%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU348+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 2.72s 1.10s
% Output : CNFRefutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 10 unt; 0 def)
% Number of atoms : 142 ( 10 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 163 ( 57 ~; 51 |; 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 : 49 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t29_lattice3,conjecture,
! [X1,X2] :
( ( latt_str(X2)
& lattice(X2)
& ~ empty_carrier(X2) )
=> ! [X3] :
( element(X3,the_carrier(poset_of_lattice(X2)))
=> ( relstr_element_smaller(poset_of_lattice(X2),X1,X3)
<=> latt_set_smaller(X2,cast_to_el_of_lattice(X2,X3),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_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/sandbox/benchmark/theBenchmark.p',d4_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/sandbox/benchmark/theBenchmark.p',dt_k5_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/sandbox/benchmark/theBenchmark.p',d3_lattice3) ).
fof(t28_lattice3,lemma,
! [X1,X2] :
( ( latt_str(X2)
& lattice(X2)
& ~ empty_carrier(X2) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> ( latt_set_smaller(X2,X3,X1)
<=> relstr_element_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_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_element_smaller(poset_of_lattice(X2),X1,X3)
<=> latt_set_smaller(X2,cast_to_el_of_lattice(X2,X3),X1) ) ) ),
inference(assume_negation,[status(cth)],[t29_lattice3]) ).
fof(c_0_6,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_7,negated_conjecture,
~ ! [X1,X2] :
( ( latt_str(X2)
& lattice(X2)
& ~ empty_carrier(X2) )
=> ! [X3] :
( element(X3,the_carrier(poset_of_lattice(X2)))
=> ( relstr_element_smaller(poset_of_lattice(X2),X1,X3)
<=> latt_set_smaller(X2,cast_to_el_of_lattice(X2,X3),X1) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_8,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_9,plain,
! [X33,X34] :
( cast_to_el_of_lattice(X33,X34) = X34
| ~ element(X34,the_carrier(poset_of_lattice(X33)))
| ~ latt_str(X33)
| ~ lattice(X33)
| empty_carrier(X33) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_10,negated_conjecture,
( ( latt_set_smaller(esk2_0,cast_to_el_of_lattice(esk2_0,esk3_0),esk1_0)
| relstr_element_smaller(poset_of_lattice(esk2_0),esk1_0,esk3_0) )
& ( ~ latt_set_smaller(esk2_0,cast_to_el_of_lattice(esk2_0,esk3_0),esk1_0)
| ~ relstr_element_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_7])])])]) ).
fof(c_0_11,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_12,plain,
! [X35,X36] :
( element(cast_to_el_of_lattice(X35,X36),the_carrier(X35))
| ~ element(X36,the_carrier(poset_of_lattice(X35)))
| ~ latt_str(X35)
| ~ lattice(X35)
| empty_carrier(X35) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_13,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_9]) ).
cnf(c_0_14,negated_conjecture,
element(esk3_0,the_carrier(poset_of_lattice(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
lattice(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
latt_str(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
~ empty_carrier(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_18,lemma,
! [X1,X2] :
( ( latt_str(X2)
& lattice(X2)
& ~ empty_carrier(X2) )
=> ! [X3] :
( element(X3,the_carrier(X2))
=> ( latt_set_smaller(X2,X3,X1)
<=> relstr_element_smaller(poset_of_lattice(X2),X1,cast_to_el_of_LattPOSet(X2,X3)) ) ) ),
inference(fof_simplification,[status(thm)],[t28_lattice3]) ).
fof(c_0_19,plain,
! [X85,X86] :
( cast_to_el_of_LattPOSet(X85,X86) = X86
| ~ element(X86,the_carrier(X85))
| ~ latt_str(X85)
| ~ lattice(X85)
| empty_carrier(X85) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
cnf(c_0_20,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_12]) ).
cnf(c_0_21,negated_conjecture,
cast_to_el_of_lattice(esk2_0,esk3_0) = esk3_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]),c_0_17]) ).
fof(c_0_22,lemma,
! [X30,X31,X32] :
( ( ~ latt_str(X31)
| ~ lattice(X31)
| empty_carrier(X31)
| ~ element(X32,the_carrier(X31))
| latt_set_smaller(X31,X32,X30)
| ~ relstr_element_smaller(poset_of_lattice(X31),X30,cast_to_el_of_LattPOSet(X31,X32)) )
& ( ~ latt_str(X31)
| ~ lattice(X31)
| empty_carrier(X31)
| ~ element(X32,the_carrier(X31))
| relstr_element_smaller(poset_of_lattice(X31),X30,cast_to_el_of_LattPOSet(X31,X32))
| ~ latt_set_smaller(X31,X32,X30) ) ),
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_18])])])])]) ).
