TSTP Solution File: NUM925+3 by E---3.1
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%------------------------------------------------------------------------------
% File : E---3.1
% Problem : NUM925+3 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 18:58:00 EDT 2023
% Result : Theorem 3.32s 1.09s
% Output : CNFRefutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 38 ( 24 unt; 0 def)
% Number of atoms : 66 ( 30 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 53 ( 25 ~; 19 |; 3 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-2 aty)
% Number of variables : 32 ( 4 sgn; 19 !; 1 ?)
% 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/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p',conj_0) ).
fof(fact_98_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.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/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p',fact_19_semiring__one__add__one__is__two) ).
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/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p',fact_231_field__power__not__zero) ).
fof(fact_789_zle__iff__zadd,axiom,
! [X26,X31] :
( is_int(X31)
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X26),X31))
<=> ? [X91] : X31 = plus_plus_int(X26,hAPP_nat_int(semiri1621563631at_int,X91)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p',fact_789_zle__iff__zadd) ).
fof(gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint,hypothesis,
! [X1,X2] :
( ( is_int(X1)
& is_int(X2) )
=> is_int(plus_plus_int(X1,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.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/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint) ).
fof(fact_807_int__le__0__conv,axiom,
! [X19] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X19)),zero_zero_int))
<=> X19 = zero_zero_nat ),
file('/export/starexec/sandbox2/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p',fact_807_int__le__0__conv) ).
fof(gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint,hypothesis,
is_int(one_one_int),
file('/export/starexec/sandbox2/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint) ).
fof(fact_254_transfer__int__nat__numerals_I2_J,axiom,
one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
file('/export/starexec/sandbox2/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p',fact_254_transfer__int__nat__numerals_I2_J) ).
fof(fact_226_one__neq__zero,axiom,
one_one_nat != zero_zero_nat,
file('/export/starexec/sandbox2/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p',fact_226_one__neq__zero) ).
fof(gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint,hypothesis,
is_int(zero_zero_int),
file('/export/starexec/sandbox2/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p',gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint) ).
fof(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(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_13,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_12]) ).
cnf(c_0_14,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_98_Pls__def]) ).
cnf(c_0_15,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_16,plain,
! [X908,X909] :
( ~ is_int(X909)
| X909 = zero_zero_int
| hAPP_nat_int(power_power_int(X909),X908) != zero_zero_int ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_231_field__power__not__zero])]) ).
cnf(c_0_17,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_13,c_0_14]) ).
cnf(c_0_18,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_15,c_0_14]) ).
fof(c_0_19,plain,
! [X1013,X1014,X1016] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1013),X1014))
| X1014 = plus_plus_int(X1013,hAPP_nat_int(semiri1621563631at_int,esk10_2(X1013,X1014)))
| ~ is_int(X1014) )
& ( X1014 != plus_plus_int(X1013,hAPP_nat_int(semiri1621563631at_int,X1016))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1013),X1014))
| ~ is_int(X1014) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_789_zle__iff__zadd])])])])]) ).
cnf(c_0_20,plain,
( X1 = zero_zero_int
| ~ is_int(X1)
| hAPP_nat_int(power_power_int(X1),X2) != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,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_17,c_0_18]) ).
fof(c_0_22,hypothesis,
! [X403,X404] :
( ~ is_int(X403)
| ~ is_int(X404)
| is_int(plus_plus_int(X403,X404)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[gsy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint])]) ).
fof(c_0_23,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_24,plain,
! [X1017] :
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1017)),zero_zero_int))
| X1017 = zero_zero_nat )
& ( X1017 != zero_zero_nat
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1017)),zero_zero_int)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_807_int__le__0__conv])]) ).
cnf(c_0_25,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X2),X1))
| X1 != plus_plus_int(X2,hAPP_nat_int(semiri1621563631at_int,X3))
| ~ is_int(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
( plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int
| ~ is_int(plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,hypothesis,
( is_int(plus_plus_int(X1,X2))
| ~ is_int(X1)
| ~ is_int(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,hypothesis,
is_int(hAPP_nat_int(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,hypothesis,
is_int(one_one_int),
inference(split_conjunct,[status(thm)],[gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint]) ).
