%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU350+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 : n017.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 02:24:48 PM UTC 2026
% Result : Theorem 0.25s 0.59s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 8 unt; 0 def)
% Number of atoms : 155 ( 8 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 186 ( 67 ~; 64 |; 30 &)
% ( 5 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t31_lattice3,conjecture,
! [X1,X2] :
( ( latt_str(X2)
& lattice(X2)
& ~ empty_carrier(X2) )
=> ! [X3] :
( element(X3,the_carrier(poset_of_lattice(X2)))
=> ( relstr_set_smaller(poset_of_lattice(X2),X1,X3)
<=> latt_element_smaller(X2,cast_to_el_of_lattice(X2,X3),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_lattice3) ).
fof(dt_k5_lattice3,axiom,
! [X1,X2] :
( ( element(X2,the_carrier(poset_of_lattice(X1)))
& latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> element(cast_to_el_of_lattice(X1,X2),the_carrier(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattice3) ).
fof(d4_lattice3,axiom,
! [X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(poset_of_lattice(X1)))
=> cast_to_el_of_lattice(X1,X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lattice3) ).
fof(t30_lattice3,axiom,
! [X1,X2] :
( ( latt_str(X2)
& lattice(X2)
& ~ empty_carrier(X2) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> ( latt_element_smaller(X2,X3,X1)
<=> relstr_set_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_lattice3) ).
fof(d3_lattice3,axiom,
! [X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> cast_to_el_of_LattPOSet(X1,X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattice3) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( ( latt_str(X2)
& lattice(X2)
& ~ empty_carrier(X2) )
=> ! [X3] :
( element(X3,the_carrier(poset_of_lattice(X2)))
=> ( relstr_set_smaller(poset_of_lattice(X2),X1,X3)
<=> latt_element_smaller(X2,cast_to_el_of_lattice(X2,X3),X1) ) ) ),
inference(assume_negation,[status(cth)],[t31_lattice3]) ).
fof(c_0_6,plain,
! [X1,X2] :
( ( element(X2,the_carrier(poset_of_lattice(X1)))
& latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> element(cast_to_el_of_lattice(X1,X2),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k5_lattice3]) ).
fof(c_0_7,plain,
! [X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(poset_of_lattice(X1)))
=> cast_to_el_of_lattice(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d4_lattice3]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2] :
( ( latt_str(X2)
& lattice(X2)
& ~ empty_carrier(X2) )
=> ! [X3] :
( element(X3,the_carrier(poset_of_lattice(X2)))
=> ( relstr_set_smaller(poset_of_lattice(X2),X1,X3)
<=> latt_element_smaller(X2,cast_to_el_of_lattice(X2,X3),X1) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_9,plain,
! [X1,X2] :
( ( latt_str(X2)
& lattice(X2)
& ~ empty_carrier(X2) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> ( latt_element_smaller(X2,X3,X1)
<=> relstr_set_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
inference(fof_simplification,[status(thm)],[t30_lattice3]) ).
fof(c_0_10,plain,
! [X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> cast_to_el_of_LattPOSet(X1,X2) = X2 ) ),
inference(fof_simplification,[status(thm)],[d3_lattice3]) ).
fof(c_0_11,plain,
! [X13,X14] :
( element(cast_to_el_of_lattice(X13,X14),the_carrier(X13))
| ~ element(X14,the_carrier(poset_of_lattice(X13)))
| ~ latt_str(X13)
| ~ lattice(X13)
| empty_carrier(X13) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_12,plain,
! [X11,X12] :
( cast_to_el_of_lattice(X11,X12) = X12
| ~ element(X12,the_carrier(poset_of_lattice(X11)))
| ~ latt_str(X11)
| ~ lattice(X11)
| empty_carrier(X11) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_13,negated_conjecture,
( ( latt_element_smaller(esk2_0,cast_to_el_of_lattice(esk2_0,esk3_0),esk1_0)
| relstr_set_smaller(poset_of_lattice(esk2_0),esk1_0,esk3_0) )
& ( ~ latt_element_smaller(esk2_0,cast_to_el_of_lattice(esk2_0,esk3_0),esk1_0)
| ~ relstr_set_smaller(poset_of_lattice(esk2_0),esk1_0,esk3_0) )
& element(esk3_0,the_carrier(poset_of_lattice(esk2_0)))
& latt_str(esk2_0)
& lattice(esk2_0)
& ~ empty_carrier(esk2_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_14,plain,
! [X8,X9,X10] :
( ( ~ latt_str(X9)
| ~ lattice(X9)
| empty_carrier(X9)
| ~ element(X10,the_carrier(X9))
| latt_element_smaller(X9,X10,X8)
| ~ relstr_set_smaller(poset_of_lattice(X9),X8,cast_to_el_of_LattPOSet(X9,X10)) )
& ( ~ latt_str(X9)
| ~ lattice(X9)
| empty_carrier(X9)
| ~ element(X10,the_carrier(X9))
| relstr_set_smaller(poset_of_lattice(X9),X8,cast_to_el_of_LattPOSet(X9,X10))
| ~ latt_element_smaller(X9,X10,X8) ) ),
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_9])])])])]) ).
