%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU681^2 : 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 : n014.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 08:25:01 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 87 ( 6 equ; 0 cnn)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 335 ( 29 ~; 25 |; 11 &; 238 @)
% ( 2 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 72 ( 6 ^; 62 !; 4 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
subset: $i > $i > $o ).
thf(decl_25,type,
subsetE: $o ).
thf(decl_26,type,
kpair: $i > $i > $i ).
thf(decl_27,type,
cartprod: $i > $i > $i ).
thf(decl_28,type,
cartprodmempair1: $o ).
thf(decl_29,type,
breln: $i > $i > $i > $o ).
thf(decl_30,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_31,type,
esk2_3: $i > $i > $i > $i ).
thf(decl_32,type,
esk3_0: $i ).
thf(decl_33,type,
esk4_0: $i ).
thf(decl_34,type,
esk5_0: $i ).
thf(decl_35,type,
epred1_0: $i > $o ).
thf(decl_36,type,
esk6_0: $i ).
thf(brelnall1,conjecture,
( subsetE
=> ( cartprodmempair1
=> ! [X1: $i,X2: $i,X7: $i] :
( ( breln @ X1 @ X2 @ X7 )
=> ! [X8: $i > $o] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X3 @ X5 ) @ X7 )
=> ( X8 @ ( kpair @ X3 @ X5 ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3 @ X7 )
=> ( X8 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.u1DIarX7vf/E---3.1_2720812.p',brelnall1) ).
thf(breln,axiom,
( breln
= ( ^ [X1: $i,X2: $i,X6: $i] : ( subset @ X6 @ ( cartprod @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.u1DIarX7vf/E---3.1_2720812.p',breln) ).
thf(subsetE,axiom,
( subsetE
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( subset @ X1 @ X2 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.u1DIarX7vf/E---3.1_2720812.p',subsetE) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X1: $i,X2: $i,X4: $i] :
( ( in @ X4 @ ( cartprod @ X1 @ X2 ) )
=> ? [X3: $i] :
( ( in @ X3 @ X1 )
& ? [X5: $i] :
( ( in @ X5 @ X2 )
& ( X4
= ( kpair @ X3 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.u1DIarX7vf/E---3.1_2720812.p',cartprodmempair1) ).
thf(c_0_4,negated_conjecture,
~ ( subsetE
=> ( cartprodmempair1
=> ! [X1: $i,X2: $i,X7: $i] :
( ( breln @ X1 @ X2 @ X7 )
=> ! [X8: $i > $o] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X3 @ X5 ) @ X7 )
=> ( X8 @ ( kpair @ X3 @ X5 ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3 @ X7 )
=> ( X8 @ X3 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[brelnall1]) ).
thf(c_0_5,plain,
( breln
= ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[breln]) ).
thf(c_0_6,negated_conjecture,
~ ( ! [X24: $i,X25: $i,X26: $i] :
( ( subset @ X24 @ X25 )
=> ( ( in @ X26 @ X24 )
=> ( in @ X26 @ X25 ) ) )
=> ( ! [X27: $i,X28: $i,X29: $i] :
( ( in @ X29 @ ( cartprod @ X27 @ X28 ) )
=> ? [X30: $i] :
( ( in @ X30 @ X27 )
& ? [X31: $i] :
( ( in @ X31 @ X28 )
& ( X29
= ( kpair @ X30 @ X31 ) ) ) ) )
=> ! [X1: $i,X2: $i,X7: $i] :
( ( subset @ X7 @ ( cartprod @ X1 @ X2 ) )
=> ! [X8: $i > $o] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X3 @ X5 ) @ X7 )
=> ( X8 @ ( kpair @ X3 @ X5 ) ) ) ) )
=> ! [X3: $i] :
( ( in @ X3 @ X7 )
=> ( X8 @ X3 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,subsetE]),c_0_5]),cartprodmempair1]) ).
