TSTP Solution File: SWV160+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV160+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n016.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 : 300s
% DateTime : Thu Aug 31 21:36:49 EDT 2023
% Result : Theorem 0.51s 0.60s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 84
% Syntax : Number of formulae : 99 ( 12 unt; 80 typ; 0 def)
% Number of atoms : 67 ( 19 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 62 ( 14 ~; 8 |; 29 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 155 ( 56 >; 99 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 2 prp; 0-4 aty)
% Number of functors : 74 ( 74 usr; 23 con; 0-7 aty)
% Number of variables : 23 ( 0 sgn; 17 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
gt: ( $i * $i ) > $o ).
tff(decl_23,type,
leq: ( $i * $i ) > $o ).
tff(decl_24,type,
lt: ( $i * $i ) > $o ).
tff(decl_25,type,
geq: ( $i * $i ) > $o ).
tff(decl_26,type,
pred: $i > $i ).
tff(decl_27,type,
succ: $i > $i ).
tff(decl_28,type,
n0: $i ).
tff(decl_29,type,
uniform_int_rnd: ( $i * $i ) > $i ).
tff(decl_30,type,
dim: ( $i * $i ) > $i ).
tff(decl_31,type,
tptp_const_array1: ( $i * $i ) > $i ).
tff(decl_32,type,
a_select2: ( $i * $i ) > $i ).
tff(decl_33,type,
tptp_const_array2: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
a_select3: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
trans: $i > $i ).
tff(decl_36,type,
inv: $i > $i ).
tff(decl_37,type,
tptp_update3: ( $i * $i * $i * $i ) > $i ).
tff(decl_38,type,
tptp_madd: ( $i * $i ) > $i ).
tff(decl_39,type,
tptp_msub: ( $i * $i ) > $i ).
tff(decl_40,type,
tptp_mmul: ( $i * $i ) > $i ).
tff(decl_41,type,
tptp_minus_1: $i ).
tff(decl_42,type,
sum: ( $i * $i * $i ) > $i ).
tff(decl_43,type,
tptp_float_0_0: $i ).
tff(decl_44,type,
n1: $i ).
tff(decl_45,type,
plus: ( $i * $i ) > $i ).
tff(decl_46,type,
n2: $i ).
tff(decl_47,type,
n3: $i ).
tff(decl_48,type,
n4: $i ).
tff(decl_49,type,
n5: $i ).
tff(decl_50,type,
minus: ( $i * $i ) > $i ).
tff(decl_51,type,
tptp_update2: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
true: $o ).
tff(decl_53,type,
def: $i ).
tff(decl_54,type,
use: $i ).
tff(decl_55,type,
pv84: $i ).
tff(decl_56,type,
x: $i ).
tff(decl_57,type,
pv10: $i ).
tff(decl_58,type,
mu: $i ).
tff(decl_59,type,
tptp_sum_index: $i ).
tff(decl_60,type,
times: ( $i * $i ) > $i ).
tff(decl_61,type,
tptp_minus_2: $i ).
tff(decl_62,type,
divide: ( $i * $i ) > $i ).
tff(decl_63,type,
sigma: $i ).
tff(decl_64,type,
exp: $i > $i ).
tff(decl_65,type,
rho: $i ).
tff(decl_66,type,
tptp_pi: $i ).
tff(decl_67,type,
sqrt: $i > $i ).
tff(decl_68,type,
pv47: $i ).
tff(decl_69,type,
n135299: $i ).
tff(decl_70,type,
q: $i ).
tff(decl_71,type,
tptp_term_equals: ( $i * $i ) > $i ).
tff(decl_72,type,
cond: ( $i * $i * $i ) > $i ).
tff(decl_73,type,
epred1_4: ( $i * $i * $i * $i ) > $o ).
tff(decl_74,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_75,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_76,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_77,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_78,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_79,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_80,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_81,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_82,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_83,type,
esk10_3: ( $i * $i * $i ) > $i ).
tff(decl_84,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_86,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_87,type,
esk14_3: ( $i * $i * $i ) > $i ).
tff(decl_88,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_89,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_90,type,
esk17_3: ( $i * $i * $i ) > $i ).
tff(decl_91,type,
esk18_3: ( $i * $i * $i ) > $i ).
tff(decl_92,type,
esk19_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_93,type,
esk20_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_94,type,
esk21_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_95,type,
esk22_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_96,type,
esk23_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_97,type,
esk24_0: $i ).
tff(decl_98,type,
esk25_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_99,type,
esk26_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_100,type,
esk27_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_101,type,
esk28_4: ( $i * $i * $i * $i ) > $i ).
