%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SEU245+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 : n026.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 02:28:42 PM UTC 2026
% Result : Theorem 0.24s 0.57s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 8 unt; 0 def)
% Number of atoms : 93 ( 16 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 104 ( 41 ~; 45 |; 11 &)
% ( 4 <=>; 3 =>; 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; 3 con; 0-3 aty)
% Number of variables : 59 ( 4 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d6_wellord1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] : relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_wellord1) ).
fof(t16_wellord1,conjecture,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_restriction(X3,X2))
<=> ( in(X1,cartesian_product2(X2,X2))
& in(X1,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_wellord1) ).
fof(c_0_4,plain,
! [X12,X13,X14,X15,X16,X17,X18,X19] :
( ( X19 = set_intersection2(X17,X18)
| in(esk4_3(X17,X18,X19),X19)
| in(esk4_3(X17,X18,X19),X18) )
& ( X19 = set_intersection2(X17,X18)
| in(esk4_3(X17,X18,X19),X19)
| in(esk4_3(X17,X18,X19),X17) )
& ( X19 = set_intersection2(X17,X18)
| ~ in(esk4_3(X17,X18,X19),X18)
| ~ in(esk4_3(X17,X18,X19),X17)
| ~ in(esk4_3(X17,X18,X19),X19) )
& ( X14 != set_intersection2(X12,X13)
| in(X16,X14)
| ~ in(X16,X13)
| ~ in(X16,X12) )
& ( X14 != set_intersection2(X12,X13)
| ~ in(X15,X14)
| in(X15,X13) )
& ( X14 != set_intersection2(X12,X13)
| ~ in(X15,X14)
| in(X15,X12) ) ),
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])])])])])])]) ).
cnf(c_0_5,plain,
( X3 != set_intersection2(X4,X2)
| ~ in(X1,X3)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_6,plain,
! [X31,X32] : set_intersection2(X31,X32) = set_intersection2(X32,X31),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_7,plain,
! [X21,X22] :
( relation_restriction(X21,X22) = set_intersection2(X21,cartesian_product2(X22,X22))
| ~ relation(X21) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_wellord1])])])]) ).
cnf(c_0_8,plain,
( ~ in(X1,set_intersection2(X3,X2))
| in(X1,X2) ),
inference(er,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_restriction(X3,X2))
<=> ( in(X1,cartesian_product2(X2,X2))
& in(X1,X3) ) ) ),
inference(assume_negation,[status(cth)],[t16_wellord1]) ).
cnf(c_0_11,plain,
( X4 != set_intersection2(X2,X3)
| ~ in(X1,X3)
| ~ in(X1,X2)
| in(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_12,plain,
( ~ relation(X1)
| relation_restriction(X1,X2) = set_intersection2(X1,cartesian_product2(X2,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( ~ in(X1,set_intersection2(X2,X3))
| in(X1,X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
fof(c_0_14,negated_conjecture,
( ( in(esk1_0,relation_restriction(esk3_0,esk2_0))
| in(esk1_0,cartesian_product2(esk2_0,esk2_0)) )
& ( in(esk1_0,relation_restriction(esk3_0,esk2_0))
| in(esk1_0,esk3_0) )
& ( ~ in(esk1_0,cartesian_product2(esk2_0,esk2_0))
| ~ in(esk1_0,esk3_0)
| ~ in(esk1_0,relation_restriction(esk3_0,esk2_0)) )
& relation(esk3_0) ),
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_10])])])])]) ).
cnf(c_0_15,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( ~ relation(X2)
| set_intersection2(cartesian_product2(X1,X1),X2) = relation_restriction(X2,X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_17,plain,
( ~ relation(X2)
| ~ in(X1,relation_restriction(X2,X3))
| in(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_18,negated_conjecture,
( in(esk1_0,relation_restriction(esk3_0,esk2_0))
| in(esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
relation(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( ~ relation(X2)
| ~ in(X1,X2)
| ~ in(X1,cartesian_product2(X3,X3))
| in(X1,relation_restriction(X2,X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( in(esk1_0,relation_restriction(esk3_0,esk2_0))
| in(esk1_0,cartesian_product2(esk2_0,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,negated_conjecture,
( ~ in(esk1_0,cartesian_product2(esk2_0,esk2_0))
| ~ in(esk1_0,esk3_0)
| ~ in(esk1_0,relation_restriction(esk3_0,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,negated_conjecture,
in(esk1_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_24,negated_conjecture,
( ~ relation(X1)
| ~ in(esk1_0,X1)
| in(esk1_0,relation_restriction(X1,esk2_0))
| in(esk1_0,relation_restriction(esk3_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( ~ in(esk1_0,cartesian_product2(esk2_0,esk2_0))
| ~ in(esk1_0,relation_restriction(esk3_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
cnf(c_0_26,negated_conjecture,
in(esk1_0,relation_restriction(esk3_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_23]),c_0_19])]) ).
cnf(c_0_27,plain,
( ~ relation(X3)
| ~ in(X1,relation_restriction(X3,X2))
| in(X1,cartesian_product2(X2,X2)) ),
inference(spm,[status(thm)],[c_0_8,c_0_12]) ).
