%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU141+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 02:23:57 PM UTC 2026
% Result : Theorem 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 51 ( 32 unt; 0 def)
% Number of atoms : 76 ( 47 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 17 ~; 17 |; 3 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 75 ( 4 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t83_xboole_1,conjecture,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(d7_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(t48_xboole_1,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(l32_xboole_1,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(t36_xboole_1,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(t39_xboole_1,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(t1_boole,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t2_boole,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
fof(c_0_12,negated_conjecture,
~ ! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
inference(assume_negation,[status(cth)],[t83_xboole_1]) ).
fof(c_0_13,plain,
! [X52,X53] :
( ( disjoint(X52,X53)
| set_intersection2(X52,X53) != empty_set )
& ( set_intersection2(X52,X53) = empty_set
| ~ disjoint(X52,X53) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])])]) ).
fof(c_0_14,lemma,
! [X112,X113] : set_difference(X112,set_difference(X112,X113)) = set_intersection2(X112,X113),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(c_0_15,plain,
! [X68,X69] :
( disjoint(X69,X68)
| ~ disjoint(X68,X69) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])])]) ).
fof(c_0_16,negated_conjecture,
( ( set_difference(esk11_0,esk12_0) = esk11_0
| disjoint(esk11_0,esk12_0) )
& ( set_difference(esk11_0,esk12_0) != esk11_0
| ~ disjoint(esk11_0,esk12_0) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])]) ).
fof(c_0_17,plain,
! [X11,X12] : set_intersection2(X11,X12) = set_intersection2(X12,X11),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_18,lemma,
! [X63,X64] :
( ( set_difference(X63,X64) = empty_set
| ~ subset(X63,X64) )
& ( subset(X63,X64)
| set_difference(X63,X64) != empty_set ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])])]) ).
fof(c_0_19,lemma,
! [X94,X95] : subset(set_difference(X94,X95),X94),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
cnf(c_0_20,plain,
( ~ disjoint(X1,X2)
| set_intersection2(X1,X2) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( ~ disjoint(X1,X2)
| disjoint(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,negated_conjecture,
( set_difference(esk11_0,esk12_0) = esk11_0
| disjoint(esk11_0,esk12_0) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_25,lemma,
! [X98,X99] : set_union2(X98,set_difference(X99,X98)) = set_union2(X98,X99),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
cnf(c_0_26,lemma,
( ~ subset(X1,X2)
| set_difference(X1,X2) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_28,plain,
! [X77] : set_union2(X77,empty_set) = X77,
inference(variable_rename,[status(thm)],[t1_boole]) ).
cnf(c_0_29,plain,
( ~ disjoint(X1,X2)
| set_difference(X1,set_difference(X1,X2)) = empty_set ),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_30,negated_conjecture,
( disjoint(esk12_0,esk11_0)
| set_difference(esk11_0,esk12_0) = esk11_0 ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_31,plain,
set_difference(X1,set_difference(X1,X2)) = set_difference(X2,set_difference(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_21]),c_0_21]) ).
fof(c_0_32,plain,
! [X9,X10] : set_union2(X9,X10) = set_union2(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_33,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_34,lemma,
set_difference(set_difference(X1,X2),X1) = empty_set,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_36,plain,
! [X86] : set_intersection2(X86,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
cnf(c_0_37,negated_conjecture,
( set_difference(esk11_0,esk12_0) = esk11_0
| set_difference(esk11_0,set_difference(esk11_0,esk12_0)) = empty_set ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_38,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,lemma,
set_union2(X1,set_difference(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_40,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_41,plain,
! [X100] : set_difference(X100,empty_set) = X100,
inference(variable_rename,[status(thm)],[t3_boole]) ).
cnf(c_0_42,negated_conjecture,
( set_difference(esk11_0,esk12_0) != esk11_0
| ~ disjoint(esk11_0,esk12_0) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_43,lemma,
set_difference(esk11_0,esk12_0) = esk11_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_37]),c_0_35]),c_0_38]),c_0_39])]) ).
cnf(c_0_44,plain,
( set_intersection2(X1,X2) != empty_set
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_45,plain,
set_difference(X1,set_difference(X1,empty_set)) = empty_set,
inference(rw,[status(thm)],[c_0_40,c_0_21]) ).
cnf(c_0_46,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_47,negated_conjecture,
~ disjoint(esk11_0,esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]) ).
cnf(c_0_48,plain,
( set_difference(X1,set_difference(X1,X2)) != empty_set
| disjoint(X1,X2) ),
inference(rw,[status(thm)],[c_0_44,c_0_21]) ).
cnf(c_0_49,plain,
set_difference(X1,X1) = empty_set,
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_43]),c_0_49])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU141+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n016.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 05:57:22 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.15/0.44 % Version: 3.5.1
% 0.15/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.44 % Starting sh5l with 300s (1) cores
% 0.15/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1703171 completed with status 0
% 0.15/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.15/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.44 % No SInE strategy applied
% 0.15/0.44 % Search class: FGHSM-FFMS32-SFFFFFNN
% 0.15/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.44 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 0.15/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.15/0.44 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with pid 1703181 completed with status 0
% 0.15/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I
% 0.15/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.44 % No SInE strategy applied
% 0.15/0.44 % Search class: FGHSM-FFMS32-SFFFFFNN
% 0.15/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.44 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S059I with 136s (1) cores
% 0.15/0.44 % Preprocessing time : 0.002 s
% 0.15/0.44 % Presaturation interreduction done
% 0.15/0.44
% 0.15/0.44 % Proof found!
