%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE069+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 : n007.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 12:58:46 PM UTC 2026
% Result : Theorem 0.58s 0.48s
% Output : CNFRefutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 41 ( 41 unt; 0 def)
% Number of atoms : 41 ( 40 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 4 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(domain3,axiom,
! [X4] : addition(domain(X4),one) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain3) ).
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(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(goals,conjecture,
! [X4,X5] : multiplication(domain(X4),addition(domain(X4),domain(X5))) = domain(X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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(domain5,axiom,
! [X4,X5] : domain(addition(X4,X5)) = addition(domain(X4),domain(X5)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain5) ).
fof(c_0_10,plain,
! [X21,X22,X23] : multiplication(addition(X21,X22),X23) = addition(multiplication(X21,X23),multiplication(X22,X23)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_11,plain,
! [X17] : multiplication(one,X17) = X17,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_12,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_13,plain,
! [X31] : addition(domain(X31),one) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_14,plain,
! [X28] : addition(X28,multiplication(domain(X28),X28)) = multiplication(domain(X28),X28),
inference(variable_rename,[status(thm)],[domain1]) ).
cnf(c_0_15,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
addition(domain(X1),one) = one,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_19,plain,
! [X18,X19,X20] : multiplication(X18,addition(X19,X20)) = addition(multiplication(X18,X19),multiplication(X18,X20)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_20,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_21,negated_conjecture,
~ ! [X4,X5] : multiplication(domain(X4),addition(domain(X4),domain(X5))) = domain(X4),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_22,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_24,plain,
addition(one,domain(X1)) = one,
inference(rw,[status(thm)],[c_0_18,c_0_17]) ).
fof(c_0_25,plain,
! [X29,X30] : domain(multiplication(X29,X30)) = domain(multiplication(X29,domain(X30))),
inference(variable_rename,[status(thm)],[domain2]) ).
cnf(c_0_26,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_28,negated_conjecture,
multiplication(domain(esk1_0),addition(domain(esk1_0),domain(esk2_0))) != domain(esk1_0),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
fof(c_0_29,plain,
! [X32,X33] : domain(addition(X32,X33)) = addition(domain(X32),domain(X33)),
inference(variable_rename,[status(thm)],[domain5]) ).
cnf(c_0_30,plain,
multiplication(domain(X1),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_17]),c_0_24]),c_0_16]) ).
cnf(c_0_31,plain,
domain(multiplication(X1,X2)) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
multiplication(domain(esk1_0),addition(domain(esk1_0),domain(esk2_0))) != domain(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
domain(addition(X1,X2)) = addition(domain(X1),domain(X2)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
multiplication(domain(X1),addition(X1,X2)) = addition(X1,multiplication(domain(X1),X2)),
inference(spm,[status(thm)],[c_0_26,c_0_30]) ).
cnf(c_0_36,plain,
domain(domain(X1)) = domain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_16]),c_0_16]) ).
cnf(c_0_37,plain,
addition(X1,multiplication(X1,domain(X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_24]),c_0_27]) ).
cnf(c_0_38,negated_conjecture,
multiplication(domain(esk1_0),domain(addition(esk1_0,esk2_0))) != domain(esk1_0),
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,plain,
multiplication(domain(X1),domain(addition(X1,X2))) = domain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_34]),c_0_36]),c_0_36]),c_0_37]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE069+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 22:40:06 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.58/0.48 % Version: 3.5.1
% 0.58/0.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.58/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.58/0.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.58/0.48 % Starting new_bool_3 with 300s (1) cores
% 0.58/0.48 % Starting new_bool_1 with 300s (1) cores
% 0.58/0.48 % Starting sh5l with 300s (1) cores
% 0.58/0.48 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3742846 completed with status 0
% 0.58/0.48 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.58/0.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.58/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.58/0.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.58/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.58/0.48 % No SInE strategy applied
% 0.58/0.48 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.58/0.48 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.58/0.48 % Starting SubtermCWHack with 136s (1) cores
% 0.58/0.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.58/0.48 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.58/0.48 % Starting G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with 136s (1) cores
% 0.58/0.48 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 0.58/0.48 % G-E--_300_C18_F1_SE_CS_SP_S0Y with pid 3742854 completed with status 0
% 0.58/0.48 % Result found by G-E--_300_C18_F1_SE_CS_SP_S0Y
% 0.58/0.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.58/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.58/0.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.58/0.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.58/0.48 % No SInE strategy applied
% 0.58/0.48 % Search class: FHUSM-FFSF21-MFFFFFNN
% 0.58/0.48 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.58/0.48 % Starting SubtermCWHack with 136s (1) cores
% 0.58/0.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.58/0.48 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 0.58/0.48 % Preprocessing time : 0.001 s
% 0.58/0.48
% 0.58/0.48 % Proof found!
