%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP152^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:04:31 AM UTC 2026
% Result : Theorem 0.21s 0.37s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 110 ( 10 ~; 11 |; 1 &; 86 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
product_prod_a_a: $tType ).
thf(decl_sort2,type,
a: $tType ).
thf(decl_sort3,type,
set_Product_prod_a_a: $tType ).
thf(decl_sort4,type,
set_a: $tType ).
thf(decl_85,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(decl_167,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(decl_168,type,
member_a: a > set_a > $o ).
thf(decl_169,type,
carrier: set_a ).
thf(decl_170,type,
relation: set_Product_prod_a_a ).
thf(decl_171,type,
x: a ).
thf(decl_172,type,
y: a ).
thf(fact_3_compl,axiom,
! [X4: a] :
( ( member_a @ X4 @ carrier )
=> ! [X5: a] :
( ( member_a @ X5 @ carrier )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ X4 @ X5 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ X5 @ X4 ) @ relation ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.m56F4HiimW/E---3.1_1239474.p',fact_3_compl) ).
thf(conj_3,conjecture,
( ( member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ y @ x ) @ relation ) ),
file('/export/starexec/sandbox2/tmp/tmp.m56F4HiimW/E---3.1_1239474.p',conj_3) ).
thf(conj_1,hypothesis,
member_a @ y @ carrier,
file('/export/starexec/sandbox2/tmp/tmp.m56F4HiimW/E---3.1_1239474.p',conj_1) ).
thf(conj_0,hypothesis,
member_a @ x @ carrier,
file('/export/starexec/sandbox2/tmp/tmp.m56F4HiimW/E---3.1_1239474.p',conj_0) ).
thf(c_0_4,plain,
! [X1036: a,X1037: a] :
( ~ ( member_a @ X1036 @ carrier )
| ~ ( member_a @ X1037 @ carrier )
| ( member449909584od_a_a @ ( product_Pair_a_a @ X1036 @ X1037 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ X1037 @ X1036 ) @ relation ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_3_compl])])])]) ).
thf(c_0_5,negated_conjecture,
~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ y @ x ) @ relation ) ),
inference(assume_negation,[status(cth)],[conj_3]) ).
thf(c_0_6,plain,
! [X1: a,X2: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ X1 @ X2 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ X2 @ X1 ) @ relation )
| ~ ( member_a @ X1 @ carrier )
| ~ ( member_a @ X2 @ carrier ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_7,hypothesis,
member_a @ y @ carrier,
inference(split_conjunct,[status(thm)],[conj_1]) ).
thf(c_0_8,negated_conjecture,
( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ y @ x ) @ relation ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])]) ).
thf(c_0_9,hypothesis,
! [X1: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ y @ X1 ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ X1 @ y ) @ relation )
| ~ ( member_a @ X1 @ carrier ) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_10,hypothesis,
member_a @ x @ carrier,
inference(split_conjunct,[status(thm)],[conj_0]) ).
thf(c_0_11,negated_conjecture,
~ ( member449909584od_a_a @ ( product_Pair_a_a @ y @ x ) @ relation ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_12,negated_conjecture,
~ ( member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,hypothesis,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP152^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n006.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 20:01:54 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running higher-order theorem proving
% 0.21/0.31 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.m56F4HiimW/E---3.1_1239474.p
% 0.21/0.37 % Version: 3.5.1-ho
% 0.21/0.37 % Preprocessing class: HSLMSMSMSSMNHFA.
% 0.21/0.37 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.37 % Starting full_lambda_6 with 1200s (4) cores
% 0.21/0.37 % Starting additional_ho_6 with 300s (1) cores
% 0.21/0.37 % Starting new_ho_9 with 300s (1) cores
% 0.21/0.37 % Starting full_lambda_3 with 300s (1) cores
% 0.21/0.37 % Starting post_as_ho6 with 300s (1) cores
% 0.21/0.37 % full_lambda_3 with pid 1239495 completed with status 0
% 0.21/0.37 % Result found by full_lambda_3
% 0.21/0.37 % Preprocessing class: HSLMSMSMSSMNHFA.
% 0.21/0.37 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.37 % Starting full_lambda_6 with 1200s (4) cores
% 0.21/0.37 % Starting additional_ho_6 with 300s (1) cores
% 0.21/0.37 % Starting new_ho_9 with 300s (1) cores
% 0.21/0.37 % Starting full_lambda_3 with 300s (1) cores
% 0.21/0.37 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountTerms,hypos,1.5,,2,20000,1.0))
% 0.21/0.37 % SinE strategy is GSinE(CountTerms,hypos,1.5,,2,20000,1.0)
% 0.21/0.37 % Search class: HGUSS-FFMM21-DHFFFFBN
% 0.21/0.37 % partial match(2): HGHSS-FFMM21-SHFFFFBN
% 0.21/0.37 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.37 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.37 % SubtermCWHack with pid 1239497 completed with status 0
% 0.21/0.37 % Result found by SubtermCWHack
% 0.21/0.37 % Preprocessing class: HSLMSMSMSSMNHFA.
