%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU658^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:24:54 AM UTC 2026
% Result : Theorem 0.25s 0.30s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 9 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 173 ( 11 ~; 7 |; 9 &; 133 @)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 42 ( 0 ^; 38 !; 4 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
kpair: $i > $i > $i ).
thf(decl_25,type,
cartprod: $i > $i > $i ).
thf(decl_26,type,
cartprodmempair1: $o ).
thf(decl_27,type,
ksnd: $i > $i ).
thf(decl_28,type,
ksndpairEq: $o ).
thf(decl_29,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_30,type,
esk2_3: $i > $i > $i > $i ).
thf(decl_31,type,
esk3_0: $i ).
thf(decl_32,type,
esk4_0: $i ).
thf(decl_33,type,
esk5_0: $i ).
thf(cartprodsndin,conjecture,
( cartprodmempair1
=> ( ksndpairEq
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ( in @ ( ksnd @ X3 ) @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vc6Io2gVtE/E---3.1_1341538.p',cartprodsndin) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ? [X4: $i] :
( ( in @ X4 @ X1 )
& ? [X5: $i] :
( ( in @ X5 @ X2 )
& ( X3
= ( kpair @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.vc6Io2gVtE/E---3.1_1341538.p',cartprodmempair1) ).
thf(ksndpairEq,axiom,
( ksndpairEq
<=> ! [X4: $i,X5: $i] :
( ( ksnd @ ( kpair @ X4 @ X5 ) )
= X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.vc6Io2gVtE/E---3.1_1341538.p',ksndpairEq) ).
thf(c_0_3,negated_conjecture,
~ ( cartprodmempair1
=> ( ksndpairEq
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ( in @ ( ksnd @ X3 ) @ X2 ) ) ) ),
inference(assume_negation,[status(cth)],[cartprodsndin]) ).
thf(c_0_4,negated_conjecture,
~ ( ! [X16: $i,X17: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X16 @ X17 ) )
=> ? [X19: $i] :
( ( in @ X19 @ X16 )
& ? [X20: $i] :
( ( in @ X20 @ X17 )
& ( X18
= ( kpair @ X19 @ X20 ) ) ) ) )
=> ( ! [X21: $i,X22: $i] :
( ( ksnd @ ( kpair @ X21 @ X22 ) )
= X22 )
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ( in @ ( ksnd @ X3 ) @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_3,cartprodmempair1]),ksndpairEq]) ).
thf(c_0_5,negated_conjecture,
! [X23: $i,X24: $i,X25: $i,X28: $i,X29: $i] :
( ( ( in @ ( esk1_3 @ X23 @ X24 @ X25 ) @ X23 )
| ~ ( in @ X25 @ ( cartprod @ X23 @ X24 ) ) )
& ( ( in @ ( esk2_3 @ X23 @ X24 @ X25 ) @ X24 )
| ~ ( in @ X25 @ ( cartprod @ X23 @ X24 ) ) )
& ( ( X25
= ( kpair @ ( esk1_3 @ X23 @ X24 @ X25 ) @ ( esk2_3 @ X23 @ X24 @ X25 ) ) )
| ~ ( in @ X25 @ ( cartprod @ X23 @ X24 ) ) )
& ( ( ksnd @ ( kpair @ X28 @ X29 ) )
= X29 )
& ( in @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ) )
& ~ ( in @ ( ksnd @ esk5_0 ) @ esk4_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_4])])])])])]) ).
thf(c_0_6,negated_conjecture,
! [X1: $i,X2: $i] :
( ( ksnd @ ( kpair @ X1 @ X2 ) )
= X2 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,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_5]) ).
thf(c_0_8,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_5]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( ( esk2_3 @ X1 @ X2 @ X3 )
= ( ksnd @ X3 ) )
| ~ ( in @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( in @ ( ksnd @ X1 ) @ X2 )
| ~ ( in @ X1 @ ( cartprod @ X3 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_11,negated_conjecture,
in @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_12,negated_conjecture,
~ ( in @ ( ksnd @ esk5_0 ) @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_13,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU658^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.21 % Computer : n002.cluster.edu
% 0.13/0.21 % Model : x86_64 x86_64
% 0.13/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.21 % Memory : 8046.5625MB
% 0.13/0.21 % OS : Linux 6.8.0-71-generic
% 0.13/0.21 % CPULimit : 300
% 0.13/0.21 % WCLimit : 300
% 0.13/0.21 % DateTime : Tue Sep 29 14:06:07 UTC 2026
% 0.13/0.21 % CPUTime :
% 0.13/0.21 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.26 Running higher-order theorem proving
% 0.13/0.27 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.vc6Io2gVtE/E---3.1_1341538.p
% 0.25/0.30 % Version: 3.5.1-ho
% 0.25/0.30 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.25/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.30 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.25/0.30 % Starting post_as_ho8 with 300s (1) cores
% 0.25/0.30 % Starting post_as_ho3 with 300s (1) cores
% 0.25/0.30 % Starting post_as_ho2 with 300s (1) cores
% 0.25/0.30 % lpo6_lambda_fix with pid 1341551 completed with status 0
% 0.25/0.30 % Result found by lpo6_lambda_fix
% 0.25/0.30 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.25/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.30 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.25/0.30 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.25/0.30 % No SInE strategy applied
% 0.25/0.30 % Search class: HHUSF-FFSF32-SFFFMFNN
% 0.25/0.30 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.30 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.30 % Starting lpo6_lambda_fix with 151s (1) cores
% 0.25/0.30 % Starting sh5l with 136s (1) cores
% 0.25/0.30 % Starting new_bool_1 with 136s (1) cores
% 0.25/0.30 % Starting new_bool_2 with 136s (1) cores
% 0.25/0.30 % SubtermCWHack with pid 1341555 completed with status 0
% 0.25/0.30 % Result found by SubtermCWHack
% 0.25/0.30 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.25/0.30 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.30 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.25/0.30 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = Auto)
% 0.25/0.30 % No SInE strategy applied
% 0.25/0.30 % Search class: HHUSF-FFSF32-SFFFMFNN
% 0.25/0.30 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.30 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.30 % Preprocessing time : 0.002 s
% 0.25/0.30
% 0.25/0.30 % Proof found!
