%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU119+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 : n004.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 02:28:07 PM UTC 2026
% Result : Theorem 0.13s 0.64s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 9 unt; 0 def)
% Number of atoms : 131 ( 30 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 157 ( 67 ~; 57 |; 28 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 77 ( 5 sgn 37 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t3_xboole_0,conjecture,
! [X1,X2] :
( ~ ( disjoint(X1,X2)
& ? [X3] :
( in(X3,X2)
& in(X3,X1) ) )
& ~ ( ! [X3] :
~ ( in(X3,X2)
& in(X3,X1) )
& ~ disjoint(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X2)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_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(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(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( ~ ( disjoint(X1,X2)
& ? [X3] :
( in(X3,X2)
& in(X3,X1) ) )
& ~ ( ! [X3] :
~ ( in(X3,X2)
& in(X3,X1) )
& ~ disjoint(X1,X2) ) ),
inference(assume_negation,[status(cth)],[t3_xboole_0]) ).
fof(c_0_6,plain,
! [X13,X14,X15,X16,X17,X18,X19,X20] :
( ( X20 = set_intersection2(X18,X19)
| in(esk2_3(X18,X19,X20),X20)
| in(esk2_3(X18,X19,X20),X19) )
& ( X20 = set_intersection2(X18,X19)
| in(esk2_3(X18,X19,X20),X20)
| in(esk2_3(X18,X19,X20),X18) )
& ( X20 = set_intersection2(X18,X19)
| ~ in(esk2_3(X18,X19,X20),X19)
| ~ in(esk2_3(X18,X19,X20),X18)
| ~ in(esk2_3(X18,X19,X20),X20) )
& ( X15 != set_intersection2(X13,X14)
| in(X17,X15)
| ~ in(X17,X14)
| ~ in(X17,X13) )
& ( X15 != set_intersection2(X13,X14)
| ~ in(X16,X15)
| in(X16,X14) )
& ( X15 != set_intersection2(X13,X14)
| ~ in(X16,X15)
| in(X16,X13) ) ),
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)],[d3_xboole_0])])])])])])]) ).
fof(c_0_7,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2] :
( ~ ( disjoint(X1,X2)
& ? [X3] :
( in(X3,X2)
& in(X3,X1) ) )
& ~ ( ! [X3] :
~ ( in(X3,X2)
& in(X3,X1) )
& ~ disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( X3 != set_intersection2(X4,X2)
| ~ in(X1,X3)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X9,X10,X11] :
( ( X11 = empty_set
| in(esk1_1(X11),X11) )
& ( ~ in(X10,X9)
| X9 != 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_7])])])])])]) ).
fof(c_0_11,plain,
! [X7,X8] : set_intersection2(X7,X8) = set_intersection2(X8,X7),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_12,negated_conjecture,
! [X31] :
( ( ~ in(X31,esk6_0)
| ~ in(X31,esk5_0)
| disjoint(esk5_0,esk6_0) )
& ( ~ in(X31,esk6_0)
| ~ in(X31,esk5_0)
| in(esk7_0,esk6_0) )
& ( ~ in(X31,esk6_0)
| ~ in(X31,esk5_0)
| in(esk7_0,esk5_0) )
& ( ~ disjoint(esk5_0,esk6_0)
| disjoint(esk5_0,esk6_0) )
& ( ~ disjoint(esk5_0,esk6_0)
| in(esk7_0,esk6_0) )
& ( ~ disjoint(esk5_0,esk6_0)
| in(esk7_0,esk5_0) ) ),
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)],[c_0_8])])])])])]) ).
cnf(c_0_13,plain,
( ~ in(X1,set_intersection2(X3,X2))
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( X1 = empty_set
| in(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X22,X23] :
( ( disjoint(X22,X23)
| set_intersection2(X22,X23) != empty_set )
& ( set_intersection2(X22,X23) = empty_set
| ~ disjoint(X22,X23) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])])]) ).
cnf(c_0_17,negated_conjecture,
( ~ in(X1,esk6_0)
| ~ in(X1,esk5_0)
| in(esk7_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( in(esk1_1(set_intersection2(X1,X2)),X2)
| set_intersection2(X1,X2) = empty_set ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
( ~ in(X1,set_intersection2(X2,X3))
| in(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( ~ disjoint(esk5_0,esk6_0)
| in(esk7_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,plain,
( set_intersection2(X1,X2) != empty_set
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( ~ in(X1,esk6_0)
| ~ in(X1,esk5_0)
| in(esk7_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,negated_conjecture,
( ~ disjoint(esk5_0,esk6_0)
| in(esk7_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_24,negated_conjecture,
( ~ in(esk1_1(set_intersection2(X1,esk6_0)),esk5_0)
| in(esk7_0,esk6_0)
| set_intersection2(X1,esk6_0) = empty_set ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,plain,
( in(esk1_1(set_intersection2(X1,X2)),X1)
| set_intersection2(X1,X2) = empty_set ),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_26,negated_conjecture,
( set_intersection2(esk5_0,esk6_0) != empty_set
| in(esk7_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
( ~ in(esk1_1(set_intersection2(X1,esk6_0)),esk5_0)
| in(esk7_0,esk5_0)
| set_intersection2(X1,esk6_0) = empty_set ),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_28,negated_conjecture,
( set_intersection2(esk5_0,esk6_0) != empty_set
| in(esk7_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_29,negated_conjecture,
( ~ in(X1,esk6_0)
| ~ in(X1,esk5_0)
| disjoint(esk5_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_30,negated_conjecture,
in(esk7_0,esk6_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_31,negated_conjecture,
in(esk7_0,esk5_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_25]),c_0_28]) ).
