%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU648^2 : 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 : n017.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 08:27:04 AM UTC 2026
% Result : Theorem 0.29s 0.29s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 30 ( 26 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 177 ( 8 ~; 4 |; 2 &; 154 @)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 42 ( 2 ^; 40 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
emptyset: $i ).
thf(decl_24,type,
setadjoin: $i > $i > $i ).
thf(decl_25,type,
kpair: $i > $i > $i ).
thf(decl_26,type,
setukpairinjL2: $o ).
thf(decl_27,type,
esk1_0: $i ).
thf(decl_28,type,
esk2_0: $i ).
thf(decl_29,type,
esk3_0: $i ).
thf(decl_30,type,
esk4_0: $i ).
thf(setukpairinjL,conjecture,
( setukpairinjL2
=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( kpair @ X1 @ X2 )
= ( kpair @ X3 @ X4 ) )
=> ( X1 = X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.le8JU4Rrff/E---3.1_384148.p',setukpairinjL) ).
thf(setukpairinjL2,axiom,
( setukpairinjL2
<=> ! [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 ) ) )
=> ( X1 = X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.le8JU4Rrff/E---3.1_384148.p',setukpairinjL2) ).
thf(kpair,axiom,
( kpair
= ( ^ [X1: $i,X2: $i] : ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.le8JU4Rrff/E---3.1_384148.p',kpair) ).
thf(c_0_3,negated_conjecture,
~ ( setukpairinjL2
=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( kpair @ X1 @ X2 )
= ( kpair @ X3 @ X4 ) )
=> ( X1 = X3 ) ) ),
inference(assume_negation,[status(cth)],[setukpairinjL]) ).
thf(c_0_4,negated_conjecture,
~ ( ! [X13: $i,X14: $i,X15: $i,X16: $i] :
( ( ( setadjoin @ ( setadjoin @ X13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X13 @ ( setadjoin @ X14 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X15 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X15 @ ( setadjoin @ X16 @ emptyset ) ) @ emptyset ) ) )
=> ( X13 = X15 ) )
=> ! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( kpair @ X1 @ X2 )
= ( kpair @ X3 @ X4 ) )
=> ( X1 = X3 ) ) ),
inference(apply_def,[status(thm)],[c_0_3,setukpairinjL2]) ).
thf(c_0_5,plain,
! [X17: $i,X18: $i] :
( ( kpair @ X17 @ X18 )
= ( setadjoin @ ( setadjoin @ X17 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X17 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[kpair])]) ).
thf(c_0_6,negated_conjecture,
! [X19: $i,X20: $i,X21: $i,X22: $i] :
( ( ( ( setadjoin @ ( setadjoin @ X19 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X19 @ ( setadjoin @ X20 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X21 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X21 @ ( setadjoin @ X22 @ emptyset ) ) @ emptyset ) ) )
| ( X19 = X21 ) )
& ( ( kpair @ esk1_0 @ esk2_0 )
= ( kpair @ esk3_0 @ esk4_0 ) )
& ( esk1_0 != esk3_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_4])])])])]) ).
thf(c_0_7,plain,
! [X27: $i,X28: $i] :
( ( kpair @ X27 @ X28 )
= ( setadjoin @ ( setadjoin @ X27 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X27 @ ( setadjoin @ X28 @ emptyset ) ) @ emptyset ) ) ),
inference(variable_rename,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X3 )
| ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,plain,
! [X1: $i,X2: $i] :
( ( kpair @ X1 @ X2 )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,negated_conjecture,
! [X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X1 = X2 )
| ( ( kpair @ X1 @ X3 )
!= ( kpair @ X2 @ X4 ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_9]) ).
thf(c_0_11,negated_conjecture,
( ( kpair @ esk1_0 @ esk2_0 )
= ( kpair @ esk3_0 @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_12,negated_conjecture,
! [X1: $i,X2: $i] :
( ( X1 = esk3_0 )
| ( ( kpair @ X1 @ X2 )
!= ( kpair @ esk1_0 @ esk2_0 ) ) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
thf(c_0_13,negated_conjecture,
esk1_0 != esk3_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_14,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_12]),c_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU648^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n017.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 13:57:52 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.26 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.le8JU4Rrff/E---3.1_384148.p
% 0.29/0.29 % Version: 3.5.1-ho
% 0.29/0.29 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.29/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.29 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.29/0.29 % Starting post_as_ho5 with 300s (1) cores
% 0.29/0.29 % Starting sh4l with 300s (1) cores
% 0.29/0.29 % Starting ho_unfolding_2 with 300s (1) cores
% 0.29/0.29 % post_as_ho5 with pid 384169 completed with status 0
% 0.29/0.29 % Result found by post_as_ho5
% 0.29/0.29 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.29/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.29 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.29/0.29 % Starting post_as_ho5 with 300s (1) cores
% 0.29/0.29 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.29/0.29 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.29/0.29 % Search class: HHUPF-FFSF22-MSFFMFNN
% 0.29/0.29 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.29/0.29 % Starting SubtermCWHack with 28s (1) cores
% 0.29/0.29 % SubtermCWHack with pid 384175 completed with status 0
% 0.29/0.29 % Result found by SubtermCWHack
% 0.29/0.29 % Preprocessing class: HSSSSMSSSLSNSFN.
