%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE143+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:58:56 PM UTC 2026
% Result : Theorem 3.88s 0.98s
% Output : CNFRefutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 58 ( 49 unt; 0 def)
% Number of atoms : 69 ( 51 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 : 6 ( 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 : 100 ( 0 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(infty_unfold1,axiom,
! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
fof(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(distributivity2,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity2) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
fof(infty_coinduction,axiom,
! [X1,X2,X3] :
( leq(X3,addition(multiplication(X1,X3),X2))
=> leq(X3,multiplication(strong_iteration(X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
fof(distributivity1,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity1) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
fof(goals,conjecture,
! [X4] : multiplication(strong_iteration(X4),strong_iteration(X4)) = strong_iteration(X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c_0_12,plain,
! [X32] : strong_iteration(X32) = addition(multiplication(X32,strong_iteration(X32)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
fof(c_0_13,plain,
! [X5,X6] : addition(X5,X6) = addition(X6,X5),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_14,plain,
! [X7,X8,X9] : addition(X9,addition(X8,X7)) = addition(addition(X9,X8),X7),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_15,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_19,plain,
! [X11] : addition(X11,X11) = X11,
inference(variable_rename,[status(thm)],[idempotence]) ).
fof(c_0_20,plain,
! [X20,X21,X22] : multiplication(addition(X20,X21),X22) = addition(multiplication(X20,X22),multiplication(X21,X22)),
inference(variable_rename,[status(thm)],[distributivity2]) ).
fof(c_0_21,plain,
! [X16] : multiplication(one,X16) = X16,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_22,plain,
addition(one,addition(multiplication(X1,strong_iteration(X1)),X2)) = addition(strong_iteration(X1),X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_26,plain,
! [X33,X34,X35] :
( leq(X35,multiplication(strong_iteration(X33),X34))
| ~ leq(X35,addition(multiplication(X33,X35),X34)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[infty_coinduction])])]) ).
fof(c_0_27,plain,
! [X12,X13,X14] : multiplication(X12,multiplication(X13,X14)) = multiplication(multiplication(X12,X13),X14),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_28,plain,
addition(strong_iteration(X1),multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_18]) ).
cnf(c_0_29,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_16]) ).
fof(c_0_30,plain,
! [X17,X18,X19] : multiplication(X17,addition(X18,X19)) = addition(multiplication(X17,X18),multiplication(X17,X19)),
inference(variable_rename,[status(thm)],[distributivity1]) ).
fof(c_0_31,plain,
! [X15] : multiplication(X15,one) = X15,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_32,plain,
( ~ leq(X1,addition(multiplication(X2,X1),X3))
| leq(X1,multiplication(strong_iteration(X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
multiplication(addition(X1,one),strong_iteration(X1)) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_35,plain,
! [X37,X38] :
( ( leq(X37,X38)
| addition(X37,X38) != X38 )
& ( addition(X37,X38) = X38
| ~ leq(X37,X38) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])]) ).
cnf(c_0_36,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_39,plain,
( ~ leq(X1,addition(X3,multiplication(X2,X1)))
| leq(X1,multiplication(strong_iteration(X2),X3)) ),
inference(spm,[status(thm)],[c_0_32,c_0_16]) ).
cnf(c_0_40,plain,
addition(one,multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2))))) = strong_iteration(multiplication(X1,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_33]) ).
cnf(c_0_41,plain,
multiplication(addition(one,X1),strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[c_0_34,c_0_16]) ).
cnf(c_0_42,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_16]) ).
cnf(c_0_44,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[c_0_38,c_0_18]) ).
cnf(c_0_45,plain,
( ~ leq(multiplication(X1,strong_iteration(multiplication(X2,X1))),strong_iteration(multiplication(X2,X1)))
| leq(multiplication(X1,strong_iteration(multiplication(X2,X1))),strong_iteration(X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_37]) ).
