%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE133+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 12:58:55 PM UTC 2026
% Result : Theorem 0.09s 0.43s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 60 ( 57 unt; 0 def)
% Number of atoms : 66 ( 65 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 9 ( 3 ~; 0 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 65 ( 5 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(goals,conjecture,
! [X4] :
( ( ! [X6] : forward_diamond(X4,forward_diamond(X4,domain(X6))) = forward_diamond(X4,domain(X6))
& ! [X5] : addition(domain(X5),forward_diamond(star(X4),domain_difference(domain(X5),forward_diamond(X4,domain(X5))))) = forward_diamond(star(X4),domain_difference(domain(X5),forward_diamond(X4,domain(X5)))) )
=> ! [X7] : addition(forward_diamond(X4,domain(X7)),forward_diamond(star(X4),domain_difference(domain(X7),forward_diamond(X4,domain(X7))))) = forward_diamond(star(X4),domain_difference(domain(X7),forward_diamond(X4,domain(X7)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(forward_diamond,axiom,
! [X4,X5] : forward_diamond(X4,X5) = domain(multiplication(X4,domain(X5))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).
fof(domain_difference,axiom,
! [X4,X5] : domain_difference(X4,X5) = multiplication(domain(X4),antidomain(X5)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',domain_difference) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(c_0_12,plain,
! [X44] : multiplication(X44,one) = X44,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_13,plain,
! [X35] : multiplication(antidomain(X35),X35) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_14,plain,
! [X38] : addition(antidomain(antidomain(X38)),antidomain(X38)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_15,plain,
! [X16] : domain(X16) = antidomain(antidomain(X16)),
inference(variable_rename,[status(thm)],[domain4]) ).
cnf(c_0_16,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,plain,
! [X40] : addition(X40,zero) = X40,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_21,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_22,negated_conjecture,
~ ! [X4] :
( ( ! [X6] : forward_diamond(X4,forward_diamond(X4,domain(X6))) = forward_diamond(X4,domain(X6))
& ! [X5] : addition(domain(X5),forward_diamond(star(X4),domain_difference(domain(X5),forward_diamond(X4,domain(X5))))) = forward_diamond(star(X4),domain_difference(domain(X5),forward_diamond(X4,domain(X5)))) )
=> ! [X7] : addition(forward_diamond(X4,domain(X7)),forward_diamond(star(X4),domain_difference(domain(X7),forward_diamond(X4,domain(X7))))) = forward_diamond(star(X4),domain_difference(domain(X7),forward_diamond(X4,domain(X7)))) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_23,plain,
! [X12,X13] : forward_diamond(X12,X13) = domain(multiplication(X12,domain(X13))),
inference(variable_rename,[status(thm)],[forward_diamond]) ).
cnf(c_0_24,plain,
addition(domain(X1),antidomain(X1)) = one,
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
multiplication(domain(X1),antidomain(X1)) = zero,
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_27,plain,
antidomain(zero) = domain(one),
inference(spm,[status(thm)],[c_0_19,c_0_21]) ).
fof(c_0_28,negated_conjecture,
! [X9,X10] :
( addition(forward_diamond(esk1_0,domain(esk2_0)),forward_diamond(star(esk1_0),domain_difference(domain(esk2_0),forward_diamond(esk1_0,domain(esk2_0))))) != forward_diamond(star(esk1_0),domain_difference(domain(esk2_0),forward_diamond(esk1_0,domain(esk2_0))))
& forward_diamond(esk1_0,forward_diamond(esk1_0,domain(X10))) = forward_diamond(esk1_0,domain(X10))
& addition(domain(X9),forward_diamond(star(esk1_0),domain_difference(domain(X9),forward_diamond(esk1_0,domain(X9))))) = forward_diamond(star(esk1_0),domain_difference(domain(X9),forward_diamond(esk1_0,domain(X9)))) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])])]) ).
fof(c_0_29,plain,
! [X14,X15] : domain_difference(X14,X15) = multiplication(domain(X14),antidomain(X15)),
inference(variable_rename,[status(thm)],[domain_difference]) ).
cnf(c_0_30,plain,
forward_diamond(X1,X2) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
domain(one) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_21]),c_0_25]) ).
