%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : PUZ107^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 08:20:35 AM UTC 2026
% Result : Theorem 0.27s 0.31s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 98 ( 77 equ; 0 cnn)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 301 ( 35 ~; 20 |; 60 &; 172 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 56 ( 56 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 122 ( 20 ^; 70 !; 32 ?; 122 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
c1: $i ).
thf(decl_24,type,
cCKB_FIN: ( $i > $i > $o ) > $o ).
thf(decl_25,type,
cCKB_INF: ( $i > $i > $o ) > $o ).
thf(decl_26,type,
cCKB_INJ: ( $i > $i > $i > $i > $o ) > $o ).
thf(decl_27,type,
cCKB_XPL: ( $i > $i > $i > $i > $o ) > ( $i > $i > $o ) > $i > $i > $o ).
thf(decl_28,type,
epred1_0: $i > $i > $i > $i > $o ).
thf(decl_29,type,
esk1_0: $i ).
thf(decl_30,type,
esk2_0: $i ).
thf(decl_31,type,
esk3_2: $i > $i > $i ).
thf(decl_32,type,
esk4_2: $i > $i > $i ).
thf(cCKB_INF_def,axiom,
( cCKB_INF
= ( ^ [X8: $i > $i > $o] :
? [X1: $i > $i > $i > $i > $o,X9: $i,X10: $i] :
( ( cCKB_INJ @ X1 )
& ( cCKB_XPL @ X1 @ X8 @ X9 @ X10 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.D2W1kAj7uh/E---3.1_2837912.p',cCKB_INF_def) ).
thf(cCKB_INJ_def,axiom,
( cCKB_INJ
= ( ^ [X1: $i > $i > $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( ( ( X1 @ X2 @ X3 @ X6 @ X7 )
& ( X1 @ X4 @ X5 @ X6 @ X7 ) )
=> ( ( X2 = X4 )
& ( X3 = X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.D2W1kAj7uh/E---3.1_2837912.p',cCKB_INJ_def) ).
thf(cCKB_XPL_def,axiom,
( cCKB_XPL
= ( ^ [X1: $i > $i > $i > $i > $o,X8: $i > $i > $o,X9: $i,X10: $i] :
( ( X8 @ X9 @ X10 )
& ! [X11: $i,X12: $i] :
( ( X8 @ X11 @ X12 )
=> ? [X6: $i,X7: $i] :
( ( X1 @ X11 @ X12 @ X6 @ X7 )
& ( X8 @ X6 @ X7 )
& ~ ( ( X6 = X9 )
& ( X7 = X10 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.D2W1kAj7uh/E---3.1_2837912.p',cCKB_XPL_def) ).
thf(cCKB_FIN_def,axiom,
( cCKB_FIN
= ( ^ [X8: $i > $i > $o] :
~ ( cCKB_INF @ X8 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.D2W1kAj7uh/E---3.1_2837912.p',cCKB_FIN_def) ).
thf(cL3000,conjecture,
( cCKB_FIN
@ ^ [X6: $i,X7: $i] :
( ( X6 = c1 )
& ( X7 = c1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.D2W1kAj7uh/E---3.1_2837912.p',cL3000) ).
thf(c_0_5,plain,
( cCKB_INF
= ( ^ [Z0: $i > $i > $o] :
? [X1: $i > $i > $i > $i > $o,X9: $i,X10: $i] :
( ! [X26: $i,X27: $i,X28: $i,X29: $i,X30: $i,X31: $i] :
( ( ( X1 @ X26 @ X27 @ X30 @ X31 )
& ( X1 @ X28 @ X29 @ X30 @ X31 ) )
=> ( ( X26 = X28 )
& ( X27 = X29 ) ) )
& ( Z0 @ X9 @ X10 )
& ! [X32: $i,X33: $i] :
( ( Z0 @ X32 @ X33 )
=> ? [X34: $i,X35: $i] :
( ( X1 @ X32 @ X33 @ X34 @ X35 )
& ( Z0 @ X34 @ X35 )
& ~ ( ( X34 = X9 )
& ( X35 = X10 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cCKB_INF_def]) ).
thf(c_0_6,plain,
( cCKB_INJ
= ( ^ [Z0: $i > $i > $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( ( ( Z0 @ X2 @ X3 @ X6 @ X7 )
& ( Z0 @ X4 @ X5 @ X6 @ X7 ) )
=> ( ( X2 = X4 )
& ( X3 = X5 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cCKB_INJ_def]) ).