cnf(c_0_46,plain,
multiplication(strong_iteration(X1),strong_iteration(multiplication(X1,strong_iteration(X1)))) = strong_iteration(multiplication(X1,strong_iteration(X1))),
inference(spm,[status(thm)],[c_0_41,c_0_18]) ).
cnf(c_0_47,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_42,c_0_23]) ).
cnf(c_0_48,plain,
addition(X1,strong_iteration(X1)) = strong_iteration(X1),
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_43,c_0_34]),c_0_17]),c_0_44]),c_0_16]),c_0_44]),c_0_34]) ).
fof(c_0_49,negated_conjecture,
~ ! [X4] : multiplication(strong_iteration(X4),strong_iteration(X4)) = strong_iteration(X4),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_50,plain,
( ~ leq(X1,X2)
| addition(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_51,plain,
leq(strong_iteration(multiplication(X1,strong_iteration(X1))),strong_iteration(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]) ).
cnf(c_0_52,plain,
addition(strong_iteration(X1),strong_iteration(multiplication(X1,strong_iteration(X1)))) = strong_iteration(multiplication(X1,strong_iteration(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_48]),c_0_44]) ).
fof(c_0_53,negated_conjecture,
multiplication(strong_iteration(esk1_0),strong_iteration(esk1_0)) != strong_iteration(esk1_0),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])]) ).
cnf(c_0_54,plain,
strong_iteration(multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_16]),c_0_52]) ).
cnf(c_0_55,negated_conjecture,
multiplication(strong_iteration(esk1_0),strong_iteration(esk1_0)) != strong_iteration(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_56,plain,
multiplication(strong_iteration(X1),strong_iteration(X1)) = strong_iteration(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_54]),c_0_54]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE143+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 22:49:21 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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/benchmark/theBenchmark.p
% 3.88/0.98 % Version: 3.5.1
% 3.88/0.98 % Preprocessing class: FSMSSMSSSSSNFFN.
% 3.88/0.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.88/0.98 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.88/0.98 % Starting new_bool_3 with 300s (1) cores
% 3.88/0.98 % Starting new_bool_1 with 300s (1) cores
% 3.88/0.98 % Starting sh5l with 300s (1) cores
% 3.88/0.98 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 4115053 completed with status 0
% 3.88/0.98 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 3.88/0.98 % Preprocessing class: FSMSSMSSSSSNFFN.
% 3.88/0.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.88/0.98 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.88/0.98 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.88/0.98 % No SInE strategy applied
% 3.88/0.98 % Search class: FHUSM-FFSF21-MFFFFFNN
% 3.88/0.98 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 3.88/0.98 % Starting SubtermCWHack with 136s (1) cores
% 3.88/0.98 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 3.88/0.98 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 3.88/0.98 % Starting G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with 136s (1) cores
% 3.88/0.98 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 3.88/0.98 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 4115064 completed with status 0
% 3.88/0.98 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 3.88/0.98 % Preprocessing class: FSMSSMSSSSSNFFN.
% 3.88/0.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.88/0.98 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.88/0.98 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.88/0.98 % No SInE strategy applied
% 3.88/0.98 % Search class: FHUSM-FFSF21-MFFFFFNN
% 3.88/0.98 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 3.88/0.98 % Starting SubtermCWHack with 136s (1) cores
% 3.88/0.98 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 3.88/0.98 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 3.88/0.98 % Starting G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with 136s (1) cores
% 3.88/0.98 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 3.88/0.98 % Preprocessing time : 0.001 s
% 3.88/0.98 % Presaturation interreduction done
% 3.88/0.98
% 3.88/0.98 % Proof found!
