%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SYO035^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:43:38 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 20 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 48 ( 6 ~; 2 |; 2 &; 28 @)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 20 ^; 15 !; 0 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
leibeq1: $i > $i > $o ).
thf(decl_24,type,
leibeq2: ( $i > $o ) > ( $i > $o ) > $o ).
thf(decl_25,type,
esk1_0: $i ).
thf(decl_26,type,
esk2_0: $i ).
thf(decl_27,type,
epred1_0: $i > $o ).
thf(conj,conjecture,
! [X1: $i,X2: $i] :
( ( leibeq2
@ ^ [X7: $i] : ( X7 = X1 )
@ ^ [X7: $i] : ( X7 = X2 ) )
=> ( leibeq1 @ X1 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.AHLx4kyi7Q/E---3.1_1247487.p',conj) ).
thf(leibeq1,axiom,
( leibeq1
= ( ^ [X1: $i,X2: $i] :
! [X3: $i > $o] :
( ( X3 @ X1 )
=> ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.AHLx4kyi7Q/E---3.1_1247487.p',leibeq1) ).
thf(leibeq2,axiom,
( leibeq2
= ( ^ [X4: $i > $o,X5: $i > $o] :
! [X6: ( $i > $o ) > $o] :
( ( X6 @ X4 )
=> ( X6 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.AHLx4kyi7Q/E---3.1_1247487.p',leibeq2) ).
thf(c_0_3,negated_conjecture,
~ ! [X1: $i,X2: $i] :
( ( leibeq2
@ ^ [X7: $i] : ( X7 = X1 )
@ ^ [X7: $i] : ( X7 = X2 ) )
=> ( leibeq1 @ X1 @ X2 ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_4,plain,
( leibeq1
= ( ^ [Z0: $i,Z1: $i] :
! [X3: $i > $o] :
( ( X3 @ Z0 )
=> ( X3 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[leibeq1]) ).
thf(c_0_5,plain,
( leibeq2
= ( ^ [Z0: $i > $o,Z1: $i > $o] :
! [X6: ( $i > $o ) > $o] :
( ( X6 @ Z0 )
=> ( X6 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[leibeq2]) ).
thf(c_0_6,negated_conjecture,
~ ! [X1: $i,X2: $i] :
( ! [X10: ( $i > $o ) > $o] :
( ( X10
@ ^ [Z0: $i] : ( Z0 = X1 ) )
=> ( X10
@ ^ [Z0: $i] : ( Z0 = X2 ) ) )
=> ! [X11: $i > $o] :
( ( X11 @ X1 )
=> ( X11 @ X2 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_3]),c_0_4]),c_0_5]) ).
thf(c_0_7,negated_conjecture,
! [X14: ( $i > $o ) > $o] :
( ( ~ ( X14
@ ^ [Z0: $i] : ( Z0 = esk1_0 ) )
| ( X14
@ ^ [Z0: $i] : ( Z0 = esk2_0 ) ) )
& ( epred1_0 @ esk1_0 )
& ~ ( epred1_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_6])])])])]) ).
thf(c_0_8,negated_conjecture,
! [X6: ( $i > $o ) > $o] :
( ( X6
@ ^ [Z0: $i] : ( Z0 = esk2_0 ) )
| ~ ( X6
@ ^ [Z0: $i] : ( Z0 = esk1_0 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,negated_conjecture,
( ( ^ [Z0: $i] : ( Z0 = esk1_0 ) )
= ( ^ [Z0: $i] : ( Z0 = esk2_0 ) ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_8]) ).
thf(c_0_10,negated_conjecture,
! [X16: $i] :
( ( X16 = esk1_0 )
<=> ( X16 = esk2_0 ) ),
inference(arg_cong,[status(thm)],[c_0_9]) ).
thf(c_0_11,negated_conjecture,
epred1_0 @ esk1_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,negated_conjecture,
esk1_0 = esk2_0,
inference(er,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_10])]) ).
