%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM329+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 0.19s 0.57s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 55 ( 26 ~; 23 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 50 ( 0 sgn 23 !; 2 ?)
% 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/sandbox2/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/sandbox2/benchmark/Axioms/NUM005+2.ax',sum_entry_point_pos_pos) ).
fof(rdn_digit_add_n0_n0_n0_n0,axiom,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n0_n0_n0_n0) ).
fof(rdn0,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn0) ).
fof(idempotent_element,conjecture,
? [X1] : sum(X1,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotent_element) ).
fof(c_0_5,plain,
! [X78,X79,X80,X81,X82] :
( rdn_add_with_carry(rdnn(X78),rdnn(X79),rdnn(X80),rdnn(X81))
| ~ rdn_digit_add(rdnn(X82),rdnn(X78),rdnn(X81),rdnn(n0))
| ~ rdn_digit_add(rdnn(X79),rdnn(X80),rdnn(X82),rdnn(n0)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[add_digit_digit_digit])])]) ).
fof(c_0_6,plain,
! [X34,X35,X36,X37,X38,X39] :
( sum(X34,X35,X36)
| ~ rdn_translate(X36,rdn_pos(X39))
| ~ rdn_add_with_carry(rdnn(n0),X37,X38,X39)
| ~ rdn_translate(X35,rdn_pos(X38))
| ~ rdn_translate(X34,rdn_pos(X37)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sum_entry_point_pos_pos])])]) ).
cnf(c_0_7,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_5]) ).
cnf(c_0_8,plain,
rdn_digit_add(rdnn(n0),rdnn(n0),rdnn(n0),rdnn(n0)),
inference(split_conjunct,[status(thm)],[rdn_digit_add_n0_n0_n0_n0]) ).
cnf(c_0_9,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_6]) ).
cnf(c_0_10,plain,
( ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(n0),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X1),rdnn(X2),rdnn(n0)) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(X4)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X5)))
| ~ rdn_translate(X3,rdn_pos(rdnn(n0)))
| ~ rdn_digit_add(rdnn(X4),rdnn(X5),rdnn(n0),rdnn(n0))
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n0)))
| ~ rdn_translate(X2,rdn_pos(rdnn(n0)))
| ~ rdn_translate(X3,rdn_pos(rdnn(n0)))
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_8]) ).
cnf(c_0_13,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(split_conjunct,[status(thm)],[rdn0]) ).
fof(c_0_14,negated_conjecture,
~ ? [X1] : sum(X1,X1,X1),
inference(assume_negation,[status(cth)],[idempotent_element]) ).
cnf(c_0_15,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n0)))
| ~ rdn_translate(X2,rdn_pos(rdnn(n0)))
| sum(X1,X2,n0) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_16,negated_conjecture,
! [X33] : ~ sum(X33,X33,X33),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
cnf(c_0_17,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n0)))
| sum(X1,n0,n0) ),
inference(spm,[status(thm)],[c_0_15,c_0_13]) ).
cnf(c_0_18,negated_conjecture,
~ sum(X1,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_13]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM329+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 02:27:08 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.43 Running first-order theorem proving
% 0.03/0.43 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/benchmark/theBenchmark.p
% 0.19/0.57 % Version: 3.5.1
% 0.19/0.57 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.19/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.57 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.19/0.57 % Starting new_bool_3 with 600s (2) cores
% 0.19/0.57 % Starting new_bool_1 with 600s (2) cores
% 0.19/0.57 % Starting sh5l with 300s (1) cores
% 0.19/0.57 % new_bool_1 with pid 1359693 completed with status 0
% 0.19/0.57 % Result found by new_bool_1
% 0.19/0.57 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.19/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.57 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.19/0.57 % Starting new_bool_3 with 600s (2) cores
% 0.19/0.57 % Starting new_bool_1 with 600s (2) cores
% 0.19/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.19/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.57 % Search class: FHUSF-FFMM21-SFFFFFNN
% 0.19/0.57 % partial match(1): FHUNF-FFMM21-SFFFFFNN
% 0.19/0.57 % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 0.19/0.57 % Starting SubtermCWHack with 61s (1) cores
% 0.19/0.57 % Starting SAT001_MinMin_p005000_rr_RG with 361s (1) cores
% 0.19/0.57 % SAT001_MinMin_p005000_rr_RG with pid 1359702 completed with status 0
% 0.19/0.57 % Result found by SAT001_MinMin_p005000_rr_RG
% 0.19/0.57 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.19/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.57 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.19/0.57 % Starting new_bool_3 with 600s (2) cores
% 0.19/0.57 % Starting new_bool_1 with 600s (2) cores
% 0.19/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.19/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.57 % Search class: FHUSF-FFMM21-SFFFFFNN
% 0.19/0.57 % partial match(1): FHUNF-FFMM21-SFFFFFNN
% 0.19/0.57 % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 0.19/0.57 % Starting SubtermCWHack with 61s (1) cores
% 0.19/0.57 % Starting SAT001_MinMin_p005000_rr_RG with 361s (1) cores
% 0.19/0.57 % Preprocessing time : 0.003 s
% 0.19/0.57 % Presaturation interreduction done
% 0.19/0.57
% 0.19/0.57 % Proof found!