fof(cl5_nebula_norm_0010,conjecture,
( ( pv84 = 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(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ! [X14] :
( ( leq(n0,X14)
& leq(X14,pred(pv47)) )
=> a_select3(q,pv10,X14) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X14)),minus(a_select2(x,pv10),a_select2(mu,X14))),tptp_minus_2),times(a_select2(sigma,X14),a_select2(sigma,X14)))),a_select2(rho,X14)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X14))),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))))) )
& ! [X18] :
( ( leq(n0,X18)
& leq(X18,pred(pv10)) )
=> sum(n0,n4,a_select3(q,X18,tptp_sum_index)) = n1 ) )
=> ! [X4] :
( ( leq(n0,X4)
& leq(X4,pred(pv10)) )
=> ( pv10 = X4
=> sum(n0,n4,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,X4,tptp_sum_index))) = n1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0010) ).
fof(pred_minus_1,axiom,
! [X1] : minus(X1,n1) = pred(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).
fof(leq_gt_pred,axiom,
! [X1,X2] :
( leq(X1,pred(X2))
<=> gt(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt_pred) ).
fof(irreflexivity_gt,axiom,
! [X1] : ~ gt(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',irreflexivity_gt) ).
fof(c_0_4,negated_conjecture,
~ ( ( pv84 = 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(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ! [X14] :
( ( leq(n0,X14)
& leq(X14,pred(pv47)) )
=> a_select3(q,pv10,X14) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X14)),minus(a_select2(x,pv10),a_select2(mu,X14))),tptp_minus_2),times(a_select2(sigma,X14),a_select2(sigma,X14)))),a_select2(rho,X14)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X14))),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))))) )
& ! [X18] :
( ( leq(n0,X18)
& leq(X18,pred(pv10)) )
=> sum(n0,n4,a_select3(q,X18,tptp_sum_index)) = n1 ) )
=> ! [X4] :
( ( leq(n0,X4)
& leq(X4,pred(pv10)) )
=> ( pv10 = X4
=> sum(n0,n4,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,X4,tptp_sum_index))) = n1 ) ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_norm_0010]) ).
fof(c_0_5,negated_conjecture,
! [X186,X187] :
( pv84 = 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(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ( ~ leq(n0,X186)
| ~ leq(X186,pred(pv47))
| a_select3(q,pv10,X186) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X186)),minus(a_select2(x,pv10),a_select2(mu,X186))),tptp_minus_2),times(a_select2(sigma,X186),a_select2(sigma,X186)))),a_select2(rho,X186)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X186))),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(n0,X187)
| ~ leq(X187,pred(pv10))
| sum(n0,n4,a_select3(q,X187,tptp_sum_index)) = n1 )
& leq(n0,esk24_0)
& leq(esk24_0,pred(pv10))
& pv10 = esk24_0
& sum(n0,n4,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,esk24_0,tptp_sum_index))) != n1 ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_6,plain,
! [X145] : minus(X145,n1) = pred(X145),
inference(variable_rename,[status(thm)],[pred_minus_1]) ).
fof(c_0_7,plain,
! [X46,X47] :
( ( ~ leq(X46,pred(X47))
| gt(X47,X46) )
& ( ~ gt(X47,X46)
| leq(X46,pred(X47)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_gt_pred])]) ).
cnf(c_0_8,negated_conjecture,
leq(esk24_0,pred(pv10)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
minus(X1,n1) = pred(X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X1] : ~ gt(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_gt]) ).
cnf(c_0_11,plain,
( gt(X2,X1)
| ~ leq(X1,pred(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
leq(esk24_0,minus(pv10,n1)),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,negated_conjecture,
pv10 = esk24_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_14,plain,
! [X33] : ~ gt(X33,X33),
inference(variable_rename,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( gt(X2,X1)
| ~ leq(X1,minus(X2,n1)) ),
inference(rw,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_16,negated_conjecture,
leq(pv10,minus(pv10,n1)),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
~ gt(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWV160+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.03/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 07:07:15 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.50/0.55 start to proof: theBenchmark
% 0.51/0.60 % Version : CSE_E---1.5
% 0.51/0.60 % Problem : theBenchmark.p
% 0.51/0.60 % Proof found
% 0.51/0.60 % SZS status Theorem for theBenchmark.p
% 0.51/0.60 % SZS output start Proof
% See solution above
% 0.51/0.60 % Total time : 0.044000 s
% 0.51/0.60 % SZS output end Proof
% 0.51/0.60 % Total time : 0.047000 s
%------------------------------------------------------------------------------