%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET183+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 : n015.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 02:13:50 PM UTC 2026
% Result : Theorem 0.12s 0.43s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 14 unt; 0 def)
% Number of atoms : 80 ( 13 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 72 ( 28 ~; 29 |; 9 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 67 ( 4 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_subset_intersection,conjecture,
! [X1,X2] :
( subset(X1,X2)
=> intersection(X1,X2) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subset_intersection) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(intersection_is_subset,axiom,
! [X1,X2] : subset(intersection(X1,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_is_subset) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,X2)
=> intersection(X1,X2) = X1 ),
inference(assume_negation,[status(cth)],[prove_subset_intersection]) ).
fof(c_0_7,plain,
! [X9,X10,X11,X12,X13] :
( ( subset(X12,X13)
| ~ member(esk1_2(X12,X13),X13) )
& ( subset(X12,X13)
| member(esk1_2(X12,X13),X12) )
& ( member(X11,X10)
| ~ member(X11,X9)
| ~ subset(X9,X10) ) ),
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,negated_conjecture,
( intersection(esk3_0,esk4_0) != esk3_0
& subset(esk3_0,esk4_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_9,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
subset(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X4,X5,X6] :
( ( member(X6,intersection(X4,X5))
| ~ member(X6,X5)
| ~ member(X6,X4) )
& ( ~ member(X6,intersection(X4,X5))
| member(X6,X5) )
& ( ~ member(X6,intersection(X4,X5))
| member(X6,X4) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])])]) ).
cnf(c_0_12,plain,
( ~ member(esk1_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
( ~ member(X1,esk3_0)
| member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( subset(X1,X2)
| member(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,negated_conjecture,
( ~ member(esk1_2(X1,esk4_0),esk3_0)
| subset(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( member(esk1_2(intersection(X1,X2),X3),X1)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
subset(intersection(esk3_0,X1),esk4_0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
( ~ member(esk1_2(X1,intersection(X2,X3)),X2)
| ~ member(esk1_2(X1,intersection(X2,X3)),X3)
| subset(X1,intersection(X2,X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
( ~ member(X1,intersection(esk3_0,X2))
| member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_19]) ).
fof(c_0_22,plain,
! [X15,X16] :
( ( X15 = X16
| ~ subset(X16,X15)
| ~ subset(X15,X16) )
& ( X15 != X16
| subset(X16,X15) )
& ( X15 != X16
| subset(X15,X16) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])]) ).
cnf(c_0_23,plain,
( ~ member(esk1_2(X1,intersection(X2,X1)),X2)
| subset(X1,intersection(X2,X1)) ),
inference(spm,[status(thm)],[c_0_20,c_0_15]) ).
fof(c_0_24,plain,
! [X7,X8] : subset(intersection(X7,X8),X7),
inference(variable_rename,[status(thm)],[intersection_is_subset]) ).
cnf(c_0_25,negated_conjecture,
( member(esk1_2(intersection(esk3_0,X1),X2),esk4_0)
| subset(intersection(esk3_0,X1),X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_26,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
subset(X1,intersection(X1,X1)),
inference(spm,[status(thm)],[c_0_23,c_0_15]) ).
cnf(c_0_28,plain,
subset(intersection(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_29,plain,
! [X17,X18] : intersection(X17,X18) = intersection(X18,X17),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_30,negated_conjecture,
subset(intersection(esk3_0,X1),intersection(esk4_0,intersection(esk3_0,X1))),
inference(spm,[status(thm)],[c_0_23,c_0_25]) ).
cnf(c_0_31,plain,
intersection(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_32,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,negated_conjecture,
subset(esk3_0,intersection(esk3_0,esk4_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_34,negated_conjecture,
intersection(esk3_0,esk4_0) != esk3_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_33]),c_0_28])]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET183+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n015.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 05:02:21 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.43 % Version: 3.5.1
% 0.12/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.43 % Starting sh5l with 300s (1) cores
% 0.12/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 615478 completed with status 0
% 0.12/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.12/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.43 % No SInE strategy applied
% 0.12/0.43 % Search class: FGUSS-FFSF22-SFFFFFNN
% 0.12/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.43 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.12/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.12/0.43 % Starting new_bool_1 with 136s (1) cores
% 0.12/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 615483 completed with status 0
% 0.12/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.12/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.43 % No SInE strategy applied
% 0.12/0.43 % Search class: FGUSS-FFSF22-SFFFFFNN
% 0.12/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.43 % Preprocessing time : 0.001 s
% 0.12/0.43 % Presaturation interreduction done
% 0.12/0.43
% 0.12/0.43 % Proof found!
