%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : KLE082+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 : n015.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 12:58:48 PM UTC 2026
% Result : Theorem 0.59s 0.48s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 46 unt; 0 def)
% Number of atoms : 55 ( 54 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 9 ( 3 ~; 0 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 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 : 81 ( 1 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5] :
( ! [X6] :
( multiplication(domain(X6),antidomain(X6)) = zero
& addition(domain(X6),antidomain(X6)) = one )
=> addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,domain(X5)))) = antidomain(multiplication(X4,domain(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(domain2,axiom,
! [X4,X5] : domain(multiplication(X4,X5)) = domain(multiplication(X4,domain(X5))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain2) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
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(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(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(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(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(c_0_10,negated_conjecture,
~ ! [X4,X5] :
( ! [X6] :
( multiplication(domain(X6),antidomain(X6)) = zero
& addition(domain(X6),antidomain(X6)) = one )
=> addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,domain(X5)))) = antidomain(multiplication(X4,domain(X5))) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_11,plain,
! [X20,X21] : domain(multiplication(X20,X21)) = domain(multiplication(X20,domain(X21))),
inference(variable_rename,[status(thm)],[domain2]) ).
fof(c_0_12,plain,
! [X35] : multiplication(one,X35) = X35,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_13,negated_conjecture,
! [X9] :
( addition(antidomain(multiplication(esk1_0,esk2_0)),antidomain(multiplication(esk1_0,domain(esk2_0)))) != antidomain(multiplication(esk1_0,domain(esk2_0)))
& multiplication(domain(X9),antidomain(X9)) = zero
& addition(domain(X9),antidomain(X9)) = one ),
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_10])])])])]) ).
cnf(c_0_14,plain,
domain(multiplication(X1,X2)) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X31] : addition(X31,zero) = X31,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_17,plain,
! [X25,X26] : addition(X25,X26) = addition(X26,X25),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_18,plain,
! [X27,X28,X29] : addition(X29,addition(X28,X27)) = addition(addition(X29,X28),X27),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_19,plain,
! [X30] : addition(X30,X30) = X30,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_20,plain,
! [X16,X17,X18] : multiplication(addition(X16,X17),X18) = addition(multiplication(X16,X18),multiplication(X17,X18)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_21,negated_conjecture,
multiplication(domain(X1),antidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
domain(domain(X1)) = domain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_15]) ).
cnf(c_0_23,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_27,plain,
! [X13,X14,X15] : multiplication(X13,addition(X14,X15)) = addition(multiplication(X13,X14),multiplication(X13,X15)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_28,plain,
! [X34] : multiplication(X34,one) = X34,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_29,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,negated_conjecture,
multiplication(domain(X1),antidomain(domain(X1))) = zero,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_31,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_32,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,negated_conjecture,
addition(domain(X1),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_34,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,negated_conjecture,
multiplication(addition(domain(X1),X2),antidomain(domain(X1))) = multiplication(X2,antidomain(domain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_37,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_32,c_0_24]) ).
cnf(c_0_38,negated_conjecture,
multiplication(addition(domain(X1),X2),antidomain(X1)) = multiplication(X2,antidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_21]),c_0_31]) ).
cnf(c_0_39,negated_conjecture,
addition(domain(X1),antidomain(domain(X1))) = one,
inference(spm,[status(thm)],[c_0_33,c_0_22]) ).
cnf(c_0_40,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_24]) ).
cnf(c_0_41,negated_conjecture,
multiplication(antidomain(X1),antidomain(domain(X1))) = antidomain(domain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_33]),c_0_15]) ).
cnf(c_0_42,negated_conjecture,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_33]),c_0_24]) ).
cnf(c_0_43,negated_conjecture,
multiplication(antidomain(domain(X1)),antidomain(X1)) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_15]) ).
cnf(c_0_44,negated_conjecture,
addition(antidomain(X1),antidomain(domain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_24]),c_0_42]),c_0_35]) ).
cnf(c_0_45,negated_conjecture,
antidomain(domain(X1)) = antidomain(X1),
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_40,c_0_43]),c_0_24]),c_0_44]),c_0_24]),c_0_42]),c_0_35]) ).
cnf(c_0_46,negated_conjecture,
addition(antidomain(multiplication(esk1_0,esk2_0)),antidomain(multiplication(esk1_0,domain(esk2_0)))) != antidomain(multiplication(esk1_0,domain(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_47,negated_conjecture,
antidomain(multiplication(X1,domain(X2))) = antidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_14]),c_0_45]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47]),c_0_26]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE082+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 22:45:21 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 0.59/0.48 % Version: 3.5.1
% 0.59/0.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.59/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.59/0.48 % Starting new_bool_3 with 300s (1) cores
% 0.59/0.48 % Starting new_bool_1 with 300s (1) cores
% 0.59/0.48 % Starting sh5l with 300s (1) cores
% 0.59/0.48 % new_bool_3 with pid 4109073 completed with status 0
% 0.59/0.48 % Result found by new_bool_3
% 0.59/0.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.59/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.59/0.48 % Starting new_bool_3 with 300s (1) cores
% 0.59/0.48 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.59/0.48 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.59/0.48 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.59/0.48 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 0.59/0.48 % Starting SubtermCWHack with 28s (1) cores
% 0.59/0.48 % SubtermCWHack with pid 4109080 completed with status 0
% 0.59/0.48 % Result found by SubtermCWHack
% 0.59/0.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.59/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.59/0.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.59/0.48 % Starting new_bool_3 with 300s (1) cores
% 0.59/0.48 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.59/0.48 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.59/0.48 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.59/0.48 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 0.59/0.48 % Starting SubtermCWHack with 28s (1) cores
% 0.59/0.48 % Preprocessing time : 0.001 s
% 0.59/0.48
% 0.59/0.48 % Proof found!
