%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET603+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 02:17:38 PM UTC 2026
% Result : Theorem 0.16s 0.50s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 11 unt; 0 def)
% Number of atoms : 85 ( 25 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 83 ( 31 ~; 38 |; 8 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 66 ( 3 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(member_equal,axiom,
! [X1,X2] :
( ! [X3] :
( member(X3,X1)
<=> member(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_equal) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(prove_th74,conjecture,
! [X1] : difference(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th74) ).
fof(c_0_5,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_6,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( ~ member(X3,X2)
& member(X3,X1) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(c_0_7,plain,
! [X8] : ~ member(X8,empty_set),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_5])]) ).
fof(c_0_8,plain,
! [X9,X10] :
( ( X9 = X10
| member(esk2_2(X9,X10),X10)
| member(esk2_2(X9,X10),X9) )
& ( X9 = X10
| ~ member(esk2_2(X9,X10),X10)
| ~ member(esk2_2(X9,X10),X9) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[member_equal])])])])]) ).
fof(c_0_9,plain,
! [X5,X6,X7] :
( ( member(X7,difference(X5,X6))
| member(X7,X6)
| ~ member(X7,X5) )
& ( ~ member(X7,difference(X5,X6))
| ~ member(X7,X6) )
& ( ~ member(X7,difference(X5,X6))
| member(X7,X5) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_10,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( X1 = X2
| member(esk2_2(X1,X2),X2)
| member(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( ~ member(X1,difference(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( member(esk2_2(X1,empty_set),X1)
| X1 = empty_set ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
fof(c_0_14,plain,
! [X12,X13,X14,X15,X16,X17] :
( ( X16 = X17
| member(esk3_2(X16,X17),X17)
| member(esk3_2(X16,X17),X16) )
& ( X16 = X17
| ~ member(esk3_2(X16,X17),X17)
| ~ member(esk3_2(X16,X17),X16) )
& ( X12 != X13
| member(X15,X12)
| ~ member(X15,X13) )
& ( X12 != X13
| member(X14,X13)
| ~ member(X14,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)],[equal_member_defn])])])])])])]) ).
cnf(c_0_15,plain,
( ~ member(esk2_2(difference(X1,X2),empty_set),X2)
| difference(X1,X2) = empty_set ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
( ~ member(X1,X2)
| member(X1,difference(X2,X3))
| member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( ~ member(X1,difference(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,plain,
( X1 = X2
| member(esk3_2(X1,X2),X2)
| member(esk3_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( ~ member(esk2_2(difference(X1,difference(X2,X3)),empty_set),X2)
| member(esk2_2(difference(X1,difference(X2,X3)),empty_set),X3)
| difference(X1,difference(X2,X3)) = empty_set ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( member(esk2_2(difference(X1,X2),X3),X1)
| member(esk2_2(difference(X1,X2),X3),X3)
| difference(X1,X2) = X3 ),
inference(spm,[status(thm)],[c_0_17,c_0_11]) ).
cnf(c_0_21,plain,
( member(esk3_2(difference(X1,X2),X3),X1)
| member(esk3_2(difference(X1,X2),X3),X3)
| difference(X1,X2) = X3 ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( member(esk2_2(difference(X1,difference(X1,X2)),empty_set),X2)
| difference(X1,difference(X1,X2)) = empty_set ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_10]) ).
fof(c_0_23,negated_conjecture,
~ ! [X1] : difference(X1,empty_set) = X1,
inference(assume_negation,[status(cth)],[prove_th74]) ).
cnf(c_0_24,plain,
( ~ member(esk3_2(X1,X2),X2)
| ~ member(esk3_2(X1,X2),X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,plain,
( member(esk3_2(difference(X1,X2),X1),X1)
| difference(X1,X2) = X1 ),
inference(ef,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
difference(X1,difference(X1,empty_set)) = empty_set,
inference(spm,[status(thm)],[c_0_10,c_0_22]) ).
fof(c_0_27,negated_conjecture,
difference(esk1_0,empty_set) != esk1_0,
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).
cnf(c_0_28,plain,
( ~ member(esk3_2(difference(X1,X2),X1),difference(X1,X2))
| difference(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
( ~ member(X1,X2)
| member(X1,difference(X2,empty_set)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_26]),c_0_10]) ).
cnf(c_0_30,negated_conjecture,
difference(esk1_0,empty_set) != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,plain,
difference(X1,empty_set) = X1,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_25]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET603+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 % Computer : n026.cluster.edu
% 0.11/0.43 % Model : x86_64 x86_64
% 0.11/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.43 % Memory : 8046.5625MB
% 0.11/0.43 % OS : Linux 6.8.0-71-generic
% 0.11/0.43 % CPULimit : 300
% 0.11/0.43 % WCLimit : 300
% 0.11/0.43 % DateTime : Mon Sep 21 05:31:06 UTC 2026
% 0.11/0.44 % CPUTime :
% 0.11/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.48 Running first-order theorem proving
% 0.16/0.48 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
% 0.16/0.50 % Version: 3.5.1
% 0.16/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.50 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.50 % Starting sh5l with 300s (1) cores
% 0.16/0.50 % new_bool_3 with pid 1460688 completed with status 0
% 0.16/0.50 % Result found by new_bool_3
% 0.16/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.50 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/0.50 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.50 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.16/0.50 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.50 % Starting SubtermCWHack with 31s (1) cores
% 0.16/0.50 % SubtermCWHack with pid 1460691 completed with status 0
% 0.16/0.50 % Result found by SubtermCWHack
% 0.16/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.50 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/0.50 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.50 % Search class: FGHSF-FFSF22-SFFFFFNN
% 0.16/0.50 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.50 % Starting SubtermCWHack with 31s (1) cores
% 0.16/0.50 % Preprocessing time : 0.001 s
% 0.16/0.50
% 0.16/0.50 % Proof found!