fof(c_0_15,plain,
! [X18,X19] :
( cast_to_el_of_LattPOSet(X18,X19) = X19
| ~ element(X19,the_carrier(X18))
| ~ latt_str(X18)
| ~ lattice(X18)
| empty_carrier(X18) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
cnf(c_0_16,plain,
( ~ element(X2,the_carrier(poset_of_lattice(X1)))
| ~ latt_str(X1)
| ~ lattice(X1)
| element(cast_to_el_of_lattice(X1,X2),the_carrier(X1))
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( ~ element(X2,the_carrier(poset_of_lattice(X1)))
| ~ latt_str(X1)
| ~ lattice(X1)
| cast_to_el_of_lattice(X1,X2) = X2
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
( ~ latt_element_smaller(esk2_0,cast_to_el_of_lattice(esk2_0,esk3_0),esk1_0)
| ~ relstr_set_smaller(poset_of_lattice(esk2_0),esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
element(esk3_0,the_carrier(poset_of_lattice(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
lattice(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
latt_str(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,negated_conjecture,
~ empty_carrier(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_element_smaller(X1,X2,X3)
| empty_carrier(X1)
| relstr_set_smaller(poset_of_lattice(X1),X3,cast_to_el_of_LattPOSet(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,plain,
( ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| cast_to_el_of_LattPOSet(X1,X2) = X2
| empty_carrier(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,plain,
( ~ latt_str(X2)
| ~ lattice(X2)
| ~ element(X1,the_carrier(poset_of_lattice(X2)))
| empty_carrier(X2)
| element(X1,the_carrier(X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_26,negated_conjecture,
( latt_element_smaller(esk2_0,cast_to_el_of_lattice(esk2_0,esk3_0),esk1_0)
| relstr_set_smaller(poset_of_lattice(esk2_0),esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_27,negated_conjecture,
( ~ latt_element_smaller(esk2_0,esk3_0,esk1_0)
| ~ relstr_set_smaller(poset_of_lattice(esk2_0),esk1_0,esk3_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_17]),c_0_19]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_28,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X3,the_carrier(X1))
| ~ latt_element_smaller(X1,X3,X2)
| empty_carrier(X1)
| relstr_set_smaller(poset_of_lattice(X1),X2,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
element(esk3_0,the_carrier(esk2_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_19]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_30,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X3,the_carrier(X1))
| ~ relstr_set_smaller(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3))
| empty_carrier(X1)
| latt_element_smaller(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_31,negated_conjecture,
( latt_element_smaller(esk2_0,esk3_0,esk1_0)
| relstr_set_smaller(poset_of_lattice(esk2_0),esk1_0,esk3_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_17]),c_0_19]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_32,negated_conjecture,
~ latt_element_smaller(esk2_0,esk3_0,esk1_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_20]),c_0_21])]),c_0_22]) ).
cnf(c_0_33,plain,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| ~ relstr_set_smaller(poset_of_lattice(X1),X3,X2)
| empty_carrier(X1)
| latt_element_smaller(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_24]) ).
cnf(c_0_34,negated_conjecture,
relstr_set_smaller(poset_of_lattice(esk2_0),esk1_0,esk3_0),
inference(sr,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,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(spm,[status(thm)],[c_0_33,c_0_34]),c_0_29]),c_0_20]),c_0_21])]),c_0_32]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU350+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.46 % Computer : n017.cluster.edu
% 0.21/0.46 % Model : x86_64 x86_64
% 0.21/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.46 % Memory : 8046.5625MB
% 0.21/0.46 % OS : Linux 6.8.0-71-generic
% 0.21/0.46 % CPULimit : 300
% 0.21/0.46 % WCLimit : 300
% 0.21/0.46 % DateTime : Mon Sep 21 06:09:57 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.52 Running first-order theorem proving
% 0.25/0.52 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
% 0.25/0.59 % Version: 3.5.1
% 0.25/0.59 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.25/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.25/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.59 % Starting sh5l with 300s (1) cores
% 0.25/0.59 % new_bool_3 with pid 1601964 completed with status 0
% 0.25/0.59 % Result found by new_bool_3
% 0.25/0.59 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.25/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.25/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.25/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.25/0.59 % Search class: FGHSF-FFSS21-SFFFFFNN
% 0.25/0.59 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.59 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.59 % SubtermCWHack with pid 1601972 completed with status 0
% 0.25/0.59 % Result found by SubtermCWHack
% 0.25/0.59 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.25/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.25/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.25/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.25/0.59 % Search class: FGHSF-FFSS21-SFFFFFNN
% 0.25/0.59 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.25/0.59 % Starting SubtermCWHack with 31s (1) cores
% 0.25/0.59 % Preprocessing time : 0.002 s
% 0.25/0.59
% 0.25/0.59 % Proof found!
