%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET143+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 : n018.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 02:13:43 PM UTC 2026
% Result : Theorem 2.40s 0.75s
% Output : CNFRefutation 2.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 33 unt; 0 def)
% Number of atoms : 101 ( 21 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 77 ( 32 ~; 33 |; 8 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 144 ( 8 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(prove_associativity_of_intersection,conjecture,
! [X1,X2,X3] : intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_intersection) ).
fof(c_0_5,plain,
! [X11,X12,X13,X14,X15] :
( ( subset(X14,X15)
| ~ member(esk1_2(X14,X15),X15) )
& ( subset(X14,X15)
| member(esk1_2(X14,X15),X14) )
& ( member(X13,X12)
| ~ member(X13,X11)
| ~ subset(X11,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)],[subset_defn])])])])])])]) ).
fof(c_0_6,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_7,plain,
( ~ member(esk1_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
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_5]) ).
cnf(c_0_11,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_7,c_0_8]) ).
cnf(c_0_12,plain,
( member(esk1_2(intersection(X1,X2),X3),X1)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( ~ member(X1,intersection(X3,X2))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
( ~ member(esk1_2(intersection(X1,X2),intersection(X3,X1)),X3)
| subset(intersection(X1,X2),intersection(X3,X1)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( member(esk1_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_10]) ).
fof(c_0_16,plain,
! [X9,X10] : intersection(X9,X10) = intersection(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_17,plain,
( ~ member(esk1_2(intersection(X1,X2),intersection(intersection(X3,X4),X1)),X3)
| ~ member(esk1_2(intersection(X1,X2),intersection(intersection(X3,X4),X1)),X4)
| subset(intersection(X1,X2),intersection(intersection(X3,X4),X1)) ),
inference(spm,[status(thm)],[c_0_14,c_0_8]) ).
cnf(c_0_18,plain,
( ~ member(esk1_2(intersection(X1,X2),intersection(X3,X2)),X3)
| subset(intersection(X1,X2),intersection(X3,X2)) ),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_19,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
( ~ member(esk1_2(intersection(X1,X2),intersection(intersection(X3,X2),X1)),X3)
| subset(intersection(X1,X2),intersection(intersection(X3,X2),X1)) ),
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_21,plain,
( member(esk1_2(intersection(intersection(X1,X2),X3),X4),X1)
| subset(intersection(intersection(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_22,plain,
( ~ member(esk1_2(intersection(X1,X2),intersection(X2,X3)),X3)
| subset(intersection(X1,X2),intersection(X2,X3)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( member(esk1_2(intersection(intersection(X1,X2),X3),X4),X2)
| subset(intersection(intersection(X1,X2),X3),X4) ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
fof(c_0_24,plain,
! [X7,X8] :
( ( X7 = X8
| ~ subset(X8,X7)
| ~ subset(X7,X8) )
& ( X7 != X8
| subset(X8,X7) )
& ( X7 != X8
| subset(X7,X8) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])]) ).
cnf(c_0_25,plain,
subset(intersection(intersection(X1,X2),X3),intersection(intersection(X1,X3),intersection(X1,X2))),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( ~ member(esk1_2(X1,intersection(X2,X1)),X2)
| subset(X1,intersection(X2,X1)) ),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_27,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X3,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
subset(intersection(intersection(X1,X2),X3),intersection(intersection(X1,X2),intersection(X1,X3))),
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_30,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X2,X3)),
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_31,plain,
subset(intersection(X1,X2),intersection(X1,intersection(X1,X2))),
inference(spm,[status(thm)],[c_0_26,c_0_12]) ).
cnf(c_0_32,plain,
subset(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_7,c_0_12]) ).
fof(c_0_33,negated_conjecture,
~ ! [X1,X2,X3] : intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
inference(assume_negation,[status(cth)],[prove_associativity_of_intersection]) ).
cnf(c_0_34,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(X1,X3)),
inference(spm,[status(thm)],[c_0_27,c_0_19]) ).
cnf(c_0_35,plain,
intersection(intersection(X1,X2),intersection(X1,X3)) = intersection(intersection(X1,X3),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_25]),c_0_27])]) ).
cnf(c_0_36,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(intersection(X2,X3),intersection(X2,X1))),
inference(spm,[status(thm)],[c_0_29,c_0_19]) ).
