%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE142+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 0.16s 0.64s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 44 ( 35 unt; 0 def)
% Number of atoms : 55 ( 35 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 : 4 ( 2 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 : 65 ( 10 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
fof(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(goals,conjecture,
! [X4] : strong_iteration(strong_iteration(X4)) = strong_iteration(one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(isolation,axiom,
! [X1] : strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',isolation) ).
fof(c_0_10,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_11,plain,
! [X16] : multiplication(one,X16) = X16,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_12,plain,
! [X7,X8,X9] : addition(X9,addition(X8,X7)) = addition(addition(X9,X8),X7),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_13,plain,
! [X11] : addition(X11,X11) = X11,
inference(variable_rename,[status(thm)],[idempotence]) ).
cnf(c_0_14,plain,
( ~ leq(X1,addition(multiplication(X2,X1),X3))
| leq(X1,multiplication(strong_iteration(X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,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_17,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( ~ leq(X1,addition(X1,X2))
| leq(X1,multiplication(strong_iteration(one),X2)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_22,plain,
! [X15] : multiplication(X15,one) = X15,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_23,plain,
leq(X1,multiplication(strong_iteration(one),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_24,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_25,plain,
! [X10] : addition(X10,zero) = X10,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_26,plain,
( ~ leq(X1,X2)
| addition(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_27,plain,
leq(X1,strong_iteration(one)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,plain,
addition(X1,strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_30,plain,
! [X5,X6] : addition(X5,X6) = addition(X6,X5),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_31,plain,
( ~ leq(X1,multiplication(X2,X1))
| leq(X1,multiplication(strong_iteration(X2),zero)) ),
inference(spm,[status(thm)],[c_0_14,c_0_28]) ).
cnf(c_0_32,plain,
leq(X1,multiplication(strong_iteration(X2),strong_iteration(one))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_29]),c_0_27])]) ).
cnf(c_0_33,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_34,negated_conjecture,
~ ! [X4] : strong_iteration(strong_iteration(X4)) = strong_iteration(one),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_35,plain,
! [X36] : strong_iteration(X36) = addition(star(X36),multiplication(strong_iteration(X36),zero)),
inference(variable_rename,[status(thm)],[isolation]) ).
cnf(c_0_36,plain,
leq(strong_iteration(one),multiplication(strong_iteration(strong_iteration(X1)),zero)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
addition(strong_iteration(one),X1) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_33,c_0_29]) ).
fof(c_0_38,negated_conjecture,
strong_iteration(strong_iteration(esk1_0)) != strong_iteration(one),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])]) ).
cnf(c_0_39,plain,
strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,plain,
multiplication(strong_iteration(strong_iteration(X1)),zero) = strong_iteration(one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_36]),c_0_37]) ).
cnf(c_0_41,negated_conjecture,
strong_iteration(strong_iteration(esk1_0)) != strong_iteration(one),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_42,plain,
strong_iteration(strong_iteration(X1)) = strong_iteration(one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_29]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE142+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.56 % Computer : n004.cluster.edu
% 0.11/0.56 % Model : x86_64 x86_64
% 0.11/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.56 % Memory : 8046.5625MB
% 0.11/0.56 % OS : Linux 6.8.0-71-generic
% 0.11/0.56 % CPULimit : 300
% 0.11/0.56 % WCLimit : 300
% 0.11/0.56 % DateTime : Sun Sep 20 22:46:06 UTC 2026
% 0.11/0.56 % CPUTime :
% 0.11/0.56 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.61 Running first-order theorem proving
% 0.11/0.61 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/benchmark/theBenchmark.p
% 0.16/0.64 % Version: 3.5.1
% 0.16/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.64 % Starting sh5l with 300s (1) cores
% 0.16/0.64 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1655768 completed with status 0
% 0.16/0.64 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.16/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.64 % No SInE strategy applied
% 0.16/0.64 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.16/0.64 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.64 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/0.64 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.16/0.64 % Starting G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with 136s (1) cores
% 0.16/0.64 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 0.16/0.64 % G-E--_300_C18_F1_SE_CS_SP_S0Y with pid 1655776 completed with status 0
% 0.16/0.64 % Result found by G-E--_300_C18_F1_SE_CS_SP_S0Y
% 0.16/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/0.64 % No SInE strategy applied
% 0.16/0.64 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.16/0.64 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/0.64 % Starting SubtermCWHack with 136s (1) cores
% 0.16/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.16/0.64 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.16/0.64 % Preprocessing time : 0.001 s
% 0.16/0.64
% 0.16/0.64 % Proof found!
