%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM330+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 : n019.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 01:44:42 PM UTC 2026
% Result : Theorem 0.21s 0.57s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 11 unt; 0 def)
% Number of atoms : 58 ( 8 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 60 ( 27 ~; 23 |; 8 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 49 ( 0 sgn 24 !; 4 ?)
% 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(rdn_digit_add_n8_n0_n8_n0,axiom,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n8_n0_n8_n0) ).
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_n4_n4_n8_n0,axiom,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n4_n4_n8_n0) ).
fof(sum_n4_n4_n8,conjecture,
? [X1,X2] :
( X2 = n4
& X1 = n4
& sum(X1,X2,n8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_n4_n4_n8) ).
fof(rdn8,axiom,
rdn_translate(n8,rdn_pos(rdnn(n8))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn8) ).
fof(rdn4,axiom,
rdn_translate(n4,rdn_pos(rdnn(n4))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn4) ).
fof(c_0_7,plain,
! [X79,X80,X81,X82,X83] :
( rdn_add_with_carry(rdnn(X79),rdnn(X80),rdnn(X81),rdnn(X82))
| ~ rdn_digit_add(rdnn(X83),rdnn(X79),rdnn(X82),rdnn(n0))
| ~ rdn_digit_add(rdnn(X80),rdnn(X81),rdnn(X83),rdnn(n0)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[add_digit_digit_digit])])]) ).
cnf(c_0_8,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_7]) ).
cnf(c_0_9,plain,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
inference(split_conjunct,[status(thm)],[rdn_digit_add_n8_n0_n8_n0]) ).
fof(c_0_10,plain,
! [X35,X36,X37,X38,X39,X40] :
( sum(X35,X36,X37)
| ~ rdn_translate(X37,rdn_pos(X40))
| ~ rdn_add_with_carry(rdnn(n0),X38,X39,X40)
| ~ rdn_translate(X36,rdn_pos(X39))
| ~ rdn_translate(X35,rdn_pos(X38)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sum_entry_point_pos_pos])])]) ).
cnf(c_0_11,plain,
( ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(n8),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X1),rdnn(X2),rdnn(n8)) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
inference(split_conjunct,[status(thm)],[rdn_digit_add_n4_n4_n8_n0]) ).
cnf(c_0_13,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_10]) ).
cnf(c_0_14,plain,
rdn_add_with_carry(rdnn(n0),rdnn(n4),rdnn(n4),rdnn(n8)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_15,negated_conjecture,
~ ? [X1,X2] :
( X2 = n4
& X1 = n4
& sum(X1,X2,n8) ),
inference(assume_negation,[status(cth)],[sum_n4_n4_n8]) ).
cnf(c_0_16,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n4)))
| ~ rdn_translate(X2,rdn_pos(rdnn(n4)))
| ~ rdn_translate(X3,rdn_pos(rdnn(n8)))
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
inference(split_conjunct,[status(thm)],[rdn8]) ).
fof(c_0_18,negated_conjecture,
! [X33,X34] :
( X34 != n4
| X33 != n4
| ~ sum(X33,X34,n8) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
cnf(c_0_19,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n4)))
| ~ rdn_translate(X2,rdn_pos(rdnn(n4)))
| sum(X1,X2,n8) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(split_conjunct,[status(thm)],[rdn4]) ).
cnf(c_0_21,negated_conjecture,
( X2 != n4
| X1 != n4
| ~ sum(X1,X2,n8) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n4)))
| sum(X1,n4,n8) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
~ sum(n4,n4,n8),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_21])]) ).
cnf(c_0_24,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_20]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM330+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 02:22:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.44 Running first-order theorem proving
% 0.10/0.45 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
% 0.21/0.57 % Version: 3.5.1
% 0.21/0.57 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.21/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.57 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.21/0.57 % Starting new_bool_3 with 600s (2) cores
% 0.21/0.57 % Starting new_bool_1 with 600s (2) cores
% 0.21/0.57 % Starting sh5l with 300s (1) cores
% 0.21/0.57 % new_bool_1 with pid 1481566 completed with status 0
% 0.21/0.57 % Result found by new_bool_1
% 0.21/0.57 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.21/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.57 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.21/0.57 % Starting new_bool_3 with 600s (2) cores
% 0.21/0.57 % Starting new_bool_1 with 600s (2) cores
% 0.21/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.57 % Search class: FHHSF-FFMM21-SFFFFFNN
% 0.21/0.57 % partial match(1): FGHSF-FFMM21-SFFFFFNN
% 0.21/0.57 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.21/0.57 % Starting SubtermCWHack with 55s (1) cores
% 0.21/0.57 % Starting new_bool_1 with 61s (1) cores
% 0.21/0.57 % new_bool_1 with pid 1481569 completed with status 0
% 0.21/0.57 % Result found by new_bool_1
% 0.21/0.57 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.21/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.57 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.21/0.57 % Starting new_bool_3 with 600s (2) cores
% 0.21/0.57 % Starting new_bool_1 with 600s (2) cores
% 0.21/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.21/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.57 % Search class: FHHSF-FFMM21-SFFFFFNN
% 0.21/0.57 % partial match(1): FGHSF-FFMM21-SFFFFFNN
% 0.21/0.57 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.21/0.57 % Starting SubtermCWHack with 55s (1) cores
% 0.21/0.57 % Starting new_bool_1 with 61s (1) cores
% 0.21/0.57 % Preprocessing time : 0.004 s
% 0.21/0.57 % Presaturation interreduction done
% 0.21/0.57
% 0.21/0.57 % Proof found!
