%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET013-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 02:13:02 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 27 ( 6 unt; 4 nHn; 21 RR)
% Number of literals : 55 ( 0 equ; 27 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 59 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(subsets_axiom2,axiom,
( ~ member(member_of_1_not_of_2(X1,X2),X2)
| subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',subsets_axiom2) ).
cnf(member_of_both_is_member_of_intersection,axiom,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',member_of_both_is_member_of_intersection) ).
cnf(member_of_intersection_is_member_of_set1,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',member_of_intersection_is_member_of_set1) ).
cnf(subsets_axiom1,axiom,
( member(member_of_1_not_of_2(X1,X2),X1)
| subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',subsets_axiom1) ).
cnf(member_of_intersection_is_member_of_set2,axiom,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',member_of_intersection_is_member_of_set2) ).
cnf(subsets_are_set_equal_sets,axiom,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| equal_sets(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',subsets_are_set_equal_sets) ).
cnf(prove_commutativity,negated_conjecture,
~ equal_sets(intersection(as,bs),intersection(bs,as)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity) ).
cnf(c_0_7,plain,
( ~ member(member_of_1_not_of_2(X1,X2),X2)
| subset(X1,X2) ),
inference(fof_simplification,[status(thm)],[subsets_axiom2]) ).
cnf(c_0_8,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
inference(fof_simplification,[status(thm)],[member_of_both_is_member_of_intersection]) ).
cnf(c_0_9,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
inference(fof_simplification,[status(thm)],[member_of_intersection_is_member_of_set1]) ).
cnf(c_0_10,plain,
( ~ member(member_of_1_not_of_2(X1,X2),X2)
| subset(X1,X2) ),
c_0_7 ).
cnf(c_0_11,plain,
( ~ member(X1,X3)
| ~ member(X1,X2)
| member(X1,intersection(X2,X3)) ),
c_0_8 ).
cnf(c_0_12,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X2) ),
c_0_9 ).
cnf(c_0_13,axiom,
( member(member_of_1_not_of_2(X1,X2),X1)
| subset(X1,X2) ),
subsets_axiom1 ).
cnf(c_0_14,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[member_of_intersection_is_member_of_set2]) ).
cnf(c_0_15,plain,
( ~ member(member_of_1_not_of_2(X1,intersection(X2,X3)),X2)
| ~ member(member_of_1_not_of_2(X1,intersection(X2,X3)),X3)
| subset(X1,intersection(X2,X3)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
( member(member_of_1_not_of_2(intersection(X1,X2),X3),X1)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( ~ member(X1,intersection(X2,X3))
| member(X1,X3) ),
c_0_14 ).
cnf(c_0_18,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| equal_sets(X2,X1) ),
inference(fof_simplification,[status(thm)],[subsets_are_set_equal_sets]) ).
cnf(c_0_19,plain,
( ~ member(member_of_1_not_of_2(intersection(X1,X2),intersection(X3,X1)),X3)
| subset(intersection(X1,X2),intersection(X3,X1)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( member(member_of_1_not_of_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
cnf(c_0_21,negated_conjecture,
~ equal_sets(intersection(as,bs),intersection(bs,as)),
inference(fof_simplification,[status(thm)],[prove_commutativity]) ).
cnf(c_0_22,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| equal_sets(X2,X1) ),
c_0_18 ).
cnf(c_0_23,plain,
subset(intersection(X1,X2),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
~ equal_sets(intersection(as,bs),intersection(bs,as)),
c_0_21 ).
cnf(c_0_25,plain,
equal_sets(intersection(X1,X2),intersection(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_23])]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET013-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 04:43:28 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.45 % Version: 3.5.1
% 0.14/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.45 % Starting sh5l with 300s (1) cores
% 0.14/0.45 % sh5l with pid 982325 completed with status 0
% 0.14/0.45 % Result found by sh5l
% 0.14/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.45 % Starting sh5l with 300s (1) cores
% 0.14/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/0.45 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/0.45 % Search class: FGUNF-FFSF22-SFFFFFNN
% 0.14/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.45 % SubtermCWHack with pid 982332 completed with status 0
% 0.14/0.45 % Result found by SubtermCWHack
% 0.14/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.45 % Starting sh5l with 300s (1) cores
% 0.14/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/0.45 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/0.45 % Search class: FGUNF-FFSF22-SFFFFFNN
% 0.14/0.45 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.45 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.45 % Preprocessing time : 0.001 s
% 0.14/0.45
% 0.14/0.45 % Proof found!
