%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW470^1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 : Wed Sep 30 08:40:08 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 100 ( 0 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 229 ( 26 ~; 7 |; 12 &; 178 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 11 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 76 ( 38 ^; 38 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
com: $tType ).
thf(decl_sort2,type,
hoare_669141180iple_a: $tType ).
thf(decl_sort3,type,
x_a: $tType ).
thf(decl_sort4,type,
state: $tType ).
thf(decl_33,type,
hoare_2128652938rivs_a: ( hoare_669141180iple_a > $o ) > ( hoare_669141180iple_a > $o ) > $o ).
thf(decl_34,type,
hoare_1295064928iple_a: ( x_a > state > $o ) > com > ( x_a > state > $o ) > hoare_669141180iple_a ).
thf(decl_35,type,
bot_bo280939947le_a_o: hoare_669141180iple_a > $o ).
thf(decl_38,type,
insert175534902iple_a: hoare_669141180iple_a > ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a > $o ).
thf(decl_42,type,
g: hoare_669141180iple_a > $o ).
thf(decl_43,type,
p: x_a > state > $o ).
thf(decl_44,type,
b: state > $o ).
thf(decl_45,type,
c: com ).
thf(conj_0,conjecture,
( hoare_2128652938rivs_a @ g
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [X19: x_a,X20: state] : ~ $true
@ c
@ ^ [X19: x_a,X20: state] :
( ( p @ X19 @ X20 )
& ~ ( b @ X20 ) ) )
@ bot_bo280939947le_a_o ) ),
file('/export/starexec/sandbox2/tmp/tmp.HFBb35Pla4/E---3.1_1481958.p',conj_0) ).
thf(fact_4_constant,axiom,
! [X14: hoare_669141180iple_a > $o,X15: x_a > state > $o,X16: com,X17: x_a > state > $o,X18: $o] :
( ( X18
=> ( hoare_2128652938rivs_a @ X14 @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ X15 @ X16 @ X17 ) @ bot_bo280939947le_a_o ) ) )
=> ( hoare_2128652938rivs_a @ X14
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [X19: x_a,X20: state] :
( ( X15 @ X19 @ X20 )
& X18 )
@ X16
@ X17 )
@ bot_bo280939947le_a_o ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HFBb35Pla4/E---3.1_1481958.p',fact_4_constant) ).
thf(fact_3_hoare__derivs_Oinsert,axiom,
! [X11: hoare_669141180iple_a > $o,X12: hoare_669141180iple_a > $o,X13: hoare_669141180iple_a] :
( ( hoare_2128652938rivs_a @ X12 @ ( insert175534902iple_a @ X13 @ bot_bo280939947le_a_o ) )
=> ( ( hoare_2128652938rivs_a @ X12 @ X11 )
=> ( hoare_2128652938rivs_a @ X12 @ ( insert175534902iple_a @ X13 @ X11 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HFBb35Pla4/E---3.1_1481958.p',fact_3_hoare__derivs_Oinsert) ).
thf(fact_0_empty,axiom,
! [X1: hoare_669141180iple_a > $o] : ( hoare_2128652938rivs_a @ X1 @ bot_bo280939947le_a_o ),
file('/export/starexec/sandbox2/tmp/tmp.HFBb35Pla4/E---3.1_1481958.p',fact_0_empty) ).
thf(c_0_4,negated_conjecture,
~ ( hoare_2128652938rivs_a @ g
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [X19: x_a,X20: state] : ~ $true
@ c
@ ^ [X19: x_a,X20: state] :
( ( p @ X19 @ X20 )
& ~ ( b @ X20 ) ) )
@ bot_bo280939947le_a_o ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_5,plain,
! [X14: hoare_669141180iple_a > $o,X15: x_a > state > $o,X16: com,X17: x_a > state > $o,X18: $o] :
( ( X18
=> ( hoare_2128652938rivs_a @ X14 @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ X15 @ X16 @ X17 ) @ bot_bo280939947le_a_o ) ) )
=> ( hoare_2128652938rivs_a @ X14
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [Z0: x_a,Z1: state] :
( ( X15 @ Z0 @ Z1 )
& X18 )
@ X16
@ X17 )
@ bot_bo280939947le_a_o ) ) ),
inference(fof_simplification,[status(thm)],[fact_4_constant]) ).