cnf(c_0_23,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_19]) ).
cnf(c_0_24,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_14]),c_0_21]),c_0_15]),c_0_16])]),c_0_17]) ).
cnf(c_0_25,lemma,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X3,the_carrier(X1))
| ~ relstr_element_smaller(poset_of_lattice(X1),X2,cast_to_el_of_LattPOSet(X1,X3))
| empty_carrier(X1)
| latt_set_smaller(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
cast_to_el_of_LattPOSet(esk2_0,esk3_0) = esk3_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_15]),c_0_16])]),c_0_17]) ).
cnf(c_0_27,negated_conjecture,
( latt_set_smaller(esk2_0,cast_to_el_of_lattice(esk2_0,esk3_0),esk1_0)
| relstr_element_smaller(poset_of_lattice(esk2_0),esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_28,negated_conjecture,
( ~ latt_set_smaller(esk2_0,cast_to_el_of_lattice(esk2_0,esk3_0),esk1_0)
| ~ relstr_element_smaller(poset_of_lattice(esk2_0),esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_29,negated_conjecture,
( ~ relstr_element_smaller(poset_of_lattice(esk2_0),X1,esk3_0)
| latt_set_smaller(esk2_0,esk3_0,X1) ),
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_25,c_0_26]),c_0_15]),c_0_24]),c_0_16])]),c_0_17]) ).
cnf(c_0_30,negated_conjecture,
( latt_set_smaller(esk2_0,esk3_0,esk1_0)
| relstr_element_smaller(poset_of_lattice(esk2_0),esk1_0,esk3_0) ),
inference(rw,[status(thm)],[c_0_27,c_0_21]) ).
cnf(c_0_31,negated_conjecture,
( ~ latt_set_smaller(esk2_0,esk3_0,esk1_0)
| ~ relstr_element_smaller(poset_of_lattice(esk2_0),esk1_0,esk3_0) ),
inference(rw,[status(thm)],[c_0_28,c_0_21]) ).
cnf(c_0_32,negated_conjecture,
latt_set_smaller(esk2_0,esk3_0,esk1_0),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,lemma,
( ~ latt_str(X1)
| ~ lattice(X1)
| ~ element(X2,the_carrier(X1))
| ~ latt_set_smaller(X1,X2,X3)
| empty_carrier(X1)
| relstr_element_smaller(poset_of_lattice(X1),X3,cast_to_el_of_LattPOSet(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_34,negated_conjecture,
~ relstr_element_smaller(poset_of_lattice(esk2_0),esk1_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_32]),c_0_26]),c_0_15]),c_0_24]),c_0_16])]),c_0_34]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU348+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n009.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 06:14:43 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.49 Running first-order theorem proving
% 0.16/0.50 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
% 2.72/1.10 % Version: 3.5.1
% 2.72/1.10 % Preprocessing class: FSLMSMSSSSSNFFN.
% 2.72/1.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.72/1.10 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 2.72/1.10 % Starting new_bool_3 with 600s (2) cores
% 2.72/1.10 % Starting new_bool_1 with 600s (2) cores
% 2.72/1.10 % Starting sh5l with 300s (1) cores
% 2.72/1.10 % new_bool_3 with pid 1022114 completed with status 0
% 2.72/1.10 % Result found by new_bool_3
% 2.72/1.10 % Preprocessing class: FSLMSMSSSSSNFFN.
% 2.72/1.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.72/1.10 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 2.72/1.10 % Starting new_bool_3 with 600s (2) cores
% 2.72/1.10 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 2.72/1.10 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.72/1.10 % Search class: FGHSM-FSLM32-MFFFFFNN
% 2.72/1.10 % Scheduled 12 strats onto 2 cores with 600 seconds (600 total)
% 2.72/1.10 % Starting SubtermCWHack with 55s (1) cores
% 2.72/1.10 % Starting new_bool_3 with 61s (1) cores
% 2.72/1.10 % new_bool_3 with pid 1022120 completed with status 0
% 2.72/1.10 % Result found by new_bool_3
% 2.72/1.10 % Preprocessing class: FSLMSMSSSSSNFFN.
% 2.72/1.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.72/1.10 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 900s (3) cores
% 2.72/1.10 % Starting new_bool_3 with 600s (2) cores
% 2.72/1.10 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 2.72/1.10 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.72/1.10 % Search class: FGHSM-FSLM32-MFFFFFNN
% 2.72/1.10 % Scheduled 12 strats onto 2 cores with 600 seconds (600 total)
% 2.72/1.10 % Starting SubtermCWHack with 55s (1) cores
% 2.72/1.10 % Starting new_bool_3 with 61s (1) cores
% 2.72/1.10 % Preprocessing time : 0.019 s
% 2.72/1.10 % Presaturation interreduction done
% 2.72/1.10
% 2.72/1.10 % Proof found!