% 0.59/0.48 % SZS status Theorem
% 0.59/0.48 % SZS output start CNFRefutation
% See solution above
% 0.59/0.48 % Parsed axioms : 18
% 0.59/0.48 % Removed by relevancy pruning/SinE : 1
% 0.59/0.48 % Initial clauses : 19
% 0.59/0.48 % Removed in clause preprocessing : 0
% 0.59/0.48 % Initial clauses in saturation : 19
% 0.59/0.48 % Processed clauses : 689
% 0.59/0.48 % ...of these trivial : 341
% 0.59/0.48 % ...subsumed : 151
% 0.59/0.48 % ...remaining for further processing : 197
% 0.59/0.48 % Other redundant clauses eliminated : 0
% 0.59/0.48 % Clauses deleted for lack of memory : 0
% 0.59/0.48 % Backward-subsumed : 0
% 0.59/0.48 % Backward-rewritten : 38
% 0.59/0.48 % Generated clauses : 14917
% 0.59/0.48 % ...of the previous two non-redundant : 6288
% 0.59/0.48 % ...aggressively subsumed : 0
% 0.59/0.48 % Contextual simplify-reflections : 0
% 0.59/0.48 % Paramodulations : 14917
% 0.59/0.48 % Factorizations : 0
% 0.59/0.48 % NegExts : 0
% 0.59/0.48 % Equation resolutions : 0
% 0.59/0.48 % Disequality decompositions : 0
% 0.59/0.48 % Total rewrite steps : 27264
% 0.59/0.48 % ...of those cached : 23836
% 0.59/0.48 % Propositional unsat checks : 0
% 0.59/0.48 % Propositional check models : 0
% 0.59/0.48 % Propositional check unsatisfiable : 0
% 0.59/0.48 % Propositional clauses : 0
% 0.59/0.48 % Propositional clauses after purity: 0
% 0.59/0.48 % Propositional unsat core size : 0
% 0.59/0.48 % Propositional preprocessing time : 0.000
% 0.59/0.48 % Propositional encoding time : 0.000
% 0.59/0.48 % Propositional solver time : 0.000
% 0.59/0.48 % Success case prop preproc time : 0.000
% 0.59/0.48 % Success case prop encoding time : 0.000
% 0.59/0.48 % Success case prop solver time : 0.000
% 0.59/0.48 % Current number of processed clauses : 159
% 0.59/0.48 % Positive orientable unit clauses : 155
% 0.59/0.48 % Positive unorientable unit clauses: 4
% 0.59/0.48 % Negative unit clauses : 0
% 0.59/0.48 % Non-unit-clauses : 0
% 0.59/0.48 % Current number of unprocessed clauses: 5591
% 0.59/0.48 % ...number of literals in the above : 5591
% 0.59/0.48 % Current number of archived formulas : 0
% 0.59/0.48 % Current number of archived clauses : 38
% 0.59/0.48 % Clause-clause subsumption calls (NU) : 0
% 0.59/0.48 % Rec. Clause-clause subsumption calls : 0
% 0.59/0.48 % Non-unit clause-clause subsumptions : 0
% 0.59/0.48 % Unit Clause-clause subsumption calls : 12
% 0.59/0.48 % Rewrite failures with RHS unbound : 0
% 0.59/0.48 % BW rewrite match attempts : 643
% 0.59/0.48 % BW rewrite match successes : 180
% 0.59/0.48 % Condensation attempts : 0
% 0.59/0.48 % Condensation successes : 0
% 0.59/0.48 % Termbank termtop insertions : 145959
% 0.59/0.48 % Search garbage collected termcells : 51
% 0.59/0.48
% 0.59/0.48 % -------------------------------------------------
% 0.59/0.48 % User time : 0.053 s
% 0.59/0.48 % System time : 0.006 s
% 0.59/0.48 % Total time : 0.059 s
% 0.59/0.48 % Maximum resident set size: 3648 pages
% 0.59/0.48
% 0.59/0.48 % -------------------------------------------------
% 0.59/0.48 % User time : 0.055 s
% 0.59/0.48 % System time : 0.007 s
% 0.59/0.48 % Total time : 0.062 s
% 0.59/0.48 % Maximum resident set size: 4608 pages
% 0.59/0.48 % E exiting
%------------------------------------------------------------------------------