%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG250^3 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 07:44:44 AM UTC 2026
% Result : Theorem 0.31s 0.43s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 4 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 143 ( 10 ~; 5 |; 4 &; 101 @)
% ( 7 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 41 ( 8 ^; 33 !; 0 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
term: $tType ).
thf(decl_sort2,type,
subst: $tType ).
thf(decl_26,type,
sub: term > subst > term ).
thf(decl_29,type,
push: term > subst > subst ).
thf(decl_31,type,
var: term > $o ).
thf(decl_70,type,
pushprop_lem3v2_lthm: $o ).
thf(decl_133,type,
pushprop_lem3v2: $o ).
thf(decl_142,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(decl_145,type,
epred1_0: term > $o ).
thf(decl_146,type,
epred2_0: term > $o ).
thf(decl_147,type,
esk1_0: term ).
thf(decl_148,type,
esk2_0: subst ).
thf(decl_149,type,
esk3_0: term ).
thf(pushprop_p_and_p_prime,axiom,
( pushprop_p_and_p_prime
= ( ^ [X1: term,X3: subst,X6: term > $o,X9: term > $o] :
! [X10: term] :
( ( X9 @ X10 )
<=> ( X6 @ ( sub @ X10 @ ( push @ X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UqPjh4Fs0D/E---3.1_1611175.p',pushprop_p_and_p_prime) ).
thf(pushprop_lem3v2,axiom,
( pushprop_lem3v2
<=> ! [X6: term > $o,X9: term > $o,X1: term,X3: subst] :
( ( pushprop_p_and_p_prime @ X1 @ X3 @ X6 @ X9 )
=> ( ! [X2: term] :
( ( var @ X2 )
=> ( X9 @ X2 ) )
=> ! [X2: term] :
( ( var @ X2 )
=> ( X6 @ ( sub @ X2 @ ( push @ X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UqPjh4Fs0D/E---3.1_1611175.p',pushprop_lem3v2) ).
thf(thm,conjecture,
pushprop_lem3v2_lthm,
file('/export/starexec/sandbox2/tmp/tmp.UqPjh4Fs0D/E---3.1_1611175.p',thm) ).
thf(pushprop_lem3v2_lthm,axiom,
( pushprop_lem3v2_lthm
<=> pushprop_lem3v2 ),
file('/export/starexec/sandbox2/tmp/tmp.UqPjh4Fs0D/E---3.1_1611175.p',pushprop_lem3v2_lthm) ).
thf(c_0_4,plain,
( pushprop_p_and_p_prime
= ( ^ [Z0: term,Z1: subst,Z2: term > $o,Z3: term > $o] :
! [X10: term] :
( ( Z3 @ X10 )
<=> ( Z2 @ ( sub @ X10 @ ( push @ Z0 @ Z1 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[pushprop_p_and_p_prime]) ).
thf(c_0_5,axiom,
( pushprop_lem3v2
= ( ! [X6: term > $o,X9: term > $o,X1: term,X3: subst] :
( ! [X3225: term] :
( ( X9 @ X3225 )
<=> ( X6 @ ( sub @ X3225 @ ( push @ X1 @ X3 ) ) ) )
=> ( ! [X2: term] :
( ( var @ X2 )
=> ( X9 @ X2 ) )
=> ! [X2: term] :
( ( var @ X2 )
=> ( X6 @ ( sub @ X2 @ ( push @ X1 @ X3 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[pushprop_lem3v2,c_0_4]) ).
thf(c_0_6,negated_conjecture,
~ pushprop_lem3v2_lthm,
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_7,axiom,
( pushprop_lem3v2_lthm
= ( ! [X1211: term > $o,X1212: term > $o,X1213: term,X1214: subst] :
( ! [X1217: term] :
( ( X1212 @ X1217 )
<=> ( X1211 @ ( sub @ X1217 @ ( push @ X1213 @ X1214 ) ) ) )
=> ( ! [X1215: term] :
( ( var @ X1215 )
=> ( X1212 @ X1215 ) )
=> ! [X1216: term] :
( ( var @ X1216 )
=> ( X1211 @ ( sub @ X1216 @ ( push @ X1213 @ X1214 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[pushprop_lem3v2_lthm,c_0_4]),c_0_5]) ).