cnf(c_0_30,plain,
( X1 = zero_zero_nat
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X1)),zero_zero_int)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
inference(split_conjunct,[status(thm)],[fact_254_transfer__int__nat__numerals_I2_J]) ).
cnf(c_0_32,plain,
one_one_nat != zero_zero_nat,
inference(split_conjunct,[status(thm)],[fact_226_one__neq__zero]) ).
cnf(c_0_33,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X1),plus_plus_int(X1,hAPP_nat_int(semiri1621563631at_int,X2))))
| ~ is_int(plus_plus_int(X1,hAPP_nat_int(semiri1621563631at_int,X2))) ),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_34,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_26,c_0_27]),c_0_28]),c_0_29])]) ).
cnf(c_0_35,hypothesis,
is_int(zero_zero_int),
inference(split_conjunct,[status(thm)],[gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint]) ).
cnf(c_0_36,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),zero_zero_int)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_37,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.23 % Problem : NUM925+3 : TPTP v8.1.2. Released v5.3.0.
% 0.11/0.24 % Command : run_E %s %d THM
% 0.23/0.43 % Computer : n016.cluster.edu
% 0.23/0.43 % Model : x86_64 x86_64
% 0.23/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.43 % Memory : 8042.1875MB
% 0.23/0.43 % OS : Linux 3.10.0-693.el7.x86_64
% 0.23/0.43 % CPULimit : 2400
% 0.23/0.43 % WCLimit : 300
% 0.23/0.43 % DateTime : Mon Oct 2 14:00:36 EDT 2023
% 0.23/0.43 % CPUTime :
% 0.44/0.63 Running first-order theorem proving
% 0.44/0.63 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/tmp/tmp.dOf1T2Dq8q/E---3.1_7572.p
% 3.32/1.09 # Version: 3.1pre001
% 3.32/1.09 # Preprocessing class: FMLSSMSMSSSNFFN.
% 3.32/1.09 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.32/1.09 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 3.32/1.09 # Starting new_bool_3 with 600s (2) cores
% 3.32/1.09 # Starting new_bool_1 with 600s (2) cores
% 3.32/1.09 # Starting sh5l with 300s (1) cores
% 3.32/1.09 # new_bool_3 with pid 7652 completed with status 0
% 3.32/1.09 # Result found by new_bool_3
% 3.32/1.09 # Preprocessing class: FMLSSMSMSSSNFFN.
% 3.32/1.09 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.32/1.09 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 3.32/1.09 # Starting new_bool_3 with 600s (2) cores
% 3.32/1.09 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 3.32/1.09 # Search class: FGHSM-SSLM31-DFFFFFNN
% 3.32/1.09 # Scheduled 6 strats onto 2 cores with 600 seconds (600 total)
% 3.32/1.09 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 325s (1) cores
% 3.32/1.09 # Starting new_bool_3 with 61s (1) cores
% 3.32/1.09 # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 7655 completed with status 0
% 3.32/1.09 # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 3.32/1.09 # Preprocessing class: FMLSSMSMSSSNFFN.
% 3.32/1.09 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.32/1.09 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 3.32/1.09 # Starting new_bool_3 with 600s (2) cores
% 3.32/1.09 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 3.32/1.09 # Search class: FGHSM-SSLM31-DFFFFFNN
% 3.32/1.09 # Scheduled 6 strats onto 2 cores with 600 seconds (600 total)
% 3.32/1.09 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 325s (1) cores
% 3.32/1.09 # Preprocessing time : 0.015 s
% 3.32/1.09 # Presaturation interreduction done
% 3.32/1.09
% 3.32/1.09 # Proof found!
