TSTP Solution File: SWV160+1 by E---3.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : SWV160+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n013.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:43:35 EDT 2023
% Result : Theorem 0.22s 0.53s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 16 unt; 0 def)
% Number of atoms : 69 ( 23 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 60 ( 13 ~; 7 |; 29 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 17 con; 0-3 aty)
% Number of variables : 25 ( 0 sgn; 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/tmp/tmp.nrxO8zR2Ng/E---3.1_22850.p',cl5_nebula_norm_0010) ).
fof(pred_minus_1,axiom,
! [X1] : minus(X1,n1) = pred(X1),
file('/export/starexec/sandbox2/tmp/tmp.nrxO8zR2Ng/E---3.1_22850.p',pred_minus_1) ).
fof(succ_pred,axiom,
! [X1] : succ(pred(X1)) = X1,
file('/export/starexec/sandbox2/tmp/tmp.nrxO8zR2Ng/E---3.1_22850.p',succ_pred) ).
fof(irreflexivity_gt,axiom,
! [X1] : ~ gt(X1,X1),
file('/export/starexec/sandbox2/tmp/tmp.nrxO8zR2Ng/E---3.1_22850.p',irreflexivity_gt) ).
fof(leq_succ_gt_equiv,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> gt(succ(X2),X1) ),
file('/export/starexec/sandbox2/tmp/tmp.nrxO8zR2Ng/E---3.1_22850.p',leq_succ_gt_equiv) ).
fof(c_0_5,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_6,negated_conjecture,
! [X28,X29] :
( 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,X28)
| ~ leq(X28,pred(pv47))
| a_select3(q,pv10,X28) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X28)),minus(a_select2(x,pv10),a_select2(mu,X28))),tptp_minus_2),times(a_select2(sigma,X28),a_select2(sigma,X28)))),a_select2(rho,X28)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X28))),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,X29)
| ~ leq(X29,pred(pv10))
| sum(n0,n4,a_select3(q,X29,tptp_sum_index)) = n1 )
& leq(n0,esk1_0)
& leq(esk1_0,pred(pv10))
& pv10 = esk1_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,esk1_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_5])])])]) ).
cnf(c_0_7,negated_conjecture,
leq(esk1_0,pred(pv10)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_8,negated_conjecture,
pv10 = esk1_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X37] : minus(X37,n1) = pred(X37),
inference(variable_rename,[status(thm)],[pred_minus_1]) ).
fof(c_0_10,plain,
! [X62] : succ(pred(X62)) = X62,
inference(variable_rename,[status(thm)],[succ_pred]) ).
fof(c_0_11,plain,
! [X1] : ~ gt(X1,X1),
inference(fof_simplification,[status(thm)],[irreflexivity_gt]) ).
fof(c_0_12,plain,
! [X53,X54] :
( ( ~ leq(X53,X54)
| gt(succ(X54),X53) )
& ( ~ gt(succ(X54),X53)
| leq(X53,X54) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[leq_succ_gt_equiv])]) ).
cnf(c_0_13,negated_conjecture,
leq(pv10,pred(pv10)),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_14,plain,
minus(X1,n1) = pred(X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
succ(pred(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X68] : ~ gt(X68,X68),
inference(variable_rename,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( gt(succ(X2),X1)
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
leq(pv10,minus(pv10,n1)),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
succ(minus(X1,n1)) = X1,
inference(rw,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_20,plain,
~ gt(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14 % Problem : SWV160+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.11/0.15 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 2400
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Oct 3 03:46:44 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.50 Running first-order theorem proving
% 0.22/0.50 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.nrxO8zR2Ng/E---3.1_22850.p
% 0.22/0.53 # Version: 3.1pre001
% 0.22/0.53 # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.22/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.53 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.22/0.53 # Starting new_bool_3 with 300s (1) cores
% 0.22/0.53 # Starting new_bool_1 with 300s (1) cores
% 0.22/0.53 # Starting sh5l with 300s (1) cores
% 0.22/0.53 # new_bool_3 with pid 22930 completed with status 0
% 0.22/0.53 # Result found by new_bool_3
% 0.22/0.53 # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.22/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.53 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.22/0.53 # Starting new_bool_3 with 300s (1) cores
% 0.22/0.53 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.53 # Search class: FGUSM-FFMM31-DFFFFFNN
% 0.22/0.53 # partial match(1): FGHSM-FFMM31-DFFFFFNN
% 0.22/0.53 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.53 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 100s (1) cores
% 0.22/0.53 # G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 22933 completed with status 0
% 0.22/0.53 # Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.22/0.53 # Preprocessing class: FSLSSMSMSSSNFFN.