thf(c_0_6,negated_conjecture,
~ ( hoare_2128652938rivs_a @ g
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [Z0: x_a,Z1: state] : ~ $true
@ c
@ ^ [Z0: x_a,Z1: state] :
( ( p @ Z0 @ Z1 )
& ~ ( b @ Z1 ) ) )
@ bot_bo280939947le_a_o ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_4])]) ).
thf(c_0_7,plain,
! [X353: hoare_669141180iple_a > $o,X354: x_a > state > $o,X355: com,X356: x_a > state > $o,X357: $o] :
( ( X357
| ( hoare_2128652938rivs_a @ X353
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [Z0: x_a,Z1: state] :
( ( X354 @ Z0 @ Z1 )
& X357 )
@ X355
@ X356 )
@ bot_bo280939947le_a_o ) ) )
& ( ~ ( hoare_2128652938rivs_a @ X353 @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ X354 @ X355 @ X356 ) @ bot_bo280939947le_a_o ) )
| ( hoare_2128652938rivs_a @ X353
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [Z0: x_a,Z1: state] :
( ( X354 @ Z0 @ Z1 )
& X357 )
@ X355
@ X356 )
@ bot_bo280939947le_a_o ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
thf(c_0_8,negated_conjecture,
~ ( hoare_2128652938rivs_a @ g
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [Z0: x_a,Z1: state] : ~ $true
@ c
@ ^ [Z0: x_a,Z1: state] :
( ( p @ Z0 @ Z1 )
& ~ ( b @ Z1 ) ) )
@ bot_bo280939947le_a_o ) ),
inference(fof_nnf,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
! [X326: hoare_669141180iple_a > $o,X327: hoare_669141180iple_a > $o,X328: hoare_669141180iple_a] :
( ~ ( hoare_2128652938rivs_a @ X327 @ ( insert175534902iple_a @ X328 @ bot_bo280939947le_a_o ) )
| ~ ( hoare_2128652938rivs_a @ X327 @ X326 )
| ( hoare_2128652938rivs_a @ X327 @ ( insert175534902iple_a @ X328 @ X326 ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_3_hoare__derivs_Oinsert])])]) ).
thf(c_0_10,plain,
! [X3: com,X2: x_a > state > $o,X1: hoare_669141180iple_a > $o,X4: x_a > state > $o] :
( hoare_2128652938rivs_a @ X1
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [Z0: x_a,Z1: state] :
( ( X2 @ Z0 @ Z1 )
& ~ $true )
@ X3
@ X4 )
@ bot_bo280939947le_a_o ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_7])])]) ).
thf(c_0_11,negated_conjecture,
~ ( hoare_2128652938rivs_a @ g
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [Z0: x_a,Z1: state] : ~ $true
@ c
@ ^ [Z0: x_a,Z1: state] :
( ( p @ Z0 @ Z1 )
& ~ ( b @ Z1 ) ) )
@ bot_bo280939947le_a_o ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,plain,
! [X1: hoare_669141180iple_a > $o,X13: hoare_669141180iple_a,X8: hoare_669141180iple_a > $o] :
( ( hoare_2128652938rivs_a @ X1 @ ( insert175534902iple_a @ X13 @ X8 ) )
| ~ ( hoare_2128652938rivs_a @ X1 @ ( insert175534902iple_a @ X13 @ bot_bo280939947le_a_o ) )
| ~ ( hoare_2128652938rivs_a @ X1 @ X8 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,plain,
! [X3: com,X1: hoare_669141180iple_a > $o,X2: x_a > state > $o] :
( hoare_2128652938rivs_a @ X1
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [Z0: x_a,Z1: state] : ~ $true
@ X3
@ X2 )
@ bot_bo280939947le_a_o ) ),
inference(cn,[status(thm)],[c_0_10]) ).
