%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET015-2 : 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 : n001.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 02:13:04 PM UTC 2026
% Result : Unsatisfiable 0.57s 0.62s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of clauses : 69 ( 14 unt; 9 nHn; 59 RR)
% Number of literals : 141 ( 0 equ; 66 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 98 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(symmetry_for_set_equal,axiom,
( ~ equal_sets(X1,X2)
| equal_sets(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',symmetry_for_set_equal) ).
cnf(transitivity_for_set_equal,axiom,
( ~ equal_sets(X2,X3)
| ~ equal_sets(X1,X2)
| equal_sets(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',transitivity_for_set_equal) ).
cnf(b_union_a_is_d,hypothesis,
equal_sets(union(bs,as),ds),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_union_a_is_d) ).
cnf(membership_in_subsets,axiom,
( ~ subset(X2,X3)
| ~ member(X1,X2)
| member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',membership_in_subsets) ).
cnf(set_equal_sets_are_subsets2,axiom,
( ~ equal_sets(X1,X2)
| subset(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',set_equal_sets_are_subsets2) ).
cnf(a_union_b_is_c,hypothesis,
equal_sets(union(as,bs),cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_union_b_is_c) ).
cnf(member_of_set2_is_member_of_union,axiom,
( ~ member(X1,X2)
| member(X1,union(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',member_of_set2_is_member_of_union) ).
cnf(member_of_union_is_member_of_one_set,axiom,
( ~ member(X1,union(X2,X3))
| member(X1,X3)
| member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',member_of_union_is_member_of_one_set) ).
cnf(member_of_set1_is_member_of_union,axiom,
( ~ member(X1,X2)
| member(X1,union(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',member_of_set1_is_member_of_union) ).
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(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(prove_c_equals_d,negated_conjecture,
~ equal_sets(cs,ds),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
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(c_0_13,plain,
( ~ equal_sets(X1,X2)
| equal_sets(X2,X1) ),
inference(fof_simplification,[status(thm)],[symmetry_for_set_equal]) ).
cnf(c_0_14,plain,
( ~ equal_sets(X2,X3)
| ~ equal_sets(X1,X2)
| equal_sets(X1,X3) ),
inference(fof_simplification,[status(thm)],[transitivity_for_set_equal]) ).
cnf(c_0_15,plain,
( ~ equal_sets(X1,X2)
| equal_sets(X2,X1) ),
c_0_13 ).
cnf(c_0_16,hypothesis,
equal_sets(union(bs,as),ds),
b_union_a_is_d ).
cnf(c_0_17,plain,
( ~ subset(X2,X3)
| ~ member(X1,X2)
| member(X1,X3) ),
inference(fof_simplification,[status(thm)],[membership_in_subsets]) ).
cnf(c_0_18,plain,
( ~ equal_sets(X1,X2)
| subset(X2,X1) ),
inference(fof_simplification,[status(thm)],[set_equal_sets_are_subsets2]) ).
cnf(c_0_19,plain,
( ~ equal_sets(X2,X3)
| ~ equal_sets(X1,X2)
| equal_sets(X1,X3) ),
c_0_14 ).
cnf(c_0_20,hypothesis,
equal_sets(ds,union(bs,as)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( ~ subset(X2,X3)
| ~ member(X1,X2)
| member(X1,X3) ),
c_0_17 ).
cnf(c_0_22,plain,
( ~ equal_sets(X1,X2)
| subset(X2,X1) ),
c_0_18 ).
cnf(c_0_23,hypothesis,
equal_sets(union(as,bs),cs),
a_union_b_is_c ).
cnf(c_0_24,hypothesis,
( ~ equal_sets(X1,ds)
| equal_sets(X1,union(bs,as)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( ~ member(X1,X3)
| ~ equal_sets(X2,X3)
| member(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,hypothesis,
equal_sets(cs,union(as,bs)),
inference(spm,[status(thm)],[c_0_15,c_0_23]) ).
cnf(c_0_27,plain,
( ~ member(X1,X2)
| member(X1,union(X3,X2)) ),
inference(fof_simplification,[status(thm)],[member_of_set2_is_member_of_union]) ).
cnf(c_0_28,plain,
( ~ member(X1,union(X2,X3))
| member(X1,X3)
| member(X1,X2) ),
inference(fof_simplification,[status(thm)],[member_of_union_is_member_of_one_set]) ).
cnf(c_0_29,plain,
( ~ member(X1,X2)
| member(X1,union(X2,X3)) ),
inference(fof_simplification,[status(thm)],[member_of_set1_is_member_of_union]) ).
