%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU171+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 02:24:07 PM UTC 2026
% Result : Theorem 0.22s 0.53s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 8 unt; 0 def)
% Number of atoms : 106 ( 20 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 120 ( 43 ~; 35 |; 16 &)
% ( 8 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 50 ( 0 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t50_subset_1,conjecture,
! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
fof(d2_subset_1,axiom,
! [X1,X2] :
( ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) )
& ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( ~ in(X4,X2)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(d5_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
inference(assume_negation,[status(cth)],[t50_subset_1]) ).
fof(c_0_6,plain,
! [X1,X2] :
( ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) )
& ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[d2_subset_1]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( ~ in(X4,X2)
& in(X4,X1) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_9,plain,
! [X7,X8] :
( ( ~ empty(X7)
| element(X8,X7)
| ~ empty(X8) )
& ( ~ empty(X7)
| empty(X8)
| ~ element(X8,X7) )
& ( empty(X7)
| element(X8,X7)
| ~ in(X8,X7) )
& ( empty(X7)
| in(X8,X7)
| ~ element(X8,X7) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_10,negated_conjecture,
( ~ in(esk9_0,subset_complement(esk7_0,esk8_0))
& ~ in(esk9_0,esk8_0)
& element(esk9_0,esk7_0)
& element(esk8_0,powerset(esk7_0))
& esk7_0 != empty_set ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_11,plain,
! [X9,X10,X11,X12,X13,X14,X15,X16] :
( ( X16 = set_difference(X14,X15)
| in(esk1_3(X14,X15,X16),X16)
| ~ in(esk1_3(X14,X15,X16),X15) )
& ( X16 = set_difference(X14,X15)
| in(esk1_3(X14,X15,X16),X16)
| in(esk1_3(X14,X15,X16),X14) )
& ( X16 = set_difference(X14,X15)
| in(esk1_3(X14,X15,X16),X15)
| ~ in(esk1_3(X14,X15,X16),X14)
| ~ in(esk1_3(X14,X15,X16),X16) )
& ( X11 != set_difference(X9,X10)
| in(X13,X11)
| in(X13,X10)
| ~ in(X13,X9) )
& ( X11 != set_difference(X9,X10)
| ~ in(X12,X11)
| ~ in(X12,X10) )
& ( X11 != set_difference(X9,X10)
| ~ in(X12,X11)
| in(X12,X9) ) ),
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)],[c_0_8])])])])])])]) ).
fof(c_0_12,plain,
! [X38] :
( X38 = empty_set
| ~ empty(X38) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])]) ).
cnf(c_0_13,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
element(esk9_0,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X18,X19] :
( subset_complement(X18,X19) = set_difference(X18,X19)
| ~ element(X19,powerset(X18)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])])]) ).
cnf(c_0_16,plain,
( X4 != set_difference(X2,X3)
| ~ in(X1,X2)
| in(X1,X4)
| in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( ~ empty(X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
( in(esk9_0,esk7_0)
| empty(esk7_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
esk7_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_20,negated_conjecture,
~ in(esk9_0,subset_complement(esk7_0,esk8_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,plain,
( ~ element(X1,powerset(X2))
| subset_complement(X2,X1) = set_difference(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,negated_conjecture,
element(esk8_0,powerset(esk7_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,plain,
( ~ in(X1,X2)
| in(X1,X3)
| in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
in(esk9_0,esk7_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_25,negated_conjecture,
~ in(esk9_0,set_difference(esk7_0,esk8_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_26,negated_conjecture,
( in(esk9_0,X1)
| in(esk9_0,set_difference(esk7_0,X1)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
~ in(esk9_0,esk8_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU171+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n006.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 05:54:12 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.49 Running first-order theorem proving
% 0.22/0.49 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
% 0.22/0.53 % Version: 3.5.1
% 0.22/0.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.53 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.53 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.53 % Starting sh5l with 300s (1) cores
% 0.22/0.53 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2137044 completed with status 0
% 0.22/0.53 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.22/0.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.53 % No SInE strategy applied
% 0.22/0.53 % Search class: FGHSM-FFMS31-SFFFFFNN
% 0.22/0.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.53 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.22/0.53 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 0.22/0.53 % Starting new_bool_3 with 136s (1) cores
% 0.22/0.53 % Starting new_bool_1 with 136s (1) cores
% 0.22/0.53 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2137050 completed with status 0
% 0.22/0.53 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.22/0.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.53 % No SInE strategy applied
% 0.22/0.53 % Search class: FGHSM-FFMS31-SFFFFFNN
% 0.22/0.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.53 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.22/0.53 % Preprocessing time : 0.001 s
% 0.22/0.53 % Presaturation interreduction done
% 0.22/0.53
% 0.22/0.53 % Proof found!
