%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE099+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 : n003.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 12:58:50 PM UTC 2026
% Result : Theorem 0.14s 0.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 63 ( 60 unt; 0 def)
% Number of atoms : 66 ( 65 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 0 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 99 ( 5 sgn 54 !; 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(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
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(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_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(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(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(goals,conjecture,
! [X4,X5,X6] :
( addition(forward_diamond(X4,domain(X5)),domain(X6)) = domain(X6)
=> multiplication(antidomain(X6),multiplication(X4,domain(X5))) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(forward_diamond,axiom,
! [X4,X5] : forward_diamond(X4,X5) = domain(multiplication(X4,domain(X5))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(c_0_15,plain,
! [X9,X10,X11] : addition(X11,addition(X10,X9)) = addition(addition(X11,X10),X9),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_16,plain,
! [X13] : addition(X13,X13) = X13,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_17,plain,
! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_18,plain,
! [X29] : multiplication(antidomain(X29),X29) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_19,plain,
! [X12] : addition(X12,zero) = X12,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_20,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_22,plain,
! [X7,X8] : addition(X7,X8) = addition(X8,X7),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_23,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_28,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_29,plain,
! [X32] : addition(antidomain(antidomain(X32)),antidomain(X32)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_30,negated_conjecture,
~ ! [X4,X5,X6] :
( addition(forward_diamond(X4,domain(X5)),domain(X6)) = domain(X6)
=> multiplication(antidomain(X6),multiplication(X4,domain(X5))) = zero ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_31,plain,
! [X42,X43] : forward_diamond(X42,X43) = domain(multiplication(X42,domain(X43))),
inference(variable_rename,[status(thm)],[forward_diamond]) ).
fof(c_0_32,plain,
! [X33] : domain(X33) = antidomain(antidomain(X33)),
inference(variable_rename,[status(thm)],[domain4]) ).
fof(c_0_33,plain,
! [X14,X15,X16] : multiplication(X14,multiplication(X15,X16)) = multiplication(multiplication(X14,X15),X16),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_34,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_35,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_36,plain,
! [X26] : multiplication(zero,X26) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_37,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_27]) ).
cnf(c_0_39,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_40,plain,
! [X18] : multiplication(one,X18) = X18,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_41,negated_conjecture,
( multiplication(antidomain(esk3_0),multiplication(esk1_0,domain(esk2_0))) != zero
& addition(forward_diamond(esk1_0,domain(esk2_0)),domain(esk3_0)) = domain(esk3_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])]) ).
cnf(c_0_42,plain,
forward_diamond(X1,X2) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_43,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_44,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_45,plain,
multiplication(antidomain(addition(X1,X2)),X2) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_24]) ).
cnf(c_0_46,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_47,plain,
multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_24]),c_0_38]) ).
cnf(c_0_48,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_39,c_0_27]) ).
cnf(c_0_49,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_50,negated_conjecture,
addition(forward_diamond(esk1_0,domain(esk2_0)),domain(esk3_0)) = domain(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_51,plain,
forward_diamond(X1,X2) = antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_43]) ).
fof(c_0_52,plain,
! [X17] : multiplication(X17,one) = X17,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_53,plain,
multiplication(antidomain(addition(X1,X2)),multiplication(X2,X3)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_54,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_55,negated_conjecture,
addition(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(esk2_0))))))),antidomain(antidomain(esk3_0))) = antidomain(antidomain(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_43]),c_0_43]),c_0_43]),c_0_51]) ).
cnf(c_0_56,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_57,negated_conjecture,
multiplication(antidomain(esk3_0),multiplication(esk1_0,domain(esk2_0))) != zero,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_58,plain,
multiplication(antidomain(addition(X1,antidomain(antidomain(X2)))),X2) = zero,
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,negated_conjecture,
addition(antidomain(antidomain(esk3_0)),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(esk2_0)))))))) = antidomain(antidomain(esk3_0)),
inference(rw,[status(thm)],[c_0_55,c_0_27]) ).
cnf(c_0_60,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_48]),c_0_56]),c_0_54]) ).
cnf(c_0_61,negated_conjecture,
multiplication(antidomain(esk3_0),multiplication(esk1_0,antidomain(antidomain(esk2_0)))) != zero,
inference(rw,[status(thm)],[c_0_57,c_0_43]) ).
cnf(c_0_62,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_60]),c_0_61]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE099+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 22:44:46 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.47 % Version: 3.5.1
% 0.14/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.47 % Starting sh5l with 300s (1) cores
% 0.14/0.47 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2779277 completed with status 0
% 0.14/0.47 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.47 % No SInE strategy applied
% 0.14/0.47 % Search class: FHUSM-FFSF21-DFFFFFNN
% 0.14/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.47 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 271s (1) cores
% 0.14/0.47 % Starting new_bool_3 with 271s (1) cores
% 0.14/0.47 % Starting U----_206d_02_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/0.47 % SubtermCWHack with pid 2779282 completed with status 0
% 0.14/0.47 % Result found by SubtermCWHack
% 0.14/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.47 % No SInE strategy applied
% 0.14/0.47 % Search class: FHUSM-FFSF21-DFFFFFNN
% 0.14/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.47 % Preprocessing time : 0.002 s
% 0.14/0.47
% 0.14/0.47 % Proof found!
