%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU651^2 : 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 : n005.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 08:24:53 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 32 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 300 ( 9 ~; 4 |; 5 &; 260 @)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 39 ( 0 ^; 39 !; 0 ?; 39 :)
% 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,
uniqinunit: $o ).
thf(decl_27,type,
secondinupair: $o ).
thf(decl_28,type,
setukpairinjR12: $o ).
thf(decl_29,type,
esk1_0: $i ).
thf(decl_30,type,
esk2_0: $i ).
thf(decl_31,type,
esk3_0: $i ).
thf(decl_32,type,
esk4_0: $i ).
thf(setukpairinjR1,conjecture,
( uniqinunit
=> ( secondinupair
=> ( setukpairinjR12
=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X3 = X4 )
=> ( X2 = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oAEoz8rDJZ/E---3.1_1717558.p',setukpairinjR1) ).
thf(uniqinunit,axiom,
( uniqinunit
<=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oAEoz8rDJZ/E---3.1_1717558.p',uniqinunit) ).
thf(secondinupair,axiom,
( secondinupair
<=> ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oAEoz8rDJZ/E---3.1_1717558.p',secondinupair) ).
thf(setukpairinjR12,axiom,
( setukpairinjR12
<=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oAEoz8rDJZ/E---3.1_1717558.p',setukpairinjR12) ).
thf(c_0_4,negated_conjecture,
~ ( uniqinunit
=> ( secondinupair
=> ( setukpairinjR12
=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X3 = X4 )
=> ( X2 = X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[setukpairinjR1]) ).
thf(c_0_5,negated_conjecture,
~ ( ! [X15: $i,X16: $i] :
( ( in @ X15 @ ( setadjoin @ X16 @ emptyset ) )
=> ( X15 = X16 ) )
=> ( ! [X17: $i,X18: $i] : ( in @ X18 @ ( setadjoin @ X17 @ ( setadjoin @ X18 @ emptyset ) ) )
=> ( ! [X19: $i,X20: $i] :
( ( X19 = X20 )
=> ( ( setadjoin @ ( setadjoin @ X19 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X19 @ ( setadjoin @ X20 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X19 @ emptyset ) @ emptyset ) ) )
=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X3 = X4 )
=> ( X2 = X4 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_4,uniqinunit]),secondinupair]),setukpairinjR12]) ).
thf(c_0_6,negated_conjecture,
! [X21: $i,X22: $i,X23: $i,X24: $i,X25: $i,X26: $i] :
( ( ~ ( in @ X21 @ ( setadjoin @ X22 @ emptyset ) )
| ( X21 = X22 ) )
& ( in @ X24 @ ( setadjoin @ X23 @ ( setadjoin @ X24 @ emptyset ) ) )
& ( ( X25 != X26 )
| ( ( setadjoin @ ( setadjoin @ X25 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X25 @ ( setadjoin @ X26 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X25 @ emptyset ) @ emptyset ) ) )
& ( ( setadjoin @ ( setadjoin @ esk1_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ esk3_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk3_0 @ ( setadjoin @ esk4_0 @ emptyset ) ) @ emptyset ) ) )
& ( esk3_0 = esk4_0 )
& ( esk2_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_5])])])])]) ).
thf(c_0_7,negated_conjecture,
! [X1: $i,X2: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) )
| ( X1 != X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_8,negated_conjecture,
! [X2: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
! [X1: $i] :
( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ),
inference(er,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_11,negated_conjecture,
! [X1: $i] : ( in @ ( setadjoin @ X1 @ ( setadjoin @ X1 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_12,negated_conjecture,
( ( setadjoin @ ( setadjoin @ esk1_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ esk3_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk3_0 @ ( setadjoin @ esk4_0 @ emptyset ) ) @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_13,negated_conjecture,
esk3_0 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_14,negated_conjecture,
! [X1: $i] :
( ( setadjoin @ X1 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X1 @ emptyset ) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_15,negated_conjecture,
( ( setadjoin @ ( setadjoin @ esk1_0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ esk3_0 @ emptyset ) @ emptyset ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_14]) ).
