%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG211+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 11:55:36 AM UTC 2026
% Result : Theorem 0.16s 5.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 5 unt; 0 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 84 ( 34 ~; 29 |; 13 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 56 ( 5 sgn 28 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(bg_2_4_2,axiom,
! [X7,X2,X8] :
( ( a_subset_of(X8,vec_to_class(X7))
& a_vector_subspace_of(X7,X2) )
=> ( lin_ind_subset(X8,X7)
<=> lin_ind_subset(X8,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_2_4_2) ).
fof(basis_of,axiom,
! [X1,X2] :
( basis_of(X1,X2)
=> ( a_subset_of(X1,vec_to_class(X2))
& lin_ind_subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',basis_of) ).
fof(bg_2_4_3,conjecture,
! [X7,X2] :
( ( a_vector_space(X2)
& a_vector_subspace_of(X7,X2) )
=> ? [X8,X9] :
( basis_of(X8,X7)
& basis_of(union(X8,X9),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_2_4_3) ).
fof(bg_2_2_5,axiom,
! [X3,X4,X2] :
( ( basis_of(X4,X2)
& lin_ind_subset(X3,X2) )
=> ? [X5] :
( basis_of(union(X3,X5),X2)
& a_subset_of(X5,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_2_2_5) ).
fof(bg_2_4_a,axiom,
! [X6,X1] :
( a_vector_subspace_of(X6,X1)
=> a_vector_space(X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_2_4_a) ).
fof(bg_remark_63_a,axiom,
! [X6] :
( a_vector_space(X6)
=> ? [X1] : basis_of(X1,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_remark_63_a) ).
fof(c_0_6,plain,
! [X22,X23,X24] :
( ( ~ a_subset_of(X24,vec_to_class(X22))
| ~ a_vector_subspace_of(X22,X23)
| lin_ind_subset(X24,X22)
| ~ lin_ind_subset(X24,X23) )
& ( ~ a_subset_of(X24,vec_to_class(X22))
| ~ a_vector_subspace_of(X22,X23)
| lin_ind_subset(X24,X23)
| ~ lin_ind_subset(X24,X22) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_2_4_2])])])]) ).
fof(c_0_7,plain,
! [X25,X26] :
( ( ~ basis_of(X25,X26)
| a_subset_of(X25,vec_to_class(X26)) )
& ( ~ basis_of(X25,X26)
| lin_ind_subset(X25,X26) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[basis_of])])])]) ).
fof(c_0_8,negated_conjecture,
~ ! [X7,X2] :
( ( a_vector_space(X2)
& a_vector_subspace_of(X7,X2) )
=> ? [X8,X9] :
( basis_of(X8,X7)
& basis_of(union(X8,X9),X2) ) ),
inference(assume_negation,[status(cth)],[bg_2_4_3]) ).
cnf(c_0_9,plain,
( ~ a_subset_of(X1,vec_to_class(X2))
| ~ a_vector_subspace_of(X2,X3)
| ~ lin_ind_subset(X1,X2)
| lin_ind_subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ basis_of(X1,X2)
| a_subset_of(X1,vec_to_class(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( ~ basis_of(X1,X2)
| lin_ind_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,negated_conjecture,
! [X12,X13] :
( ( ~ basis_of(X12,esk1_0)
| ~ basis_of(union(X12,X13),esk2_0) )
& a_vector_space(esk2_0)
& a_vector_subspace_of(esk1_0,esk2_0) ),
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_8])])])])]) ).
fof(c_0_13,plain,
! [X16,X17,X18] :
( ( ~ basis_of(X17,X18)
| ~ lin_ind_subset(X16,X18)
| basis_of(union(X16,esk4_3(X16,X17,X18)),X18) )
& ( ~ basis_of(X17,X18)
| ~ lin_ind_subset(X16,X18)
| a_subset_of(esk4_3(X16,X17,X18),X17) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_2_2_5])])])])]) ).
cnf(c_0_14,plain,
( ~ basis_of(X1,X3)
| ~ a_vector_subspace_of(X3,X2)
| lin_ind_subset(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_15,negated_conjecture,
a_vector_subspace_of(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X20,X21] :
( a_vector_space(X20)
| ~ a_vector_subspace_of(X20,X21) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_2_4_a])])]) ).
cnf(c_0_17,negated_conjecture,
( ~ basis_of(X1,esk1_0)
| ~ basis_of(union(X1,X2),esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( ~ basis_of(X2,X3)
| ~ lin_ind_subset(X1,X3)
| basis_of(union(X1,esk4_3(X1,X2,X3)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
( ~ basis_of(X1,esk1_0)
| lin_ind_subset(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_20,plain,
! [X14] :
( basis_of(esk3_1(X14),X14)
| ~ a_vector_space(X14) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_remark_63_a])])])]) ).
