%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM344+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 : n018.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 0.62s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 15 unt; 0 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 81 ( 37 ~; 33 |; 8 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 68 ( 0 sgn 32 !; 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(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_n9_n0_n9_n0,axiom,
rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(n9),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n9_n0_n9_n0) ).
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(rdn_digit_add_n8_n1_n9_n0,axiom,
rdn_digit_add(rdnn(n8),rdnn(n1),rdnn(n9),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n8_n1_n9_n0) ).
fof(exist_bigger_plus_one,conjecture,
? [X1,X2] :
( less(X1,X2)
& sum(X1,n1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exist_bigger_plus_one) ).
fof(rdn9,axiom,
rdn_translate(n9,rdn_pos(rdnn(n9))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn9) ).
fof(rdn8,axiom,
rdn_translate(n8,rdn_pos(rdnn(n8))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn8) ).
fof(rdn_positive_less89,axiom,
rdn_positive_less(rdnn(n8),rdnn(n9)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less89) ).
fof(rdn1,axiom,
rdn_translate(n1,rdn_pos(rdnn(n1))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn1) ).
fof(c_0_10,plain,
! [X111,X112,X113,X114,X115] :
( rdn_add_with_carry(rdnn(X111),rdnn(X112),rdnn(X113),rdnn(X114))
| ~ rdn_digit_add(rdnn(X115),rdnn(X111),rdnn(X114),rdnn(n0))
| ~ rdn_digit_add(rdnn(X112),rdnn(X113),rdnn(X115),rdnn(n0)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[add_digit_digit_digit])])]) ).
fof(c_0_11,plain,
! [X54,X55,X56,X57,X58,X59] :
( sum(X54,X55,X56)
| ~ rdn_translate(X56,rdn_pos(X59))
| ~ rdn_add_with_carry(rdnn(n0),X57,X58,X59)
| ~ rdn_translate(X55,rdn_pos(X58))
| ~ rdn_translate(X54,rdn_pos(X57)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sum_entry_point_pos_pos])])]) ).
cnf(c_0_12,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_10]) ).
cnf(c_0_13,plain,
rdn_digit_add(rdnn(n9),rdnn(n0),rdnn(n9),rdnn(n0)),
inference(split_conjunct,[status(thm)],[rdn_digit_add_n9_n0_n9_n0]) ).
cnf(c_0_14,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_11]) ).
cnf(c_0_15,plain,
( ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(n9),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X1),rdnn(X2),rdnn(n9)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_16,plain,
! [X35,X36,X37,X38] :
( less(X35,X36)
| ~ rdn_positive_less(X37,X38)
| ~ rdn_translate(X36,rdn_pos(X38))
| ~ rdn_translate(X35,rdn_pos(X37)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less_entry_point_pos_pos])])]) ).
cnf(c_0_17,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(X4)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X5)))
| ~ rdn_translate(X3,rdn_pos(rdnn(n9)))
| ~ rdn_digit_add(rdnn(X4),rdnn(X5),rdnn(n9),rdnn(n0))
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
rdn_digit_add(rdnn(n8),rdnn(n1),rdnn(n9),rdnn(n0)),
inference(split_conjunct,[status(thm)],[rdn_digit_add_n8_n1_n9_n0]) ).
fof(c_0_19,negated_conjecture,
~ ? [X1,X2] :
( less(X1,X2)
& sum(X1,n1,X2) ),
inference(assume_negation,[status(cth)],[exist_bigger_plus_one]) ).
cnf(c_0_20,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_16]) ).
cnf(c_0_21,plain,
rdn_translate(n9,rdn_pos(rdnn(n9))),
inference(split_conjunct,[status(thm)],[rdn9]) ).
cnf(c_0_22,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n8)))
| ~ rdn_translate(X2,rdn_pos(rdnn(n1)))
| ~ rdn_translate(X3,rdn_pos(rdnn(n9)))
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_23,negated_conjecture,
! [X33,X34] :
( ~ less(X33,X34)
| ~ sum(X33,n1,X34) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_24,plain,
( ~ rdn_translate(X1,rdn_pos(X2))
| ~ rdn_positive_less(X2,rdnn(n9))
| less(X1,n9) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
inference(split_conjunct,[status(thm)],[rdn8]) ).
cnf(c_0_26,plain,
rdn_positive_less(rdnn(n8),rdnn(n9)),
inference(split_conjunct,[status(thm)],[rdn_positive_less89]) ).
cnf(c_0_27,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n8)))
| ~ rdn_translate(X2,rdn_pos(rdnn(n1)))
| sum(X1,X2,n9) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_28,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(split_conjunct,[status(thm)],[rdn1]) ).