% 0.12/0.43 % SZS status Theorem
% 0.12/0.43 % SZS output start CNFRefutation
% See solution above
% 0.12/0.44 % Parsed axioms : 8
% 0.12/0.44 % Removed by relevancy pruning/SinE : 0
% 0.12/0.44 % Initial clauses : 18
% 0.12/0.44 % Removed in clause preprocessing : 2
% 0.12/0.44 % Initial clauses in saturation : 16
% 0.12/0.44 % Processed clauses : 82
% 0.12/0.44 % ...of these trivial : 2
% 0.12/0.44 % ...subsumed : 26
% 0.12/0.44 % ...remaining for further processing : 54
% 0.12/0.44 % Other redundant clauses eliminated : 2
% 0.12/0.44 % Clauses deleted for lack of memory : 0
% 0.12/0.44 % Backward-subsumed : 0
% 0.12/0.44 % Backward-rewritten : 1
% 0.12/0.44 % Generated clauses : 147
% 0.12/0.44 % ...of the previous two non-redundant : 113
% 0.12/0.44 % ...aggressively subsumed : 0
% 0.12/0.44 % Contextual simplify-reflections : 0
% 0.12/0.44 % Paramodulations : 143
% 0.12/0.44 % Factorizations : 2
% 0.12/0.44 % NegExts : 0
% 0.12/0.44 % Equation resolutions : 2
% 0.12/0.44 % Disequality decompositions : 0
% 0.12/0.44 % Total rewrite steps : 30
% 0.12/0.44 % ...of those cached : 16
% 0.12/0.44 % Propositional unsat checks : 0
% 0.12/0.44 % Propositional check models : 0
% 0.12/0.44 % Propositional check unsatisfiable : 0
% 0.12/0.44 % Propositional clauses : 0
% 0.12/0.44 % Propositional clauses after purity: 0
% 0.12/0.44 % Propositional unsat core size : 0
% 0.12/0.44 % Propositional preprocessing time : 0.000
% 0.12/0.44 % Propositional encoding time : 0.000
% 0.12/0.44 % Propositional solver time : 0.000
% 0.12/0.44 % Success case prop preproc time : 0.000
% 0.12/0.44 % Success case prop encoding time : 0.000
% 0.12/0.44 % Success case prop solver time : 0.000
% 0.12/0.44 % Current number of processed clauses : 37
% 0.12/0.44 % Positive orientable unit clauses : 9
% 0.12/0.44 % Positive unorientable unit clauses: 1
% 0.12/0.44 % Negative unit clauses : 1
% 0.12/0.44 % Non-unit-clauses : 26
% 0.12/0.44 % Current number of unprocessed clauses: 61
% 0.12/0.44 % ...number of literals in the above : 136
% 0.12/0.44 % Current number of archived formulas : 0
% 0.12/0.44 % Current number of archived clauses : 15
% 0.12/0.44 % Clause-clause subsumption calls (NU) : 154
% 0.12/0.44 % Rec. Clause-clause subsumption calls : 153
% 0.12/0.44 % Non-unit clause-clause subsumptions : 26
% 0.12/0.44 % Unit Clause-clause subsumption calls : 20
% 0.12/0.44 % Rewrite failures with RHS unbound : 0
% 0.12/0.44 % BW rewrite match attempts : 29
% 0.12/0.44 % BW rewrite match successes : 11
% 0.12/0.44 % Condensation attempts : 0
% 0.12/0.44 % Condensation successes : 0
% 0.12/0.44 % Termbank termtop insertions : 2483
% 0.12/0.44 % Search garbage collected termcells : 282
% 0.12/0.44
% 0.12/0.44 % -------------------------------------------------
% 0.12/0.44 % User time : 0.006 s
% 0.12/0.44 % System time : 0.003 s
% 0.12/0.44 % Total time : 0.009 s
% 0.12/0.44 % Maximum resident set size: 3632 pages
% 0.12/0.44
% 0.12/0.44 % -------------------------------------------------
% 0.12/0.44 % User time : 0.020 s
% 0.12/0.44 % System time : 0.013 s
% 0.12/0.44 % Total time : 0.033 s
% 0.12/0.44 % Maximum resident set size: 4864 pages
% 0.12/0.44 % E exiting
%------------------------------------------------------------------------------