thf(c_0_7,negated_conjecture,
! [X32: $i,X33: $i,X34: $i,X35: $i,X36: $i,X37: $i,X44: $i,X45: $i] :
( ( ~ ( subset @ X32 @ X33 )
| ~ ( in @ X34 @ X32 )
| ( in @ X34 @ X33 ) )
& ( ( in @ ( esk1_3 @ X35 @ X36 @ X37 ) @ X35 )
| ~ ( in @ X37 @ ( cartprod @ X35 @ X36 ) ) )
& ( ( in @ ( esk2_3 @ X35 @ X36 @ X37 ) @ X36 )
| ~ ( in @ X37 @ ( cartprod @ X35 @ X36 ) ) )
& ( ( X37
= ( kpair @ ( esk1_3 @ X35 @ X36 @ X37 ) @ ( esk2_3 @ X35 @ X36 @ X37 ) ) )
| ~ ( in @ X37 @ ( cartprod @ X35 @ X36 ) ) )
& ( subset @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ) )
& ( ~ ( in @ X44 @ esk3_0 )
| ~ ( in @ X45 @ esk4_0 )
| ~ ( in @ ( kpair @ X44 @ X45 ) @ esk5_0 )
| ( epred1_0 @ ( kpair @ X44 @ X45 ) ) )
& ( in @ esk6_0 @ esk5_0 )
& ~ ( epred1_0 @ esk6_0 ) ),
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_6])])])])])]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i,X2: $i] :
( ( epred1_0 @ ( kpair @ X1 @ X2 ) )
| ~ ( in @ X1 @ esk3_0 )
| ~ ( in @ X2 @ esk4_0 )
| ~ ( in @ ( kpair @ X1 @ X2 ) @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( X1
= ( kpair @ ( esk1_3 @ X2 @ X3 @ X1 ) @ ( esk2_3 @ X2 @ X3 @ X1 ) ) )
| ~ ( in @ X1 @ ( cartprod @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( epred1_0 @ X1 )
| ~ ( in @ ( esk2_3 @ X2 @ X3 @ X1 ) @ esk4_0 )
| ~ ( in @ ( esk1_3 @ X2 @ X3 @ X1 ) @ esk3_0 )
| ~ ( in @ X1 @ ( cartprod @ X2 @ X3 ) )
| ~ ( in @ X1 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ ( esk2_3 @ X1 @ X2 @ X3 ) @ X2 )
| ~ ( in @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_12,negated_conjecture,
! [X3: $i,X2: $i,X1: $i] :
( ( in @ X3 @ X2 )
| ~ ( subset @ X1 @ X2 )
| ~ ( in @ X3 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_13,negated_conjecture,
subset @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_14,negated_conjecture,
! [X2: $i,X1: $i] :
( ( epred1_0 @ X1 )
| ~ ( in @ ( esk1_3 @ X2 @ esk4_0 @ X1 ) @ esk3_0 )
| ~ ( in @ X1 @ ( cartprod @ X2 @ esk4_0 ) )
| ~ ( in @ X1 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ ( esk1_3 @ X1 @ X2 @ X3 ) @ X1 )
| ~ ( in @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_16,negated_conjecture,
! [X1: $i] :
( ( in @ X1 @ ( cartprod @ esk3_0 @ esk4_0 ) )
| ~ ( in @ X1 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i] :
( ( epred1_0 @ X1 )
| ~ ( in @ X1 @ esk5_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
thf(c_0_18,negated_conjecture,
in @ esk6_0 @ esk5_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_19,negated_conjecture,
~ ( epred1_0 @ esk6_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_20,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU681^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.16 % Computer : n014.cluster.edu
% 0.07/0.16 % Model : x86_64 x86_64
% 0.07/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.16 % Memory : 8046.5625MB
% 0.07/0.16 % OS : Linux 6.8.0-71-generic
% 0.07/0.16 % CPULimit : 300
% 0.07/0.16 % WCLimit : 300
% 0.07/0.16 % DateTime : Tue Sep 29 14:09:30 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 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.u1DIarX7vf/E---3.1_2720812.p
% 0.07/0.24 % Version: 3.5.1-ho
% 0.07/0.24 % partial match(1): HSSSSLSSSLMNSSA
% 0.07/0.24 % Preprocessing class: HSSSSLSSSLSNSSA.
% 0.07/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.24 % Starting new_bool_2 with 300s (1) cores
% 0.07/0.24 % Starting new_bool_9 with 300s (1) cores
% 0.07/0.24 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 0.07/0.24 % new_bool_9 with pid 2720827 completed with status 0
% 0.07/0.24 % Result found by new_bool_9
% 0.07/0.24 % partial match(1): HSSSSLSSSLMNSSA
% 0.07/0.24 % Preprocessing class: HSSSSLSSSLSNSSA.
% 0.07/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.24 % Starting new_bool_2 with 300s (1) cores
% 0.07/0.24 % Starting new_bool_9 with 300s (1) cores
% 0.07/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1,,2,20000,1.0))
% 0.07/0.24 % SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 0.07/0.24 % Search class: HHUSF-FFSF32-SSSFMFNN
% 0.07/0.24 % partial match(2): HHUSF-FFSF32-SFFFMFNN
% 0.07/0.24 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.24 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.24 % SubtermCWHack with pid 2720831 completed with status 0
% 0.07/0.24 % Result found by SubtermCWHack
% 0.07/0.24 % partial match(1): HSSSSLSSSLMNSSA
% 0.07/0.24 % Preprocessing class: HSSSSLSSSLSNSSA.
