TSTP Solution File: NUM925+5 by E---3.2.0
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%------------------------------------------------------------------------------
% File : E---3.2.0
% Problem : NUM925+5 : TPTP v8.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n001.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 : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 12:39:05 EDT 2024
% Result : Theorem 0.19s 0.54s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 50 ( 41 unt; 0 def)
% Number of atoms : 72 ( 50 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 43 ( 21 ~; 16 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 39 ( 4 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_92_Bit1__def,axiom,
! [X19] : bit1(X19) = plus_plus(int,plus_plus(int,one_one(int),X19),X19),
file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',fact_92_Bit1__def) ).
fof(fact_47_zadd__commute,axiom,
! [X15,X7] : plus_plus(int,X15,X7) = plus_plus(int,X7,X15),
file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',fact_47_zadd__commute) ).
fof(fact_76_add__Pls,axiom,
! [X19] : plus_plus(int,pls,X19) = X19,
file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',fact_76_add__Pls) ).
fof(fact_75_add__Pls__right,axiom,
! [X19] : plus_plus(int,X19,pls) = X19,
file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',fact_75_add__Pls__right) ).
fof(fact_2_sum__power2__eq__zero__iff,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X4,X5] :
( plus_plus(X1,power_power(X1,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(X1,X5,number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X1)
<=> ( ti(X1,X4) = zero_zero(X1)
& ti(X1,X5) = zero_zero(X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',fact_2_sum__power2__eq__zero__iff) ).
fof(conj_0,conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int),
file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',conj_0) ).
fof(fact_29_nat__1__add__1,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',fact_29_nat__1__add__1) ).
fof(fact_73_Pls__def,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',fact_73_Pls__def) ).
fof(fact_85_add__numeral__0__right,axiom,
! [X1] :
( number_ring(X1)
=> ! [X30] : plus_plus(X1,X30,number_number_of(X1,pls)) = ti(X1,X30) ),
file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',fact_85_add__numeral__0__right) ).
fof(fact_19_zero__is__num__zero,axiom,
zero_zero(int) = number_number_of(int,pls),
file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',fact_19_zero__is__num__zero) ).
fof(arity_Int_Oint___Int_Onumber__ring,axiom,
number_ring(int),
file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',arity_Int_Oint___Int_Onumber__ring) ).
fof(arity_Int_Oint___Rings_Olinordered__idom,axiom,
linordered_idom(int),
file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',arity_Int_Oint___Rings_Olinordered__idom) ).
fof(fact_32_rel__simps_I2_J,axiom,
~ ord_less(int,pls,pls),
file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',fact_32_rel__simps_I2_J) ).
fof(fact_0_n1pos,axiom,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
file('/export/starexec/sandbox2/tmp/tmp.9xVFQLMyCN/E---3.1_18066.p',fact_0_n1pos) ).
fof(c_0_14,plain,
! [X79] : bit1(X79) = plus_plus(int,plus_plus(int,one_one(int),X79),X79),
inference(variable_rename,[status(thm)],[fact_92_Bit1__def]) ).
fof(c_0_15,plain,
! [X116,X117] : plus_plus(int,X116,X117) = plus_plus(int,X117,X116),
inference(variable_rename,[status(thm)],[fact_47_zadd__commute]) ).
fof(c_0_16,plain,
! [X83] : plus_plus(int,pls,X83) = X83,
inference(variable_rename,[status(thm)],[fact_76_add__Pls]) ).
cnf(c_0_17,plain,
bit1(X1) = plus_plus(int,plus_plus(int,one_one(int),X1),X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
plus_plus(int,X1,X2) = plus_plus(int,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X82] : plus_plus(int,X82,pls) = X82,
inference(variable_rename,[status(thm)],[fact_75_add__Pls__right]) ).
fof(c_0_20,plain,
! [X88,X89,X90] :
( ( ti(X88,X89) = zero_zero(X88)
| plus_plus(X88,power_power(X88,X89,number_number_of(nat,bit0(bit1(pls)))),power_power(X88,X90,number_number_of(nat,bit0(bit1(pls))))) != zero_zero(X88)
| ~ linordered_idom(X88) )
& ( ti(X88,X90) = zero_zero(X88)
| plus_plus(X88,power_power(X88,X89,number_number_of(nat,bit0(bit1(pls)))),power_power(X88,X90,number_number_of(nat,bit0(bit1(pls))))) != zero_zero(X88)
| ~ linordered_idom(X88) )
& ( ti(X88,X89) != zero_zero(X88)
| ti(X88,X90) != zero_zero(X88)
| plus_plus(X88,power_power(X88,X89,number_number_of(nat,bit0(bit1(pls)))),power_power(X88,X90,number_number_of(nat,bit0(bit1(pls))))) = zero_zero(X88)
| ~ linordered_idom(X88) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_2_sum__power2__eq__zero__iff])])])])]) ).
