TSTP Solution File: ITP042^1 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : ITP042^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat May 4 08:06:45 EDT 2024
% Result : Theorem 0.43s 0.63s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 23
% Syntax : Number of formulae : 35 ( 3 unt; 18 typ; 0 def)
% Number of atoms : 64 ( 17 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 169 ( 7 ~; 3 |; 13 &; 142 @)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 36 ( 11 ^ 12 !; 13 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
sum_su1965225555um_c_b: $tType ).
thf(decl_sort2,type,
set_Su111624115um_c_b: $tType ).
thf(decl_sort3,type,
denota723907260t_unit: $tType ).
thf(decl_sort4,type,
a: $tType ).
thf(decl_sort5,type,
trm_a_b: $tType ).
thf(decl_sort6,type,
set_a: $tType ).
thf(decl_22,type,
denota896875430_a_c_b: denota723907260t_unit > denota723907260t_unit > set_Su111624115um_c_b > $o ).
thf(decl_83,type,
collec1166375742um_c_b: ( sum_su1965225555um_c_b > $o ) > set_Su111624115um_c_b ).
thf(decl_90,type,
static_SIGT_a_b: trm_a_b > set_a ).
thf(decl_92,type,
sum_In811702836um_c_b: a > sum_su1965225555um_c_b ).
thf(decl_95,type,
times_a_b: trm_a_b > trm_a_b > trm_a_b ).
thf(decl_110,type,
member_a: a > set_a > $o ).
thf(decl_111,type,
i: denota723907260t_unit ).
thf(decl_112,type,
j: denota723907260t_unit ).
thf(decl_115,type,
theta_1: trm_a_b ).
thf(decl_116,type,
theta_2: trm_a_b ).
thf(decl_137,type,
epred1_0: sum_su1965225555um_c_b > $o ).
thf(decl_140,type,
epred4_0: sum_su1965225555um_c_b > $o ).
thf(conj_0,conjecture,
( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [X3: sum_su1965225555um_c_b] :
? [X4: a] :
( ( X3
= ( sum_In811702836um_c_b @ X4 ) )
& ( member_a @ X4 @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.j5bUwAcIm6/E---3.1_7453.p',conj_0) ).
thf(fact_0__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0621_125_092_060close_062,axiom,
! [X1: denota723907260t_unit,X2: denota723907260t_unit] :
( ( denota896875430_a_c_b @ X1 @ X2
@ ( collec1166375742um_c_b
@ ^ [X3: sum_su1965225555um_c_b] :
? [X4: a] :
( ( X3
= ( sum_In811702836um_c_b @ X4 ) )
& ( member_a @ X4 @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) )
=> ( denota896875430_a_c_b @ X1 @ X2
@ ( collec1166375742um_c_b
@ ^ [X3: sum_su1965225555um_c_b] :
? [X4: a] :
( ( X3
= ( sum_In811702836um_c_b @ X4 ) )
& ( member_a @ X4 @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.j5bUwAcIm6/E---3.1_7453.p',fact_0__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0621_125_092_060close_062) ).
thf(fact_3_dfree__Times_Oprems_I2_J,axiom,
( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [X3: sum_su1965225555um_c_b] :
? [X4: a] :
( ( X3
= ( sum_In811702836um_c_b @ X4 ) )
& ( member_a @ X4 @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.j5bUwAcIm6/E---3.1_7453.p',fact_3_dfree__Times_Oprems_I2_J) ).
thf(c_0_3,negated_conjecture,
~ ( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [Z0: sum_su1965225555um_c_b] :
? [X4: a] :
( ( Z0
= ( sum_In811702836um_c_b @ X4 ) )
& ( member_a @ X4 @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])])]) ).
thf(c_0_4,plain,
! [X1: denota723907260t_unit,X2: denota723907260t_unit] :
( ( denota896875430_a_c_b @ X1 @ X2
@ ( collec1166375742um_c_b
@ ^ [Z0: sum_su1965225555um_c_b] :
? [X4: a] :
( ( Z0
= ( sum_In811702836um_c_b @ X4 ) )
& ( member_a @ X4 @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) )
=> ( denota896875430_a_c_b @ X1 @ X2
@ ( collec1166375742um_c_b
@ ^ [Z0: sum_su1965225555um_c_b] :
? [X4: a] :
( ( Z0
= ( sum_In811702836um_c_b @ X4 ) )
& ( member_a @ X4 @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_0__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0621_125_092_060close_062]) ).
thf(c_0_5,negated_conjecture,
~ ( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [Z0: sum_su1965225555um_c_b] :
? [X4: a] :
( ( Z0
= ( sum_In811702836um_c_b @ X4 ) )
& ( member_a @ X4 @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[c_0_3]) ).
thf(c_0_6,plain,
! [X1345: sum_su1965225555um_c_b] :
( ( epred1_0 @ X1345 )
<=> ? [X1344: a] :
( ( X1345
= ( sum_In811702836um_c_b @ X1344 ) )
& ( member_a @ X1344 @ ( static_SIGT_a_b @ theta_1 ) ) ) ),
introduced(definition) ).
