TSTP Solution File: KLE137+1 by E-SAT---3.1
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%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : KLE137+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n009.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 18:05:14 EDT 2023
% Result : Theorem 0.15s 0.43s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 61 ( 42 unt; 0 def)
% Number of atoms : 82 ( 40 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 20 ~; 17 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 90 ( 5 sgn; 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(star_induction2,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X3,X1),X2),X3)
=> leq(multiplication(X2,star(X1)),X3) ),
file('/export/starexec/sandbox/tmp/tmp.8TZTf7Uj3v/E---3.1_27364.p',star_induction2) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/tmp/tmp.8TZTf7Uj3v/E---3.1_27364.p',multiplicative_right_identity) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/tmp/tmp.8TZTf7Uj3v/E---3.1_27364.p',additive_associativity) ).
fof(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/tmp/tmp.8TZTf7Uj3v/E---3.1_27364.p',idempotence) ).
fof(infty_unfold1,axiom,
! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
file('/export/starexec/sandbox/tmp/tmp.8TZTf7Uj3v/E---3.1_27364.p',infty_unfold1) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.8TZTf7Uj3v/E---3.1_27364.p',additive_commutativity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/tmp/tmp.8TZTf7Uj3v/E---3.1_27364.p',multiplicative_left_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.8TZTf7Uj3v/E---3.1_27364.p',order) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/tmp/tmp.8TZTf7Uj3v/E---3.1_27364.p',left_annihilation) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/tmp/tmp.8TZTf7Uj3v/E---3.1_27364.p',additive_identity) ).
fof(star_unfold2,axiom,
! [X1] : addition(one,multiplication(star(X1),X1)) = star(X1),
file('/export/starexec/sandbox/tmp/tmp.8TZTf7Uj3v/E---3.1_27364.p',star_unfold2) ).
fof(infty_coinduction,axiom,
! [X1,X2,X3] :
( leq(X3,addition(multiplication(X1,X3),X2))
=> leq(X3,multiplication(strong_iteration(X1),X2)) ),
file('/export/starexec/sandbox/tmp/tmp.8TZTf7Uj3v/E---3.1_27364.p',infty_coinduction) ).
fof(goals,conjecture,
! [X4] : leq(X4,strong_iteration(one)),
file('/export/starexec/sandbox/tmp/tmp.8TZTf7Uj3v/E---3.1_27364.p',goals) ).
fof(c_0_13,plain,
! [X9,X10,X11] :
( ~ leq(addition(multiplication(X11,X9),X10),X11)
| leq(multiplication(X10,star(X9)),X11) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction2])]) ).
fof(c_0_14,plain,
! [X19] : multiplication(X19,one) = X19,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_15,plain,
! [X34,X35,X36] : addition(X36,addition(X35,X34)) = addition(addition(X36,X35),X34),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_16,plain,
! [X37] : addition(X37,X37) = X37,
inference(variable_rename,[status(thm)],[idempotence]) ).
fof(c_0_17,plain,
! [X17] : strong_iteration(X17) = addition(multiplication(X17,strong_iteration(X17)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
fof(c_0_18,plain,
! [X32,X33] : addition(X32,X33) = addition(X33,X32),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_19,plain,
( leq(multiplication(X3,star(X2)),X1)
| ~ leq(addition(multiplication(X1,X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( leq(multiplication(X1,star(one)),X2)
| ~ leq(addition(X2,X1),X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_28,plain,
! [X20] : multiplication(one,X20) = X20,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_29,plain,
( leq(multiplication(X1,star(one)),X2)
| ~ leq(addition(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_30,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_32,plain,
! [X15,X16] :
( ( ~ leq(X15,X16)
| addition(X15,X16) = X16 )
& ( addition(X15,X16) != X16
| leq(X15,X16) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_33,plain,
! [X39] : multiplication(zero,X39) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_34,plain,
! [X38] : addition(X38,zero) = X38,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_35,plain,
( leq(star(one),strong_iteration(X1))
| ~ leq(strong_iteration(X1),strong_iteration(X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_36,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_39,plain,
! [X22] : addition(one,multiplication(star(X22),X22)) = star(X22),
inference(variable_rename,[status(thm)],[star_unfold2]) ).
