%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU107+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 : n001.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 02:23:49 PM UTC 2026
% Result : Theorem 0.23s 0.57s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 12 unt; 0 def)
% Number of atoms : 128 ( 9 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 133 ( 49 ~; 47 |; 25 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 75 ( 2 sgn 43 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rc3_finset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( finite(X2)
& ~ empty(X2)
& element(X2,powerset(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
fof(dt_k2_finsub_1,axiom,
! [X1,X2,X3] :
( ( element(X3,X1)
& element(X2,X1)
& preboolean(X1)
& ~ empty(X1) )
=> element(prebool_difference(X1,X2,X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_finsub_1) ).
fof(redefinition_k2_finsub_1,axiom,
! [X1,X2,X3] :
( ( element(X3,X1)
& element(X2,X1)
& preboolean(X1)
& ~ empty(X1) )
=> prebool_difference(X1,X2,X3) = set_difference(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_finsub_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(t37_xboole_1,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( in(X1,X2)
| empty(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(t18_finsub_1,conjecture,
! [X1] :
( ( preboolean(X1)
& ~ empty(X1) )
=> in(empty_set,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_finsub_1) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(c_0_9,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( finite(X2)
& ~ empty(X2)
& element(X2,powerset(X1)) ) ),
inference(fof_simplification,[status(thm)],[rc3_finset_1]) ).
fof(c_0_10,plain,
! [X1,X2,X3] :
( ( element(X3,X1)
& element(X2,X1)
& preboolean(X1)
& ~ empty(X1) )
=> element(prebool_difference(X1,X2,X3),X1) ),
inference(fof_simplification,[status(thm)],[dt_k2_finsub_1]) ).
fof(c_0_11,plain,
! [X1,X2,X3] :
( ( element(X3,X1)
& element(X2,X1)
& preboolean(X1)
& ~ empty(X1) )
=> prebool_difference(X1,X2,X3) = set_difference(X2,X3) ),
inference(fof_simplification,[status(thm)],[redefinition_k2_finsub_1]) ).
fof(c_0_12,plain,
! [X48,X49,X50] :
( element(X48,X50)
| ~ element(X49,powerset(X50))
| ~ in(X48,X49) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])])]) ).
fof(c_0_13,plain,
! [X29] :
( ( empty(X29)
| finite(esk9_1(X29)) )
& ( empty(X29)
| ~ empty(esk9_1(X29)) )
& ( empty(X29)
| element(esk9_1(X29),powerset(X29)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])]) ).
fof(c_0_14,plain,
! [X11,X12,X13] :
( element(prebool_difference(X11,X12,X13),X11)
| ~ element(X13,X11)
| ~ element(X12,X11)
| ~ preboolean(X11)
| empty(X11) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_15,plain,
! [X33,X34,X35] :
( prebool_difference(X33,X34,X35) = set_difference(X34,X35)
| ~ element(X35,X33)
| ~ element(X34,X33)
| ~ preboolean(X33)
| empty(X33) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_16,plain,
! [X42,X43] :
( ( set_difference(X42,X43) = empty_set
| ~ subset(X42,X43) )
& ( subset(X42,X43)
| set_difference(X42,X43) != empty_set ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])])]) ).
fof(c_0_17,plain,
! [X36] : subset(X36,X36),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_18,plain,
( ~ element(X2,powerset(X3))
| ~ in(X1,X2)
| element(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( empty(X1)
| element(esk9_1(X1),powerset(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_20,plain,
! [X40,X41] :
( in(X40,X41)
| empty(X41)
| ~ element(X40,X41) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])]) ).
fof(c_0_21,negated_conjecture,
~ ! [X1] :
( ( preboolean(X1)
& ~ empty(X1) )
=> in(empty_set,X1) ),
inference(assume_negation,[status(cth)],[t18_finsub_1]) ).
cnf(c_0_22,plain,
( ~ element(X3,X1)
| ~ element(X2,X1)
| ~ preboolean(X1)
| element(prebool_difference(X1,X2,X3),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
( ~ element(X3,X1)
| ~ element(X2,X1)
| ~ preboolean(X1)
| prebool_difference(X1,X2,X3) = set_difference(X2,X3)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
( ~ subset(X1,X2)
| set_difference(X1,X2) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
( ~ in(X1,esk9_1(X2))
| empty(X2)
| element(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,plain,
( ~ element(X1,X2)
| in(X1,X2)
| empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
( ~ empty(esk9_1(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_29,plain,
! [X14] : element(esk1_1(X14),X14),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_30,negated_conjecture,
~ ! [X1] :
( ( preboolean(X1)
& ~ empty(X1) )
=> in(empty_set,X1) ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
cnf(c_0_31,plain,
( ~ preboolean(X3)
| ~ element(X1,X3)
| ~ element(X2,X3)
| empty(X3)
| element(set_difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_32,plain,
set_difference(X1,X1) = empty_set,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,plain,
( ~ element(X1,esk9_1(X2))
| empty(X2)
| element(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_34,plain,
element(esk1_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_35,negated_conjecture,
( ~ in(empty_set,esk11_0)
& preboolean(esk11_0)
& ~ empty(esk11_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])]) ).
