%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG249^3 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 0.34s 0.46s
% Output : CNFRefutation 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 56 ( 15 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 240 ( 10 ~; 6 |; 7 &; 182 @)
% ( 9 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 9 con; 0-4 aty)
% Number of variables : 70 ( 8 ^; 62 !; 0 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
term: $tType ).
thf(decl_sort2,type,
subst: $tType ).
thf(decl_26,type,
sub: term > subst > term ).
thf(decl_28,type,
sh: subst ).
thf(decl_29,type,
push: term > subst > subst ).
thf(decl_30,type,
comp: subst > subst > subst ).
thf(decl_31,type,
var: term > $o ).
thf(decl_81,type,
pushprop_lem2v2: $o ).
thf(decl_83,type,
axclos: $o ).
thf(decl_127,type,
pushprop_lem2v2_lthm: $o ).
thf(decl_137,type,
axshiftcons: $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/sandbox/tmp/tmp.bhwfBMOLXm/E---3.1_919537.p',pushprop_p_and_p_prime) ).
thf(pushprop_lem2v2,axiom,
( pushprop_lem2v2
<=> ! [X6: term > $o,X9: term > $o,X1: term,X3: subst] :
( ( pushprop_p_and_p_prime @ X1 @ X3 @ X6 @ X9 )
=> ( ! [X2: term] :
( ( var @ X2 )
=> ( X6 @ ( sub @ X2 @ X3 ) ) )
=> ! [X7: term] :
( ( var @ X7 )
=> ( ( X9 @ X7 )
=> ( X9 @ ( sub @ X7 @ sh ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bhwfBMOLXm/E---3.1_919537.p',pushprop_lem2v2) ).
thf(thm,conjecture,
pushprop_lem2v2_lthm,
file('/export/starexec/sandbox/tmp/tmp.bhwfBMOLXm/E---3.1_919537.p',thm) ).
thf(pushprop_lem2v2_lthm,axiom,
( pushprop_lem2v2_lthm
<=> ( axclos
=> ( axshiftcons
=> pushprop_lem2v2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bhwfBMOLXm/E---3.1_919537.p',pushprop_lem2v2_lthm) ).
thf(axclos,axiom,
( axclos
<=> ! [X1: term,X3: subst,X4: subst] :
( ( sub @ ( sub @ X1 @ X3 ) @ X4 )
= ( sub @ X1 @ ( comp @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.bhwfBMOLXm/E---3.1_919537.p',axclos) ).
thf(axshiftcons,axiom,
( axshiftcons
<=> ! [X1: term,X3: subst] :
( ( comp @ sh @ ( push @ X1 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.bhwfBMOLXm/E---3.1_919537.p',axshiftcons) ).
thf(c_0_6,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_7,axiom,
( pushprop_lem2v2
= ( ! [X6: term > $o,X9: term > $o,X1: term,X3: subst] :
( ! [X1716: term] :
( ( X9 @ X1716 )
<=> ( X6 @ ( sub @ X1716 @ ( push @ X1 @ X3 ) ) ) )
=> ( ! [X2: term] :
( ( var @ X2 )
=> ( X6 @ ( sub @ X2 @ X3 ) ) )
=> ! [X7: term] :
( ( var @ X7 )
=> ( ( X9 @ X7 )
=> ( X9 @ ( sub @ X7 @ sh ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[pushprop_lem2v2,c_0_6]) ).
thf(c_0_8,negated_conjecture,
~ pushprop_lem2v2_lthm,
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_9,axiom,
( pushprop_lem2v2_lthm
= ( ! [X3138: term,X3139: subst,X3140: subst] :
( ( sub @ ( sub @ X3138 @ X3139 ) @ X3140 )
= ( sub @ X3138 @ ( comp @ X3139 @ X3140 ) ) )
=> ( ! [X3141: term,X3142: subst] :
( ( comp @ sh @ ( push @ X3141 @ X3142 ) )
= X3142 )
=> ! [X3143: term > $o,X3144: term > $o,X3145: term,X3146: subst] :
( ! [X3147: term] :
( ( X3144 @ X3147 )
<=> ( X3143 @ ( sub @ X3147 @ ( push @ X3145 @ X3146 ) ) ) )
=> ( ! [X3148: term] :
( ( var @ X3148 )
=> ( X3143 @ ( sub @ X3148 @ X3146 ) ) )
=> ! [X3149: term] :
( ( var @ X3149 )
=> ( ( X3144 @ X3149 )
=> ( X3144 @ ( sub @ X3149 @ sh ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[pushprop_lem2v2_lthm,axclos]),axshiftcons]),c_0_7]) ).
