TSTP Solution File: SEU664^2 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU664^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n023.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 : Tue May 21 03:28:58 EDT 2024
% Result : Theorem 0.20s 0.51s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 36 ( 10 unt; 13 typ; 0 def)
% Number of atoms : 70 ( 22 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 286 ( 19 ~; 16 |; 10 &; 220 @)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 64 ( 0 ^ 60 !; 4 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
in: $i > $i > $o ).
thf(decl_23,type,
kpair: $i > $i > $i ).
thf(decl_24,type,
cartprod: $i > $i > $i ).
thf(decl_25,type,
cartprodmempair1: $o ).
thf(decl_26,type,
kfst: $i > $i ).
thf(decl_27,type,
ksnd: $i > $i ).
thf(decl_28,type,
cartprodfstpairEq: $o ).
thf(decl_29,type,
cartprodsndpairEq: $o ).
thf(decl_30,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_31,type,
esk2_3: $i > $i > $i > $i ).
thf(decl_32,type,
esk3_0: $i ).
thf(decl_33,type,
esk4_0: $i ).
thf(decl_34,type,
esk5_0: $i ).
thf(cartprodpairsurjEq,conjecture,
( cartprodmempair1
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ? [X4: $i] :
( ( in @ X4 @ X1 )
& ? [X5: $i] :
( ( in @ X5 @ X2 )
& ( X3
= ( kpair @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
<=> ! [X1: $i,X2: $i,X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( kfst @ ( kpair @ X4 @ X5 ) )
= X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(cartprodsndpairEq,axiom,
( cartprodsndpairEq
<=> ! [X1: $i,X2: $i,X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( ksnd @ ( kpair @ X4 @ X5 ) )
= X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(c_0_4,negated_conjecture,
~ ( ! [X22: $i,X23: $i,X24: $i] :
( ( in @ X24 @ ( cartprod @ X22 @ X23 ) )
=> ? [X25: $i] :
( ( in @ X25 @ X22 )
& ? [X26: $i] :
( ( in @ X26 @ X23 )
& ( X24
= ( kpair @ X25 @ X26 ) ) ) ) )
=> ( ! [X27: $i,X28: $i,X29: $i] :
( ( in @ X29 @ X27 )
=> ! [X30: $i] :
( ( in @ X30 @ X28 )
=> ( ( kfst @ ( kpair @ X29 @ X30 ) )
= X29 ) ) )
=> ( ! [X31: $i,X32: $i,X33: $i] :
( ( in @ X33 @ X31 )
=> ! [X34: $i] :
( ( in @ X34 @ X32 )
=> ( ( ksnd @ ( kpair @ X33 @ X34 ) )
= X34 ) ) )
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
= X3 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[cartprodpairsurjEq]),cartprodmempair1]),cartprodfstpairEq]),cartprodsndpairEq]) ).
thf(c_0_5,negated_conjecture,
! [X35: $i,X36: $i,X37: $i,X40: $i,X41: $i,X42: $i,X43: $i,X44: $i,X45: $i,X46: $i,X47: $i] :
( ( ( in @ ( esk1_3 @ X35 @ X36 @ X37 ) @ X35 )
| ~ ( in @ X37 @ ( cartprod @ X35 @ X36 ) ) )
& ( ( in @ ( esk2_3 @ X35 @ X36 @ X37 ) @ X36 )
| ~ ( in @ X37 @ ( cartprod @ X35 @ X36 ) ) )
& ( ( X37
= ( kpair @ ( esk1_3 @ X35 @ X36 @ X37 ) @ ( esk2_3 @ X35 @ X36 @ X37 ) ) )
| ~ ( in @ X37 @ ( cartprod @ X35 @ X36 ) ) )
& ( ~ ( in @ X42 @ X40 )
| ~ ( in @ X43 @ X41 )
| ( ( kfst @ ( kpair @ X42 @ X43 ) )
= X42 ) )
& ( ~ ( in @ X46 @ X44 )
| ~ ( in @ X47 @ X45 )
| ( ( ksnd @ ( kpair @ X46 @ X47 ) )
= X47 ) )
& ( in @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ) )
& ( ( kpair @ ( kfst @ esk5_0 ) @ ( ksnd @ esk5_0 ) )
!= esk5_0 ) ),
inference(distribute,[status(thm)],[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_4])])])])])]) ).
