%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU611^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:24:43 AM UTC 2026
% Result : Theorem 0.10s 0.24s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 99 ( 4 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 347 ( 38 ~; 31 |; 6 &; 229 @)
% ( 5 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 82 ( 14 ^; 68 !; 0 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_25,type,
dsetconstrEL: $o ).
thf(decl_26,type,
dsetconstrER: $o ).
thf(decl_27,type,
binunion: $i > $i > $i ).
thf(decl_28,type,
binunionE: $o ).
thf(decl_29,type,
symdiff: $i > $i > $i ).
thf(decl_30,type,
esk1_0: $i ).
thf(decl_31,type,
esk2_0: $i ).
thf(decl_32,type,
esk3_0: $i ).
thf(decl_33,type,
epred1_0: $o ).
thf(symdiffE,conjecture,
( dsetconstrEL
=> ( dsetconstrER
=> ( binunionE
=> ! [X1: $i,X5: $i,X3: $i] :
( ( in @ X3 @ ( symdiff @ X1 @ X5 ) )
=> ! [X6: $o] :
( ( ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ X5 )
=> X6 ) )
=> ( ( ~ ( in @ X3 @ X1 )
=> ( ( in @ X3 @ X5 )
=> X6 ) )
=> X6 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4LPEHUxhKS/E---3.1_2547173.p',symdiffE) ).
thf(dsetconstrEL,axiom,
( dsetconstrEL
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
=> ( in @ X3 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4LPEHUxhKS/E---3.1_2547173.p',dsetconstrEL) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
=> ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4LPEHUxhKS/E---3.1_2547173.p',dsetconstrER) ).
thf(binunionE,axiom,
( binunionE
<=> ! [X1: $i,X5: $i,X3: $i] :
( ( in @ X3 @ ( binunion @ X1 @ X5 ) )
=> ( ( in @ X3 @ X1 )
| ( in @ X3 @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4LPEHUxhKS/E---3.1_2547173.p',binunionE) ).
thf(symdiff,axiom,
( symdiff
= ( ^ [X1: $i,X5: $i] :
( dsetconstr @ ( binunion @ X1 @ X5 )
@ ^ [X3: $i] :
( ~ ( in @ X3 @ X1 )
| ~ ( in @ X3 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4LPEHUxhKS/E---3.1_2547173.p',symdiff) ).
thf(c_0_5,negated_conjecture,
~ ( dsetconstrEL
=> ( dsetconstrER
=> ( binunionE
=> ! [X1: $i,X5: $i,X3: $i] :
( ( in @ X3 @ ( symdiff @ X1 @ X5 ) )
=> ! [X6: $o] :
( ( ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ X5 )
=> X6 ) )
=> ( ( ~ ( in @ X3 @ X1 )
=> ( ( in @ X3 @ X5 )
=> X6 ) )
=> X6 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[symdiffE]) ).
thf(c_0_6,plain,
( dsetconstrEL
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) )
=> ( in @ X3 @ X1 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrEL]) ).
thf(c_0_7,plain,
( dsetconstrER
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) )
=> ( X2 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrER]) ).
thf(c_0_8,negated_conjecture,
~ ( ! [X20: $i,X21: $i > $o,X22: $i] :
( ( in @ X22 @ ( dsetconstr @ X20 @ X21 ) )
=> ( in @ X22 @ X20 ) )
=> ( ! [X23: $i,X24: $i > $o,X25: $i] :
( ( in @ X25 @ ( dsetconstr @ X23 @ X24 ) )
=> ( X24 @ X25 ) )
=> ( ! [X26: $i,X27: $i,X28: $i] :
( ( in @ X28 @ ( binunion @ X26 @ X27 ) )
=> ( ( in @ X28 @ X26 )
| ( in @ X28 @ X27 ) ) )
=> ! [X1: $i,X5: $i,X3: $i] :
( ( in @ X3 @ ( symdiff @ X1 @ X5 ) )
=> ! [X6: $o] :
( ( ( in @ X3 @ X1 )
=> ( ~ ( in @ X3 @ X5 )
=> X6 ) )
=> ( ( ~ ( in @ X3 @ X1 )
=> ( ( in @ X3 @ X5 )
=> X6 ) )
=> X6 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_5,c_0_6]),c_0_7]),binunionE])])]) ).
thf(c_0_9,plain,
( symdiff
= ( ^ [Z0: $i,Z1: $i] :
( dsetconstr @ ( binunion @ Z0 @ Z1 )
@ ^ [Z2: $i] :
( ~ ( in @ Z2 @ Z0 )
| ~ ( in @ Z2 @ Z1 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[symdiff]) ).
