%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV156+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 20:30:18 EDT 2022
% Result : Theorem 1.30s 1.48s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 20 unt; 0 def)
% Number of atoms : 121 ( 42 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 113 ( 32 ~; 19 |; 46 &)
% ( 3 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 12 con; 0-3 aty)
% Number of variables : 38 ( 0 sgn 27 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexivity_gt,axiom,
! [X] : ~ gt(X,X) ).
fof(leq_succ_gt_equiv,axiom,
! [X,Y] :
( leq(X,Y)
<=> gt(succ(Y),X) ) ).
fof(succ_pred,axiom,
! [X] : succ(pred(X)) = X ).
fof(cl5_nebula_norm_0006,conjecture,
( ( 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)))))
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,n135299)
& leq(pv12,n4)
& ! [A] :
( ( leq(n0,A)
& leq(A,pred(pv12)) )
=> 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)))))) )
& ! [B] :
( ( leq(n0,B)
& leq(B,pred(pv10)) )
=> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) )
=> ! [C] :
( ( leq(n0,C)
& leq(C,pred(pv10)) )
=> ( 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 ) ) ) ).
fof(subgoal_0,plain,
( ( 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)))))
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,n135299)
& leq(pv12,n4)
& ! [A] :
( ( leq(n0,A)
& leq(A,pred(pv12)) )
=> 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)))))) )
& ! [B] :
( ( leq(n0,B)
& leq(B,pred(pv10)) )
=> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) )
=> ! [C] :
( ( leq(n0,C)
& leq(C,pred(pv10))
& 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(strip,[],[cl5_nebula_norm_0006]) ).
fof(negate_0_0,plain,
~ ( ( 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)))))
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,n135299)
& leq(pv12,n4)
& ! [A] :
( ( leq(n0,A)
& leq(A,pred(pv12)) )
=> 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)))))) )
& ! [B] :
( ( leq(n0,B)
& leq(B,pred(pv10)) )
=> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) )
=> ! [C] :
( ( leq(n0,C)
& leq(C,pred(pv10))
& 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(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( 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)))))
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,n135299)
& leq(pv12,n4)
& ? [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) )
& ! [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)))))) )
& ! [B] :
( ~ leq(B,pred(pv10))
| ~ leq(n0,B)
| sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,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) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,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,skolemFOFtoCNF_C,tptp_sum_index))) != n1
& pv10 = skolemFOFtoCNF_C
& leq(n0,skolemFOFtoCNF_C)
& leq(skolemFOFtoCNF_C,pred(pv10)) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
leq(skolemFOFtoCNF_C,pred(pv10)),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
pv10 = skolemFOFtoCNF_C,
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ gt(succ(Y),X)
<=> ~ leq(X,Y) ),
inference(canonicalize,[],[leq_succ_gt_equiv]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ gt(succ(Y),X)
<=> ~ leq(X,Y) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ( ~ gt(succ(Y),X)
| leq(X,Y) )
& ( ~ leq(X,Y)
| gt(succ(Y),X) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ leq(X,Y)
| gt(succ(Y),X) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X] : succ(pred(X)) = X,
inference(canonicalize,[],[succ_pred]) ).
fof(normalize_0_10,plain,
! [X] : succ(pred(X)) = X,
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X] : ~ gt(X,X),
inference(canonicalize,[],[irreflexivity_gt]) ).
fof(normalize_0_12,plain,
! [X] : ~ gt(X,X),
inference(specialize,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
leq(skolemFOFtoCNF_C,pred(pv10)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
pv10 = skolemFOFtoCNF_C,
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_3,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_4,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( pv10 != skolemFOFtoCNF_C
| skolemFOFtoCNF_C = pv10 ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(pv10)),bind(Y0,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_6,plain,
skolemFOFtoCNF_C = pv10,
inference(resolve,[$cnf( $equal(pv10,skolemFOFtoCNF_C) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( skolemFOFtoCNF_C != pv10
| ~ leq(skolemFOFtoCNF_C,pred(pv10))
| leq(pv10,pred(pv10)) ),
introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_C,pred(pv10)) ),[0],$fot(pv10)]]) ).
cnf(refute_0_8,plain,
( ~ leq(skolemFOFtoCNF_C,pred(pv10))
| leq(pv10,pred(pv10)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C,pv10) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
leq(pv10,pred(pv10)),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_C,pred(pv10)) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ leq(X,Y)
| gt(succ(Y),X) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_11,plain,
( ~ leq(pv10,pred(pv10))
| gt(succ(pred(pv10)),pv10) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(pv10)),bind(Y,$fot(pred(pv10)))]]) ).
cnf(refute_0_12,plain,
gt(succ(pred(pv10)),pv10),
inference(resolve,[$cnf( leq(pv10,pred(pv10)) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
succ(pred(X)) = X,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_14,plain,
succ(pred(pv10)) = pv10,
inference(subst,[],[refute_0_13:[bind(X,$fot(pv10))]]) ).
cnf(refute_0_15,plain,
( succ(pred(pv10)) != pv10
| ~ gt(succ(pred(pv10)),pv10)
| gt(pv10,pv10) ),
introduced(tautology,[equality,[$cnf( gt(succ(pred(pv10)),pv10) ),[0],$fot(pv10)]]) ).
cnf(refute_0_16,plain,
( ~ gt(succ(pred(pv10)),pv10)
| gt(pv10,pv10) ),
inference(resolve,[$cnf( $equal(succ(pred(pv10)),pv10) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
gt(pv10,pv10),
inference(resolve,[$cnf( gt(succ(pred(pv10)),pv10) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
~ gt(X,X),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_19,plain,
~ gt(pv10,pv10),
inference(subst,[],[refute_0_18:[bind(X,$fot(pv10))]]) ).
cnf(refute_0_20,plain,
$false,
inference(resolve,[$cnf( gt(pv10,pv10) )],[refute_0_17,refute_0_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV156+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jun 15 06:58:56 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.30/1.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.30/1.48
% 1.30/1.48 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.30/1.48
%------------------------------------------------------------------------------