% 0.19/0.57 % SZS status Theorem
% 0.19/0.57 % SZS output start CNFRefutation
% See solution above
% 0.19/0.57 % Parsed axioms : 402
% 0.19/0.57 % Removed by relevancy pruning/SinE : 262
% 0.19/0.57 % Initial clauses : 140
% 0.19/0.57 % Removed in clause preprocessing : 0
% 0.19/0.57 % Initial clauses in saturation : 140
% 0.19/0.57 % Processed clauses : 1023
% 0.19/0.57 % ...of these trivial : 0
% 0.19/0.57 % ...subsumed : 120
% 0.19/0.57 % ...remaining for further processing : 903
% 0.19/0.57 % Other redundant clauses eliminated : 0
% 0.19/0.57 % Clauses deleted for lack of memory : 0
% 0.19/0.57 % Backward-subsumed : 0
% 0.19/0.57 % Backward-rewritten : 0
% 0.19/0.57 % Generated clauses : 1318
% 0.19/0.57 % ...of the previous two non-redundant : 1317
% 0.19/0.57 % ...aggressively subsumed : 0
% 0.19/0.57 % Contextual simplify-reflections : 0
% 0.19/0.57 % Paramodulations : 1318
% 0.19/0.57 % Factorizations : 0
% 0.19/0.57 % NegExts : 0
% 0.19/0.57 % Equation resolutions : 0
% 0.19/0.57 % Disequality decompositions : 0
% 0.19/0.57 % Total rewrite steps : 0
% 0.19/0.57 % ...of those cached : 0
% 0.19/0.57 % Propositional unsat checks : 0
% 0.19/0.57 % Propositional check models : 0
% 0.19/0.57 % Propositional check unsatisfiable : 0
% 0.19/0.57 % Propositional clauses : 0
% 0.19/0.57 % Propositional clauses after purity: 0
% 0.19/0.57 % Propositional unsat core size : 0
% 0.19/0.57 % Propositional preprocessing time : 0.000
% 0.19/0.57 % Propositional encoding time : 0.000
% 0.19/0.57 % Propositional solver time : 0.000
% 0.19/0.57 % Success case prop preproc time : 0.000
% 0.19/0.57 % Success case prop encoding time : 0.000
% 0.19/0.57 % Success case prop solver time : 0.000
% 0.19/0.57 % Current number of processed clauses : 763
% 0.19/0.57 % Positive orientable unit clauses : 173
% 0.19/0.57 % Positive unorientable unit clauses: 0
% 0.19/0.57 % Negative unit clauses : 1
% 0.19/0.57 % Non-unit-clauses : 589
% 0.19/0.57 % Current number of unprocessed clauses: 574
% 0.19/0.57 % ...number of literals in the above : 2743
% 0.19/0.57 % Current number of archived formulas : 0
% 0.19/0.57 % Current number of archived clauses : 140
% 0.19/0.57 % Clause-clause subsumption calls (NU) : 80755
% 0.19/0.57 % Rec. Clause-clause subsumption calls : 49532
% 0.19/0.57 % Non-unit clause-clause subsumptions : 120
% 0.19/0.57 % Unit Clause-clause subsumption calls : 56
% 0.19/0.57 % Rewrite failures with RHS unbound : 0
% 0.19/0.57 % BW rewrite match attempts : 0
% 0.19/0.57 % BW rewrite match successes : 0
% 0.19/0.57 % Condensation attempts : 0
% 0.19/0.57 % Condensation successes : 0
% 0.19/0.57 % Termbank termtop insertions : 47389
% 0.19/0.57 % Search garbage collected termcells : 1766
% 0.19/0.57
% 0.19/0.57 % -------------------------------------------------
% 0.19/0.57 % User time : 0.087 s
% 0.19/0.57 % System time : 0.011 s
% 0.19/0.57 % Total time : 0.098 s
% 0.19/0.57 % Maximum resident set size: 4712 pages
% 0.19/0.57
% 0.19/0.57 % -------------------------------------------------
% 0.19/0.57 % User time : 0.171 s
% 0.19/0.57 % System time : 0.023 s
% 0.19/0.57 % Total time : 0.194 s
% 0.19/0.57 % Maximum resident set size: 5120 pages
% 0.19/0.57 % E exiting
%------------------------------------------------------------------------------