%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU660^2 : 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 : n018.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 08:24:55 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 13 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 192 ( 13 ~; 9 |; 9 &; 146 @)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 55 ( 0 ^; 51 !; 4 ?; 55 :)
% 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,
setukpairinjR: $o ).
thf(decl_28,type,
esk1_3: $i > $i > $i > $i ).
thf(decl_29,type,
esk2_3: $i > $i > $i > $i ).
thf(decl_30,type,
esk3_0: $i ).
thf(decl_31,type,
esk4_0: $i ).
thf(decl_32,type,
esk5_0: $i ).
thf(decl_33,type,
esk6_0: $i ).
thf(cartprodpairmemER,conjecture,
( cartprodmempair1
=> ( setukpairinjR
=> ! [X1: $i,X2: $i,X4: $i,X5: $i] :
( ( in @ ( kpair @ X4 @ X5 ) @ ( cartprod @ X1 @ X2 ) )
=> ( in @ X5 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.GnvfkAC7Q9/E---3.1_125963.p',cartprodpairmemER) ).
thf(setukpairinjR,axiom,
( setukpairinjR
<=> ! [X4: $i,X5: $i,X6: $i,X3: $i] :
( ( ( kpair @ X4 @ X5 )
= ( kpair @ X6 @ X3 ) )
=> ( X5 = X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.GnvfkAC7Q9/E---3.1_125963.p',setukpairinjR) ).
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.GnvfkAC7Q9/E---3.1_125963.p',cartprodmempair1) ).
thf(c_0_3,negated_conjecture,
~ ( cartprodmempair1
=> ( setukpairinjR
=> ! [X1: $i,X2: $i,X4: $i,X5: $i] :
( ( in @ ( kpair @ X4 @ X5 ) @ ( cartprod @ X1 @ X2 ) )
=> ( in @ X5 @ X2 ) ) ) ),
inference(assume_negation,[status(cth)],[cartprodpairmemER]) ).
thf(c_0_4,negated_conjecture,
~ ( ! [X20: $i,X21: $i,X22: $i] :
( ( in @ X22 @ ( cartprod @ X20 @ X21 ) )
=> ? [X23: $i] :
( ( in @ X23 @ X20 )
& ? [X24: $i] :
( ( in @ X24 @ X21 )
& ( X22
= ( kpair @ X23 @ X24 ) ) ) ) )
=> ( ! [X25: $i,X26: $i,X27: $i,X28: $i] :
( ( ( kpair @ X25 @ X26 )
= ( kpair @ X27 @ X28 ) )
=> ( X26 = X28 ) )
=> ! [X1: $i,X2: $i,X4: $i,X5: $i] :
( ( in @ ( kpair @ X4 @ X5 ) @ ( cartprod @ X1 @ X2 ) )
=> ( in @ X5 @ X2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_3,setukpairinjR]),cartprodmempair1]) ).
thf(c_0_5,negated_conjecture,
! [X29: $i,X30: $i,X31: $i,X34: $i,X35: $i,X36: $i,X37: $i] :
( ( ( in @ ( esk1_3 @ X29 @ X30 @ X31 ) @ X29 )
| ~ ( in @ X31 @ ( cartprod @ X29 @ X30 ) ) )
& ( ( in @ ( esk2_3 @ X29 @ X30 @ X31 ) @ X30 )
| ~ ( in @ X31 @ ( cartprod @ X29 @ X30 ) ) )
& ( ( X31
= ( kpair @ ( esk1_3 @ X29 @ X30 @ X31 ) @ ( esk2_3 @ X29 @ X30 @ X31 ) ) )
| ~ ( in @ X31 @ ( cartprod @ X29 @ X30 ) ) )
& ( ( ( kpair @ X34 @ X35 )
!= ( kpair @ X36 @ X37 ) )
| ( X35 = X37 ) )
& ( in @ ( kpair @ esk5_0 @ esk6_0 ) @ ( cartprod @ esk3_0 @ esk4_0 ) )
& ~ ( in @ esk6_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,X3: $i,X4: $i] :
( ( X2 = X4 )
| ( ( kpair @ X1 @ X2 )
!= ( kpair @ X3 @ X4 ) ) ),
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,X4: $i,X3: $i,X2: $i] :
( ( ( esk2_3 @ X1 @ X2 @ ( kpair @ X3 @ X4 ) )
= X4 )
| ~ ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7])]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X4: $i,X3: $i,X2: $i] :
( ( in @ X1 @ X2 )
| ~ ( in @ ( kpair @ X3 @ X1 ) @ ( cartprod @ X4 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_11,negated_conjecture,
in @ ( kpair @ esk5_0 @ esk6_0 ) @ ( cartprod @ esk3_0 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_12,negated_conjecture,
~ ( in @ esk6_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 : SEU660^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n018.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:06:20 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 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.GnvfkAC7Q9/E---3.1_125963.p