cnf(c_0_37,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_30,c_0_19]) ).
cnf(c_0_38,plain,
subset(intersection(X1,X2),intersection(X2,intersection(X1,X2))),
inference(spm,[status(thm)],[c_0_31,c_0_19]) ).
cnf(c_0_39,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_32,c_0_19]) ).
fof(c_0_40,negated_conjecture,
intersection(intersection(esk3_0,esk4_0),esk5_0) != intersection(esk3_0,intersection(esk4_0,esk5_0)),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])]) ).
cnf(c_0_41,plain,
subset(intersection(intersection(X1,X2),X3),intersection(intersection(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(intersection(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_43,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X2,intersection(X1,X3))),
inference(spm,[status(thm)],[c_0_37,c_0_35]) ).
cnf(c_0_44,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X1,intersection(intersection(X1,X2),X3))),
inference(spm,[status(thm)],[c_0_26,c_0_21]) ).
cnf(c_0_45,plain,
intersection(X1,intersection(X2,X1)) = intersection(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_38]),c_0_39])]) ).
cnf(c_0_46,negated_conjecture,
intersection(intersection(esk3_0,esk4_0),esk5_0) != intersection(esk3_0,intersection(esk4_0,esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_47,plain,
intersection(intersection(X1,X2),X3) = intersection(intersection(X1,X3),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_41]),c_0_41])]) ).
cnf(c_0_48,plain,
intersection(intersection(X1,X2),X3) = intersection(X2,intersection(X1,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_42]),c_0_43])]) ).
cnf(c_0_49,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(X2,intersection(X1,intersection(X2,X3)))),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,negated_conjecture,
intersection(esk5_0,intersection(esk3_0,esk4_0)) != intersection(esk3_0,intersection(esk4_0,esk5_0)),
inference(rw,[status(thm)],[c_0_46,c_0_19]) ).
cnf(c_0_51,plain,
intersection(X1,intersection(X2,X3)) = intersection(X3,intersection(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48]),c_0_48]) ).
cnf(c_0_52,plain,
intersection(X1,intersection(X2,intersection(X1,X3))) = intersection(X2,intersection(X1,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_49]),c_0_39])]) ).
cnf(c_0_53,negated_conjecture,
intersection(esk4_0,intersection(esk3_0,esk5_0)) != intersection(esk3_0,intersection(esk4_0,esk5_0)),
inference(rw,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,plain,
intersection(X1,intersection(X2,X3)) = intersection(X2,intersection(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_45]),c_0_48]),c_0_48]),c_0_52]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET143+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 04:57:58 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 2.40/0.75 % Version: 3.5.1
% 2.40/0.75 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.40/0.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.40/0.75 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.40/0.75 % Starting new_bool_3 with 300s (1) cores
% 2.40/0.75 % Starting new_bool_1 with 300s (1) cores
% 2.40/0.75 % Starting sh5l with 300s (1) cores
% 2.40/0.75 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1010939 completed with status 0
% 2.40/0.75 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 2.40/0.75 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.40/0.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.40/0.75 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.40/0.75 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.40/0.75 % No SInE strategy applied
% 2.40/0.75 % Search class: FGUSS-FFSF22-SFFFFFNN
% 2.40/0.75 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.40/0.75 % Starting SubtermCWHack with 136s (1) cores
% 2.40/0.75 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 2.40/0.75 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.40/0.75 % Starting new_bool_3 with 136s (1) cores
% 2.40/0.75 % Starting new_bool_1 with 136s (1) cores
% 2.40/0.75 % U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 1010946 completed with status 0
% 2.40/0.75 % Result found by U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 2.40/0.75 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.40/0.75 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.40/0.75 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.40/0.75 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.40/0.75 % No SInE strategy applied
% 2.40/0.75 % Search class: FGUSS-FFSF22-SFFFFFNN
% 2.40/0.75 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.40/0.75 % Starting SubtermCWHack with 136s (1) cores
% 2.40/0.75 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 2.40/0.75 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 2.40/0.75 % Preprocessing time : 0.001 s
% 2.40/0.75 % Presaturation interreduction done
% 2.40/0.75
% 2.40/0.75 % Proof found!
