%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE093+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 : n006.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 12:58:50 PM UTC 2026
% Result : Theorem 0.14s 0.50s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 43 ( 40 unt; 0 def)
% Number of atoms : 48 ( 40 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 11 ( 6 ~; 3 |; 1 &)
% ( 1 <=>; 0 =>; 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 58 ( 5 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(domain2,axiom,
! [X4,X5] : domain(multiplication(X4,X5)) = domain(multiplication(X4,domain(X5))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain2) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_left_identity) ).
fof(domain5,axiom,
! [X4,X5] : domain(addition(X4,X5)) = addition(domain(X4),domain(X5)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain5) ).
fof(domain3,axiom,
! [X4] : addition(domain(X4),one) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain3) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).
fof(domain1,axiom,
! [X4] : addition(X4,multiplication(domain(X4),X4)) = multiplication(domain(X4),X4),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain1) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',order) ).
fof(star_unfold_right,axiom,
! [X1] : leq(addition(one,multiplication(X1,star(X1))),star(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_associativity) ).
fof(goals,conjecture,
! [X4] : domain(star(X4)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c_0_11,plain,
! [X37,X38] : domain(multiplication(X37,X38)) = domain(multiplication(X37,domain(X38))),
inference(variable_rename,[status(thm)],[domain2]) ).
fof(c_0_12,plain,
! [X17] : multiplication(one,X17) = X17,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_13,plain,
! [X40,X41] : domain(addition(X40,X41)) = addition(domain(X40),domain(X41)),
inference(variable_rename,[status(thm)],[domain5]) ).
cnf(c_0_14,plain,
domain(multiplication(X1,X2)) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X39] : addition(domain(X39),one) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_17,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_18,plain,
domain(addition(X1,X2)) = addition(domain(X1),domain(X2)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
domain(domain(X1)) = domain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_15]) ).
cnf(c_0_20,plain,
addition(domain(X1),one) = one,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,plain,
! [X36] : addition(X36,multiplication(domain(X36),X36)) = multiplication(domain(X36),X36),
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_23,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_24,plain,
domain(addition(X1,domain(X2))) = domain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_18]) ).
cnf(c_0_25,plain,
addition(one,domain(X1)) = one,
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_28,plain,
! [X26,X27] :
( ( leq(X26,X27)
| addition(X26,X27) != X27 )
& ( addition(X26,X27) = X27
| ~ leq(X26,X27) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])])]) ).
fof(c_0_29,plain,
! [X28] : leq(addition(one,multiplication(X28,star(X28))),star(X28)),
inference(variable_rename,[status(thm)],[star_unfold_right]) ).
fof(c_0_30,plain,
! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_31,negated_conjecture,
~ ! [X4] : domain(star(X4)) = one,
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_32,plain,
domain(addition(one,X1)) = domain(one),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,plain,
domain(one) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_25]) ).
cnf(c_0_34,plain,
( ~ leq(X1,X2)
| addition(X1,X2) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_37,negated_conjecture,
domain(star(esk1_0)) != one,
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).
cnf(c_0_38,plain,
domain(addition(one,X1)) = one,
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,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_34,c_0_35]),c_0_36]),c_0_21]) ).
cnf(c_0_40,negated_conjecture,
domain(star(esk1_0)) != one,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_41,plain,
domain(star(X1)) = one,
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE093+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n006.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 22:42:42 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 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/benchmark/theBenchmark.p
% 0.14/0.50 % Version: 3.5.1
% 0.14/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.50 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.50 % Starting sh5l with 300s (1) cores
% 0.14/0.50 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1417615 completed with status 0
% 0.14/0.50 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.50 % No SInE strategy applied
% 0.14/0.50 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.14/0.50 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.50 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.14/0.50 % Starting G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with 136s (1) cores
% 0.14/0.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 0.14/0.50 % SubtermCWHack with pid 1417619 completed with status 0
% 0.14/0.50 % Result found by SubtermCWHack
% 0.14/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.50 % No SInE strategy applied
% 0.14/0.50 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.14/0.50 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.50 % Preprocessing time : 0.002 s
% 0.14/0.50
% 0.14/0.50 % Proof found!
