TSTP Solution File: KLE151+1 by E-SAT---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : KLE151+1 : TPTP v8.1.2. Released v4.0.0.
% 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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 18:05:18 EDT 2023
% Result : Theorem 84.53s 11.20s
% Output : CNFRefutation 84.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 51 ( 42 unt; 0 def)
% Number of atoms : 62 ( 43 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 11 ~; 8 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn; 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(infty_unfold1,axiom,
! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',infty_unfold1) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',additive_commutativity) ).
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.ZM0SnZjvGd/E---3.1_26734.p',infty_coinduction) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',multiplicative_associativity) ).
fof(distributivity2,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',distributivity2) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',multiplicative_left_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',order) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',additive_associativity) ).
fof(distributivity1,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',distributivity1) ).
fof(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',idempotence) ).
fof(goals,conjecture,
! [X4,X5] : leq(multiplication(X4,strong_iteration(multiplication(X5,X4))),multiplication(strong_iteration(multiplication(X4,X5)),X4)),
file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',goals) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/tmp/tmp.ZM0SnZjvGd/E---3.1_26734.p',multiplicative_right_identity) ).
fof(c_0_12,plain,
! [X33] : strong_iteration(X33) = addition(multiplication(X33,strong_iteration(X33)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
fof(c_0_13,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_14,plain,
! [X34,X35,X36] :
( ~ leq(X36,addition(multiplication(X34,X36),X35))
| leq(X36,multiplication(strong_iteration(X34),X35)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[infty_coinduction])]) ).
fof(c_0_15,plain,
! [X13,X14,X15] : multiplication(X13,multiplication(X14,X15)) = multiplication(multiplication(X13,X14),X15),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_16,plain,
! [X21,X22,X23] : multiplication(addition(X21,X22),X23) = addition(multiplication(X21,X23),multiplication(X22,X23)),
inference(variable_rename,[status(thm)],[distributivity2]) ).
fof(c_0_17,plain,
! [X17] : multiplication(one,X17) = X17,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_18,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_22,plain,
! [X38,X39] :
( ( ~ leq(X38,X39)
| addition(X38,X39) = X39 )
& ( addition(X38,X39) != X39
| leq(X38,X39) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_23,plain,
! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_24,plain,
! [X18,X19,X20] : multiplication(X18,addition(X19,X20)) = addition(multiplication(X18,X19),multiplication(X18,X20)),
inference(variable_rename,[status(thm)],[distributivity1]) ).
cnf(c_0_25,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_28,plain,
! [X12] : addition(X12,X12) = X12,
inference(variable_rename,[status(thm)],[idempotence]) ).
fof(c_0_29,negated_conjecture,
~ ! [X4,X5] : leq(multiplication(X4,strong_iteration(multiplication(X5,X4))),multiplication(strong_iteration(multiplication(X4,X5)),X4)),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_30,plain,
( leq(X1,multiplication(strong_iteration(multiplication(X2,X3)),X4))
| ~ leq(X1,addition(multiplication(X2,multiplication(X3,X1)),X4)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_31,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_19]) ).
cnf(c_0_35,plain,
addition(one,multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2))))) = strong_iteration(multiplication(X1,X2)),
inference(spm,[status(thm)],[c_0_27,c_0_21]) ).
fof(c_0_36,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_37,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_38,negated_conjecture,
~ leq(multiplication(esk1_0,strong_iteration(multiplication(esk2_0,esk1_0))),multiplication(strong_iteration(multiplication(esk1_0,esk2_0)),esk1_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).
cnf(c_0_39,plain,
( leq(X1,multiplication(strong_iteration(multiplication(X2,X3)),X4))
| addition(X1,addition(multiplication(X2,multiplication(X3,X1)),X4)) != addition(multiplication(X2,multiplication(X3,X1)),X4) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,plain,
addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4)) = addition(multiplication(X1,addition(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_41,plain,
addition(X1,multiplication(X2,multiplication(X3,X1))) = multiplication(addition(one,multiplication(X2,X3)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_21]),c_0_19]) ).
cnf(c_0_42,plain,
addition(one,addition(multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2)))),X3)) = addition(strong_iteration(multiplication(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_32,c_0_35]) ).
cnf(c_0_43,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_32,c_0_37]) ).
cnf(c_0_45,negated_conjecture,
~ leq(multiplication(esk1_0,strong_iteration(multiplication(esk2_0,esk1_0))),multiplication(strong_iteration(multiplication(esk1_0,esk2_0)),esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
( leq(multiplication(X1,X2),multiplication(strong_iteration(multiplication(X1,X3)),X4))
| addition(multiplication(X1,multiplication(addition(one,multiplication(X3,X1)),X2)),X4) != addition(multiplication(X1,multiplication(X3,multiplication(X1,X2))),X4) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_47,plain,
multiplication(addition(one,multiplication(X1,X2)),strong_iteration(multiplication(X1,X2))) = strong_iteration(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_37]),c_0_35]),c_0_41]) ).
cnf(c_0_48,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_43]),c_0_19]) ).
cnf(c_0_49,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[c_0_44,c_0_27]) ).
cnf(c_0_50,negated_conjecture,
$false,
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(rw,[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_47]),c_0_19]),c_0_48]),c_0_19]),c_0_49]),c_0_19]),c_0_48]),c_0_19]),c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE151+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n001.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 2400
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Oct 3 05:16:37 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.48 Running first-order model finding
% 0.20/0.48 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.ZM0SnZjvGd/E---3.1_26734.p
% 84.53/11.20 # Version: 3.1pre001
% 84.53/11.20 # Preprocessing class: FSMSSMSSSSSNFFN.
