%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU664^2 : 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 08:24:56 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 85 ( 24 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 367 ( 30 ~; 25 |; 10 &; 277 @)
% ( 3 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 10 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 : 95 ( 0 ^; 91 !; 4 ?; 95 :)
% 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,
kfst: $i > $i ).
thf(decl_28,type,
ksnd: $i > $i ).
thf(decl_29,type,
cartprodfstpairEq: $o ).
thf(decl_30,type,
cartprodsndpairEq: $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(cartprodpairsurjEq,conjecture,
( cartprodmempair1
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TyokCCWVaG/E---3.1_126940.p',cartprodpairsurjEq) ).
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.TyokCCWVaG/E---3.1_126940.p',cartprodmempair1) ).
thf(cartprodfstpairEq,axiom,
( cartprodfstpairEq
<=> ! [X1: $i,X2: $i,X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( kfst @ ( kpair @ X4 @ X5 ) )
= X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TyokCCWVaG/E---3.1_126940.p',cartprodfstpairEq) ).
thf(cartprodsndpairEq,axiom,
( cartprodsndpairEq
<=> ! [X1: $i,X2: $i,X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X2 )
=> ( ( ksnd @ ( kpair @ X4 @ X5 ) )
= X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TyokCCWVaG/E---3.1_126940.p',cartprodsndpairEq) ).
thf(c_0_4,negated_conjecture,
~ ( cartprodmempair1
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
= X3 ) ) ) ) ),
inference(assume_negation,[status(cth)],[cartprodpairsurjEq]) ).
thf(c_0_5,negated_conjecture,
~ ( ! [X22: $i,X23: $i,X24: $i] :
( ( in @ X24 @ ( cartprod @ X22 @ X23 ) )
=> ? [X25: $i] :
( ( in @ X25 @ X22 )
& ? [X26: $i] :
( ( in @ X26 @ X23 )
& ( X24
= ( kpair @ X25 @ X26 ) ) ) ) )
=> ( ! [X27: $i,X28: $i,X29: $i] :
( ( in @ X29 @ X27 )
=> ! [X30: $i] :
( ( in @ X30 @ X28 )
=> ( ( kfst @ ( kpair @ X29 @ X30 ) )
= X29 ) ) )
=> ( ! [X31: $i,X32: $i,X33: $i] :
( ( in @ X33 @ X31 )
=> ! [X34: $i] :
( ( in @ X34 @ X32 )
=> ( ( ksnd @ ( kpair @ X33 @ X34 ) )
= X34 ) ) )
=> ! [X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
=> ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
= X3 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,cartprodmempair1]),cartprodfstpairEq]),cartprodsndpairEq]) ).
thf(c_0_6,negated_conjecture,
! [X35: $i,X36: $i,X37: $i,X40: $i,X41: $i,X42: $i,X43: $i,X44: $i,X45: $i,X46: $i,X47: $i] :
( ( ( 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 ) ) )
& ( ~ ( in @ X42 @ X40 )
| ~ ( in @ X43 @ X41 )
| ( ( kfst @ ( kpair @ X42 @ X43 ) )
= X42 ) )
& ( ~ ( in @ X46 @ X44 )
| ~ ( in @ X47 @ X45 )
| ( ( ksnd @ ( kpair @ X46 @ X47 ) )
= X47 ) )
& ( in @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ) )
& ( ( kpair @ ( kfst @ esk5_0 ) @ ( ksnd @ esk5_0 ) )
!= esk5_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_5])])])])])]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( kfst @ ( kpair @ X1 @ X3 ) )
= X1 )
| ~ ( in @ X1 @ X2 )
| ~ ( in @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
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_6]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i,X3: $i,X2: $i,X4: $i,X5: $i] :
( ( ( kfst @ ( kpair @ X1 @ ( esk2_3 @ X2 @ X3 @ X4 ) ) )
= X1 )
| ~ ( in @ X4 @ ( cartprod @ X2 @ X3 ) )
| ~ ( in @ X1 @ X5 ) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
thf(c_0_10,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_6]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i,X6: $i,X5: $i,X4: $i,X3: $i,X2: $i] :
( ( ( kfst @ ( kpair @ ( esk1_3 @ X1 @ X2 @ X3 ) @ ( esk2_3 @ X4 @ X5 @ X6 ) ) )
= ( esk1_3 @ X1 @ X2 @ X3 ) )
| ~ ( in @ X6 @ ( cartprod @ X4 @ X5 ) )
| ~ ( in @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
thf(c_0_12,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_6]) ).