thf(c_0_16,negated_conjecture,
in @ ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) ) @ ( setadjoin @ ( setadjoin @ esk3_0 @ emptyset ) @ emptyset ),
inference(spm,[status(thm)],[c_0_8,c_0_15]) ).
thf(c_0_17,negated_conjecture,
( ( setadjoin @ esk1_0 @ ( setadjoin @ esk2_0 @ emptyset ) )
= ( setadjoin @ esk3_0 @ emptyset ) ),
inference(spm,[status(thm)],[c_0_10,c_0_16]) ).
thf(c_0_18,negated_conjecture,
esk2_0 != esk4_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_19,negated_conjecture,
in @ esk2_0 @ ( setadjoin @ esk3_0 @ emptyset ),
inference(spm,[status(thm)],[c_0_8,c_0_17]) ).
thf(c_0_20,negated_conjecture,
esk2_0 != esk3_0,
inference(rw,[status(thm)],[c_0_18,c_0_13]) ).
thf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_19]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU651^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.16 % Computer : n005.cluster.edu
% 0.07/0.16 % Model : x86_64 x86_64
% 0.07/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.16 % Memory : 8046.5625MB
% 0.07/0.16 % OS : Linux 6.8.0-71-generic
% 0.07/0.16 % CPULimit : 300
% 0.07/0.16 % WCLimit : 300
% 0.07/0.16 % DateTime : Tue Sep 29 14:02:31 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 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.oAEoz8rDJZ/E---3.1_1717558.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 1717572 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-FFSF22-MFFFMFNN
% 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 1717575 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-FFSF22-MFFFMFNN
% 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 : 10
% 0.07/0.24 % Removed by relevancy pruning/SinE : 6
% 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 : 14
% 0.07/0.24 % ...of these trivial : 1
% 0.07/0.24 % ...subsumed : 0
% 0.07/0.24 % ...remaining for further processing : 13
% 0.07/0.24 % Other redundant clauses eliminated : 1
% 0.07/0.24 % Clauses deleted for lack of memory : 0
% 0.07/0.24 % Backward-subsumed : 0
% 0.07/0.24 % Backward-rewritten : 2
% 0.07/0.24 % Generated clauses : 10
% 0.07/0.24 % ...of the previous two non-redundant : 9
% 0.07/0.24 % ...aggressively subsumed : 0
% 0.07/0.24 % Contextual simplify-reflections : 0
% 0.07/0.24 % Paramodulations : 9
% 0.07/0.24 % Factorizations : 0
% 0.07/0.24 % NegExts : 0
% 0.07/0.24 % Equation resolutions : 1
% 0.07/0.24 % Disequality decompositions : 0
% 0.07/0.24 % Total rewrite steps : 9
% 0.07/0.24 % ...of those cached : 1
% 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 : 10
% 0.07/0.24 % Positive orientable unit clauses : 8
% 0.07/0.24 % Positive unorientable unit clauses: 0
% 0.07/0.24 % Negative unit clauses : 1
% 0.07/0.24 % Non-unit-clauses : 1
% 0.07/0.24 % Current number of unprocessed clauses: 1
% 0.07/0.24 % ...number of literals in the above : 1
% 0.07/0.24 % Current number of archived formulas : 0
% 0.07/0.24 % Current number of archived clauses : 2
% 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 : 5
% 0.07/0.24 % BW rewrite match successes : 2
% 0.07/0.24 % Condensation attempts : 0
% 0.07/0.24 % Condensation successes : 0
% 0.07/0.24 % Termbank termtop insertions : 896
% 0.07/0.24 % Search garbage collected termcells : 224
% 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: 3632 pages
% 0.07/0.24
% 0.07/0.24 % -------------------------------------------------
% 0.07/0.24 % User time : 0.005 s
% 0.07/0.24 % System time : 0.004 s
% 0.07/0.24 % Total time : 0.010 s
% 0.07/0.24 % Maximum resident set size: 4608 pages
% 0.07/0.24 % E exiting
%------------------------------------------------------------------------------