%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE088+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 : n005.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 12:58:49 PM UTC 2026
% Result : Theorem 1.04s 0.68s
% Output : CNFRefutation 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 60 ( 57 unt; 0 def)
% Number of atoms : 63 ( 62 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 0 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 78 ( 1 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5] :
( multiplication(domain(X4),X5) = zero
=> addition(domain(X4),antidomain(X5)) = antidomain(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
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(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(domain2,axiom,
! [X4,X5] : addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,antidomain(antidomain(X5))))) = antidomain(multiplication(X4,antidomain(antidomain(X5)))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain2) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(c_0_13,negated_conjecture,
~ ! [X4,X5] :
( multiplication(domain(X4),X5) = zero
=> addition(domain(X4),antidomain(X5)) = antidomain(X5) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_14,plain,
! [X31] : addition(antidomain(antidomain(X31)),antidomain(X31)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_15,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_16,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_17,plain,
! [X28] : multiplication(antidomain(X28),X28) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_18,plain,
! [X11] : addition(X11,zero) = X11,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_19,plain,
! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_20,plain,
! [X12] : addition(X12,X12) = X12,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_21,negated_conjecture,
( addition(domain(esk1_0),antidomain(esk2_0)) != antidomain(esk2_0)
& multiplication(domain(esk1_0),esk2_0) = zero ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
fof(c_0_22,plain,
! [X32] : domain(X32) = antidomain(antidomain(X32)),
inference(variable_rename,[status(thm)],[domain4]) ).
cnf(c_0_23,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_30,plain,
! [X29,X30] : addition(antidomain(multiplication(X29,X30)),antidomain(multiplication(X29,antidomain(antidomain(X30))))) = antidomain(multiplication(X29,antidomain(antidomain(X30)))),
inference(variable_rename,[status(thm)],[domain2]) ).
cnf(c_0_31,negated_conjecture,
multiplication(domain(esk1_0),esk2_0) = zero,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_32,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_34,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_35,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_36,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_37,plain,
! [X21,X22,X23] : multiplication(addition(X21,X22),X23) = addition(multiplication(X21,X23),multiplication(X22,X23)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_38,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,negated_conjecture,
multiplication(antidomain(antidomain(esk1_0)),esk2_0) = zero,
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_40,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_41,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_33]),c_0_24]) ).
fof(c_0_42,plain,
! [X17] : multiplication(one,X17) = X17,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_43,plain,
! [X18,X19,X20] : multiplication(X18,addition(X19,X20)) = addition(multiplication(X18,X19),multiplication(X18,X20)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_44,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,negated_conjecture,
antidomain(multiplication(antidomain(antidomain(esk1_0)),antidomain(antidomain(esk2_0)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41]) ).
cnf(c_0_46,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_47,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_48,plain,
multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_26]),c_0_35]) ).
cnf(c_0_49,negated_conjecture,
multiplication(antidomain(antidomain(esk1_0)),antidomain(antidomain(esk2_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_45]),c_0_46]) ).
cnf(c_0_50,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_26]),c_0_27]) ).
cnf(c_0_51,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_33]),c_0_46]) ).
cnf(c_0_52,negated_conjecture,
addition(domain(esk1_0),antidomain(esk2_0)) != antidomain(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_53,negated_conjecture,
multiplication(antidomain(antidomain(esk1_0)),addition(antidomain(antidomain(esk2_0)),X1)) = multiplication(antidomain(antidomain(esk1_0)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_49]),c_0_35]) ).
cnf(c_0_54,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_33]),c_0_25]),c_0_51]) ).
cnf(c_0_55,negated_conjecture,
addition(antidomain(antidomain(esk1_0)),antidomain(esk2_0)) != antidomain(esk2_0),
inference(rw,[status(thm)],[c_0_52,c_0_32]) ).
cnf(c_0_56,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_46]),c_0_24]) ).
cnf(c_0_57,negated_conjecture,
multiplication(antidomain(antidomain(esk1_0)),antidomain(esk2_0)) = antidomain(antidomain(esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_33]),c_0_25]),c_0_54]) ).
cnf(c_0_58,negated_conjecture,
addition(antidomain(esk2_0),antidomain(antidomain(esk1_0))) != antidomain(esk2_0),
inference(rw,[status(thm)],[c_0_55,c_0_24]) ).
