%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM334+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 : n001.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 0.47s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 17 unt; 0 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 65 ( 31 ~; 26 |; 5 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 55 ( 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/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_n7_n0_n7_n0,axiom,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n7_n0_n7_n0) ).
fof(diff_n7_n5_n2,conjecture,
difference(n7,n5,n2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diff_n7_n5_n2) ).
fof(rdn_digit_add_n5_n2_n7_n0,axiom,
rdn_digit_add(rdnn(n5),rdnn(n2),rdnn(n7),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n5_n2_n7_n0) ).
fof(rdn7,axiom,
rdn_translate(n7,rdn_pos(rdnn(n7))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn7) ).
fof(minus_entry_point,axiom,
! [X1,X2,X3] :
( sum(X2,X3,X1)
<=> difference(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',minus_entry_point) ).
fof(rdn2,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn2) ).
fof(rdn5,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn5) ).
fof(c_0_9,plain,
! [X80,X81,X82,X83,X84] :
( rdn_add_with_carry(rdnn(X80),rdnn(X81),rdnn(X82),rdnn(X83))
| ~ rdn_digit_add(rdnn(X84),rdnn(X80),rdnn(X83),rdnn(n0))
| ~ rdn_digit_add(rdnn(X81),rdnn(X82),rdnn(X84),rdnn(n0)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[add_digit_digit_digit])])]) ).
fof(c_0_10,plain,
! [X36,X37,X38,X39,X40,X41] :
( sum(X36,X37,X38)
| ~ rdn_translate(X38,rdn_pos(X41))
| ~ rdn_add_with_carry(rdnn(n0),X39,X40,X41)
| ~ rdn_translate(X37,rdn_pos(X40))
| ~ rdn_translate(X36,rdn_pos(X39)) ),
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(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_9]) ).
cnf(c_0_12,plain,
rdn_digit_add(rdnn(n7),rdnn(n0),rdnn(n7),rdnn(n0)),
inference(split_conjunct,[status(thm)],[rdn_digit_add_n7_n0_n7_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_digit_add(rdnn(X1),rdnn(X2),rdnn(n7),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X1),rdnn(X2),rdnn(n7)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_15,negated_conjecture,
~ difference(n7,n5,n2),
inference(assume_negation,[status(cth)],[diff_n7_n5_n2]) ).
cnf(c_0_16,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(X4)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X5)))
| ~ rdn_translate(X3,rdn_pos(rdnn(n7)))
| ~ rdn_digit_add(rdnn(X4),rdnn(X5),rdnn(n7),rdnn(n0))
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
rdn_digit_add(rdnn(n5),rdnn(n2),rdnn(n7),rdnn(n0)),
inference(split_conjunct,[status(thm)],[rdn_digit_add_n5_n2_n7_n0]) ).
fof(c_0_18,negated_conjecture,
~ difference(n7,n5,n2),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X2,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X3,rdn_pos(rdnn(n7)))
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
rdn_translate(n7,rdn_pos(rdnn(n7))),
inference(split_conjunct,[status(thm)],[rdn7]) ).
fof(c_0_21,negated_conjecture,
~ difference(n7,n5,n2),
inference(fof_nnf,[status(thm)],[c_0_18]) ).
fof(c_0_22,plain,
! [X33,X34,X35] :
( ( sum(X34,X35,X33)
| ~ difference(X33,X34,X35) )
& ( difference(X33,X34,X35)
| ~ sum(X34,X35,X33) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[minus_entry_point])])]) ).
cnf(c_0_23,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n5)))
| ~ rdn_translate(X2,rdn_pos(rdnn(n2)))
| sum(X1,X2,n7) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(split_conjunct,[status(thm)],[rdn2]) ).
cnf(c_0_25,negated_conjecture,
~ difference(n7,n5,n2),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
( ~ sum(X1,X2,X3)
| difference(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n5)))
| sum(X1,n2,n7) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(split_conjunct,[status(thm)],[rdn5]) ).
cnf(c_0_29,negated_conjecture,
~ sum(n5,n2,n7),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM334+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n001.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 02:27:59 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.19/0.47 % Version: 3.5.1
% 0.19/0.47 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.19/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.47 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.19/0.47 % Starting new_bool_3 with 600s (2) cores
% 0.19/0.47 % Starting new_bool_1 with 600s (2) cores
% 0.19/0.47 % Starting sh5l with 300s (1) cores
% 0.19/0.47 % new_bool_3 with pid 1991111 completed with status 0
% 0.19/0.47 % Result found by new_bool_3
% 0.19/0.47 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.19/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.47 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.19/0.47 % Starting new_bool_3 with 600s (2) cores
% 0.19/0.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.19/0.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.47 % Search class: FHUSF-FFMM21-SFFFFFNN
% 0.19/0.47 % partial match(1): FHUNF-FFMM21-SFFFFFNN
% 0.19/0.47 % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 0.19/0.47 % Starting SubtermCWHack with 61s (1) cores
% 0.19/0.47 % Starting SAT001_MinMin_p005000_rr_RG with 361s (1) cores
% 0.19/0.47 % SAT001_MinMin_p005000_rr_RG with pid 1991117 completed with status 0
% 0.19/0.47 % Result found by SAT001_MinMin_p005000_rr_RG
% 0.19/0.47 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.19/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.47 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.19/0.47 % Starting new_bool_3 with 600s (2) cores
% 0.19/0.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.19/0.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.47 % Search class: FHUSF-FFMM21-SFFFFFNN
% 0.19/0.47 % partial match(1): FHUNF-FFMM21-SFFFFFNN
% 0.19/0.47 % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 0.19/0.47 % Starting SubtermCWHack with 61s (1) cores
% 0.19/0.47 % Starting SAT001_MinMin_p005000_rr_RG with 361s (1) cores
% 0.19/0.47 % Preprocessing time : 0.002 s
% 0.19/0.47 % Presaturation interreduction done
% 0.19/0.47
% 0.19/0.47 % Proof found!