cnf(c_0_32,plain,
multiplication(domain(zero),domain(one)) = zero,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_33,plain,
! [X41] : multiplication(X41,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_34,negated_conjecture,
addition(domain(X1),forward_diamond(star(esk1_0),domain_difference(domain(X1),forward_diamond(esk1_0,domain(X1))))) = forward_diamond(star(esk1_0),domain_difference(domain(X1),forward_diamond(esk1_0,domain(X1)))),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
domain_difference(X1,X2) = multiplication(domain(X1),antidomain(X2)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,negated_conjecture,
forward_diamond(esk1_0,forward_diamond(esk1_0,domain(X1))) = forward_diamond(esk1_0,domain(X1)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,plain,
forward_diamond(X1,one) = domain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_16]) ).
cnf(c_0_38,plain,
antidomain(domain(X1)) = domain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_19,c_0_19]) ).
cnf(c_0_39,plain,
domain(zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_31]),c_0_16]) ).
cnf(c_0_40,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_41,plain,
! [X20,X21] : addition(X20,X21) = addition(X21,X20),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_42,negated_conjecture,
addition(domain(X1),forward_diamond(star(esk1_0),multiplication(domain(domain(X1)),antidomain(forward_diamond(esk1_0,domain(X1)))))) = forward_diamond(star(esk1_0),multiplication(domain(domain(X1)),antidomain(forward_diamond(esk1_0,domain(X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_35]) ).
cnf(c_0_43,negated_conjecture,
forward_diamond(esk1_0,domain(esk1_0)) = domain(esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_31]),c_0_37]),c_0_37]) ).
cnf(c_0_44,plain,
multiplication(domain(domain(X1)),domain(antidomain(X1))) = zero,
inference(spm,[status(thm)],[c_0_26,c_0_38]) ).
cnf(c_0_45,plain,
forward_diamond(X1,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_39]),c_0_40]),c_0_39]) ).
cnf(c_0_46,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_47,plain,
! [X42] : multiplication(zero,X42) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_48,negated_conjecture,
domain(esk1_0) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_38]),c_0_44]),c_0_45]),c_0_25]),c_0_38]),c_0_44]),c_0_45]) ).
cnf(c_0_49,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_46]) ).
fof(c_0_50,plain,
! [X45] : multiplication(one,X45) = X45,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_51,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_52,negated_conjecture,
antidomain(esk1_0) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_48]),c_0_49]) ).
cnf(c_0_53,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_54,plain,
forward_diamond(zero,X1) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_51]),c_0_39]) ).
cnf(c_0_55,negated_conjecture,
zero = esk1_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_52]),c_0_53]) ).
cnf(c_0_56,negated_conjecture,
addition(forward_diamond(esk1_0,domain(esk2_0)),forward_diamond(star(esk1_0),domain_difference(domain(esk2_0),forward_diamond(esk1_0,domain(esk2_0))))) != forward_diamond(star(esk1_0),domain_difference(domain(esk2_0),forward_diamond(esk1_0,domain(esk2_0)))),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_57,plain,
forward_diamond(esk1_0,X1) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55]),c_0_55]) ).
cnf(c_0_58,plain,
addition(esk1_0,X1) = X1,
inference(rw,[status(thm)],[c_0_49,c_0_55]) ).
cnf(c_0_59,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57]),c_0_57]),c_0_35]),c_0_52]),c_0_16]),c_0_58]),c_0_57]),c_0_35]),c_0_52]),c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE133+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 22:50:59 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.43 % Version: 3.5.1
% 0.09/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.43 % Starting sh5l with 300s (1) cores
% 0.09/0.43 % new_bool_3 with pid 1576999 completed with status 0
% 0.09/0.43 % Result found by new_bool_3
% 0.09/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.43 % Search class: FHUPM-FFMF21-MFFFFFNN
% 0.09/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.43 % SubtermCWHack with pid 1577002 completed with status 0
% 0.09/0.43 % Result found by SubtermCWHack
% 0.09/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.09/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.09/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.09/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.09/0.43 % Search class: FHUPM-FFMF21-MFFFFFNN
% 0.09/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.09/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.09/0.43 % Preprocessing time : 0.002 s
% 0.09/0.43
% 0.09/0.43 % Proof found!
