%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE141+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 : n001.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 0.13s 0.53s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 27 unt; 0 def)
% Number of atoms : 47 ( 30 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 : 49 ( 4 sgn 28 !; 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/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
fof(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(isolation,axiom,
! [X1] : strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',isolation) ).
fof(goals,conjecture,
! [X4] : multiplication(strong_iteration(one),X4) = strong_iteration(one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
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(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
fof(c_0_9,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_10,plain,
! [X16] : multiplication(one,X16) = X16,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_11,plain,
( ~ leq(X1,addition(multiplication(X2,X1),X3))
| leq(X1,multiplication(strong_iteration(X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,plain,
! [X10] : addition(X10,zero) = X10,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_14,plain,
( ~ leq(X1,addition(X1,X2))
| leq(X1,multiplication(strong_iteration(one),X2)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
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])])]) ).
fof(c_0_17,plain,
! [X11] : addition(X11,X11) = X11,
inference(variable_rename,[status(thm)],[idempotence]) ).
cnf(c_0_18,plain,
( ~ leq(X1,X1)
| leq(X1,multiplication(strong_iteration(one),zero)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_21,plain,
! [X36] : strong_iteration(X36) = addition(star(X36),multiplication(strong_iteration(X36),zero)),
inference(variable_rename,[status(thm)],[isolation]) ).
cnf(c_0_22,plain,
( ~ leq(X1,X2)
| addition(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
leq(X1,multiplication(strong_iteration(one),zero)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
fof(c_0_24,negated_conjecture,
~ ! [X4] : multiplication(strong_iteration(one),X4) = strong_iteration(one),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_25,plain,
! [X12,X13,X14] : multiplication(X12,multiplication(X13,X14)) = multiplication(multiplication(X12,X13),X14),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_26,plain,
strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
addition(X1,multiplication(strong_iteration(one),zero)) = multiplication(strong_iteration(one),zero),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_28,plain,
! [X23] : multiplication(zero,X23) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_29,negated_conjecture,
multiplication(strong_iteration(one),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_24])])])]) ).
cnf(c_0_30,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
multiplication(strong_iteration(one),zero) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,negated_conjecture,
multiplication(strong_iteration(one),esk1_0) != strong_iteration(one),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,plain,
multiplication(strong_iteration(one),X1) = strong_iteration(one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_31]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE141+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 : n001.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 22:51:29 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 0.13/0.53 % Version: 3.5.1
% 0.13/0.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.53 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.53 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.53 % Starting sh5l with 300s (1) cores
% 0.13/0.53 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1578484 completed with status 0
% 0.13/0.53 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.53 % No SInE strategy applied
% 0.13/0.53 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.13/0.53 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.53 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.53 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.13/0.53 % Starting G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with 136s (1) cores
% 0.13/0.53 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 0.13/0.53 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1578489 completed with status 0
% 0.13/0.53 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.53 % No SInE strategy applied
% 0.13/0.53 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.13/0.53 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.53 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.53 % Preprocessing time : 0.002 s
% 0.13/0.53 % Presaturation interreduction done
% 0.13/0.53
% 0.13/0.53 % Proof found!
% 0.13/0.53 % SZS status Theorem
% 0.13/0.53 % SZS output start CNFRefutation
% See solution above
% 0.13/0.53 % Parsed axioms : 19
% 0.13/0.53 % Removed by relevancy pruning/SinE : 0
% 0.13/0.53 % Initial clauses : 20
% 0.13/0.53 % Removed in clause preprocessing : 0
% 0.13/0.53 % Initial clauses in saturation : 20
% 0.13/0.53 % Processed clauses : 84
% 0.13/0.53 % ...of these trivial : 5
% 0.13/0.53 % ...subsumed : 5
% 0.13/0.53 % ...remaining for further processing : 74
% 0.13/0.53 % Other redundant clauses eliminated : 0
% 0.13/0.53 % Clauses deleted for lack of memory : 0
% 0.13/0.53 % Backward-subsumed : 0
% 0.13/0.53 % Backward-rewritten : 19
% 0.13/0.53 % Generated clauses : 343
% 0.13/0.53 % ...of the previous two non-redundant : 225
% 0.13/0.53 % ...aggressively subsumed : 0
% 0.13/0.53 % Contextual simplify-reflections : 1
% 0.13/0.53 % Paramodulations : 343
% 0.13/0.53 % Factorizations : 0
% 0.13/0.53 % NegExts : 0
% 0.13/0.53 % Equation resolutions : 0
% 0.13/0.53 % Disequality decompositions : 0
% 0.13/0.53 % Total rewrite steps : 284
% 0.13/0.53 % ...of those cached : 152
% 0.13/0.53 % Propositional unsat checks : 0
% 0.13/0.53 % Propositional check models : 0
% 0.13/0.53 % Propositional check unsatisfiable : 0
% 0.13/0.53 % Propositional clauses : 0
% 0.13/0.53 % Propositional clauses after purity: 0
% 0.13/0.53 % Propositional unsat core size : 0
% 0.13/0.53 % Propositional preprocessing time : 0.000
% 0.13/0.53 % Propositional encoding time : 0.000
% 0.13/0.53 % Propositional solver time : 0.000
% 0.13/0.53 % Success case prop preproc time : 0.000
% 0.13/0.53 % Success case prop encoding time : 0.000
% 0.13/0.53 % Success case prop solver time : 0.000
% 0.13/0.53 % Current number of processed clauses : 35
% 0.13/0.53 % Positive orientable unit clauses : 25
% 0.13/0.53 % Positive unorientable unit clauses: 1
% 0.13/0.53 % Negative unit clauses : 0
% 0.13/0.53 % Non-unit-clauses : 9
% 0.13/0.53 % Current number of unprocessed clauses: 176
% 0.13/0.53 % ...number of literals in the above : 300
% 0.13/0.53 % Current number of archived formulas : 0
% 0.13/0.53 % Current number of archived clauses : 39
% 0.13/0.53 % Clause-clause subsumption calls (NU) : 35
% 0.13/0.53 % Rec. Clause-clause subsumption calls : 35
% 0.13/0.53 % Non-unit clause-clause subsumptions : 6
% 0.13/0.53 % Unit Clause-clause subsumption calls : 5
% 0.13/0.53 % Rewrite failures with RHS unbound : 0
% 0.13/0.53 % BW rewrite match attempts : 45
% 0.13/0.53 % BW rewrite match successes : 34
% 0.13/0.53 % Condensation attempts : 0
% 0.13/0.53 % Condensation successes : 0
% 0.13/0.53 % Termbank termtop insertions : 4549
% 0.13/0.53 % Search garbage collected termcells : 69
% 0.13/0.53
% 0.13/0.53 % -------------------------------------------------
% 0.13/0.53 % User time : 0.017 s
% 0.13/0.53 % System time : 0.006 s
% 0.13/0.53 % Total time : 0.023 s
% 0.13/0.53 % Maximum resident set size: 3652 pages
% 0.13/0.53
% 0.13/0.53 % -------------------------------------------------
% 0.13/0.53 % User time : 0.099 s
% 0.13/0.53 % System time : 0.023 s
% 0.13/0.53 % Total time : 0.122 s
% 0.13/0.53 % Maximum resident set size: 4864 pages
% 0.13/0.53 % E exiting
%------------------------------------------------------------------------------