%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM925+3 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 01:51:02 PM UTC 2026
% Result : Theorem 1.10s 0.56s
% Output : CNFRefutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 25 unt; 0 def)
% Number of atoms : 48 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 21 ~; 9 |; 1 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 20 ( 3 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_231_field__power__not__zero,axiom,
! [X65,X66] :
( is_int(X66)
=> ( X66 != zero_zero_int
=> hAPP_nat_int(power_power_int(X66),X65) != zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_field__power__not__zero) ).
fof(fact_98_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Pls__def) ).
fof(fact_19_semiring__one__add__one__is__two,axiom,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_semiring__one__add__one__is__two) ).
fof(fact_79_bin__less__0__simps_I1_J,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_bin__less__0__simps_I1_J) ).
fof(gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint,hypothesis,
! [X1,X2] :
( ( is_int(X2)
& is_int(X1) )
=> is_int(plus_plus_int(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint,hypothesis,
! [X1,X2] : is_int(hAPP_nat_int(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint) ).
fof(gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint,hypothesis,
is_int(one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint) ).
fof(fact_0_n1pos,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
fof(c_0_9,negated_conjecture,
~ ( hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_10,negated_conjecture,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(fof_simplification,[status(thm)],[c_0_9]) ).
fof(c_0_11,plain,
! [X65,X66] :
( is_int(X66)
=> ( X66 != zero_zero_int
=> hAPP_nat_int(power_power_int(X66),X65) != zero_zero_int ) ),
inference(fof_simplification,[status(thm)],[fact_231_field__power__not__zero]) ).
cnf(c_0_12,negated_conjecture,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_98_Pls__def]) ).
cnf(c_0_14,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
inference(split_conjunct,[status(thm)],[fact_19_semiring__one__add__one__is__two]) ).
fof(c_0_15,plain,
! [X908,X909] :
( hAPP_nat_int(power_power_int(X909),X908) != zero_zero_int
| X909 = zero_zero_int
| ~ is_int(X909) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
cnf(c_0_16,negated_conjecture,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(zero_zero_int)))) = zero_zero_int,
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
number_number_of_nat(bit0(bit1(zero_zero_int))) = plus_plus_nat(one_one_nat,one_one_nat),
inference(rw,[status(thm)],[c_0_14,c_0_13]) ).
fof(c_0_18,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
inference(fof_simplification,[status(thm)],[fact_79_bin__less__0__simps_I1_J]) ).
cnf(c_0_19,plain,
( hAPP_nat_int(power_power_int(X1),X2) != zero_zero_int
| ~ is_int(X1)
| X1 = zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
hAPP_nat_int(power_power_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))),plus_plus_nat(one_one_nat,one_one_nat)) = zero_zero_int,
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_21,hypothesis,
! [X403,X404] :
( is_int(plus_plus_int(X403,X404))
| ~ is_int(X404)
| ~ is_int(X403) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint])])]) ).
fof(c_0_22,hypothesis,
! [X407,X408] : is_int(hAPP_nat_int(X407,X408)),
inference(variable_rename,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint]) ).
fof(c_0_23,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
inference(fof_nnf,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))
| plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,hypothesis,
( ~ is_int(X2)
| ~ is_int(X1)
| is_int(plus_plus_int(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,hypothesis,
is_int(hAPP_nat_int(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,hypothesis,
is_int(one_one_int),
inference(split_conjunct,[status(thm)],[gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint]) ).
cnf(c_0_28,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
inference(split_conjunct,[status(thm)],[fact_0_n1pos]) ).
cnf(c_0_30,hypothesis,
plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27])]) ).
cnf(c_0_31,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),zero_zero_int)),
inference(rw,[status(thm)],[c_0_28,c_0_13]) ).
cnf(c_0_32,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM925+3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Mon Sep 21 03:17:08 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.34 Running first-order theorem proving
% 0.06/0.34 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
% 1.10/0.56 % Version: 3.5.1
% 1.10/0.56 % Preprocessing class: FMLSSMSMSSSNFFN.
% 1.10/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.10/0.56 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 1.10/0.56 % Starting new_bool_3 with 600s (2) cores
% 1.10/0.56 % Starting new_bool_1 with 600s (2) cores
% 1.10/0.56 % Starting sh5l with 300s (1) cores
% 1.10/0.56 % new_bool_1 with pid 1447602 completed with status 0
% 1.10/0.56 % Result found by new_bool_1
% 1.10/0.56 % Preprocessing class: FMLSSMSMSSSNFFN.
% 1.10/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.10/0.56 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 1.10/0.56 % Starting new_bool_3 with 600s (2) cores
% 1.10/0.56 % Starting new_bool_1 with 600s (2) cores
% 1.10/0.56 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.10/0.56 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.10/0.56 % Search class: FGHSM-SSLM31-DFFFFFNN
% 1.10/0.56 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 1.10/0.56 % Starting SubtermCWHack with 55s (1) cores
% 1.10/0.56 % Starting new_bool_1 with 61s (1) cores
% 1.10/0.56 % new_bool_1 with pid 1447616 completed with status 0
% 1.10/0.56 % Result found by new_bool_1
% 1.10/0.56 % Preprocessing class: FMLSSMSMSSSNFFN.
