%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU472^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:23:53 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 70 ( 25 equ; 0 cnn)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 280 ( 14 ~; 20 |; 27 &; 187 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 73 ( 73 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 118 ( 37 ^; 81 !; 0 ?; 118 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(decl_26,type,
infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(decl_30,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf(decl_34,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(decl_35,type,
trans: ( $i > $i > $o ) > $o ).
thf(decl_36,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(decl_38,type,
trsc: ( $i > $i > $o ) > $i > $i > $o ).
thf(decl_52,type,
epred1_0: $i > $i > $o ).
thf(decl_53,type,
esk1_0: $i ).
thf(decl_54,type,
esk2_0: $i ).
thf(decl_55,type,
epred2_0: $i > $i > $o ).
thf(decl_56,type,
epred3_0: $i > $i > $o ).
thf(transitive_closure,axiom,
( tc
= ( ^ [X1: $i > $i > $o,X3: $i,X4: $i] :
! [X2: $i > $i > $o] :
( ( ( trans @ X2 )
& ( subrel @ X1 @ X2 ) )
=> ( X2 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xljV2EdyX6/E---3.1_784193.p',transitive_closure) ).
thf(subrel,axiom,
( subrel
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xljV2EdyX6/E---3.1_784193.p',subrel) ).
thf(transitive,axiom,
( trans
= ( ^ [X1: $i > $i > $o] :
! [X3: $i,X4: $i,X6: $i] :
( ( ( X1 @ X3 @ X4 )
& ( X1 @ X4 @ X6 ) )
=> ( X1 @ X3 @ X6 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xljV2EdyX6/E---3.1_784193.p',transitive) ).
thf(transitive_reflexive_symmetric_closure,axiom,
( trsc
= ( ^ [X1: $i > $i > $o] : ( sc @ ( rc @ ( tc @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xljV2EdyX6/E---3.1_784193.p',transitive_reflexive_symmetric_closure) ).
thf(reflexive_closure,axiom,
( rc
= ( ^ [X1: $i > $i > $o,X3: $i,X4: $i] :
( ( X3 = X4 )
| ( X1 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xljV2EdyX6/E---3.1_784193.p',reflexive_closure) ).
thf(symmetric_closure,axiom,
( sc
= ( ^ [X1: $i > $i > $o,X3: $i,X4: $i] :
( ( X1 @ X4 @ X3 )
| ( X1 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xljV2EdyX6/E---3.1_784193.p',symmetric_closure) ).
thf(inflationary,axiom,
( infl
= ( ^ [X5: ( $i > $i > $o ) > $i > $i > $o] :
! [X1: $i > $i > $o] : ( subrel @ X1 @ ( X5 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xljV2EdyX6/E---3.1_784193.p',inflationary) ).
thf(transitive_reflexive_symmetric_closure_op_is_inflationary,conjecture,
infl @ trsc,
file('/export/starexec/sandbox2/tmp/tmp.xljV2EdyX6/E---3.1_784193.p',transitive_reflexive_symmetric_closure_op_is_inflationary) ).
thf(c_0_8,plain,
( tc
= ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
! [X2: $i > $i > $o] :
( ( ! [X11: $i,X12: $i,X13: $i] :
( ( ( X2 @ X11 @ X12 )
& ( X2 @ X12 @ X13 ) )
=> ( X2 @ X11 @ X13 ) )
& ! [X14: $i,X15: $i] :
( ( Z0 @ X14 @ X15 )
=> ( X2 @ X14 @ X15 ) ) )
=> ( X2 @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[transitive_closure]) ).
thf(c_0_9,plain,
( subrel
= ( ^ [Z0: $i > $i > $o,Z1: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( Z0 @ X3 @ X4 )
=> ( Z1 @ X3 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[subrel]) ).
thf(c_0_10,plain,
( trans
= ( ^ [Z0: $i > $i > $o] :
! [X3: $i,X4: $i,X6: $i] :
( ( ( Z0 @ X3 @ X4 )
& ( Z0 @ X4 @ X6 ) )
=> ( Z0 @ X3 @ X6 ) ) ) ),
inference(fof_simplification,[status(thm)],[transitive]) ).
