%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU933^5 : 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 : n012.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 08:28:08 AM UTC 2026
% Result : Theorem 0.07s 0.23s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 19 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 272 ( 33 ~; 35 |; 12 &; 174 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 73 ( 35 ^; 38 !; 0 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
b: $i ).
thf(decl_24,type,
a: $i ).
thf(decl_25,type,
epred1_2: ( $i > $i ) > ( $i > $i ) > ( $i > $i ) > $o ).
thf(decl_26,type,
esk1_3: ( $i > $i ) > ( $i > $i ) > ( ( $i > $i ) > $o ) > $i > $i ).
thf(cTHM196B_pme,conjecture,
( ( a != b )
=> ~ ! [X1: $i > $i,X2: $i > $i] :
( ! [X3: ( $i > $i ) > $o] :
( ( ( X3 @ X1 )
& ! [X4: $i > $i] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i] : ( X1 @ ( X4 @ X5 ) ) ) ) )
=> ( X3
@ ^ [X5: $i] : ( X2 @ ( X1 @ X5 ) ) ) )
=> ! [X3: ( $i > $i ) > $o] :
( ( ( X3 @ X1 )
& ! [X6: $i > $i] :
( ( X3 @ X6 )
=> ( X3
@ ^ [X5: $i] : ( X1 @ ( X6 @ X5 ) ) ) ) )
=> ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.GiT4UxGhVQ/E---3.1_204748.p',cTHM196B_pme) ).
thf(c_0_1,negated_conjecture,
~ ( ( a != b )
=> ~ ! [X1: $i > $i,X2: $i > $i] :
( ! [X3: ( $i > $i ) > $o] :
( ( ( X3 @ X1 )
& ! [X4: $i > $i] :
( ( X3 @ X4 )
=> ( X3
@ ^ [X5: $i] : ( X1 @ ( X4 @ X5 ) ) ) ) )
=> ( X3
@ ^ [X5: $i] : ( X2 @ ( X1 @ X5 ) ) ) )
=> ! [X3: ( $i > $i ) > $o] :
( ( ( X3 @ X1 )
& ! [X6: $i > $i] :
( ( X3 @ X6 )
=> ( X3
@ ^ [X5: $i] : ( X1 @ ( X6 @ X5 ) ) ) ) )
=> ( X3 @ X2 ) ) ) ),
inference(assume_negation,[status(cth)],[cTHM196B_pme]) ).
thf(c_0_2,negated_conjecture,
~ ( ( a != b )
=> ~ ! [X1: $i > $i,X2: $i > $i] :
( ! [X3: ( $i > $i ) > $o] :
( ( ( X3 @ X1 )
& ! [X4: $i > $i] :
( ( X3 @ X4 )
=> ( X3
@ ^ [Z0: $i] : ( X1 @ ( X4 @ Z0 ) ) ) ) )
=> ( X3
@ ^ [Z0: $i] : ( X2 @ ( X1 @ Z0 ) ) ) )
=> ! [X3: ( $i > $i ) > $o] :
( ( ( X3 @ X1 )
& ! [X6: $i > $i] :
( ( X3 @ X6 )
=> ( X3
@ ^ [Z0: $i] : ( X1 @ ( X6 @ Z0 ) ) ) ) )
=> ( X3 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_1])]) ).
