%------------------------------------------------------------------------------
% File : E-SAT---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 : 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 12:59:15 PM UTC 2026
% Result : Theorem 0.27s 0.65s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 28 unt; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 0 |; 1 &)
% ( 0 <=>; 1 =>; 2 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 44 ( 3 sgn 26 !; 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(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(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_7,plain,
! [X24,X25,X26] : multiplication(addition(X24,X25),X26) = addition(multiplication(X24,X26),multiplication(X25,X26)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_8,plain,
! [X31] : multiplication(one,X31) = X31,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_9,plain,
! [X14,X15] : addition(X14,X15) = addition(X15,X14),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_10,plain,
! [X11] : addition(domain(X11),one) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_11,plain,
! [X8] : addition(X8,multiplication(domain(X8),X8)) = multiplication(domain(X8),X8),
inference(variable_rename,[status(thm)],[domain1]) ).
cnf(c_0_12,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
addition(domain(X1),one) = one,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,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_17,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_19,plain,
addition(one,domain(X1)) = one,
inference(rw,[status(thm)],[c_0_15,c_0_14]) ).
fof(c_0_20,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_16]) ).
cnf(c_0_21,plain,
multiplication(domain(X1),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_14]),c_0_19]),c_0_13]) ).
fof(c_0_22,plain,
! [X12,X13] : domain(addition(X12,X13)) = addition(domain(X12),domain(X13)),
inference(variable_rename,[status(thm)],[domain5]) ).
fof(c_0_23,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_20])])])]) ).
cnf(c_0_24,plain,
multiplication(addition(domain(X1),X2),X1) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_21]),c_0_18]) ).
cnf(c_0_25,plain,
domain(addition(X1,X2)) = addition(domain(X1),domain(X2)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
addition(domain(esk1_0),domain(esk2_0)) = domain(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,negated_conjecture,
addition(esk1_0,multiplication(domain(esk2_0),esk1_0)) != multiplication(domain(esk2_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
multiplication(domain(addition(X1,X2)),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_14]),c_0_19]),c_0_13]) ).
cnf(c_0_29,negated_conjecture,
domain(addition(esk1_0,esk2_0)) = domain(esk2_0),
inference(rw,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_30,negated_conjecture,
multiplication(domain(esk2_0),esk1_0) != esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_18]),c_0_14]),c_0_19]),c_0_13]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE064+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.44 % Computer : n004.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sun Sep 20 22:41:50 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.53 Running first-order theorem proving
% 0.27/0.53 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
% 0.27/0.65 % Version: 3.5.1
% 0.27/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.65 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.65 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.65 % Starting sh5l with 300s (1) cores
% 0.27/0.65 % sh5l with pid 1650345 completed with status 0
% 0.27/0.65 % Result found by sh5l
% 0.27/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.65 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.65 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.65 % Starting sh5l with 300s (1) cores
% 0.27/0.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.27/0.65 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.27/0.65 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.27/0.65 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.65 % Starting SubtermCWHack with 28s (1) cores
% 0.27/0.65 % SubtermCWHack with pid 1650353 completed with status 0
% 0.27/0.65 % Result found by SubtermCWHack
% 0.27/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.27/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.27/0.65 % Starting new_bool_3 with 300s (1) cores
% 0.27/0.65 % Starting new_bool_1 with 300s (1) cores
% 0.27/0.65 % Starting sh5l with 300s (1) cores
% 0.27/0.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.27/0.65 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.27/0.65 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.27/0.65 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.65 % Starting SubtermCWHack with 28s (1) cores
% 0.27/0.65 % Preprocessing time : 0.002 s
% 0.27/0.65
% 0.27/0.65 % Proof found!