cnf(c_0_40,plain,
leq(star(one),strong_iteration(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_22])]) ).
cnf(c_0_41,plain,
strong_iteration(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_37]),c_0_38]) ).
cnf(c_0_42,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_43,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_44,plain,
leq(star(one),one),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_26,c_0_42]) ).
cnf(c_0_46,plain,
star(one) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_24]),c_0_45]) ).
fof(c_0_47,plain,
! [X12,X13,X14] :
( ~ leq(X14,addition(multiplication(X12,X14),X13))
| leq(X14,multiplication(strong_iteration(X12),X13)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[infty_coinduction])]) ).
cnf(c_0_48,plain,
( leq(X1,X2)
| ~ leq(addition(X1,X2),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_24]),c_0_46]),c_0_20]) ).
cnf(c_0_49,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_50,plain,
( leq(X1,X2)
| ~ leq(addition(X2,X1),X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_24]) ).
cnf(c_0_51,plain,
( leq(X1,multiplication(strong_iteration(one),X2))
| ~ leq(X1,addition(X1,X2)) ),
inference(spm,[status(thm)],[c_0_49,c_0_31]) ).
cnf(c_0_52,plain,
( leq(X1,X2)
| addition(X2,addition(X1,X2)) != X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_36]),c_0_21]) ).
fof(c_0_53,negated_conjecture,
~ ! [X4] : leq(X4,strong_iteration(one)),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_54,plain,
( leq(X1,multiplication(strong_iteration(one),X2))
| ~ leq(X1,addition(X2,X1)) ),
inference(spm,[status(thm)],[c_0_51,c_0_24]) ).
cnf(c_0_55,plain,
( leq(X1,X2)
| addition(X2,X1) != X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_24]),c_0_26]) ).
fof(c_0_56,negated_conjecture,
~ leq(esk1_0,strong_iteration(one)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])]) ).
cnf(c_0_57,plain,
leq(X1,multiplication(strong_iteration(one),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_21]),c_0_22])]) ).
cnf(c_0_58,negated_conjecture,
~ leq(esk1_0,strong_iteration(one)),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_59,plain,
leq(X1,strong_iteration(one)),
inference(spm,[status(thm)],[c_0_57,c_0_20]) ).
cnf(c_0_60,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : KLE137+1 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.10 % Command : run_E %s %d THM
% 0.10/0.30 % Computer : n009.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 2400
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue Oct 3 04:39:29 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.15/0.40 Running first-order model finding
% 0.15/0.40 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.8TZTf7Uj3v/E---3.1_27364.p
% 0.15/0.43 # Version: 3.1pre001
% 0.15/0.43 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.43 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.43 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.43 # Starting new_bool_3 with 300s (1) cores
% 0.15/0.43 # Starting new_bool_1 with 300s (1) cores
% 0.15/0.43 # Starting sh5l with 300s (1) cores
% 0.15/0.43 # new_bool_1 with pid 27444 completed with status 0
% 0.15/0.43 # Result found by new_bool_1
% 0.15/0.43 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.43 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.43 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.43 # Starting new_bool_3 with 300s (1) cores
% 0.15/0.43 # Starting new_bool_1 with 300s (1) cores
% 0.15/0.43 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.43 # Search class: FHUSM-FFSF21-MFFFFFNN
% 0.15/0.43 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.43 # Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 28s (1) cores
% 0.15/0.43 # G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 27452 completed with status 0
% 0.15/0.43 # Result found by G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.15/0.43 # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.43 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.43 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.43 # Starting new_bool_3 with 300s (1) cores
% 0.15/0.43 # Starting new_bool_1 with 300s (1) cores
% 0.15/0.43 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.43 # Search class: FHUSM-FFSF21-MFFFFFNN
% 0.15/0.43 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.43 # Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 28s (1) cores
% 0.15/0.43 # Preprocessing time : 0.001 s
% 0.15/0.43 # Presaturation interreduction done
% 0.15/0.43
% 0.15/0.43 # Proof found!
