%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU668^2 : 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 : n015.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 08:24:57 AM UTC 2026
% Result : Theorem 0.27s 0.32s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 80 ( 32 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 279 ( 13 ~; 8 |; 24 &; 205 @)
% ( 4 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 10 con; 0-3 aty)
% Number of variables : 95 ( 17 ^; 66 !; 12 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
in: $i > $i > $o ).
thf(decl_24,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(decl_25,type,
dsetconstrER: $o ).
thf(decl_26,type,
kpair: $i > $i > $i ).
thf(decl_27,type,
cartprod: $i > $i > $i ).
thf(decl_28,type,
setukpairinjL: $o ).
thf(decl_29,type,
setukpairinjR: $o ).
thf(decl_30,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(decl_31,type,
esk1_0: $i ).
thf(decl_32,type,
esk2_0: $i ).
thf(decl_33,type,
epred1_0: $i > $i > $o ).
thf(decl_34,type,
esk3_0: $i ).
thf(decl_35,type,
esk4_0: $i ).
thf(decl_36,type,
esk5_0: $i ).
thf(decl_37,type,
esk6_0: $i ).
thf(dpsetconstrERa,conjecture,
( dsetconstrER
=> ( setukpairinjL
=> ( setukpairinjR
=> ! [X1: $i,X7: $i,X9: $i > $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X7 )
=> ( ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X1 @ X7
@ ^ [X5: $i,X6: $i] : ( X9 @ X5 @ X6 ) ) )
=> ( X9 @ X3 @ X4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.09R4mtc1CY/E---3.1_3579795.p',dpsetconstrERa) ).
thf(dpsetconstr,axiom,
( dpsetconstr
= ( ^ [X1: $i,X7: $i,X8: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X1 @ X7 )
@ ^ [X6: $i] :
? [X3: $i] :
( ( in @ X3 @ X1 )
& ? [X4: $i] :
( ( in @ X4 @ X7 )
& ( X8 @ X3 @ X4 )
& ( X6
= ( kpair @ X3 @ X4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.09R4mtc1CY/E---3.1_3579795.p',dpsetconstr) ).
thf(dsetconstrER,axiom,
( dsetconstrER
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) )
=> ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.09R4mtc1CY/E---3.1_3579795.p',dsetconstrER) ).
thf(setukpairinjR,axiom,
( setukpairinjR
<=> ! [X3: $i,X4: $i,X5: $i,X6: $i] :
( ( ( kpair @ X3 @ X4 )
= ( kpair @ X5 @ X6 ) )
=> ( X4 = X6 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.09R4mtc1CY/E---3.1_3579795.p',setukpairinjR) ).
thf(setukpairinjL,axiom,
( setukpairinjL
<=> ! [X3: $i,X4: $i,X5: $i,X6: $i] :
( ( ( kpair @ X3 @ X4 )
= ( kpair @ X5 @ X6 ) )
=> ( X3 = X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.09R4mtc1CY/E---3.1_3579795.p',setukpairinjL) ).
thf(c_0_5,negated_conjecture,
~ ( dsetconstrER
=> ( setukpairinjL
=> ( setukpairinjR
=> ! [X1: $i,X7: $i,X9: $i > $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X7 )
=> ( ( in @ ( kpair @ X3 @ X4 )
@ ( dpsetconstr @ X1 @ X7
@ ^ [X5: $i,X6: $i] : ( X9 @ X5 @ X6 ) ) )
=> ( X9 @ X3 @ X4 ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[dpsetconstrERa]) ).
thf(c_0_6,plain,
( dpsetconstr
= ( ^ [Z0: $i,Z1: $i,Z2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Z0 @ Z1 )
@ ^ [Z3: $i] :
? [X3: $i] :
( ( in @ X3 @ Z0 )
& ? [X4: $i] :
( ( in @ X4 @ Z1 )
& ( Z2 @ X3 @ X4 )
& ( Z3
= ( kpair @ X3 @ X4 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[dpsetconstr]) ).
thf(c_0_7,plain,
( dsetconstrER
<=> ! [X1: $i,X2: $i > $o,X3: $i] :
( ( in @ X3
@ ( dsetconstr @ X1
@ ^ [Z0: $i] : ( X2 @ Z0 ) ) )
=> ( X2 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[dsetconstrER]) ).
