%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE064+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 : n020.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 0.14s 0.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 19 unt; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 1 &)
% ( 0 <=>; 1 =>; 2 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
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(goals,conjecture,
! [X4,X5] :
( addition(X4,multiplication(domain(X5),X4)) = multiplication(domain(X5),X4)
<= addition(domain(X4),domain(X5)) = domain(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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(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_5,plain,
! [X15,X16,X17] : addition(X17,addition(X16,X15)) = addition(addition(X17,X16),X15),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_6,plain,
! [X8] : addition(X8,multiplication(domain(X8),X8)) = multiplication(domain(X8),X8),
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_7,negated_conjecture,
~ ! [X4,X5] :
( addition(X4,multiplication(domain(X5),X4)) = multiplication(domain(X5),X4)
<= addition(domain(X4),domain(X5)) = domain(X5) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_8,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X22,X23,X24] : multiplication(addition(X22,X23),X24) = addition(multiplication(X22,X24),multiplication(X23,X24)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_11,negated_conjecture,
~ ! [X4,X5] :
( addition(domain(X4),domain(X5)) = domain(X5)
=> addition(X4,multiplication(domain(X5),X4)) = multiplication(domain(X5),X4) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
addition(X1,addition(multiplication(domain(X1),X1),X2)) = addition(multiplication(domain(X1),X1),X2),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X11,X12] : domain(addition(X11,X12)) = addition(domain(X11),domain(X12)),
inference(variable_rename,[status(thm)],[domain5]) ).
fof(c_0_15,negated_conjecture,
( addition(esk1_0,multiplication(domain(esk2_0),esk1_0)) != multiplication(domain(esk2_0),esk1_0)
& addition(domain(esk1_0),domain(esk2_0)) = domain(esk2_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
cnf(c_0_16,plain,
addition(X1,multiplication(addition(domain(X1),X2),X1)) = multiplication(addition(domain(X1),X2),X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
domain(addition(X1,X2)) = addition(domain(X1),domain(X2)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
addition(domain(esk1_0),domain(esk2_0)) = domain(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
addition(X1,multiplication(domain(addition(X1,X2)),X1)) = multiplication(domain(addition(X1,X2)),X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
domain(addition(esk1_0,esk2_0)) = domain(esk2_0),
inference(rw,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
addition(esk1_0,multiplication(domain(esk2_0),esk1_0)) != multiplication(domain(esk2_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE064+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 : n020.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 22:42:48 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.46 % Version: 3.5.1
% 0.14/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.46 % Starting sh5l with 300s (1) cores
% 0.14/0.46 % new_bool_3 with pid 1387320 completed with status 0
% 0.14/0.46 % Result found by new_bool_3
% 0.14/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.46 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.14/0.46 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.14/0.46 % SubtermCWHack with pid 1387326 completed with status 0
% 0.14/0.46 % Result found by SubtermCWHack
% 0.14/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.46 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.14/0.46 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.14/0.46 % Preprocessing time : 0.001 s
% 0.14/0.46
% 0.14/0.46 % Proof found!
% 0.14/0.46 % SZS status Theorem
% 0.14/0.46 % SZS output start CNFRefutation
% See solution above
% 0.14/0.46 % Parsed axioms : 18
% 0.14/0.46 % Removed by relevancy pruning/SinE : 4
% 0.14/0.46 % Initial clauses : 15
% 0.14/0.46 % Removed in clause preprocessing : 0
% 0.14/0.46 % Initial clauses in saturation : 15
% 0.14/0.46 % Processed clauses : 466
% 0.14/0.46 % ...of these trivial : 279
% 0.14/0.46 % ...subsumed : 104
% 0.14/0.46 % ...remaining for further processing : 83
% 0.14/0.46 % Other redundant clauses eliminated : 0
% 0.14/0.46 % Clauses deleted for lack of memory : 0
% 0.14/0.46 % Backward-subsumed : 0
% 0.14/0.46 % Backward-rewritten : 7
% 0.14/0.46 % Generated clauses : 3517
% 0.14/0.46 % ...of the previous two non-redundant : 2785
% 0.14/0.46 % ...aggressively subsumed : 0
% 0.14/0.46 % Contextual simplify-reflections : 0
% 0.14/0.46 % Paramodulations : 3517
% 0.14/0.46 % Factorizations : 0
% 0.14/0.46 % NegExts : 0
% 0.14/0.46 % Equation resolutions : 0
% 0.14/0.46 % Disequality decompositions : 0
% 0.14/0.46 % Total rewrite steps : 4946
% 0.14/0.46 % ...of those cached : 2744
% 0.14/0.46 % Propositional unsat checks : 0
% 0.14/0.46 % Propositional check models : 0
% 0.14/0.46 % Propositional check unsatisfiable : 0
% 0.14/0.46 % Propositional clauses : 0
% 0.14/0.46 % Propositional clauses after purity: 0
% 0.14/0.46 % Propositional unsat core size : 0
% 0.14/0.46 % Propositional preprocessing time : 0.000
% 0.14/0.46 % Propositional encoding time : 0.000
% 0.14/0.46 % Propositional solver time : 0.000
% 0.14/0.46 % Success case prop preproc time : 0.000
% 0.14/0.46 % Success case prop encoding time : 0.000
% 0.14/0.46 % Success case prop solver time : 0.000
% 0.14/0.46 % Current number of processed clauses : 76
% 0.14/0.46 % Positive orientable unit clauses : 70
% 0.14/0.46 % Positive unorientable unit clauses: 5
% 0.14/0.46 % Negative unit clauses : 1
% 0.14/0.46 % Non-unit-clauses : 0
% 0.14/0.46 % Current number of unprocessed clauses: 2249
% 0.14/0.46 % ...number of literals in the above : 2249
% 0.14/0.46 % Current number of archived formulas : 0
% 0.14/0.46 % Current number of archived clauses : 7
% 0.14/0.46 % Clause-clause subsumption calls (NU) : 0
% 0.14/0.46 % Rec. Clause-clause subsumption calls : 0
% 0.14/0.46 % Non-unit clause-clause subsumptions : 0
% 0.14/0.46 % Unit Clause-clause subsumption calls : 13
% 0.14/0.46 % Rewrite failures with RHS unbound : 0
% 0.14/0.46 % BW rewrite match attempts : 209
% 0.14/0.46 % BW rewrite match successes : 49
% 0.14/0.46 % Condensation attempts : 0
% 0.14/0.46 % Condensation successes : 0
% 0.14/0.46 % Termbank termtop insertions : 60582
% 0.14/0.46 % Search garbage collected termcells : 45
% 0.14/0.46
% 0.14/0.46 % -------------------------------------------------
% 0.14/0.46 % User time : 0.030 s
% 0.14/0.46 % System time : 0.000 s
% 0.14/0.46 % Total time : 0.030 s
% 0.14/0.46 % Maximum resident set size: 3648 pages
% 0.14/0.46
% 0.14/0.46 % -------------------------------------------------
% 0.14/0.46 % User time : 0.031 s
% 0.14/0.46 % System time : 0.003 s
% 0.14/0.46 % Total time : 0.034 s
% 0.14/0.46 % Maximum resident set size: 4608 pages
% 0.14/0.46 % E exiting
%------------------------------------------------------------------------------