thf(c_0_10,negated_conjecture,
~ ( ! [X3373: term,X3374: subst,X3375: subst] :
( ( sub @ ( sub @ X3373 @ X3374 ) @ X3375 )
= ( sub @ X3373 @ ( comp @ X3374 @ X3375 ) ) )
=> ( ! [X3376: term,X3377: subst] :
( ( comp @ sh @ ( push @ X3376 @ X3377 ) )
= X3377 )
=> ! [X3378: term > $o,X3379: term > $o,X3380: term,X3381: subst] :
( ! [X3382: term] :
( ( X3379 @ X3382 )
<=> ( X3378 @ ( sub @ X3382 @ ( push @ X3380 @ X3381 ) ) ) )
=> ( ! [X3383: term] :
( ( var @ X3383 )
=> ( X3378 @ ( sub @ X3383 @ X3381 ) ) )
=> ! [X3384: term] :
( ( var @ X3384 )
=> ( ( X3379 @ X3384 )
=> ( X3379 @ ( sub @ X3384 @ sh ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X3397: term,X3398: subst,X3399: subst,X3400: term,X3401: subst,X3406: term,X3407: term] :
( ( ( sub @ ( sub @ X3397 @ X3398 ) @ X3399 )
= ( sub @ X3397 @ ( comp @ X3398 @ X3399 ) ) )
& ( ( comp @ sh @ ( push @ X3400 @ X3401 ) )
= X3401 )
& ( ~ ( epred2_0 @ X3406 )
| ( epred1_0 @ ( sub @ X3406 @ ( push @ esk1_0 @ esk2_0 ) ) ) )
& ( ~ ( epred1_0 @ ( sub @ X3406 @ ( push @ esk1_0 @ esk2_0 ) ) )
| ( epred2_0 @ X3406 ) )
& ( ~ ( var @ X3407 )
| ( epred1_0 @ ( sub @ X3407 @ esk2_0 ) ) )
& ( var @ esk3_0 )
& ( epred2_0 @ esk3_0 )
& ~ ( epred2_0 @ ( sub @ esk3_0 @ sh ) ) ),
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_10])])])])]) ).
thf(c_0_12,negated_conjecture,
! [X1: term,X3: subst,X4: subst] :
( ( sub @ ( sub @ X1 @ X3 ) @ X4 )
= ( sub @ X1 @ ( comp @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_13,negated_conjecture,
! [X1: term,X3: subst] :
( ( comp @ sh @ ( push @ X1 @ X3 ) )
= X3 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X1: term] :
( ( epred2_0 @ X1 )
| ~ ( epred1_0 @ ( sub @ X1 @ ( push @ esk1_0 @ esk2_0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_15,negated_conjecture,
! [X1: term,X2: term,X3: subst] :
( ( sub @ ( sub @ X1 @ sh ) @ ( push @ X2 @ X3 ) )
= ( sub @ X1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_16,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ ( sub @ X1 @ esk2_0 ) )
| ~ ( var @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_17,negated_conjecture,
var @ esk3_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_18,negated_conjecture,
! [X1: term] :
( ( epred2_0 @ ( sub @ X1 @ sh ) )
| ~ ( epred1_0 @ ( sub @ X1 @ esk2_0 ) ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_19,negated_conjecture,
epred1_0 @ ( sub @ esk3_0 @ esk2_0 ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_20,negated_conjecture,
~ ( epred2_0 @ ( sub @ esk3_0 @ sh ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG249^3 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 % Computer : n026.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.25 % CPULimit : 300
% 0.11/0.25 % WCLimit : 300
% 0.11/0.25 % DateTime : Tue Sep 29 17:34:57 UTC 2026
% 0.11/0.25 % CPUTime :
% 0.11/0.25 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.32 Running higher-order theorem proving
% 0.34/0.38 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.bhwfBMOLXm/E---3.1_919537.p
% 0.34/0.46 % Version: 3.5.1-ho
% 0.34/0.46 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.34/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.34/0.46 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.34/0.46 % Starting post_as_ho1 with 300s (1) cores
% 0.34/0.46 % Starting post_as_ho5 with 300s (1) cores
% 0.34/0.46 % Starting post_as_ho10 with 300s (1) cores
% 0.34/0.46 % post_as_ho1 with pid 919551 completed with status 0
% 0.34/0.46 % Result found by post_as_ho1
% 0.34/0.46 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.34/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.34/0.46 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.34/0.46 % Starting post_as_ho1 with 300s (1) cores
% 0.34/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.34/0.46 % No SInE strategy applied
% 0.34/0.46 % Search class: HHUSM-FFSF32-SHFMMFNN
% 0.34/0.46 % partial match(1): HHUSS-FFSF32-SHFMMFNN
% 0.34/0.46 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.34/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.34/0.46 % SubtermCWHack with pid 919556 completed with status 0
% 0.34/0.46 % Result found by SubtermCWHack
% 0.34/0.46 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.34/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.34/0.46 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.34/0.46 % Starting post_as_ho1 with 300s (1) cores
% 0.34/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.34/0.46 % No SInE strategy applied
% 0.34/0.46 % Search class: HHUSM-FFSF32-SHFMMFNN
% 0.34/0.46 % partial match(1): HHUSS-FFSF32-SHFMMFNN
% 0.34/0.46 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.34/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.34/0.46 % Preprocessing time : 0.002 s
% 0.34/0.46
% 0.34/0.46 % Proof found!