% 3.88/0.98 % SZS status Theorem
% 3.88/0.98 % SZS output start CNFRefutation
% See solution above
% 3.88/0.98 % Parsed axioms : 19
% 3.88/0.98 % Removed by relevancy pruning/SinE : 0
% 3.88/0.98 % Initial clauses : 20
% 3.88/0.98 % Removed in clause preprocessing : 0
% 3.88/0.98 % Initial clauses in saturation : 20
% 3.88/0.98 % Processed clauses : 4550
% 3.88/0.98 % ...of these trivial : 493
% 3.88/0.98 % ...subsumed : 3355
% 3.88/0.98 % ...remaining for further processing : 702
% 3.88/0.98 % Other redundant clauses eliminated : 357
% 3.88/0.98 % Clauses deleted for lack of memory : 0
% 3.88/0.98 % Backward-subsumed : 13
% 3.88/0.98 % Backward-rewritten : 68
% 3.88/0.98 % Generated clauses : 52604
% 3.88/0.98 % ...of the previous two non-redundant : 23263
% 3.88/0.98 % ...aggressively subsumed : 0
% 3.88/0.98 % Contextual simplify-reflections : 0
% 3.88/0.98 % Paramodulations : 52246
% 3.88/0.98 % Factorizations : 0
% 3.88/0.98 % NegExts : 0
% 3.88/0.98 % Equation resolutions : 358
% 3.88/0.98 % Disequality decompositions : 0
% 3.88/0.98 % Total rewrite steps : 107613
% 3.88/0.98 % ...of those cached : 100394
% 3.88/0.98 % Propositional unsat checks : 0
% 3.88/0.98 % Propositional check models : 0
% 3.88/0.98 % Propositional check unsatisfiable : 0
% 3.88/0.98 % Propositional clauses : 0
% 3.88/0.98 % Propositional clauses after purity: 0
% 3.88/0.98 % Propositional unsat core size : 0
% 3.88/0.98 % Propositional preprocessing time : 0.000
% 3.88/0.98 % Propositional encoding time : 0.000
% 3.88/0.98 % Propositional solver time : 0.000
% 3.88/0.98 % Success case prop preproc time : 0.000
% 3.88/0.98 % Success case prop encoding time : 0.000
% 3.88/0.98 % Success case prop solver time : 0.000
% 3.88/0.98 % Current number of processed clauses : 601
% 3.88/0.98 % Positive orientable unit clauses : 311
% 3.88/0.98 % Positive unorientable unit clauses: 4
% 3.88/0.98 % Negative unit clauses : 0
% 3.88/0.98 % Non-unit-clauses : 286
% 3.88/0.98 % Current number of unprocessed clauses: 18515
% 3.88/0.98 % ...number of literals in the above : 31091
% 3.88/0.98 % Current number of archived formulas : 0
% 3.88/0.98 % Current number of archived clauses : 101
% 3.88/0.98 % Clause-clause subsumption calls (NU) : 19980
% 3.88/0.98 % Rec. Clause-clause subsumption calls : 19923
% 3.88/0.98 % Non-unit clause-clause subsumptions : 3257
% 3.88/0.98 % Unit Clause-clause subsumption calls : 511
% 3.88/0.98 % Rewrite failures with RHS unbound : 0
% 3.88/0.98 % BW rewrite match attempts : 795
% 3.88/0.98 % BW rewrite match successes : 191
% 3.88/0.98 % Condensation attempts : 0
% 3.88/0.98 % Condensation successes : 0
% 3.88/0.98 % Termbank termtop insertions : 620624
% 3.88/0.98 % Search garbage collected termcells : 70
% 3.88/0.98
% 3.88/0.98 % -------------------------------------------------
% 3.88/0.98 % User time : 0.512 s
% 3.88/0.98 % System time : 0.026 s
% 3.88/0.98 % Total time : 0.538 s
% 3.88/0.98 % Maximum resident set size: 3652 pages
% 3.88/0.98
% 3.88/0.98 % -------------------------------------------------
% 3.88/0.98 % User time : 2.514 s
% 3.88/0.98 % System time : 0.127 s
% 3.88/0.98 % Total time : 2.641 s
% 3.88/0.98 % Maximum resident set size: 4608 pages
% 3.88/0.98 % E exiting
%------------------------------------------------------------------------------