%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM310+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 : n013.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 1.15s 0.63s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 21 unt; 0 def)
% Number of atoms : 102 ( 10 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 108 ( 50 ~; 41 |; 11 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 82 ( 0 sgn 44 !; 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_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/sandbox/benchmark/Axioms/NUM005+2.ax',sum_entry_point_pos_pos) ).
fof(rdn_digit_add_n6_n0_n6_n0,axiom,
rdn_digit_add(rdnn(n6),rdnn(n0),rdnn(n6),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n6_n0_n6_n0) ).
fof(rdn_digit_add_n3_n3_n6_n0,axiom,
rdn_digit_add(rdnn(n3),rdnn(n3),rdnn(n6),rdnn(n0)),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',rdn_digit_add_n3_n3_n6_n0) ).
fof(sum_n2_n3_not_n6,conjecture,
~ sum(n2,n3,n6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_n2_n3_not_n6) ).
fof(rdn6,axiom,
rdn_translate(n6,rdn_pos(rdnn(n6))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn6) ).
fof(less_entry_point_pos_pos,axiom,
! [X1,X2,X10,X11] :
( ( rdn_positive_less(X10,X11)
& rdn_translate(X2,rdn_pos(X11))
& rdn_translate(X1,rdn_pos(X10)) )
=> less(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',less_entry_point_pos_pos) ).
fof(unique_LHS,axiom,
! [X17,X18,X2,X3] :
( ( sum(X18,X2,X3)
& sum(X17,X2,X3) )
=> X17 = X18 ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+2.ax',unique_LHS) ).
fof(rdn3,axiom,
rdn_translate(n3,rdn_pos(rdnn(n3))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn3) ).
fof(less_property,axiom,
! [X1,X2] :
( less(X1,X2)
<=> ( X2 != X1
& ~ less(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+1.ax',less_property) ).
fof(rdn2,axiom,
rdn_translate(n2,rdn_pos(rdnn(n2))),
file('/export/starexec/sandbox/benchmark/Axioms/NUM005+0.ax',rdn2) ).
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,
! [X33,X34,X35,X36,X37,X38] :
( sum(X33,X34,X35)
| ~ rdn_translate(X35,rdn_pos(X38))
| ~ rdn_add_with_carry(rdnn(n0),X36,X37,X38)
| ~ rdn_translate(X34,rdn_pos(X37))
| ~ rdn_translate(X33,rdn_pos(X36)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sum_entry_point_pos_pos])])]) ).
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(n6),rdnn(n0),rdnn(n6),rdnn(n0)),
inference(split_conjunct,[status(thm)],[rdn_digit_add_n6_n0_n6_n0]) ).
cnf(c_0_16,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_13]) ).
cnf(c_0_17,plain,
( ~ rdn_digit_add(rdnn(X1),rdnn(X2),rdnn(n6),rdnn(n0))
| rdn_add_with_carry(rdnn(n0),rdnn(X1),rdnn(X2),rdnn(n6)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(X4)))
| ~ rdn_translate(X2,rdn_pos(rdnn(X5)))
| ~ rdn_translate(X3,rdn_pos(rdnn(n6)))
| ~ rdn_digit_add(rdnn(X4),rdnn(X5),rdnn(n6),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(n3),rdnn(n3),rdnn(n6),rdnn(n0)),
inference(split_conjunct,[status(thm)],[rdn_digit_add_n3_n3_n6_n0]) ).
fof(c_0_20,negated_conjecture,
~ ~ sum(n2,n3,n6),
inference(assume_negation,[status(cth)],[sum_n2_n3_not_n6]) ).
cnf(c_0_21,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X2,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X3,rdn_pos(rdnn(n6)))
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
rdn_translate(n6,rdn_pos(rdnn(n6))),
inference(split_conjunct,[status(thm)],[rdn6]) ).
fof(c_0_23,plain,
! [X129,X130,X131,X132] :
( less(X129,X130)
| ~ rdn_positive_less(X131,X132)
| ~ rdn_translate(X130,rdn_pos(X132))
| ~ rdn_translate(X129,rdn_pos(X131)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less_entry_point_pos_pos])])]) ).
fof(c_0_24,plain,
! [X69,X70,X71,X72] :
( X69 = X70
| ~ sum(X70,X71,X72)
| ~ sum(X69,X71,X72) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unique_LHS])])]) ).
