%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM345+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 : Thu Sep 24 01:44:43 PM UTC 2026
% Result : Theorem 0.24s 0.63s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 42 ( 20 unt; 0 def)
% Number of atoms : 92 ( 5 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 89 ( 39 ~; 36 |; 8 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 75 ( 0 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(add_digit_digit_digit,axiom,
! [X21,X22,X23,X24,X25] :
( ( rdn_digit_add(rdnn(X25),rdnn(X21),rdnn(X24),rdnn(n0))
& rdn_digit_add(rdnn(X22),rdnn(X23),rdnn(X25),rdnn(n0)) )
=> rdn_add_with_carry(rdnn(X21),rdnn(X22),rdnn(X23),rdnn(X24)) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',add_digit_digit_digit) ).
fof(sum_entry_point_pos_pos,axiom,
! [X1,X2,X3,X10,X11,X12] :
( ( rdn_translate(X3,rdn_pos(X12))
& rdn_add_with_carry(rdnn(n0),X10,X11,X12)
& rdn_translate(X2,rdn_pos(X11))
& rdn_translate(X1,rdn_pos(X10)) )
=> sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',sum_entry_point_pos_pos) ).
fof(rdn_digit_add_n5_n0_n5_n0,axiom,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n5_n0_n5_n0) ).
fof(rdn_digit_add_n2_n3_n5_n0,axiom,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n2_n3_n5_n0) ).
fof(sum_n2_n3_less_n6,conjecture,
! [X1] :
( sum(n2,n3,X1)
=> less(X1,n6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_n2_n3_less_n6) ).
fof(rdn5,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn5) ).
fof(unique_sum,axiom,
! [X1,X2,X15,X16] :
( ( sum(X1,X2,X16)
& sum(X1,X2,X15) )
=> X15 = X16 ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',unique_sum) ).
fof(rdn3,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn3) ).
fof(less_entry_point_pos_pos,axiom,
! [X1,X2,X10,X11] :
( ( rdn_positive_less(X10,X11)
& rdn_translate(X2,rdn_pos(X11))
& rdn_translate(X1,rdn_pos(X10)) )
=> less(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',less_entry_point_pos_pos) ).
fof(rdn2,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn2) ).
fof(rdn6,axiom,
rdn_translate(n6,rdn_pos(rdnn(n6))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn6) ).
fof(rdn_positive_less56,axiom,
rdn_positive_less(rdnn(n5),rdnn(n6)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less56) ).
fof(c_0_12,plain,
! [X99,X100,X101,X102,X103] :
( rdn_add_with_carry(rdnn(X99),rdnn(X100),rdnn(X101),rdnn(X102))
| ~ rdn_digit_add(rdnn(X103),rdnn(X99),rdnn(X102),rdnn(n0))
| ~ rdn_digit_add(rdnn(X100),rdnn(X101),rdnn(X103),rdnn(n0)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[add_digit_digit_digit])])]) ).
fof(c_0_13,plain,
! [X48,X49,X50,X51,X52,X53] :
( sum(X48,X49,X50)
| ~ rdn_translate(X50,rdn_pos(X53))
| ~ rdn_add_with_carry(rdnn(n0),X51,X52,X53)
| ~ rdn_translate(X49,rdn_pos(X52))
| ~ rdn_translate(X48,rdn_pos(X51)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sum_entry_point_pos_pos])])]) ).
cnf(c_0_14,plain,
( ~ rdn_digit_add(rdnn(X3),rdnn(X4),rdnn(X5),rdnn(n0))
| ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(X3),rdnn(n0))
| rdn_add_with_carry(rdnn(X4),rdnn(X1),rdnn(X2),rdnn(X5)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,plain,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(split_conjunct,[status(thm)],[rdn_digit_add_n5_n0_n5_n0]) ).
cnf(c_0_16,plain,
( ~ rdn_translate(X6,rdn_pos(X5))
| ~ rdn_add_with_carry(rdnn(n0),X2,X4,X5)
| ~ rdn_translate(X3,rdn_pos(X4))
| ~ rdn_translate(X1,rdn_pos(X2))
| sum(X1,X3,X6) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
( ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(n5),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X1),rdnn(X2),rdnn(n5)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(X4)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X5)))
| ~ rdn_translate(X3,rdn_pos(rdnn(n5)))
| ~ rdn_digit_add(rdnn(X4),rdnn(X5),rdnn(n5),rdnn(n0))
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,plain,
rdn_digit_add(rdnn(n2),rdnn(n3),rdnn(n5),rdnn(n0)),
inference(split_conjunct,[status(thm)],[rdn_digit_add_n2_n3_n5_n0]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1] :
( sum(n2,n3,X1)
=> less(X1,n6) ),
inference(assume_negation,[status(cth)],[sum_n2_n3_less_n6]) ).