% 0.09/0.43 % SZS status Theorem
% 0.09/0.43 % SZS output start CNFRefutation
% See solution above
% 0.09/0.43 % Parsed axioms : 29
% 0.09/0.43 % Removed by relevancy pruning/SinE : 7
% 0.09/0.43 % Initial clauses : 24
% 0.09/0.43 % Removed in clause preprocessing : 0
% 0.09/0.43 % Initial clauses in saturation : 24
% 0.09/0.43 % Processed clauses : 132
% 0.09/0.43 % ...of these trivial : 41
% 0.09/0.43 % ...subsumed : 0
% 0.09/0.43 % ...remaining for further processing : 90
% 0.09/0.43 % Other redundant clauses eliminated : 0
% 0.09/0.43 % Clauses deleted for lack of memory : 0
% 0.09/0.43 % Backward-subsumed : 0
% 0.09/0.43 % Backward-rewritten : 41
% 0.09/0.43 % Generated clauses : 670
% 0.09/0.43 % ...of the previous two non-redundant : 390
% 0.09/0.43 % ...aggressively subsumed : 0
% 0.09/0.43 % Contextual simplify-reflections : 0
% 0.09/0.43 % Paramodulations : 670
% 0.09/0.43 % Factorizations : 0
% 0.09/0.43 % NegExts : 0
% 0.09/0.43 % Equation resolutions : 0
% 0.09/0.43 % Disequality decompositions : 0
% 0.09/0.43 % Total rewrite steps : 1267
% 0.09/0.43 % ...of those cached : 965
% 0.09/0.43 % Propositional unsat checks : 0
% 0.09/0.43 % Propositional check models : 0
% 0.09/0.43 % Propositional check unsatisfiable : 0
% 0.09/0.43 % Propositional clauses : 0
% 0.09/0.43 % Propositional clauses after purity: 0
% 0.09/0.43 % Propositional unsat core size : 0
% 0.09/0.43 % Propositional preprocessing time : 0.000
% 0.09/0.43 % Propositional encoding time : 0.000
% 0.09/0.43 % Propositional solver time : 0.000
% 0.09/0.43 % Success case prop preproc time : 0.000
% 0.09/0.43 % Success case prop encoding time : 0.000
% 0.09/0.43 % Success case prop solver time : 0.000
% 0.09/0.43 % Current number of processed clauses : 49
% 0.09/0.43 % Positive orientable unit clauses : 47
% 0.09/0.43 % Positive unorientable unit clauses: 1
% 0.09/0.43 % Negative unit clauses : 0
% 0.09/0.43 % Non-unit-clauses : 1
% 0.09/0.43 % Current number of unprocessed clauses: 269
% 0.09/0.43 % ...number of literals in the above : 286
% 0.09/0.43 % Current number of archived formulas : 0
% 0.09/0.43 % Current number of archived clauses : 41
% 0.09/0.43 % Clause-clause subsumption calls (NU) : 0
% 0.09/0.43 % Rec. Clause-clause subsumption calls : 0
% 0.09/0.43 % Non-unit clause-clause subsumptions : 0
% 0.09/0.43 % Unit Clause-clause subsumption calls : 2
% 0.09/0.43 % Rewrite failures with RHS unbound : 0
% 0.09/0.43 % BW rewrite match attempts : 22
% 0.09/0.43 % BW rewrite match successes : 13
% 0.09/0.43 % Condensation attempts : 0
% 0.09/0.43 % Condensation successes : 0
% 0.09/0.43 % Termbank termtop insertions : 7555
% 0.09/0.43 % Search garbage collected termcells : 117
% 0.09/0.43
% 0.09/0.43 % -------------------------------------------------
% 0.09/0.43 % User time : 0.008 s
% 0.09/0.43 % System time : 0.005 s
% 0.09/0.43 % Total time : 0.013 s
% 0.09/0.43 % Maximum resident set size: 3664 pages
% 0.09/0.43
% 0.09/0.43 % -------------------------------------------------
% 0.09/0.43 % User time : 0.009 s
% 0.09/0.43 % System time : 0.011 s
% 0.09/0.43 % Total time : 0.020 s
% 0.09/0.43 % Maximum resident set size: 4864 pages
% 0.09/0.43 % E exiting
%------------------------------------------------------------------------------