cnf(c_0_30,hypothesis,
( ~ equal_sets(X1,union(as,bs))
| equal_sets(X1,cs) ),
inference(spm,[status(thm)],[c_0_19,c_0_23]) ).
cnf(c_0_31,hypothesis,
( ~ equal_sets(X1,ds)
| equal_sets(union(bs,as),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_24]) ).
cnf(c_0_32,plain,
( ~ member(member_of_1_not_of_2(X1,X2),X2)
| subset(X1,X2) ),
inference(fof_simplification,[status(thm)],[subsets_axiom2]) ).
cnf(c_0_33,hypothesis,
( ~ member(X1,union(as,bs))
| member(X1,cs) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,plain,
( ~ member(X1,X2)
| member(X1,union(X3,X2)) ),
c_0_27 ).
cnf(c_0_35,plain,
( ~ member(X1,union(X2,X3))
| member(X1,X3)
| member(X1,X2) ),
c_0_28 ).
cnf(c_0_36,hypothesis,
( ~ member(X1,ds)
| member(X1,union(bs,as)) ),
inference(spm,[status(thm)],[c_0_25,c_0_16]) ).
cnf(c_0_37,plain,
( ~ member(X1,X2)
| member(X1,union(X2,X3)) ),
c_0_29 ).
cnf(c_0_38,hypothesis,
( ~ equal_sets(union(as,bs),ds)
| equal_sets(union(bs,as),cs) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_39,hypothesis,
( ~ equal_sets(X1,cs)
| equal_sets(X1,union(as,bs)) ),
inference(spm,[status(thm)],[c_0_19,c_0_26]) ).
cnf(c_0_40,plain,
( ~ member(member_of_1_not_of_2(X1,X2),X2)
| subset(X1,X2) ),
c_0_32 ).
cnf(c_0_41,hypothesis,
( ~ member(X1,bs)
| member(X1,cs) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_42,hypothesis,
( ~ member(X1,ds)
| member(X1,bs)
| member(X1,as) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,axiom,
( member(member_of_1_not_of_2(X1,X2),X1)
| subset(X1,X2) ),
subsets_axiom1 ).
cnf(c_0_44,hypothesis,
( ~ member(X1,as)
| member(X1,cs) ),
inference(spm,[status(thm)],[c_0_33,c_0_37]) ).
cnf(c_0_45,hypothesis,
( ~ equal_sets(union(as,bs),ds)
| equal_sets(cs,union(bs,as)) ),
inference(spm,[status(thm)],[c_0_15,c_0_38]) ).
cnf(c_0_46,hypothesis,
( ~ equal_sets(X1,cs)
| equal_sets(union(as,bs),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_39]) ).
cnf(c_0_47,negated_conjecture,
~ equal_sets(cs,ds),
inference(fof_simplification,[status(thm)],[prove_c_equals_d]) ).
cnf(c_0_48,hypothesis,
( ~ member(X1,union(bs,as))
| member(X1,ds) ),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_49,hypothesis,
( ~ member(X1,cs)
| member(X1,union(as,bs)) ),
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_50,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| equal_sets(X2,X1) ),
inference(fof_simplification,[status(thm)],[subsets_are_set_equal_sets]) ).
cnf(c_0_51,hypothesis,
( ~ member(member_of_1_not_of_2(X1,cs),bs)
| subset(X1,cs) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_52,hypothesis,
( member(member_of_1_not_of_2(ds,X1),as)
| member(member_of_1_not_of_2(ds,X1),bs)
| subset(ds,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_53,hypothesis,
( ~ member(member_of_1_not_of_2(X1,cs),as)
| subset(X1,cs) ),
inference(spm,[status(thm)],[c_0_40,c_0_44]) ).
cnf(c_0_54,hypothesis,
( ~ equal_sets(X1,union(bs,as))
| equal_sets(X1,ds) ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_55,hypothesis,
( ~ equal_sets(ds,cs)
| equal_sets(cs,union(bs,as)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_56,negated_conjecture,
~ equal_sets(cs,ds),
c_0_47 ).
cnf(c_0_57,hypothesis,
( ~ member(X1,bs)
| member(X1,ds) ),
inference(spm,[status(thm)],[c_0_48,c_0_37]) ).
cnf(c_0_58,hypothesis,
( ~ member(X1,cs)
| member(X1,as)
| member(X1,bs) ),
inference(spm,[status(thm)],[c_0_35,c_0_49]) ).
cnf(c_0_59,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| equal_sets(X2,X1) ),
c_0_50 ).
