%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM325+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 01:51:38 PM UTC 2026
% Result : Theorem 0.57s 0.73s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 22 unt; 0 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 87 ( 41 ~; 37 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-1 aty)
% Number of variables : 63 ( 1 sgn 29 !; 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/sandbox/benchmark/Axioms/NUM005+2.ax',add_digit_digit_digit) ).
fof(sum_entry_point_pos_neg_2,axiom,
! [X1,X2,X3,X10,X11,X12] :
( ( rdn_translate(X3,rdn_pos(X12))
& rdn_add_with_carry(rdnn(n0),X11,X12,X10)
& rdn_positive_less(X11,X10)
& rdn_translate(X2,rdn_neg(X11))
& rdn_translate(X1,rdn_pos(X10)) )
=> sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',sum_entry_point_pos_neg_2) ).
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(rdn_positive_less_transitivity,axiom,
! [X1,X2,X3] :
( ( rdn_positive_less(rdnn(X2),rdnn(X3))
& rdn_positive_less(rdnn(X1),rdnn(X2)) )
=> rdn_positive_less(rdnn(X1),rdnn(X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less_transitivity) ).
fof(rdn5,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn5) ).
fof(sum_what_nn2_n3,conjecture,
? [X1] : sum(X1,nn2,n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_what_nn2_n3) ).
fof(rdn_positive_less45,axiom,
rdn_positive_less(rdnn(n4),rdnn(n5)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less45) ).
fof(rdn3,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn3) ).
fof(rdnn2,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdnn2) ).
fof(rdn_positive_less34,axiom,
rdn_positive_less(rdnn(n3),rdnn(n4)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less34) ).
fof(rdn_positive_less23,axiom,
rdn_positive_less(rdnn(n2),rdnn(n3)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less23) ).
fof(c_0_12,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_13,plain,
! [X52,X53,X54,X55,X56,X57] :
( sum(X52,X53,X54)
| ~ rdn_translate(X54,rdn_pos(X57))
| ~ rdn_add_with_carry(rdnn(n0),X56,X57,X55)
| ~ rdn_positive_less(X56,X55)
| ~ rdn_translate(X53,rdn_neg(X56))
| ~ rdn_translate(X52,rdn_pos(X55)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sum_entry_point_pos_neg_2])])]) ).
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),X4,X5,X2)
| ~ rdn_positive_less(X4,X2)
| ~ rdn_translate(X3,rdn_neg(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(X2,rdn_neg(rdnn(X4)))
| ~ rdn_translate(X3,rdn_pos(rdnn(X5)))
| ~ rdn_translate(X1,rdn_pos(rdnn(n5)))
| ~ rdn_positive_less(rdnn(X4),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,plain,
! [X117,X118,X119] :
( rdn_positive_less(rdnn(X117),rdnn(X119))
| ~ rdn_positive_less(rdnn(X118),rdnn(X119))
| ~ rdn_positive_less(rdnn(X117),rdnn(X118)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rdn_positive_less_transitivity])])]) ).
cnf(c_0_21,plain,
( ~ rdn_translate(X2,rdn_neg(rdnn(n2)))
| ~ rdn_translate(X3,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X1,rdn_pos(rdnn(n5)))
| ~ rdn_positive_less(rdnn(n2),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,negated_conjecture,
~ ? [X1] : sum(X1,nn2,n3),
inference(assume_negation,[status(cth)],[sum_what_nn2_n3]) ).
cnf(c_0_24,plain,
( ~ rdn_positive_less(rdnn(X2),rdnn(X3))
| ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| rdn_positive_less(rdnn(X1),rdnn(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(split_conjunct,[status(thm)],[rdn_positive_less45]) ).
cnf(c_0_26,plain,
( ~ rdn_translate(X1,rdn_neg(rdnn(n2)))
| ~ rdn_translate(X2,rdn_pos(rdnn(n3)))
| ~ rdn_positive_less(rdnn(n2),rdnn(n5))
| sum(n5,X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(split_conjunct,[status(thm)],[rdn3]) ).
