%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU118+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 : Thu Sep 24 02:23:51 PM UTC 2026
% Result : Theorem 0.14s 5.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 9 unt; 0 def)
% Number of atoms : 83 ( 8 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 94 ( 37 ~; 37 |; 9 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 1 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d5_finsub_1,axiom,
! [X1,X2] :
( preboolean(X2)
=> ( X2 = finite_subsets(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( finite(X3)
& subset(X3,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_finsub_1) ).
fof(dt_k5_finsub_1,axiom,
! [X1] : preboolean(finite_subsets(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(t34_finsub_1,conjecture,
! [X1,X2] :
( element(X2,powerset(X1))
=> ( finite(X1)
=> element(X2,finite_subsets(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_finsub_1) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(cc2_finset_1,axiom,
! [X1] :
( finite(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> finite(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(c_0_6,plain,
! [X32,X33,X34,X35] :
( ( ~ preboolean(X33)
| X33 = finite_subsets(X32)
| in(esk8_2(X32,X33),X33)
| finite(esk8_2(X32,X33)) )
& ( ~ preboolean(X33)
| X33 = finite_subsets(X32)
| in(esk8_2(X32,X33),X33)
| subset(esk8_2(X32,X33),X32) )
& ( ~ preboolean(X33)
| X33 = finite_subsets(X32)
| ~ finite(esk8_2(X32,X33))
| ~ subset(esk8_2(X32,X33),X32)
| ~ in(esk8_2(X32,X33),X33) )
& ( ~ preboolean(X33)
| X33 != finite_subsets(X32)
| in(X35,X33)
| ~ finite(X35)
| ~ subset(X35,X32) )
& ( ~ preboolean(X33)
| X33 != finite_subsets(X32)
| ~ in(X34,X33)
| finite(X34) )
& ( ~ preboolean(X33)
| X33 != finite_subsets(X32)
| ~ in(X34,X33)
| subset(X34,X32) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_finsub_1])])])])])])]) ).
fof(c_0_7,plain,
! [X37] : preboolean(finite_subsets(X37)),
inference(variable_rename,[status(thm)],[dt_k5_finsub_1]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(X1))
=> ( finite(X1)
=> element(X2,finite_subsets(X1)) ) ),
inference(assume_negation,[status(cth)],[t34_finsub_1]) ).
fof(c_0_9,plain,
! [X20,X21] :
( element(X20,X21)
| ~ in(X20,X21) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])])]) ).
cnf(c_0_10,plain,
( ~ preboolean(X3)
| X3 != finite_subsets(X2)
| ~ finite(X1)
| ~ subset(X1,X2)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
preboolean(finite_subsets(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
! [X6,X7] :
( finite(X7)
| ~ element(X7,powerset(X6))
| ~ finite(X6) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_finset_1])])])]) ).
fof(c_0_13,negated_conjecture,
( ~ element(esk2_0,finite_subsets(esk1_0))
& finite(esk1_0)
& element(esk2_0,powerset(esk1_0)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_14,plain,
( ~ in(X1,X2)
| element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ finite(X1)
| ~ subset(X1,X2)
| in(X1,finite_subsets(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_10]),c_0_11])]) ).
cnf(c_0_16,plain,
( ~ element(X2,powerset(X1))
| ~ finite(X1)
| finite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
element(esk2_0,powerset(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
finite(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
~ element(esk2_0,finite_subsets(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( ~ finite(X1)
| ~ subset(X1,X2)
| element(X1,finite_subsets(X2)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
finite(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
fof(c_0_22,plain,
! [X24,X25] :
( ( element(X24,powerset(X25))
| ~ subset(X24,X25) )
& ( subset(X24,X25)
| ~ element(X24,powerset(X25)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])]) ).
cnf(c_0_23,negated_conjecture,
~ subset(esk2_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_24,plain,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU118+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/5.37 % Computer : n002.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Mon Sep 21 05:54:07 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.44 % Version: 3.5.1
% 0.14/5.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.44 % Starting sh5l with 300s (1) cores
% 0.14/5.44 % sh5l with pid 2569385 completed with status 0
% 0.14/5.44 % Result found by sh5l
% 0.14/5.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.44 % Starting sh5l with 300s (1) cores
% 0.14/5.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/5.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/5.44 % Search class: FGHSM-FFMM21-SFFFFFNN
% 0.14/5.44 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.44 % Starting SubtermCWHack with 28s (1) cores
% 0.14/5.44 % SubtermCWHack with pid 2569391 completed with status 0
% 0.14/5.44 % Result found by SubtermCWHack
% 0.14/5.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/5.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/5.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/5.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/5.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/5.44 % Starting sh5l with 300s (1) cores
% 0.14/5.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/5.44 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/5.44 % Search class: FGHSM-FFMM21-SFFFFFNN
% 0.14/5.44 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.14/5.44 % Starting SubtermCWHack with 28s (1) cores
% 0.14/5.44 % Preprocessing time : 0.001 s
% 0.14/5.44
% 0.14/5.44 % Proof found!