thf(c_0_7,plain,
( cCKB_XPL
= ( ^ [Z0: $i > $i > $i > $i > $o,Z1: $i > $i > $o,Z2: $i,Z3: $i] :
( ( Z1 @ Z2 @ Z3 )
& ! [X11: $i,X12: $i] :
( ( Z1 @ X11 @ X12 )
=> ? [X6: $i,X7: $i] :
( ( Z0 @ X11 @ X12 @ X6 @ X7 )
& ( Z1 @ X6 @ X7 )
& ~ ( X6
& ( X7 = Z3 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cCKB_XPL_def]) ).
thf(c_0_8,plain,
( cCKB_FIN
= ( ^ [Z0: $i > $i > $o] :
~ ? [X13: $i > $i > $i > $i > $o,X14: $i,X15: $i] :
( ! [X16: $i,X17: $i,X18: $i,X19: $i,X20: $i,X21: $i] :
( ( ( X13 @ X16 @ X17 @ X20 @ X21 )
& ( X13 @ X18 @ X19 @ X20 @ X21 ) )
=> ( ( X16 = X18 )
& ( X17 = X19 ) ) )
& ( Z0 @ X14 @ X15 )
& ! [X22: $i,X23: $i] :
( ( Z0 @ X22 @ X23 )
=> ? [X24: $i,X25: $i] :
( ( X13 @ X22 @ X23 @ X24 @ X25 )
& ( Z0 @ X24 @ X25 )
& ~ ( ( X24 = X14 )
& ( X25 = X15 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[cCKB_FIN_def]) ).
thf(c_0_9,plain,
( cCKB_INF
= ( ^ [Z0: $i > $i > $o] :
? [X1: $i > $i > $i > $i > $o,X9: $i,X10: $i] :
( ! [X26: $i,X27: $i,X28: $i,X29: $i,X30: $i,X31: $i] :
( ( ( X1 @ X26 @ X27 @ X30 @ X31 )
& ( X1 @ X28 @ X29 @ X30 @ X31 ) )
=> ( ( X26 = X28 )
& ( X27 = X29 ) ) )
& ( Z0 @ X9 @ X10 )
& ! [X32: $i,X33: $i] :
( ( Z0 @ X32 @ X33 )
=> ? [X34: $i,X35: $i] :
( ( X1 @ X32 @ X33 @ X34 @ X35 )
& ( Z0 @ X34 @ X35 )
& ~ ( ( X34 = X9 )
& ( X35 = X10 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_5,c_0_6]),c_0_7]) ).
thf(c_0_10,negated_conjecture,
~ ( cCKB_FIN
@ ^ [X6: $i,X7: $i] :
( ( X6 = c1 )
& ( X7 = c1 ) ) ),
inference(assume_negation,[status(cth)],[cL3000]) ).
thf(c_0_11,plain,
( cCKB_FIN
= ( ^ [Z0: $i > $i > $o] :
~ ? [X13: $i > $i > $i > $i > $o,X14: $i,X15: $i] :
( ! [X16: $i,X17: $i,X18: $i,X19: $i,X20: $i,X21: $i] :
( ( ( X13 @ X16 @ X17 @ X20 @ X21 )
& ( X13 @ X18 @ X19 @ X20 @ X21 ) )
=> ( ( X16 = X18 )
& ( X17 = X19 ) ) )
& ( Z0 @ X14 @ X15 )
& ! [X22: $i,X23: $i] :
( ( Z0 @ X22 @ X23 )
=> ? [X24: $i,X25: $i] :
( ( X13 @ X22 @ X23 @ X24 @ X25 )
& ( Z0 @ X24 @ X25 )
& ~ ( ( X24 = X14 )
& ( X25 = X15 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_8,c_0_6]),c_0_7]),c_0_9]) ).
thf(c_0_12,negated_conjecture,
~ ~ ? [X36: $i > $i > $i > $i > $o,X37: $i,X38: $i] :
( ! [X39: $i,X40: $i,X41: $i,X42: $i,X43: $i,X44: $i] :
( ( ( X36 @ X39 @ X40 @ X43 @ X44 )
& ( X36 @ X41 @ X42 @ X43 @ X44 ) )
=> ( ( X39 = X41 )
& ( X40 = X42 ) ) )
& ( X37 = c1 )
& ( X38 = c1 )
& ! [X45: $i,X46: $i] :
( ( ( X45 = c1 )
& ( X46 = c1 ) )
=> ? [X47: $i,X48: $i] :
( ( X36 @ X45 @ X46 @ X47 @ X48 )
& ( X47 = c1 )
& ( X48 = c1 )
& ~ ( ( X47 = X37 )
& ( X48 = X38 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_10]),c_0_11]) ).