% 0.15/0.43 # SZS status Theorem
% 0.15/0.43 # SZS output start CNFRefutation
% See solution above
% 0.15/0.43 # Parsed axioms : 19
% 0.15/0.43 # Removed by relevancy pruning/SinE : 0
% 0.15/0.43 # Initial clauses : 20
% 0.15/0.43 # Removed in clause preprocessing : 0
% 0.15/0.43 # Initial clauses in saturation : 20
% 0.15/0.43 # Processed clauses : 156
% 0.15/0.43 # ...of these trivial : 13
% 0.15/0.43 # ...subsumed : 20
% 0.15/0.43 # ...remaining for further processing : 123
% 0.15/0.43 # Other redundant clauses eliminated : 2
% 0.15/0.43 # Clauses deleted for lack of memory : 0
% 0.15/0.43 # Backward-subsumed : 1
% 0.15/0.43 # Backward-rewritten : 37
% 0.15/0.43 # Generated clauses : 861
% 0.15/0.43 # ...of the previous two non-redundant : 582
% 0.15/0.43 # ...aggressively subsumed : 0
% 0.15/0.43 # Contextual simplify-reflections : 1
% 0.15/0.43 # Paramodulations : 859
% 0.15/0.43 # Factorizations : 0
% 0.15/0.43 # NegExts : 0
% 0.15/0.43 # Equation resolutions : 2
% 0.15/0.43 # Total rewrite steps : 792
% 0.15/0.43 # Propositional unsat checks : 0
% 0.15/0.43 # Propositional check models : 0
% 0.15/0.43 # Propositional check unsatisfiable : 0
% 0.15/0.43 # Propositional clauses : 0
% 0.15/0.43 # Propositional clauses after purity: 0
% 0.15/0.43 # Propositional unsat core size : 0
% 0.15/0.43 # Propositional preprocessing time : 0.000
% 0.15/0.43 # Propositional encoding time : 0.000
% 0.15/0.43 # Propositional solver time : 0.000
% 0.15/0.43 # Success case prop preproc time : 0.000
% 0.15/0.43 # Success case prop encoding time : 0.000
% 0.15/0.43 # Success case prop solver time : 0.000
% 0.15/0.43 # Current number of processed clauses : 65
% 0.15/0.43 # Positive orientable unit clauses : 39
% 0.15/0.43 # Positive unorientable unit clauses: 3
% 0.15/0.43 # Negative unit clauses : 1
% 0.15/0.43 # Non-unit-clauses : 22
% 0.15/0.43 # Current number of unprocessed clauses: 455
% 0.15/0.43 # ...number of literals in the above : 691
% 0.15/0.43 # Current number of archived formulas : 0
% 0.15/0.43 # Current number of archived clauses : 58
% 0.15/0.43 # Clause-clause subsumption calls (NU) : 124
% 0.15/0.43 # Rec. Clause-clause subsumption calls : 124
% 0.15/0.43 # Non-unit clause-clause subsumptions : 19
% 0.15/0.43 # Unit Clause-clause subsumption calls : 62
% 0.15/0.43 # Rewrite failures with RHS unbound : 0
% 0.15/0.43 # BW rewrite match attempts : 119
% 0.15/0.43 # BW rewrite match successes : 69
% 0.15/0.43 # Condensation attempts : 0
% 0.15/0.43 # Condensation successes : 0
% 0.15/0.43 # Termbank termtop insertions : 9097
% 0.15/0.43
% 0.15/0.43 # -------------------------------------------------
% 0.15/0.43 # User time : 0.014 s
% 0.15/0.43 # System time : 0.002 s
% 0.15/0.43 # Total time : 0.016 s
% 0.15/0.43 # Maximum resident set size: 1716 pages
% 0.15/0.43
% 0.15/0.43 # -------------------------------------------------
% 0.15/0.43 # User time : 0.014 s
% 0.15/0.43 # System time : 0.004 s
% 0.15/0.43 # Total time : 0.018 s
% 0.15/0.43 # Maximum resident set size: 1684 pages
% 0.15/0.43 % E---3.1 exiting
%------------------------------------------------------------------------------