thf(c_0_8,negated_conjecture,
~ ( ! [X26: $i,X27: $i > $o,X28: $i] :
( ( in @ X28 @ ( dsetconstr @ X26 @ X27 ) )
=> ( X27 @ X28 ) )
=> ( ! [X29: $i,X30: $i,X31: $i,X32: $i] :
( ( ( kpair @ X29 @ X30 )
= ( kpair @ X31 @ X32 ) )
=> ( X29 = X31 ) )
=> ( ! [X33: $i,X34: $i,X35: $i,X36: $i] :
( ( ( kpair @ X33 @ X34 )
= ( kpair @ X35 @ X36 ) )
=> ( X34 = X36 ) )
=> ! [X1: $i,X7: $i,X9: $i > $i > $o,X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X7 )
=> ( ( in @ ( kpair @ X3 @ X4 )
@ ( dsetconstr @ ( cartprod @ X1 @ X7 )
@ ^ [Z0: $i] :
? [X37: $i] :
( ( in @ X37 @ X1 )
& ? [X38: $i] :
( ( in @ X38 @ X7 )
& ( X9 @ X37 @ X38 )
& ( Z0
= ( kpair @ X37 @ X38 ) ) ) ) ) )
=> ( X9 @ X3 @ X4 ) ) ) ) ) ) ),
inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_5]),setukpairinjR]),setukpairinjL]),c_0_6]),c_0_7])]) ).
thf(c_0_9,negated_conjecture,
! [X39: $i,X40: $i > $o,X41: $i,X42: $i,X43: $i,X44: $i,X45: $i,X46: $i,X47: $i,X48: $i,X49: $i] :
( ( ~ ( in @ X41 @ ( dsetconstr @ X39 @ X40 ) )
| ( X40 @ X41 ) )
& ( ( ( kpair @ X42 @ X43 )
!= ( kpair @ X44 @ X45 ) )
| ( X42 = X44 ) )
& ( ( ( kpair @ X46 @ X47 )
!= ( kpair @ X48 @ X49 ) )
| ( X47 = X49 ) )
& ( in @ esk3_0 @ esk1_0 )
& ( in @ esk4_0 @ esk2_0 )
& ( in @ ( kpair @ esk3_0 @ esk4_0 )
@ ( dsetconstr @ ( cartprod @ esk1_0 @ esk2_0 )
@ ^ [Z0: $i] :
? [X37: $i] :
( ( in @ X37 @ esk1_0 )
& ? [X38: $i] :
( ( in @ X38 @ esk2_0 )
& ( epred1_0 @ X37 @ X38 )
& ( Z0
= ( kpair @ X37 @ X38 ) ) ) ) ) )
& ~ ( epred1_0 @ esk3_0 @ esk4_0 ) ),
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,
! [X1: $i,X3: $i,X2: $i > $o] :
( ( X2 @ X1 )
| ~ ( in @ X1 @ ( dsetconstr @ X3 @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_11,negated_conjecture,
( in @ ( kpair @ esk3_0 @ esk4_0 )
@ ( dsetconstr @ ( cartprod @ esk1_0 @ esk2_0 )
@ ^ [Z0: $i] :
? [X59: $i] :
( ( in @ X59 @ esk1_0 )
& ? [X60: $i] :
( ( in @ X60 @ esk2_0 )
& ( epred1_0 @ X59 @ X60 )
& ( Z0
= ( kpair @ X59 @ X60 ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_12,negated_conjecture,
? [X61: $i] :
( ( in @ X61 @ esk1_0 )
& ? [X62: $i] :
( ( in @ X62 @ esk2_0 )
& ( epred1_0 @ X61 @ X62 )
& ( ( kpair @ esk3_0 @ esk4_0 )
= ( kpair @ X61 @ X62 ) ) ) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_13,negated_conjecture,
! [X1: $i,X3: $i,X4: $i,X5: $i] :
( ( X1 = X4 )
| ( ( kpair @ X1 @ X3 )
!= ( kpair @ X4 @ X5 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_14,negated_conjecture,
( ( kpair @ esk3_0 @ esk4_0 )
= ( kpair @ esk5_0 @ esk6_0 ) ),
inference(dynamic_cnf,[status(thm)],[c_0_12]) ).