thf(c_0_13,negated_conjecture,
! [X52: $i,X53: $i,X54: $i,X55: $i,X56: $i,X57: $i,X58: $i,X59: $i] :
( ( ( X52 = X54 )
| ~ ( epred1_0 @ X52 @ X53 @ X56 @ X57 )
| ~ ( epred1_0 @ X54 @ X55 @ X56 @ X57 ) )
& ( ( X53 = X55 )
| ~ ( epred1_0 @ X52 @ X53 @ X56 @ X57 )
| ~ ( epred1_0 @ X54 @ X55 @ X56 @ X57 ) )
& ( esk1_0 = c1 )
& ( esk2_0 = c1 )
& ( ( epred1_0 @ X58 @ X59 @ ( esk3_2 @ X58 @ X59 ) @ ( esk4_2 @ X58 @ X59 ) )
| ( X58 != c1 )
| ( X59 != c1 ) )
& ( ( ( esk3_2 @ X58 @ X59 )
= c1 )
| ( X58 != c1 )
| ( X59 != c1 ) )
& ( ( ( esk4_2 @ X58 @ X59 )
= c1 )
| ( X58 != c1 )
| ( X59 != c1 ) )
& ( ( ( esk3_2 @ X58 @ X59 )
!= esk1_0 )
| ( ( esk4_2 @ X58 @ X59 )
!= esk2_0 )
| ( X58 != c1 )
| ( X59 != c1 ) ) ),
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_12])])])])])]) ).
thf(c_0_14,negated_conjecture,
! [X2: $i,X3: $i] :
( ( ( esk3_2 @ X2 @ X3 )
= c1 )
| ( X2 != c1 )
| ( X3 != c1 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_15,negated_conjecture,
! [X2: $i,X3: $i] :
( ( ( esk4_2 @ X2 @ X3 )
= c1 )
| ( X2 != c1 )
| ( X3 != c1 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_16,negated_conjecture,
! [X2: $i,X3: $i] :
( ( ( esk3_2 @ X2 @ X3 )
!= esk1_0 )
| ( ( esk4_2 @ X2 @ X3 )
!= esk2_0 )
| ( X2 != c1 )
| ( X3 != c1 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_17,negated_conjecture,
esk1_0 = c1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_18,negated_conjecture,
esk2_0 = c1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_19,negated_conjecture,
( ( esk3_2 @ c1 @ c1 )
= c1 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_14])]) ).
thf(c_0_20,negated_conjecture,
( ( esk4_2 @ c1 @ c1 )
= c1 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_15])]) ).
thf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_18])])]),c_0_19]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ107^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 % Computer : n010.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 13:24:03 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.28 Running higher-order theorem proving
% 0.27/0.29 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.D2W1kAj7uh/E---3.1_2837912.p
% 0.27/0.31 % Version: 3.5.1-ho
% 0.27/0.31 % Preprocessing class: HSSSSMSSSLMNHSN.
% 0.27/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.31 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.27/0.31 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.27/0.31 % Starting sh2l with 300s (1) cores
% 0.27/0.31 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.27/0.31 % sh2l with pid 2837927 completed with status 0
% 0.27/0.31 % Result found by sh2l
% 0.27/0.31 % Preprocessing class: HSSSSMSSSLMNHSN.
% 0.27/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.31 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.27/0.31 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.27/0.31 % Starting sh2l with 300s (1) cores
% 0.27/0.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf120_gu_RUU_F100_L01000)
% 0.27/0.31 % SinE strategy is gf120_gu_RUU_F100_L01000
% 0.27/0.31 % Search class: HHHSF-FFSF22-SHSFMFNN
% 0.27/0.31 % partial match(2): HHHSF-FFSF11-SHSFMFNN
% 0.27/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.27/0.31 % SubtermCWHack with pid 2837932 completed with status 0
% 0.27/0.31 % Result found by SubtermCWHack
% 0.27/0.31 % Preprocessing class: HSSSSMSSSLMNHSN.
% 0.27/0.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.31 % Starting ho_unfolding_6 with 1500s (5) cores
% 0.27/0.31 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.27/0.31 % Starting sh2l with 300s (1) cores
% 0.27/0.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf120_gu_RUU_F100_L01000)
% 0.27/0.31 % SinE strategy is gf120_gu_RUU_F100_L01000
% 0.27/0.31 % Search class: HHHSF-FFSF22-SHSFMFNN
% 0.27/0.31 % partial match(2): HHHSF-FFSF11-SHSFMFNN
% 0.27/0.31 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.31 % Starting SubtermCWHack with 28s (1) cores
% 0.27/0.31 % Preprocessing time : 0.001 s
% 0.27/0.31
% 0.27/0.31 % Proof found!