thf(c_0_7,plain,
! [X1091: denota723907260t_unit,X1092: denota723907260t_unit] :
( ~ ( denota896875430_a_c_b @ X1091 @ X1092
@ ( collec1166375742um_c_b
@ ^ [Z0: sum_su1965225555um_c_b] :
? [X4: a] :
( ( Z0
= ( sum_In811702836um_c_b @ X4 ) )
& ( member_a @ X4 @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) )
| ( denota896875430_a_c_b @ X1091 @ X1092
@ ( collec1166375742um_c_b
@ ^ [Z0: sum_su1965225555um_c_b] :
? [X4: a] :
( ( Z0
= ( sum_In811702836um_c_b @ X4 ) )
& ( member_a @ X4 @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
thf(c_0_8,plain,
! [X1353: sum_su1965225555um_c_b] :
( ( epred4_0 @ X1353 )
<=> ? [X1352: a] :
( ( X1353
= ( sum_In811702836um_c_b @ X1352 ) )
& ( member_a @ X1352 @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ),
introduced(definition) ).
thf(c_0_9,plain,
( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [Z0: sum_su1965225555um_c_b] :
? [X4: a] :
( ( Z0
= ( sum_In811702836um_c_b @ X4 ) )
& ( member_a @ X4 @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_3_dfree__Times_Oprems_I2_J]) ).
thf(c_0_10,negated_conjecture,
( ( denota896875430_a_c_b @ i @ j @ ( collec1166375742um_c_b @ epred1_0 ) )
!= $true ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_5]),c_0_6]) ).
thf(c_0_11,plain,
! [X1: denota723907260t_unit,X2: denota723907260t_unit] :
( ( ( denota896875430_a_c_b @ X1 @ X2 @ ( collec1166375742um_c_b @ epred1_0 ) )
= $true )
| ( ( denota896875430_a_c_b @ X1 @ X2 @ ( collec1166375742um_c_b @ epred4_0 ) )
!= $true ) ),
inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_7]),c_0_8]),c_0_6]) ).
thf(c_0_12,plain,
( ( denota896875430_a_c_b @ i @ j @ ( collec1166375742um_c_b @ epred4_0 ) )
= $true ),
inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_9]),c_0_8]) ).
thf(c_0_13,negated_conjecture,
~ ( denota896875430_a_c_b @ i @ j @ ( collec1166375742um_c_b @ epred1_0 ) ),
inference(cn,[status(thm)],[c_0_10]) ).
thf(c_0_14,plain,
! [X1: denota723907260t_unit,X2: denota723907260t_unit] :
( ( denota896875430_a_c_b @ X1 @ X2 @ ( collec1166375742um_c_b @ epred1_0 ) )
| ~ ( denota896875430_a_c_b @ X1 @ X2 @ ( collec1166375742um_c_b @ epred4_0 ) ) ),
inference(cn,[status(thm)],[c_0_11]) ).
thf(c_0_15,plain,
denota896875430_a_c_b @ i @ j @ ( collec1166375742um_c_b @ epred4_0 ),
inference(cn,[status(thm)],[c_0_12]) ).
thf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.17 % Problem : ITP042^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.18 % Command : run_E %s %d THM
% 0.18/0.40 % Computer : n010.cluster.edu
% 0.18/0.40 % Model : x86_64 x86_64
% 0.18/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.40 % Memory : 8042.1875MB
% 0.18/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.40 % CPULimit : 300
% 0.18/0.40 % WCLimit : 300
% 0.18/0.40 % DateTime : Fri May 3 12:13:03 EDT 2024
% 0.18/0.40 % CPUTime :
% 0.25/0.57 Running higher-order theorem proving
% 0.25/0.57 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.j5bUwAcIm6/E---3.1_7453.p
% 0.43/0.63 # Version: 3.1.0-ho
% 0.43/0.63 # Preprocessing class: HSLSSMSMSSLNHSA.
% 0.43/0.63 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.63 # Starting ho_unfolding_8 with 900s (3) cores
% 0.43/0.63 # Starting new_bool_8 with 300s (1) cores
% 0.43/0.63 # Starting post_as_ho6 with 300s (1) cores
% 0.43/0.63 # Starting ho_unfolding_1 with 300s (1) cores
% 0.43/0.63 # Starting full_lambda_4 with 300s (1) cores
% 0.43/0.63 # Starting pre_casc_5 with 300s (1) cores
% 0.43/0.63 # new_bool_8 with pid 7597 completed with status 0
% 0.43/0.63 # Result found by new_bool_8
% 0.43/0.63 # Preprocessing class: HSLSSMSMSSLNHSA.
% 0.43/0.63 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.63 # Starting ho_unfolding_8 with 900s (3) cores
% 0.43/0.63 # Starting new_bool_8 with 300s (1) cores
% 0.43/0.63 # SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 0.43/0.63 # Search class: HGUSM-FFLM32-MHSFFSBN
% 0.43/0.63 # partial match(1): HGUSM-FSLM32-MHSFFSBN
% 0.43/0.63 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.43/0.63 # Starting lpo8_s with 163s (1) cores
% 0.43/0.63 # lpo8_s with pid 7605 completed with status 0
% 0.43/0.63 # Result found by lpo8_s
% 0.43/0.63 # Preprocessing class: HSLSSMSMSSLNHSA.
