%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU646^2 : 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 : n001.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 08:24:51 AM UTC 2026
% Result : Theorem 0.10s 0.24s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 16 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 274 ( 10 ~; 6 |; 11 &; 233 @)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 50 ( 4 ^; 40 !; 6 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
emptyset: $i ).
thf(decl_25,type,
setadjoin: $i > $i > $i ).
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,
kfst: $i > $i ).
thf(decl_30,type,
kfstpairEq: $o ).
thf(decl_31,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_32,type,
esk2_3: $i > $i > $i > $i ).
thf(decl_33,type,
esk3_0: $i ).
thf(decl_34,type,
esk4_0: $i ).
thf(decl_35,type,
esk5_0: $i ).
thf(kpair,axiom,
( kpair
= ( ^ [X1: $i,X2: $i] : ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fSPt2w5ZYs/E---3.1_1295431.p',kpair) ).
thf(cartprodfstin,conjecture,
( cartprodmempair1
=> ( kfstpairEq
=> ! [X3: $i,X4: $i,X5: $i] :
( ( in @ X5 @ ( cartprod @ X3 @ X4 ) )
=> ( in @ ( kfst @ X5 ) @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fSPt2w5ZYs/E---3.1_1295431.p',cartprodfstin) ).
thf(kfstpairEq,axiom,
( kfstpairEq
<=> ! [X1: $i,X2: $i] :
( ( kfst @ ( kpair @ X1 @ X2 ) )
= X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.fSPt2w5ZYs/E---3.1_1295431.p',kfstpairEq) ).
thf(cartprodmempair1,axiom,
( cartprodmempair1
<=> ! [X3: $i,X4: $i,X5: $i] :
( ( in @ X5 @ ( cartprod @ X3 @ X4 ) )
=> ? [X1: $i] :
( ( in @ X1 @ X3 )
& ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X5
= ( kpair @ X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fSPt2w5ZYs/E---3.1_1295431.p',cartprodmempair1) ).
thf(c_0_4,plain,
( kpair
= ( ^ [Z0: $i,Z1: $i] : ( setadjoin @ ( setadjoin @ Z0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Z0 @ ( setadjoin @ Z1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fof_simplification,[status(thm)],[kpair]) ).
thf(c_0_5,negated_conjecture,
~ ( cartprodmempair1
=> ( kfstpairEq
=> ! [X3: $i,X4: $i,X5: $i] :
( ( in @ X5 @ ( cartprod @ X3 @ X4 ) )
=> ( in @ ( kfst @ X5 ) @ X3 ) ) ) ),
inference(assume_negation,[status(cth)],[cartprodfstin]) ).
thf(c_0_6,axiom,
( kfstpairEq
= ( ! [X1: $i,X2: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
= X1 ) ) ),
inference(apply_def,[status(thm)],[kfstpairEq,c_0_4]) ).
thf(c_0_7,axiom,
( cartprodmempair1
= ( ! [X3: $i,X4: $i,X5: $i] :
( ( in @ X5 @ ( cartprod @ X3 @ X4 ) )
=> ? [X1: $i] :
( ( in @ X1 @ X3 )
& ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( X5
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[cartprodmempair1,c_0_4]) ).
thf(c_0_8,negated_conjecture,
~ ( ! [X16: $i,X17: $i,X18: $i] :
( ( in @ X18 @ ( cartprod @ X16 @ X17 ) )
=> ? [X19: $i] :
( ( in @ X19 @ X16 )
& ? [X20: $i] :
( ( in @ X20 @ X17 )
& ( X18
= ( setadjoin @ ( setadjoin @ X19 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X19 @ ( setadjoin @ X20 @ emptyset ) ) @ emptyset ) ) ) ) ) )
=> ( ! [X21: $i,X22: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X21 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X21 @ ( setadjoin @ X22 @ emptyset ) ) @ emptyset ) ) )
= X21 )
=> ! [X3: $i,X4: $i,X5: $i] :
( ( in @ X5 @ ( cartprod @ X3 @ X4 ) )
=> ( in @ ( kfst @ X5 ) @ X3 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_5,c_0_6]),c_0_7]) ).
thf(c_0_9,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
= ( setadjoin @ ( setadjoin @ ( esk1_3 @ X23 @ X24 @ X25 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk1_3 @ X23 @ X24 @ X25 ) @ ( setadjoin @ ( esk2_3 @ X23 @ X24 @ X25 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X25 @ ( cartprod @ X23 @ X24 ) ) )
& ( ( kfst @ ( setadjoin @ ( setadjoin @ X28 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X28 @ ( setadjoin @ X29 @ emptyset ) ) @ emptyset ) ) )
= X28 )
& ( in @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ) )
& ~ ( in @ ( kfst @ esk5_0 ) @ esk3_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_8])])])])])]) ).
