%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYN056^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:41:00 AM UTC 2026
% Result : Theorem 0.10s 0.28s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 22 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 113 ( 0 equ; 0 cnn)
% Maximal formula atoms : 36 ( 5 avg)
% Number of connectives : 245 ( 42 ~; 45 |; 22 &; 112 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 5 con; 0-1 aty)
% Number of variables : 40 ( 0 ^; 32 !; 8 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
cR: $i > $o ).
thf(decl_24,type,
cP: $i > $o ).
thf(decl_25,type,
cS: $i > $o ).
thf(decl_26,type,
cQ: $i > $o ).
thf(decl_27,type,
esk1_0: $i ).
thf(decl_28,type,
esk2_0: $i ).
thf(decl_29,type,
esk3_0: $i ).
thf(decl_30,type,
esk4_0: $i ).
thf(cPELL26,conjecture,
( ( ( ? [X1: $i] : ( cP @ X1 )
=> ? [X1: $i] : ( cQ @ X1 ) )
& ( ? [X1: $i] : ( cQ @ X1 )
=> ? [X1: $i] : ( cP @ X1 ) )
& ! [X1: $i,X2: $i] :
( ( ( cP @ X1 )
& ( cQ @ X2 ) )
=> ( ( ( cR @ X1 )
=> ( cS @ X2 ) )
& ( ( cS @ X2 )
=> ( cR @ X1 ) ) ) ) )
=> ( ( ! [X1: $i] :
( ( cP @ X1 )
=> ( cR @ X1 ) )
=> ! [X1: $i] :
( ( cQ @ X1 )
=> ( cS @ X1 ) ) )
& ( ! [X1: $i] :
( ( cQ @ X1 )
=> ( cS @ X1 ) )
=> ! [X1: $i] :
( ( cP @ X1 )
=> ( cR @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.aIY1v1yTXN/E---3.1_923058.p',cPELL26) ).
thf(c_0_1,negated_conjecture,
~ ( ( ( ? [X1: $i] : ( cP @ X1 )
=> ? [X1: $i] : ( cQ @ X1 ) )
& ( ? [X1: $i] : ( cQ @ X1 )
=> ? [X1: $i] : ( cP @ X1 ) )
& ! [X1: $i,X2: $i] :
( ( ( cP @ X1 )
& ( cQ @ X2 ) )
=> ( ( ( cR @ X1 )
=> ( cS @ X2 ) )
& ( ( cS @ X2 )
=> ( cR @ X1 ) ) ) ) )
=> ( ( ! [X1: $i] :
( ( cP @ X1 )
=> ( cR @ X1 ) )
=> ! [X1: $i] :
( ( cQ @ X1 )
=> ( cS @ X1 ) ) )
& ( ! [X1: $i] :
( ( cQ @ X1 )
=> ( cS @ X1 ) )
=> ! [X1: $i] :
( ( cP @ X1 )
=> ( cR @ X1 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cPELL26]) ).
thf(c_0_2,negated_conjecture,
! [X13: $i,X15: $i,X17: $i,X18: $i,X19: $i,X21: $i] :
( ( ~ ( cP @ X13 )
| ( cQ @ esk1_0 ) )
& ( ~ ( cQ @ X15 )
| ( cP @ esk2_0 ) )
& ( ~ ( cR @ X17 )
| ( cS @ X18 )
| ~ ( cP @ X17 )
| ~ ( cQ @ X18 ) )
& ( ~ ( cS @ X18 )
| ( cR @ X17 )
| ~ ( cP @ X17 )
| ~ ( cQ @ X18 ) )
& ( ~ ( cQ @ X21 )
| ( cS @ X21 )
| ~ ( cP @ X19 )
| ( cR @ X19 ) )
& ( ( cP @ esk4_0 )
| ~ ( cP @ X19 )
| ( cR @ X19 ) )
& ( ~ ( cR @ esk4_0 )
| ~ ( cP @ X19 )
| ( cR @ X19 ) )
& ( ~ ( cQ @ X21 )
| ( cS @ X21 )
| ( cQ @ esk3_0 ) )
& ( ( cP @ esk4_0 )
| ( cQ @ esk3_0 ) )
& ( ~ ( cR @ esk4_0 )
| ( cQ @ esk3_0 ) )
& ( ~ ( cQ @ X21 )
| ( cS @ X21 )
| ~ ( cS @ esk3_0 ) )
& ( ( cP @ esk4_0 )
| ~ ( cS @ esk3_0 ) )
& ( ~ ( cR @ esk4_0 )
| ~ ( cS @ esk3_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_1])])])])])]) ).