% 0.34/0.46 % SZS status Theorem
% 0.34/0.46 % SZS output start CNFRefutation
% See solution above
% 0.34/0.46 % Parsed axioms : 238
% 0.34/0.46 % Removed by relevancy pruning/SinE : 0
% 0.34/0.46 % Initial clauses : 134
% 0.34/0.46 % Removed in clause preprocessing : 124
% 0.34/0.46 % Initial clauses in saturation : 10
% 0.34/0.46 % Processed clauses : 21
% 0.34/0.46 % ...of these trivial : 0
% 0.34/0.46 % ...subsumed : 6
% 0.34/0.46 % ...remaining for further processing : 15
% 0.34/0.46 % Other redundant clauses eliminated : 0
% 0.34/0.46 % Clauses deleted for lack of memory : 0
% 0.34/0.46 % Backward-subsumed : 0
% 0.34/0.46 % Backward-rewritten : 0
% 0.34/0.46 % Generated clauses : 15
% 0.34/0.46 % ...of the previous two non-redundant : 12
% 0.34/0.46 % ...aggressively subsumed : 0
% 0.34/0.46 % Contextual simplify-reflections : 0
% 0.34/0.46 % Paramodulations : 15
% 0.34/0.46 % Factorizations : 0
% 0.34/0.46 % NegExts : 0
% 0.34/0.46 % Equation resolutions : 0
% 0.34/0.46 % Disequality decompositions : 0
% 0.34/0.46 % Total rewrite steps : 0
% 0.34/0.46 % ...of those cached : 0
% 0.34/0.46 % Propositional unsat checks : 0
% 0.34/0.46 % Propositional check models : 0
% 0.34/0.46 % Propositional check unsatisfiable : 0
% 0.34/0.46 % Propositional clauses : 0
% 0.34/0.46 % Propositional clauses after purity: 0
% 0.34/0.46 % Propositional unsat core size : 0
% 0.34/0.46 % Propositional preprocessing time : 0.000
% 0.34/0.46 % Propositional encoding time : 0.000
% 0.34/0.46 % Propositional solver time : 0.000
% 0.34/0.46 % Success case prop preproc time : 0.000
% 0.34/0.46 % Success case prop encoding time : 0.000
% 0.34/0.46 % Success case prop solver time : 0.000
% 0.34/0.46 % Current number of processed clauses : 15
% 0.34/0.46 % Positive orientable unit clauses : 7
% 0.34/0.46 % Positive unorientable unit clauses: 2
% 0.34/0.46 % Negative unit clauses : 1
% 0.34/0.46 % Non-unit-clauses : 5
% 0.34/0.46 % Current number of unprocessed clauses: 1
% 0.34/0.46 % ...number of literals in the above : 1
% 0.34/0.46 % Current number of archived formulas : 0
% 0.34/0.46 % Current number of archived clauses : 0
% 0.34/0.46 % Clause-clause subsumption calls (NU) : 2
% 0.34/0.46 % Rec. Clause-clause subsumption calls : 2
% 0.34/0.46 % Non-unit clause-clause subsumptions : 0
% 0.34/0.46 % Unit Clause-clause subsumption calls : 3
% 0.34/0.46 % Rewrite failures with RHS unbound : 16
% 0.34/0.46 % BW rewrite match attempts : 2
% 0.34/0.46 % BW rewrite match successes : 2
% 0.34/0.46 % Condensation attempts : 0
% 0.34/0.46 % Condensation successes : 0
% 0.34/0.46 % Termbank termtop insertions : 26936
% 0.34/0.46 % Search garbage collected termcells : 1855
% 0.34/0.46
% 0.34/0.46 % -------------------------------------------------
% 0.34/0.46 % User time : 0.025 s
% 0.34/0.46 % System time : 0.015 s
% 0.34/0.46 % Total time : 0.040 s
% 0.34/0.46 % Maximum resident set size: 7820 pages
% 0.34/0.46
% 0.34/0.46 % -------------------------------------------------
% 0.34/0.46 % User time : 0.033 s
% 0.34/0.46 % System time : 0.024 s
% 0.34/0.46 % Total time : 0.056 s
% 0.34/0.46 % Maximum resident set size: 4864 pages
% 0.34/0.46 % E exiting
%------------------------------------------------------------------------------