TSTP Solution File: KLE040+1 by E---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : KLE040+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n004.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 18:03:59 EDT 2023
% Result : Timeout 4.39s 300.18s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 39 unt; 0 def)
% Number of atoms : 85 ( 44 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 47 ( 23 ~; 20 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn; 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p',additive_idempotence) ).
fof(star_induction_right,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X2),X3),X1)
=> leq(multiplication(X3,star(X2)),X1) ),
file('/export/starexec/sandbox/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p',star_induction_right) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p',multiplicative_right_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p',additive_commutativity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p',order) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p',multiplicative_left_identity) ).
fof(star_unfold_right,axiom,
! [X1] : leq(addition(one,multiplication(X1,star(X1))),star(X1)),
file('/export/starexec/sandbox/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p',star_unfold_right) ).
fof(star_induction_left,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X2),X3),X2)
=> leq(multiplication(star(X1),X3),X2) ),
file('/export/starexec/sandbox/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p',star_induction_left) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p',right_distributivity) ).
fof(goals,conjecture,
! [X4] : multiplication(star(X4),star(X4)) = star(X4),
file('/export/starexec/sandbox/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p',goals) ).
fof(c_0_11,plain,
! [X31,X32,X33] : addition(X33,addition(X32,X31)) = addition(addition(X33,X32),X31),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_12,plain,
! [X35] : addition(X35,X35) = X35,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_13,plain,
! [X11,X12,X13] :
( ~ leq(addition(multiplication(X11,X12),X13),X11)
| leq(multiplication(X13,star(X12)),X11) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction_right])]) ).
fof(c_0_14,plain,
! [X17] : multiplication(X17,one) = X17,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_15,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X29,X30] : addition(X29,X30) = addition(X30,X29),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_18,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_19,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_20,plain,
! [X27,X28] :
( ( ~ leq(X27,X28)
| addition(X27,X28) = X28 )
& ( addition(X27,X28) != X28
| leq(X27,X28) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
cnf(c_0_21,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( leq(multiplication(X1,star(one)),X2)
| ~ leq(addition(X2,X1),X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_26,plain,
! [X18] : multiplication(one,X18) = X18,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_27,plain,
! [X6] : leq(addition(one,multiplication(X6,star(X6))),star(X6)),
inference(variable_rename,[status(thm)],[star_unfold_right]) ).
cnf(c_0_28,plain,
( leq(multiplication(X1,star(one)),X2)
| addition(X1,X2) != X2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_15]),c_0_25]) ).
cnf(c_0_29,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,plain,
( leq(star(one),X1)
| addition(one,X1) != X1 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
leq(addition(one,star(one)),star(one)),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_34,plain,
( addition(star(one),X1) = X1
| addition(one,X1) != X1 ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
addition(one,star(one)) = star(one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_33]),c_0_15]),c_0_16]) ).
cnf(c_0_36,plain,
( addition(X1,star(one)) = X1
| addition(one,X1) != X1 ),
inference(spm,[status(thm)],[c_0_22,c_0_34]) ).
cnf(c_0_37,plain,
( leq(multiplication(X1,star(X2)),X3)
| ~ leq(addition(X1,multiplication(X3,X2)),X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_38,plain,
star(one) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_16])]) ).
cnf(c_0_39,plain,
( leq(X1,X2)
| ~ leq(addition(X1,X2),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_19]),c_0_38]),c_0_19]) ).
cnf(c_0_40,plain,
( leq(addition(X1,X2),X3)
| ~ leq(addition(X1,addition(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_39,c_0_15]) ).
fof(c_0_41,plain,
! [X8,X9,X10] :
( ~ leq(addition(multiplication(X8,X9),X10),X9)
| leq(multiplication(star(X8),X10),X9) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction_left])]) ).
cnf(c_0_42,plain,
( leq(addition(X1,X2),X1)
| ~ leq(addition(X2,X1),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_16]),c_0_15]),c_0_25]) ).
cnf(c_0_43,plain,
( leq(multiplication(star(X1),X3),X2)
| ~ leq(addition(multiplication(X1,X2),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_44,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_30]),c_0_15]),c_0_22]) ).