cnf(c_0_21,plain,
plus_plus(int,pls,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
plus_plus(int,X1,plus_plus(int,one_one(int),X1)) = bit1(X1),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
plus_plus(int,X1,pls) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_24,negated_conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(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_25,plain,
( ti(X1,X2) = zero_zero(X1)
| plus_plus(X1,power_power(X1,X3,number_number_of(nat,bit0(bit1(pls)))),power_power(X1,X2,number_number_of(nat,bit0(bit1(pls))))) != zero_zero(X1)
| ~ linordered_idom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
inference(split_conjunct,[status(thm)],[fact_29_nat__1__add__1]) ).
cnf(c_0_27,plain,
bit1(pls) = one_one(int),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_28,negated_conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
pls = zero_zero(int),
inference(split_conjunct,[status(thm)],[fact_73_Pls__def]) ).
fof(c_0_30,plain,
! [X178,X179] :
( ~ number_ring(X178)
| plus_plus(X178,X179,number_number_of(X178,pls)) = ti(X178,X179) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_85_add__numeral__0__right])])])]) ).
cnf(c_0_31,plain,
zero_zero(int) = number_number_of(int,pls),
inference(split_conjunct,[status(thm)],[fact_19_zero__is__num__zero]) ).
cnf(c_0_32,plain,
( ti(X1,X2) = zero_zero(X1)
| plus_plus(X1,power_power(X1,X3,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X1,X2,plus_plus(nat,one_one(nat),one_one(nat)))) != zero_zero(X1)
| ~ linordered_idom(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_26]) ).
cnf(c_0_33,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(one_one(int))),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,negated_conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(nat,one_one(nat),one_one(nat))) = pls,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_26]),c_0_29]) ).
cnf(c_0_35,plain,
( plus_plus(X1,X2,number_number_of(X1,pls)) = ti(X1,X2)
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,plain,
number_ring(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Int_Onumber__ring]) ).
cnf(c_0_37,plain,
number_number_of(int,pls) = pls,
inference(rw,[status(thm)],[c_0_31,c_0_29]) ).
cnf(c_0_38,plain,
( ti(X1,X2) = zero_zero(X1)
| plus_plus(X1,power_power(X1,X3,number_number_of(nat,bit0(one_one(int)))),power_power(X1,X2,number_number_of(nat,bit0(one_one(int))))) != zero_zero(X1)
| ~ linordered_idom(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_33]) ).
cnf(c_0_39,negated_conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(one_one(int)))) = pls,
inference(rw,[status(thm)],[c_0_34,c_0_33]) ).
cnf(c_0_40,plain,
ti(int,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_23]) ).
cnf(c_0_41,plain,
linordered_idom(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Olinordered__idom]) ).
fof(c_0_42,plain,
~ ord_less(int,pls,pls),
inference(fof_simplification,[status(thm)],[fact_32_rel__simps_I2_J]) ).
cnf(c_0_43,plain,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(split_conjunct,[status(thm)],[fact_0_n1pos]) ).
cnf(c_0_44,negated_conjecture,
( plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) = pls
| power_power(int,X1,number_number_of(nat,bit0(one_one(int)))) != pls ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_29]),c_0_23]),c_0_29]),c_0_41])]) ).
fof(c_0_45,plain,
~ ord_less(int,pls,pls),
inference(fof_nnf,[status(thm)],[c_0_42]) ).
cnf(c_0_46,plain,
ord_less(int,pls,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(rw,[status(thm)],[c_0_43,c_0_29]) ).
cnf(c_0_47,negated_conjecture,
plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) = pls,
inference(spm,[status(thm)],[c_0_44,c_0_39]) ).
cnf(c_0_48,plain,
~ ord_less(int,pls,pls),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_49,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47]),c_0_48]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : NUM925+5 : TPTP v8.2.0. Released v5.3.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.35 % DateTime : Sat Jun 22 23:54:54 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.19/0.49 Running first-order theorem proving
% 0.19/0.49 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.9xVFQLMyCN/E---3.1_18066.p
% 0.19/0.54 # Version: 3.2.0
% 0.19/0.54 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.19/0.54 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.54 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.19/0.54 # Starting new_bool_3 with 300s (1) cores
% 0.19/0.54 # Starting new_bool_1 with 300s (1) cores
% 0.19/0.54 # Starting sh5l with 300s (1) cores
% 0.19/0.54 # new_bool_1 with pid 18147 completed with status 0
% 0.19/0.54 # Result found by new_bool_1
% 0.19/0.54 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.19/0.54 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.54 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.19/0.54 # Starting new_bool_3 with 300s (1) cores
% 0.19/0.54 # Starting new_bool_1 with 300s (1) cores
% 0.19/0.54 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.54 # Search class: FGHSM-FFLM31-MFFFFFNN
% 0.19/0.54 # Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.54 # Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 109s (1) cores
% 0.19/0.54 # 208_C09_12_F1_SE_CS_SP_PS_S070I with pid 18154 completed with status 0
% 0.19/0.54 # Result found by 208_C09_12_F1_SE_CS_SP_PS_S070I
% 0.19/0.54 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.19/0.54 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.54 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.19/0.54 # Starting new_bool_3 with 300s (1) cores
% 0.19/0.54 # Starting new_bool_1 with 300s (1) cores
% 0.19/0.54 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.54 # Search class: FGHSM-FFLM31-MFFFFFNN
% 0.19/0.54 # Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.54 # Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 109s (1) cores
% 0.19/0.54 # Preprocessing time : 0.002 s
% 0.19/0.54 # Presaturation interreduction done
% 0.19/0.54
% 0.19/0.54 # Proof found!