thf(c_0_15,negated_conjecture,
! [X1: $i,X3: $i] :
( ( esk3_0 = X1 )
| ( ( kpair @ esk5_0 @ esk6_0 )
!= ( kpair @ X1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_16,negated_conjecture,
esk3_0 = esk5_0,
inference(er,[status(thm)],[c_0_15]) ).
thf(c_0_17,negated_conjecture,
! [X1: $i,X3: $i,X4: $i,X5: $i] :
( ( X3 = X5 )
| ( ( kpair @ X1 @ X3 )
!= ( kpair @ X4 @ X5 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_18,negated_conjecture,
( ( kpair @ esk5_0 @ esk4_0 )
= ( kpair @ esk5_0 @ esk6_0 ) ),
inference(rw,[status(thm)],[c_0_14,c_0_16]) ).
thf(c_0_19,negated_conjecture,
~ ( epred1_0 @ esk3_0 @ esk4_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_20,negated_conjecture,
! [X3: $i,X1: $i] :
( ( X1 = esk4_0 )
| ( ( kpair @ X3 @ X1 )
!= ( kpair @ esk5_0 @ esk6_0 ) ) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_21,negated_conjecture,
~ ( epred1_0 @ esk5_0 @ esk4_0 ),
inference(rw,[status(thm)],[c_0_19,c_0_16]) ).
thf(c_0_22,negated_conjecture,
esk4_0 = esk6_0,
inference(er,[status(thm)],[c_0_20]) ).
thf(c_0_23,negated_conjecture,
epred1_0 @ esk5_0 @ esk6_0,
inference(dynamic_cnf,[status(thm)],[c_0_12]) ).
thf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU668^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n015.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:10:03 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.27 Running higher-order theorem proving
% 0.27/0.29 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.09R4mtc1CY/E---3.1_3579795.p
% 0.27/0.32 % Version: 3.5.1-ho
% 0.27/0.32 % Preprocessing class: HSSSSLSSSLMNHSA.
% 0.27/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.32 % Starting new_ho_10 with 1500s (5) cores
% 0.27/0.32 % Starting new_ho_7 with 300s (1) cores
% 0.27/0.32 % Starting lpo8_lambda_fix with 300s (1) cores
% 0.27/0.32 % Starting lpo9_lambda_fix with 300s (1) cores
% 0.27/0.32 % new_ho_7 with pid 3579809 completed with status 0
% 0.27/0.32 % Result found by new_ho_7
% 0.27/0.32 % Preprocessing class: HSSSSLSSSLMNHSA.
% 0.27/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.32 % Starting new_ho_10 with 1500s (5) cores
% 0.27/0.32 % Starting new_ho_7 with 300s (1) cores
% 0.27/0.32 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,3,,5,20000,1.0,true))
% 0.27/0.32 % SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 0.27/0.32 % Search class: HHUSF-FFSS22-DHSFMSBN
% 0.27/0.32 % partial match(2): HHUSF-FFSS22-SSSFMSBN
% 0.27/0.32 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.32 % Starting SubtermCWHack with 28s (1) cores
% 0.27/0.32 % SubtermCWHack with pid 3579812 completed with status 0
% 0.27/0.32 % Result found by SubtermCWHack
% 0.27/0.32 % Preprocessing class: HSSSSLSSSLMNHSA.
% 0.27/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.27/0.32 % Starting new_ho_10 with 1500s (5) cores
% 0.27/0.32 % Starting new_ho_7 with 300s (1) cores
% 0.27/0.32 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,3,,5,20000,1.0,true))
% 0.27/0.32 % SinE strategy is GSinE(CountFormulas,hypos,3,,5,20000,1.0,true)
% 0.27/0.32 % Search class: HHUSF-FFSS22-DHSFMSBN
% 0.27/0.32 % partial match(2): HHUSF-FFSS22-SSSFMSBN
% 0.27/0.32 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.27/0.32 % Starting SubtermCWHack with 28s (1) cores
% 0.27/0.32 % Preprocessing time : 0.001 s
% 0.27/0.32
% 0.27/0.32 % Proof found!
