%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP330_1 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:55:25 PM UTC 2026
% Result : Theorem 0.20s 0.52s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 11 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 26 ( 13 ~; 8 |; 2 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 12 ( 11 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 20 !; 1 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
'A_m_vec_set$': $tType ).
tff(decl_sort2,type,
'M_a_m_vec_fun$': $tType ).
tff(decl_sort3,type,
'M_set$': $tType ).
tff(decl_sort4,type,
'A_n_vec$': $tType ).
tff(decl_sort5,type,
'N_a_n_vec_fun$': $tType ).
tff(decl_sort6,type,
'M_a_fun$': $tType ).
tff(decl_sort7,type,
'A_m_vec$': $tType ).
tff(decl_sort8,type,
'N$': $tType ).
tff(decl_sort9,type,
'A_n_vec_n_vec$': $tType ).
tff(decl_sort10,type,
'A_n_vec_a_m_vec_fun$': $tType ).
tff(decl_sort11,type,
'A_m_vec_bool_fun$': $tType ).
tff(decl_35,type,
'vec_nth$a': 'A_n_vec_n_vec$' > 'N_a_n_vec_fun$' ).
tff(decl_69,type,
'cart_basis_Rn$': 'A_n_vec_n_vec$' ).
tff(decl_83,type,
'fun_app$ar': ( 'A_n_vec$' * 'A_n_vec_a_m_vec_fun$' ) > 'A_m_vec$' ).
tff(decl_97,type,
'member$a': ( 'A_m_vec_set$' * 'A_m_vec$' ) > $o ).
tff(decl_104,type,
'collect$': 'A_m_vec_bool_fun$' > 'A_m_vec_set$' ).
tff(decl_204,type,
'top$': 'M_set$' ).
tff(decl_273,type,
'sum$': ( 'M_set$' * 'M_a_m_vec_fun$' ) > 'A_m_vec$' ).
tff(decl_288,type,
'j$': 'N$' ).
tff(decl_307,type,
'thesis$': $o ).
tff(decl_375,type,
'uu$': 'M_a_fun$' > 'M_a_m_vec_fun$' ).
tff(decl_419,type,
'fun_app$a': ( 'N$' * 'N_a_n_vec_fun$' ) > 'A_n_vec$' ).
tff(decl_440,type,
'top$b': 'A_m_vec_set$' ).
tff(decl_531,type,
'fun_app$': ( 'A_m_vec$' * 'A_m_vec_bool_fun$' ) > $o ).
tff(decl_601,type,
'f$': 'A_n_vec_a_m_vec_fun$' ).
tff(decl_625,type,
'uua$': 'A_m_vec_bool_fun$' ).
tff(decl_652,type,
esk6_1: 'A_m_vec$' > 'M_a_fun$' ).
fof(conjecture283,conjecture,
'thesis$',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture283) ).
tff(axiom520,axiom,
! [X1: 'A_m_vec$',X1556: 'A_m_vec_bool_fun$'] :
( 'member$a'(X1,'collect$'(X1556))
<=> 'fun_app$'(X1556,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom520) ).
tff(axiom319,axiom,
! [X1: 'A_m_vec$'] : 'member$a'(X1,'top$b'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom319) ).
tff(hypothesis284,hypothesis,
! [X845: 'M_a_fun$'] :
( ( 'sum$'('uu$'(X845),'top$') = 'fun_app$ar'('f$','fun_app$a'('vec_nth$a'('cart_basis_Rn$'),'j$')) )
=> 'thesis$' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis284) ).
tff(axiom0,axiom,
! [X1: 'A_m_vec$'] :
( 'fun_app$'('uua$',X1)
<=> ? [X2: 'M_a_fun$'] : ( 'sum$'('uu$'(X2),'top$') = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom0) ).
tff(axiom287,axiom,
'top$b' = 'collect$'('uua$'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom287) ).
fof(c_0_6,negated_conjecture,
~ 'thesis$',
inference(assume_negation,[status(cth)],[conjecture283]) ).
fof(c_0_7,negated_conjecture,
~ 'thesis$',
inference(fof_simplification,[status(thm)],[c_0_6]) ).
tff(c_0_8,plain,
! [X2671: 'A_m_vec$',X2672: 'A_m_vec_bool_fun$'] :
( ( 'member$a'(X2671,'collect$'(X2672))
| ~ 'fun_app$'(X2672,X2671) )
& ( 'fun_app$'(X2672,X2671)
| ~ 'member$a'(X2671,'collect$'(X2672)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom520])])]) ).