thf(c_0_13,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_11,c_0_12]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( ksnd @ ( kpair @ X1 @ X3 ) )
= X3 )
| ~ ( in @ X1 @ X2 )
| ~ ( in @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( in @ ( kfst @ X1 ) @ X2 )
| ~ ( in @ X1 @ ( cartprod @ X2 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_10,c_0_13]) ).
thf(c_0_16,negated_conjecture,
in @ esk5_0 @ ( cartprod @ esk3_0 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i,X3: $i,X2: $i,X4: $i,X5: $i] :
( ( ( ksnd @ ( kpair @ X1 @ ( esk2_3 @ X2 @ X3 @ X4 ) ) )
= ( esk2_3 @ X2 @ X3 @ X4 ) )
| ~ ( in @ X4 @ ( cartprod @ X2 @ X3 ) )
| ~ ( in @ X1 @ X5 ) ),
inference(spm,[status(thm)],[c_0_14,c_0_8]) ).
thf(c_0_18,negated_conjecture,
in @ ( kfst @ esk5_0 ) @ esk3_0,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i,X3: $i,X2: $i] :
( ( ( ksnd @ ( kpair @ ( kfst @ esk5_0 ) @ ( esk2_3 @ X1 @ X2 @ X3 ) ) )
= ( esk2_3 @ X1 @ X2 @ X3 ) )
| ~ ( in @ X3 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ ( kfst @ X1 ) @ ( esk2_3 @ X2 @ X3 @ X1 ) )
= X1 )
| ~ ( in @ X1 @ ( cartprod @ X2 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_21,negated_conjecture,
! [X1: $i,X2: $i] :
( ( ( esk2_3 @ X1 @ X2 @ esk5_0 )
= ( ksnd @ esk5_0 ) )
| ~ ( in @ esk5_0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_22,negated_conjecture,
( ( kpair @ ( kfst @ esk5_0 ) @ ( ksnd @ esk5_0 ) )
!= esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i,X2: $i] :
~ ( in @ esk5_0 @ ( cartprod @ X1 @ X2 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
thf(c_0_24,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_16,c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU664^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n018.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:06:43 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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.TyokCCWVaG/E---3.1_126940.p
% 0.08/0.25 % Version: 3.5.1-ho
% 0.08/0.25 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.08/0.25 % Starting post_as_ho8 with 300s (1) cores
% 0.08/0.25 % Starting post_as_ho3 with 300s (1) cores
% 0.08/0.25 % Starting post_as_ho2 with 300s (1) cores
% 0.08/0.25 % post_as_ho8 with pid 126954 completed with status 0
% 0.08/0.25 % Result found by post_as_ho8
% 0.08/0.25 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.08/0.25 % Starting post_as_ho8 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.08/0.25 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.08/0.25 % Search class: HHUSF-FFSF32-SFFFMFNN
% 0.08/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.25 % SubtermCWHack with pid 126958 completed with status 0
% 0.08/0.25 % Result found by SubtermCWHack
% 0.08/0.25 % Preprocessing class: HSSSSLSSSLSNFFN.
% 0.08/0.25 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.25 % Starting lpo6_lambda_fix with 1500s (5) cores
% 0.08/0.25 % Starting post_as_ho8 with 300s (1) cores
% 0.08/0.25 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true))
% 0.08/0.25 % SinE strategy is GSinE(CountFormulas,,true,1.5,0,3,20000,1.0,true)
% 0.08/0.25 % Search class: HHUSF-FFSF32-SFFFMFNN
% 0.08/0.25 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.25 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.25 % Preprocessing time : 0.001 s
% 0.08/0.25
% 0.08/0.25 % Proof found!
