%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM342+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 : n002.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 0.28s 0.71s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 15 unt; 0 def)
% Number of atoms : 89 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 95 ( 45 ~; 40 |; 7 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 78 ( 0 sgn 30 !; 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/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_n8_n0_n8_n0,axiom,
rdn_digit_add(rdnn(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n8_n0_n8_n0) ).
fof(rdn_digit_add_n4_n0_n4_n0,axiom,
rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n4_n0_n4_n0) ).
fof(rdn_digit_add_n4_n4_n8_n0,axiom,
rdn_digit_add(rdnn(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n4_n4_n8_n0) ).
fof(sum_and_difference,conjecture,
? [X1,X2] :
( difference(X1,X2,n0)
& sum(X1,X2,n8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_and_difference) ).
fof(rdn8,axiom,
rdn_translate(n8,rdn_pos(rdnn(n8))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn8) ).
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(rdn4,axiom,
rdn_translate(n4,rdn_pos(rdnn(n4))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn4) ).
fof(rdn0,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn0) ).
fof(c_0_10,plain,
! [X82,X83,X84,X85,X86] :
( rdn_add_with_carry(rdnn(X82),rdnn(X83),rdnn(X84),rdnn(X85))
| ~ rdn_digit_add(rdnn(X86),rdnn(X82),rdnn(X85),rdnn(n0))
| ~ rdn_digit_add(rdnn(X83),rdnn(X84),rdnn(X86),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,
! [X38,X39,X40,X41,X42,X43] :
( sum(X38,X39,X40)
| ~ rdn_translate(X40,rdn_pos(X43))
| ~ rdn_add_with_carry(rdnn(n0),X41,X42,X43)
| ~ rdn_translate(X39,rdn_pos(X42))
| ~ rdn_translate(X38,rdn_pos(X41)) ),
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(n8),rdnn(n0),rdnn(n8),rdnn(n0)),
inference(split_conjunct,[status(thm)],[rdn_digit_add_n8_n0_n8_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(n8),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X1),rdnn(X2),rdnn(n8)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
rdn_digit_add(rdnn(n4),rdnn(n0),rdnn(n4),rdnn(n0)),
inference(split_conjunct,[status(thm)],[rdn_digit_add_n4_n0_n4_n0]) ).
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(n8)))
| ~ rdn_digit_add(rdnn(X4),rdnn(X5),rdnn(n8),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(n4),rdnn(n4),rdnn(n8),rdnn(n0)),
inference(split_conjunct,[status(thm)],[rdn_digit_add_n4_n4_n8_n0]) ).
cnf(c_0_19,plain,
( ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(n4),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X1),rdnn(X2),rdnn(n4)) ),
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
fof(c_0_20,negated_conjecture,
~ ? [X1,X2] :
( difference(X1,X2,n0)
& sum(X1,X2,n8) ),
inference(assume_negation,[status(cth)],[sum_and_difference]) ).
cnf(c_0_21,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n4)))
| ~ rdn_translate(X2,rdn_pos(rdnn(n4)))
| ~ rdn_translate(X3,rdn_pos(rdnn(n8)))
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
rdn_translate(n8,rdn_pos(rdnn(n8))),
inference(split_conjunct,[status(thm)],[rdn8]) ).
cnf(c_0_23,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(X4)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X5)))
| ~ rdn_translate(X3,rdn_pos(rdnn(n4)))
| ~ rdn_digit_add(rdnn(X4),rdnn(X5),rdnn(n4),rdnn(n0))
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_19]) ).
fof(c_0_24,negated_conjecture,
! [X33,X34] :
( ~ difference(X33,X34,n0)
| ~ sum(X33,X34,n8) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
fof(c_0_25,plain,
! [X35,X36,X37] :
( ( sum(X36,X37,X35)
| ~ difference(X35,X36,X37) )
& ( difference(X35,X36,X37)
| ~ sum(X36,X37,X35) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[minus_entry_point])])]) ).
cnf(c_0_26,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n4)))
| ~ rdn_translate(X2,rdn_pos(rdnn(n4)))
| sum(X1,X2,n8) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
rdn_translate(n4,rdn_pos(rdnn(n4))),
inference(split_conjunct,[status(thm)],[rdn4]) ).
cnf(c_0_28,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n4)))
| ~ rdn_translate(X2,rdn_pos(rdnn(n0)))
| ~ rdn_translate(X3,rdn_pos(rdnn(n4)))
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
cnf(c_0_29,negated_conjecture,
( ~ difference(X1,X2,n0)
| ~ sum(X1,X2,n8) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
( ~ sum(X1,X2,X3)
| difference(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n4)))
| sum(X1,n4,n8) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n4)))
| ~ rdn_translate(X2,rdn_pos(rdnn(n0)))
| sum(X1,X2,n4) ),
inference(spm,[status(thm)],[c_0_28,c_0_27]) ).
cnf(c_0_33,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(split_conjunct,[status(thm)],[rdn0]) ).
cnf(c_0_34,negated_conjecture,
( ~ sum(X2,n0,X1)
| ~ sum(X1,X2,n8) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
sum(n4,n4,n8),
inference(spm,[status(thm)],[c_0_31,c_0_27]) ).
