%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU305+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 02:24:38 PM UTC 2026
% Result : Theorem 0.26s 0.54s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 9 unt; 0 def)
% Number of atoms : 146 ( 22 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 179 ( 62 ~; 58 |; 35 &)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 57 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_lattices,axiom,
! [X1,X2,X3] :
( ( element(X3,the_carrier(X1))
& element(X2,the_carrier(X1))
& join_semilatt_str(X1)
& join_commutative(X1)
& ~ empty_carrier(X1) )
=> join_commut(X1,X2,X3) = join_commut(X1,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_lattices) ).
fof(redefinition_k3_lattices,axiom,
! [X1,X2,X3] :
( ( element(X3,the_carrier(X1))
& element(X2,the_carrier(X1))
& join_semilatt_str(X1)
& join_commutative(X1)
& ~ empty_carrier(X1) )
=> join_commut(X1,X2,X3) = join(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k3_lattices) ).
fof(d3_lattices,axiom,
! [X1] :
( ( join_semilatt_str(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below(X1,X2,X3)
<=> join(X1,X2,X3) = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattices) ).
fof(t26_lattices,conjecture,
! [X1] :
( ( join_semilatt_str(X1)
& join_commutative(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( below(X1,X3,X2)
& below(X1,X2,X3) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_lattices) ).
fof(c_0_4,plain,
! [X1,X2,X3] :
( ( element(X3,the_carrier(X1))
& element(X2,the_carrier(X1))
& join_semilatt_str(X1)
& join_commutative(X1)
& ~ empty_carrier(X1) )
=> join_commut(X1,X2,X3) = join_commut(X1,X3,X2) ),
inference(fof_simplification,[status(thm)],[commutativity_k3_lattices]) ).
fof(c_0_5,plain,
! [X1,X2,X3] :
( ( element(X3,the_carrier(X1))
& element(X2,the_carrier(X1))
& join_semilatt_str(X1)
& join_commutative(X1)
& ~ empty_carrier(X1) )
=> join_commut(X1,X2,X3) = join(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[redefinition_k3_lattices]) ).
fof(c_0_6,plain,
! [X16,X17,X18] :
( join_commut(X16,X17,X18) = join_commut(X16,X18,X17)
| ~ element(X18,the_carrier(X16))
| ~ element(X17,the_carrier(X16))
| ~ join_semilatt_str(X16)
| ~ join_commutative(X16)
| empty_carrier(X16) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_7,plain,
! [X22,X23,X24] :
( join_commut(X22,X23,X24) = join(X22,X23,X24)
| ~ element(X24,the_carrier(X22))
| ~ element(X23,the_carrier(X22))
| ~ join_semilatt_str(X22)
| ~ join_commutative(X22)
| empty_carrier(X22) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,plain,
! [X1] :
( ( join_semilatt_str(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below(X1,X2,X3)
<=> join(X1,X2,X3) = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[d3_lattices]) ).
cnf(c_0_9,plain,
( ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1)
| join_commut(X1,X2,X3) = join_commut(X1,X3,X2)
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1)
| join_commut(X1,X2,X3) = join(X1,X2,X3)
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X10,X11,X12] :
( ( ~ join_semilatt_str(X10)
| empty_carrier(X10)
| ~ element(X11,the_carrier(X10))
| ~ element(X12,the_carrier(X10))
| below(X10,X11,X12)
| join(X10,X11,X12) != X12 )
& ( ~ join_semilatt_str(X10)
| empty_carrier(X10)
| ~ element(X11,the_carrier(X10))
| ~ element(X12,the_carrier(X10))
| join(X10,X11,X12) = X12
| ~ below(X10,X11,X12) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])]) ).
cnf(c_0_12,plain,
( ~ join_commutative(X1)
| ~ join_semilatt_str(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| empty_carrier(X1)
| join_commut(X1,X2,X3) = join(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ( join_semilatt_str(X1)
& join_commutative(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( below(X1,X3,X2)
& below(X1,X2,X3) )
=> X2 = X3 ) ) ) ),
inference(assume_negation,[status(cth)],[t26_lattices]) ).
cnf(c_0_14,plain,
( ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ below(X1,X2,X3)
| empty_carrier(X1)
| join(X1,X2,X3) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( ~ join_commutative(X1)
| ~ join_semilatt_str(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| empty_carrier(X1)
| join(X1,X2,X3) = join(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_12]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ( join_semilatt_str(X1)
& join_commutative(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( below(X1,X3,X2)
& below(X1,X2,X3) )
=> X2 = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
( ~ join_commutative(X1)
| ~ join_semilatt_str(X1)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ below(X1,X3,X2)
| empty_carrier(X1)
| join(X1,X2,X3) = X2 ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_18,negated_conjecture,
( esk2_0 != esk3_0
& below(esk1_0,esk3_0,esk2_0)
& below(esk1_0,esk2_0,esk3_0)
& element(esk3_0,the_carrier(esk1_0))
& element(esk2_0,the_carrier(esk1_0))
& join_semilatt_str(esk1_0)
& join_commutative(esk1_0)
& ~ empty_carrier(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
cnf(c_0_19,plain,
( ~ join_commutative(X3)
| ~ join_semilatt_str(X3)
| ~ element(X1,the_carrier(X3))
| ~ element(X2,the_carrier(X3))
| ~ below(X3,X2,X1)
| ~ below(X3,X1,X2)
| empty_carrier(X3)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
below(esk1_0,esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,negated_conjecture,
below(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
element(esk2_0,the_carrier(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
element(esk3_0,the_carrier(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
join_semilatt_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,negated_conjecture,
join_commutative(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
esk2_0 != esk3_0,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,negated_conjecture,
~ empty_carrier(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[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(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22]),c_0_23]),c_0_24]),c_0_25])]),c_0_26]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU305+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n008.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 06:10:54 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.51 Running first-order theorem proving
% 0.26/0.51 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
% 0.26/0.54 % Version: 3.5.1
% 0.26/0.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.26/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.26/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.26/0.54 % Starting sh5l with 300s (1) cores
% 0.26/0.54 % new_bool_3 with pid 311695 completed with status 0
% 0.26/0.54 % Result found by new_bool_3
% 0.26/0.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.26/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.26/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.26/0.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.26/0.54 % Search class: FGUSF-FFSM32-SFFFFFNN
% 0.26/0.54 % partial match(1): FGUPF-FFSM32-SFFFFFNN
% 0.26/0.54 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.54 % Starting SubtermCWHack with 31s (1) cores
% 0.26/0.54 % SubtermCWHack with pid 311698 completed with status 0
% 0.26/0.54 % Result found by SubtermCWHack
% 0.26/0.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.26/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.26/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.54 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.26/0.54 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.26/0.54 % Search class: FGUSF-FFSM32-SFFFFFNN
% 0.26/0.54 % partial match(1): FGUPF-FFSM32-SFFFFFNN
% 0.26/0.54 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.54 % Starting SubtermCWHack with 31s (1) cores
% 0.26/0.54 % Preprocessing time : 0.002 s
% 0.26/0.54
% 0.26/0.54 % Proof found!