% 0.07/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.24 % Starting new_ho_10 with 1500s (5) cores
% 0.07/0.24 % Starting new_bool_2 with 300s (1) cores
% 0.07/0.24 % Starting new_bool_9 with 300s (1) cores
% 0.07/0.24 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1,,2,20000,1.0))
% 0.07/0.24 % SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 0.07/0.24 % Search class: HHUSF-FFSF32-SSSFMFNN
% 0.07/0.24 % partial match(2): HHUSF-FFSF32-SFFFMFNN
% 0.07/0.24 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.24 % Starting SubtermCWHack with 31s (1) cores
% 0.07/0.24 % Preprocessing time : 0.001 s
% 0.07/0.24
% 0.07/0.24 % Proof found!
% 0.07/0.24 % SZS status Theorem
% 0.07/0.24 % SZS output start CNFRefutation
% See solution above
% 0.07/0.24 % Parsed axioms : 11
% 0.07/0.24 % Removed by relevancy pruning/SinE : 7
% 0.07/0.24 % Initial clauses : 8
% 0.07/0.24 % Removed in clause preprocessing : 0
% 0.07/0.24 % Initial clauses in saturation : 8
% 0.07/0.24 % Processed clauses : 12
% 0.07/0.24 % ...of these trivial : 0
% 0.07/0.24 % ...subsumed : 0
% 0.07/0.24 % ...remaining for further processing : 12
% 0.07/0.24 % Other redundant clauses eliminated : 0
% 0.07/0.24 % Clauses deleted for lack of memory : 0
% 0.07/0.24 % Backward-subsumed : 3
% 0.07/0.24 % Backward-rewritten : 0
% 0.07/0.24 % Generated clauses : 7
% 0.07/0.24 % ...of the previous two non-redundant : 4
% 0.07/0.24 % ...aggressively subsumed : 0
% 0.07/0.24 % Contextual simplify-reflections : 1
% 0.07/0.24 % Paramodulations : 7
% 0.07/0.24 % Factorizations : 0
% 0.07/0.24 % NegExts : 0
% 0.07/0.24 % Equation resolutions : 0
% 0.07/0.24 % Disequality decompositions : 0
% 0.07/0.24 % Total rewrite steps : 0
% 0.07/0.24 % ...of those cached : 0
% 0.07/0.24 % Propositional unsat checks : 0
% 0.07/0.24 % Propositional check models : 0
% 0.07/0.24 % Propositional check unsatisfiable : 0
% 0.07/0.24 % Propositional clauses : 0
% 0.07/0.24 % Propositional clauses after purity: 0
% 0.07/0.24 % Propositional unsat core size : 0
% 0.07/0.24 % Propositional preprocessing time : 0.000
% 0.07/0.24 % Propositional encoding time : 0.000
% 0.07/0.24 % Propositional solver time : 0.000
% 0.07/0.24 % Success case prop preproc time : 0.000
% 0.07/0.24 % Success case prop encoding time : 0.000
% 0.07/0.24 % Success case prop solver time : 0.000
% 0.07/0.24 % Current number of processed clauses : 9
% 0.07/0.24 % Positive orientable unit clauses : 2
% 0.07/0.24 % Positive unorientable unit clauses: 0
% 0.07/0.24 % Negative unit clauses : 1
% 0.07/0.24 % Non-unit-clauses : 6
% 0.07/0.24 % Current number of unprocessed clauses: 0
% 0.07/0.24 % ...number of literals in the above : 0
% 0.07/0.24 % Current number of archived formulas : 0
% 0.07/0.24 % Current number of archived clauses : 3
% 0.07/0.24 % Clause-clause subsumption calls (NU) : 18
% 0.07/0.24 % Rec. Clause-clause subsumption calls : 11
% 0.07/0.24 % Non-unit clause-clause subsumptions : 4
% 0.07/0.24 % Unit Clause-clause subsumption calls : 0
% 0.07/0.24 % Rewrite failures with RHS unbound : 0
% 0.07/0.24 % BW rewrite match attempts : 0
% 0.07/0.24 % BW rewrite match successes : 0
% 0.07/0.24 % Condensation attempts : 0
% 0.07/0.24 % Condensation successes : 0
% 0.07/0.24 % Termbank termtop insertions : 1225
% 0.07/0.24 % Search garbage collected termcells : 392
% 0.07/0.24
% 0.07/0.24 % -------------------------------------------------
% 0.07/0.24 % User time : 0.002 s
% 0.07/0.24 % System time : 0.003 s
% 0.07/0.24 % Total time : 0.005 s
% 0.07/0.24 % Maximum resident set size: 3640 pages
% 0.07/0.24
% 0.07/0.24 % -------------------------------------------------
% 0.07/0.24 % User time : 0.003 s
% 0.07/0.24 % System time : 0.007 s
% 0.07/0.24 % Total time : 0.010 s
% 0.07/0.24 % Maximum resident set size: 4864 pages
% 0.07/0.24 % E exiting
%------------------------------------------------------------------------------