% 2.72/1.10 % SZS status Theorem
% 2.72/1.10 % SZS output start CNFRefutation
% See solution above
% 2.72/1.10 % Parsed axioms : 636
% 2.72/1.10 % Removed by relevancy pruning/SinE : 511
% 2.72/1.10 % Initial clauses : 583
% 2.72/1.10 % Removed in clause preprocessing : 4
% 2.72/1.10 % Initial clauses in saturation : 579
% 2.72/1.10 % Processed clauses : 1821
% 2.72/1.10 % ...of these trivial : 8
% 2.72/1.10 % ...subsumed : 546
% 2.72/1.10 % ...remaining for further processing : 1267
% 2.72/1.10 % Other redundant clauses eliminated : 243
% 2.72/1.10 % Clauses deleted for lack of memory : 0
% 2.72/1.10 % Backward-subsumed : 10
% 2.72/1.10 % Backward-rewritten : 20
% 2.72/1.10 % Generated clauses : 3984
% 2.72/1.10 % ...of the previous two non-redundant : 3754
% 2.72/1.10 % ...aggressively subsumed : 0
% 2.72/1.10 % Contextual simplify-reflections : 56
% 2.72/1.10 % Paramodulations : 3784
% 2.72/1.10 % Factorizations : 0
% 2.72/1.10 % NegExts : 0
% 2.72/1.10 % Equation resolutions : 247
% 2.72/1.10 % Disequality decompositions : 0
% 2.72/1.10 % Total rewrite steps : 351
% 2.72/1.10 % ...of those cached : 269
% 2.72/1.10 % Propositional unsat checks : 0
% 2.72/1.10 % Propositional check models : 0
% 2.72/1.10 % Propositional check unsatisfiable : 0
% 2.72/1.10 % Propositional clauses : 0
% 2.72/1.10 % Propositional clauses after purity: 0
% 2.72/1.10 % Propositional unsat core size : 0
% 2.72/1.10 % Propositional preprocessing time : 0.000
% 2.72/1.10 % Propositional encoding time : 0.000
% 2.72/1.10 % Propositional solver time : 0.000
% 2.72/1.10 % Success case prop preproc time : 0.000
% 2.72/1.10 % Success case prop encoding time : 0.000
% 2.72/1.10 % Success case prop solver time : 0.000
% 2.72/1.10 % Current number of processed clauses : 540
% 2.72/1.10 % Positive orientable unit clauses : 134
% 2.72/1.10 % Positive unorientable unit clauses: 0
% 2.72/1.10 % Negative unit clauses : 87
% 2.72/1.10 % Non-unit-clauses : 319
% 2.72/1.10 % Current number of unprocessed clauses: 3016
% 2.72/1.10 % ...number of literals in the above : 11662
% 2.72/1.10 % Current number of archived formulas : 0
% 2.72/1.10 % Current number of archived clauses : 567
% 2.72/1.10 % Clause-clause subsumption calls (NU) : 159851
% 2.72/1.10 % Rec. Clause-clause subsumption calls : 21643
% 2.72/1.10 % Non-unit clause-clause subsumptions : 313
% 2.72/1.10 % Unit Clause-clause subsumption calls : 2857
% 2.72/1.10 % Rewrite failures with RHS unbound : 0
% 2.72/1.10 % BW rewrite match attempts : 21
% 2.72/1.10 % BW rewrite match successes : 10
% 2.72/1.10 % Condensation attempts : 0
% 2.72/1.10 % Condensation successes : 0
% 2.72/1.10 % Termbank termtop insertions : 105608
% 2.72/1.10 % Search garbage collected termcells : 11695
% 2.72/1.10
% 2.72/1.10 % -------------------------------------------------
% 2.72/1.10 % User time : 0.444 s
% 2.72/1.10 % System time : 0.020 s
% 2.72/1.10 % Total time : 0.464 s
% 2.72/1.10 % Maximum resident set size: 5788 pages
% 2.72/1.10
% 2.72/1.10 % -------------------------------------------------
% 2.72/1.10 % User time : 0.816 s
% 2.72/1.10 % System time : 0.052 s
% 2.72/1.10 % Total time : 0.868 s
% 2.72/1.10 % Maximum resident set size: 5376 pages
% 2.72/1.10 % E exiting
%------------------------------------------------------------------------------