% 0.08/0.25 % SZS status Theorem
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25 % Parsed axioms : 12
% 0.08/0.25 % Removed by relevancy pruning/SinE : 8
% 0.08/0.25 % Initial clauses : 7
% 0.08/0.25 % Removed in clause preprocessing : 0
% 0.08/0.25 % Initial clauses in saturation : 7
% 0.08/0.25 % Processed clauses : 58
% 0.08/0.25 % ...of these trivial : 0
% 0.08/0.25 % ...subsumed : 0
% 0.08/0.25 % ...remaining for further processing : 58
% 0.08/0.25 % Other redundant clauses eliminated : 0
% 0.08/0.25 % Clauses deleted for lack of memory : 0
% 0.08/0.25 % Backward-subsumed : 1
% 0.08/0.25 % Backward-rewritten : 0
% 0.08/0.25 % Generated clauses : 152
% 0.08/0.25 % ...of the previous two non-redundant : 144
% 0.08/0.25 % ...aggressively subsumed : 0
% 0.08/0.25 % Contextual simplify-reflections : 0
% 0.08/0.25 % Paramodulations : 151
% 0.08/0.25 % Factorizations : 0
% 0.08/0.25 % NegExts : 0
% 0.08/0.25 % Equation resolutions : 0
% 0.08/0.25 % Disequality decompositions : 0
% 0.08/0.25 % Total rewrite steps : 7
% 0.08/0.25 % ...of those cached : 1
% 0.08/0.25 % Propositional unsat checks : 0
% 0.08/0.25 % Propositional check models : 0
% 0.08/0.25 % Propositional check unsatisfiable : 0
% 0.08/0.25 % Propositional clauses : 0
% 0.08/0.25 % Propositional clauses after purity: 0
% 0.08/0.25 % Propositional unsat core size : 0
% 0.08/0.25 % Propositional preprocessing time : 0.000
% 0.08/0.25 % Propositional encoding time : 0.000
% 0.08/0.25 % Propositional solver time : 0.000
% 0.08/0.25 % Success case prop preproc time : 0.000
% 0.08/0.25 % Success case prop encoding time : 0.000
% 0.08/0.25 % Success case prop solver time : 0.000
% 0.08/0.25 % Current number of processed clauses : 56
% 0.08/0.25 % Positive orientable unit clauses : 9
% 0.08/0.25 % Positive unorientable unit clauses: 0
% 0.08/0.25 % Negative unit clauses : 2
% 0.08/0.25 % Non-unit-clauses : 45
% 0.08/0.25 % Current number of unprocessed clauses: 93
% 0.08/0.25 % ...number of literals in the above : 225
% 0.08/0.25 % Current number of archived formulas : 0
% 0.08/0.25 % Current number of archived clauses : 2
% 0.08/0.25 % Clause-clause subsumption calls (NU) : 163
% 0.08/0.25 % Rec. Clause-clause subsumption calls : 163
% 0.08/0.25 % Non-unit clause-clause subsumptions : 0
% 0.08/0.25 % Unit Clause-clause subsumption calls : 10
% 0.08/0.25 % Rewrite failures with RHS unbound : 0
% 0.08/0.25 % BW rewrite match attempts : 0
% 0.08/0.25 % BW rewrite match successes : 0
% 0.08/0.25 % Condensation attempts : 0
% 0.08/0.25 % Condensation successes : 0
% 0.08/0.25 % Termbank termtop insertions : 3729
% 0.08/0.25 % Search garbage collected termcells : 358
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.006 s
% 0.08/0.25 % System time : 0.002 s
% 0.08/0.25 % Total time : 0.007 s
% 0.08/0.25 % Maximum resident set size: 3636 pages
% 0.08/0.25
% 0.08/0.25 % -------------------------------------------------
% 0.08/0.25 % User time : 0.007 s
% 0.08/0.25 % System time : 0.006 s
% 0.08/0.25 % Total time : 0.013 s
% 0.08/0.25 % Maximum resident set size: 4864 pages
% 0.08/0.25 % E exiting
%------------------------------------------------------------------------------