thf(c_0_10,negated_conjecture,
! [X29: $i,X30: $i > $o,X31: $i,X32: $i,X33: $i > $o,X34: $i,X35: $i,X36: $i,X37: $i] :
( ( ~ ( in @ X31 @ ( dsetconstr @ X29 @ X30 ) )
| ( in @ X31 @ X29 ) )
& ( ~ ( in @ X34 @ ( dsetconstr @ X32 @ X33 ) )
| ( X33 @ X34 ) )
& ( ~ ( in @ X37 @ ( binunion @ X35 @ X36 ) )
| ( in @ X37 @ X35 )
| ( in @ X37 @ X36 ) )
& ( in @ esk3_0 @ ( symdiff @ esk1_0 @ esk2_0 ) )
& ( ~ ( in @ esk3_0 @ esk1_0 )
| ( in @ esk3_0 @ esk2_0 )
| epred1_0 )
& ( ( in @ esk3_0 @ esk1_0 )
| ~ ( in @ esk3_0 @ esk2_0 )
| epred1_0 )
& ~ epred1_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_8])])])])]) ).
thf(c_0_11,plain,
( symdiff
= ( ^ [Z0: $i,Z1: $i] :
( dsetconstr @ ( binunion @ Z0 @ Z1 )
@ ^ [Z2: $i] :
( ~ ( in @ Z2 @ Z0 )
| ~ ( in @ Z2 @ Z1 ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $o] :
( ( in @ X1 @ X3 )
| ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_13,plain,
! [X1: $i,X3: $i] :
( ( dsetconstr @ ( binunion @ X1 @ X3 )
@ ^ [Z0: $i] :
( ~ ( in @ Z0 @ X1 )
| ~ ( in @ Z0 @ X3 ) ) )
= ( symdiff @ X1 @ X3 ) ),
inference(arg_cong,[status(thm)],[c_0_11]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X3: $i,X4: $i] :
( ( in @ X1 @ X3 )
| ( in @ X1 @ X4 )
| ~ ( in @ X1 @ ( binunion @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X3: $i,X4: $i] :
( ( in @ X1 @ ( binunion @ X3 @ X4 ) )
| ~ ( in @ X1 @ ( symdiff @ X3 @ X4 ) ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_16,negated_conjecture,
( ( in @ esk3_0 @ esk2_0 )
| epred1_0
| ~ ( in @ esk3_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_17,negated_conjecture,
~ epred1_0,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_18,negated_conjecture,
! [X1: $i,X3: $i,X2: $i > $o] :
( ( X2 @ X1 )
| ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_19,negated_conjecture,
( ( in @ esk3_0 @ esk1_0 )
| epred1_0
| ~ ( in @ esk3_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i,X4: $i,X3: $i] :
( ( in @ X1 @ X3 )
| ( in @ X1 @ X4 )
| ~ ( in @ X1 @ ( symdiff @ X4 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_21,negated_conjecture,
in @ esk3_0 @ ( symdiff @ esk1_0 @ esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_22,negated_conjecture,
( ( in @ esk3_0 @ esk2_0 )
| ~ ( in @ esk3_0 @ esk1_0 ) ),
inference(sr,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i,X3: $i,X4: $i] :
( ~ ( in @ X1 @ X3 )
| ~ ( in @ X1 @ X4 )
| ~ ( in @ X1 @ ( symdiff @ X3 @ X4 ) ) ),
inference(spm,[status(thm)],[c_0_18,c_0_13]) ).
thf(c_0_24,negated_conjecture,
( ( in @ esk3_0 @ esk1_0 )
| ~ ( in @ esk3_0 @ esk2_0 ) ),
inference(sr,[status(thm)],[c_0_19,c_0_17]) ).
thf(c_0_25,negated_conjecture,
in @ esk3_0 @ esk2_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
thf(c_0_26,negated_conjecture,
! [X1: $i,X3: $i,X4: $i] :
( ~ ( in @ X1 @ ( symdiff @ X3 @ X4 ) )
| ~ ( in @ X1 @ X3 )
| ~ ( in @ X1 @ X4 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_23]) ).
thf(c_0_27,negated_conjecture,
in @ esk3_0 @ esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
thf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_21]),c_0_27]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU611^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n003.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 13:59:52 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.22 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.4LPEHUxhKS/E---3.1_2547173.p
% 0.10/0.24 % Version: 3.5.1-ho
% 0.10/0.24 % Preprocessing class: HSSSSLSSSLMNSFA.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.24 % Starting full_lambda_3 with 300s (1) cores
% 0.10/0.24 % Starting ho_unfolding_6 with 300s (1) cores
% 0.10/0.24 % Starting sh4l with 300s (1) cores
% 0.10/0.24 % full_lambda_3 with pid 2547204 completed with status 0
% 0.10/0.24 % Result found by full_lambda_3
% 0.10/0.24 % Preprocessing class: HSSSSLSSSLMNSFA.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.24 % Starting full_lambda_3 with 300s (1) cores
% 0.10/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountTerms,hypos,1.5,,2,20000,1.0))
% 0.10/0.24 % SinE strategy is GSinE(CountTerms,hypos,1.5,,2,20000,1.0)
% 0.10/0.24 % Search class: HGUSF-FFSF22-DSFFMSBN
% 0.10/0.24 % partial match(2): HGHSF-FFSF22-SSFFMSBN
% 0.10/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.24 % SubtermCWHack with pid 2547209 completed with status 0
% 0.10/0.24 % Result found by SubtermCWHack
% 0.10/0.24 % Preprocessing class: HSSSSLSSSLMNSFA.
