%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV156+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Sun Sep 27 09:06:55 AM UTC 2026
% Result : Theorem 17.97s 2.89s
% Output : CNFRefutation 17.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 11 unt; 0 def)
% Number of atoms : 75 ( 24 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 72 ( 14 ~; 9 |; 38 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 12 con; 0-3 aty)
% Number of variables : 19 ( 0 sgn 14 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexivity_gt,axiom,
! [X] : ~ gt(X,X),
file('theBenchmark.p',irreflexivity_gt) ).
fof(leq_succ_gt_equiv,axiom,
! [X,Y] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
file('theBenchmark.p',leq_succ_gt_equiv) ).
fof(succ_pred,axiom,
! [X] : succ(pred(X)) = X,
file('theBenchmark.p',succ_pred) ).
fof(cl5_nebula_norm_0006,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('theBenchmark.p',cl5_nebula_norm_0006) ).
fof(cl5_nebula_norm_0006_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(assume_negation,[status(cth)],[cl5_nebula_norm_0006]) ).
cnf(c_63,plain,
~ gt(A,A),
inference(clausify,[status(thm)],[irreflexivity_gt]) ).
cnf(c_72,plain,
( gt(succ(B),A)
| ~ leq(A,B) ),
inference(clausify,[status(thm)],[leq_succ_gt_equiv]) ).
cnf(c_302,plain,
succ(pred(A)) = A,
inference(clausify,[status(thm)],[succ_pred]) ).
fof(nnf_56,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] :
( 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)))))) = a_select3(q,pv10,A)
| ~ leq(A,pred(pv12))
| ~ leq(n0,A) )
& leq(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,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))))) = pv70 ),
inference(fof_nnf,[status(thm)],[cl5_nebula_norm_0006_neg]) ).
fof(sk_cl5_nebula_norm_0006_neg,plain,
( 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,sK0,tptp_sum_index))) != n1
& pv10 = sK0
& leq(sK0,pred(pv10))
& leq(n0,sK0)
& ! [B] :
( sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1
| ~ leq(B,pred(pv10))
| ~ leq(n0,B) )
& ! [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)))))) = a_select3(q,pv10,A)
| ~ leq(A,pred(pv12))
| ~ leq(n0,A) )
& leq(pv12,n4)
& leq(pv10,n135299)
& leq(n0,pv12)
& leq(n0,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))))) = pv70 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0)],[nnf_56]) ).
cnf(c_374,negated_conjecture,
leq(sK0,pred(pv10)),
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_norm_0006_neg]) ).
cnf(c_375,negated_conjecture,
pv10 = sK0,
inference(split_conjunct,[status(thm)],[sk_cl5_nebula_norm_0006_neg]) ).
cnf(c_376,negated_conjecture,
sK0 = pv10,
inference(copy,[status(thm)],[c_375]) ).
cnf(c_841,negated_conjecture,
leq(pv10,pred(pv10)),
inference(paramod,[status(thm)],[c_376,c_374]) ).
cnf(c_2955,negated_conjecture,
gt(succ(pred(pv10)),pv10),
inference(resolve,[status(thm)],[c_841,c_72]) ).
cnf(c_2956,negated_conjecture,
gt(pv10,pv10),
inference(paramod,[status(thm)],[c_302,c_2955]) ).
cnf(c_2954,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_63,c_2956]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV156+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n004.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 13:16:36 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 1799945 was started by sandbox on n004,
% 0.17/0.44 % Sat Sep 26 13:16:36 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.26/0.56
% 0.26/0.56 % From the command line: assign(max_seconds, 300).
% 17.97/2.89
% 17.97/2.89 % given #500 (I,wt=173): 579 leq(n0,f19(A,B,C,D,E,F,n0,V6)) | leq(f21(A,B,C,D,E,F,n0,V6),n0) | a_select3(F,f24(A,B,C,D,E,F,n0,V6),f23(A,B,C,D,E,F,n0,V6)) != a_select3(F,f23(A,B,C,D,E,F,n0,V6),f24(A,B,C,D,E,F,n0,V6)) | -leq(n0,V7) | -leq(V7,n0) | a_select3(tptp_madd(A,tptp_mmul(B,tptp_mmul(tptp_madd(tptp_mmul(C,tptp_mmul(D,trans(C))),tptp_mmul(E,tptp_mmul(F,trans(E)))),trans(B)))),n0,V7) = a_select3(tptp_madd(A,tptp_mmul(B,tptp_mmul(tptp_madd(tptp_mmul(C,tptp_mmul(D,trans(C))),tptp_mmul(E,tptp_mmul(F,trans(E)))),trans(B)))),V7,n0). [factor(162,d,e),flip(g),unit_del(d,64)].
% 17.97/2.89
% 17.97/2.89 % SZS status Theorem for theBenchmark
% 17.97/2.89
% 17.97/2.89 % Proof 1 at 1.84 (+ 0.26) seconds.
% 17.97/2.89 % Length of proof is 12.
% 17.97/2.89 % Level of proof is 4.
% 17.97/2.89 % Maximum clause weight is 20.000.
% 17.97/2.89 % Given clauses 762.
% 17.97/2.89
% 17.97/2.89 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------