cnf(c_0_29,negated_conjecture,
( ~ less(X1,X2)
| ~ sum(X1,n1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
less(n8,n9),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_31,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n8)))
| sum(X1,n1,n9) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
~ sum(n8,n1,n9),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_25]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM344+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n018.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 02:24:58 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.51 Running first-order theorem proving
% 0.24/0.51 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
% 0.24/0.62 % Version: 3.5.1
% 0.24/0.62 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.24/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.62 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.24/0.62 % Starting new_bool_3 with 600s (2) cores
% 0.24/0.62 % Starting new_bool_1 with 600s (2) cores
% 0.24/0.62 % Starting sh5l with 300s (1) cores
% 0.24/0.62 % sh5l with pid 762321 completed with status 0
% 0.24/0.62 % Result found by sh5l
% 0.24/0.62 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.24/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.62 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.24/0.62 % Starting new_bool_3 with 600s (2) cores
% 0.24/0.62 % Starting new_bool_1 with 600s (2) cores
% 0.24/0.62 % Starting sh5l with 300s (1) cores
% 0.24/0.62 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.24/0.62 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.24/0.62 % Search class: FGHSF-FFLM21-SFFFFFNN
% 0.24/0.62 % partial match(1): FGHSF-FFMM21-SFFFFFNN
% 0.24/0.62 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.62 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.62 % SubtermCWHack with pid 762324 completed with status 0
% 0.24/0.62 % Result found by SubtermCWHack
% 0.24/0.62 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.24/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.62 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.24/0.62 % Starting new_bool_3 with 600s (2) cores
% 0.24/0.62 % Starting new_bool_1 with 600s (2) cores
% 0.24/0.62 % Starting sh5l with 300s (1) cores
% 0.24/0.62 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.24/0.62 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.24/0.62 % Search class: FGHSF-FFLM21-SFFFFFNN
% 0.24/0.62 % partial match(1): FGHSF-FFMM21-SFFFFFNN
% 0.24/0.62 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.62 % Starting SubtermCWHack with 28s (1) cores
% 0.24/0.62 % Preprocessing time : 0.002 s
% 0.24/0.62
% 0.24/0.62 % Proof found!
% 0.24/0.62 % SZS status Theorem
% 0.24/0.62 % SZS output start CNFRefutation
% See solution above
% 0.24/0.62 % Parsed axioms : 402
% 0.24/0.62 % Removed by relevancy pruning/SinE : 247
% 0.24/0.62 % Initial clauses : 159
% 0.24/0.62 % Removed in clause preprocessing : 0
% 0.24/0.62 % Initial clauses in saturation : 159
% 0.24/0.62 % Processed clauses : 944
% 0.24/0.62 % ...of these trivial : 0
% 0.24/0.62 % ...subsumed : 404
% 0.24/0.62 % ...remaining for further processing : 540
% 0.24/0.62 % Other redundant clauses eliminated : 2
% 0.24/0.62 % Clauses deleted for lack of memory : 0
% 0.24/0.62 % Backward-subsumed : 0
% 0.24/0.62 % Backward-rewritten : 0
% 0.24/0.62 % Generated clauses : 1022
% 0.24/0.62 % ...of the previous two non-redundant : 998
% 0.24/0.62 % ...aggressively subsumed : 0
% 0.24/0.62 % Contextual simplify-reflections : 0
% 0.24/0.62 % Paramodulations : 1018
% 0.24/0.62 % Factorizations : 2
% 0.24/0.62 % NegExts : 0
% 0.24/0.62 % Equation resolutions : 2
% 0.24/0.62 % Disequality decompositions : 0
% 0.24/0.62 % Total rewrite steps : 27
% 0.24/0.62 % ...of those cached : 9
% 0.24/0.62 % Propositional unsat checks : 0
% 0.24/0.62 % Propositional check models : 0
% 0.24/0.62 % Propositional check unsatisfiable : 0
% 0.24/0.62 % Propositional clauses : 0
% 0.24/0.62 % Propositional clauses after purity: 0
% 0.24/0.62 % Propositional unsat core size : 0
% 0.24/0.62 % Propositional preprocessing time : 0.000
% 0.24/0.62 % Propositional encoding time : 0.000
% 0.24/0.62 % Propositional solver time : 0.000
% 0.24/0.62 % Success case prop preproc time : 0.000
% 0.24/0.62 % Success case prop encoding time : 0.000
% 0.24/0.62 % Success case prop solver time : 0.000
% 0.24/0.62 % Current number of processed clauses : 538
% 0.24/0.62 % Positive orientable unit clauses : 139
% 0.24/0.62 % Positive unorientable unit clauses: 0
% 0.24/0.62 % Negative unit clauses : 74
% 0.24/0.62 % Non-unit-clauses : 325
% 0.24/0.62 % Current number of unprocessed clauses: 213
% 0.24/0.62 % ...number of literals in the above : 1075
% 0.24/0.62 % Current number of archived formulas : 0
% 0.24/0.62 % Current number of archived clauses : 0
% 0.24/0.62 % Clause-clause subsumption calls (NU) : 33422
% 0.24/0.62 % Rec. Clause-clause subsumption calls : 28246
% 0.24/0.62 % Non-unit clause-clause subsumptions : 230
% 0.24/0.62 % Unit Clause-clause subsumption calls : 5197
% 0.24/0.62 % Rewrite failures with RHS unbound : 0
% 0.24/0.62 % BW rewrite match attempts : 0
% 0.24/0.62 % BW rewrite match successes : 0
% 0.24/0.62 % Condensation attempts : 0
% 0.24/0.62 % Condensation successes : 0
% 0.24/0.62 % Termbank termtop insertions : 28986
% 0.24/0.62 % Search garbage collected termcells : 1860
% 0.24/0.62
% 0.24/0.62 % -------------------------------------------------
% 0.24/0.62 % User time : 0.047 s
% 0.24/0.62 % System time : 0.008 s
% 0.24/0.62 % Total time : 0.055 s
% 0.24/0.62 % Maximum resident set size: 4508 pages
% 0.24/0.62
% 0.24/0.62 % -------------------------------------------------
% 0.24/0.62 % User time : 0.059 s
% 0.24/0.62 % System time : 0.014 s
% 0.24/0.62 % Total time : 0.073 s
% 0.24/0.62 % Maximum resident set size: 5120 pages
% 0.24/0.62 % E exiting
%------------------------------------------------------------------------------