) ).
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(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,B)),minus(a_select2(x,pv10),a_select2(mu,B))),tptp_minus_2),times(a_select2(sigma,B),a_select2(sigma,B)))),a_select2(rho,B)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,B))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) ) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f52_nnf,plain,
( ? [B] :
( a_select3(q,pv10,B) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,B)),minus(a_select2(x,pv10),a_select2(mu,B))),tptp_minus_2),times(a_select2(sigma,B),a_select2(sigma,B)))),a_select2(rho,B)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,B))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))))
& 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(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sk27)),minus(a_select2(x,pv10),a_select2(mu,sk27))),tptp_minus_2),times(a_select2(sigma,sk27),a_select2(sigma,sk27)))),a_select2(rho,sk27)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sk27))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))))
& 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(p316,plain,
( leq(n0,X0)
| ~ leq(sk27,X0) ),
inference(resolution,[status(thm)],[c4,c258]) ).
cnf(c259,plain,
leq(sk27,tptp_minus_1),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(p13187,plain,
leq(n0,tptp_minus_1),
inference(resolution,[status(thm)],[p316,c259]) ).
fof(f12,axiom,
! [X,Y] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_gt_equiv) ).
fof(f12_nnf,plain,
! [X,Y] :
( ( ~ gt(succ(Y),X)
| leq(X,Y) )
& ( gt(succ(Y),X)
| ~ leq(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y] :
( ( ~ gt(succ(Y),X)
| leq(X,Y) )
& ( gt(succ(Y),X)
| ~ leq(X,Y) ) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c15,plain,
( gt(succ(X1),X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p13191,plain,
gt(n0,n0),
inference(resolution,[status(thm)],[p13187,c15]) ).
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(p13326,plain,
$false,
inference(resolution,[status(thm)],[p13191,c2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV164+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 18:39:17 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 47.22/6.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 47.22/6.50 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------