% 0.27/0.32 % SZS status Theorem
% 0.27/0.32 % SZS output start CNFRefutation
% See solution above
% 0.27/0.32 % Parsed axioms : 13
% 0.27/0.32 % Removed by relevancy pruning/SinE : 8
% 0.27/0.32 % Initial clauses : 7
% 0.27/0.32 % Removed in clause preprocessing : 0
% 0.27/0.32 % Initial clauses in saturation : 7
% 0.27/0.32 % Processed clauses : 20
% 0.27/0.32 % ...of these trivial : 0
% 0.27/0.32 % ...subsumed : 2
% 0.27/0.32 % ...remaining for further processing : 18
% 0.27/0.32 % Other redundant clauses eliminated : 0
% 0.27/0.32 % Clauses deleted for lack of memory : 0
% 0.27/0.32 % Backward-subsumed : 0
% 0.27/0.32 % Backward-rewritten : 9
% 0.27/0.32 % Generated clauses : 17
% 0.27/0.32 % ...of the previous two non-redundant : 20
% 0.27/0.32 % ...aggressively subsumed : 0
% 0.27/0.32 % Contextual simplify-reflections : 0
% 0.27/0.32 % Paramodulations : 9
% 0.27/0.32 % Factorizations : 0
% 0.27/0.32 % NegExts : 0
% 0.27/0.32 % Equation resolutions : 4
% 0.27/0.32 % Disequality decompositions : 0
% 0.27/0.32 % Total rewrite steps : 12
% 0.27/0.32 % ...of those cached : 6
% 0.27/0.32 % Propositional unsat checks : 0
% 0.27/0.32 % Propositional check models : 0
% 0.27/0.32 % Propositional check unsatisfiable : 0
% 0.27/0.32 % Propositional clauses : 0
% 0.27/0.32 % Propositional clauses after purity: 0
% 0.27/0.32 % Propositional unsat core size : 0
% 0.27/0.32 % Propositional preprocessing time : 0.000
% 0.27/0.32 % Propositional encoding time : 0.000
% 0.27/0.32 % Propositional solver time : 0.000
% 0.27/0.32 % Success case prop preproc time : 0.000
% 0.27/0.32 % Success case prop encoding time : 0.000
% 0.27/0.32 % Success case prop solver time : 0.000
% 0.27/0.32 % Current number of processed clauses : 8
% 0.27/0.32 % Positive orientable unit clauses : 5
% 0.27/0.32 % Positive unorientable unit clauses: 0
% 0.27/0.32 % Negative unit clauses : 0
% 0.27/0.32 % Non-unit-clauses : 3
% 0.27/0.32 % Current number of unprocessed clauses: 3
% 0.27/0.32 % ...number of literals in the above : 5
% 0.27/0.32 % Current number of archived formulas : 0
% 0.27/0.32 % Current number of archived clauses : 10
% 0.27/0.32 % Clause-clause subsumption calls (NU) : 8
% 0.27/0.32 % Rec. Clause-clause subsumption calls : 8
% 0.27/0.32 % Non-unit clause-clause subsumptions : 2
% 0.27/0.32 % Unit Clause-clause subsumption calls : 0
% 0.27/0.32 % Rewrite failures with RHS unbound : 0
% 0.27/0.32 % BW rewrite match attempts : 3
% 0.27/0.32 % BW rewrite match successes : 3
% 0.27/0.32 % Condensation attempts : 0
% 0.27/0.32 % Condensation successes : 0
% 0.27/0.32 % Termbank termtop insertions : 1384
% 0.27/0.32 % Search garbage collected termcells : 442
% 0.27/0.32
% 0.27/0.32 % -------------------------------------------------
% 0.27/0.32 % User time : 0.006 s
% 0.27/0.32 % System time : 0.003 s
% 0.27/0.32 % Total time : 0.009 s
% 0.27/0.32 % Maximum resident set size: 3588 pages
% 0.27/0.32
% 0.27/0.32 % -------------------------------------------------
% 0.27/0.32 % User time : 0.011 s
% 0.27/0.32 % System time : 0.005 s
% 0.27/0.32 % Total time : 0.015 s
% 0.27/0.32 % Maximum resident set size: 4864 pages
% 0.27/0.32 % E exiting
%------------------------------------------------------------------------------