% 0.16/0.64 % SZS status Theorem
% 0.16/0.64 % SZS output start CNFRefutation
% See solution above
% 0.16/0.64 % Parsed axioms : 19
% 0.16/0.64 % Removed by relevancy pruning/SinE : 0
% 0.16/0.64 % Initial clauses : 20
% 0.16/0.64 % Removed in clause preprocessing : 0
% 0.16/0.64 % Initial clauses in saturation : 20
% 0.16/0.64 % Processed clauses : 66
% 0.16/0.64 % ...of these trivial : 7
% 0.16/0.64 % ...subsumed : 0
% 0.16/0.64 % ...remaining for further processing : 59
% 0.16/0.64 % Other redundant clauses eliminated : 1
% 0.16/0.64 % Clauses deleted for lack of memory : 0
% 0.16/0.64 % Backward-subsumed : 0
% 0.16/0.64 % Backward-rewritten : 18
% 0.16/0.64 % Generated clauses : 317
% 0.16/0.64 % ...of the previous two non-redundant : 183
% 0.16/0.64 % ...aggressively subsumed : 0
% 0.16/0.64 % Contextual simplify-reflections : 0
% 0.16/0.64 % Paramodulations : 316
% 0.16/0.64 % Factorizations : 0
% 0.16/0.64 % NegExts : 0
% 0.16/0.64 % Equation resolutions : 1
% 0.16/0.64 % Disequality decompositions : 0
% 0.16/0.64 % Total rewrite steps : 308
% 0.16/0.64 % ...of those cached : 172
% 0.16/0.64 % Propositional unsat checks : 0
% 0.16/0.64 % Propositional check models : 0
% 0.16/0.64 % Propositional check unsatisfiable : 0
% 0.16/0.64 % Propositional clauses : 0
% 0.16/0.64 % Propositional clauses after purity: 0
% 0.16/0.64 % Propositional unsat core size : 0
% 0.16/0.64 % Propositional preprocessing time : 0.000
% 0.16/0.64 % Propositional encoding time : 0.000
% 0.16/0.64 % Propositional solver time : 0.000
% 0.16/0.64 % Success case prop preproc time : 0.000
% 0.16/0.64 % Success case prop encoding time : 0.000
% 0.16/0.64 % Success case prop solver time : 0.000
% 0.16/0.64 % Current number of processed clauses : 41
% 0.16/0.64 % Positive orientable unit clauses : 31
% 0.16/0.64 % Positive unorientable unit clauses: 1
% 0.16/0.64 % Negative unit clauses : 0
% 0.16/0.64 % Non-unit-clauses : 9
% 0.16/0.64 % Current number of unprocessed clauses: 123
% 0.16/0.64 % ...number of literals in the above : 197
% 0.16/0.64 % Current number of archived formulas : 0
% 0.16/0.64 % Current number of archived clauses : 18
% 0.16/0.64 % Clause-clause subsumption calls (NU) : 13
% 0.16/0.64 % Rec. Clause-clause subsumption calls : 13
% 0.16/0.64 % Non-unit clause-clause subsumptions : 0
% 0.16/0.64 % Unit Clause-clause subsumption calls : 0
% 0.16/0.64 % Rewrite failures with RHS unbound : 0
% 0.16/0.64 % BW rewrite match attempts : 25
% 0.16/0.64 % BW rewrite match successes : 18
% 0.16/0.64 % Condensation attempts : 0
% 0.16/0.64 % Condensation successes : 0
% 0.16/0.64 % Termbank termtop insertions : 3946
% 0.16/0.64 % Search garbage collected termcells : 70
% 0.16/0.64
% 0.16/0.64 % -------------------------------------------------
% 0.16/0.64 % User time : 0.009 s
% 0.16/0.64 % System time : 0.003 s
% 0.16/0.64 % Total time : 0.013 s
% 0.16/0.64 % Maximum resident set size: 3652 pages
% 0.16/0.64
% 0.16/0.64 % -------------------------------------------------
% 0.16/0.64 % User time : 0.038 s
% 0.16/0.64 % System time : 0.018 s
% 0.16/0.64 % Total time : 0.056 s
% 0.16/0.64 % Maximum resident set size: 4864 pages
% 0.16/0.64 % E exiting
%------------------------------------------------------------------------------