cnf(c_0_45,plain,
( leq(multiplication(X1,star(one)),X2)
| ~ leq(addition(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_46,plain,
( leq(addition(X1,X2),X1)
| addition(X2,X1) != X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_24]),c_0_15]),c_0_16]) ).
cnf(c_0_47,plain,
( leq(multiplication(star(X1),X2),X3)
| ~ leq(addition(X2,multiplication(X1,X3)),X3) ),
inference(spm,[status(thm)],[c_0_43,c_0_22]) ).
cnf(c_0_48,plain,
addition(star(X1),multiplication(X1,star(X1))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_44]),c_0_15]),c_0_22]),c_0_21]) ).
cnf(c_0_49,plain,
leq(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_38]),c_0_19]),c_0_16])]) ).
fof(c_0_50,plain,
! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_51,negated_conjecture,
~ ! [X4] : multiplication(star(X4),star(X4)) = star(X4),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_52,plain,
leq(multiplication(star(X1),star(X1)),star(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
cnf(c_0_53,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
fof(c_0_54,negated_conjecture,
multiplication(star(esk1_0),star(esk1_0)) != star(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])]) ).
cnf(c_0_55,plain,
addition(star(X1),multiplication(star(X1),star(X1))) = star(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_52]),c_0_22]) ).
cnf(c_0_56,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_19]),c_0_22]) ).
cnf(c_0_57,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_21,c_0_44]) ).
cnf(c_0_58,negated_conjecture,
multiplication(star(esk1_0),star(esk1_0)) != star(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_59,plain,
multiplication(star(X1),star(X1)) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56]),c_0_22]),c_0_57]) ).
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
% 0.06/0.11 % Problem : KLE040+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n004.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 2400
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Oct 3 04:48:59 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.17/0.44 Running first-order theorem proving
% 0.17/0.44 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/tmp/tmp.QLRnZWL4DE/E---3.1_31930.p
% 4.39/300.18 # Version: 3.1pre001
% 4.39/300.18 # Preprocessing class: FSMSSMSSSSSNFFN.
% 4.39/300.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.39/300.18 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.39/300.18 # Starting new_bool_3 with 300s (1) cores
% 4.39/300.18 # Starting new_bool_1 with 300s (1) cores
% 4.39/300.18 # Starting sh5l with 300s (1) cores
% 4.39/300.18 # sh5l with pid 32011 completed with status 0
% 4.39/300.18 # Result found by sh5l
% 4.39/300.18 # Preprocessing class: FSMSSMSSSSSNFFN.
% 4.39/300.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.39/300.18 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.39/300.18 # Starting new_bool_3 with 300s (1) cores
% 4.39/300.18 # Starting new_bool_1 with 300s (1) cores
% 4.39/300.18 # Starting sh5l with 300s (1) cores
% 4.39/300.18 # SinE strategy is gf500_gu_R04_F100_L20000
% 4.39/300.18 # Search class: FHUSM-FFSF21-MFFFFFNN
% 4.39/300.18 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 4.39/300.18 # Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 28s (1) cores
% 4.39/300.18 # G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 32018 completed with status 0
% 4.39/300.18 # Result found by G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 4.39/300.18 # Preprocessing class: FSMSSMSSSSSNFFN.
% 4.39/300.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.39/300.18 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.39/300.18 # Starting new_bool_3 with 300s (1) cores
% 4.39/300.18 # Starting new_bool_1 with 300s (1) cores
% 4.39/300.18 # Starting sh5l with 300s (1) cores
% 4.39/300.18 # SinE strategy is gf500_gu_R04_F100_L20000
% 4.39/300.18 # Search class: FHUSM-FFSF21-MFFFFFNN
% 4.39/300.18 # Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 4.39/300.18 # Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 28s (1) cores
% 4.39/300.18 # Preprocessing time : 0.001 s
% 4.39/300.18 # Presaturation interreduction done
% 4.39/300.18
% 4.39/300.18 # Proof found!
