%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET578+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 02:17:21 PM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 10 unt; 0 def)
% Number of atoms : 105 ( 16 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 105 ( 37 ~; 46 |; 13 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 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 : 71 ( 2 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th19,conjecture,
! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( member(X4,X3)
& member(X4,X2) ) )
=> X1 = intersection(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th19) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X2)
& member(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( ! [X4] :
( member(X4,X1)
<=> ( member(X4,X3)
& member(X4,X2) ) )
=> X1 = intersection(X2,X3) ),
inference(assume_negation,[status(cth)],[prove_th19]) ).
fof(c_0_6,negated_conjecture,
! [X29] :
( esk3_0 != intersection(esk4_0,esk5_0)
& ( member(X29,esk3_0)
| ~ member(X29,esk5_0)
| ~ member(X29,esk4_0) )
& ( ~ member(X29,esk3_0)
| member(X29,esk5_0) )
& ( ~ member(X29,esk3_0)
| member(X29,esk4_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_5])])])])])]) ).
fof(c_0_7,plain,
! [X12,X13,X14,X15,X16] :
( ( subset(X15,X16)
| ~ member(esk1_2(X15,X16),X16) )
& ( subset(X15,X16)
| member(esk1_2(X15,X16),X15) )
& ( member(X14,X13)
| ~ member(X14,X12)
| ~ subset(X12,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)],[subset_defn])])])])])])]) ).
fof(c_0_8,plain,
! [X5,X6,X7] :
( ( member(X7,intersection(X5,X6))
| ~ member(X7,X6)
| ~ member(X7,X5) )
& ( ~ member(X7,intersection(X5,X6))
| member(X7,X6) )
& ( ~ member(X7,intersection(X5,X6))
| member(X7,X5) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])])]) ).
cnf(c_0_9,negated_conjecture,
( ~ member(X1,esk3_0)
| member(X1,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( member(esk1_2(esk3_0,X1),esk4_0)
| subset(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( ~ member(X1,esk3_0)
| member(X1,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_14,plain,
! [X10,X11] : intersection(X10,X11) = intersection(X11,X10),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_15,negated_conjecture,
( ~ member(esk1_2(esk3_0,X1),X2)
| member(esk1_2(esk3_0,X1),intersection(X2,esk4_0))
| subset(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( member(esk1_2(esk3_0,X1),esk5_0)
| subset(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_17,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( ~ member(esk1_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
( member(esk1_2(esk3_0,X1),intersection(esk4_0,esk5_0))
| subset(esk3_0,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_20,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_21,negated_conjecture,
subset(esk3_0,intersection(esk4_0,esk5_0)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_22,plain,
! [X19,X20,X21,X22,X23,X24] :
( ( X23 = X24
| member(esk2_2(X23,X24),X24)
| member(esk2_2(X23,X24),X23) )
& ( X23 = X24
| ~ member(esk2_2(X23,X24),X24)
| ~ member(esk2_2(X23,X24),X23) )
& ( X19 != X20
| member(X22,X19)
| ~ member(X22,X20) )
& ( X19 != X20
| member(X21,X20)
| ~ member(X21,X19) ) ),
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_23,negated_conjecture,
( ~ member(X1,esk3_0)
| member(X1,intersection(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
( X1 = X2
| member(esk2_2(X1,X2),X2)
| member(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,negated_conjecture,
( member(esk2_2(esk3_0,X1),X1)
| member(esk2_2(esk3_0,X1),intersection(esk4_0,esk5_0))
| esk3_0 = X1 ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,negated_conjecture,
esk3_0 != intersection(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_27,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_28,negated_conjecture,
member(esk2_2(esk3_0,intersection(esk4_0,esk5_0)),intersection(esk4_0,esk5_0)),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_25]),c_0_26]) ).
cnf(c_0_29,plain,
( ~ member(esk2_2(X1,X2),X2)
| ~ member(esk2_2(X1,X2),X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,negated_conjecture,
( ~ member(X1,esk5_0)
| ~ member(X1,esk4_0)
| member(X1,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_31,negated_conjecture,
member(esk2_2(esk3_0,intersection(esk4_0,esk5_0)),esk4_0),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
~ member(esk2_2(esk3_0,intersection(esk4_0,esk5_0)),esk3_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_28]),c_0_26]) ).
cnf(c_0_33,plain,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_34,negated_conjecture,
~ member(esk2_2(esk3_0,intersection(esk4_0,esk5_0)),esk5_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_35,plain,
( member(esk2_2(X1,intersection(X2,X3)),X3)
| member(esk2_2(X1,intersection(X2,X3)),X1)
| X1 = intersection(X2,X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_24]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_26]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET578+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:27:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.45 % Version: 3.5.1
% 0.10/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.45 % Starting sh5l with 300s (1) cores
% 0.10/0.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1768520 completed with status 0
% 0.10/0.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.10/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.45 % No SInE strategy applied
% 0.10/0.45 % Search class: FGUSS-FFSF22-SFFFFFNN
% 0.10/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.45 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.10/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.10/0.45 % Starting new_bool_1 with 136s (1) cores
% 0.10/0.45 % new_bool_3 with pid 1768529 completed with status 0
% 0.10/0.45 % Result found by new_bool_3
% 0.10/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.45 % No SInE strategy applied
% 0.10/0.45 % Search class: FGUSS-FFSF22-SFFFFFNN
% 0.10/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.45 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.10/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.10/0.45 % Preprocessing time : 0.001 s
% 0.10/0.45 % Presaturation interreduction done
% 0.10/0.45
% 0.10/0.45 % Proof found!