% 0.19/0.54 # SZS status Theorem
% 0.19/0.54 # SZS output start CNFRefutation
% See solution above
% 0.19/0.54 # Parsed axioms : 153
% 0.19/0.54 # Removed by relevancy pruning/SinE : 43
% 0.19/0.54 # Initial clauses : 148
% 0.19/0.54 # Removed in clause preprocessing : 3
% 0.19/0.54 # Initial clauses in saturation : 145
% 0.19/0.54 # Processed clauses : 674
% 0.19/0.54 # ...of these trivial : 13
% 0.19/0.54 # ...subsumed : 320
% 0.19/0.54 # ...remaining for further processing : 341
% 0.19/0.54 # Other redundant clauses eliminated : 6
% 0.19/0.54 # Clauses deleted for lack of memory : 0
% 0.19/0.54 # Backward-subsumed : 1
% 0.19/0.54 # Backward-rewritten : 24
% 0.19/0.54 # Generated clauses : 1218
% 0.19/0.54 # ...of the previous two non-redundant : 997
% 0.19/0.54 # ...aggressively subsumed : 0
% 0.19/0.54 # Contextual simplify-reflections : 0
% 0.19/0.54 # Paramodulations : 1207
% 0.19/0.54 # Factorizations : 2
% 0.19/0.54 # NegExts : 0
% 0.19/0.54 # Equation resolutions : 9
% 0.19/0.54 # Disequality decompositions : 0
% 0.19/0.54 # Total rewrite steps : 1460
% 0.19/0.54 # ...of those cached : 1317
% 0.19/0.54 # Propositional unsat checks : 0
% 0.19/0.54 # Propositional check models : 0
% 0.19/0.54 # Propositional check unsatisfiable : 0
% 0.19/0.54 # Propositional clauses : 0
% 0.19/0.54 # Propositional clauses after purity: 0
% 0.19/0.54 # Propositional unsat core size : 0
% 0.19/0.54 # Propositional preprocessing time : 0.000
% 0.19/0.54 # Propositional encoding time : 0.000
% 0.19/0.54 # Propositional solver time : 0.000
% 0.19/0.54 # Success case prop preproc time : 0.000
% 0.19/0.54 # Success case prop encoding time : 0.000
% 0.19/0.54 # Success case prop solver time : 0.000
% 0.19/0.54 # Current number of processed clauses : 195
% 0.19/0.54 # Positive orientable unit clauses : 55
% 0.19/0.54 # Positive unorientable unit clauses: 2
% 0.19/0.54 # Negative unit clauses : 35
% 0.19/0.54 # Non-unit-clauses : 103
% 0.19/0.54 # Current number of unprocessed clauses: 575
% 0.19/0.54 # ...number of literals in the above : 1228
% 0.19/0.54 # Current number of archived formulas : 0
% 0.19/0.54 # Current number of archived clauses : 142
% 0.19/0.54 # Clause-clause subsumption calls (NU) : 1664
% 0.19/0.54 # Rec. Clause-clause subsumption calls : 1409
% 0.19/0.54 # Non-unit clause-clause subsumptions : 75
% 0.19/0.54 # Unit Clause-clause subsumption calls : 140
% 0.19/0.54 # Rewrite failures with RHS unbound : 0
% 0.19/0.54 # BW rewrite match attempts : 217
% 0.19/0.54 # BW rewrite match successes : 43
% 0.19/0.54 # Condensation attempts : 0
% 0.19/0.54 # Condensation successes : 0
% 0.19/0.54 # Termbank termtop insertions : 29932
% 0.19/0.54 # Search garbage collected termcells : 1367
% 0.19/0.54
% 0.19/0.54 # -------------------------------------------------
% 0.19/0.54 # User time : 0.035 s
% 0.19/0.54 # System time : 0.005 s
% 0.19/0.54 # Total time : 0.040 s
% 0.19/0.54 # Maximum resident set size: 2220 pages
% 0.19/0.54
% 0.19/0.54 # -------------------------------------------------
% 0.19/0.54 # User time : 0.037 s
% 0.19/0.54 # System time : 0.008 s
% 0.19/0.54 # Total time : 0.044 s
% 0.19/0.54 # Maximum resident set size: 1856 pages
% 0.19/0.54 % E---3.1 exiting
% 0.19/0.54 % E exiting
%------------------------------------------------------------------------------