thf(c_0_3,negated_conjecture,
! [X13: $i > $i,X14: $i > $i,X16: $i > $i,X17: ( $i > $i ) > $o] :
( ( a != b )
& ( ( X17 @ ( esk1_3 @ X13 @ X14 @ X17 ) )
| ~ ( X17 @ X13 )
| ( X17 @ X14 )
| ( epred1_2 @ X13 @ X14 @ X13 ) )
& ( ~ ( X17
@ ^ [Z0: $i] : ( X13 @ ( esk1_3 @ X13 @ X14 @ X17 @ Z0 ) ) )
| ~ ( X17 @ X13 )
| ( X17 @ X14 )
| ( epred1_2 @ X13 @ X14 @ X13 ) )
& ( ( X17 @ ( esk1_3 @ X13 @ X14 @ X17 ) )
| ~ ( X17 @ X13 )
| ( X17 @ X14 )
| ~ ( epred1_2 @ X13 @ X14 @ X16 )
| ( epred1_2 @ X13 @ X14
@ ^ [Z0: $i] : ( X13 @ ( X16 @ Z0 ) ) ) )
& ( ~ ( X17
@ ^ [Z0: $i] : ( X13 @ ( esk1_3 @ X13 @ X14 @ X17 @ Z0 ) ) )
| ~ ( X17 @ X13 )
| ( X17 @ X14 )
| ~ ( epred1_2 @ X13 @ X14 @ X16 )
| ( epred1_2 @ X13 @ X14
@ ^ [Z0: $i] : ( X13 @ ( X16 @ Z0 ) ) ) )
& ( ( X17 @ ( esk1_3 @ X13 @ X14 @ X17 ) )
| ~ ( X17 @ X13 )
| ( X17 @ X14 )
| ~ ( epred1_2 @ X13 @ X14
@ ^ [Z0: $i] : ( X14 @ ( X13 @ Z0 ) ) ) )
& ( ~ ( X17
@ ^ [Z0: $i] : ( X13 @ ( esk1_3 @ X13 @ X14 @ X17 @ Z0 ) ) )
| ~ ( X17 @ X13 )
| ( X17 @ X14 )
| ~ ( epred1_2 @ X13 @ X14
@ ^ [Z0: $i] : ( X14 @ ( X13 @ Z0 ) ) ) ) ),
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_2])])])])])]) ).
thf(c_0_4,negated_conjecture,
! [X3: ( $i > $i ) > $o,X2: $i > $i,X1: $i > $i] :
( ( X3 @ X2 )
| ( epred1_2 @ X1 @ X2 @ X1 )
| ~ ( X3
@ ^ [Z0: $i] : ( X1 @ ( esk1_3 @ X1 @ X2 @ X3 @ Z0 ) ) )
| ~ ( X3 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_5,negated_conjecture,
! [X2: $i > $i,X1: $i > $i] :
( ( ( ^ [Z0: $i] :
( X1
@ ( esk1_3 @ X1 @ X2
@ ^ [Z1: $i > $i] : ( Z1 != X2 )
@ Z0 ) ) )
= X2 )
| ( X1 = X2 )
| ( epred1_2 @ X1 @ X2 @ X1 ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_4]) ).
thf(c_0_6,negated_conjecture,
a != b,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_7,negated_conjecture,
! [X5: $i,X2: $i > $i,X1: $i > $i] :
( ( ( X1
@ ( esk1_3 @ X1 @ X2
@ ^ [Z0: $i > $i] : ( Z0 != X2 )
@ X5 ) )
= ( X2 @ X5 ) )
| ( X1 = X2 )
| ( epred1_2 @ X1 @ X2 @ X1 ) ),
inference(arg_cong,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
! [X3: ( $i > $i ) > $o,X2: $i > $i,X1: $i > $i] :
( ( X3 @ X2 )
| ~ ( X3
@ ^ [Z0: $i] : ( X1 @ ( esk1_3 @ X1 @ X2 @ X3 @ Z0 ) ) )
| ~ ( X3 @ X1 )
| ~ ( epred1_2 @ X1 @ X2
@ ^ [Z0: $i] : ( X2 @ ( X1 @ Z0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i > $i,X5: $i] :
( ( ( ^ [Z0: $i] : b )
= X1 )
| ( epred1_2
@ ^ [Z0: $i] : b
@ X1
@ ^ [Z0: $i] : b )
| ( ( X1 @ X5 )
!= a ) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X2: $i > $i,X1: $i > $i] :
( ( ( ^ [Z0: $i] :
( X1
@ ( esk1_3 @ X1 @ X2
@ ^ [Z1: $i > $i] : ( Z1 != X2 )
@ Z0 ) ) )
= X2 )
| ( X1 = X2 )
| ~ ( epred1_2 @ X1 @ X2
@ ^ [Z0: $i] : ( X2 @ ( X1 @ Z0 ) ) ) ),
inference(eliminate_leibniz_eq,[status(thm)],[inference(cn,[status(thm)],[]),c_0_8]) ).