cnf(c_0_21,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X2,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X3,rdn_pos(rdnn(n5)))
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(split_conjunct,[status(thm)],[rdn5]) ).
fof(c_0_23,plain,
! [X80,X81,X82,X83] :
( X82 = X83
| ~ sum(X80,X81,X83)
| ~ sum(X80,X81,X82) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unique_sum])])]) ).
fof(c_0_24,negated_conjecture,
( ~ less(esk1_0,n6)
& sum(n2,n3,esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
cnf(c_0_25,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X2,rdn_pos(rdnn(n3)))
| sum(X1,X2,n5) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(split_conjunct,[status(thm)],[rdn3]) ).
fof(c_0_27,plain,
! [X34,X35,X36,X37] :
( less(X34,X35)
| ~ rdn_positive_less(X36,X37)
| ~ rdn_translate(X35,rdn_pos(X37))
| ~ rdn_translate(X34,rdn_pos(X36)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less_entry_point_pos_pos])])]) ).
cnf(c_0_28,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,negated_conjecture,
sum(n2,n3,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n2)))
| sum(X1,n3,n5) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(split_conjunct,[status(thm)],[rdn2]) ).
cnf(c_0_32,plain,
( ~ rdn_positive_less(X2,X4)
| ~ rdn_translate(X3,rdn_pos(X4))
| ~ rdn_translate(X1,rdn_pos(X2))
| less(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
rdn_translate(n6,rdn_pos(rdnn(n6))),
inference(split_conjunct,[status(thm)],[rdn6]) ).
cnf(c_0_34,negated_conjecture,
( ~ sum(n2,n3,X1)
| X1 = esk1_0 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
sum(n2,n3,n5),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
( ~ rdn_translate(X1,rdn_pos(X2))
| ~ rdn_positive_less(X2,rdnn(n6))
| less(X1,n6) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
rdn_positive_less(rdnn(n5),rdnn(n6)),
inference(split_conjunct,[status(thm)],[rdn_positive_less56]) ).
cnf(c_0_38,negated_conjecture,
~ less(esk1_0,n6),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_39,negated_conjecture,
esk1_0 = n5,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
less(n5,n6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_22]),c_0_37])]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM345+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.41 % Computer : n017.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Mon Sep 21 02:18:11 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.48 Running first-order theorem proving
% 0.16/0.48 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.24/0.63 % Version: 3.5.1
% 0.24/0.63 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.24/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.63 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.24/0.63 % Starting new_bool_3 with 600s (2) cores
% 0.24/0.63 % Starting new_bool_1 with 600s (2) cores
% 0.24/0.63 % Starting sh5l with 300s (1) cores
% 0.24/0.63 % new_bool_1 with pid 1213490 completed with status 0
% 0.24/0.63 % Result found by new_bool_1
% 0.24/0.63 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.24/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.63 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.24/0.63 % Starting new_bool_3 with 600s (2) cores
% 0.24/0.63 % Starting new_bool_1 with 600s (2) cores
% 0.24/0.63 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/0.63 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/0.63 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.24/0.63 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.24/0.63 % Starting SubtermCWHack with 55s (1) cores
% 0.24/0.63 % Starting new_bool_1 with 61s (1) cores
% 0.24/0.63 % SubtermCWHack with pid 1213492 completed with status 0
% 0.24/0.63 % Result found by SubtermCWHack
% 0.24/0.63 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.24/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.63 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.24/0.63 % Starting new_bool_3 with 600s (2) cores
% 0.24/0.63 % Starting new_bool_1 with 600s (2) cores
% 0.24/0.63 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/0.63 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/0.63 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.24/0.63 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.24/0.63 % Starting SubtermCWHack with 55s (1) cores
% 0.24/0.63 % Preprocessing time : 0.002 s
% 0.24/0.63
% 0.24/0.63 % Proof found!