% 0.29/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.29/0.29 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.29/0.29 % Starting post_as_ho5 with 300s (1) cores
% 0.29/0.29 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 0.29/0.29 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 0.29/0.29 % Search class: HHUPF-FFSF22-MSFFMFNN
% 0.29/0.29 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.29/0.29 % Starting SubtermCWHack with 28s (1) cores
% 0.29/0.29 % Preprocessing time : 0.001 s
% 0.29/0.29
% 0.29/0.29 % Proof found!
% 0.29/0.29 % SZS status Theorem
% 0.29/0.29 % SZS output start CNFRefutation
% See solution above
% 0.29/0.29 % Parsed axioms : 7
% 0.29/0.29 % Removed by relevancy pruning/SinE : 4
% 0.29/0.29 % Initial clauses : 4
% 0.29/0.29 % Removed in clause preprocessing : 0
% 0.29/0.29 % Initial clauses in saturation : 4
% 0.29/0.29 % Processed clauses : 7
% 0.29/0.29 % ...of these trivial : 0
% 0.29/0.29 % ...subsumed : 0
% 0.29/0.29 % ...remaining for further processing : 7
% 0.29/0.29 % Other redundant clauses eliminated : 0
% 0.29/0.29 % Clauses deleted for lack of memory : 0
% 0.29/0.29 % Backward-subsumed : 0
% 0.29/0.29 % Backward-rewritten : 0
% 0.29/0.29 % Generated clauses : 8
% 0.29/0.29 % ...of the previous two non-redundant : 4
% 0.29/0.29 % ...aggressively subsumed : 0
% 0.29/0.29 % Contextual simplify-reflections : 0
% 0.29/0.29 % Paramodulations : 6
% 0.29/0.29 % Factorizations : 0
% 0.29/0.29 % NegExts : 0
% 0.29/0.29 % Equation resolutions : 2
% 0.29/0.29 % Disequality decompositions : 0
% 0.29/0.29 % Total rewrite steps : 7
% 0.29/0.29 % ...of those cached : 1
% 0.29/0.29 % Propositional unsat checks : 0
% 0.29/0.29 % Propositional check models : 0
% 0.29/0.29 % Propositional check unsatisfiable : 0
% 0.29/0.29 % Propositional clauses : 0
% 0.29/0.29 % Propositional clauses after purity: 0
% 0.29/0.29 % Propositional unsat core size : 0
% 0.29/0.29 % Propositional preprocessing time : 0.000
% 0.29/0.29 % Propositional encoding time : 0.000
% 0.29/0.29 % Propositional solver time : 0.000
% 0.29/0.29 % Success case prop preproc time : 0.000
% 0.29/0.29 % Success case prop encoding time : 0.000
% 0.29/0.29 % Success case prop solver time : 0.000
% 0.29/0.29 % Current number of processed clauses : 7
% 0.29/0.29 % Positive orientable unit clauses : 4
% 0.29/0.29 % Positive unorientable unit clauses: 0
% 0.29/0.29 % Negative unit clauses : 1
% 0.29/0.29 % Non-unit-clauses : 2
% 0.29/0.29 % Current number of unprocessed clauses: 1
% 0.29/0.29 % ...number of literals in the above : 2
% 0.29/0.29 % Current number of archived formulas : 0
% 0.29/0.29 % Current number of archived clauses : 0
% 0.29/0.29 % Clause-clause subsumption calls (NU) : 1
% 0.29/0.29 % Rec. Clause-clause subsumption calls : 1
% 0.29/0.29 % Non-unit clause-clause subsumptions : 0
% 0.29/0.29 % Unit Clause-clause subsumption calls : 0
% 0.29/0.29 % Rewrite failures with RHS unbound : 0
% 0.29/0.29 % BW rewrite match attempts : 1
% 0.29/0.29 % BW rewrite match successes : 0
% 0.29/0.29 % Condensation attempts : 0
% 0.29/0.29 % Condensation successes : 0
% 0.29/0.29 % Termbank termtop insertions : 709
% 0.29/0.29 % Search garbage collected termcells : 138
% 0.29/0.29
% 0.29/0.29 % -------------------------------------------------
% 0.29/0.29 % User time : 0.005 s
% 0.29/0.29 % System time : 0.002 s
% 0.29/0.29 % Total time : 0.006 s
% 0.29/0.29 % Maximum resident set size: 3632 pages
% 0.29/0.29
% 0.29/0.29 % -------------------------------------------------
% 0.29/0.29 % User time : 0.007 s
% 0.29/0.29 % System time : 0.008 s
% 0.29/0.29 % Total time : 0.014 s
% 0.29/0.29 % Maximum resident set size: 4864 pages
% 0.29/0.29 % E exiting
%------------------------------------------------------------------------------