fof(c_0_28,negated_conjecture,
! [X33] : ~ sum(X33,nn2,n3),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
cnf(c_0_29,plain,
( ~ rdn_positive_less(rdnn(X1),rdnn(n4))
| rdn_positive_less(rdnn(X1),rdnn(n5)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
( ~ rdn_translate(X1,rdn_neg(rdnn(n2)))
| ~ rdn_positive_less(rdnn(n2),rdnn(n5))
| sum(n5,X1,n3) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(split_conjunct,[status(thm)],[rdnn2]) ).
cnf(c_0_32,negated_conjecture,
~ sum(X1,nn2,n3),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,plain,
( ~ rdn_positive_less(rdnn(X1),rdnn(X2))
| ~ rdn_positive_less(rdnn(X2),rdnn(n4))
| rdn_positive_less(rdnn(X1),rdnn(n5)) ),
inference(spm,[status(thm)],[c_0_24,c_0_29]) ).
cnf(c_0_34,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(split_conjunct,[status(thm)],[rdn_positive_less34]) ).
cnf(c_0_35,plain,
~ rdn_positive_less(rdnn(n2),rdnn(n5)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_36,plain,
( ~ rdn_positive_less(rdnn(X1),rdnn(n3))
| rdn_positive_less(rdnn(X1),rdnn(n5)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(split_conjunct,[status(thm)],[rdn_positive_less23]) ).
cnf(c_0_38,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM325+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.45 % Computer : n018.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Mon Sep 21 02:24:28 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 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
% 0.57/0.73 % Version: 3.5.1
% 0.57/0.73 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.57/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.73 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.57/0.73 % Starting new_bool_3 with 600s (2) cores
% 0.57/0.73 % Starting new_bool_1 with 600s (2) cores
% 0.57/0.73 % Starting sh5l with 300s (1) cores
% 0.57/0.73 % new_bool_3 with pid 761493 completed with status 0
% 0.57/0.73 % Result found by new_bool_3
% 0.57/0.73 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.57/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.73 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.57/0.73 % Starting new_bool_3 with 600s (2) cores
% 0.57/0.73 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.57/0.73 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.57/0.73 % Search class: FHUSF-FFMM21-SFFFFFNN
% 0.57/0.73 % partial match(1): FHUNF-FFMM21-SFFFFFNN
% 0.57/0.73 % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 0.57/0.73 % Starting SubtermCWHack with 61s (1) cores
% 0.57/0.73 % Starting SAT001_MinMin_p005000_rr_RG with 361s (1) cores
% 0.57/0.73 % SAT001_MinMin_p005000_rr_RG with pid 761499 completed with status 0
% 0.57/0.73 % Result found by SAT001_MinMin_p005000_rr_RG
% 0.57/0.73 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.57/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.73 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.57/0.73 % Starting new_bool_3 with 600s (2) cores
% 0.57/0.73 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.57/0.73 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.57/0.73 % Search class: FHUSF-FFMM21-SFFFFFNN
% 0.57/0.73 % partial match(1): FHUNF-FFMM21-SFFFFFNN
% 0.57/0.73 % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 0.57/0.73 % Starting SubtermCWHack with 61s (1) cores
% 0.57/0.73 % Starting SAT001_MinMin_p005000_rr_RG with 361s (1) cores
% 0.57/0.73 % Preprocessing time : 0.002 s
% 0.57/0.73 % Presaturation interreduction done
% 0.57/0.73
% 0.57/0.73 % Proof found!