tff(c_0_9,plain,
! [X2676: 'A_m_vec$'] : 'member$a'(X2676,'top$b'),
inference(variable_rename,[status(thm)],[axiom319]) ).
tff(c_0_10,hypothesis,
! [X2567: 'M_a_fun$'] :
( 'thesis$'
| ( 'sum$'('uu$'(X2567),'top$') != 'fun_app$ar'('f$','fun_app$a'('vec_nth$a'('cart_basis_Rn$'),'j$')) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[hypothesis284])])]) ).
fof(c_0_11,negated_conjecture,
~ 'thesis$',
inference(fof_nnf,[status(thm)],[c_0_7]) ).
tff(c_0_12,plain,
! [X2595: 'A_m_vec$',X2597: 'A_m_vec$',X2598: 'M_a_fun$'] :
( ( 'fun_app$'('uua$',X2597)
| ( 'sum$'('uu$'(X2598),'top$') != X2597 ) )
& ( ( 'sum$'('uu$'(esk6_1(X2595)),'top$') = X2595 )
| ~ 'fun_app$'('uua$',X2595) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom0])])])])])]) ).
tcf(c_0_13,plain,
! [X1: 'A_m_vec$',X1556: 'A_m_vec_bool_fun$'] :
( ~ 'member$a'(X1,'collect$'(X1556))
| 'fun_app$'(X1556,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tcf(c_0_14,plain,
'top$b' = 'collect$'('uua$'),
inference(split_conjunct,[status(thm)],[axiom287]) ).
tcf(c_0_15,plain,
! [X1: 'A_m_vec$'] : 'member$a'(X1,'top$b'),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_16,hypothesis,
! [X2: 'M_a_fun$'] :
( ( 'sum$'('uu$'(X2),'top$') != 'fun_app$ar'('f$','fun_app$a'('vec_nth$a'('cart_basis_Rn$'),'j$')) )
| 'thesis$' ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
~ 'thesis$',
inference(split_conjunct,[status(thm)],[c_0_11]) ).
tcf(c_0_18,plain,
! [X1: 'A_m_vec$'] :
( ~ 'fun_app$'('uua$',X1)
| ( 'sum$'('uu$'(esk6_1(X1)),'top$') = X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tcf(c_0_19,plain,
! [X1: 'A_m_vec$'] : 'fun_app$'('uua$',X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
tcf(c_0_20,hypothesis,
! [X2: 'M_a_fun$'] : 'sum$'('uu$'(X2),'top$') != 'fun_app$ar'('f$','fun_app$a'('vec_nth$a'('cart_basis_Rn$'),'j$')),
inference(sr,[status(thm)],[c_0_16,c_0_17]) ).
tcf(c_0_21,plain,
! [X1: 'A_m_vec$'] : 'sum$'('uu$'(esk6_1(X1)),'top$') = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]) ).
cnf(c_0_22,hypothesis,
$false,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP330_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 22:37:36 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.42 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
% 0.20/0.52 % Version: 3.5.1
% 0.20/0.52 % partial match(1): FMLMSLSMSSSNFFN
% 0.20/0.52 % Preprocessing class: FMLMSLLMSSSNFFN.
% 0.20/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.52 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 0.20/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.20/0.52 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.52 % Starting sh5l with 300s (1) cores
% 0.20/0.52 % new_bool_3 with pid 4091206 completed with status 0
% 0.20/0.52 % Result found by new_bool_3
% 0.20/0.52 % partial match(1): FMLMSLSMSSSNFFN
% 0.20/0.52 % Preprocessing class: FMLMSLLMSSSNFFN.
% 0.20/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.52 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 0.20/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.20/0.52 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.20/0.52 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.52 % Search class: FGUSM-FFMM31-DFFFFFNN
% 0.20/0.52 % partial match(1): FGHSM-FFMM31-DFFFFFNN
% 0.20/0.52 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.52 % Starting SubtermCWHack with 31s (1) cores
% 0.20/0.52 % SubtermCWHack with pid 4091209 completed with status 0
% 0.20/0.52 % Result found by SubtermCWHack
% 0.20/0.52 % partial match(1): FMLMSLSMSSSNFFN
% 0.20/0.52 % Preprocessing class: FMLMSLLMSSSNFFN.
% 0.20/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.52 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 0.20/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.20/0.52 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.20/0.52 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.52 % Search class: FGUSM-FFMM31-DFFFFFNN
% 0.20/0.52 % partial match(1): FGHSM-FFMM31-DFFFFFNN
% 0.20/0.52 % Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.52 % Starting SubtermCWHack with 31s (1) cores
% 0.20/0.52 % Preprocessing time : 0.005 s
% 0.20/0.52
% 0.20/0.52 % Proof found!