cnf(c_0_21,plain,
( ~ a_vector_subspace_of(X1,X2)
| a_vector_space(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( ~ basis_of(X2,esk2_0)
| ~ basis_of(X1,esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_23,plain,
( ~ a_vector_space(X1)
| basis_of(esk3_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
a_vector_space(esk1_0),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_25,negated_conjecture,
~ basis_of(X1,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_26,negated_conjecture,
a_vector_space(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_23]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG211+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/5.39 % Computer : n009.cluster.edu
% 0.13/5.39 % Model : x86_64 x86_64
% 0.13/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.39 % Memory : 8046.5625MB
% 0.13/5.39 % OS : Linux 6.8.0-71-generic
% 0.13/5.40 % CPULimit : 300
% 0.13/5.40 % WCLimit : 300
% 0.13/5.40 % DateTime : Mon Sep 21 13:01:48 UTC 2026
% 0.16/5.40 % CPUTime :
% 0.16/5.40 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/5.44 Running first-order theorem proving
% 0.16/5.44 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
% 0.16/5.46 % Version: 3.5.1
% 0.16/5.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/5.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/5.46 % Starting new_bool_3 with 300s (1) cores
% 0.16/5.46 % Starting new_bool_1 with 300s (1) cores
% 0.16/5.46 % Starting sh5l with 300s (1) cores
% 0.16/5.46 % new_bool_3 with pid 1805984 completed with status 0
% 0.16/5.46 % Result found by new_bool_3
% 0.16/5.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/5.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/5.46 % Starting new_bool_3 with 300s (1) cores
% 0.16/5.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/5.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/5.46 % Search class: FHHNF-FFSF31-SFFFFFNN
% 0.16/5.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/5.46 % Starting SubtermCWHack with 31s (1) cores
% 0.16/5.46 % SubtermCWHack with pid 1805987 completed with status 0
% 0.16/5.46 % Result found by SubtermCWHack
% 0.16/5.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/5.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/5.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/5.46 % Starting new_bool_3 with 300s (1) cores
% 0.16/5.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/5.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/5.46 % Search class: FHHNF-FFSF31-SFFFFFNN
% 0.16/5.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/5.46 % Starting SubtermCWHack with 31s (1) cores
% 0.16/5.46 % Preprocessing time : 0.001 s
% 0.16/5.46
% 0.16/5.46 % Proof found!
% 0.16/5.46 % SZS status Theorem
% 0.16/5.46 % SZS output start CNFRefutation
% See solution above
% 0.16/5.46 % Parsed axioms : 6
% 0.16/5.46 % Removed by relevancy pruning/SinE : 0
% 0.16/5.46 % Initial clauses : 11
% 0.16/5.46 % Removed in clause preprocessing : 0
% 0.16/5.46 % Initial clauses in saturation : 11
% 0.16/5.46 % Processed clauses : 17
% 0.16/5.46 % ...of these trivial : 0
% 0.16/5.46 % ...subsumed : 1
% 0.16/5.46 % ...remaining for further processing : 16
% 0.16/5.46 % Other redundant clauses eliminated : 0
% 0.16/5.46 % Clauses deleted for lack of memory : 0
% 0.16/5.46 % Backward-subsumed : 2
% 0.16/5.46 % Backward-rewritten : 0
% 0.16/5.46 % Generated clauses : 11
% 0.16/5.46 % ...of the previous two non-redundant : 9
% 0.16/5.46 % ...aggressively subsumed : 0
% 0.16/5.46 % Contextual simplify-reflections : 2
% 0.16/5.46 % Paramodulations : 11
% 0.16/5.46 % Factorizations : 0
% 0.16/5.46 % NegExts : 0
% 0.16/5.46 % Equation resolutions : 0
% 0.16/5.46 % Disequality decompositions : 0
% 0.16/5.46 % Total rewrite steps : 2
% 0.16/5.46 % ...of those cached : 0
% 0.16/5.46 % Propositional unsat checks : 0
% 0.16/5.46 % Propositional check models : 0
% 0.16/5.46 % Propositional check unsatisfiable : 0
% 0.16/5.46 % Propositional clauses : 0
% 0.16/5.46 % Propositional clauses after purity: 0
% 0.16/5.46 % Propositional unsat core size : 0
% 0.16/5.46 % Propositional preprocessing time : 0.000
% 0.16/5.46 % Propositional encoding time : 0.000
% 0.16/5.46 % Propositional solver time : 0.000
% 0.16/5.46 % Success case prop preproc time : 0.000
% 0.16/5.46 % Success case prop encoding time : 0.000
% 0.16/5.46 % Success case prop solver time : 0.000
% 0.16/5.46 % Current number of processed clauses : 14
% 0.16/5.46 % Positive orientable unit clauses : 3
% 0.16/5.46 % Positive unorientable unit clauses: 0
% 0.16/5.46 % Negative unit clauses : 1
% 0.16/5.46 % Non-unit-clauses : 10
% 0.16/5.46 % Current number of unprocessed clauses: 3
% 0.16/5.46 % ...number of literals in the above : 13
% 0.16/5.46 % Current number of archived formulas : 0
% 0.16/5.46 % Current number of archived clauses : 2
% 0.16/5.46 % Clause-clause subsumption calls (NU) : 24
% 0.16/5.46 % Rec. Clause-clause subsumption calls : 22
% 0.16/5.46 % Non-unit clause-clause subsumptions : 4
% 0.16/5.46 % Unit Clause-clause subsumption calls : 8
% 0.16/5.46 % Rewrite failures with RHS unbound : 0
% 0.16/5.46 % BW rewrite match attempts : 0
% 0.16/5.46 % BW rewrite match successes : 0
% 0.16/5.46 % Condensation attempts : 0
% 0.16/5.46 % Condensation successes : 0
% 0.16/5.46 % Termbank termtop insertions : 895
% 0.16/5.46 % Search garbage collected termcells : 181
% 0.16/5.46
% 0.16/5.46 % -------------------------------------------------
% 0.16/5.46 % User time : 0.004 s
% 0.16/5.46 % System time : 0.001 s
% 0.16/5.46 % Total time : 0.005 s
% 0.16/5.46 % Maximum resident set size: 3636 pages
% 0.16/5.46
% 0.16/5.46 % -------------------------------------------------
% 0.16/5.46 % User time : 0.007 s
% 0.16/5.46 % System time : 0.004 s
% 0.16/5.46 % Total time : 0.011 s
% 0.16/5.46 % Maximum resident set size: 4864 pages
% 0.16/5.46 % E exiting
%------------------------------------------------------------------------------