%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU174+2 : 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 : 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 : Thu Sep 24 02:28:24 PM UTC 2026
% Result : Theorem 0.93s 0.76s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 8 unt; 0 def)
% Number of atoms : 94 ( 27 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 115 ( 51 ~; 40 |; 11 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 54 ( 3 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t46_setfam_1,conjecture,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( complements_of_subsets(X1,X2) = empty_set
& X2 != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_setfam_1) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(d8_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ! [X3] :
( element(X3,powerset(powerset(X1)))
=> ( X3 = complements_of_subsets(X1,X2)
<=> ! [X4] :
( element(X4,powerset(X1))
=> ( in(X4,X3)
<=> in(subset_complement(X1,X4),X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_setfam_1) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X3))
& in(X1,X2) )
=> element(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(dt_k7_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(involutiveness_k7_setfam_1,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( complements_of_subsets(X1,X2) = empty_set
& X2 != empty_set ) ),
inference(assume_negation,[status(cth)],[t46_setfam_1]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( complements_of_subsets(X1,X2) = empty_set
& X2 != empty_set ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_8,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_9,plain,
! [X115,X116,X117,X118] :
( ( ~ element(X116,powerset(powerset(X115)))
| ~ element(X117,powerset(powerset(X115)))
| X117 = complements_of_subsets(X115,X116)
| in(subset_complement(X115,esk17_3(X115,X116,X117)),X116)
| in(esk17_3(X115,X116,X117),X117) )
& ( ~ element(X116,powerset(powerset(X115)))
| ~ element(X117,powerset(powerset(X115)))
| X117 = complements_of_subsets(X115,X116)
| ~ in(subset_complement(X115,esk17_3(X115,X116,X117)),X116)
| ~ in(esk17_3(X115,X116,X117),X117) )
& ( ~ element(X116,powerset(powerset(X115)))
| ~ element(X117,powerset(powerset(X115)))
| X117 = complements_of_subsets(X115,X116)
| element(esk17_3(X115,X116,X117),powerset(X115)) )
& ( ~ element(X116,powerset(powerset(X115)))
| ~ element(X117,powerset(powerset(X115)))
| X117 != complements_of_subsets(X115,X116)
| ~ element(X118,powerset(X115))
| in(X118,X117)
| ~ in(subset_complement(X115,X118),X116) )
& ( ~ element(X116,powerset(powerset(X115)))
| ~ element(X117,powerset(powerset(X115)))
| X117 != complements_of_subsets(X115,X116)
| ~ element(X118,powerset(X115))
| in(subset_complement(X115,X118),X116)
| ~ in(X118,X117) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_setfam_1])])])])])]) ).
fof(c_0_10,plain,
! [X269,X270,X271] :
( element(X269,X271)
| ~ element(X270,powerset(X271))
| ~ in(X269,X270) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])])]) ).
fof(c_0_11,plain,
! [X124,X125] :
( element(complements_of_subsets(X124,X125),powerset(powerset(X124)))
| ~ element(X125,powerset(powerset(X124))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_setfam_1])])]) ).
fof(c_0_12,negated_conjecture,
( complements_of_subsets(esk27_0,esk28_0) = empty_set
& esk28_0 != empty_set
& element(esk28_0,powerset(powerset(esk27_0))) ),
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_13,plain,
! [X139,X140] :
( complements_of_subsets(X139,complements_of_subsets(X139,X140)) = X140
| ~ element(X140,powerset(powerset(X139))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k7_setfam_1])])]) ).
fof(c_0_14,plain,
! [X26,X27,X28] :
( ( X28 = empty_set
| in(esk2_1(X28),X28) )
& ( ~ in(X27,X26)
| X26 != empty_set ) ),
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])])])])])]) ).
cnf(c_0_15,plain,
( ~ element(X4,powerset(powerset(X3)))
| ~ element(X2,powerset(powerset(X3)))
| X2 != complements_of_subsets(X3,X4)
| ~ element(X1,powerset(X3))
| ~ in(X1,X2)
| in(subset_complement(X3,X1),X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( ~ element(X2,powerset(X3))
| ~ in(X1,X2)
| element(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( ~ element(X1,powerset(powerset(X2)))
| element(complements_of_subsets(X2,X1),powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
element(esk28_0,powerset(powerset(esk27_0))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
complements_of_subsets(esk27_0,esk28_0) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( ~ element(X1,powerset(powerset(X2)))
| complements_of_subsets(X2,complements_of_subsets(X2,X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( ~ in(X2,X1)
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( ~ in(X2,complements_of_subsets(X1,X3))
| ~ element(X3,powerset(powerset(X1)))
| in(subset_complement(X1,X2),X3) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(csr,[status(thm)],[c_0_15,c_0_16])]),c_0_17]) ).
cnf(c_0_23,negated_conjecture,
element(empty_set,powerset(powerset(esk27_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_24,negated_conjecture,
complements_of_subsets(esk27_0,empty_set) = esk28_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_18]),c_0_19]) ).
cnf(c_0_25,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_26,negated_conjecture,
~ in(X1,esk28_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25]) ).