% 0.57/0.73 % SZS status Theorem
% 0.57/0.73 % SZS output start CNFRefutation
% See solution above
% 0.57/0.73 % Parsed axioms : 402
% 0.57/0.73 % Removed by relevancy pruning/SinE : 261
% 0.57/0.73 % Initial clauses : 141
% 0.57/0.73 % Removed in clause preprocessing : 0
% 0.57/0.73 % Initial clauses in saturation : 141
% 0.57/0.73 % Processed clauses : 1495
% 0.57/0.73 % ...of these trivial : 0
% 0.57/0.73 % ...subsumed : 252
% 0.57/0.73 % ...remaining for further processing : 1243
% 0.57/0.73 % Other redundant clauses eliminated : 0
% 0.57/0.73 % Clauses deleted for lack of memory : 0
% 0.57/0.73 % Backward-subsumed : 26
% 0.57/0.73 % Backward-rewritten : 0
% 0.57/0.73 % Generated clauses : 2221
% 0.57/0.73 % ...of the previous two non-redundant : 2217
% 0.57/0.73 % ...aggressively subsumed : 0
% 0.57/0.73 % Contextual simplify-reflections : 0
% 0.57/0.73 % Paramodulations : 2221
% 0.57/0.73 % Factorizations : 0
% 0.57/0.73 % NegExts : 0
% 0.57/0.73 % Equation resolutions : 0
% 0.57/0.73 % Disequality decompositions : 0
% 0.57/0.73 % Total rewrite steps : 10
% 0.57/0.73 % ...of those cached : 4
% 0.57/0.73 % Propositional unsat checks : 0
% 0.57/0.73 % Propositional check models : 0
% 0.57/0.73 % Propositional check unsatisfiable : 0
% 0.57/0.73 % Propositional clauses : 0
% 0.57/0.73 % Propositional clauses after purity: 0
% 0.57/0.73 % Propositional unsat core size : 0
% 0.57/0.73 % Propositional preprocessing time : 0.000
% 0.57/0.73 % Propositional encoding time : 0.000
% 0.57/0.73 % Propositional solver time : 0.000
% 0.57/0.73 % Success case prop preproc time : 0.000
% 0.57/0.73 % Success case prop encoding time : 0.000
% 0.57/0.73 % Success case prop solver time : 0.000
% 0.57/0.73 % Current number of processed clauses : 1076
% 0.57/0.73 % Positive orientable unit clauses : 176
% 0.57/0.73 % Positive unorientable unit clauses: 0
% 0.57/0.73 % Negative unit clauses : 2
% 0.57/0.73 % Non-unit-clauses : 898
% 0.57/0.73 % Current number of unprocessed clauses: 1003
% 0.57/0.73 % ...number of literals in the above : 4927
% 0.57/0.73 % Current number of archived formulas : 0
% 0.57/0.73 % Current number of archived clauses : 167
% 0.57/0.73 % Clause-clause subsumption calls (NU) : 258958
% 0.57/0.73 % Rec. Clause-clause subsumption calls : 107200
% 0.57/0.73 % Non-unit clause-clause subsumptions : 271
% 0.57/0.73 % Unit Clause-clause subsumption calls : 221
% 0.57/0.73 % Rewrite failures with RHS unbound : 0
% 0.57/0.73 % BW rewrite match attempts : 0
% 0.57/0.73 % BW rewrite match successes : 0
% 0.57/0.73 % Condensation attempts : 0
% 0.57/0.73 % Condensation successes : 0
% 0.57/0.73 % Termbank termtop insertions : 75681
% 0.57/0.73 % Search garbage collected termcells : 1762
% 0.57/0.73
% 0.57/0.73 % -------------------------------------------------
% 0.57/0.73 % User time : 0.156 s
% 0.57/0.73 % System time : 0.007 s
% 0.57/0.73 % Total time : 0.163 s
% 0.57/0.73 % Maximum resident set size: 4764 pages
% 0.57/0.73
% 0.57/0.73 % -------------------------------------------------
% 0.57/0.73 % User time : 0.317 s
% 0.57/0.73 % System time : 0.021 s
% 0.57/0.73 % Total time : 0.338 s
% 0.57/0.73 % Maximum resident set size: 5120 pages
% 0.57/0.73 % E exiting
%------------------------------------------------------------------------------