% 0.58/0.48 % SZS status Theorem
% 0.58/0.48 % SZS output start CNFRefutation
% See solution above
% 0.58/0.48 % Parsed axioms : 18
% 0.58/0.48 % Removed by relevancy pruning/SinE : 0
% 0.58/0.48 % Initial clauses : 19
% 0.58/0.48 % Removed in clause preprocessing : 0
% 0.58/0.48 % Initial clauses in saturation : 19
% 0.58/0.48 % Processed clauses : 330
% 0.58/0.48 % ...of these trivial : 99
% 0.58/0.48 % ...subsumed : 123
% 0.58/0.48 % ...remaining for further processing : 108
% 0.58/0.48 % Other redundant clauses eliminated : 0
% 0.58/0.48 % Clauses deleted for lack of memory : 0
% 0.58/0.48 % Backward-subsumed : 0
% 0.58/0.48 % Backward-rewritten : 24
% 0.58/0.48 % Generated clauses : 5170
% 0.58/0.48 % ...of the previous two non-redundant : 2479
% 0.58/0.48 % ...aggressively subsumed : 0
% 0.58/0.48 % Contextual simplify-reflections : 0
% 0.58/0.48 % Paramodulations : 5170
% 0.58/0.48 % Factorizations : 0
% 0.58/0.48 % NegExts : 0
% 0.58/0.48 % Equation resolutions : 0
% 0.58/0.48 % Disequality decompositions : 0
% 0.58/0.48 % Total rewrite steps : 8393
% 0.58/0.48 % ...of those cached : 6927
% 0.58/0.48 % Propositional unsat checks : 0
% 0.58/0.48 % Propositional check models : 0
% 0.58/0.48 % Propositional check unsatisfiable : 0
% 0.58/0.48 % Propositional clauses : 0
% 0.58/0.48 % Propositional clauses after purity: 0
% 0.58/0.48 % Propositional unsat core size : 0
% 0.58/0.48 % Propositional preprocessing time : 0.000
% 0.58/0.48 % Propositional encoding time : 0.000
% 0.58/0.48 % Propositional solver time : 0.000
% 0.58/0.48 % Success case prop preproc time : 0.000
% 0.58/0.48 % Success case prop encoding time : 0.000
% 0.58/0.48 % Success case prop solver time : 0.000
% 0.58/0.48 % Current number of processed clauses : 84
% 0.58/0.48 % Positive orientable unit clauses : 74
% 0.58/0.48 % Positive unorientable unit clauses: 8
% 0.58/0.48 % Negative unit clauses : 0
% 0.58/0.48 % Non-unit-clauses : 2
% 0.58/0.48 % Current number of unprocessed clauses: 2151
% 0.58/0.48 % ...number of literals in the above : 2151
% 0.58/0.48 % Current number of archived formulas : 0
% 0.58/0.48 % Current number of archived clauses : 24
% 0.58/0.48 % Clause-clause subsumption calls (NU) : 0
% 0.58/0.48 % Rec. Clause-clause subsumption calls : 0
% 0.58/0.48 % Non-unit clause-clause subsumptions : 0
% 0.58/0.48 % Unit Clause-clause subsumption calls : 21
% 0.58/0.48 % Rewrite failures with RHS unbound : 0
% 0.58/0.48 % BW rewrite match attempts : 308
% 0.58/0.48 % BW rewrite match successes : 122
% 0.58/0.48 % Condensation attempts : 0
% 0.58/0.48 % Condensation successes : 0
% 0.58/0.48 % Termbank termtop insertions : 51550
% 0.58/0.48 % Search garbage collected termcells : 37
% 0.58/0.48
% 0.58/0.48 % -------------------------------------------------
% 0.58/0.48 % User time : 0.047 s
% 0.58/0.48 % System time : 0.006 s
% 0.58/0.48 % Total time : 0.053 s
% 0.58/0.48 % Maximum resident set size: 3648 pages
% 0.58/0.48
% 0.58/0.48 % -------------------------------------------------
% 0.58/0.48 % User time : 0.237 s
% 0.58/0.48 % System time : 0.026 s
% 0.58/0.48 % Total time : 0.263 s
% 0.58/0.48 % Maximum resident set size: 4608 pages
% 0.58/0.48 % E exiting
%------------------------------------------------------------------------------