thf(c_0_11,negated_conjecture,
( ( ( ^ [Z0: $i] : Z0 )
= ( ^ [Z0: $i] : b ) )
| ( epred1_2
@ ^ [Z0: $i] : b
@ ^ [Z0: $i] : Z0
@ ^ [Z0: $i] : b ) ),
inference(er,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
( ( ^ [Z0: $i] : Z0 )
= ( ^ [Z0: $i] : b ) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_13,negated_conjecture,
! [X5: $i] : ( X5 = b ),
inference(arg_cong,[status(thm)],[c_0_12]) ).
thf(c_0_14,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_6,c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU933^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.09 % Computer : n012.cluster.edu
% 0.00/0.09 % Model : x86_64 x86_64
% 0.00/0.09 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.09 % Memory : 8046.5625MB
% 0.00/0.09 % OS : Linux 6.8.0-71-generic
% 0.00/0.09 % CPULimit : 300
% 0.00/0.09 % WCLimit : 300
% 0.00/0.09 % DateTime : Tue Sep 29 14:46:33 UTC 2026
% 0.00/0.09 % CPUTime :
% 0.00/0.09 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.11 Running higher-order theorem proving
% 0.07/0.12 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.GiT4UxGhVQ/E---3.1_204748.p
% 0.07/0.23 % Version: 3.5.1-ho
% 0.07/0.23 % Preprocessing class: HSSSSMSSSSMNHHA.
% 0.07/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.23 % Starting post_as_ho5 with 1500s (5) cores
% 0.07/0.23 % Starting sh2lt with 300s (1) cores
% 0.07/0.23 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.07/0.23 % Starting post_as_ho10 with 300s (1) cores
% 0.07/0.23 % post_as_ho5 with pid 204761 completed with status 0
% 0.07/0.23 % Result found by post_as_ho5
% 0.07/0.23 % Preprocessing class: HSSSSMSSSSMNHHA.
% 0.07/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.23 % Starting post_as_ho5 with 1500s (5) cores
% 0.07/0.23 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.07/0.23 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.07/0.23 % Search class: HGUSF-FFSF33-MHHFFMBN
% 0.07/0.23 % partial match(2): HGUSF-FFSF31-SHHFFMBN
% 0.07/0.23 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.23 % Starting SubtermCWHack with 136s (1) cores
% 0.07/0.23 % Starting post_as_ho5 with 151s (1) cores
% 0.07/0.23 % Starting lpo8_s with 136s (1) cores
% 0.07/0.23 % Starting sh2lt with 136s (1) cores
% 0.07/0.23 % Starting sh2l with 136s (1) cores
% 0.07/0.23 % SubtermCWHack with pid 204765 completed with status 10
% 0.07/0.23 % Starting full_lambda_4 with 136s (1) cores
% 0.07/0.23 % full_lambda_4 with pid 204773 completed with status 10
% 0.07/0.23 % Starting new_ho_10 with 669s (1) cores
% 0.07/0.23 % new_ho_10 with pid 204776 completed with status 10
% 0.07/0.23 % post_as_ho5 with pid 204766 completed with status 0
% 0.07/0.23 % Result found by post_as_ho5
% 0.07/0.23 % Preprocessing class: HSSSSMSSSSMNHHA.
% 0.07/0.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.23 % Starting post_as_ho5 with 1500s (5) cores
% 0.07/0.23 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.07/0.23 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.07/0.23 % Search class: HGUSF-FFSF33-MHHFFMBN
% 0.07/0.23 % partial match(2): HGUSF-FFSF31-SHHFFMBN
% 0.07/0.23 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.07/0.23 % Starting SubtermCWHack with 136s (1) cores
% 0.07/0.23 % Starting post_as_ho5 with 151s (1) cores
% 0.07/0.23 % Preprocessing time : 0.001 s
% 0.07/0.23 % Presaturation interreduction done
% 0.07/0.23
% 0.07/0.23 % Proof found!