% 1.10/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.10/0.56 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 1.10/0.56 % Starting new_bool_3 with 600s (2) cores
% 1.10/0.56 % Starting new_bool_1 with 600s (2) cores
% 1.10/0.56 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.10/0.56 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.10/0.56 % Search class: FGHSM-SSLM31-DFFFFFNN
% 1.10/0.56 % Scheduled 7 strats onto 2 cores with 600 seconds (600 total)
% 1.10/0.56 % Starting SubtermCWHack with 55s (1) cores
% 1.10/0.56 % Starting new_bool_1 with 61s (1) cores
% 1.10/0.56 % Preprocessing time : 0.012 s
% 1.10/0.56 % Presaturation interreduction done
% 1.10/0.56
% 1.10/0.56 % Proof found!
% 1.10/0.56 % SZS status Theorem
% 1.10/0.56 % SZS output start CNFRefutation
% See solution above
% 1.10/0.56 % Parsed axioms : 1233
% 1.10/0.56 % Removed by relevancy pruning/SinE : 363
% 1.10/0.56 % Initial clauses : 1289
% 1.10/0.56 % Removed in clause preprocessing : 98
% 1.10/0.56 % Initial clauses in saturation : 1191
% 1.10/0.56 % Processed clauses : 2867
% 1.10/0.56 % ...of these trivial : 126
% 1.10/0.56 % ...subsumed : 1243
% 1.10/0.56 % ...remaining for further processing : 1498
% 1.10/0.56 % Other redundant clauses eliminated : 140
% 1.10/0.56 % Clauses deleted for lack of memory : 0
% 1.10/0.56 % Backward-subsumed : 8
% 1.10/0.56 % Backward-rewritten : 207
% 1.10/0.56 % Generated clauses : 6734
% 1.10/0.56 % ...of the previous two non-redundant : 5955
% 1.10/0.56 % ...aggressively subsumed : 0
% 1.10/0.56 % Contextual simplify-reflections : 2
% 1.10/0.56 % Paramodulations : 6597
% 1.10/0.56 % Factorizations : 0
% 1.10/0.56 % NegExts : 0
% 1.10/0.56 % Equation resolutions : 149
% 1.10/0.56 % Disequality decompositions : 0
% 1.10/0.56 % Total rewrite steps : 4289
% 1.10/0.56 % ...of those cached : 3136
% 1.10/0.56 % Propositional unsat checks : 0
% 1.10/0.56 % Propositional check models : 0
% 1.10/0.56 % Propositional check unsatisfiable : 0
% 1.10/0.56 % Propositional clauses : 0
% 1.10/0.56 % Propositional clauses after purity: 0
% 1.10/0.56 % Propositional unsat core size : 0
% 1.10/0.56 % Propositional preprocessing time : 0.000
% 1.10/0.56 % Propositional encoding time : 0.000
% 1.10/0.56 % Propositional solver time : 0.000
% 1.10/0.56 % Success case prop preproc time : 0.000
% 1.10/0.56 % Success case prop encoding time : 0.000
% 1.10/0.56 % Success case prop solver time : 0.000
% 1.10/0.56 % Current number of processed clauses : 452
% 1.10/0.56 % Positive orientable unit clauses : 235
% 1.10/0.56 % Positive unorientable unit clauses: 15
% 1.10/0.56 % Negative unit clauses : 129
% 1.10/0.56 % Non-unit-clauses : 73
% 1.10/0.56 % Current number of unprocessed clauses: 4932
% 1.10/0.56 % ...number of literals in the above : 7151
% 1.10/0.56 % Current number of archived formulas : 0
% 1.10/0.56 % Current number of archived clauses : 937
% 1.10/0.56 % Clause-clause subsumption calls (NU) : 72465
% 1.10/0.56 % Rec. Clause-clause subsumption calls : 41865
% 1.10/0.56 % Non-unit clause-clause subsumptions : 296
% 1.10/0.56 % Unit Clause-clause subsumption calls : 3889
% 1.10/0.56 % Rewrite failures with RHS unbound : 0
% 1.10/0.56 % BW rewrite match attempts : 858
% 1.10/0.56 % BW rewrite match successes : 492
% 1.10/0.56 % Condensation attempts : 0
% 1.10/0.56 % Condensation successes : 0
% 1.10/0.56 % Termbank termtop insertions : 206729
% 1.10/0.56 % Search garbage collected termcells : 17549
% 1.10/0.56
% 1.10/0.56 % -------------------------------------------------
% 1.10/0.56 % User time : 0.171 s
% 1.10/0.56 % System time : 0.016 s
% 1.10/0.56 % Total time : 0.187 s
% 1.10/0.56 % Maximum resident set size: 8816 pages
% 1.10/0.56
% 1.10/0.56 % -------------------------------------------------
% 1.10/0.56 % User time : 0.332 s
% 1.10/0.56 % System time : 0.029 s
% 1.10/0.56 % Total time : 0.361 s
% 1.10/0.56 % Maximum resident set size: 6656 pages
% 1.10/0.56 % E exiting
%------------------------------------------------------------------------------