% 0.21/0.57 % SZS status Theorem
% 0.21/0.57 % SZS output start CNFRefutation
% See solution above
% 0.21/0.57 % Parsed axioms : 402
% 0.21/0.57 % Removed by relevancy pruning/SinE : 262
% 0.21/0.57 % Initial clauses : 140
% 0.21/0.57 % Removed in clause preprocessing : 0
% 0.21/0.57 % Initial clauses in saturation : 140
% 0.21/0.57 % Processed clauses : 604
% 0.21/0.57 % ...of these trivial : 0
% 0.21/0.57 % ...subsumed : 0
% 0.21/0.57 % ...remaining for further processing : 604
% 0.21/0.57 % Other redundant clauses eliminated : 2
% 0.21/0.57 % Clauses deleted for lack of memory : 0
% 0.21/0.57 % Backward-subsumed : 5
% 0.21/0.57 % Backward-rewritten : 5
% 0.21/0.57 % Generated clauses : 718
% 0.21/0.57 % ...of the previous two non-redundant : 628
% 0.21/0.58 % ...aggressively subsumed : 0
% 0.21/0.58 % Contextual simplify-reflections : 0
% 0.21/0.58 % Paramodulations : 717
% 0.21/0.58 % Factorizations : 0
% 0.21/0.58 % NegExts : 0
% 0.21/0.58 % Equation resolutions : 2
% 0.21/0.58 % Disequality decompositions : 0
% 0.21/0.58 % Total rewrite steps : 122
% 0.21/0.58 % ...of those cached : 80
% 0.21/0.58 % Propositional unsat checks : 0
% 0.21/0.58 % Propositional check models : 0
% 0.21/0.58 % Propositional check unsatisfiable : 0
% 0.21/0.58 % Propositional clauses : 0
% 0.21/0.58 % Propositional clauses after purity: 0
% 0.21/0.58 % Propositional unsat core size : 0
% 0.21/0.58 % Propositional preprocessing time : 0.000
% 0.21/0.58 % Propositional encoding time : 0.000
% 0.21/0.58 % Propositional solver time : 0.000
% 0.21/0.58 % Success case prop preproc time : 0.000
% 0.21/0.58 % Success case prop encoding time : 0.000
% 0.21/0.58 % Success case prop solver time : 0.000
% 0.21/0.58 % Current number of processed clauses : 453
% 0.21/0.58 % Positive orientable unit clauses : 235
% 0.21/0.58 % Positive unorientable unit clauses: 0
% 0.21/0.58 % Negative unit clauses : 1
% 0.21/0.58 % Non-unit-clauses : 217
% 0.21/0.58 % Current number of unprocessed clauses: 304
% 0.21/0.58 % ...number of literals in the above : 829
% 0.21/0.58 % Current number of archived formulas : 0
% 0.21/0.58 % Current number of archived clauses : 150
% 0.21/0.58 % Clause-clause subsumption calls (NU) : 7271
% 0.21/0.58 % Rec. Clause-clause subsumption calls : 4564
% 0.21/0.58 % Non-unit clause-clause subsumptions : 5
% 0.21/0.58 % Unit Clause-clause subsumption calls : 25
% 0.21/0.58 % Rewrite failures with RHS unbound : 0
% 0.21/0.58 % BW rewrite match attempts : 1001
% 0.21/0.58 % BW rewrite match successes : 5
% 0.21/0.58 % Condensation attempts : 0
% 0.21/0.58 % Condensation successes : 0
% 0.21/0.58 % Termbank termtop insertions : 27312
% 0.21/0.58 % Search garbage collected termcells : 1786
% 0.21/0.58
% 0.21/0.58 % -------------------------------------------------
% 0.21/0.58 % User time : 0.076 s
% 0.21/0.58 % System time : 0.009 s
% 0.21/0.58 % Total time : 0.085 s
% 0.21/0.58 % Maximum resident set size: 4764 pages
% 0.21/0.58
% 0.21/0.58 % -------------------------------------------------
% 0.21/0.58 % User time : 0.131 s
% 0.21/0.58 % System time : 0.017 s
% 0.21/0.58 % Total time : 0.147 s
% 0.21/0.58 % Maximum resident set size: 4864 pages
% 0.21/0.58 % E exiting
%------------------------------------------------------------------------------