% 0.22/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.53 # Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.22/0.53 # Starting new_bool_3 with 300s (1) cores
% 0.22/0.53 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.53 # Search class: FGUSM-FFMM31-DFFFFFNN
% 0.22/0.53 # partial match(1): FGHSM-FFMM31-DFFFFFNN
% 0.22/0.53 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.53 # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 100s (1) cores
% 0.22/0.53 # Preprocessing time : 0.003 s
% 0.22/0.53 # Presaturation interreduction done
% 0.22/0.53
% 0.22/0.53 # Proof found!
% 0.22/0.53 # SZS status Theorem
% 0.22/0.53 # SZS output start CNFRefutation
% See solution above
% 0.22/0.53 # Parsed axioms : 100
% 0.22/0.53 # Removed by relevancy pruning/SinE : 23
% 0.22/0.53 # Initial clauses : 90
% 0.22/0.53 # Removed in clause preprocessing : 0
% 0.22/0.53 # Initial clauses in saturation : 90
% 0.22/0.53 # Processed clauses : 162
% 0.22/0.53 # ...of these trivial : 1
% 0.22/0.53 # ...subsumed : 0
% 0.22/0.53 # ...remaining for further processing : 161
% 0.22/0.53 # Other redundant clauses eliminated : 0
% 0.22/0.53 # Clauses deleted for lack of memory : 0
% 0.22/0.53 # Backward-subsumed : 0
% 0.22/0.53 # Backward-rewritten : 2
% 0.22/0.53 # Generated clauses : 43
% 0.22/0.53 # ...of the previous two non-redundant : 26
% 0.22/0.53 # ...aggressively subsumed : 0
% 0.22/0.53 # Contextual simplify-reflections : 0
% 0.22/0.53 # Paramodulations : 43
% 0.22/0.53 # Factorizations : 0
% 0.22/0.53 # NegExts : 0
% 0.22/0.53 # Equation resolutions : 0
% 0.22/0.53 # Total rewrite steps : 38
% 0.22/0.53 # Propositional unsat checks : 0
% 0.22/0.53 # Propositional check models : 0
% 0.22/0.53 # Propositional check unsatisfiable : 0
% 0.22/0.53 # Propositional clauses : 0
% 0.22/0.53 # Propositional clauses after purity: 0
% 0.22/0.53 # Propositional unsat core size : 0
% 0.22/0.53 # Propositional preprocessing time : 0.000
% 0.22/0.53 # Propositional encoding time : 0.000
% 0.22/0.53 # Propositional solver time : 0.000
% 0.22/0.53 # Success case prop preproc time : 0.000
% 0.22/0.53 # Success case prop encoding time : 0.000
% 0.22/0.53 # Success case prop solver time : 0.000
% 0.22/0.53 # Current number of processed clauses : 70
% 0.22/0.53 # Positive orientable unit clauses : 61
% 0.22/0.53 # Positive unorientable unit clauses: 0
% 0.22/0.53 # Negative unit clauses : 1
% 0.22/0.53 # Non-unit-clauses : 8
% 0.22/0.53 # Current number of unprocessed clauses: 41
% 0.22/0.53 # ...number of literals in the above : 96
% 0.22/0.53 # Current number of archived formulas : 0
% 0.22/0.53 # Current number of archived clauses : 91
% 0.22/0.53 # Clause-clause subsumption calls (NU) : 173
% 0.22/0.53 # Rec. Clause-clause subsumption calls : 73
% 0.22/0.53 # Non-unit clause-clause subsumptions : 0
% 0.22/0.53 # Unit Clause-clause subsumption calls : 5
% 0.22/0.53 # Rewrite failures with RHS unbound : 0
% 0.22/0.53 # BW rewrite match attempts : 10
% 0.22/0.53 # BW rewrite match successes : 2
% 0.22/0.53 # Condensation attempts : 0
% 0.22/0.53 # Condensation successes : 0
% 0.22/0.53 # Termbank termtop insertions : 5217
% 0.22/0.53
% 0.22/0.53 # -------------------------------------------------
% 0.22/0.53 # User time : 0.013 s
% 0.22/0.53 # System time : 0.001 s
% 0.22/0.53 # Total time : 0.014 s
% 0.22/0.53 # Maximum resident set size: 2088 pages
% 0.22/0.53
% 0.22/0.53 # -------------------------------------------------
% 0.22/0.53 # User time : 0.015 s
% 0.22/0.53 # System time : 0.004 s
% 0.22/0.53 # Total time : 0.019 s
% 0.22/0.53 # Maximum resident set size: 1808 pages
% 0.22/0.53 % E---3.1 exiting
% 0.22/0.53 % E---3.1 exiting
%------------------------------------------------------------------------------