cnf(c_0_28,negated_conjecture,
~ in(esk1_0,cartesian_product2(esk2_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_26]),c_0_19])]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU245+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.45 % Computer : n026.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Mon Sep 21 06:05:52 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.53 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
% 0.24/0.57 % Version: 3.5.1
% 0.24/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.57 % Starting sh5l with 300s (1) cores
% 0.24/0.57 % new_bool_1 with pid 1526953 completed with status 0
% 0.24/0.57 % Result found by new_bool_1
% 0.24/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/0.57 % Search class: FGHSS-FFSM32-SFFFFFNN
% 0.24/0.57 % partial match(1): FGHSS-FFSF32-SFFFFFNN
% 0.24/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.24/0.57 % SubtermCWHack with pid 1526958 completed with status 0
% 0.24/0.57 % Result found by SubtermCWHack
% 0.24/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.24/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.24/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.24/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.24/0.57 % Search class: FGHSS-FFSM32-SFFFFFNN
% 0.24/0.57 % partial match(1): FGHSS-FFSF32-SFFFFFNN
% 0.24/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.24/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.24/0.57 % Preprocessing time : 0.002 s
% 0.24/0.57
% 0.24/0.57 % Proof found!
% 0.24/0.57 % SZS status Theorem
% 0.24/0.57 % SZS output start CNFRefutation
% See solution above
% 0.24/0.57 % Parsed axioms : 26
% 0.24/0.57 % Removed by relevancy pruning/SinE : 12
% 0.24/0.57 % Initial clauses : 25
% 0.24/0.57 % Removed in clause preprocessing : 0
% 0.24/0.57 % Initial clauses in saturation : 25
% 0.24/0.57 % Processed clauses : 159
% 0.24/0.57 % ...of these trivial : 1
% 0.24/0.57 % ...subsumed : 63
% 0.24/0.57 % ...remaining for further processing : 94
% 0.24/0.57 % Other redundant clauses eliminated : 3
% 0.24/0.57 % Clauses deleted for lack of memory : 0
% 0.24/0.57 % Backward-subsumed : 1
% 0.24/0.57 % Backward-rewritten : 11
% 0.24/0.57 % Generated clauses : 335
% 0.24/0.57 % ...of the previous two non-redundant : 300
% 0.24/0.57 % ...aggressively subsumed : 0
% 0.24/0.57 % Contextual simplify-reflections : 1
% 0.24/0.57 % Paramodulations : 328
% 0.24/0.57 % Factorizations : 4
% 0.24/0.57 % NegExts : 0
% 0.24/0.57 % Equation resolutions : 3
% 0.24/0.57 % Disequality decompositions : 0
% 0.24/0.57 % Total rewrite steps : 58
% 0.24/0.57 % ...of those cached : 46
% 0.24/0.57 % Propositional unsat checks : 0
% 0.24/0.57 % Propositional check models : 0
% 0.24/0.57 % Propositional check unsatisfiable : 0
% 0.24/0.57 % Propositional clauses : 0
% 0.24/0.57 % Propositional clauses after purity: 0
% 0.24/0.57 % Propositional unsat core size : 0
% 0.24/0.57 % Propositional preprocessing time : 0.000
% 0.24/0.57 % Propositional encoding time : 0.000
% 0.24/0.57 % Propositional solver time : 0.000
% 0.24/0.57 % Success case prop preproc time : 0.000
% 0.24/0.57 % Success case prop encoding time : 0.000
% 0.24/0.57 % Success case prop solver time : 0.000
% 0.24/0.57 % Current number of processed clauses : 79
% 0.24/0.57 % Positive orientable unit clauses : 13
% 0.24/0.57 % Positive unorientable unit clauses: 1
% 0.24/0.57 % Negative unit clauses : 7
% 0.24/0.57 % Non-unit-clauses : 58
% 0.24/0.57 % Current number of unprocessed clauses: 166
% 0.24/0.57 % ...number of literals in the above : 572
% 0.24/0.57 % Current number of archived formulas : 0
% 0.24/0.57 % Current number of archived clauses : 12
% 0.24/0.57 % Clause-clause subsumption calls (NU) : 862
% 0.24/0.57 % Rec. Clause-clause subsumption calls : 725
% 0.24/0.57 % Non-unit clause-clause subsumptions : 57
% 0.24/0.57 % Unit Clause-clause subsumption calls : 21
% 0.24/0.57 % Rewrite failures with RHS unbound : 0
% 0.24/0.57 % BW rewrite match attempts : 5
% 0.24/0.57 % BW rewrite match successes : 5
% 0.24/0.57 % Condensation attempts : 0
% 0.24/0.57 % Condensation successes : 0
% 0.24/0.57 % Termbank termtop insertions : 5311
% 0.24/0.57 % Search garbage collected termcells : 370
% 0.24/0.57
% 0.24/0.57 % -------------------------------------------------
% 0.24/0.57 % User time : 0.019 s
% 0.24/0.57 % System time : 0.006 s
% 0.24/0.57 % Total time : 0.025 s
% 0.24/0.57 % Maximum resident set size: 3648 pages
% 0.24/0.57
% 0.24/0.57 % -------------------------------------------------
% 0.24/0.57 % User time : 0.021 s
% 0.24/0.57 % System time : 0.013 s
% 0.24/0.57 % Total time : 0.034 s
% 0.24/0.57 % Maximum resident set size: 4864 pages
% 0.24/0.57 % E exiting
%------------------------------------------------------------------------------