% 0.22/0.53 % SZS status Theorem
% 0.22/0.53 % SZS output start CNFRefutation
% See solution above
% 0.22/0.53 % Parsed axioms : 23
% 0.22/0.53 % Removed by relevancy pruning/SinE : 0
% 0.22/0.53 % Initial clauses : 37
% 0.22/0.53 % Removed in clause preprocessing : 4
% 0.22/0.53 % Initial clauses in saturation : 33
% 0.22/0.53 % Processed clauses : 90
% 0.22/0.53 % ...of these trivial : 0
% 0.22/0.53 % ...subsumed : 5
% 0.22/0.53 % ...remaining for further processing : 85
% 0.22/0.53 % Other redundant clauses eliminated : 3
% 0.22/0.53 % Clauses deleted for lack of memory : 0
% 0.22/0.53 % Backward-subsumed : 2
% 0.22/0.53 % Backward-rewritten : 4
% 0.22/0.53 % Generated clauses : 70
% 0.22/0.53 % ...of the previous two non-redundant : 58
% 0.22/0.53 % ...aggressively subsumed : 0
% 0.22/0.53 % Contextual simplify-reflections : 1
% 0.22/0.53 % Paramodulations : 65
% 0.22/0.53 % Factorizations : 2
% 0.22/0.53 % NegExts : 0
% 0.22/0.53 % Equation resolutions : 3
% 0.22/0.53 % Disequality decompositions : 0
% 0.22/0.53 % Total rewrite steps : 11
% 0.22/0.53 % ...of those cached : 4
% 0.22/0.53 % Propositional unsat checks : 0
% 0.22/0.53 % Propositional check models : 0
% 0.22/0.53 % Propositional check unsatisfiable : 0
% 0.22/0.53 % Propositional clauses : 0
% 0.22/0.53 % Propositional clauses after purity: 0
% 0.22/0.53 % Propositional unsat core size : 0
% 0.22/0.53 % Propositional preprocessing time : 0.000
% 0.22/0.53 % Propositional encoding time : 0.000
% 0.22/0.53 % Propositional solver time : 0.000
% 0.22/0.53 % Success case prop preproc time : 0.000
% 0.22/0.53 % Success case prop encoding time : 0.000
% 0.22/0.53 % Success case prop solver time : 0.000
% 0.22/0.53 % Current number of processed clauses : 43
% 0.22/0.53 % Positive orientable unit clauses : 12
% 0.22/0.53 % Positive unorientable unit clauses: 0
% 0.22/0.53 % Negative unit clauses : 10
% 0.22/0.53 % Non-unit-clauses : 21
% 0.22/0.53 % Current number of unprocessed clauses: 28
% 0.22/0.53 % ...number of literals in the above : 75
% 0.22/0.53 % Current number of archived formulas : 0
% 0.22/0.53 % Current number of archived clauses : 39
% 0.22/0.53 % Clause-clause subsumption calls (NU) : 126
% 0.22/0.53 % Rec. Clause-clause subsumption calls : 89
% 0.22/0.53 % Non-unit clause-clause subsumptions : 3
% 0.22/0.53 % Unit Clause-clause subsumption calls : 47
% 0.22/0.53 % Rewrite failures with RHS unbound : 0
% 0.22/0.53 % BW rewrite match attempts : 3
% 0.22/0.53 % BW rewrite match successes : 3
% 0.22/0.53 % Condensation attempts : 0
% 0.22/0.53 % Condensation successes : 0
% 0.22/0.53 % Termbank termtop insertions : 2746
% 0.22/0.53 % Search garbage collected termcells : 409
% 0.22/0.53
% 0.22/0.53 % -------------------------------------------------
% 0.22/0.53 % User time : 0.009 s
% 0.22/0.53 % System time : 0.005 s
% 0.22/0.53 % Total time : 0.014 s
% 0.22/0.53 % Maximum resident set size: 3388 pages
% 0.22/0.53
% 0.22/0.53 % -------------------------------------------------
% 0.22/0.53 % User time : 0.021 s
% 0.22/0.53 % System time : 0.021 s
% 0.22/0.53 % Total time : 0.042 s
% 0.22/0.53 % Maximum resident set size: 4608 pages
% 0.22/0.53 % E exiting
%------------------------------------------------------------------------------