% 0.24/0.63 % SZS status Theorem
% 0.24/0.63 % SZS output start CNFRefutation
% See solution above
% 0.24/0.63 % Parsed axioms : 402
% 0.24/0.63 % Removed by relevancy pruning/SinE : 258
% 0.24/0.63 % Initial clauses : 147
% 0.24/0.63 % Removed in clause preprocessing : 0
% 1.13/0.63 % Initial clauses in saturation : 147
% 1.13/0.63 % Processed clauses : 1308
% 1.13/0.63 % ...of these trivial : 0
% 1.13/0.63 % ...subsumed : 350
% 1.13/0.63 % ...remaining for further processing : 958
% 1.13/0.63 % Other redundant clauses eliminated : 1
% 1.13/0.63 % Clauses deleted for lack of memory : 0
% 1.13/0.63 % Backward-subsumed : 39
% 1.13/0.63 % Backward-rewritten : 6
% 1.13/0.63 % Generated clauses : 2086
% 1.13/0.63 % ...of the previous two non-redundant : 2068
% 1.13/0.63 % ...aggressively subsumed : 0
% 1.13/0.63 % Contextual simplify-reflections : 0
% 1.13/0.63 % Paramodulations : 2083
% 1.13/0.63 % Factorizations : 2
% 1.13/0.63 % NegExts : 0
% 1.13/0.63 % Equation resolutions : 1
% 1.13/0.63 % Disequality decompositions : 0
% 1.13/0.63 % Total rewrite steps : 39
% 1.13/0.63 % ...of those cached : 15
% 1.13/0.63 % Propositional unsat checks : 0
% 1.13/0.63 % Propositional check models : 0
% 1.13/0.63 % Propositional check unsatisfiable : 0
% 1.13/0.63 % Propositional clauses : 0
% 1.13/0.63 % Propositional clauses after purity: 0
% 1.13/0.63 % Propositional unsat core size : 0
% 1.13/0.63 % Propositional preprocessing time : 0.000
% 1.13/0.63 % Propositional encoding time : 0.000
% 1.13/0.63 % Propositional solver time : 0.000
% 1.13/0.63 % Success case prop preproc time : 0.000
% 1.13/0.63 % Success case prop encoding time : 0.000
% 1.13/0.63 % Success case prop solver time : 0.000
% 1.13/0.63 % Current number of processed clauses : 912
% 1.13/0.63 % Positive orientable unit clauses : 173
% 1.13/0.63 % Positive unorientable unit clauses: 0
% 1.13/0.63 % Negative unit clauses : 68
% 1.13/0.63 % Non-unit-clauses : 671
% 1.13/0.63 % Current number of unprocessed clauses: 903
% 1.13/0.63 % ...number of literals in the above : 4671
% 1.13/0.63 % Current number of archived formulas : 0
% 1.13/0.63 % Current number of archived clauses : 45
% 1.13/0.63 % Clause-clause subsumption calls (NU) : 102199
% 1.13/0.63 % Rec. Clause-clause subsumption calls : 63624
% 1.13/0.63 % Non-unit clause-clause subsumptions : 199
% 1.13/0.63 % Unit Clause-clause subsumption calls : 5179
% 1.13/0.63 % Rewrite failures with RHS unbound : 0
% 1.13/0.63 % BW rewrite match attempts : 3
% 1.13/0.63 % BW rewrite match successes : 1
% 1.13/0.63 % Condensation attempts : 0
% 1.13/0.63 % Condensation successes : 0
% 1.13/0.63 % Termbank termtop insertions : 64241
% 1.13/0.63 % Search garbage collected termcells : 1851
% 1.13/0.63
% 1.13/0.63 % -------------------------------------------------
% 1.13/0.63 % User time : 0.102 s
% 1.13/0.63 % System time : 0.009 s
% 1.13/0.63 % Total time : 0.111 s
% 1.13/0.63 % Maximum resident set size: 4508 pages
% 1.13/0.63
% 1.13/0.63 % -------------------------------------------------
% 1.13/0.63 % User time : 0.205 s
% 1.13/0.63 % System time : 0.026 s
% 1.13/0.63 % Total time : 0.231 s
% 1.13/0.63 % Maximum resident set size: 5120 pages
% 1.13/0.63 % E exiting
%------------------------------------------------------------------------------