thf(c_0_6,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ ( esk2_3 @ X1 @ X2 @ X3 ) @ X2 )
| ~ ( in @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
in @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( ksnd @ ( kpair @ X1 @ X3 ) )
= X3 )
| ~ ( in @ X1 @ X2 )
| ~ ( in @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,negated_conjecture,
in @ ( esk2_3 @ esk3_0 @ esk4_0 @ esk5_0 ) @ esk4_0,
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X1 )
| ~ ( in @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( X1
= ( kpair @ ( esk1_3 @ X2 @ X3 @ X1 ) @ ( esk2_3 @ X2 @ X3 @ X1 ) ) )
| ~ ( in @ X1 @ ( cartprod @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X2: $i] :
( ( ( ksnd @ ( kpair @ X1 @ ( esk2_3 @ esk3_0 @ esk4_0 @ esk5_0 ) ) )
= ( esk2_3 @ esk3_0 @ esk4_0 @ esk5_0 ) )
| ~ ( in @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_13,negated_conjecture,
in @ ( esk1_3 @ esk3_0 @ esk4_0 @ esk5_0 ) @ esk3_0,
inference(spm,[status(thm)],[c_0_10,c_0_7]) ).
thf(c_0_14,negated_conjecture,
( ( kpair @ ( esk1_3 @ esk3_0 @ esk4_0 @ esk5_0 ) @ ( esk2_3 @ esk3_0 @ esk4_0 @ esk5_0 ) )
= esk5_0 ),
inference(spm,[status(thm)],[c_0_11,c_0_7]) ).
thf(c_0_15,negated_conjecture,
( ( esk2_3 @ esk3_0 @ esk4_0 @ esk5_0 )
= ( ksnd @ esk5_0 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( kfst @ ( kpair @ X1 @ X3 ) )
= X1 )
| ~ ( in @ X1 @ X2 )
| ~ ( in @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_17,negated_conjecture,
in @ ( ksnd @ esk5_0 ) @ esk4_0,
inference(rw,[status(thm)],[c_0_9,c_0_15]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i,X2: $i] :
( ( ( kfst @ ( kpair @ X1 @ ( ksnd @ esk5_0 ) ) )
= X1 )
| ~ ( in @ X1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_19,negated_conjecture,
( ( kpair @ ( esk1_3 @ esk3_0 @ esk4_0 @ esk5_0 ) @ ( ksnd @ esk5_0 ) )
= esk5_0 ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_20,negated_conjecture,
( ( esk1_3 @ esk3_0 @ esk4_0 @ esk5_0 )
= ( kfst @ esk5_0 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_13]),c_0_19]) ).
thf(c_0_21,negated_conjecture,
( ( kpair @ ( kfst @ esk5_0 ) @ ( ksnd @ esk5_0 ) )
!= esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU664^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.14 % Command : run_E %s %d THM
% 0.13/0.36 % Computer : n023.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sun May 19 16:00:08 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.20/0.49 Running higher-order theorem proving
% 0.20/0.49 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/benchmark/theBenchmark.p
% 0.20/0.51 # Version: 3.1.0-ho
% 0.20/0.51 # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.20/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.51 # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.20/0.51 # Starting post_as_ho8 with 300s (1) cores
% 0.20/0.51 # Starting post_as_ho3 with 300s (1) cores
% 0.20/0.51 # Starting post_as_ho2 with 300s (1) cores
% 0.20/0.51 # lpo6_lambda_fix with pid 17204 completed with status 0
% 0.20/0.51 # Result found by lpo6_lambda_fix
% 0.20/0.51 # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.20/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.51 # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.20/0.51 # No SInE strategy applied
% 0.20/0.51 # Search class: HHUSF-FFSF32-SFFFMFNN
% 0.20/0.51 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.51 # Starting new_ho_10 with 811s (1) cores
% 0.20/0.51 # Starting lpo6_lambda_fix with 151s (1) cores
% 0.20/0.51 # Starting new_bool_1 with 136s (1) cores
% 0.20/0.51 # Starting new_bool_2 with 136s (1) cores
% 0.20/0.51 # Starting new_bool_9 with 136s (1) cores
% 0.20/0.51 # new_bool_1 with pid 17210 completed with status 0
% 0.20/0.51 # Result found by new_bool_1
% 0.20/0.51 # Preprocessing class: HSSSSLSSSLSNFFN.
% 0.20/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.51 # Starting lpo6_lambda_fix with 1500s (5) cores
% 0.20/0.51 # No SInE strategy applied
% 0.20/0.51 # Search class: HHUSF-FFSF32-SFFFMFNN
% 0.20/0.51 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.51 # Starting new_ho_10 with 811s (1) cores
% 0.20/0.51 # Starting lpo6_lambda_fix with 151s (1) cores
% 0.20/0.51 # Starting new_bool_1 with 136s (1) cores
% 0.20/0.51 # Preprocessing time : 0.001 s
% 0.20/0.51 # Presaturation interreduction done
% 0.20/0.51
% 0.20/0.51 # Proof found!