thf(c_0_11,plain,
( trsc
= ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
( Z2
| ! [X22: $i > $i > $o] :
( ( ! [X23: $i,X24: $i,X25: $i] :
( ( ( X22 @ X23 @ X24 )
& ( X22 @ X24 @ X25 ) )
=> ( X22 @ X23 @ X25 ) )
& ! [X26: $i,X27: $i] :
( ( Z0 @ X26 @ X27 )
=> ( X22 @ X26 @ X27 ) ) )
=> ( X22 @ Z2 @ Z1 ) )
| ( Z1 = Z2 )
| ! [X22: $i > $i > $o] :
( ( ! [X23: $i,X24: $i,X25: $i] :
( ( ( X22 @ X23 @ X24 )
& ( X22 @ X24 @ X25 ) )
=> ( X22 @ X23 @ X25 ) )
& ! [X26: $i,X27: $i] :
( ( Z0 @ X26 @ X27 )
=> ( X22 @ X26 @ X27 ) ) )
=> ( X22 @ Z1 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[transitive_reflexive_symmetric_closure]) ).
thf(c_0_12,plain,
( rc
= ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
( ( Z1 = Z2 )
| ( Z0 @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[reflexive_closure]) ).
thf(c_0_13,plain,
( sc
= ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
( ( Z0 @ Z2 @ Z1 )
| ( Z0 @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[symmetric_closure]) ).
thf(c_0_14,plain,
( tc
= ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
! [X2: $i > $i > $o] :
( ( ! [X11: $i,X12: $i,X13: $i] :
( ( ( X2 @ X11 @ X12 )
& ( X2 @ X12 @ X13 ) )
=> ( X2 @ X11 @ X13 ) )
& ! [X14: $i,X15: $i] :
( ( Z0 @ X14 @ X15 )
=> ( X2 @ X14 @ X15 ) ) )
=> ( X2 @ Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
thf(c_0_15,plain,
( infl
= ( ^ [Z0: ( $i > $i > $o ) > $i > $i > $o] :
! [X1: $i > $i > $o,X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( Z0 @ X1 @ X9 @ X10 ) ) ) ),
inference(fof_simplification,[status(thm)],[inflationary]) ).
thf(c_0_16,negated_conjecture,
~ ( infl @ trsc ),
inference(assume_negation,[status(cth)],[transitive_reflexive_symmetric_closure_op_is_inflationary]) ).
thf(c_0_17,plain,
( trsc
= ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
( Z2
| ! [X22: $i > $i > $o] :
( ( ! [X23: $i,X24: $i,X25: $i] :
( ( ( X22 @ X23 @ X24 )
& ( X22 @ X24 @ X25 ) )
=> ( X22 @ X23 @ X25 ) )
& ! [X26: $i,X27: $i] :
( ( Z0 @ X26 @ X27 )
=> ( X22 @ X26 @ X27 ) ) )
=> ( X22 @ Z2 @ Z1 ) )
| ( Z1 = Z2 )
| ! [X22: $i > $i > $o] :
( ( ! [X23: $i,X24: $i,X25: $i] :
( ( ( X22 @ X23 @ X24 )
& ( X22 @ X24 @ X25 ) )
=> ( X22 @ X23 @ X25 ) )
& ! [X26: $i,X27: $i] :
( ( Z0 @ X26 @ X27 )
=> ( X22 @ X26 @ X27 ) ) )
=> ( X22 @ Z1 @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14]) ).
thf(c_0_18,plain,
( infl
= ( ^ [Z0: ( $i > $i > $o ) > $i > $i > $o] :
! [X1: $i > $i > $o,X9: $i,X10: $i] :
( ( X1 @ X9 @ X10 )
=> ( Z0 @ X1 @ X9 @ X10 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_15,c_0_9]) ).