thf(c_0_14,plain,
! [X322: hoare_669141180iple_a > $o] : ( hoare_2128652938rivs_a @ X322 @ bot_bo280939947le_a_o ),
inference(variable_rename,[status(thm)],[fact_0_empty]) ).
thf(c_0_15,negated_conjecture,
~ ( hoare_2128652938rivs_a @ g
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [Z0: x_a,Z1: state] : ~ $true
@ c
@ ^ [Z0: x_a,Z1: state] :
( ( p @ Z0 @ Z1 )
& ~ ( b @ Z1 ) ) )
@ bot_bo280939947le_a_o ) ),
inference(cn,[status(thm)],[c_0_11]) ).
thf(c_0_16,plain,
! [X3: com,X2: x_a > state > $o,X1: hoare_669141180iple_a > $o,X8: hoare_669141180iple_a > $o] :
( ( hoare_2128652938rivs_a @ X1
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [Z0: x_a,Z1: state] : ~ $true
@ X3
@ X2 )
@ X8 ) )
| ~ ( hoare_2128652938rivs_a @ X1 @ X8 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_17,plain,
! [X1: hoare_669141180iple_a > $o] : ( hoare_2128652938rivs_a @ X1 @ bot_bo280939947le_a_o ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW470^1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n004.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:04:51 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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.HFBb35Pla4/E---3.1_1481958.p
% 0.21/0.27 % Version: 3.5.1-ho
% 0.21/0.27 % Preprocessing class: HSLSSMSSSSLCHSA.
% 0.21/0.27 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.27 % Starting sh2 with 1200s (4) cores
% 0.21/0.27 % Starting full_lambda_3 with 300s (1) cores
% 0.21/0.27 % Starting ehoh_best7_lambda with 300s (1) cores
% 0.21/0.27 % Starting post_as_ho9 with 300s (1) cores
% 0.21/0.27 % Starting almost_fo_4 with 300s (1) cores
% 0.21/0.27 % post_as_ho9 with pid 1481974 completed with status 0
% 0.21/0.27 % Result found by post_as_ho9
% 0.21/0.27 % Preprocessing class: HSLSSMSSSSLCHSA.
% 0.21/0.27 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.27 % Starting sh2 with 1200s (4) cores
% 0.21/0.27 % Starting full_lambda_3 with 300s (1) cores
% 0.21/0.27 % Starting ehoh_best7_lambda with 300s (1) cores
% 0.21/0.27 % Starting post_as_ho9 with 300s (1) cores
% 0.21/0.27 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,,true,1,0,2,20000,1.0,true))
% 0.21/0.27 % SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
% 0.21/0.27 % Search class: HGUSM-FFMF33-DHSFFSBN
% 0.21/0.27 % partial match(3): HGUSM-FFMF32-SHSFMSBN
% 0.21/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.27 % SubtermCWHack with pid 1481977 completed with status 0
% 0.21/0.27 % Result found by SubtermCWHack
% 0.21/0.27 % Preprocessing class: HSLSSMSSSSLCHSA.
% 0.21/0.27 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.27 % Starting sh2 with 1200s (4) cores
% 0.21/0.27 % Starting full_lambda_3 with 300s (1) cores
% 0.21/0.27 % Starting ehoh_best7_lambda with 300s (1) cores
% 0.21/0.27 % Starting post_as_ho9 with 300s (1) cores
% 0.21/0.27 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,,true,1,0,2,20000,1.0,true))
% 0.21/0.27 % SinE strategy is GSinE(CountFormulas,,true,1,0,2,20000,1.0,true)
% 0.21/0.27 % Search class: HGUSM-FFMF33-DHSFFSBN
% 0.21/0.27 % partial match(3): HGUSM-FFMF32-SHSFMSBN
% 0.21/0.27 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.27 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.27 % Preprocessing time : 0.001 s
% 0.21/0.27
% 0.21/0.27 % Proof found!