% 0.21/0.37 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.37 % Starting full_lambda_6 with 1200s (4) cores
% 0.21/0.37 % Starting additional_ho_6 with 300s (1) cores
% 0.21/0.37 % Starting new_ho_9 with 300s (1) cores
% 0.21/0.37 % Starting full_lambda_3 with 300s (1) cores
% 0.21/0.37 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountTerms,hypos,1.5,,2,20000,1.0))
% 0.21/0.37 % SinE strategy is GSinE(CountTerms,hypos,1.5,,2,20000,1.0)
% 0.21/0.37 % Search class: HGUSS-FFMM21-DHFFFFBN
% 0.21/0.37 % partial match(2): HGHSS-FFMM21-SHFFFFBN
% 0.21/0.37 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.37 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.37 % Preprocessing time : 0.003 s
% 0.21/0.37
% 0.21/0.37 % Proof found!
% 0.21/0.37 % SZS status Theorem
% 0.21/0.37 % SZS output start CNFRefutation
% See solution above
% 0.21/0.37 % Parsed axioms : 531
% 0.21/0.37 % Removed by relevancy pruning/SinE : 501
% 0.21/0.37 % Initial clauses : 48
% 0.21/0.37 % Removed in clause preprocessing : 7
% 0.21/0.37 % Initial clauses in saturation : 41
% 0.21/0.37 % Processed clauses : 50
% 0.21/0.37 % ...of these trivial : 5
% 0.21/0.37 % ...subsumed : 7
% 0.21/0.37 % ...remaining for further processing : 38
% 0.21/0.37 % Other redundant clauses eliminated : 10
% 0.21/0.37 % Clauses deleted for lack of memory : 0
% 0.21/0.37 % Backward-subsumed : 0
% 0.21/0.37 % Backward-rewritten : 5
% 0.21/0.37 % Generated clauses : 49
% 0.21/0.37 % ...of the previous two non-redundant : 34
% 0.21/0.37 % ...aggressively subsumed : 0
% 0.21/0.37 % Contextual simplify-reflections : 0
% 0.21/0.37 % Paramodulations : 37
% 0.21/0.37 % Factorizations : 0
% 0.21/0.37 % NegExts : 0
% 0.21/0.37 % Equation resolutions : 12
% 0.21/0.37 % Disequality decompositions : 0
% 0.21/0.37 % Total rewrite steps : 17
% 0.21/0.37 % ...of those cached : 7
% 0.21/0.37 % Propositional unsat checks : 0
% 0.21/0.37 % Propositional check models : 0
% 0.21/0.37 % Propositional check unsatisfiable : 0
% 0.21/0.37 % Propositional clauses : 0
% 0.21/0.37 % Propositional clauses after purity: 0
% 0.21/0.37 % Propositional unsat core size : 0
% 0.21/0.37 % Propositional preprocessing time : 0.000
% 0.21/0.37 % Propositional encoding time : 0.000
% 0.21/0.37 % Propositional solver time : 0.000
% 0.21/0.37 % Success case prop preproc time : 0.000
% 0.21/0.37 % Success case prop encoding time : 0.000
% 0.21/0.37 % Success case prop solver time : 0.000
% 0.21/0.37 % Current number of processed clauses : 33
% 0.21/0.37 % Positive orientable unit clauses : 11
% 0.21/0.37 % Positive unorientable unit clauses: 0
% 0.21/0.37 % Negative unit clauses : 3
% 0.21/0.37 % Non-unit-clauses : 19
% 0.21/0.37 % Current number of unprocessed clauses: 16
% 0.21/0.37 % ...number of literals in the above : 74
% 0.21/0.37 % Current number of archived formulas : 0
% 0.21/0.37 % Current number of archived clauses : 5
% 0.21/0.37 % Clause-clause subsumption calls (NU) : 62
% 0.21/0.37 % Rec. Clause-clause subsumption calls : 53
% 0.21/0.37 % Non-unit clause-clause subsumptions : 7
% 0.21/0.37 % Unit Clause-clause subsumption calls : 13
% 0.21/0.37 % Rewrite failures with RHS unbound : 0
% 0.21/0.37 % BW rewrite match attempts : 4
% 0.21/0.37 % BW rewrite match successes : 4
% 0.21/0.37 % Condensation attempts : 0
% 0.21/0.37 % Condensation successes : 0
% 0.21/0.37 % Termbank termtop insertions : 11002
% 0.21/0.37 % Search garbage collected termcells : 5421
% 0.21/0.37
% 0.21/0.37 % -------------------------------------------------
% 0.21/0.37 % User time : 0.008 s
% 0.21/0.37 % System time : 0.007 s
% 0.21/0.37 % Total time : 0.014 s
% 0.21/0.37 % Maximum resident set size: 5220 pages
% 0.21/0.37
% 0.21/0.37 % -------------------------------------------------
% 0.21/0.37 % User time : 0.024 s
% 0.21/0.37 % System time : 0.016 s
% 0.21/0.37 % Total time : 0.040 s
% 0.21/0.37 % Maximum resident set size: 5888 pages
% 0.21/0.37 % E exiting
%------------------------------------------------------------------------------