%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV156+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 03:12:23 PM UTC 2026
% Result : Theorem 24.23s 3.57s
% Output : Proof 24.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 81 ( 21 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 84 ( 20 ~; 13 |; 40 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 12 con; 0-3 aty)
% Number of variables : 23 ( 0 sgn 19 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f52,conjecture,
( ( ! [B] :
( ( leq(B,pred(pv10))
& leq(n0,B) )
=> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 )
& ! [A] :
( ( leq(A,pred(pv12))
& leq(n0,A) )
=> a_select3(q,pv10,A) = divide(sqrt(times(minus(a_select3(center,A,n0),a_select2(x,pv10)),minus(a_select3(center,A,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(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,pv10)
& pv70 = 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))))) )
=> ! [C] :
( ( leq(C,pred(pv10))
& leq(n0,C) )
=> ( pv10 = C
=> sum(n0,n4,cond(tptp_term_equals(pv12,tptp_sum_index),divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70),a_select3(q,C,tptp_sum_index))) = n1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_norm_0006) ).
fof(f52_neg,negated_conjecture,
~ ( ( ! [B] :
( ( leq(B,pred(pv10))
& leq(n0,B) )
=> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 )
& ! [A] :
( ( leq(A,pred(pv12))
& leq(n0,A) )
=> a_select3(q,pv10,A) = divide(sqrt(times(minus(a_select3(center,A,n0),a_select2(x,pv10)),minus(a_select3(center,A,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(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,pv10)
& pv70 = 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))))) )
=> ! [C] :
( ( leq(C,pred(pv10))
& leq(n0,C) )
=> ( pv10 = C
=> sum(n0,n4,cond(tptp_term_equals(pv12,tptp_sum_index),divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70),a_select3(q,C,tptp_sum_index))) = n1 ) ) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f52_nnf,plain,
( ? [C] :
( sum(n0,n4,cond(tptp_term_equals(pv12,tptp_sum_index),divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70),a_select3(q,C,tptp_sum_index))) != n1
& pv10 = C
& leq(C,pred(pv10))
& leq(n0,C) )
& ! [B] :
( sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1
| ~ leq(B,pred(pv10))
| ~ leq(n0,B) )
& ! [A] :
( a_select3(q,pv10,A) = divide(sqrt(times(minus(a_select3(center,A,n0),a_select2(x,pv10)),minus(a_select3(center,A,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(A,pred(pv12))
| ~ leq(n0,A) )
& leq(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,pv10)
& pv70 = 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(nnf_transformation,[status(thm)],[f52_neg]) ).
fof(f52_sk,plain,
! [A,B] :
( sum(n0,n4,cond(tptp_term_equals(pv12,tptp_sum_index),divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70),a_select3(q,sk27,tptp_sum_index))) != n1
& pv10 = sk27
& leq(sk27,pred(pv10))
& leq(n0,sk27)
& ( sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1
| ~ leq(B,pred(pv10))
| ~ leq(n0,B) )
& ( a_select3(q,pv10,A) = divide(sqrt(times(minus(a_select3(center,A,n0),a_select2(x,pv10)),minus(a_select3(center,A,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(A,pred(pv12))
| ~ leq(n0,A) )
& leq(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,pv10)
& pv70 = 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(skolemisation,[status(esa),new_symbols(skolem,[sk27])],[f52_nnf]) ).
cnf(c264,plain,
pv10 = sk27,
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c263,plain,
leq(sk27,pred(pv10)),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
fof(f9,axiom,
! [X,Y] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt_pred) ).
fof(f9_nnf,plain,
! [X,Y] :
( ( ~ gt(Y,X)
| leq(X,pred(Y)) )
& ( gt(Y,X)
| ~ leq(X,pred(Y)) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y] :
( ( ~ gt(Y,X)
| leq(X,pred(Y)) )
& ( gt(Y,X)
| ~ leq(X,pred(Y)) ) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c11,plain,
( gt(X1,X0)
| ~ leq(X0,pred(X1)) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p859,plain,
gt(pv10,sk27),
inference(resolution,[status(thm)],[c263,c11]) ).
cnf(p865,plain,
gt(pv10,pv10),
inference(superposition,[status(thm)],[c264,p859]) ).
fof(f2,axiom,
! [X] : ~ gt(X,X),
file('/export/starexec/sandbox2/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(p868,plain,
$false,
inference(resolution,[status(thm)],[p865,c2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV156+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.44 % Computer : n017.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Thu Sep 24 18:34:01 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.23/3.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.23/3.57 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------