% 0.10/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.10/0.24 % Starting full_lambda_3 with 300s (1) cores
% 0.10/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountTerms,hypos,1.5,,2,20000,1.0))
% 0.10/0.24 % SinE strategy is GSinE(CountTerms,hypos,1.5,,2,20000,1.0)
% 0.10/0.24 % Search class: HGUSF-FFSF22-DSFFMSBN
% 0.10/0.24 % partial match(2): HGHSF-FFSF22-SSFFMSBN
% 0.10/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.24 % Preprocessing time : 0.001 s
% 0.10/0.24
% 0.10/0.24 % Proof found!
% 0.10/0.24 % SZS status Theorem
% 0.10/0.24 % SZS output start CNFRefutation
% See solution above
% 0.10/0.24 % Parsed axioms : 12
% 0.10/0.24 % Removed by relevancy pruning/SinE : 7
% 0.10/0.24 % Initial clauses : 8
% 0.10/0.24 % Removed in clause preprocessing : 0
% 0.10/0.24 % Initial clauses in saturation : 8
% 0.10/0.24 % Processed clauses : 17
% 0.10/0.24 % ...of these trivial : 1
% 0.10/0.24 % ...subsumed : 0
% 0.10/0.24 % ...remaining for further processing : 16
% 0.10/0.24 % Other redundant clauses eliminated : 0
% 0.10/0.24 % Clauses deleted for lack of memory : 0
% 0.10/0.24 % Backward-subsumed : 1
% 0.10/0.24 % Backward-rewritten : 1
% 0.10/0.24 % Generated clauses : 10
% 0.10/0.24 % ...of the previous two non-redundant : 9
% 0.10/0.24 % ...aggressively subsumed : 0
% 0.10/0.24 % Contextual simplify-reflections : 1
% 0.10/0.24 % Paramodulations : 6
% 0.10/0.24 % Factorizations : 0
% 0.10/0.24 % NegExts : 0
% 0.10/0.24 % Equation resolutions : 0
% 0.10/0.24 % Disequality decompositions : 0
% 0.10/0.24 % Total rewrite steps : 4
% 0.10/0.24 % ...of those cached : 1
% 0.10/0.24 % Propositional unsat checks : 0
% 0.10/0.24 % Propositional check models : 0
% 0.10/0.24 % Propositional check unsatisfiable : 0
% 0.10/0.24 % Propositional clauses : 0
% 0.10/0.24 % Propositional clauses after purity: 0
% 0.10/0.24 % Propositional unsat core size : 0
% 0.10/0.24 % Propositional preprocessing time : 0.000
% 0.10/0.24 % Propositional encoding time : 0.000
% 0.10/0.24 % Propositional solver time : 0.000
% 0.10/0.24 % Success case prop preproc time : 0.000
% 0.10/0.24 % Success case prop encoding time : 0.000
% 0.10/0.24 % Success case prop solver time : 0.000
% 0.10/0.24 % Current number of processed clauses : 13
% 0.10/0.24 % Positive orientable unit clauses : 6
% 0.10/0.24 % Positive unorientable unit clauses: 0
% 0.10/0.24 % Negative unit clauses : 1
% 0.10/0.24 % Non-unit-clauses : 6
% 0.10/0.24 % Current number of unprocessed clauses: 0
% 0.10/0.24 % ...number of literals in the above : 0
% 0.10/0.24 % Current number of archived formulas : 0
% 0.10/0.24 % Current number of archived clauses : 3
% 0.10/0.24 % Clause-clause subsumption calls (NU) : 4
% 0.10/0.24 % Rec. Clause-clause subsumption calls : 4
% 0.10/0.24 % Non-unit clause-clause subsumptions : 1
% 0.10/0.24 % Unit Clause-clause subsumption calls : 1
% 0.10/0.24 % Rewrite failures with RHS unbound : 0
% 0.10/0.24 % BW rewrite match attempts : 2
% 0.10/0.24 % BW rewrite match successes : 1
% 0.10/0.24 % Condensation attempts : 0
% 0.10/0.24 % Condensation successes : 0
% 0.10/0.24 % Termbank termtop insertions : 1481
% 0.10/0.24 % Search garbage collected termcells : 377
% 0.10/0.24
% 0.10/0.24 % -------------------------------------------------
% 0.10/0.24 % User time : 0.005 s
% 0.10/0.24 % System time : 0.001 s
% 0.10/0.24 % Total time : 0.006 s
% 0.10/0.24 % Maximum resident set size: 3640 pages
% 0.10/0.24
% 0.10/0.24 % -------------------------------------------------
% 0.10/0.24 % User time : 0.007 s
% 0.10/0.24 % System time : 0.005 s
% 0.10/0.24 % Total time : 0.012 s
% 0.10/0.24 % Maximum resident set size: 4608 pages
% 0.10/0.24 % E exiting
%------------------------------------------------------------------------------