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 % SZS output start CNFRefutation
% See solution above
% 0.19/0.47 % Parsed axioms : 402
% 0.19/0.47 % Removed by relevancy pruning/SinE : 265
% 0.19/0.47 % Initial clauses : 138
% 0.19/0.47 % Removed in clause preprocessing : 0
% 0.19/0.47 % Initial clauses in saturation : 138
% 0.19/0.47 % Processed clauses : 712
% 0.19/0.47 % ...of these trivial : 0
% 0.19/0.47 % ...subsumed : 120
% 0.19/0.47 % ...remaining for further processing : 592
% 0.19/0.47 % Other redundant clauses eliminated : 0
% 0.19/0.47 % Clauses deleted for lack of memory : 0
% 0.19/0.47 % Backward-subsumed : 0
% 0.19/0.47 % Backward-rewritten : 0
% 0.19/0.47 % Generated clauses : 594
% 0.19/0.47 % ...of the previous two non-redundant : 592
% 0.19/0.47 % ...aggressively subsumed : 0
% 0.19/0.47 % Contextual simplify-reflections : 0
% 0.19/0.47 % Paramodulations : 594
% 0.19/0.47 % Factorizations : 0
% 0.19/0.47 % NegExts : 0
% 0.19/0.47 % Equation resolutions : 0
% 0.19/0.47 % Disequality decompositions : 0
% 0.19/0.47 % Total rewrite steps : 0
% 0.19/0.47 % ...of those cached : 0
% 0.19/0.47 % Propositional unsat checks : 0
% 0.19/0.47 % Propositional check models : 0
% 0.19/0.47 % Propositional check unsatisfiable : 0
% 0.19/0.47 % Propositional clauses : 0
% 0.19/0.47 % Propositional clauses after purity: 0
% 0.19/0.47 % Propositional unsat core size : 0
% 0.19/0.47 % Propositional preprocessing time : 0.000
% 0.19/0.47 % Propositional encoding time : 0.000
% 0.19/0.47 % Propositional solver time : 0.000
% 0.19/0.47 % Success case prop preproc time : 0.000
% 0.19/0.47 % Success case prop encoding time : 0.000
% 0.19/0.47 % Success case prop solver time : 0.000
% 0.19/0.47 % Current number of processed clauses : 454
% 0.19/0.47 % Positive orientable unit clauses : 144
% 0.19/0.47 % Positive unorientable unit clauses: 0
% 0.19/0.47 % Negative unit clauses : 2
% 0.19/0.47 % Non-unit-clauses : 308
% 0.19/0.47 % Current number of unprocessed clauses: 156
% 0.19/0.47 % ...number of literals in the above : 932
% 0.19/0.47 % Current number of archived formulas : 0
% 0.19/0.47 % Current number of archived clauses : 138
% 0.19/0.47 % Clause-clause subsumption calls (NU) : 21759
% 0.19/0.47 % Rec. Clause-clause subsumption calls : 16623
% 0.19/0.47 % Non-unit clause-clause subsumptions : 120
% 0.19/0.47 % Unit Clause-clause subsumption calls : 21
% 0.19/0.47 % Rewrite failures with RHS unbound : 0
% 0.19/0.47 % BW rewrite match attempts : 0
% 0.19/0.47 % BW rewrite match successes : 0
% 0.19/0.47 % Condensation attempts : 0
% 0.19/0.47 % Condensation successes : 0
% 0.19/0.47 % Termbank termtop insertions : 26329
% 0.19/0.47 % Search garbage collected termcells : 1756
% 0.19/0.47
% 0.19/0.47 % -------------------------------------------------
% 0.19/0.47 % User time : 0.029 s
% 0.19/0.47 % System time : 0.008 s
% 0.19/0.47 % Total time : 0.037 s
% 0.19/0.47 % Maximum resident set size: 4508 pages
% 0.19/0.47
% 0.19/0.47 % -------------------------------------------------
% 0.19/0.47 % User time : 0.060 s
% 0.19/0.47 % System time : 0.019 s
% 0.19/0.47 % Total time : 0.079 s
% 0.19/0.47 % Maximum resident set size: 4864 pages
% 0.19/0.47 % E exiting
%------------------------------------------------------------------------------