cnf(c_0_32,plain,
( X4 != set_intersection2(X2,X3)
| ~ in(X1,X3)
| ~ in(X1,X2)
| in(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_33,plain,
( ~ disjoint(X1,X2)
| set_intersection2(X1,X2) = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_34,negated_conjecture,
disjoint(esk5_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_35,plain,
( ~ in(X2,X1)
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_36,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_37,negated_conjecture,
set_intersection2(esk5_0,esk6_0) = empty_set,
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( ~ in(X1,esk5_0)
| ~ in(X1,esk6_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_30]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU119+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.57 % Computer : n004.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Mon Sep 21 05:51:20 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.57 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.61 Running first-order theorem proving
% 0.09/0.61 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
% 0.13/0.64 % Version: 3.5.1
% 0.13/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.64 % Starting sh5l with 300s (1) cores
% 0.13/0.64 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2380872 completed with status 0
% 0.13/0.64 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.64 % No SInE strategy applied
% 0.13/0.64 % Search class: FGHSS-FFSF32-SFFFFFNN
% 0.13/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.64 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.64 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.13/0.64 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.64 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.64 % SubtermCWHack with pid 2380876 completed with status 0
% 0.13/0.64 % Result found by SubtermCWHack
% 0.13/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.64 % No SInE strategy applied
% 0.13/0.64 % Search class: FGHSS-FFSF32-SFFFFFNN
% 0.13/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.64 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.64 % Preprocessing time : 0.001 s
% 0.13/0.64
% 0.13/0.64 % Proof found!
% 0.13/0.64 % SZS status Theorem
% 0.13/0.64 % SZS output start CNFRefutation
% See solution above
% 0.13/0.64 % Parsed axioms : 13
% 0.13/0.64 % Removed by relevancy pruning/SinE : 0
% 0.13/0.64 % Initial clauses : 25
% 0.13/0.64 % Removed in clause preprocessing : 3
% 0.13/0.64 % Initial clauses in saturation : 22
% 0.13/0.64 % Processed clauses : 107
% 0.13/0.64 % ...of these trivial : 3
% 0.13/0.64 % ...subsumed : 33
% 0.13/0.64 % ...remaining for further processing : 71
% 0.13/0.64 % Other redundant clauses eliminated : 4
% 0.13/0.64 % Clauses deleted for lack of memory : 0
% 0.13/0.64 % Backward-subsumed : 0
% 0.13/0.64 % Backward-rewritten : 17
% 0.13/0.64 % Generated clauses : 224
% 0.13/0.64 % ...of the previous two non-redundant : 175
% 0.13/0.64 % ...aggressively subsumed : 0
% 0.13/0.64 % Contextual simplify-reflections : 2
% 0.13/0.64 % Paramodulations : 216
% 0.13/0.64 % Factorizations : 4
% 0.13/0.64 % NegExts : 0
% 0.13/0.64 % Equation resolutions : 4
% 0.13/0.64 % Disequality decompositions : 0
% 0.13/0.64 % Total rewrite steps : 48
% 0.13/0.64 % ...of those cached : 38
% 0.13/0.64 % Propositional unsat checks : 0
% 0.13/0.64 % Propositional check models : 0
% 0.13/0.64 % Propositional check unsatisfiable : 0
% 0.13/0.64 % Propositional clauses : 0
% 0.13/0.64 % Propositional clauses after purity: 0
% 0.13/0.64 % Propositional unsat core size : 0
% 0.13/0.64 % Propositional preprocessing time : 0.000
% 0.13/0.64 % Propositional encoding time : 0.000
% 0.13/0.64 % Propositional solver time : 0.000
% 0.13/0.64 % Success case prop preproc time : 0.000
% 0.13/0.64 % Success case prop encoding time : 0.000
% 0.13/0.64 % Success case prop solver time : 0.000
% 0.13/0.64 % Current number of processed clauses : 50
% 0.13/0.64 % Positive orientable unit clauses : 10
% 0.13/0.64 % Positive unorientable unit clauses: 1
% 0.13/0.64 % Negative unit clauses : 4
% 0.13/0.64 % Non-unit-clauses : 35
% 0.13/0.64 % Current number of unprocessed clauses: 88
% 0.13/0.64 % ...number of literals in the above : 249
% 0.13/0.64 % Current number of archived formulas : 0
% 0.13/0.64 % Current number of archived clauses : 17
% 0.13/0.64 % Clause-clause subsumption calls (NU) : 399
% 0.13/0.64 % Rec. Clause-clause subsumption calls : 364
% 0.13/0.64 % Non-unit clause-clause subsumptions : 30
% 0.13/0.64 % Unit Clause-clause subsumption calls : 9
% 0.13/0.64 % Rewrite failures with RHS unbound : 0
% 0.13/0.64 % BW rewrite match attempts : 5
% 0.13/0.64 % BW rewrite match successes : 5
% 0.13/0.64 % Condensation attempts : 0
% 0.13/0.64 % Condensation successes : 0
% 0.13/0.64 % Termbank termtop insertions : 3684
% 0.13/0.64 % Search garbage collected termcells : 308
% 0.13/0.64
% 0.13/0.64 % -------------------------------------------------
% 0.13/0.64 % User time : 0.009 s
% 0.13/0.64 % System time : 0.001 s
% 0.13/0.64 % Total time : 0.010 s
% 0.13/0.64 % Maximum resident set size: 3636 pages
% 0.13/0.64
% 0.13/0.64 % -------------------------------------------------
% 0.13/0.64 % User time : 0.023 s
% 0.13/0.64 % System time : 0.010 s
% 0.13/0.64 % Total time : 0.034 s
% 0.13/0.64 % Maximum resident set size: 4608 pages
% 0.13/0.64 % E exiting
%------------------------------------------------------------------------------