% 0.14/5.44 % SZS status Theorem
% 0.14/5.44 % SZS output start CNFRefutation
% See solution above
% 0.14/5.44 % Parsed axioms : 33
% 0.14/5.44 % Removed by relevancy pruning/SinE : 3
% 0.14/5.44 % Initial clauses : 56
% 0.14/5.44 % Removed in clause preprocessing : 0
% 0.14/5.44 % Initial clauses in saturation : 56
% 0.14/5.44 % Processed clauses : 85
% 0.14/5.44 % ...of these trivial : 1
% 0.14/5.44 % ...subsumed : 7
% 0.14/5.44 % ...remaining for further processing : 77
% 0.14/5.44 % Other redundant clauses eliminated : 3
% 0.14/5.44 % Clauses deleted for lack of memory : 0
% 0.14/5.44 % Backward-subsumed : 1
% 0.14/5.44 % Backward-rewritten : 3
% 0.14/5.44 % Generated clauses : 64
% 0.14/5.44 % ...of the previous two non-redundant : 45
% 0.14/5.44 % ...aggressively subsumed : 0
% 0.14/5.44 % Contextual simplify-reflections : 0
% 0.14/5.44 % Paramodulations : 61
% 0.14/5.44 % Factorizations : 0
% 0.14/5.44 % NegExts : 0
% 0.14/5.44 % Equation resolutions : 3
% 0.14/5.44 % Disequality decompositions : 0
% 0.14/5.44 % Total rewrite steps : 20
% 0.14/5.44 % ...of those cached : 6
% 0.14/5.44 % Propositional unsat checks : 0
% 0.14/5.44 % Propositional check models : 0
% 0.14/5.44 % Propositional check unsatisfiable : 0
% 0.14/5.44 % Propositional clauses : 0
% 0.14/5.44 % Propositional clauses after purity: 0
% 0.14/5.44 % Propositional unsat core size : 0
% 0.14/5.44 % Propositional preprocessing time : 0.000
% 0.14/5.44 % Propositional encoding time : 0.000
% 0.14/5.44 % Propositional solver time : 0.000
% 0.14/5.44 % Success case prop preproc time : 0.000
% 0.14/5.44 % Success case prop encoding time : 0.000
% 0.14/5.44 % Success case prop solver time : 0.000
% 0.14/5.44 % Current number of processed clauses : 70
% 0.14/5.44 % Positive orientable unit clauses : 24
% 0.14/5.44 % Positive unorientable unit clauses: 0
% 0.14/5.44 % Negative unit clauses : 7
% 0.14/5.44 % Non-unit-clauses : 39
% 0.14/5.44 % Current number of unprocessed clauses: 9
% 0.14/5.44 % ...number of literals in the above : 33
% 0.14/5.44 % Current number of archived formulas : 0
% 0.14/5.44 % Current number of archived clauses : 4
% 0.14/5.44 % Clause-clause subsumption calls (NU) : 113
% 0.14/5.44 % Rec. Clause-clause subsumption calls : 91
% 0.14/5.44 % Non-unit clause-clause subsumptions : 6
% 0.14/5.44 % Unit Clause-clause subsumption calls : 17
% 0.14/5.44 % Rewrite failures with RHS unbound : 0
% 0.14/5.44 % BW rewrite match attempts : 8
% 0.14/5.44 % BW rewrite match successes : 2
% 0.14/5.44 % Condensation attempts : 0
% 0.14/5.44 % Condensation successes : 0
% 0.14/5.44 % Termbank termtop insertions : 3548
% 0.14/5.44 % Search garbage collected termcells : 570
% 0.14/5.44
% 0.14/5.44 % -------------------------------------------------
% 0.14/5.44 % User time : 0.007 s
% 0.14/5.44 % System time : 0.002 s
% 0.14/5.44 % Total time : 0.009 s
% 0.14/5.44 % Maximum resident set size: 3660 pages
% 0.14/5.44
% 0.14/5.44 % -------------------------------------------------
% 0.14/5.44 % User time : 0.009 s
% 0.14/5.44 % System time : 0.006 s
% 0.14/5.44 % Total time : 0.016 s
% 0.14/5.44 % Maximum resident set size: 4864 pages
% 0.14/5.44 % E exiting
%------------------------------------------------------------------------------