% 3.32/1.09 # SZS status Theorem
% 3.32/1.09 # SZS output start CNFRefutation
% See solution above
% 3.32/1.09 # Parsed axioms : 1233
% 3.32/1.09 # Removed by relevancy pruning/SinE : 363
% 3.32/1.09 # Initial clauses : 1289
% 3.32/1.09 # Removed in clause preprocessing : 98
% 3.32/1.09 # Initial clauses in saturation : 1191
% 3.32/1.09 # Processed clauses : 2368
% 3.32/1.09 # ...of these trivial : 135
% 3.32/1.09 # ...subsumed : 527
% 3.32/1.09 # ...remaining for further processing : 1706
% 3.32/1.09 # Other redundant clauses eliminated : 196
% 3.32/1.09 # Clauses deleted for lack of memory : 0
% 3.32/1.09 # Backward-subsumed : 9
% 3.32/1.09 # Backward-rewritten : 25
% 3.32/1.09 # Generated clauses : 11702
% 3.32/1.09 # ...of the previous two non-redundant : 10243
% 3.32/1.09 # ...aggressively subsumed : 0
% 3.32/1.09 # Contextual simplify-reflections : 2
% 3.32/1.09 # Paramodulations : 11490
% 3.32/1.09 # Factorizations : 9
% 3.32/1.09 # NegExts : 0
% 3.32/1.09 # Equation resolutions : 215
% 3.32/1.09 # Total rewrite steps : 5778
% 3.32/1.09 # Propositional unsat checks : 0
% 3.32/1.09 # Propositional check models : 0
% 3.32/1.09 # Propositional check unsatisfiable : 0
% 3.32/1.09 # Propositional clauses : 0
% 3.32/1.09 # Propositional clauses after purity: 0
% 3.32/1.09 # Propositional unsat core size : 0
% 3.32/1.09 # Propositional preprocessing time : 0.000
% 3.32/1.09 # Propositional encoding time : 0.000
% 3.32/1.09 # Propositional solver time : 0.000
% 3.32/1.09 # Success case prop preproc time : 0.000
% 3.32/1.09 # Success case prop encoding time : 0.000
% 3.32/1.09 # Success case prop solver time : 0.000
% 3.32/1.09 # Current number of processed clauses : 839
% 3.32/1.09 # Positive orientable unit clauses : 189
% 3.32/1.09 # Positive unorientable unit clauses: 15
% 3.32/1.09 # Negative unit clauses : 75
% 3.32/1.09 # Non-unit-clauses : 560
% 3.32/1.09 # Current number of unprocessed clauses: 9762
% 3.32/1.09 # ...number of literals in the above : 23504
% 3.32/1.09 # Current number of archived formulas : 0
% 3.32/1.09 # Current number of archived clauses : 758
% 3.32/1.09 # Clause-clause subsumption calls (NU) : 112406
% 3.32/1.09 # Rec. Clause-clause subsumption calls : 60293
% 3.32/1.09 # Non-unit clause-clause subsumptions : 293
% 3.32/1.09 # Unit Clause-clause subsumption calls : 14448
% 3.32/1.09 # Rewrite failures with RHS unbound : 0
% 3.32/1.09 # BW rewrite match attempts : 541
% 3.32/1.09 # BW rewrite match successes : 205
% 3.32/1.09 # Condensation attempts : 0
% 3.32/1.09 # Condensation successes : 0
% 3.32/1.09 # Termbank termtop insertions : 319548
% 3.32/1.09
% 3.32/1.09 # -------------------------------------------------
% 3.32/1.09 # User time : 0.399 s
% 3.32/1.09 # System time : 0.015 s
% 3.32/1.09 # Total time : 0.414 s
% 3.32/1.09 # Maximum resident set size: 7080 pages
% 3.32/1.09
% 3.32/1.09 # -------------------------------------------------
% 3.32/1.09 # User time : 0.783 s
% 3.32/1.09 # System time : 0.020 s
% 3.32/1.09 # Total time : 0.803 s
% 3.32/1.09 # Maximum resident set size: 3560 pages
% 3.32/1.09 % E---3.1 exiting
% 3.32/1.09 % E---3.1 exiting
%------------------------------------------------------------------------------