thf(c_0_19,negated_conjecture,
~ ! [X91: $i > $i > $o,X92: $i,X93: $i] :
( ( X91 @ X92 @ X93 )
=> ( ( X93 = X92 )
| ! [X79: $i > $i > $o] :
( ( ! [X80: $i,X81: $i,X82: $i] :
( ( ( X79 @ X80 @ X81 )
& ( X79 @ X81 @ X82 ) )
=> ( X79 @ X80 @ X82 ) )
& ! [X83: $i,X84: $i] :
( ( X91 @ X83 @ X84 )
=> ( X79 @ X83 @ X84 ) ) )
=> ( X79 @ X93 @ X92 ) )
| ( X92 = X93 )
| ! [X85: $i > $i > $o] :
( ( ! [X86: $i,X87: $i,X88: $i] :
( ( ( X85 @ X86 @ X87 )
& ( X85 @ X87 @ X88 ) )
=> ( X85 @ X86 @ X88 ) )
& ! [X89: $i,X90: $i] :
( ( X91 @ X89 @ X90 )
=> ( X85 @ X89 @ X90 ) ) )
=> ( X85 @ X92 @ X93 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
thf(c_0_20,negated_conjecture,
! [X98: $i,X99: $i,X100: $i,X101: $i,X102: $i,X104: $i,X105: $i,X106: $i,X107: $i,X108: $i] :
( ( epred1_0 @ esk1_0 @ esk2_0 )
& ( esk2_0 != esk1_0 )
& ( ~ ( epred2_0 @ X98 @ X99 )
| ~ ( epred2_0 @ X99 @ X100 )
| ( epred2_0 @ X98 @ X100 ) )
& ( ~ ( epred1_0 @ X101 @ X102 )
| ( epred2_0 @ X101 @ X102 ) )
& ~ ( epred2_0 @ esk2_0 @ esk1_0 )
& ( esk1_0 != esk2_0 )
& ( ~ ( epred3_0 @ X104 @ X105 )
| ~ ( epred3_0 @ X105 @ X106 )
| ( epred3_0 @ X104 @ X106 ) )
& ( ~ ( epred1_0 @ X107 @ X108 )
| ( epred3_0 @ X107 @ X108 ) )
& ~ ( epred3_0 @ 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_19])])])])]) ).
thf(c_0_21,negated_conjecture,
! [X3: $i,X4: $i] :
( ( epred3_0 @ X3 @ X4 )
| ~ ( epred1_0 @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_22,negated_conjecture,
epred1_0 @ esk1_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_23,negated_conjecture,
~ ( epred3_0 @ esk1_0 @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_24,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU472^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n019.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 13:42:47 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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.xljV2EdyX6/E---3.1_784193.p
% 0.08/0.26 % Version: 3.5.1-ho
% 0.08/0.26 % Preprocessing class: HSSSSMSSMLSNHHN.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.26 % Starting pre_casc_5 with 300s (1) cores
% 0.08/0.26 % Starting post_as_ho11 with 300s (1) cores
% 0.08/0.26 % Starting ho_unfolding_1 with 300s (1) cores
% 0.08/0.26 % pre_casc_5 with pid 784207 completed with status 0
% 0.08/0.26 % Result found by pre_casc_5
% 0.08/0.26 % Preprocessing class: HSSSSMSSMLSNHHN.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.26 % Starting pre_casc_5 with 300s (1) cores
% 0.08/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,3,,5,20000,1.0,true))
% 0.08/0.26 % SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 0.08/0.26 % Search class: HHUSF-FFSF00-SHHSMFNN
% 0.08/0.26 % partial match(1): HHUNF-FFSF00-SHHSMFNN
% 0.08/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.26 % SubtermCWHack with pid 784210 completed with status 0
% 0.08/0.26 % Result found by SubtermCWHack
% 0.08/0.26 % Preprocessing class: HSSSSMSSMLSNHHN.
% 0.08/0.26 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.26 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.26 % Starting pre_casc_5 with 300s (1) cores
% 0.08/0.26 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,3,,5,20000,1.0,true))
% 0.08/0.26 % SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 0.08/0.26 % Search class: HHUSF-FFSF00-SHHSMFNN
% 0.08/0.26 % partial match(1): HHUNF-FFSF00-SHHSMFNN
% 0.08/0.26 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.26 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.26 % Preprocessing time : 0.001 s
% 0.08/0.26
% 0.08/0.26 % Proof found!