% 2.40/0.75 % SZS status Theorem
% 2.40/0.75 % SZS output start CNFRefutation
% See solution above
% 2.40/0.75 % Parsed axioms : 7
% 2.40/0.75 % Removed by relevancy pruning/SinE : 0
% 2.40/0.75 % Initial clauses : 16
% 2.40/0.75 % Removed in clause preprocessing : 2
% 2.40/0.75 % Initial clauses in saturation : 14
% 2.40/0.75 % Processed clauses : 2764
% 2.40/0.75 % ...of these trivial : 627
% 2.40/0.75 % ...subsumed : 1735
% 2.40/0.75 % ...remaining for further processing : 402
% 2.40/0.75 % Other redundant clauses eliminated : 2
% 2.40/0.75 % Clauses deleted for lack of memory : 0
% 2.40/0.75 % Backward-subsumed : 0
% 2.40/0.75 % Backward-rewritten : 234
% 2.40/0.75 % Generated clauses : 25536
% 2.40/0.75 % ...of the previous two non-redundant : 18263
% 2.40/0.75 % ...aggressively subsumed : 0
% 2.40/0.75 % Contextual simplify-reflections : 2
% 2.40/0.75 % Paramodulations : 25462
% 2.40/0.75 % Factorizations : 72
% 2.40/0.75 % NegExts : 0
% 2.40/0.75 % Equation resolutions : 2
% 2.40/0.75 % Disequality decompositions : 0
% 2.40/0.75 % Total rewrite steps : 21410
% 2.40/0.75 % ...of those cached : 19320
% 2.40/0.75 % Propositional unsat checks : 0
% 2.40/0.75 % Propositional check models : 0
% 2.40/0.75 % Propositional check unsatisfiable : 0
% 2.40/0.75 % Propositional clauses : 0
% 2.40/0.75 % Propositional clauses after purity: 0
% 2.40/0.75 % Propositional unsat core size : 0
% 2.40/0.75 % Propositional preprocessing time : 0.000
% 2.40/0.75 % Propositional encoding time : 0.000
% 2.40/0.75 % Propositional solver time : 0.000
% 2.40/0.75 % Success case prop preproc time : 0.000
% 2.40/0.75 % Success case prop encoding time : 0.000
% 2.40/0.75 % Success case prop solver time : 0.000
% 2.40/0.75 % Current number of processed clauses : 154
% 2.40/0.75 % Positive orientable unit clauses : 30
% 2.40/0.75 % Positive unorientable unit clauses: 4
% 2.40/0.75 % Negative unit clauses : 0
% 2.40/0.75 % Non-unit-clauses : 120
% 2.40/0.75 % Current number of unprocessed clauses: 15295
% 2.40/0.75 % ...number of literals in the above : 31834
% 2.40/0.75 % Current number of archived formulas : 0
% 2.40/0.75 % Current number of archived clauses : 246
% 2.40/0.75 % Clause-clause subsumption calls (NU) : 23038
% 2.40/0.75 % Rec. Clause-clause subsumption calls : 20202
% 2.40/0.75 % Non-unit clause-clause subsumptions : 1646
% 2.40/0.75 % Unit Clause-clause subsumption calls : 2290
% 2.40/0.75 % Rewrite failures with RHS unbound : 0
% 2.40/0.75 % BW rewrite match attempts : 3302
% 2.40/0.75 % BW rewrite match successes : 555
% 2.40/0.75 % Condensation attempts : 0
% 2.40/0.75 % Condensation successes : 0
% 2.40/0.75 % Termbank termtop insertions : 304815
% 2.40/0.75 % Search garbage collected termcells : 276
% 2.40/0.75
% 2.40/0.75 % -------------------------------------------------
% 2.40/0.75 % User time : 0.234 s
% 2.40/0.75 % System time : 0.019 s
% 2.40/0.75 % Total time : 0.254 s
% 2.40/0.75 % Maximum resident set size: 3632 pages
% 2.40/0.75
% 2.40/0.75 % -------------------------------------------------
% 2.40/0.75 % User time : 1.316 s
% 2.40/0.75 % System time : 0.091 s
% 2.40/0.75 % Total time : 1.407 s
% 2.40/0.75 % Maximum resident set size: 4608 pages
% 2.40/0.75 % E exiting
%------------------------------------------------------------------------------