% 0.25/0.30 % SZS status Theorem
% 0.25/0.30 % SZS output start CNFRefutation
% See solution above
% 0.25/0.30 % Parsed axioms : 9
% 0.25/0.30 % Removed by relevancy pruning/SinE : 0
% 0.25/0.30 % Initial clauses : 12
% 0.25/0.30 % Removed in clause preprocessing : 6
% 0.25/0.30 % Initial clauses in saturation : 6
% 0.25/0.30 % Processed clauses : 8
% 0.25/0.30 % ...of these trivial : 0
% 0.25/0.30 % ...subsumed : 0
% 0.25/0.30 % ...remaining for further processing : 8
% 0.25/0.30 % Other redundant clauses eliminated : 0
% 0.25/0.30 % Clauses deleted for lack of memory : 0
% 0.25/0.30 % Backward-subsumed : 0
% 0.25/0.30 % Backward-rewritten : 0
% 0.25/0.30 % Generated clauses : 6
% 0.25/0.30 % ...of the previous two non-redundant : 3
% 0.25/0.30 % ...aggressively subsumed : 0
% 0.25/0.30 % Contextual simplify-reflections : 0
% 0.25/0.30 % Paramodulations : 6
% 0.25/0.30 % Factorizations : 0
% 0.25/0.30 % NegExts : 0
% 0.25/0.30 % Equation resolutions : 0
% 0.25/0.30 % Disequality decompositions : 0
% 0.25/0.30 % Total rewrite steps : 0
% 0.25/0.30 % ...of those cached : 0
% 0.25/0.30 % Propositional unsat checks : 0
% 0.25/0.30 % Propositional check models : 0
% 0.25/0.30 % Propositional check unsatisfiable : 0
% 0.25/0.30 % Propositional clauses : 0
% 0.25/0.30 % Propositional clauses after purity: 0
% 0.25/0.30 % Propositional unsat core size : 0
% 0.25/0.30 % Propositional preprocessing time : 0.000
% 0.25/0.30 % Propositional encoding time : 0.000
% 0.25/0.30 % Propositional solver time : 0.000
% 0.25/0.30 % Success case prop preproc time : 0.000
% 0.25/0.30 % Success case prop encoding time : 0.000
% 0.25/0.30 % Success case prop solver time : 0.000
% 0.25/0.30 % Current number of processed clauses : 8
% 0.25/0.30 % Positive orientable unit clauses : 2
% 0.25/0.30 % Positive unorientable unit clauses: 0
% 0.25/0.30 % Negative unit clauses : 1
% 0.25/0.30 % Non-unit-clauses : 5
% 0.25/0.30 % Current number of unprocessed clauses: 1
% 0.25/0.30 % ...number of literals in the above : 2
% 0.25/0.30 % Current number of archived formulas : 0
% 0.25/0.30 % Current number of archived clauses : 0
% 0.25/0.30 % Clause-clause subsumption calls (NU) : 0
% 0.25/0.30 % Rec. Clause-clause subsumption calls : 0
% 0.25/0.30 % Non-unit clause-clause subsumptions : 0
% 0.25/0.30 % Unit Clause-clause subsumption calls : 0
% 0.25/0.30 % Rewrite failures with RHS unbound : 0
% 0.25/0.30 % BW rewrite match attempts : 0
% 0.25/0.30 % BW rewrite match successes : 0
% 0.25/0.30 % Condensation attempts : 0
% 0.25/0.30 % Condensation successes : 0
% 0.25/0.30 % Termbank termtop insertions : 713
% 0.25/0.30 % Search garbage collected termcells : 206
% 0.25/0.30
% 0.25/0.30 % -------------------------------------------------
% 0.25/0.30 % User time : 0.005 s
% 0.25/0.30 % System time : 0.003 s
% 0.25/0.30 % Total time : 0.008 s
% 0.25/0.30 % Maximum resident set size: 3632 pages
% 0.25/0.30
% 0.25/0.30 % -------------------------------------------------
% 0.25/0.30 % User time : 0.012 s
% 0.25/0.30 % System time : 0.014 s
% 0.25/0.30 % Total time : 0.026 s
% 0.25/0.30 % Maximum resident set size: 4864 pages
% 0.25/0.30 % E exiting
%------------------------------------------------------------------------------