%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM317+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 : n003.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 01:44:40 PM UTC 2026
% Result : Theorem 1.82s 0.76s
% Output : CNFRefutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 40 ( 24 unt; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 84 ( 40 ~; 35 |; 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 : 57 ( 0 sgn 28 !; 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_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(sum_n5_nn2_n3,conjecture,
sum(n5,nn2,n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_n5_nn2_n3) ).
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(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(rdn_positive_less34,axiom,
rdn_positive_less(rdnn(n3),rdnn(n4)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',rdn_positive_less34) ).
fof(rdnn2,axiom,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdnn2) ).
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,
! [X77,X78,X79,X80,X81] :
( rdn_add_with_carry(rdnn(X77),rdnn(X78),rdnn(X79),rdnn(X80))
| ~ rdn_digit_add(rdnn(X81),rdnn(X77),rdnn(X80),rdnn(n0))
| ~ rdn_digit_add(rdnn(X78),rdnn(X79),rdnn(X81),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,
! [X51,X52,X53,X54,X55,X56] :
( sum(X51,X52,X53)
| ~ rdn_translate(X53,rdn_pos(X56))
| ~ rdn_add_with_carry(rdnn(n0),X55,X56,X54)
| ~ rdn_positive_less(X55,X54)
| ~ rdn_translate(X52,rdn_neg(X55))
| ~ rdn_translate(X51,rdn_pos(X54)) ),
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,negated_conjecture,
~ sum(n5,nn2,n3),
inference(assume_negation,[status(cth)],[sum_n5_nn2_n3]) ).
fof(c_0_21,plain,
! [X116,X117,X118] :
( rdn_positive_less(rdnn(X116),rdnn(X118))
| ~ rdn_positive_less(rdnn(X117),rdnn(X118))
| ~ rdn_positive_less(rdnn(X116),rdnn(X117)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rdn_positive_less_transitivity])])]) ).
cnf(c_0_22,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_23,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(split_conjunct,[status(thm)],[rdn5]) ).
fof(c_0_24,negated_conjecture,
~ sum(n5,nn2,n3),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
cnf(c_0_25,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_21]) ).
cnf(c_0_26,plain,
rdn_positive_less(rdnn(n4),rdnn(n5)),
inference(split_conjunct,[status(thm)],[rdn_positive_less45]) ).
cnf(c_0_27,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_22,c_0_23]) ).
cnf(c_0_28,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(split_conjunct,[status(thm)],[rdn3]) ).
fof(c_0_29,negated_conjecture,
~ sum(n5,nn2,n3),
inference(fof_nnf,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
( ~ rdn_positive_less(rdnn(X1),rdnn(n4))
| rdn_positive_less(rdnn(X1),rdnn(n5)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
rdn_positive_less(rdnn(n3),rdnn(n4)),
inference(split_conjunct,[status(thm)],[rdn_positive_less34]) ).
cnf(c_0_32,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_27,c_0_28]) ).
cnf(c_0_33,plain,
rdn_translate(nn2,rdn_neg(rdnn(n2))),
inference(split_conjunct,[status(thm)],[rdnn2]) ).
cnf(c_0_34,negated_conjecture,
~ sum(n5,nn2,n3),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
rdn_positive_less(rdnn(n3),rdnn(n5)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
~ rdn_positive_less(rdnn(n2),rdnn(n5)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_37,plain,
( ~ rdn_positive_less(rdnn(X1),rdnn(n3))
| rdn_positive_less(rdnn(X1),rdnn(n5)) ),
inference(spm,[status(thm)],[c_0_25,c_0_35]) ).
cnf(c_0_38,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(split_conjunct,[status(thm)],[rdn_positive_less23]) ).
cnf(c_0_39,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM317+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.33 % Computer : n003.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Mon Sep 21 02:23:32 UTC 2026
% 0.06/0.34 % CPUTime :
% 0.06/0.34 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 1.82/0.76 % Version: 3.5.1
% 1.82/0.76 % Preprocessing class: FSLMSMSLSSSNFFN.
% 1.82/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.82/0.76 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 1.82/0.76 % Starting new_bool_3 with 600s (2) cores
% 1.82/0.76 % Starting new_bool_1 with 600s (2) cores
% 1.82/0.76 % Starting sh5l with 300s (1) cores
% 1.82/0.76 % new_bool_1 with pid 3199505 completed with status 0
% 1.82/0.76 % Result found by new_bool_1
% 1.82/0.76 % Preprocessing class: FSLMSMSLSSSNFFN.
% 1.82/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.82/0.76 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 1.82/0.76 % Starting new_bool_3 with 600s (2) cores
% 1.82/0.76 % Starting new_bool_1 with 600s (2) cores
% 1.82/0.76 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.82/0.76 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.82/0.76 % Search class: FHUSF-FFMM21-SFFFFFNN
% 1.82/0.76 % partial match(1): FHUNF-FFMM21-SFFFFFNN
% 1.82/0.76 % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 1.82/0.76 % Starting SubtermCWHack with 61s (1) cores
% 1.82/0.76 % Starting SAT001_MinMin_p005000_rr_RG with 361s (1) cores
% 1.82/0.76 % SAT001_MinMin_p005000_rr_RG with pid 3199511 completed with status 0
% 1.82/0.76 % Result found by SAT001_MinMin_p005000_rr_RG
% 1.82/0.76 % Preprocessing class: FSLMSMSLSSSNFFN.