% 0.25/0.59 % SZS status Theorem
% 0.25/0.59 % SZS output start CNFRefutation
% See solution above
% 0.25/0.59 % Parsed axioms : 65
% 0.25/0.59 % Removed by relevancy pruning/SinE : 57
% 0.25/0.59 % Initial clauses : 14
% 0.25/0.59 % Removed in clause preprocessing : 0
% 0.25/0.59 % Initial clauses in saturation : 14
% 0.25/0.59 % Processed clauses : 27
% 0.25/0.59 % ...of these trivial : 0
% 0.25/0.59 % ...subsumed : 1
% 0.25/0.59 % ...remaining for further processing : 26
% 0.25/0.59 % Other redundant clauses eliminated : 0
% 0.25/0.59 % Clauses deleted for lack of memory : 0
% 0.25/0.59 % Backward-subsumed : 1
% 0.25/0.59 % Backward-rewritten : 2
% 0.25/0.59 % Generated clauses : 24
% 0.25/0.59 % ...of the previous two non-redundant : 17
% 0.25/0.59 % ...aggressively subsumed : 0
% 0.25/0.59 % Contextual simplify-reflections : 0
% 0.25/0.59 % Paramodulations : 23
% 0.25/0.59 % Factorizations : 0
% 0.25/0.59 % NegExts : 0
% 0.25/0.59 % Equation resolutions : 0
% 0.25/0.59 % Disequality decompositions : 0
% 0.25/0.59 % Total rewrite steps : 19
% 0.25/0.59 % ...of those cached : 14
% 0.25/0.59 % Propositional unsat checks : 0
% 0.25/0.59 % Propositional check models : 0
% 0.25/0.59 % Propositional check unsatisfiable : 0
% 0.25/0.59 % Propositional clauses : 0
% 0.25/0.59 % Propositional clauses after purity: 0
% 0.25/0.59 % Propositional unsat core size : 0
% 0.25/0.59 % Propositional preprocessing time : 0.000
% 0.25/0.59 % Propositional encoding time : 0.000
% 0.25/0.59 % Propositional solver time : 0.000
% 0.25/0.59 % Success case prop preproc time : 0.000
% 0.25/0.59 % Success case prop encoding time : 0.000
% 0.25/0.59 % Success case prop solver time : 0.000
% 0.25/0.59 % Current number of processed clauses : 22
% 0.25/0.59 % Positive orientable unit clauses : 7
% 0.25/0.59 % Positive unorientable unit clauses: 0
% 0.25/0.59 % Negative unit clauses : 3
% 0.25/0.59 % Non-unit-clauses : 12
% 0.25/0.59 % Current number of unprocessed clauses: 4
% 0.25/0.59 % ...number of literals in the above : 30
% 0.25/0.59 % Current number of archived formulas : 0
% 0.25/0.59 % Current number of archived clauses : 4
% 0.25/0.59 % Clause-clause subsumption calls (NU) : 34
% 0.25/0.59 % Rec. Clause-clause subsumption calls : 6
% 0.25/0.59 % Non-unit clause-clause subsumptions : 0
% 0.25/0.59 % Unit Clause-clause subsumption calls : 2
% 0.25/0.59 % Rewrite failures with RHS unbound : 0
% 0.25/0.59 % BW rewrite match attempts : 1
% 0.25/0.59 % BW rewrite match successes : 1
% 0.25/0.59 % Condensation attempts : 0
% 0.25/0.59 % Condensation successes : 0
% 0.25/0.59 % Termbank termtop insertions : 2563
% 0.25/0.59 % Search garbage collected termcells : 583
% 0.25/0.59
% 0.25/0.59 % -------------------------------------------------
% 0.25/0.59 % User time : 0.010 s
% 0.25/0.59 % System time : 0.003 s
% 0.25/0.59 % Total time : 0.013 s
% 0.25/0.59 % Maximum resident set size: 3700 pages
% 0.25/0.59
% 0.25/0.59 % -------------------------------------------------
% 0.25/0.59 % User time : 0.017 s
% 0.25/0.59 % System time : 0.006 s
% 0.25/0.59 % Total time : 0.024 s
% 0.25/0.59 % Maximum resident set size: 4864 pages
% 0.25/0.59 % E exiting
%------------------------------------------------------------------------------