thf(c_0_13,negated_conjecture,
~ ( epred1_0 @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_14,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO035^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n020.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 16:24:19 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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.AHLx4kyi7Q/E---3.1_1247487.p
% 0.08/0.25 % Version: 3.5.1-ho
% 0.08/0.25 % Preprocessing class: HSSSSMSSSLMNHSN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.08/0.25 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.08/0.25 % Starting sh2l with 300s (1) cores
% 0.08/0.25 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.08/0.25 % ho_unfolding_6 with pid 1247519 completed with status 0
% 0.08/0.25 % Result found by ho_unfolding_6
% 0.08/0.25 % Preprocessing class: HSSSSMSSSLMNHSN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.25 % No SInE strategy applied
% 0.08/0.25 % Search class: HHUNF-FFSF00-SHSFMSBN
% 0.08/0.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.25 % Starting SubtermCWHack with 136s (1) cores
% 0.08/0.25 % Starting ho_unfolding_6 with 151s (1) cores
% 0.08/0.25 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.08/0.25 % Starting sh5l with 136s (1) cores
% 0.08/0.25 % Starting new_bool_3 with 136s (1) cores
% 0.08/0.25 % ho_unfolding_6 with pid 1247527 completed with status 0
% 0.08/0.25 % Result found by ho_unfolding_6
% 0.08/0.25 % Preprocessing class: HSSSSMSSSLMNHSN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.08/0.25 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.25 % No SInE strategy applied
% 0.08/0.25 % Search class: HHUNF-FFSF00-SHSFMSBN
% 0.08/0.25 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.25 % Starting SubtermCWHack with 136s (1) cores
% 0.08/0.25 % Starting ho_unfolding_6 with 151s (1) cores
% 0.08/0.25 % Preprocessing time : 0.001 s
% 0.08/0.25
% 0.08/0.25 % Proof found!
% 0.08/0.25 % SZS status Theorem
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25 % Parsed axioms : 5
% 0.08/0.25 % Removed by relevancy pruning/SinE : 0
% 0.08/0.25 % Initial clauses : 5
% 0.08/0.25 % Removed in clause preprocessing : 2
% 0.08/0.25 % Initial clauses in saturation : 3
% 0.08/0.25 % Processed clauses : 7
% 0.08/0.25 % ...of these trivial : 1
% 0.08/0.25 % ...subsumed : 0
% 0.08/0.25 % ...remaining for further processing : 6
% 0.08/0.25 % Other redundant clauses eliminated : 2
% 0.08/0.25 % Clauses deleted for lack of memory : 0
% 0.08/0.25 % Backward-subsumed : 0
% 0.08/0.25 % Backward-rewritten : 2
% 0.08/0.25 % Generated clauses : 7
% 0.08/0.25 % ...of the previous two non-redundant : 5
% 0.08/0.25 % ...aggressively subsumed : 0
% 0.08/0.25 % Contextual simplify-reflections : 0
% 0.08/0.25 % Paramodulations : 0
% 0.08/0.25 % Factorizations : 0
% 0.08/0.25 % NegExts : 0
% 0.08/0.25 % Equation resolutions : 2
% 0.08/0.25 % Disequality decompositions : 0
% 0.08/0.25 % Total rewrite steps : 3
% 0.08/0.25 % ...of those cached : 1
% 0.08/0.25 % Propositional unsat checks : 0
% 0.08/0.25 % Propositional check models : 0
% 0.08/0.25 % Propositional check unsatisfiable : 0
% 0.08/0.25 % Propositional clauses : 0
% 0.08/0.25 % Propositional clauses after purity: 0
% 0.08/0.25 % Propositional unsat core size : 0
% 0.08/0.25 % Propositional preprocessing time : 0.000
% 0.08/0.25 % Propositional encoding time : 0.000
% 0.08/0.25 % Propositional solver time : 0.000
% 0.08/0.25 % Success case prop preproc time : 0.000
% 0.08/0.25 % Success case prop encoding time : 0.000
% 0.08/0.25 % Success case prop solver time : 0.000
% 0.08/0.25 % Current number of processed clauses : 3
% 0.08/0.25 % Positive orientable unit clauses : 2
% 0.08/0.25 % Positive unorientable unit clauses: 0
% 0.08/0.25 % Negative unit clauses : 1
% 0.08/0.25 % Non-unit-clauses : 0
% 0.08/0.25 % Current number of unprocessed clauses: 1
% 0.08/0.25 % ...number of literals in the above : 1
% 0.08/0.25 % Current number of archived formulas : 0
% 0.08/0.25 % Current number of archived clauses : 3
% 0.08/0.25 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.25 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.25 % Non-unit clause-clause subsumptions : 0
% 0.08/0.25 % Unit Clause-clause subsumption calls : 0
% 0.08/0.25 % Rewrite failures with RHS unbound : 0
% 0.08/0.25 % BW rewrite match attempts : 2
% 0.08/0.25 % BW rewrite match successes : 2
% 0.08/0.25 % Condensation attempts : 7
% 0.08/0.25 % Condensation successes : 0
% 0.08/0.25 % Termbank termtop insertions : 488
% 0.08/0.25 % Search garbage collected termcells : 138
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.003 s
% 0.08/0.25 % System time : 0.002 s
% 0.08/0.25 % Total time : 0.005 s
% 0.08/0.25 % Maximum resident set size: 3636 pages
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.008 s
% 0.08/0.25 % System time : 0.008 s
% 0.08/0.25 % Total time : 0.016 s
% 0.08/0.25 % Maximum resident set size: 4864 pages
% 0.08/0.25 % E exiting
%------------------------------------------------------------------------------