% 0.07/0.24 % Version: 3.5.1-ho
% 0.07/0.24 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.07/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.24 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.07/0.24 % Starting post_as_ho8 with 300s (1) cores
% 0.07/0.24 % Starting post_as_ho3 with 300s (1) cores
% 0.07/0.24 % Starting post_as_ho2 with 300s (1) cores
% 0.07/0.24 % post_as_ho8 with pid 125977 completed with status 0
% 0.07/0.24 % Result found by post_as_ho8
% 0.07/0.24 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.07/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.24 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.07/0.24 % Starting post_as_ho8 with 300s (1) cores
% 0.07/0.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.07/0.24 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.07/0.24 % Search class: HHUSF-FFSF32-SFFFMFNN
% 0.07/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.24 % Starting SubtermCWHack with 28s (1) cores
% 0.07/0.24 % SubtermCWHack with pid 125980 completed with status 0
% 0.07/0.24 % Result found by SubtermCWHack
% 0.07/0.24 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.07/0.24 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.07/0.24 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.07/0.24 % Starting post_as_ho8 with 300s (1) cores
% 0.07/0.24 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.07/0.24 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.07/0.24 % Search class: HHUSF-FFSF32-SFFFMFNN
% 0.07/0.24 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.07/0.24 % Starting SubtermCWHack with 28s (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 : 8
% 0.07/0.24 % Removed by relevancy pruning/SinE : 5
% 0.07/0.24 % Initial clauses : 6
% 0.07/0.24 % Removed in clause preprocessing : 0
% 0.07/0.24 % Initial clauses in saturation : 6
% 0.07/0.24 % Processed clauses : 8
% 0.07/0.24 % ...of these trivial : 0
% 0.07/0.24 % ...subsumed : 0
% 0.07/0.24 % ...remaining for further processing : 8
% 0.07/0.24 % Other redundant clauses eliminated : 2
% 0.07/0.24 % Clauses deleted for lack of memory : 0
% 0.07/0.24 % Backward-subsumed : 0
% 0.07/0.24 % Backward-rewritten : 0
% 0.07/0.24 % Generated clauses : 10
% 0.07/0.24 % ...of the previous two non-redundant : 6
% 0.07/0.24 % ...aggressively subsumed : 0
% 0.07/0.24 % Contextual simplify-reflections : 0
% 0.07/0.24 % Paramodulations : 7
% 0.07/0.24 % Factorizations : 0
% 0.07/0.24 % NegExts : 0
% 0.07/0.24 % Equation resolutions : 3
% 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 : 8
% 0.07/0.24 % Positive orientable unit clauses : 1
% 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: 3
% 0.07/0.24 % ...number of literals in the above : 7
% 0.07/0.24 % Current number of archived formulas : 0
% 0.07/0.24 % Current number of archived clauses : 0
% 0.07/0.24 % Clause-clause subsumption calls (NU) : 0
% 0.07/0.24 % Rec. Clause-clause subsumption calls : 0
% 0.07/0.24 % Non-unit clause-clause subsumptions : 0
% 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 : 744
% 0.07/0.24 % Search garbage collected termcells : 250
% 0.07/0.24
% 0.07/0.24 % -------------------------------------------------
% 0.07/0.24 % User time : 0.003 s
% 0.07/0.24 % System time : 0.001 s
% 0.07/0.24 % Total time : 0.004 s
% 0.07/0.24 % Maximum resident set size: 3888 pages
% 0.07/0.24
% 0.07/0.24 % -------------------------------------------------
% 0.07/0.24 % User time : 0.004 s
% 0.07/0.24 % System time : 0.006 s
% 0.07/0.24 % Total time : 0.009 s
% 0.07/0.24 % Maximum resident set size: 4864 pages
% 0.07/0.24 % E exiting
%------------------------------------------------------------------------------