fof(c_0_25,negated_conjecture,
sum(n2,n3,n6),
inference(fof_simplification,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n3)))
| ~ rdn_translate(X2,rdn_pos(rdnn(n3)))
| sum(X1,X2,n6) ),
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,plain,
! [X1,X2] :
( less(X1,X2)
<=> ( X2 != X1
& ~ less(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[less_property]) ).
cnf(c_0_29,plain,
( ~ rdn_positive_less(X2,X4)
| ~ rdn_translate(X3,rdn_pos(X4))
| ~ rdn_translate(X1,rdn_pos(X2))
| less(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( ~ sum(X4,X2,X3)
| ~ sum(X1,X2,X3)
| X1 = X4 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
sum(n2,n3,n6),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
( ~ rdn_translate(X1,rdn_pos(rdnn(n3)))
| sum(X1,n3,n6) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_33,plain,
! [X144,X145] :
( ( less(X144,X145)
| X145 = X144
| less(X145,X144) )
& ( ~ less(X144,X145)
| X145 != X144 )
& ( ~ less(X144,X145)
| ~ less(X145,X144) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])]) ).
cnf(c_0_34,plain,
( ~ rdn_translate(X1,rdn_pos(X2))
| ~ rdn_positive_less(X2,rdnn(n3))
| less(X1,n3) ),
inference(spm,[status(thm)],[c_0_29,c_0_27]) ).
cnf(c_0_35,plain,
rdn_translate(n2,rdn_pos(rdnn(n2))),
inference(split_conjunct,[status(thm)],[rdn2]) ).
cnf(c_0_36,plain,
rdn_positive_less(rdnn(n2),rdnn(n3)),
inference(split_conjunct,[status(thm)],[rdn_positive_less23]) ).
cnf(c_0_37,negated_conjecture,
( ~ sum(X1,n3,n6)
| X1 = n2 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,plain,
sum(n3,n3,n6),
inference(spm,[status(thm)],[c_0_32,c_0_27]) ).
cnf(c_0_39,plain,
( ~ less(X2,X1)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,plain,
less(n2,n3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_41,negated_conjecture,
n3 = n2,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
~ less(X1,X1),
inference(er,[status(thm)],[c_0_39]) ).
cnf(c_0_43,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM310+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 02:21:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 1.15/0.63 % Version: 3.5.1
% 1.15/0.63 % Preprocessing class: FSLMSMSLSSSNFFN.
% 1.15/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.15/0.63 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 1.15/0.63 % Starting new_bool_3 with 600s (2) cores
% 1.15/0.63 % Starting new_bool_1 with 600s (2) cores
% 1.15/0.63 % Starting sh5l with 300s (1) cores
% 1.15/0.63 % sh5l with pid 3938039 completed with status 0
% 1.15/0.63 % Result found by sh5l
% 1.15/0.63 % Preprocessing class: FSLMSMSLSSSNFFN.
% 1.15/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.15/0.63 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 1.15/0.63 % Starting new_bool_3 with 600s (2) cores
% 1.15/0.63 % Starting new_bool_1 with 600s (2) cores
% 1.15/0.63 % Starting sh5l with 300s (1) cores
% 1.15/0.63 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 1.15/0.63 % SinE strategy is gf500_gu_R04_F100_L20000
% 1.15/0.63 % Search class: FGHSF-FFLM21-SFFFFFNN
% 1.15/0.63 % partial match(1): FGHSF-FFMM21-SFFFFFNN
% 1.15/0.63 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.15/0.63 % Starting SubtermCWHack with 28s (1) cores
% 1.15/0.63 % SubtermCWHack with pid 3938044 completed with status 0
% 1.15/0.63 % Result found by SubtermCWHack
% 1.15/0.63 % Preprocessing class: FSLMSMSLSSSNFFN.
% 1.15/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.15/0.63 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 1.15/0.63 % Starting new_bool_3 with 600s (2) cores
% 1.15/0.63 % Starting new_bool_1 with 600s (2) cores
% 1.15/0.63 % Starting sh5l with 300s (1) cores
% 1.15/0.63 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 1.15/0.63 % SinE strategy is gf500_gu_R04_F100_L20000
% 1.15/0.63 % Search class: FGHSF-FFLM21-SFFFFFNN
% 1.15/0.63 % partial match(1): FGHSF-FFMM21-SFFFFFNN
% 1.15/0.63 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.15/0.63 % Starting SubtermCWHack with 28s (1) cores
% 1.15/0.63 % Preprocessing time : 0.003 s
% 1.15/0.63
% 1.15/0.63 % Proof found!