% 0.10/0.45 % SZS status Theorem
% 0.10/0.45 % SZS output start CNFRefutation
% See solution above
% 0.10/0.45 % Parsed axioms : 7
% 0.10/0.45 % Removed by relevancy pruning/SinE : 0
% 0.10/0.45 % Initial clauses : 19
% 0.10/0.45 % Removed in clause preprocessing : 2
% 0.10/0.45 % Initial clauses in saturation : 17
% 0.10/0.45 % Processed clauses : 307
% 0.10/0.45 % ...of these trivial : 3
% 0.10/0.45 % ...subsumed : 170
% 0.10/0.45 % ...remaining for further processing : 134
% 0.10/0.45 % Other redundant clauses eliminated : 2
% 0.10/0.45 % Clauses deleted for lack of memory : 0
% 0.10/0.45 % Backward-subsumed : 0
% 0.10/0.45 % Backward-rewritten : 10
% 0.10/0.45 % Generated clauses : 817
% 0.10/0.45 % ...of the previous two non-redundant : 777
% 0.10/0.45 % ...aggressively subsumed : 0
% 0.10/0.45 % Contextual simplify-reflections : 1
% 0.10/0.45 % Paramodulations : 795
% 0.10/0.45 % Factorizations : 20
% 0.10/0.45 % NegExts : 0
% 0.10/0.45 % Equation resolutions : 2
% 0.10/0.45 % Disequality decompositions : 0
% 0.10/0.45 % Total rewrite steps : 138
% 0.10/0.45 % ...of those cached : 107
% 0.10/0.45 % Propositional unsat checks : 0
% 0.10/0.45 % Propositional check models : 0
% 0.10/0.45 % Propositional check unsatisfiable : 0
% 0.10/0.45 % Propositional clauses : 0
% 0.10/0.45 % Propositional clauses after purity: 0
% 0.10/0.45 % Propositional unsat core size : 0
% 0.10/0.45 % Propositional preprocessing time : 0.000
% 0.10/0.45 % Propositional encoding time : 0.000
% 0.10/0.45 % Propositional solver time : 0.000
% 0.10/0.45 % Success case prop preproc time : 0.000
% 0.10/0.45 % Success case prop encoding time : 0.000
% 0.10/0.45 % Success case prop solver time : 0.000
% 0.10/0.45 % Current number of processed clauses : 107
% 0.10/0.45 % Positive orientable unit clauses : 17
% 0.10/0.45 % Positive unorientable unit clauses: 1
% 0.10/0.45 % Negative unit clauses : 4
% 0.10/0.45 % Non-unit-clauses : 85
% 0.10/0.45 % Current number of unprocessed clauses: 482
% 0.10/0.45 % ...number of literals in the above : 1334
% 0.10/0.45 % Current number of archived formulas : 0
% 0.10/0.45 % Current number of archived clauses : 25
% 0.10/0.45 % Clause-clause subsumption calls (NU) : 1269
% 0.10/0.45 % Rec. Clause-clause subsumption calls : 1118
% 0.10/0.45 % Non-unit clause-clause subsumptions : 171
% 0.10/0.45 % Unit Clause-clause subsumption calls : 103
% 0.10/0.45 % Rewrite failures with RHS unbound : 0
% 0.10/0.45 % BW rewrite match attempts : 31
% 0.10/0.45 % BW rewrite match successes : 12
% 0.10/0.45 % Condensation attempts : 0
% 0.10/0.45 % Condensation successes : 0
% 0.10/0.45 % Termbank termtop insertions : 11824
% 0.10/0.45 % Search garbage collected termcells : 355
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.013 s
% 0.10/0.45 % System time : 0.004 s
% 0.10/0.45 % Total time : 0.018 s
% 0.10/0.45 % Maximum resident set size: 3632 pages
% 0.10/0.45
% 0.10/0.45 % -------------------------------------------------
% 0.10/0.45 % User time : 0.061 s
% 0.10/0.45 % System time : 0.017 s
% 0.10/0.45 % Total time : 0.078 s
% 0.10/0.45 % Maximum resident set size: 4864 pages
% 0.10/0.45 % E exiting
%------------------------------------------------------------------------------