% 0.26/0.54 % SZS status Theorem
% 0.26/0.54 % SZS output start CNFRefutation
% See solution above
% 0.26/0.54 % Parsed axioms : 42
% 0.26/0.54 % Removed by relevancy pruning/SinE : 34
% 0.26/0.54 % Initial clauses : 16
% 0.26/0.54 % Removed in clause preprocessing : 0
% 0.26/0.54 % Initial clauses in saturation : 16
% 0.26/0.54 % Processed clauses : 33
% 0.26/0.54 % ...of these trivial : 0
% 0.26/0.54 % ...subsumed : 12
% 0.26/0.54 % ...remaining for further processing : 21
% 0.26/0.54 % Other redundant clauses eliminated : 2
% 0.26/0.54 % Clauses deleted for lack of memory : 0
% 0.26/0.54 % Backward-subsumed : 0
% 0.26/0.54 % Backward-rewritten : 0
% 0.26/0.54 % Generated clauses : 30
% 0.26/0.54 % ...of the previous two non-redundant : 20
% 0.26/0.54 % ...aggressively subsumed : 0
% 0.26/0.54 % Contextual simplify-reflections : 0
% 0.26/0.54 % Paramodulations : 28
% 0.26/0.54 % Factorizations : 0
% 0.26/0.54 % NegExts : 0
% 0.26/0.54 % Equation resolutions : 2
% 0.26/0.54 % Disequality decompositions : 0
% 0.26/0.54 % Total rewrite steps : 5
% 0.26/0.54 % ...of those cached : 0
% 0.26/0.54 % Propositional unsat checks : 0
% 0.26/0.54 % Propositional check models : 0
% 0.26/0.54 % Propositional check unsatisfiable : 0
% 0.26/0.54 % Propositional clauses : 0
% 0.26/0.54 % Propositional clauses after purity: 0
% 0.26/0.54 % Propositional unsat core size : 0
% 0.26/0.54 % Propositional preprocessing time : 0.000
% 0.26/0.54 % Propositional encoding time : 0.000
% 0.26/0.54 % Propositional solver time : 0.000
% 0.26/0.54 % Success case prop preproc time : 0.000
% 0.26/0.54 % Success case prop encoding time : 0.000
% 0.26/0.54 % Success case prop solver time : 0.000
% 0.26/0.54 % Current number of processed clauses : 21
% 0.26/0.54 % Positive orientable unit clauses : 8
% 0.26/0.54 % Positive unorientable unit clauses: 0
% 0.26/0.54 % Negative unit clauses : 2
% 0.26/0.54 % Non-unit-clauses : 11
% 0.26/0.54 % Current number of unprocessed clauses: 3
% 0.26/0.54 % ...number of literals in the above : 21
% 0.26/0.54 % Current number of archived formulas : 0
% 0.26/0.54 % Current number of archived clauses : 0
% 0.26/0.54 % Clause-clause subsumption calls (NU) : 34
% 0.26/0.54 % Rec. Clause-clause subsumption calls : 12
% 0.26/0.54 % Non-unit clause-clause subsumptions : 12
% 0.26/0.54 % Unit Clause-clause subsumption calls : 0
% 0.26/0.54 % Rewrite failures with RHS unbound : 0
% 0.26/0.54 % BW rewrite match attempts : 0
% 0.26/0.54 % BW rewrite match successes : 0
% 0.26/0.54 % Condensation attempts : 0
% 0.26/0.54 % Condensation successes : 0
% 0.26/0.54 % Termbank termtop insertions : 2744
% 0.26/0.54 % Search garbage collected termcells : 472
% 0.26/0.54
% 0.26/0.54 % -------------------------------------------------
% 0.26/0.54 % User time : 0.006 s
% 0.26/0.54 % System time : 0.003 s
% 0.26/0.54 % Total time : 0.009 s
% 0.26/0.54 % Maximum resident set size: 3624 pages
% 0.26/0.54
% 0.26/0.54 % -------------------------------------------------
% 0.26/0.54 % User time : 0.010 s
% 0.26/0.54 % System time : 0.008 s
% 0.26/0.54 % Total time : 0.018 s
% 0.26/0.54 % Maximum resident set size: 4864 pages
% 0.26/0.54 % E exiting
%------------------------------------------------------------------------------