cnf(c_0_36,plain,
( ~ preboolean(X1)
| ~ element(X2,X1)
| empty(X1)
| element(empty_set,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
( empty(X1)
| element(esk1_1(esk9_1(X1)),X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
~ in(empty_set,esk11_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_39,negated_conjecture,
~ empty(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,plain,
( ~ preboolean(X1)
| empty(X1)
| element(empty_set,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
preboolean(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,negated_conjecture,
~ element(empty_set,esk11_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_27]),c_0_39]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU107+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.44 % Computer : n001.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.44 % CPULimit : 300
% 0.20/0.44 % WCLimit : 300
% 0.20/0.44 % DateTime : Mon Sep 21 05:56:28 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.52 Running first-order theorem proving
% 0.23/0.52 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
% 0.23/0.57 % Version: 3.5.1
% 0.23/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.57 % Starting sh5l with 300s (1) cores
% 0.23/0.57 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2328270 completed with status 0
% 0.23/0.57 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.23/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.57 % No SInE strategy applied
% 0.23/0.57 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.23/0.57 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.57 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.23/0.57 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 0.23/0.57 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.23/0.57 % Starting G-E--_208_B07----D_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.23/0.57 % G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with pid 2328280 completed with status 0
% 0.23/0.57 % Result found by G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y
% 0.23/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.57 % No SInE strategy applied
% 0.23/0.57 % Search class: FGHSM-FFMM31-SFFFFFNN
% 0.23/0.57 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.57 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.23/0.57 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 136s (1) cores
% 0.23/0.57 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 0.23/0.57 % Preprocessing time : 0.002 s
% 0.23/0.57
% 0.23/0.57 % Proof found!
% 0.23/0.57 % SZS status Theorem
% 0.23/0.57 % SZS output start CNFRefutation
% See solution above
% 0.23/0.57 % Parsed axioms : 33
% 0.23/0.57 % Removed by relevancy pruning/SinE : 0
% 0.23/0.57 % Initial clauses : 58
% 0.23/0.57 % Removed in clause preprocessing : 0
% 0.23/0.57 % Initial clauses in saturation : 58
% 0.23/0.57 % Processed clauses : 194
% 0.23/0.57 % ...of these trivial : 2
% 0.23/0.57 % ...subsumed : 46
% 0.23/0.57 % ...remaining for further processing : 146
% 0.23/0.57 % Other redundant clauses eliminated : 0
% 0.23/0.57 % Clauses deleted for lack of memory : 0
% 0.23/0.57 % Backward-subsumed : 7
% 0.23/0.57 % Backward-rewritten : 13
% 0.23/0.57 % Generated clauses : 312
% 0.23/0.57 % ...of the previous two non-redundant : 244
% 0.23/0.57 % ...aggressively subsumed : 0
% 0.23/0.57 % Contextual simplify-reflections : 7
% 0.23/0.57 % Paramodulations : 311
% 0.23/0.57 % Factorizations : 0
% 0.23/0.57 % NegExts : 0
% 0.23/0.57 % Equation resolutions : 1
% 0.23/0.57 % Disequality decompositions : 0
% 0.23/0.57 % Total rewrite steps : 92
% 0.23/0.57 % ...of those cached : 76
% 0.23/0.57 % Propositional unsat checks : 0
% 0.23/0.57 % Propositional check models : 0
% 0.23/0.57 % Propositional check unsatisfiable : 0
% 0.23/0.57 % Propositional clauses : 0
% 0.23/0.57 % Propositional clauses after purity: 0
% 0.23/0.57 % Propositional unsat core size : 0
% 0.23/0.57 % Propositional preprocessing time : 0.000
% 0.23/0.57 % Propositional encoding time : 0.000
% 0.23/0.57 % Propositional solver time : 0.000
% 0.23/0.57 % Success case prop preproc time : 0.000
% 0.23/0.57 % Success case prop encoding time : 0.000
% 0.23/0.57 % Success case prop solver time : 0.000
% 0.23/0.57 % Current number of processed clauses : 126
% 0.23/0.57 % Positive orientable unit clauses : 32
% 0.23/0.57 % Positive unorientable unit clauses: 0
% 0.23/0.57 % Negative unit clauses : 13
% 0.23/0.57 % Non-unit-clauses : 81
% 0.23/0.57 % Current number of unprocessed clauses: 94
% 0.23/0.57 % ...number of literals in the above : 411
% 0.23/0.57 % Current number of archived formulas : 0
% 0.23/0.57 % Current number of archived clauses : 20
% 0.23/0.57 % Clause-clause subsumption calls (NU) : 1279
% 0.23/0.57 % Rec. Clause-clause subsumption calls : 778
% 0.23/0.57 % Non-unit clause-clause subsumptions : 49
% 0.23/0.57 % Unit Clause-clause subsumption calls : 276
% 0.23/0.57 % Rewrite failures with RHS unbound : 0
% 0.23/0.57 % BW rewrite match attempts : 13
% 0.23/0.57 % BW rewrite match successes : 3
% 0.23/0.57 % Condensation attempts : 0
% 0.23/0.57 % Condensation successes : 0
% 0.23/0.57 % Termbank termtop insertions : 7034
% 0.23/0.57 % Search garbage collected termcells : 478
% 0.23/0.57
% 0.23/0.57 % -------------------------------------------------
% 0.23/0.57 % User time : 0.018 s
% 0.23/0.57 % System time : 0.005 s
% 0.23/0.57 % Total time : 0.023 s
% 0.23/0.57 % Maximum resident set size: 3660 pages
% 0.23/0.57
% 0.23/0.57 % -------------------------------------------------
% 0.23/0.57 % User time : 0.069 s
% 0.23/0.57 % System time : 0.025 s
% 0.23/0.57 % Total time : 0.095 s
% 0.23/0.57 % Maximum resident set size: 4864 pages
% 0.23/0.57 % E exiting
%------------------------------------------------------------------------------