thf(c_0_3,negated_conjecture,
! [X1: $i] :
( ( cP @ esk2_0 )
| ~ ( cQ @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_4,negated_conjecture,
( ( cP @ esk4_0 )
| ( cQ @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_5,negated_conjecture,
! [X2: $i,X1: $i] :
( ( cR @ X2 )
| ~ ( cS @ X1 )
| ~ ( cP @ X2 )
| ~ ( cQ @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_6,negated_conjecture,
! [X1: $i,X2: $i] :
( ( cS @ X1 )
| ( cR @ X2 )
| ~ ( cQ @ X1 )
| ~ ( cP @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i] :
( ( cQ @ esk1_0 )
| ~ ( cP @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_8,negated_conjecture,
( ( cP @ esk4_0 )
| ( cP @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X2: $i] :
( ( cR @ X1 )
| ~ ( cP @ X1 )
| ~ ( cQ @ X2 ) ),
inference(csr,[status(thm)],[c_0_5,c_0_6]) ).
thf(c_0_10,negated_conjecture,
cQ @ esk1_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_7]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i] :
( ( cS @ X2 )
| ~ ( cR @ X1 )
| ~ ( cP @ X1 )
| ~ ( cQ @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i] :
( ( cR @ X1 )
| ~ ( cP @ X1 ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_13,negated_conjecture,
( ~ ( cR @ esk4_0 )
| ~ ( cS @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_14,negated_conjecture,
( ( cP @ esk4_0 )
| ~ ( cS @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_15,negated_conjecture,
! [X2: $i,X1: $i] :
( ( cS @ X1 )
| ~ ( cP @ X2 )
| ~ ( cQ @ X1 ) ),
inference(csr,[status(thm)],[c_0_11,c_0_12]) ).
thf(c_0_16,negated_conjecture,
cP @ esk2_0,
inference(spm,[status(thm)],[c_0_3,c_0_10]) ).
thf(c_0_17,negated_conjecture,
( ( cQ @ esk3_0 )
| ~ ( cR @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
thf(c_0_18,negated_conjecture,
~ ( cS @ esk3_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_12]),c_0_14]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i] :
( ( cS @ X1 )
| ~ ( cQ @ X1 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_20,negated_conjecture,
cQ @ esk3_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_12]),c_0_4]) ).
thf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN056^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 % Computer : n006.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 16:14:09 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.26 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.aIY1v1yTXN/E---3.1_923058.p
% 0.10/0.28 % Version: 3.5.1-ho
% 0.10/0.28 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.10/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.28 % Starting full_lambda_5 with 300s (1) cores
% 0.10/0.28 % Starting new_ho_10_unif with 300s (1) cores
% 0.10/0.28 % new_bool_1 with pid 923093 completed with status 0
% 0.10/0.28 % Result found by new_bool_1
% 0.10/0.28 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.10/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.28 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.28 % Search class: HGHNF-FFSF00-SFFFFFNN
% 0.10/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.28 % SubtermCWHack with pid 923098 completed with status 0
% 0.10/0.28 % Result found by SubtermCWHack
% 0.10/0.28 % Preprocessing class: HSMSSMSSSSSNFFN.
% 0.10/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.28 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.28 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.28 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.28 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.28 % Search class: HGHNF-FFSF00-SFFFFFNN
% 0.10/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.28 % Preprocessing time : 0.001 s
% 0.10/0.28
% 0.10/0.28 % Proof found!