thf(c_0_10,negated_conjecture,
! [X2: $i,X1: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( X1
= ( setadjoin @ ( setadjoin @ ( esk1_3 @ X2 @ X3 @ X1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( esk1_3 @ X2 @ X3 @ X1 ) @ ( setadjoin @ ( esk2_3 @ X2 @ X3 @ X1 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X1 @ ( cartprod @ X2 @ X3 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( ( esk1_3 @ X1 @ X2 @ X3 )
= ( kfst @ X3 ) )
| ~ ( in @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_13,negated_conjecture,
in @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,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_9]) ).
thf(c_0_15,negated_conjecture,
( ( esk1_3 @ esk3_0 @ esk4_0 @ esk5_0 )
= ( kfst @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_16,negated_conjecture,
~ ( in @ ( kfst @ esk5_0 ) @ esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_17,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_13])]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU646^2 : 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 : n001.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 14:07:50 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.fSPt2w5ZYs/E---3.1_1295431.p
% 0.10/0.24 % Version: 3.5.1-ho
% 0.10/0.24 % Preprocessing class: HSSSSLSSSLSNSFN.
% 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 ehoh_best_sine_rwall with 300s (1) cores
% 0.10/0.24 % Starting lpo1_def_fix with 300s (1) cores
% 0.10/0.24 % Starting ehoh_best8_lambda with 300s (1) cores
% 0.10/0.24 % ehoh_best_sine_rwall with pid 1295475 completed with status 0
% 0.10/0.24 % Result found by ehoh_best_sine_rwall
% 0.10/0.24 % Preprocessing class: HSSSSLSSSLSNSFN.
% 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 ehoh_best_sine_rwall with 300s (1) cores
% 0.10/0.24 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.24 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.24 % Search class: HHUSF-FFSF32-MSFFMFNN
% 0.10/0.24 % partial match(2): HHUSF-FFSF32-SFFFMFNN
% 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 1295479 completed with status 0
% 0.10/0.24 % Result found by SubtermCWHack
% 0.10/0.24 % Preprocessing class: HSSSSLSSSLSNSFN.
% 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 ehoh_best_sine_rwall with 300s (1) cores
% 0.10/0.24 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.24 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.24 % Search class: HHUSF-FFSF32-MSFFMFNN
% 0.10/0.24 % partial match(2): HHUSF-FFSF32-SFFFMFNN
% 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 : 8
% 0.10/0.24 % Initial clauses : 6
% 0.10/0.24 % Removed in clause preprocessing : 0
% 0.10/0.24 % Initial clauses in saturation : 6
% 0.10/0.24 % Processed clauses : 8
% 0.10/0.24 % ...of these trivial : 0
% 0.10/0.24 % ...subsumed : 0
% 0.10/0.24 % ...remaining for further processing : 8
% 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 : 0
% 0.10/0.24 % Backward-rewritten : 0
% 0.10/0.24 % Generated clauses : 7
% 0.10/0.24 % ...of the previous two non-redundant : 5
% 0.10/0.24 % ...aggressively subsumed : 0
% 0.10/0.24 % Contextual simplify-reflections : 0
% 0.10/0.24 % Paramodulations : 7
% 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 : 1
% 0.10/0.24 % ...of those cached : 0
% 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 : 8
% 0.10/0.24 % Positive orientable unit clauses : 3
% 0.10/0.24 % Positive unorientable unit clauses: 0
% 0.10/0.24 % Negative unit clauses : 1
% 0.10/0.24 % Non-unit-clauses : 4
% 0.10/0.24 % Current number of unprocessed clauses: 3
% 0.10/0.24 % ...number of literals in the above : 6
% 0.10/0.24 % Current number of archived formulas : 0
% 0.10/0.24 % Current number of archived clauses : 0
% 0.10/0.24 % Clause-clause subsumption calls (NU) : 0
% 0.10/0.24 % Rec. Clause-clause subsumption calls : 0
% 0.10/0.24 % Non-unit clause-clause subsumptions : 0
% 0.10/0.24 % Unit Clause-clause subsumption calls : 0
% 0.10/0.24 % Rewrite failures with RHS unbound : 0
% 0.10/0.24 % BW rewrite match attempts : 0
% 0.10/0.24 % BW rewrite match successes : 0
% 0.10/0.24 % Condensation attempts : 0
% 0.10/0.24 % Condensation successes : 0
% 0.10/0.24 % Termbank termtop insertions : 815
% 0.10/0.24 % Search garbage collected termcells : 212
% 0.10/0.24
% 0.10/0.24 % -------------------------------------------------
% 0.10/0.24 % User time : 0.003 s
% 0.10/0.24 % System time : 0.001 s
% 0.10/0.24 % Total time : 0.004 s
% 0.10/0.24 % Maximum resident set size: 3636 pages
% 0.10/0.24
% 0.10/0.24 % -------------------------------------------------
% 0.10/0.24 % User time : 0.006 s
% 0.10/0.24 % System time : 0.004 s
% 0.10/0.24 % Total time : 0.010 s
% 0.10/0.24 % Maximum resident set size: 4608 pages
% 0.10/0.24 % E exiting
%------------------------------------------------------------------------------