% 0.14/0.47 % SZS status Theorem
% 0.14/0.47 % SZS output start CNFRefutation
% See solution above
% 0.14/0.47 % Parsed axioms : 27
% 0.14/0.47 % Removed by relevancy pruning/SinE : 0
% 0.14/0.47 % Initial clauses : 29
% 0.14/0.47 % Removed in clause preprocessing : 8
% 0.14/0.47 % Initial clauses in saturation : 21
% 0.14/0.47 % Processed clauses : 200
% 0.14/0.47 % ...of these trivial : 55
% 0.14/0.47 % ...subsumed : 53
% 0.14/0.47 % ...remaining for further processing : 92
% 0.14/0.47 % Other redundant clauses eliminated : 0
% 0.14/0.47 % Clauses deleted for lack of memory : 0
% 0.14/0.47 % Backward-subsumed : 0
% 0.14/0.47 % Backward-rewritten : 14
% 0.14/0.47 % Generated clauses : 2347
% 0.14/0.47 % ...of the previous two non-redundant : 960
% 0.14/0.47 % ...aggressively subsumed : 0
% 0.14/0.47 % Contextual simplify-reflections : 0
% 0.14/0.47 % Paramodulations : 2347
% 0.14/0.47 % Factorizations : 0
% 0.14/0.47 % NegExts : 0
% 0.14/0.47 % Equation resolutions : 0
% 0.14/0.47 % Disequality decompositions : 0
% 0.14/0.47 % Total rewrite steps : 3338
% 0.14/0.47 % ...of those cached : 2573
% 0.14/0.47 % Propositional unsat checks : 0
% 0.14/0.47 % Propositional check models : 0
% 0.14/0.47 % Propositional check unsatisfiable : 0
% 0.14/0.47 % Propositional clauses : 0
% 0.14/0.47 % Propositional clauses after purity: 0
% 0.14/0.47 % Propositional unsat core size : 0
% 0.14/0.47 % Propositional preprocessing time : 0.000
% 0.14/0.47 % Propositional encoding time : 0.000
% 0.14/0.47 % Propositional solver time : 0.000
% 0.14/0.47 % Success case prop preproc time : 0.000
% 0.14/0.47 % Success case prop encoding time : 0.000
% 0.14/0.47 % Success case prop solver time : 0.000
% 0.14/0.47 % Current number of processed clauses : 78
% 0.14/0.47 % Positive orientable unit clauses : 72
% 0.14/0.47 % Positive unorientable unit clauses: 3
% 0.14/0.47 % Negative unit clauses : 1
% 0.14/0.47 % Non-unit-clauses : 2
% 0.14/0.47 % Current number of unprocessed clauses: 755
% 0.14/0.47 % ...number of literals in the above : 755
% 0.14/0.47 % Current number of archived formulas : 0
% 0.14/0.47 % Current number of archived clauses : 22
% 0.14/0.47 % Clause-clause subsumption calls (NU) : 0
% 0.14/0.47 % Rec. Clause-clause subsumption calls : 0
% 0.14/0.47 % Non-unit clause-clause subsumptions : 0
% 0.14/0.47 % Unit Clause-clause subsumption calls : 3
% 0.14/0.47 % Rewrite failures with RHS unbound : 0
% 0.14/0.47 % BW rewrite match attempts : 114
% 0.14/0.47 % BW rewrite match successes : 51
% 0.14/0.47 % Condensation attempts : 0
% 0.14/0.47 % Condensation successes : 0
% 0.14/0.47 % Termbank termtop insertions : 20676
% 0.14/0.47 % Search garbage collected termcells : 56
% 0.14/0.47
% 0.14/0.47 % -------------------------------------------------
% 0.14/0.47 % User time : 0.032 s
% 0.14/0.47 % System time : 0.012 s
% 0.14/0.47 % Total time : 0.044 s
% 0.14/0.47 % Maximum resident set size: 3660 pages
% 0.14/0.47
% 0.14/0.47 % -------------------------------------------------
% 0.14/0.47 % User time : 0.166 s
% 0.14/0.47 % System time : 0.039 s
% 0.14/0.47 % Total time : 0.206 s
% 0.14/0.47 % Maximum resident set size: 4608 pages
% 0.14/0.47 % E exiting
%------------------------------------------------------------------------------