% 0.20/0.52 % SZS status Theorem
% 0.20/0.52 % SZS output start CNFRefutation
% See solution above
% 0.20/0.52 % Parsed axioms : 1643
% 0.20/0.52 % Removed by relevancy pruning/SinE : 1587
% 0.20/0.52 % Initial clauses : 85
% 0.20/0.52 % Removed in clause preprocessing : 14
% 0.20/0.52 % Initial clauses in saturation : 71
% 0.20/0.52 % Processed clauses : 59
% 0.20/0.52 % ...of these trivial : 7
% 0.20/0.52 % ...subsumed : 10
% 0.20/0.52 % ...remaining for further processing : 42
% 0.20/0.52 % Other redundant clauses eliminated : 7
% 0.20/0.52 % Clauses deleted for lack of memory : 0
% 0.20/0.52 % Backward-subsumed : 0
% 0.20/0.52 % Backward-rewritten : 2
% 0.20/0.52 % Generated clauses : 29
% 0.20/0.52 % ...of the previous two non-redundant : 18
% 0.20/0.52 % ...aggressively subsumed : 0
% 0.20/0.52 % Contextual simplify-reflections : 0
% 0.20/0.52 % Paramodulations : 18
% 0.20/0.52 % Factorizations : 0
% 0.20/0.52 % NegExts : 0
% 0.20/0.52 % Equation resolutions : 11
% 0.20/0.52 % Disequality decompositions : 0
% 0.20/0.52 % Total rewrite steps : 17
% 0.20/0.52 % ...of those cached : 3
% 0.20/0.52 % Propositional unsat checks : 0
% 0.20/0.52 % Propositional check models : 0
% 0.20/0.52 % Propositional check unsatisfiable : 0
% 0.20/0.52 % Propositional clauses : 0
% 0.20/0.52 % Propositional clauses after purity: 0
% 0.20/0.52 % Propositional unsat core size : 0
% 0.20/0.52 % Propositional preprocessing time : 0.000
% 0.20/0.52 % Propositional encoding time : 0.000
% 0.20/0.52 % Propositional solver time : 0.000
% 0.20/0.52 % Success case prop preproc time : 0.000
% 0.20/0.52 % Success case prop encoding time : 0.000
% 0.20/0.52 % Success case prop solver time : 0.000
% 0.20/0.52 % Current number of processed clauses : 34
% 0.20/0.52 % Positive orientable unit clauses : 13
% 0.20/0.52 % Positive unorientable unit clauses: 2
% 0.20/0.52 % Negative unit clauses : 2
% 0.20/0.52 % Non-unit-clauses : 17
% 0.20/0.52 % Current number of unprocessed clauses: 30
% 0.20/0.52 % ...number of literals in the above : 63
% 0.20/0.52 % Current number of archived formulas : 0
% 0.20/0.52 % Current number of archived clauses : 2
% 0.20/0.52 % Clause-clause subsumption calls (NU) : 34
% 0.20/0.52 % Rec. Clause-clause subsumption calls : 33
% 0.20/0.52 % Non-unit clause-clause subsumptions : 0
% 0.20/0.52 % Unit Clause-clause subsumption calls : 2
% 0.20/0.52 % Rewrite failures with RHS unbound : 24
% 0.20/0.52 % BW rewrite match attempts : 2
% 0.20/0.52 % BW rewrite match successes : 2
% 0.20/0.52 % Condensation attempts : 0
% 0.20/0.52 % Condensation successes : 0
% 0.20/0.52 % Termbank termtop insertions : 16402
% 0.20/0.52 % Search garbage collected termcells : 10872
% 0.20/0.52
% 0.20/0.52 % -------------------------------------------------
% 0.20/0.52 % User time : 0.016 s
% 0.20/0.52 % System time : 0.013 s
% 0.20/0.52 % Total time : 0.029 s
% 0.20/0.52 % Maximum resident set size: 7908 pages
% 0.20/0.52
% 0.20/0.52 % -------------------------------------------------
% 0.20/0.52 % User time : 0.074 s
% 0.20/0.52 % System time : 0.021 s
% 0.20/0.52 % Total time : 0.094 s
% 0.20/0.52 % Maximum resident set size: 7680 pages
% 0.20/0.52 % E exiting
%------------------------------------------------------------------------------