%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ALG211+1 : TPTP v9.3.1. Released v3.1.0.
% 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 12:01:38 PM UTC 2026
% Result : Theorem 0.15s 0.43s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 7 unt; 0 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 82 ( 33 ~; 28 |; 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 : 55 ( 4 sgn 28 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',basis_of) ).
fof(bg_remark_63_a,axiom,
! [X6] :
( a_vector_space(X6)
=> ? [X1] : basis_of(X1,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_remark_63_a) ).
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/sandbox/benchmark/theBenchmark.p',bg_2_4_3) ).
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/sandbox/benchmark/theBenchmark.p',bg_2_4_2) ).
fof(bg_2_4_a,axiom,
! [X6,X1] :
( a_vector_subspace_of(X6,X1)
=> a_vector_space(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_a) ).
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/sandbox/benchmark/theBenchmark.p',bg_2_2_5) ).
fof(c_0_6,plain,
! [X10,X11] :
( ( ~ basis_of(X10,X11)
| a_subset_of(X10,vec_to_class(X11)) )
& ( ~ basis_of(X10,X11)
| lin_ind_subset(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[basis_of])])])]) ).
fof(c_0_7,plain,
! [X16] :
( basis_of(esk2_1(X16),X16)
| ~ a_vector_space(X16) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_remark_63_a])])])]) ).
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]) ).
fof(c_0_9,plain,
! [X20,X21,X22] :
( ( ~ a_subset_of(X22,vec_to_class(X20))
| ~ a_vector_subspace_of(X20,X21)
| lin_ind_subset(X22,X20)
| ~ lin_ind_subset(X22,X21) )
& ( ~ a_subset_of(X22,vec_to_class(X20))
| ~ a_vector_subspace_of(X20,X21)
| lin_ind_subset(X22,X21)
| ~ lin_ind_subset(X22,X20) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_2_4_2])])])]) ).
cnf(c_0_10,plain,
( ~ basis_of(X1,X2)
| a_subset_of(X1,vec_to_class(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( ~ a_vector_space(X1)
| basis_of(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( ~ basis_of(X1,X2)
| lin_ind_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_13,plain,
! [X18,X19] :
( a_vector_space(X18)
| ~ a_vector_subspace_of(X18,X19) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[bg_2_4_a])])]) ).
fof(c_0_14,negated_conjecture,
! [X25,X26] :
( ( ~ basis_of(X25,esk3_0)
| ~ basis_of(union(X25,X26),esk4_0) )
& a_vector_space(esk4_0)
& a_vector_subspace_of(esk3_0,esk4_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])])])])]) ).
cnf(c_0_15,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_9]) ).
cnf(c_0_16,plain,
( ~ a_vector_space(X1)
| a_subset_of(esk2_1(X1),vec_to_class(X1)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_17,plain,
( ~ a_vector_space(X1)
| lin_ind_subset(esk2_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_18,plain,
( ~ a_vector_subspace_of(X1,X2)
| a_vector_space(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
a_vector_subspace_of(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_20,plain,
! [X12,X13,X14] :
( ( ~ basis_of(X13,X14)
| ~ lin_ind_subset(X12,X14)
| basis_of(union(X12,esk1_3(X12,X13,X14)),X14) )
& ( ~ basis_of(X13,X14)
| ~ lin_ind_subset(X12,X14)
| a_subset_of(esk1_3(X12,X13,X14),X13) ) ),
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_21,plain,
( ~ a_vector_subspace_of(X1,X2)
| lin_ind_subset(esk2_1(X1),X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( ~ basis_of(X1,esk3_0)
| ~ basis_of(union(X1,X2),esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,negated_conjecture,
a_vector_space(esk3_0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( ~ basis_of(X2,X3)
| ~ lin_ind_subset(X1,X3)
| basis_of(union(X1,esk1_3(X1,X2,X3)),X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
lin_ind_subset(esk2_1(esk3_0),esk4_0),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_26,negated_conjecture,
~ basis_of(union(esk2_1(esk3_0),X1),esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_11]),c_0_23])]) ).
cnf(c_0_27,negated_conjecture,
~ basis_of(X1,esk4_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_28,negated_conjecture,
a_vector_space(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_11]),c_0_28])]),
[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/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 13:01:42 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 0.15/0.43 % Version: 3.5.1
% 0.15/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.43 % Starting sh5l with 300s (1) cores
% 0.15/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1805791 completed with status 0
% 0.15/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.15/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.43 % No SInE strategy applied
% 0.15/0.43 % Search class: FHHNF-FFSF31-SFFFFFNN
% 0.15/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.15/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.15/0.43 % Starting new_bool_1 with 136s (1) cores
% 0.15/0.43 % new_bool_1 with pid 1805799 completed with status 0
% 0.15/0.43 % Result found by new_bool_1
% 0.15/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.43 % No SInE strategy applied
% 0.15/0.43 % Search class: FHHNF-FFSF31-SFFFFFNN
% 0.15/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.15/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.15/0.43 % Starting new_bool_1 with 136s (1) cores
% 0.15/0.43 % Preprocessing time : 0.001 s
% 0.15/0.43 % Presaturation interreduction done
% 0.15/0.43
% 0.15/0.43 % Proof found!