% 0.20/0.51 # SZS status Theorem
% 0.20/0.51 # SZS output start CNFRefutation
% See solution above
% 0.20/0.51 # Parsed axioms : 12
% 0.20/0.51 # Removed by relevancy pruning/SinE : 0
% 0.20/0.51 # Initial clauses : 15
% 0.20/0.51 # Removed in clause preprocessing : 8
% 0.20/0.51 # Initial clauses in saturation : 7
% 0.20/0.51 # Processed clauses : 52
% 0.20/0.51 # ...of these trivial : 5
% 0.20/0.51 # ...subsumed : 1
% 0.20/0.51 # ...remaining for further processing : 46
% 0.20/0.51 # Other redundant clauses eliminated : 0
% 0.20/0.51 # Clauses deleted for lack of memory : 0
% 0.20/0.51 # Backward-subsumed : 0
% 0.20/0.51 # Backward-rewritten : 10
% 0.20/0.51 # Generated clauses : 44
% 0.20/0.51 # ...of the previous two non-redundant : 48
% 0.20/0.51 # ...aggressively subsumed : 0
% 0.20/0.51 # Contextual simplify-reflections : 0
% 0.20/0.51 # Paramodulations : 44
% 0.20/0.51 # Factorizations : 0
% 0.20/0.51 # NegExts : 0
% 0.20/0.51 # Equation resolutions : 0
% 0.20/0.51 # Disequality decompositions : 0
% 0.20/0.51 # Total rewrite steps : 20
% 0.20/0.51 # ...of those cached : 12
% 0.20/0.51 # Propositional unsat checks : 0
% 0.20/0.51 # Propositional check models : 0
% 0.20/0.51 # Propositional check unsatisfiable : 0
% 0.20/0.51 # Propositional clauses : 0
% 0.20/0.51 # Propositional clauses after purity: 0
% 0.20/0.51 # Propositional unsat core size : 0
% 0.20/0.51 # Propositional preprocessing time : 0.000
% 0.20/0.51 # Propositional encoding time : 0.000
% 0.20/0.51 # Propositional solver time : 0.000
% 0.20/0.51 # Success case prop preproc time : 0.000
% 0.20/0.51 # Success case prop encoding time : 0.000
% 0.20/0.51 # Success case prop solver time : 0.000
% 0.20/0.51 # Current number of processed clauses : 29
% 0.20/0.51 # Positive orientable unit clauses : 17
% 0.20/0.51 # Positive unorientable unit clauses: 0
% 0.20/0.51 # Negative unit clauses : 1
% 0.20/0.51 # Non-unit-clauses : 11
% 0.20/0.51 # Current number of unprocessed clauses: 5
% 0.20/0.51 # ...number of literals in the above : 5
% 0.20/0.51 # Current number of archived formulas : 0
% 0.20/0.51 # Current number of archived clauses : 17
% 0.20/0.51 # Clause-clause subsumption calls (NU) : 8
% 0.20/0.51 # Rec. Clause-clause subsumption calls : 8
% 0.20/0.51 # Non-unit clause-clause subsumptions : 1
% 0.20/0.51 # Unit Clause-clause subsumption calls : 0
% 0.20/0.51 # Rewrite failures with RHS unbound : 0
% 0.20/0.51 # BW rewrite match attempts : 2
% 0.20/0.51 # BW rewrite match successes : 2
% 0.20/0.51 # Condensation attempts : 0
% 0.20/0.51 # Condensation successes : 0
% 0.20/0.51 # Termbank termtop insertions : 1984
% 0.20/0.51 # Search garbage collected termcells : 358
% 0.20/0.51
% 0.20/0.51 # -------------------------------------------------
% 0.20/0.51 # User time : 0.002 s
% 0.20/0.51 # System time : 0.007 s
% 0.20/0.51 # Total time : 0.008 s
% 0.20/0.51 # Maximum resident set size: 1824 pages
% 0.20/0.51
% 0.20/0.51 # -------------------------------------------------
% 0.20/0.51 # User time : 0.019 s
% 0.20/0.51 # System time : 0.014 s
% 0.20/0.51 # Total time : 0.033 s
% 0.20/0.51 # Maximum resident set size: 1700 pages
% 0.20/0.51 % E---3.1 exiting
% 0.20/0.51 % E exiting
%------------------------------------------------------------------------------