% 0.07/0.23 % SZS status Theorem
% 0.07/0.23 % SZS output start CNFRefutation
% See solution above
% 0.07/0.23 % Parsed axioms : 3
% 0.07/0.23 % Removed by relevancy pruning/SinE : 2
% 0.07/0.23 % Initial clauses : 7
% 0.07/0.23 % Removed in clause preprocessing : 0
% 0.07/0.23 % Initial clauses in saturation : 7
% 0.07/0.23 % Processed clauses : 191
% 0.07/0.23 % ...of these trivial : 6
% 0.07/0.23 % ...subsumed : 93
% 0.07/0.23 % ...remaining for further processing : 92
% 0.07/0.23 % Other redundant clauses eliminated : 221
% 0.07/0.23 % Clauses deleted for lack of memory : 0
% 0.07/0.23 % Backward-subsumed : 0
% 0.07/0.23 % Backward-rewritten : 44
% 0.07/0.23 % Generated clauses : 2406
% 0.07/0.23 % ...of the previous two non-redundant : 1889
% 0.07/0.23 % ...aggressively subsumed : 0
% 0.07/0.23 % Contextual simplify-reflections : 0
% 0.07/0.23 % Paramodulations : 1928
% 0.07/0.23 % Factorizations : 9
% 0.07/0.23 % NegExts : 17
% 0.07/0.23 % Equation resolutions : 269
% 0.07/0.23 % Disequality decompositions : 0
% 0.07/0.23 % Total rewrite steps : 391
% 0.07/0.23 % ...of those cached : 367
% 0.07/0.23 % Propositional unsat checks : 0
% 0.07/0.23 % Propositional check models : 0
% 0.07/0.23 % Propositional check unsatisfiable : 0
% 0.07/0.23 % Propositional clauses : 0
% 0.07/0.23 % Propositional clauses after purity: 0
% 0.07/0.23 % Propositional unsat core size : 0
% 0.07/0.23 % Propositional preprocessing time : 0.000
% 0.07/0.23 % Propositional encoding time : 0.000
% 0.07/0.23 % Propositional solver time : 0.000
% 0.07/0.23 % Success case prop preproc time : 0.000
% 0.07/0.23 % Success case prop encoding time : 0.000
% 0.07/0.23 % Success case prop solver time : 0.000
% 0.07/0.23 % Current number of processed clauses : 39
% 0.07/0.23 % Positive orientable unit clauses : 1
% 0.07/0.23 % Positive unorientable unit clauses: 1
% 0.07/0.23 % Negative unit clauses : 0
% 0.07/0.23 % Non-unit-clauses : 37
% 0.07/0.23 % Current number of unprocessed clauses: 1703
% 0.07/0.23 % ...number of literals in the above : 7945
% 0.07/0.23 % Current number of archived formulas : 0
% 0.07/0.23 % Current number of archived clauses : 53
% 0.07/0.23 % Clause-clause subsumption calls (NU) : 1988
% 0.07/0.23 % Rec. Clause-clause subsumption calls : 931
% 0.07/0.23 % Non-unit clause-clause subsumptions : 87
% 0.07/0.23 % Unit Clause-clause subsumption calls : 15
% 0.07/0.23 % Rewrite failures with RHS unbound : 0
% 0.07/0.23 % BW rewrite match attempts : 79
% 0.07/0.23 % BW rewrite match successes : 23
% 0.07/0.23 % Condensation attempts : 0
% 0.07/0.23 % Condensation successes : 0
% 0.07/0.23 % Termbank termtop insertions : 336010
% 0.07/0.23 % Search garbage collected termcells : 297
% 0.07/0.23
% 0.07/0.23 % -------------------------------------------------
% 0.07/0.23 % User time : 0.101 s
% 0.07/0.23 % System time : 0.006 s
% 0.07/0.23 % Total time : 0.107 s
% 0.07/0.23 % Maximum resident set size: 3584 pages
% 0.07/0.23
% 0.07/0.23 % -------------------------------------------------
% 0.07/0.23 % User time : 0.394 s
% 0.07/0.23 % System time : 0.014 s
% 0.07/0.23 % Total time : 0.408 s
% 0.07/0.23 % Maximum resident set size: 4608 pages
% 0.07/0.23 % E exiting
%------------------------------------------------------------------------------