% 0.27/0.31 % SZS status Theorem
% 0.27/0.31 % SZS output start CNFRefutation
% See solution above
% 0.27/0.31 % Parsed axioms : 10
% 0.27/0.31 % Removed by relevancy pruning/SinE : 5
% 0.27/0.31 % Initial clauses : 8
% 0.27/0.31 % Removed in clause preprocessing : 0
% 0.27/0.31 % Initial clauses in saturation : 8
% 0.27/0.31 % Processed clauses : 11
% 0.27/0.31 % ...of these trivial : 0
% 0.27/0.31 % ...subsumed : 0
% 0.27/0.31 % ...remaining for further processing : 11
% 0.27/0.31 % Other redundant clauses eliminated : 8
% 0.27/0.31 % Clauses deleted for lack of memory : 0
% 0.27/0.31 % Backward-subsumed : 0
% 0.27/0.31 % Backward-rewritten : 0
% 0.27/0.31 % Generated clauses : 6
% 0.27/0.31 % ...of the previous two non-redundant : 5
% 0.27/0.31 % ...aggressively subsumed : 0
% 0.27/0.31 % Contextual simplify-reflections : 0
% 0.27/0.31 % Paramodulations : 2
% 0.27/0.31 % Factorizations : 0
% 0.27/0.31 % NegExts : 0
% 0.27/0.31 % Equation resolutions : 8
% 0.27/0.31 % Disequality decompositions : 0
% 0.27/0.31 % Total rewrite steps : 6
% 0.27/0.31 % ...of those cached : 2
% 0.27/0.31 % Propositional unsat checks : 0
% 0.27/0.31 % Propositional check models : 0
% 0.27/0.31 % Propositional check unsatisfiable : 0
% 0.27/0.31 % Propositional clauses : 0
% 0.27/0.32 % Propositional clauses after purity: 0
% 0.27/0.32 % Propositional unsat core size : 0
% 0.27/0.32 % Propositional preprocessing time : 0.000
% 0.27/0.32 % Propositional encoding time : 0.000
% 0.27/0.32 % Propositional solver time : 0.000
% 0.27/0.32 % Success case prop preproc time : 0.000
% 0.27/0.32 % Success case prop encoding time : 0.000
% 0.27/0.32 % Success case prop solver time : 0.000
% 0.27/0.32 % Current number of processed clauses : 7
% 0.27/0.32 % Positive orientable unit clauses : 5
% 0.27/0.32 % Positive unorientable unit clauses: 0
% 0.27/0.32 % Negative unit clauses : 0
% 0.27/0.32 % Non-unit-clauses : 2
% 0.27/0.32 % Current number of unprocessed clauses: 2
% 0.27/0.32 % ...number of literals in the above : 4
% 0.27/0.32 % Current number of archived formulas : 0
% 0.27/0.32 % Current number of archived clauses : 0
% 0.27/0.32 % Clause-clause subsumption calls (NU) : 2
% 0.27/0.32 % Rec. Clause-clause subsumption calls : 2
% 0.27/0.32 % Non-unit clause-clause subsumptions : 0
% 0.27/0.32 % Unit Clause-clause subsumption calls : 0
% 0.27/0.32 % Rewrite failures with RHS unbound : 0
% 0.27/0.32 % BW rewrite match attempts : 0
% 0.27/0.32 % BW rewrite match successes : 0
% 0.27/0.32 % Condensation attempts : 0
% 0.27/0.32 % Condensation successes : 0
% 0.27/0.32 % Termbank termtop insertions : 985
% 0.27/0.32 % Search garbage collected termcells : 331
% 0.27/0.32
% 0.27/0.32 % -------------------------------------------------
% 0.27/0.32 % User time : 0.004 s
% 0.27/0.32 % System time : 0.003 s
% 0.27/0.32 % Total time : 0.007 s
% 0.27/0.32 % Maximum resident set size: 3644 pages
% 0.27/0.32
% 0.27/0.32 % -------------------------------------------------
% 0.27/0.32 % User time : 0.006 s
% 0.27/0.32 % System time : 0.007 s
% 0.27/0.32 % Total time : 0.013 s
% 0.27/0.32 % Maximum resident set size: 4864 pages
% 0.27/0.32 % E exiting
%------------------------------------------------------------------------------