cnf(c_0_36,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n4)))
| sum(X1,n0,n4) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
~ sum(n4,n0,n4),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_27]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM342+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 % Computer : n002.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Mon Sep 21 02:25:31 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.51 Running first-order theorem proving
% 0.27/0.51 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
% 0.28/0.71 % Version: 3.5.1
% 0.28/0.71 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.28/0.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.71 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.28/0.71 % Starting new_bool_3 with 600s (2) cores
% 0.28/0.71 % Starting new_bool_1 with 600s (2) cores
% 0.28/0.71 % Starting sh5l with 300s (1) cores
% 0.28/0.71 % new_bool_3 with pid 2227744 completed with status 0
% 0.28/0.71 % Result found by new_bool_3
% 0.28/0.71 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.28/0.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.71 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.28/0.71 % Starting new_bool_3 with 600s (2) cores
% 0.28/0.71 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.28/0.71 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.28/0.71 % Search class: FHHSF-FFMM21-SFFFFFNN
% 0.28/0.71 % partial match(1): FGHSF-FFMM21-SFFFFFNN
% 0.28/0.71 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.28/0.71 % Starting SubtermCWHack with 55s (1) cores
% 0.28/0.71 % Starting new_bool_3 with 61s (1) cores
% 0.28/0.71 % SubtermCWHack with pid 2227753 completed with status 0
% 0.28/0.71 % Result found by SubtermCWHack
% 0.28/0.71 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.28/0.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.71 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.28/0.71 % Starting new_bool_3 with 600s (2) cores
% 0.28/0.71 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.28/0.71 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.28/0.71 % Search class: FHHSF-FFMM21-SFFFFFNN
% 0.28/0.71 % partial match(1): FGHSF-FFMM21-SFFFFFNN
% 0.28/0.71 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 0.28/0.71 % Starting SubtermCWHack with 55s (1) cores
% 0.28/0.71 % Preprocessing time : 0.004 s
% 0.28/0.71
% 0.28/0.71 % Proof found!
% 0.28/0.71 % SZS status Theorem
% 0.28/0.71 % SZS output start CNFRefutation
% See solution above
% 0.28/0.71 % Parsed axioms : 402
% 0.28/0.71 % Removed by relevancy pruning/SinE : 261
% 0.28/0.71 % Initial clauses : 142
% 0.28/0.71 % Removed in clause preprocessing : 0
% 0.28/0.71 % Initial clauses in saturation : 142
% 0.28/0.71 % Processed clauses : 905
% 0.28/0.71 % ...of these trivial : 0
% 0.28/0.71 % ...subsumed : 120
% 0.28/0.71 % ...remaining for further processing : 785
% 0.28/0.71 % Other redundant clauses eliminated : 0
% 0.28/0.71 % Clauses deleted for lack of memory : 0
% 0.28/0.71 % Backward-subsumed : 0
% 0.28/0.71 % Backward-rewritten : 0
% 0.28/0.71 % Generated clauses : 1661
% 0.28/0.71 % ...of the previous two non-redundant : 1659
% 0.28/0.71 % ...aggressively subsumed : 0
% 0.28/0.71 % Contextual simplify-reflections : 0
% 0.28/0.71 % Paramodulations : 1661
% 0.28/0.71 % Factorizations : 0
% 0.28/0.71 % NegExts : 0
% 0.28/0.71 % Equation resolutions : 0
% 0.28/0.71 % Disequality decompositions : 0
% 0.28/0.71 % Total rewrite steps : 0
% 0.28/0.71 % ...of those cached : 0
% 0.28/0.71 % Propositional unsat checks : 0
% 0.28/0.71 % Propositional check models : 0
% 0.28/0.71 % Propositional check unsatisfiable : 0
% 0.28/0.71 % Propositional clauses : 0
% 0.28/0.71 % Propositional clauses after purity: 0
% 0.28/0.71 % Propositional unsat core size : 0
% 0.28/0.71 % Propositional preprocessing time : 0.000
% 0.28/0.71 % Propositional encoding time : 0.000
% 0.28/0.71 % Propositional solver time : 0.000
% 0.28/0.71 % Success case prop preproc time : 0.000
% 0.28/0.71 % Success case prop encoding time : 0.000
% 0.28/0.71 % Success case prop solver time : 0.000
% 0.28/0.71 % Current number of processed clauses : 785
% 0.28/0.71 % Positive orientable unit clauses : 165
% 0.28/0.71 % Positive unorientable unit clauses: 0
% 0.28/0.71 % Negative unit clauses : 9
% 0.28/0.71 % Non-unit-clauses : 611
% 0.28/0.71 % Current number of unprocessed clauses: 896
% 0.28/0.71 % ...number of literals in the above : 4639
% 0.28/0.71 % Current number of archived formulas : 0
% 0.28/0.71 % Current number of archived clauses : 0
% 0.28/0.71 % Clause-clause subsumption calls (NU) : 75140
% 0.28/0.71 % Rec. Clause-clause subsumption calls : 43676
% 0.28/0.71 % Non-unit clause-clause subsumptions : 120
% 0.28/0.71 % Unit Clause-clause subsumption calls : 3018
% 0.28/0.71 % Rewrite failures with RHS unbound : 0
% 0.28/0.71 % BW rewrite match attempts : 3
% 0.28/0.71 % BW rewrite match successes : 0
% 0.28/0.71 % Condensation attempts : 0
% 0.28/0.71 % Condensation successes : 0
% 0.28/0.71 % Termbank termtop insertions : 61098
% 0.28/0.71 % Search garbage collected termcells : 1793
% 0.28/0.71
% 0.28/0.71 % -------------------------------------------------
% 0.28/0.71 % User time : 0.138 s
% 0.28/0.71 % System time : 0.005 s
% 0.28/0.71 % Total time : 0.143 s
% 0.28/0.71 % Maximum resident set size: 4764 pages
% 0.28/0.71
% 0.28/0.71 % -------------------------------------------------
% 0.28/0.71 % User time : 0.250 s
% 0.28/0.71 % System time : 0.019 s
% 0.28/0.71 % Total time : 0.269 s
% 0.28/0.71 % Maximum resident set size: 4864 pages
% 0.28/0.71 % E exiting
%------------------------------------------------------------------------------