% 0.08/0.26 % SZS status Theorem
% 0.08/0.26 % SZS output start CNFRefutation
% See solution above
% 0.08/0.26 % Parsed axioms : 59
% 0.08/0.26 % Removed by relevancy pruning/SinE : 45
% 0.08/0.26 % Initial clauses : 9
% 0.08/0.26 % Removed in clause preprocessing : 0
% 0.08/0.26 % Initial clauses in saturation : 9
% 0.08/0.26 % Processed clauses : 8
% 0.08/0.26 % ...of these trivial : 0
% 0.08/0.26 % ...subsumed : 1
% 0.08/0.26 % ...remaining for further processing : 7
% 0.08/0.26 % Other redundant clauses eliminated : 0
% 0.08/0.26 % Clauses deleted for lack of memory : 0
% 0.08/0.26 % Backward-subsumed : 0
% 0.08/0.26 % Backward-rewritten : 0
% 0.08/0.26 % Generated clauses : 2
% 0.08/0.26 % ...of the previous two non-redundant : 1
% 0.08/0.26 % ...aggressively subsumed : 0
% 0.08/0.26 % Contextual simplify-reflections : 0
% 0.08/0.26 % Paramodulations : 2
% 0.08/0.26 % Factorizations : 0
% 0.08/0.26 % NegExts : 0
% 0.08/0.26 % Equation resolutions : 0
% 0.08/0.26 % Disequality decompositions : 0
% 0.08/0.26 % Total rewrite steps : 0
% 0.08/0.26 % ...of those cached : 0
% 0.08/0.26 % Propositional unsat checks : 0
% 0.08/0.26 % Propositional check models : 0
% 0.08/0.26 % Propositional check unsatisfiable : 0
% 0.08/0.26 % Propositional clauses : 0
% 0.08/0.26 % Propositional clauses after purity: 0
% 0.08/0.26 % Propositional unsat core size : 0
% 0.08/0.26 % Propositional preprocessing time : 0.000
% 0.08/0.26 % Propositional encoding time : 0.000
% 0.08/0.26 % Propositional solver time : 0.000
% 0.08/0.26 % Success case prop preproc time : 0.000
% 0.08/0.26 % Success case prop encoding time : 0.000
% 0.08/0.26 % Success case prop solver time : 0.000
% 0.08/0.26 % Current number of processed clauses : 7
% 0.08/0.26 % Positive orientable unit clauses : 2
% 0.08/0.26 % Positive unorientable unit clauses: 0
% 0.08/0.26 % Negative unit clauses : 3
% 0.08/0.26 % Non-unit-clauses : 2
% 0.08/0.26 % Current number of unprocessed clauses: 2
% 0.08/0.26 % ...number of literals in the above : 6
% 0.08/0.26 % Current number of archived formulas : 0
% 0.08/0.26 % Current number of archived clauses : 0
% 0.08/0.26 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.26 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.26 % Non-unit clause-clause subsumptions : 0
% 0.08/0.26 % Unit Clause-clause subsumption calls : 0
% 0.08/0.26 % Rewrite failures with RHS unbound : 0
% 0.08/0.26 % BW rewrite match attempts : 0
% 0.08/0.26 % BW rewrite match successes : 0
% 0.08/0.26 % Condensation attempts : 0
% 0.08/0.26 % Condensation successes : 0
% 0.08/0.26 % Termbank termtop insertions : 2169
% 0.08/0.26 % Search garbage collected termcells : 856
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.003 s
% 0.08/0.26 % System time : 0.002 s
% 0.08/0.26 % Total time : 0.004 s
% 0.08/0.26 % Maximum resident set size: 3888 pages
% 0.08/0.26
% 0.08/0.26 % -------------------------------------------------
% 0.08/0.26 % User time : 0.006 s
% 0.08/0.26 % System time : 0.005 s
% 0.08/0.26 % Total time : 0.011 s
% 0.08/0.26 % Maximum resident set size: 4864 pages
% 0.08/0.26 % E exiting
%------------------------------------------------------------------------------