% 0.27/0.65 % SZS status Theorem
% 0.27/0.65 % SZS output start CNFRefutation
% See solution above
% 0.27/0.65 % Parsed axioms : 18
% 0.27/0.65 % Removed by relevancy pruning/SinE : 1
% 0.27/0.65 % Initial clauses : 18
% 0.27/0.65 % Removed in clause preprocessing : 0
% 0.27/0.65 % Initial clauses in saturation : 18
% 0.27/0.65 % Processed clauses : 323
% 0.27/0.65 % ...of these trivial : 100
% 0.27/0.65 % ...subsumed : 122
% 0.27/0.65 % ...remaining for further processing : 101
% 0.27/0.65 % Other redundant clauses eliminated : 0
% 0.27/0.65 % Clauses deleted for lack of memory : 0
% 0.27/0.65 % Backward-subsumed : 0
% 0.27/0.65 % Backward-rewritten : 12
% 0.27/0.65 % Generated clauses : 3863
% 0.27/0.65 % ...of the previous two non-redundant : 2099
% 0.27/0.65 % ...aggressively subsumed : 0
% 0.27/0.65 % Contextual simplify-reflections : 0
% 0.27/0.65 % Paramodulations : 3863
% 0.27/0.65 % Factorizations : 0
% 0.27/0.65 % NegExts : 0
% 0.27/0.65 % Equation resolutions : 0
% 0.27/0.65 % Disequality decompositions : 0
% 0.27/0.65 % Total rewrite steps : 5261
% 0.27/0.65 % ...of those cached : 3748
% 0.27/0.65 % Propositional unsat checks : 0
% 0.27/0.65 % Propositional check models : 0
% 0.27/0.65 % Propositional check unsatisfiable : 0
% 0.27/0.65 % Propositional clauses : 0
% 0.27/0.65 % Propositional clauses after purity: 0
% 0.27/0.65 % Propositional unsat core size : 0
% 0.27/0.65 % Propositional preprocessing time : 0.000
% 0.27/0.65 % Propositional encoding time : 0.000
% 0.27/0.65 % Propositional solver time : 0.000
% 0.27/0.65 % Success case prop preproc time : 0.000
% 0.27/0.65 % Success case prop encoding time : 0.000
% 0.27/0.65 % Success case prop solver time : 0.000
% 0.27/0.65 % Current number of processed clauses : 89
% 0.27/0.65 % Positive orientable unit clauses : 84
% 0.27/0.65 % Positive unorientable unit clauses: 4
% 0.27/0.65 % Negative unit clauses : 1
% 0.27/0.65 % Non-unit-clauses : 0
% 0.27/0.65 % Current number of unprocessed clauses: 1723
% 0.27/0.65 % ...number of literals in the above : 1723
% 0.27/0.65 % Current number of archived formulas : 0
% 0.27/0.65 % Current number of archived clauses : 12
% 0.27/0.65 % Clause-clause subsumption calls (NU) : 0
% 0.27/0.65 % Rec. Clause-clause subsumption calls : 0
% 0.27/0.65 % Non-unit clause-clause subsumptions : 0
% 0.27/0.65 % Unit Clause-clause subsumption calls : 7
% 0.27/0.65 % Rewrite failures with RHS unbound : 0
% 0.27/0.65 % BW rewrite match attempts : 279
% 0.27/0.65 % BW rewrite match successes : 97
% 0.27/0.65 % Condensation attempts : 0
% 0.27/0.65 % Condensation successes : 0
% 0.27/0.65 % Termbank termtop insertions : 39112
% 0.27/0.65 % Search garbage collected termcells : 35
% 0.27/0.65
% 0.27/0.65 % -------------------------------------------------
% 0.27/0.65 % User time : 0.059 s
% 0.27/0.65 % System time : 0.005 s
% 0.27/0.65 % Total time : 0.065 s
% 0.27/0.65 % Maximum resident set size: 3904 pages
% 0.27/0.65
% 0.27/0.65 % -------------------------------------------------
% 0.27/0.65 % User time : 0.060 s
% 0.27/0.65 % System time : 0.013 s
% 0.27/0.65 % Total time : 0.073 s
% 0.27/0.65 % Maximum resident set size: 4608 pages
% 0.27/0.65 % E exiting
%------------------------------------------------------------------------------