% 0.43/0.63 # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 0.43/0.63 # Starting ho_unfolding_8 with 900s (3) cores
% 0.43/0.63 # Starting new_bool_8 with 300s (1) cores
% 0.43/0.63 # SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 0.43/0.63 # Search class: HGUSM-FFLM32-MHSFFSBN
% 0.43/0.63 # partial match(1): HGUSM-FSLM32-MHSFFSBN
% 0.43/0.63 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.43/0.63 # Starting lpo8_s with 163s (1) cores
% 0.43/0.63 # Preprocessing time : 0.004 s
% 0.43/0.63 # Presaturation interreduction done
% 0.43/0.63
% 0.43/0.63 # Proof found!
% 0.43/0.63 # SZS status Theorem
% 0.43/0.63 # SZS output start CNFRefutation
% See solution above
% 0.43/0.63 # Parsed axioms : 482
% 0.43/0.63 # Removed by relevancy pruning/SinE : 365
% 0.43/0.63 # Initial clauses : 182
% 0.43/0.63 # Removed in clause preprocessing : 6
% 0.43/0.63 # Initial clauses in saturation : 176
% 0.43/0.63 # Processed clauses : 211
% 0.43/0.63 # ...of these trivial : 13
% 0.43/0.63 # ...subsumed : 52
% 0.43/0.63 # ...remaining for further processing : 146
% 0.43/0.63 # Other redundant clauses eliminated : 28
% 0.43/0.63 # Clauses deleted for lack of memory : 0
% 0.43/0.63 # Backward-subsumed : 0
% 0.43/0.63 # Backward-rewritten : 0
% 0.43/0.63 # Generated clauses : 42
% 0.43/0.63 # ...of the previous two non-redundant : 17
% 0.43/0.63 # ...aggressively subsumed : 0
% 0.43/0.63 # Contextual simplify-reflections : 0
% 0.43/0.63 # Paramodulations : 3
% 0.43/0.63 # Factorizations : 0
% 0.43/0.63 # NegExts : 2
% 0.43/0.63 # Equation resolutions : 28
% 0.43/0.63 # Disequality decompositions : 0
% 0.43/0.63 # Total rewrite steps : 32
% 0.43/0.63 # ...of those cached : 19
% 0.43/0.63 # Propositional unsat checks : 0
% 0.43/0.63 # Propositional check models : 0
% 0.43/0.63 # Propositional check unsatisfiable : 0
% 0.43/0.63 # Propositional clauses : 0
% 0.43/0.63 # Propositional clauses after purity: 0
% 0.43/0.63 # Propositional unsat core size : 0
% 0.43/0.63 # Propositional preprocessing time : 0.000
% 0.43/0.63 # Propositional encoding time : 0.000
% 0.43/0.63 # Propositional solver time : 0.000
% 0.43/0.63 # Success case prop preproc time : 0.000
% 0.43/0.63 # Success case prop encoding time : 0.000
% 0.43/0.63 # Success case prop solver time : 0.000
% 0.43/0.63 # Current number of processed clauses : 24
% 0.43/0.63 # Positive orientable unit clauses : 12
% 0.43/0.63 # Positive unorientable unit clauses: 0
% 0.43/0.63 # Negative unit clauses : 3
% 0.43/0.63 # Non-unit-clauses : 9
% 0.43/0.63 # Current number of unprocessed clauses: 80
% 0.43/0.63 # ...number of literals in the above : 180
% 0.43/0.63 # Current number of archived formulas : 0
% 0.43/0.63 # Current number of archived clauses : 103
% 0.43/0.63 # Clause-clause subsumption calls (NU) : 1512
% 0.43/0.63 # Rec. Clause-clause subsumption calls : 1205
% 0.43/0.63 # Non-unit clause-clause subsumptions : 51
% 0.43/0.63 # Unit Clause-clause subsumption calls : 23
% 0.43/0.63 # Rewrite failures with RHS unbound : 0
% 0.43/0.63 # BW rewrite match attempts : 16
% 0.43/0.63 # BW rewrite match successes : 0
% 0.43/0.63 # Condensation attempts : 211
% 0.43/0.63 # Condensation successes : 0
% 0.43/0.63 # Termbank termtop insertions : 18218
% 0.43/0.63 # Search garbage collected termcells : 5762
% 0.43/0.63
% 0.43/0.63 # -------------------------------------------------
% 0.43/0.63 # User time : 0.023 s
% 0.43/0.63 # System time : 0.009 s
% 0.43/0.63 # Total time : 0.032 s
% 0.43/0.63 # Maximum resident set size: 3496 pages
% 0.43/0.63
% 0.43/0.63 # -------------------------------------------------
% 0.43/0.63 # User time : 0.036 s
% 0.43/0.63 # System time : 0.013 s
% 0.43/0.63 # Total time : 0.049 s
% 0.43/0.63 # Maximum resident set size: 2676 pages
% 0.43/0.63 % E---3.1 exiting
% 0.43/0.64 % E exiting
%------------------------------------------------------------------------------