% 1.15/0.63 % SZS status Theorem
% 1.15/0.63 % SZS output start CNFRefutation
% See solution above
% 1.15/0.63 % Parsed axioms : 402
% 1.15/0.63 % Removed by relevancy pruning/SinE : 247
% 1.15/0.63 % Initial clauses : 159
% 1.15/0.63 % Removed in clause preprocessing : 0
% 1.15/0.63 % Initial clauses in saturation : 159
% 1.15/0.63 % Processed clauses : 1689
% 1.15/0.63 % ...of these trivial : 0
% 1.15/0.63 % ...subsumed : 661
% 1.15/0.63 % ...remaining for further processing : 1028
% 1.15/0.63 % Other redundant clauses eliminated : 2
% 1.15/0.63 % Clauses deleted for lack of memory : 0
% 1.15/0.63 % Backward-subsumed : 21
% 1.15/0.63 % Backward-rewritten : 61
% 1.15/0.63 % Generated clauses : 3249
% 1.15/0.63 % ...of the previous two non-redundant : 3098
% 1.15/0.63 % ...aggressively subsumed : 0
% 1.15/0.63 % Contextual simplify-reflections : 0
% 1.15/0.63 % Paramodulations : 3245
% 1.15/0.63 % Factorizations : 2
% 1.15/0.63 % NegExts : 0
% 1.15/0.63 % Equation resolutions : 2
% 1.15/0.63 % Disequality decompositions : 0
% 1.15/0.63 % Total rewrite steps : 158
% 1.15/0.63 % ...of those cached : 135
% 1.15/0.63 % Propositional unsat checks : 0
% 1.15/0.63 % Propositional check models : 0
% 1.15/0.63 % Propositional check unsatisfiable : 0
% 1.15/0.63 % Propositional clauses : 0
% 1.15/0.63 % Propositional clauses after purity: 0
% 1.15/0.63 % Propositional unsat core size : 0
% 1.15/0.63 % Propositional preprocessing time : 0.000
% 1.15/0.63 % Propositional encoding time : 0.000
% 1.15/0.63 % Propositional solver time : 0.000
% 1.15/0.63 % Success case prop preproc time : 0.000
% 1.15/0.63 % Success case prop encoding time : 0.000
% 1.15/0.63 % Success case prop solver time : 0.000
% 1.15/0.63 % Current number of processed clauses : 944
% 1.15/0.63 % Positive orientable unit clauses : 163
% 1.15/0.63 % Positive unorientable unit clauses: 0
% 1.15/0.63 % Negative unit clauses : 64
% 1.15/0.63 % Non-unit-clauses : 717
% 1.15/0.63 % Current number of unprocessed clauses: 1531
% 1.15/0.63 % ...number of literals in the above : 8216
% 1.15/0.63 % Current number of archived formulas : 0
% 1.15/0.63 % Current number of archived clauses : 82
% 1.15/0.63 % Clause-clause subsumption calls (NU) : 147059
% 1.15/0.63 % Rec. Clause-clause subsumption calls : 69617
% 1.15/0.63 % Non-unit clause-clause subsumptions : 443
% 1.15/0.63 % Unit Clause-clause subsumption calls : 4929
% 1.15/0.63 % Rewrite failures with RHS unbound : 0
% 1.15/0.63 % BW rewrite match attempts : 1
% 1.15/0.63 % BW rewrite match successes : 1
% 1.15/0.63 % Condensation attempts : 0
% 1.15/0.63 % Condensation successes : 0
% 1.15/0.63 % Termbank termtop insertions : 93637
% 1.15/0.63 % Search garbage collected termcells : 1847
% 1.15/0.63
% 1.15/0.63 % -------------------------------------------------
% 1.15/0.63 % User time : 0.172 s
% 1.15/0.63 % System time : 0.013 s
% 1.15/0.63 % Total time : 0.185 s
% 1.15/0.63 % Maximum resident set size: 4508 pages
% 1.15/0.63
% 1.15/0.63 % -------------------------------------------------
% 1.15/0.63 % User time : 0.182 s
% 1.15/0.63 % System time : 0.015 s
% 1.15/0.63 % Total time : 0.197 s
% 1.15/0.63 % Maximum resident set size: 5120 pages
% 1.15/0.63 % E exiting
%------------------------------------------------------------------------------