thf(c_0_8,negated_conjecture,
~ ! [X3373: term > $o,X3374: term > $o,X3375: term,X3376: subst] :
( ! [X3377: term] :
( ( X3374 @ X3377 )
<=> ( X3373 @ ( sub @ X3377 @ ( push @ X3375 @ X3376 ) ) ) )
=> ( ! [X3378: term] :
( ( var @ X3378 )
=> ( X3374 @ X3378 ) )
=> ! [X3379: term] :
( ( var @ X3379 )
=> ( X3373 @ ( sub @ X3379 @ ( push @ X3375 @ X3376 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X3396: term,X3397: term] :
( ( ~ ( epred2_0 @ X3396 )
| ( epred1_0 @ ( sub @ X3396 @ ( push @ esk1_0 @ esk2_0 ) ) ) )
& ( ~ ( epred1_0 @ ( sub @ X3396 @ ( push @ esk1_0 @ esk2_0 ) ) )
| ( epred2_0 @ X3396 ) )
& ( ~ ( var @ X3397 )
| ( epred2_0 @ X3397 ) )
& ( var @ esk3_0 )
& ~ ( epred1_0 @ ( sub @ esk3_0 @ ( push @ esk1_0 @ esk2_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])])])])]) ).
thf(c_0_10,negated_conjecture,
~ ( epred1_0 @ ( sub @ esk3_0 @ ( push @ esk1_0 @ esk2_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ ( sub @ X1 @ ( push @ esk1_0 @ esk2_0 ) ) )
| ~ ( epred2_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X1: term] :
( ( epred2_0 @ X1 )
| ~ ( var @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,negated_conjecture,
var @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,negated_conjecture,
~ ( epred2_0 @ esk3_0 ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_15,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG250^3 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 % Computer : n002.cluster.edu
% 0.08/0.23 % Model : x86_64 x86_64
% 0.08/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.23 % Memory : 8046.5625MB
% 0.08/0.23 % OS : Linux 6.8.0-71-generic
% 0.08/0.23 % CPULimit : 300
% 0.08/0.23 % WCLimit : 300
% 0.08/0.23 % DateTime : Tue Sep 29 17:34:52 UTC 2026
% 0.08/0.23 % CPUTime :
% 0.08/0.23 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.30 Running higher-order theorem proving
% 0.24/0.33 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.UqPjh4Fs0D/E---3.1_1611175.p
% 0.31/0.43 % Version: 3.5.1-ho
% 0.31/0.43 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.31/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/0.43 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.31/0.43 % Starting post_as_ho1 with 300s (1) cores
% 0.31/0.43 % Starting post_as_ho5 with 300s (1) cores
% 0.31/0.43 % Starting post_as_ho10 with 300s (1) cores
% 0.31/0.43 % new_ho_10_cnf2 with pid 1611188 completed with status 0
% 0.31/0.43 % Result found by new_ho_10_cnf2
% 0.31/0.43 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.31/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/0.43 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.31/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.31/0.43 % No SInE strategy applied
% 0.31/0.43 % Search class: HHUSS-FFSF32-SHFMMFNN
% 0.31/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.31/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.31/0.43 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.31/0.43 % Starting sh5l with 136s (1) cores
% 0.31/0.43 % Starting new_bool_1 with 136s (1) cores
% 0.31/0.43 % Starting new_bool_2 with 136s (1) cores
% 0.31/0.43 % new_bool_2 with pid 1611208 completed with status 0
% 0.31/0.43 % Result found by new_bool_2
% 0.31/0.43 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.31/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/0.43 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.31/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.31/0.43 % No SInE strategy applied
% 0.31/0.43 % Search class: HHUSS-FFSF32-SHFMMFNN
% 0.31/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.31/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.31/0.43 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.31/0.43 % Starting sh5l with 136s (1) cores
% 0.31/0.43 % Starting new_bool_1 with 136s (1) cores
% 0.31/0.43 % Starting new_bool_2 with 136s (1) cores
% 0.31/0.43 % Preprocessing time : 0.002 s
% 0.31/0.43 % Presaturation interreduction done
% 0.31/0.43
% 0.31/0.43 % Proof found!