% 0.14/0.50 % SZS status Theorem
% 0.14/0.50 % SZS output start CNFRefutation
% See solution above
% 0.14/0.50 % Parsed axioms : 22
% 0.14/0.50 % Removed by relevancy pruning/SinE : 0
% 0.14/0.50 % Initial clauses : 23
% 0.14/0.50 % Removed in clause preprocessing : 0
% 0.14/0.50 % Initial clauses in saturation : 23
% 0.14/0.50 % Processed clauses : 113
% 0.14/0.50 % ...of these trivial : 37
% 0.14/0.50 % ...subsumed : 5
% 0.14/0.50 % ...remaining for further processing : 71
% 0.14/0.50 % Other redundant clauses eliminated : 0
% 0.14/0.50 % Clauses deleted for lack of memory : 0
% 0.14/0.50 % Backward-subsumed : 3
% 0.14/0.50 % Backward-rewritten : 13
% 0.14/0.50 % Generated clauses : 599
% 0.14/0.50 % ...of the previous two non-redundant : 290
% 0.14/0.50 % ...aggressively subsumed : 0
% 0.14/0.50 % Contextual simplify-reflections : 0
% 0.14/0.50 % Paramodulations : 599
% 0.14/0.50 % Factorizations : 0
% 0.14/0.50 % NegExts : 0
% 0.14/0.50 % Equation resolutions : 0
% 0.14/0.50 % Disequality decompositions : 0
% 0.14/0.50 % Total rewrite steps : 753
% 0.14/0.50 % ...of those cached : 528
% 0.14/0.50 % Propositional unsat checks : 0
% 0.14/0.50 % Propositional check models : 0
% 0.14/0.50 % Propositional check unsatisfiable : 0
% 0.14/0.50 % Propositional clauses : 0
% 0.14/0.50 % Propositional clauses after purity: 0
% 0.14/0.50 % Propositional unsat core size : 0
% 0.14/0.50 % Propositional preprocessing time : 0.000
% 0.14/0.50 % Propositional encoding time : 0.000
% 0.14/0.50 % Propositional solver time : 0.000
% 0.14/0.50 % Success case prop preproc time : 0.000
% 0.14/0.50 % Success case prop encoding time : 0.000
% 0.14/0.50 % Success case prop solver time : 0.000
% 0.14/0.50 % Current number of processed clauses : 55
% 0.14/0.50 % Positive orientable unit clauses : 47
% 0.14/0.50 % Positive unorientable unit clauses: 1
% 0.14/0.50 % Negative unit clauses : 2
% 0.14/0.50 % Non-unit-clauses : 5
% 0.14/0.50 % Current number of unprocessed clauses: 190
% 0.14/0.50 % ...number of literals in the above : 235
% 0.14/0.50 % Current number of archived formulas : 0
% 0.14/0.50 % Current number of archived clauses : 16
% 0.14/0.50 % Clause-clause subsumption calls (NU) : 7
% 0.14/0.50 % Rec. Clause-clause subsumption calls : 7
% 0.14/0.50 % Non-unit clause-clause subsumptions : 0
% 0.14/0.50 % Unit Clause-clause subsumption calls : 6
% 0.14/0.50 % Rewrite failures with RHS unbound : 0
% 0.14/0.50 % BW rewrite match attempts : 54
% 0.14/0.50 % BW rewrite match successes : 18
% 0.14/0.50 % Condensation attempts : 0
% 0.14/0.50 % Condensation successes : 0
% 0.14/0.50 % Termbank termtop insertions : 5638
% 0.14/0.50 % Search garbage collected termcells : 57
% 0.14/0.50
% 0.14/0.50 % -------------------------------------------------
% 0.14/0.50 % User time : 0.014 s
% 0.14/0.50 % System time : 0.006 s
% 0.14/0.50 % Total time : 0.019 s
% 0.14/0.50 % Maximum resident set size: 3656 pages
% 0.14/0.50
% 0.14/0.50 % -------------------------------------------------
% 0.14/0.50 % User time : 0.052 s
% 0.14/0.50 % System time : 0.022 s
% 0.14/0.50 % Total time : 0.074 s
% 0.14/0.50 % Maximum resident set size: 4608 pages
% 0.14/0.50 % E exiting
%------------------------------------------------------------------------------