% 0.15/0.44 % SZS status Theorem
% 0.15/0.44 % SZS output start CNFRefutation
% See solution above
% 0.15/0.44 % Parsed axioms : 57
% 0.15/0.44 % Removed by relevancy pruning/SinE : 0
% 0.15/0.44 % Initial clauses : 87
% 0.15/0.44 % Removed in clause preprocessing : 5
% 0.15/0.44 % Initial clauses in saturation : 82
% 0.15/0.44 % Processed clauses : 212
% 0.15/0.44 % ...of these trivial : 3
% 0.15/0.44 % ...subsumed : 61
% 0.15/0.44 % ...remaining for further processing : 148
% 0.15/0.44 % Other redundant clauses eliminated : 18
% 0.15/0.44 % Clauses deleted for lack of memory : 0
% 0.15/0.44 % Backward-subsumed : 0
% 0.15/0.44 % Backward-rewritten : 8
% 0.15/0.44 % Generated clauses : 240
% 0.15/0.44 % ...of the previous two non-redundant : 168
% 0.15/0.44 % ...aggressively subsumed : 0
% 0.15/0.44 % Contextual simplify-reflections : 0
% 0.15/0.44 % Paramodulations : 222
% 0.15/0.44 % Factorizations : 0
% 0.15/0.44 % NegExts : 0
% 0.15/0.44 % Equation resolutions : 18
% 0.15/0.44 % Disequality decompositions : 0
% 0.15/0.44 % Total rewrite steps : 134
% 0.15/0.44 % ...of those cached : 95
% 0.15/0.44 % Propositional unsat checks : 0
% 0.15/0.44 % Propositional check models : 0
% 0.15/0.44 % Propositional check unsatisfiable : 0
% 0.15/0.44 % Propositional clauses : 0
% 0.15/0.44 % Propositional clauses after purity: 0
% 0.15/0.44 % Propositional unsat core size : 0
% 0.15/0.44 % Propositional preprocessing time : 0.000
% 0.15/0.44 % Propositional encoding time : 0.000
% 0.15/0.44 % Propositional solver time : 0.000
% 0.15/0.44 % Success case prop preproc time : 0.000
% 0.15/0.44 % Success case prop encoding time : 0.000
% 0.15/0.44 % Success case prop solver time : 0.000
% 0.15/0.44 % Current number of processed clauses : 54
% 0.15/0.44 % Positive orientable unit clauses : 18
% 0.15/0.44 % Positive unorientable unit clauses: 2
% 0.15/0.44 % Negative unit clauses : 9
% 0.15/0.44 % Non-unit-clauses : 25
% 0.15/0.44 % Current number of unprocessed clauses: 111
% 0.15/0.44 % ...number of literals in the above : 218
% 0.15/0.44 % Current number of archived formulas : 0
% 0.15/0.44 % Current number of archived clauses : 82
% 0.15/0.44 % Clause-clause subsumption calls (NU) : 614
% 0.15/0.44 % Rec. Clause-clause subsumption calls : 461
% 0.15/0.44 % Non-unit clause-clause subsumptions : 15
% 0.15/0.44 % Unit Clause-clause subsumption calls : 35
% 0.15/0.44 % Rewrite failures with RHS unbound : 0
% 0.15/0.44 % BW rewrite match attempts : 40
% 0.15/0.44 % BW rewrite match successes : 27
% 0.15/0.44 % Condensation attempts : 0
% 0.15/0.44 % Condensation successes : 0
% 0.15/0.44 % Termbank termtop insertions : 6856
% 0.15/0.44 % Search garbage collected termcells : 1170
% 0.15/0.44
% 0.15/0.44 % -------------------------------------------------
% 0.15/0.44 % User time : 0.017 s
% 0.15/0.44 % System time : 0.004 s
% 0.15/0.44 % Total time : 0.021 s
% 0.15/0.44 % Maximum resident set size: 3932 pages
% 0.15/0.44
% 0.15/0.44 % -------------------------------------------------
% 0.15/0.44 % User time : 0.064 s
% 0.15/0.44 % System time : 0.015 s
% 0.15/0.44 % Total time : 0.079 s
% 0.15/0.44 % Maximum resident set size: 4864 pages
% 0.15/0.44 % E exiting
%------------------------------------------------------------------------------