cnf(c_0_27,plain,
( X1 = empty_set
| in(esk2_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_28,negated_conjecture,
esk28_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU174+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n015.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 05:58:05 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.53 Running first-order theorem proving
% 0.25/0.53 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
% 0.93/0.76 % Version: 3.5.1
% 0.93/0.76 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.93/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.93/0.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.93/0.76 % Starting new_bool_3 with 300s (1) cores
% 0.93/0.76 % Starting new_bool_1 with 300s (1) cores
% 0.93/0.76 % Starting sh5l with 300s (1) cores
% 0.93/0.76 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 711094 completed with status 0
% 0.93/0.76 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.93/0.76 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.93/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.93/0.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.93/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.93/0.76 % No SInE strategy applied
% 0.93/0.76 % Search class: FGHSM-FSLS32-MFFFFFNN
% 0.93/0.76 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.93/0.76 % Starting SubtermCWHack with 136s (1) cores
% 0.93/0.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.93/0.76 % Starting G-E--_200_C45_F1_SE_CS_SP_PI_CO_S0V with 169s (1) cores
% 0.93/0.76 % Starting new_bool_3 with 169s (1) cores
% 0.93/0.76 % Starting new_bool_1 with 169s (1) cores
% 0.93/0.76 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 711100 completed with status 0
% 0.93/0.76 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.93/0.76 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.93/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.93/0.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.93/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.93/0.76 % No SInE strategy applied
% 0.93/0.76 % Search class: FGHSM-FSLS32-MFFFFFNN
% 0.93/0.76 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.93/0.76 % Starting SubtermCWHack with 136s (1) cores
% 0.93/0.76 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.93/0.76 % Preprocessing time : 0.006 s
% 0.93/0.76 % Presaturation interreduction done
% 0.93/0.76
% 0.93/0.76 % Proof found!
% 0.93/0.76 % SZS status Theorem
% 0.93/0.76 % SZS output start CNFRefutation
% See solution above
% 0.93/0.76 % Parsed axioms : 122
% 0.93/0.76 % Removed by relevancy pruning/SinE : 0
% 0.93/0.76 % Initial clauses : 211
% 0.93/0.76 % Removed in clause preprocessing : 14
% 0.93/0.76 % Initial clauses in saturation : 197
% 0.93/0.76 % Processed clauses : 407
% 0.93/0.76 % ...of these trivial : 3
% 0.93/0.76 % ...subsumed : 19
% 0.93/0.76 % ...remaining for further processing : 385
% 0.93/0.76 % Other redundant clauses eliminated : 102
% 0.93/0.76 % Clauses deleted for lack of memory : 0
% 0.93/0.76 % Backward-subsumed : 0
% 0.93/0.76 % Backward-rewritten : 3
% 0.93/0.76 % Generated clauses : 2322
% 0.93/0.76 % ...of the previous two non-redundant : 2157
% 0.93/0.76 % ...aggressively subsumed : 0
% 0.93/0.76 % Contextual simplify-reflections : 3
% 0.93/0.76 % Paramodulations : 2205
% 0.93/0.76 % Factorizations : 14
% 0.93/0.76 % NegExts : 0
% 0.93/0.76 % Equation resolutions : 107
% 0.93/0.76 % Disequality decompositions : 0
% 0.93/0.76 % Total rewrite steps : 228
% 0.93/0.76 % ...of those cached : 184
% 0.93/0.76 % Propositional unsat checks : 0
% 0.93/0.76 % Propositional check models : 0
% 0.93/0.76 % Propositional check unsatisfiable : 0
% 0.93/0.76 % Propositional clauses : 0
% 0.93/0.76 % Propositional clauses after purity: 0
% 0.93/0.76 % Propositional unsat core size : 0
% 0.93/0.76 % Propositional preprocessing time : 0.000
% 0.93/0.76 % Propositional encoding time : 0.000
% 0.93/0.76 % Propositional solver time : 0.000
% 0.93/0.76 % Success case prop preproc time : 0.000
% 0.93/0.76 % Success case prop encoding time : 0.000
% 0.93/0.76 % Success case prop solver time : 0.000
% 0.93/0.76 % Current number of processed clauses : 178
% 0.93/0.76 % Positive orientable unit clauses : 26
% 0.93/0.76 % Positive unorientable unit clauses: 3
% 0.93/0.76 % Negative unit clauses : 12
% 0.93/0.76 % Non-unit-clauses : 137
% 0.93/0.76 % Current number of unprocessed clauses: 2099
% 0.93/0.76 % ...number of literals in the above : 6974
% 0.93/0.76 % Current number of archived formulas : 0
% 0.93/0.76 % Current number of archived clauses : 177
% 0.93/0.76 % Clause-clause subsumption calls (NU) : 7678
% 0.93/0.76 % Rec. Clause-clause subsumption calls : 5156
% 0.93/0.76 % Non-unit clause-clause subsumptions : 19
% 0.93/0.76 % Unit Clause-clause subsumption calls : 483
% 0.93/0.76 % Rewrite failures with RHS unbound : 0
% 0.93/0.76 % BW rewrite match attempts : 59
% 0.93/0.76 % BW rewrite match successes : 40
% 0.93/0.76 % Condensation attempts : 0
% 0.93/0.76 % Condensation successes : 0
% 0.93/0.76 % Termbank termtop insertions : 39286
% 0.93/0.76 % Search garbage collected termcells : 3100
% 0.93/0.76
% 0.93/0.76 % -------------------------------------------------
% 0.93/0.76 % User time : 0.123 s
% 0.93/0.76 % System time : 0.007 s
% 0.93/0.76 % Total time : 0.130 s
% 0.93/0.76 % Maximum resident set size: 4256 pages
% 0.93/0.76
% 0.93/0.76 % -------------------------------------------------
% 0.93/0.76 % User time : 0.673 s
% 0.93/0.76 % System time : 0.054 s
% 0.93/0.76 % Total time : 0.728 s
% 0.93/0.76 % Maximum resident set size: 4864 pages
% 0.93/0.76 % E exiting
%------------------------------------------------------------------------------