% 0.10/0.28 % SZS status Theorem
% 0.10/0.28 % SZS output start CNFRefutation
% See solution above
% 0.10/0.28 % Parsed axioms : 5
% 0.10/0.28 % Removed by relevancy pruning/SinE : 4
% 0.10/0.28 % Initial clauses : 13
% 0.10/0.28 % Removed in clause preprocessing : 0
% 0.10/0.28 % Initial clauses in saturation : 13
% 0.10/0.28 % Processed clauses : 24
% 0.10/0.28 % ...of these trivial : 0
% 0.10/0.28 % ...subsumed : 0
% 0.10/0.28 % ...remaining for further processing : 24
% 0.10/0.28 % Other redundant clauses eliminated : 0
% 0.10/0.28 % Clauses deleted for lack of memory : 0
% 0.10/0.28 % Backward-subsumed : 12
% 0.10/0.28 % Backward-rewritten : 5
% 0.10/0.28 % Generated clauses : 19
% 0.10/0.28 % ...of the previous two non-redundant : 12
% 0.10/0.28 % ...aggressively subsumed : 0
% 0.10/0.28 % Contextual simplify-reflections : 6
% 0.10/0.28 % Paramodulations : 19
% 0.10/0.28 % Factorizations : 0
% 0.10/0.28 % NegExts : 0
% 0.10/0.28 % Equation resolutions : 0
% 0.10/0.28 % Disequality decompositions : 0
% 0.10/0.28 % Total rewrite steps : 6
% 0.10/0.28 % ...of those cached : 2
% 0.10/0.28 % Propositional unsat checks : 0
% 0.10/0.28 % Propositional check models : 0
% 0.10/0.28 % Propositional check unsatisfiable : 0
% 0.10/0.28 % Propositional clauses : 0
% 0.10/0.28 % Propositional clauses after purity: 0
% 0.10/0.28 % Propositional unsat core size : 0
% 0.10/0.28 % Propositional preprocessing time : 0.000
% 0.10/0.28 % Propositional encoding time : 0.000
% 0.10/0.28 % Propositional solver time : 0.000
% 0.10/0.28 % Success case prop preproc time : 0.000
% 0.10/0.28 % Success case prop encoding time : 0.000
% 0.10/0.28 % Success case prop solver time : 0.000
% 0.10/0.28 % Current number of processed clauses : 7
% 0.10/0.28 % Positive orientable unit clauses : 4
% 0.10/0.28 % Positive unorientable unit clauses: 0
% 0.10/0.28 % Negative unit clauses : 1
% 0.10/0.28 % Non-unit-clauses : 2
% 0.10/0.28 % Current number of unprocessed clauses: 1
% 0.10/0.28 % ...number of literals in the above : 3
% 0.10/0.28 % Current number of archived formulas : 0
% 0.10/0.28 % Current number of archived clauses : 17
% 0.10/0.28 % Clause-clause subsumption calls (NU) : 14
% 0.10/0.28 % Rec. Clause-clause subsumption calls : 14
% 0.10/0.28 % Non-unit clause-clause subsumptions : 11
% 0.10/0.28 % Unit Clause-clause subsumption calls : 10
% 0.10/0.28 % Rewrite failures with RHS unbound : 0
% 0.10/0.28 % BW rewrite match attempts : 4
% 0.10/0.28 % BW rewrite match successes : 4
% 0.10/0.28 % Condensation attempts : 0
% 0.10/0.28 % Condensation successes : 0
% 0.10/0.28 % Termbank termtop insertions : 1283
% 0.10/0.28 % Search garbage collected termcells : 325
% 0.10/0.28
% 0.10/0.28 % -------------------------------------------------
% 0.10/0.28 % User time : 0.005 s
% 0.10/0.28 % System time : 0.002 s
% 0.10/0.28 % Total time : 0.006 s
% 0.10/0.28 % Maximum resident set size: 3628 pages
% 0.10/0.28
% 0.10/0.28 % -------------------------------------------------
% 0.10/0.28 % User time : 0.007 s
% 0.10/0.28 % System time : 0.005 s
% 0.10/0.28 % Total time : 0.012 s
% 0.10/0.28 % Maximum resident set size: 4864 pages
% 0.10/0.28 % E exiting
%------------------------------------------------------------------------------