% 0.15/0.43 % SZS status Theorem
% 0.15/0.43 % SZS output start CNFRefutation
% See solution above
% 0.15/0.43 % Parsed axioms : 6
% 0.15/0.43 % Removed by relevancy pruning/SinE : 0
% 0.15/0.43 % Initial clauses : 11
% 0.15/0.43 % Removed in clause preprocessing : 0
% 0.15/0.43 % Initial clauses in saturation : 11
% 0.15/0.43 % Processed clauses : 30
% 0.15/0.43 % ...of these trivial : 0
% 0.15/0.43 % ...subsumed : 1
% 0.15/0.43 % ...remaining for further processing : 29
% 0.15/0.43 % Other redundant clauses eliminated : 0
% 0.15/0.43 % Clauses deleted for lack of memory : 0
% 0.15/0.43 % Backward-subsumed : 2
% 0.15/0.43 % Backward-rewritten : 0
% 0.15/0.43 % Generated clauses : 12
% 0.15/0.43 % ...of the previous two non-redundant : 11
% 0.15/0.43 % ...aggressively subsumed : 0
% 0.15/0.43 % Contextual simplify-reflections : 2
% 0.15/0.43 % Paramodulations : 12
% 0.15/0.43 % Factorizations : 0
% 0.15/0.43 % NegExts : 0
% 0.15/0.43 % Equation resolutions : 0
% 0.15/0.43 % Disequality decompositions : 0
% 0.15/0.43 % Total rewrite steps : 2
% 0.15/0.43 % ...of those cached : 0
% 0.15/0.43 % Propositional unsat checks : 0
% 0.15/0.43 % Propositional check models : 0
% 0.15/0.43 % Propositional check unsatisfiable : 0
% 0.15/0.43 % Propositional clauses : 0
% 0.15/0.43 % Propositional clauses after purity: 0
% 0.15/0.43 % Propositional unsat core size : 0
% 0.15/0.43 % Propositional preprocessing time : 0.000
% 0.15/0.43 % Propositional encoding time : 0.000
% 0.15/0.43 % Propositional solver time : 0.000
% 0.15/0.43 % Success case prop preproc time : 0.000
% 0.15/0.43 % Success case prop encoding time : 0.000
% 0.15/0.43 % Success case prop solver time : 0.000
% 0.15/0.43 % Current number of processed clauses : 16
% 0.15/0.43 % Positive orientable unit clauses : 4
% 0.15/0.43 % Positive unorientable unit clauses: 0
% 0.15/0.43 % Negative unit clauses : 1
% 0.15/0.43 % Non-unit-clauses : 11
% 0.15/0.43 % Current number of unprocessed clauses: 3
% 0.15/0.43 % ...number of literals in the above : 8
% 0.15/0.43 % Current number of archived formulas : 0
% 0.15/0.43 % Current number of archived clauses : 13
% 0.15/0.43 % Clause-clause subsumption calls (NU) : 30
% 0.15/0.43 % Rec. Clause-clause subsumption calls : 21
% 0.15/0.43 % Non-unit clause-clause subsumptions : 3
% 0.15/0.43 % Unit Clause-clause subsumption calls : 9
% 0.15/0.43 % Rewrite failures with RHS unbound : 0
% 0.15/0.43 % BW rewrite match attempts : 0
% 0.15/0.43 % BW rewrite match successes : 0
% 0.15/0.43 % Condensation attempts : 0
% 0.15/0.43 % Condensation successes : 0
% 0.15/0.43 % Termbank termtop insertions : 1011
% 0.15/0.43 % Search garbage collected termcells : 181
% 0.15/0.43
% 0.15/0.43 % -------------------------------------------------
% 0.15/0.43 % User time : 0.004 s
% 0.15/0.43 % System time : 0.001 s
% 0.15/0.43 % Total time : 0.005 s
% 0.15/0.43 % Maximum resident set size: 3636 pages
% 0.15/0.43
% 0.15/0.43 % -------------------------------------------------
% 0.15/0.43 % User time : 0.014 s
% 0.15/0.43 % System time : 0.010 s
% 0.15/0.43 % Total time : 0.023 s
% 0.15/0.43 % Maximum resident set size: 4864 pages
% 0.15/0.43 % E exiting
%------------------------------------------------------------------------------