% 1.82/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.82/0.76 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 1.82/0.76 % Starting new_bool_3 with 600s (2) cores
% 1.82/0.76 % Starting new_bool_1 with 600s (2) cores
% 1.82/0.76 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.82/0.76 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.82/0.76 % Search class: FHUSF-FFMM21-SFFFFFNN
% 1.82/0.76 % partial match(1): FHUNF-FFMM21-SFFFFFNN
% 1.82/0.76 % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 1.82/0.76 % Starting SubtermCWHack with 61s (1) cores
% 1.82/0.76 % Starting SAT001_MinMin_p005000_rr_RG with 361s (1) cores
% 1.82/0.76 % Preprocessing time : 0.005 s
% 1.82/0.76 % Presaturation interreduction done
% 1.82/0.76
% 1.82/0.76 % Proof found!
% 1.82/0.76 % SZS status Theorem
% 1.82/0.76 % SZS output start CNFRefutation
% See solution above
% 1.82/0.76 % Parsed axioms : 402
% 1.82/0.76 % Removed by relevancy pruning/SinE : 261
% 1.82/0.76 % Initial clauses : 141
% 1.82/0.76 % Removed in clause preprocessing : 0
% 1.82/0.76 % Initial clauses in saturation : 141
% 1.82/0.76 % Processed clauses : 1529
% 1.82/0.76 % ...of these trivial : 0
% 1.82/0.76 % ...subsumed : 250
% 1.82/0.76 % ...remaining for further processing : 1279
% 1.82/0.76 % Other redundant clauses eliminated : 0
% 1.82/0.76 % Clauses deleted for lack of memory : 0
% 1.82/0.76 % Backward-subsumed : 28
% 1.82/0.76 % Backward-rewritten : 0
% 1.82/0.76 % Generated clauses : 2330
% 1.82/0.76 % ...of the previous two non-redundant : 2326
% 1.82/0.76 % ...aggressively subsumed : 0
% 1.82/0.76 % Contextual simplify-reflections : 0
% 1.82/0.76 % Paramodulations : 2330
% 1.82/0.76 % Factorizations : 0
% 1.82/0.76 % NegExts : 0
% 1.82/0.76 % Equation resolutions : 0
% 1.82/0.76 % Disequality decompositions : 0
% 1.82/0.76 % Total rewrite steps : 11
% 1.82/0.76 % ...of those cached : 4
% 1.82/0.76 % Propositional unsat checks : 0
% 1.82/0.76 % Propositional check models : 0
% 1.82/0.76 % Propositional check unsatisfiable : 0
% 1.82/0.76 % Propositional clauses : 0
% 1.82/0.76 % Propositional clauses after purity: 0
% 1.82/0.76 % Propositional unsat core size : 0
% 1.82/0.76 % Propositional preprocessing time : 0.000
% 1.82/0.76 % Propositional encoding time : 0.000
% 1.82/0.76 % Propositional solver time : 0.000
% 1.82/0.76 % Success case prop preproc time : 0.000
% 1.82/0.76 % Success case prop encoding time : 0.000
% 1.82/0.76 % Success case prop solver time : 0.000
% 1.82/0.76 % Current number of processed clauses : 1110
% 1.82/0.76 % Positive orientable unit clauses : 177
% 1.82/0.76 % Positive unorientable unit clauses: 0
% 1.82/0.76 % Negative unit clauses : 2
% 1.82/0.76 % Non-unit-clauses : 931
% 1.82/0.76 % Current number of unprocessed clauses: 1079
% 1.82/0.76 % ...number of literals in the above : 5364
% 1.82/0.76 % Current number of archived formulas : 0
% 1.82/0.76 % Current number of archived clauses : 169
% 1.82/0.76 % Clause-clause subsumption calls (NU) : 268305
% 1.82/0.76 % Rec. Clause-clause subsumption calls : 111386
% 1.82/0.76 % Non-unit clause-clause subsumptions : 275
% 1.82/0.76 % Unit Clause-clause subsumption calls : 244
% 1.82/0.76 % Rewrite failures with RHS unbound : 0
% 1.82/0.76 % BW rewrite match attempts : 0
% 1.82/0.76 % BW rewrite match successes : 0
% 1.82/0.76 % Condensation attempts : 0
% 1.82/0.76 % Condensation successes : 0
% 1.82/0.76 % Termbank termtop insertions : 79700
% 1.82/0.76 % Search garbage collected termcells : 1755
% 1.82/0.76
% 1.82/0.76 % -------------------------------------------------
% 1.82/0.76 % User time : 0.304 s
% 1.82/0.76 % System time : 0.015 s
% 1.82/0.76 % Total time : 0.319 s
% 1.82/0.76 % Maximum resident set size: 4508 pages
% 1.82/0.76
% 1.82/0.76 % -------------------------------------------------
% 1.82/0.76 % User time : 0.542 s
% 1.82/0.76 % System time : 0.035 s
% 1.82/0.76 % Total time : 0.577 s
% 1.82/0.76 % Maximum resident set size: 4864 pages
% 2.26/0.76 % E exiting
%------------------------------------------------------------------------------