%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM312+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 : n020.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 0.25s 0.60s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 14 unt; 0 def)
% Number of atoms : 71 ( 8 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 70 ( 31 ~; 28 |; 6 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 61 ( 0 sgn 32 !; 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_n5_n0_n5_n0,axiom,
rdn_digit_add(rdnn(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n2_n3_n5_n0) ).
fof(sum_only_n2_n3_n5,conjecture,
! [X1] :
( sum(X1,n3,n5)
=> X1 = n2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_only_n2_n3_n5) ).
fof(rdn5,axiom,
rdn_translate(n5,rdn_pos(rdnn(n5))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn5) ).
fof(unique_LHS,axiom,
! [X17,X18,X2,X3] :
( ( sum(X18,X2,X3)
& sum(X17,X2,X3) )
=> X17 = X18 ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+2.ax',unique_LHS) ).
fof(rdn3,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn3) ).
fof(rdn2,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM005+0.ax',rdn2) ).
fof(c_0_9,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_10,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_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(n5),rdnn(n0),rdnn(n5),rdnn(n0)),
inference(split_conjunct,[status(thm)],[rdn_digit_add_n5_n0_n5_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(n5),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X1),rdnn(X2),rdnn(n5)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(X4)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X5)))
| ~ rdn_translate(X3,rdn_pos(rdnn(n5)))
| ~ rdn_digit_add(rdnn(X4),rdnn(X5),rdnn(n5),rdnn(n0))
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,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_17,negated_conjecture,
~ ! [X1] :
( sum(X1,n3,n5)
=> X1 = n2 ),
inference(assume_negation,[status(cth)],[sum_only_n2_n3_n5]) ).
cnf(c_0_18,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X2,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X3,rdn_pos(rdnn(n5)))
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
rdn_translate(n5,rdn_pos(rdnn(n5))),
inference(split_conjunct,[status(thm)],[rdn5]) ).
fof(c_0_20,plain,
! [X70,X71,X72,X73] :
( X70 = X71
| ~ sum(X71,X72,X73)
| ~ sum(X70,X72,X73) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unique_LHS])])]) ).
fof(c_0_21,negated_conjecture,
( esk1_0 != n2
& sum(esk1_0,n3,n5) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
cnf(c_0_22,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n2)))
| ~ rdn_translate(X2,rdn_pos(rdnn(n3)))
| sum(X1,X2,n5) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
rdn_translate(n3,rdn_pos(rdnn(n3))),
inference(split_conjunct,[status(thm)],[rdn3]) ).
cnf(c_0_24,plain,
( ~ sum(X4,X2,X3)
| ~ sum(X1,X2,X3)
| X1 = X4 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
sum(esk1_0,n3,n5),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n2)))
| sum(X1,n3,n5) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(split_conjunct,[status(thm)],[rdn2]) ).
cnf(c_0_28,negated_conjecture,
( ~ sum(X1,n3,n5)
| X1 = esk1_0 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
sum(n2,n3,n5),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
esk1_0 != n2,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM312+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.43 % Computer : n020.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Mon Sep 21 02:22:32 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.50 Running first-order theorem proving
% 0.25/0.50 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
% 0.25/0.60 % Version: 3.5.1
% 0.25/0.60 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.25/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.60 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.25/0.60 % Starting new_bool_3 with 600s (2) cores
% 0.25/0.60 % Starting new_bool_1 with 600s (2) cores
% 0.25/0.60 % Starting sh5l with 300s (1) cores
% 0.25/0.60 % new_bool_3 with pid 1784121 completed with status 0
% 0.25/0.60 % Result found by new_bool_3
% 0.25/0.60 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.25/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.60 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.25/0.60 % Starting new_bool_3 with 600s (2) cores
% 0.25/0.60 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.25/0.60 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.25/0.60 % Search class: FHUSF-FFMM21-SFFFFFNN
% 0.25/0.60 % partial match(1): FHUNF-FFMM21-SFFFFFNN
% 0.25/0.60 % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 0.25/0.60 % Starting SubtermCWHack with 61s (1) cores
% 0.25/0.60 % Starting SAT001_MinMin_p005000_rr_RG with 361s (1) cores
% 0.25/0.60 % SAT001_MinMin_p005000_rr_RG with pid 1784127 completed with status 0
% 0.25/0.60 % Result found by SAT001_MinMin_p005000_rr_RG
% 0.25/0.60 % Preprocessing class: FSLMSMSLSSSNFFN.