cnf(c_0_59,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_24]),c_0_41]),c_0_46]),c_0_58]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE088+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.46 % Computer : n005.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Sun Sep 20 22:42:33 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.53 Running first-order theorem proving
% 0.23/0.53 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
% 1.04/0.68 % Version: 3.5.1
% 1.04/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.04/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.04/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.04/0.68 % Starting new_bool_3 with 300s (1) cores
% 1.04/0.68 % Starting new_bool_1 with 300s (1) cores
% 1.04/0.68 % Starting sh5l with 300s (1) cores
% 1.04/0.68 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1916924 completed with status 0
% 1.04/0.68 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.04/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.04/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.04/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.04/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.04/0.68 % No SInE strategy applied
% 1.04/0.68 % Search class: FHUSM-FFSF21-MFFFFFNN
% 1.04/0.68 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 1.04/0.68 % Starting SubtermCWHack with 136s (1) cores
% 1.04/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.04/0.68 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 1.04/0.68 % Starting G-E--_092_C01_F1_AE_CS_SP_PS_CO_S0Y with 136s (1) cores
% 1.04/0.68 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 1.04/0.68 % G-E--_300_C18_F1_SE_CS_SP_S0Y with pid 1916933 completed with status 0
% 1.04/0.68 % Result found by G-E--_300_C18_F1_SE_CS_SP_S0Y
% 1.04/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.04/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.04/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.04/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.04/0.68 % No SInE strategy applied
% 1.04/0.68 % Search class: FHUSM-FFSF21-MFFFFFNN
% 1.04/0.68 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 1.04/0.68 % Starting SubtermCWHack with 136s (1) cores
% 1.04/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.04/0.68 % Starting G-E--_300_C18_F1_SE_CS_SP_S0Y with 136s (1) cores
% 1.04/0.68 % Preprocessing time : 0.002 s
% 1.04/0.68
% 1.04/0.68 % Proof found!
% 1.04/0.68 % SZS status Theorem
% 1.04/0.68 % SZS output start CNFRefutation
% See solution above
% 1.04/0.68 % Parsed axioms : 21
% 1.04/0.68 % Removed by relevancy pruning/SinE : 0
% 1.04/0.68 % Initial clauses : 23
% 1.04/0.68 % Removed in clause preprocessing : 2
% 1.04/0.68 % Initial clauses in saturation : 21
% 1.04/0.68 % Processed clauses : 465
% 1.04/0.68 % ...of these trivial : 187
% 1.04/0.68 % ...subsumed : 64
% 1.04/0.68 % ...remaining for further processing : 214
% 1.04/0.68 % Other redundant clauses eliminated : 0
% 1.04/0.68 % Clauses deleted for lack of memory : 0
% 1.04/0.68 % Backward-subsumed : 0
% 1.04/0.68 % Backward-rewritten : 48
% 1.04/0.68 % Generated clauses : 7253
% 1.04/0.68 % ...of the previous two non-redundant : 3053
% 1.04/0.68 % ...aggressively subsumed : 0
% 1.04/0.68 % Contextual simplify-reflections : 0
% 1.04/0.68 % Paramodulations : 7253
% 1.04/0.68 % Factorizations : 0
% 1.04/0.68 % NegExts : 0
% 1.04/0.68 % Equation resolutions : 0
% 1.04/0.68 % Disequality decompositions : 0
% 1.04/0.68 % Total rewrite steps : 11167
% 1.04/0.68 % ...of those cached : 8863
% 1.04/0.68 % Propositional unsat checks : 0
% 1.04/0.68 % Propositional check models : 0
% 1.04/0.68 % Propositional check unsatisfiable : 0
% 1.04/0.68 % Propositional clauses : 0
% 1.04/0.68 % Propositional clauses after purity: 0
% 1.04/0.68 % Propositional unsat core size : 0
% 1.04/0.68 % Propositional preprocessing time : 0.000
% 1.04/0.68 % Propositional encoding time : 0.000
% 1.04/0.68 % Propositional solver time : 0.000
% 1.04/0.68 % Success case prop preproc time : 0.000
% 1.04/0.68 % Success case prop encoding time : 0.000
% 1.04/0.68 % Success case prop solver time : 0.000
% 1.04/0.68 % Current number of processed clauses : 166
% 1.04/0.68 % Positive orientable unit clauses : 160
% 1.04/0.68 % Positive unorientable unit clauses: 3
% 1.04/0.68 % Negative unit clauses : 1
% 1.04/0.68 % Non-unit-clauses : 2
% 1.04/0.68 % Current number of unprocessed clauses: 2508
% 1.04/0.68 % ...number of literals in the above : 2508
% 1.04/0.68 % Current number of archived formulas : 0
% 1.04/0.68 % Current number of archived clauses : 50
% 1.04/0.68 % Clause-clause subsumption calls (NU) : 0
% 1.04/0.68 % Rec. Clause-clause subsumption calls : 0
% 1.04/0.68 % Non-unit clause-clause subsumptions : 0
% 1.04/0.68 % Unit Clause-clause subsumption calls : 3
% 1.04/0.68 % Rewrite failures with RHS unbound : 0
% 1.04/0.68 % BW rewrite match attempts : 368
% 1.04/0.68 % BW rewrite match successes : 83
% 1.04/0.68 % Condensation attempts : 0
% 1.04/0.68 % Condensation successes : 0
% 1.04/0.68 % Termbank termtop insertions : 76875
% 1.04/0.68 % Search garbage collected termcells : 49
% 1.04/0.68
% 1.04/0.68 % -------------------------------------------------
% 1.04/0.68 % User time : 0.109 s
% 1.04/0.68 % System time : 0.010 s
% 1.04/0.68 % Total time : 0.119 s
% 1.04/0.68 % Maximum resident set size: 3652 pages
% 1.04/0.68
% 1.04/0.68 % -------------------------------------------------
% 1.04/0.68 % User time : 0.488 s
% 1.04/0.68 % System time : 0.048 s
% 1.04/0.68 % Total time : 0.536 s
% 1.04/0.68 % Maximum resident set size: 4608 pages
% 1.04/0.68 % E exiting
%------------------------------------------------------------------------------