% 0.16/0.50 % SZS status Theorem
% 0.16/0.50 % SZS output start CNFRefutation
% See solution above
% 0.16/0.51 % Parsed axioms : 9
% 0.16/0.51 % Removed by relevancy pruning/SinE : 4
% 0.16/0.51 % Initial clauses : 11
% 0.16/0.51 % Removed in clause preprocessing : 2
% 0.16/0.51 % Initial clauses in saturation : 9
% 0.16/0.51 % Processed clauses : 153
% 0.16/0.51 % ...of these trivial : 0
% 0.16/0.51 % ...subsumed : 99
% 0.16/0.51 % ...remaining for further processing : 54
% 0.16/0.51 % Other redundant clauses eliminated : 0
% 0.16/0.51 % Clauses deleted for lack of memory : 0
% 0.16/0.51 % Backward-subsumed : 0
% 0.16/0.51 % Backward-rewritten : 3
% 0.16/0.51 % Generated clauses : 436
% 0.16/0.51 % ...of the previous two non-redundant : 268
% 0.16/0.51 % ...aggressively subsumed : 0
% 0.16/0.51 % Contextual simplify-reflections : 1
% 0.16/0.51 % Paramodulations : 424
% 0.16/0.51 % Factorizations : 12
% 0.16/0.51 % NegExts : 0
% 0.16/0.51 % Equation resolutions : 0
% 0.16/0.51 % Disequality decompositions : 0
% 0.16/0.51 % Total rewrite steps : 243
% 0.16/0.51 % ...of those cached : 230
% 0.16/0.51 % Propositional unsat checks : 0
% 0.16/0.51 % Propositional check models : 0
% 0.16/0.51 % Propositional check unsatisfiable : 0
% 0.16/0.51 % Propositional clauses : 0
% 0.16/0.51 % Propositional clauses after purity: 0
% 0.16/0.51 % Propositional unsat core size : 0
% 0.16/0.51 % Propositional preprocessing time : 0.000
% 0.16/0.51 % Propositional encoding time : 0.000
% 0.16/0.51 % Propositional solver time : 0.000
% 0.16/0.51 % Success case prop preproc time : 0.000
% 0.16/0.51 % Success case prop encoding time : 0.000
% 0.16/0.51 % Success case prop solver time : 0.000
% 0.16/0.51 % Current number of processed clauses : 51
% 0.16/0.51 % Positive orientable unit clauses : 5
% 0.16/0.51 % Positive unorientable unit clauses: 0
% 0.16/0.51 % Negative unit clauses : 1
% 0.16/0.51 % Non-unit-clauses : 45
% 0.16/0.51 % Current number of unprocessed clauses: 124
% 0.16/0.51 % ...number of literals in the above : 342
% 0.16/0.51 % Current number of archived formulas : 0
% 0.16/0.51 % Current number of archived clauses : 3
% 0.16/0.51 % Clause-clause subsumption calls (NU) : 665
% 0.16/0.51 % Rec. Clause-clause subsumption calls : 527
% 0.16/0.51 % Non-unit clause-clause subsumptions : 78
% 0.16/0.51 % Unit Clause-clause subsumption calls : 79
% 0.16/0.51 % Rewrite failures with RHS unbound : 0
% 0.16/0.51 % BW rewrite match attempts : 8
% 0.16/0.51 % BW rewrite match successes : 3
% 0.16/0.51 % Condensation attempts : 0
% 0.16/0.51 % Condensation successes : 0
% 0.16/0.51 % Termbank termtop insertions : 6129
% 0.16/0.51 % Search garbage collected termcells : 233
% 0.16/0.51
% 0.16/0.51 % -------------------------------------------------
% 0.16/0.51 % User time : 0.004 s
% 0.16/0.51 % System time : 0.006 s
% 0.16/0.51 % Total time : 0.010 s
% 0.16/0.51 % Maximum resident set size: 3636 pages
% 0.16/0.51
% 0.16/0.51 % -------------------------------------------------
% 0.16/0.51 % User time : 0.005 s
% 0.16/0.51 % System time : 0.010 s
% 0.16/0.51 % Total time : 0.015 s
% 0.16/0.51 % Maximum resident set size: 4608 pages
% 0.16/0.51 % E exiting
%------------------------------------------------------------------------------