% 84.53/11.20 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 84.53/11.20 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 84.53/11.20 # Starting new_bool_3 with 300s (1) cores
% 84.53/11.20 # Starting new_bool_1 with 300s (1) cores
% 84.53/11.20 # Starting sh5l with 300s (1) cores
% 84.53/11.20 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 26811 completed with status 0
% 84.53/11.20 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 84.53/11.20 # Preprocessing class: FSMSSMSSSSSNFFN.
% 84.53/11.20 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 84.53/11.20 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 84.53/11.20 # No SInE strategy applied
% 84.53/11.20 # Search class: FHUSM-FFSF21-MFFFFFNN
% 84.53/11.20 # Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 84.53/11.20 # Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 84.53/11.20 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 84.53/11.20 # Starting G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with 136s (1) cores
% 84.53/11.20 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 84.53/11.20 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2U with 136s (1) cores
% 84.53/11.20 # G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2U with pid 26821 completed with status 0
% 84.53/11.20 # Result found by G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2U
% 84.53/11.20 # Preprocessing class: FSMSSMSSSSSNFFN.
% 84.53/11.20 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 84.53/11.20 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 84.53/11.20 # No SInE strategy applied
% 84.53/11.20 # Search class: FHUSM-FFSF21-MFFFFFNN
% 84.53/11.20 # Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 84.53/11.20 # Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 84.53/11.20 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 84.53/11.20 # Starting G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with 136s (1) cores
% 84.53/11.20 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 84.53/11.20 # Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2U with 136s (1) cores
% 84.53/11.20 # Preprocessing time : 0.001 s
% 84.53/11.20 # Presaturation interreduction done
% 84.53/11.20
% 84.53/11.20 # Proof found!
% 84.53/11.20 # SZS status Theorem
% 84.53/11.20 # SZS output start CNFRefutation
% See solution above
% 84.53/11.20 # Parsed axioms : 19
% 84.53/11.20 # Removed by relevancy pruning/SinE : 0
% 84.53/11.20 # Initial clauses : 20
% 84.53/11.20 # Removed in clause preprocessing : 0
% 84.53/11.20 # Initial clauses in saturation : 20
% 84.53/11.20 # Processed clauses : 26923
% 84.53/11.20 # ...of these trivial : 438
% 84.53/11.20 # ...subsumed : 24063
% 84.53/11.20 # ...remaining for further processing : 2422
% 84.53/11.20 # Other redundant clauses eliminated : 52
% 84.53/11.20 # Clauses deleted for lack of memory : 0
% 84.53/11.20 # Backward-subsumed : 244
% 84.53/11.20 # Backward-rewritten : 107
% 84.53/11.20 # Generated clauses : 561759
% 84.53/11.20 # ...of the previous two non-redundant : 492711
% 84.53/11.20 # ...aggressively subsumed : 0
% 84.53/11.20 # Contextual simplify-reflections : 15
% 84.53/11.20 # Paramodulations : 561497
% 84.53/11.20 # Factorizations : 0
% 84.53/11.20 # NegExts : 0
% 84.53/11.20 # Equation resolutions : 262
% 84.53/11.20 # Total rewrite steps : 860075
% 84.53/11.20 # Propositional unsat checks : 0
% 84.53/11.20 # Propositional check models : 0
% 84.53/11.20 # Propositional check unsatisfiable : 0
% 84.53/11.20 # Propositional clauses : 0
% 84.53/11.20 # Propositional clauses after purity: 0
% 84.53/11.20 # Propositional unsat core size : 0
% 84.53/11.20 # Propositional preprocessing time : 0.000
% 84.53/11.20 # Propositional encoding time : 0.000
% 84.53/11.20 # Propositional solver time : 0.000
% 84.53/11.20 # Success case prop preproc time : 0.000
% 84.53/11.20 # Success case prop encoding time : 0.000
% 84.53/11.20 # Success case prop solver time : 0.000
% 84.53/11.20 # Current number of processed clauses : 2051
% 84.53/11.20 # Positive orientable unit clauses : 218
% 84.53/11.20 # Positive unorientable unit clauses: 18
% 84.53/11.20 # Negative unit clauses : 117
% 84.53/11.20 # Non-unit-clauses : 1698
% 84.53/11.20 # Current number of unprocessed clauses: 463470
% 84.53/11.20 # ...number of literals in the above : 1184262
% 84.53/11.20 # Current number of archived formulas : 0
% 84.53/11.20 # Current number of archived clauses : 371
% 84.53/11.20 # Clause-clause subsumption calls (NU) : 347748
% 84.53/11.20 # Rec. Clause-clause subsumption calls : 286109
% 84.53/11.20 # Non-unit clause-clause subsumptions : 5881
% 84.53/11.20 # Unit Clause-clause subsumption calls : 7835
% 84.53/11.20 # Rewrite failures with RHS unbound : 0
% 84.53/11.20 # BW rewrite match attempts : 1913
% 84.53/11.20 # BW rewrite match successes : 365
% 84.53/11.20 # Condensation attempts : 0
% 84.53/11.20 # Condensation successes : 0
% 84.53/11.20 # Termbank termtop insertions : 11526935
% 84.53/11.20
% 84.53/11.20 # -------------------------------------------------
% 84.53/11.20 # User time : 10.135 s
% 84.53/11.20 # System time : 0.316 s
% 84.53/11.20 # Total time : 10.451 s
% 84.53/11.20 # Maximum resident set size: 1752 pages
% 84.53/11.20
% 84.53/11.20 # -------------------------------------------------
% 84.53/11.20 # User time : 50.904 s
% 84.53/11.20 # System time : 1.757 s
% 84.53/11.20 # Total time : 52.660 s
% 84.53/11.20 # Maximum resident set size: 1688 pages
% 84.53/11.20 % E---3.1 exiting
%------------------------------------------------------------------------------