% 4.39/300.18 # SZS status Theorem
% 4.39/300.18 # SZS output start CNFRefutation
% See solution above
% 4.39/300.18 # Parsed axioms : 17
% 4.39/300.18 # Removed by relevancy pruning/SinE : 0
% 4.39/300.18 # Initial clauses : 18
% 4.39/300.18 # Removed in clause preprocessing : 0
% 4.39/300.18 # Initial clauses in saturation : 18
% 4.39/300.18 # Processed clauses : 381
% 4.39/300.18 # ...of these trivial : 35
% 4.39/300.18 # ...subsumed : 167
% 4.39/300.18 # ...remaining for further processing : 179
% 4.39/300.18 # Other redundant clauses eliminated : 13
% 4.39/300.18 # Clauses deleted for lack of memory : 0
% 4.39/300.18 # Backward-subsumed : 16
% 4.39/300.18 # Backward-rewritten : 43
% 4.39/300.18 # Generated clauses : 2283
% 4.39/300.18 # ...of the previous two non-redundant : 1284
% 4.39/300.18 # ...aggressively subsumed : 0
% 4.39/300.18 # Contextual simplify-reflections : 1
% 4.39/300.18 # Paramodulations : 2270
% 4.39/300.18 # Factorizations : 0
% 4.39/300.18 # NegExts : 0
% 4.39/300.18 # Equation resolutions : 13
% 4.39/300.18 # Total rewrite steps : 3272
% 4.39/300.18 # Propositional unsat checks : 0
% 4.39/300.18 # Propositional check models : 0
% 4.39/300.18 # Propositional check unsatisfiable : 0
% 4.39/300.18 # Propositional clauses : 0
% 4.39/300.18 # Propositional clauses after purity: 0
% 4.39/300.18 # Propositional unsat core size : 0
% 4.39/300.18 # Propositional preprocessing time : 0.000
% 4.39/300.18 # Propositional encoding time : 0.000
% 4.39/300.18 # Propositional solver time : 0.000
% 4.39/300.18 # Success case prop preproc time : 0.000
% 4.39/300.18 # Success case prop encoding time : 0.000
% 4.39/300.18 # Success case prop solver time : 0.000
% 4.39/300.18 # Current number of processed clauses : 102
% 4.39/300.18 # Positive orientable unit clauses : 43
% 4.39/300.18 # Positive unorientable unit clauses: 4
% 4.39/300.18 # Negative unit clauses : 6
% 4.39/300.18 # Non-unit-clauses : 49
% 4.39/300.18 # Current number of unprocessed clauses: 889
% 4.39/300.18 # ...number of literals in the above : 1596
% 4.39/300.18 # Current number of archived formulas : 0
% 4.39/300.18 # Current number of archived clauses : 77
% 4.39/300.18 # Clause-clause subsumption calls (NU) : 813
% 4.39/300.18 # Rec. Clause-clause subsumption calls : 797
% 4.39/300.18 # Non-unit clause-clause subsumptions : 150
% 4.39/300.18 # Unit Clause-clause subsumption calls : 127
% 4.39/300.18 # Rewrite failures with RHS unbound : 0
% 4.39/300.18 # BW rewrite match attempts : 199
% 4.39/300.18 # BW rewrite match successes : 58
% 4.39/300.18 # Condensation attempts : 0
% 4.39/300.18 # Condensation successes : 0
% 4.39/300.18 # Termbank termtop insertions : 23844
% 4.39/300.18
% 4.39/300.18 # -------------------------------------------------
% 4.39/300.18 # User time : 0.029 s
% 4.39/300.18 # System time : 0.002 s
% 4.39/300.18 # Total time : 0.031 s
% 4.39/300.18 # Maximum resident set size: 1740 pages
% 4.39/300.18
% 4.39/300.18 # -------------------------------------------------
% 4.39/300.18 # User time : 0.029 s
% 4.39/300.18 # System time : 0.004 s
% 4.39/300.18 # Total time : 0.034 s
% 4.39/300.18 # Maximum resident set size: 1688 pages
% 4.39/300.18 % E---3.1 exiting
% 4.39/300.18 % E---3.1 exiting
%------------------------------------------------------------------------------