% 0.14/0.45 % SZS status Unsatisfiable
% 0.14/0.45 % SZS output start CNFRefutation
% See solution above
% 0.14/0.45 % Parsed axioms : 22
% 0.14/0.45 % Removed by relevancy pruning/SinE : 6
% 0.14/0.45 % Initial clauses : 16
% 0.14/0.45 % Removed in clause preprocessing : 0
% 0.14/0.45 % Initial clauses in saturation : 16
% 0.14/0.45 % Processed clauses : 311
% 0.14/0.45 % ...of these trivial : 4
% 0.14/0.45 % ...subsumed : 134
% 0.14/0.45 % ...remaining for further processing : 173
% 0.14/0.45 % Other redundant clauses eliminated : 0
% 0.14/0.45 % Clauses deleted for lack of memory : 0
% 0.14/0.45 % Backward-subsumed : 0
% 0.14/0.45 % Backward-rewritten : 1
% 0.14/0.45 % Generated clauses : 1387
% 0.14/0.45 % ...of the previous two non-redundant : 1268
% 0.14/0.45 % ...aggressively subsumed : 0
% 0.14/0.45 % Contextual simplify-reflections : 0
% 0.14/0.45 % Paramodulations : 1381
% 0.14/0.45 % Factorizations : 6
% 0.14/0.45 % NegExts : 0
% 0.14/0.45 % Equation resolutions : 0
% 0.14/0.45 % Disequality decompositions : 0
% 0.14/0.45 % Total rewrite steps : 67
% 0.14/0.45 % ...of those cached : 42
% 0.14/0.45 % Propositional unsat checks : 0
% 0.14/0.45 % Propositional check models : 0
% 0.14/0.45 % Propositional check unsatisfiable : 0
% 0.14/0.45 % Propositional clauses : 0
% 0.14/0.45 % Propositional clauses after purity: 0
% 0.14/0.45 % Propositional unsat core size : 0
% 0.14/0.45 % Propositional preprocessing time : 0.000
% 0.14/0.45 % Propositional encoding time : 0.000
% 0.14/0.45 % Propositional solver time : 0.000
% 0.14/0.45 % Success case prop preproc time : 0.000
% 0.14/0.45 % Success case prop encoding time : 0.000
% 0.14/0.45 % Success case prop solver time : 0.000
% 0.14/0.45 % Current number of processed clauses : 172
% 0.14/0.45 % Positive orientable unit clauses : 69
% 0.14/0.45 % Positive unorientable unit clauses: 0
% 0.14/0.45 % Negative unit clauses : 0
% 0.14/0.45 % Non-unit-clauses : 103
% 0.14/0.45 % Current number of unprocessed clauses: 973
% 0.14/0.45 % ...number of literals in the above : 2263
% 0.14/0.45 % Current number of archived formulas : 0
% 0.14/0.45 % Current number of archived clauses : 1
% 0.14/0.45 % Clause-clause subsumption calls (NU) : 1584
% 0.14/0.45 % Rec. Clause-clause subsumption calls : 1567
% 0.14/0.45 % Non-unit clause-clause subsumptions : 134
% 0.14/0.45 % Unit Clause-clause subsumption calls : 149
% 0.14/0.45 % Rewrite failures with RHS unbound : 0
% 0.14/0.45 % BW rewrite match attempts : 117
% 0.14/0.45 % BW rewrite match successes : 1
% 0.14/0.45 % Condensation attempts : 0
% 0.14/0.45 % Condensation successes : 0
% 0.14/0.45 % Termbank termtop insertions : 18626
% 0.14/0.45 % Search garbage collected termcells : 55
% 0.14/0.45
% 0.14/0.45 % -------------------------------------------------
% 0.14/0.45 % User time : 0.024 s
% 0.14/0.45 % System time : 0.003 s
% 0.14/0.45 % Total time : 0.027 s
% 0.14/0.45 % Maximum resident set size: 3648 pages
% 0.14/0.45
% 0.14/0.45 % -------------------------------------------------
% 0.14/0.45 % User time : 0.027 s
% 0.14/0.45 % System time : 0.006 s
% 0.14/0.45 % Total time : 0.033 s
% 0.14/0.45 % Maximum resident set size: 4608 pages
% 0.14/0.45 % E exiting
%------------------------------------------------------------------------------