% 0.25/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.60 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 0.25/0.60 % Starting new_bool_3 with 600s (2) cores
% 0.25/0.60 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.25/0.60 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.25/0.60 % Search class: FHUSF-FFMM21-SFFFFFNN
% 0.25/0.60 % partial match(1): FHUNF-FFMM21-SFFFFFNN
% 0.25/0.60 % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 0.25/0.60 % Starting SubtermCWHack with 61s (1) cores
% 0.25/0.60 % Starting SAT001_MinMin_p005000_rr_RG with 361s (1) cores
% 0.25/0.60 % Preprocessing time : 0.002 s
% 0.25/0.60 % Presaturation interreduction done
% 0.25/0.60
% 0.25/0.60 % Proof found!
% 0.25/0.60 % SZS status Theorem
% 0.25/0.60 % SZS output start CNFRefutation
% See solution above
% 0.25/0.60 % Parsed axioms : 402
% 0.25/0.60 % Removed by relevancy pruning/SinE : 262
% 0.25/0.60 % Initial clauses : 141
% 0.25/0.60 % Removed in clause preprocessing : 0
% 0.25/0.60 % Initial clauses in saturation : 141
% 0.25/0.60 % Processed clauses : 854
% 0.25/0.60 % ...of these trivial : 0
% 0.25/0.60 % ...subsumed : 120
% 0.25/0.60 % ...remaining for further processing : 734
% 0.25/0.60 % Other redundant clauses eliminated : 0
% 0.25/0.60 % Clauses deleted for lack of memory : 0
% 0.25/0.60 % Backward-subsumed : 0
% 0.25/0.60 % Backward-rewritten : 0
% 0.25/0.60 % Generated clauses : 821
% 0.25/0.60 % ...of the previous two non-redundant : 820
% 0.25/0.61 % ...aggressively subsumed : 0
% 0.25/0.61 % Contextual simplify-reflections : 0
% 0.25/0.61 % Paramodulations : 821
% 0.25/0.61 % Factorizations : 0
% 0.25/0.61 % NegExts : 0
% 0.25/0.61 % Equation resolutions : 0
% 0.25/0.61 % Disequality decompositions : 0
% 0.25/0.61 % Total rewrite steps : 0
% 0.25/0.61 % ...of those cached : 0
% 0.25/0.61 % Propositional unsat checks : 0
% 0.25/0.61 % Propositional check models : 0
% 0.25/0.61 % Propositional check unsatisfiable : 0
% 0.25/0.61 % Propositional clauses : 0
% 0.25/0.61 % Propositional clauses after purity: 0
% 0.25/0.61 % Propositional unsat core size : 0
% 0.25/0.61 % Propositional preprocessing time : 0.000
% 0.25/0.61 % Propositional encoding time : 0.000
% 0.25/0.61 % Propositional solver time : 0.000
% 0.25/0.61 % Success case prop preproc time : 0.000
% 0.25/0.61 % Success case prop encoding time : 0.000
% 0.25/0.61 % Success case prop solver time : 0.000
% 0.25/0.61 % Current number of processed clauses : 593
% 0.25/0.61 % Positive orientable unit clauses : 159
% 0.25/0.61 % Positive unorientable unit clauses: 0
% 0.25/0.61 % Negative unit clauses : 1
% 0.25/0.61 % Non-unit-clauses : 433
% 0.25/0.61 % Current number of unprocessed clauses: 245
% 0.25/0.61 % ...number of literals in the above : 1106
% 0.25/0.61 % Current number of archived formulas : 0
% 0.25/0.61 % Current number of archived clauses : 141
% 0.25/0.61 % Clause-clause subsumption calls (NU) : 44376
% 0.25/0.61 % Rec. Clause-clause subsumption calls : 31401
% 0.25/0.61 % Non-unit clause-clause subsumptions : 120
% 0.25/0.61 % Unit Clause-clause subsumption calls : 56
% 0.25/0.61 % Rewrite failures with RHS unbound : 0
% 0.25/0.61 % BW rewrite match attempts : 0
% 0.25/0.61 % BW rewrite match successes : 0
% 0.25/0.61 % Condensation attempts : 0
% 0.25/0.61 % Condensation successes : 0
% 0.25/0.61 % Termbank termtop insertions : 32191
% 0.25/0.61 % Search garbage collected termcells : 1780
% 0.25/0.61
% 0.25/0.61 % -------------------------------------------------
% 0.25/0.61 % User time : 0.061 s
% 0.25/0.61 % System time : 0.008 s
% 0.25/0.61 % Total time : 0.069 s
% 0.25/0.61 % Maximum resident set size: 4764 pages
% 0.25/0.61
% 0.25/0.61 % -------------------------------------------------
% 0.25/0.61 % User time : 0.100 s
% 0.25/0.61 % System time : 0.019 s
% 0.25/0.61 % Total time : 0.119 s
% 0.25/0.61 % Maximum resident set size: 5120 pages
% 0.25/0.61 % E exiting
%------------------------------------------------------------------------------