% 0.21/0.27 % SZS status Theorem
% 0.21/0.27 % SZS output start CNFRefutation
% See solution above
% 0.21/0.27 % Parsed axioms : 125
% 0.21/0.27 % Removed by relevancy pruning/SinE : 106
% 0.21/0.27 % Initial clauses : 37
% 0.21/0.27 % Removed in clause preprocessing : 2
% 0.21/0.27 % Initial clauses in saturation : 35
% 0.21/0.27 % Processed clauses : 99
% 0.21/0.27 % ...of these trivial : 10
% 0.21/0.27 % ...subsumed : 30
% 0.21/0.27 % ...remaining for further processing : 59
% 0.21/0.27 % Other redundant clauses eliminated : 13
% 0.21/0.27 % Clauses deleted for lack of memory : 0
% 0.21/0.27 % Backward-subsumed : 0
% 0.21/0.27 % Backward-rewritten : 0
% 0.21/0.27 % Generated clauses : 266
% 0.21/0.27 % ...of the previous two non-redundant : 141
% 0.21/0.27 % ...aggressively subsumed : 0
% 0.21/0.27 % Contextual simplify-reflections : 0
% 0.21/0.27 % Paramodulations : 219
% 0.21/0.27 % Factorizations : 0
% 0.21/0.27 % NegExts : 0
% 0.21/0.27 % Equation resolutions : 21
% 0.21/0.27 % Disequality decompositions : 0
% 0.21/0.27 % Total rewrite steps : 114
% 0.21/0.27 % ...of those cached : 77
% 0.21/0.27 % Propositional unsat checks : 0
% 0.21/0.27 % Propositional check models : 0
% 0.21/0.27 % Propositional check unsatisfiable : 0
% 0.21/0.27 % Propositional clauses : 0
% 0.21/0.27 % Propositional clauses after purity: 0
% 0.21/0.27 % Propositional unsat core size : 0
% 0.21/0.27 % Propositional preprocessing time : 0.000
% 0.21/0.27 % Propositional encoding time : 0.000
% 0.21/0.27 % Propositional solver time : 0.000
% 0.21/0.27 % Success case prop preproc time : 0.000
% 0.21/0.27 % Success case prop encoding time : 0.000
% 0.21/0.27 % Success case prop solver time : 0.000
% 0.21/0.27 % Current number of processed clauses : 51
% 0.21/0.27 % Positive orientable unit clauses : 15
% 0.21/0.27 % Positive unorientable unit clauses: 1
% 0.21/0.27 % Negative unit clauses : 2
% 0.21/0.27 % Non-unit-clauses : 33
% 0.21/0.27 % Current number of unprocessed clauses: 77
% 0.21/0.27 % ...number of literals in the above : 167
% 0.21/0.27 % Current number of archived formulas : 0
% 0.21/0.27 % Current number of archived clauses : 6
% 0.21/0.27 % Clause-clause subsumption calls (NU) : 176
% 0.21/0.27 % Rec. Clause-clause subsumption calls : 170
% 0.21/0.27 % Non-unit clause-clause subsumptions : 24
% 0.21/0.27 % Unit Clause-clause subsumption calls : 4
% 0.21/0.27 % Rewrite failures with RHS unbound : 0
% 0.21/0.27 % BW rewrite match attempts : 27
% 0.21/0.27 % BW rewrite match successes : 2
% 0.21/0.27 % Condensation attempts : 0
% 0.21/0.27 % Condensation successes : 0
% 0.21/0.27 % Termbank termtop insertions : 8500
% 0.21/0.27 % Search garbage collected termcells : 1897
% 0.21/0.27
% 0.21/0.27 % -------------------------------------------------
% 0.21/0.27 % User time : 0.011 s
% 0.21/0.27 % System time : 0.002 s
% 0.21/0.27 % Total time : 0.012 s
% 0.21/0.27 % Maximum resident set size: 4168 pages
% 0.21/0.27
% 0.21/0.27 % -------------------------------------------------
% 0.21/0.27 % User time : 0.015 s
% 0.21/0.27 % System time : 0.008 s
% 0.21/0.27 % Total time : 0.023 s
% 0.21/0.27 % Maximum resident set size: 5120 pages
% 0.21/0.27 % E exiting
%------------------------------------------------------------------------------