% 0.31/0.43 % SZS status Theorem
% 0.31/0.43 % SZS output start CNFRefutation
% See solution above
% 0.31/0.43 % Parsed axioms : 238
% 0.31/0.43 % Removed by relevancy pruning/SinE : 0
% 0.31/0.43 % Initial clauses : 131
% 0.31/0.43 % Removed in clause preprocessing : 124
% 0.31/0.43 % Initial clauses in saturation : 7
% 0.31/0.43 % Processed clauses : 14
% 0.31/0.43 % ...of these trivial : 0
% 0.31/0.43 % ...subsumed : 0
% 0.31/0.43 % ...remaining for further processing : 13
% 0.31/0.43 % Other redundant clauses eliminated : 0
% 0.31/0.43 % Clauses deleted for lack of memory : 0
% 0.31/0.43 % Backward-subsumed : 0
% 0.31/0.43 % Backward-rewritten : 0
% 0.31/0.43 % Generated clauses : 3
% 0.31/0.43 % ...of the previous two non-redundant : 2
% 0.31/0.43 % ...aggressively subsumed : 0
% 0.31/0.43 % Contextual simplify-reflections : 0
% 0.31/0.43 % Paramodulations : 3
% 0.31/0.43 % Factorizations : 0
% 0.31/0.43 % NegExts : 0
% 0.31/0.43 % Equation resolutions : 0
% 0.31/0.43 % Disequality decompositions : 0
% 0.31/0.43 % Total rewrite steps : 0
% 0.31/0.43 % ...of those cached : 0
% 0.31/0.43 % Propositional unsat checks : 0
% 0.31/0.43 % Propositional check models : 0
% 0.31/0.43 % Propositional check unsatisfiable : 0
% 0.31/0.43 % Propositional clauses : 0
% 0.31/0.43 % Propositional clauses after purity: 0
% 0.31/0.43 % Propositional unsat core size : 0
% 0.31/0.43 % Propositional preprocessing time : 0.000
% 0.31/0.43 % Propositional encoding time : 0.000
% 0.31/0.43 % Propositional solver time : 0.000
% 0.31/0.43 % Success case prop preproc time : 0.000
% 0.31/0.43 % Success case prop encoding time : 0.000
% 0.31/0.43 % Success case prop solver time : 0.000
% 0.31/0.43 % Current number of processed clauses : 6
% 0.31/0.43 % Positive orientable unit clauses : 1
% 0.31/0.43 % Positive unorientable unit clauses: 0
% 0.31/0.43 % Negative unit clauses : 2
% 0.31/0.43 % Non-unit-clauses : 3
% 0.31/0.43 % Current number of unprocessed clauses: 2
% 0.31/0.43 % ...number of literals in the above : 2
% 0.31/0.43 % Current number of archived formulas : 0
% 0.31/0.43 % Current number of archived clauses : 7
% 0.31/0.43 % Clause-clause subsumption calls (NU) : 2
% 0.31/0.43 % Rec. Clause-clause subsumption calls : 2
% 0.31/0.43 % Non-unit clause-clause subsumptions : 0
% 0.31/0.43 % Unit Clause-clause subsumption calls : 4
% 0.31/0.43 % Rewrite failures with RHS unbound : 0
% 0.31/0.43 % BW rewrite match attempts : 0
% 0.31/0.43 % BW rewrite match successes : 0
% 0.31/0.43 % Condensation attempts : 0
% 0.31/0.43 % Condensation successes : 0
% 0.31/0.43 % Termbank termtop insertions : 26654
% 0.31/0.43 % Search garbage collected termcells : 1769
% 0.31/0.43
% 0.31/0.43 % -------------------------------------------------
% 0.31/0.43 % User time : 0.046 s
% 0.31/0.43 % System time : 0.012 s
% 0.31/0.43 % Total time : 0.058 s
% 0.31/0.43 % Maximum resident set size: 7564 pages
% 0.31/0.43
% 0.31/0.43 % -------------------------------------------------
% 0.31/0.43 % User time : 0.063 s
% 0.31/0.43 % System time : 0.028 s
% 0.31/0.43 % Total time : 0.090 s
% 0.31/0.43 % Maximum resident set size: 4608 pages
% 0.31/0.43 % E exiting
%------------------------------------------------------------------------------