cnf(c_0_60,hypothesis,
subset(ds,cs),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
cnf(c_0_61,hypothesis,
~ equal_sets(ds,cs),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
cnf(c_0_62,hypothesis,
( ~ member(X1,as)
| member(X1,ds) ),
inference(spm,[status(thm)],[c_0_48,c_0_34]) ).
cnf(c_0_63,hypothesis,
( ~ member(member_of_1_not_of_2(X1,ds),bs)
| subset(X1,ds) ),
inference(spm,[status(thm)],[c_0_40,c_0_57]) ).
cnf(c_0_64,hypothesis,
( member(member_of_1_not_of_2(cs,X1),bs)
| member(member_of_1_not_of_2(cs,X1),as)
| subset(cs,X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_43]) ).
cnf(c_0_65,hypothesis,
~ subset(cs,ds),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).
cnf(c_0_66,hypothesis,
( ~ member(member_of_1_not_of_2(X1,ds),as)
| subset(X1,ds) ),
inference(spm,[status(thm)],[c_0_40,c_0_62]) ).
cnf(c_0_67,hypothesis,
member(member_of_1_not_of_2(cs,ds),as),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]) ).
cnf(c_0_68,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_65]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET015-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n001.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
% 0.10/0.38 % DateTime : Mon Sep 21 04:47:29 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.44 Running first-order theorem proving
% 0.15/0.44 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
% 0.57/0.62 % Version: 3.5.1
% 0.57/0.62 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.57/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.57/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.57/0.62 % Starting new_bool_1 with 300s (1) cores
% 0.57/0.62 % Starting sh5l with 300s (1) cores
% 0.57/0.62 % sh5l with pid 2213002 completed with status 0
% 0.57/0.62 % Result found by sh5l
% 0.57/0.62 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.57/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.57/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.57/0.62 % Starting new_bool_1 with 300s (1) cores
% 0.57/0.62 % Starting sh5l with 300s (1) cores
% 0.57/0.62 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.57/0.62 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.57/0.62 % Search class: FGUNF-FFSF22-SFFFFFNN
% 0.57/0.62 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.57/0.62 % Starting SubtermCWHack with 31s (1) cores
% 0.57/0.62 % SubtermCWHack with pid 2213008 completed with status 0
% 0.57/0.62 % Result found by SubtermCWHack
% 0.57/0.62 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.57/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.57/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.57/0.62 % Starting new_bool_1 with 300s (1) cores
% 0.57/0.62 % Starting sh5l with 300s (1) cores
% 0.57/0.62 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.57/0.62 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.57/0.62 % Search class: FGUNF-FFSF22-SFFFFFNN
% 0.57/0.62 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.57/0.62 % Starting SubtermCWHack with 31s (1) cores
% 0.57/0.62 % Preprocessing time : 0.001 s
% 0.57/0.62
% 0.57/0.62 % Proof found!
% 0.57/0.62 % SZS status Unsatisfiable
% 0.57/0.62 % SZS output start CNFRefutation
% See solution above
% 0.57/0.62 % Parsed axioms : 24
% 0.57/0.62 % Removed by relevancy pruning/SinE : 6
% 0.57/0.62 % Initial clauses : 18
% 0.57/0.62 % Removed in clause preprocessing : 0
% 0.57/0.62 % Initial clauses in saturation : 18
% 0.57/0.62 % Processed clauses : 771
% 0.57/0.62 % ...of these trivial : 5
% 0.57/0.62 % ...subsumed : 260
% 0.57/0.62 % ...remaining for further processing : 506
% 0.57/0.62 % Other redundant clauses eliminated : 0
% 0.57/0.62 % Clauses deleted for lack of memory : 0
% 0.57/0.62 % Backward-subsumed : 5
% 0.57/0.62 % Backward-rewritten : 3
% 0.57/0.62 % Generated clauses : 3356
% 0.57/0.62 % ...of the previous two non-redundant : 3125
% 0.57/0.62 % ...aggressively subsumed : 0
% 0.57/0.62 % Contextual simplify-reflections : 1
% 0.57/0.62 % Paramodulations : 3350
% 0.57/0.62 % Factorizations : 6
% 0.57/0.62 % NegExts : 0
% 0.57/0.62 % Equation resolutions : 0
% 0.57/0.62 % Disequality decompositions : 0
% 0.57/0.62 % Total rewrite steps : 209
% 0.57/0.62 % ...of those cached : 24
% 0.57/0.62 % Propositional unsat checks : 0
% 0.57/0.62 % Propositional check models : 0
% 0.57/0.62 % Propositional check unsatisfiable : 0
% 0.57/0.62 % Propositional clauses : 0
% 0.57/0.62 % Propositional clauses after purity: 0
% 0.57/0.62 % Propositional unsat core size : 0
% 0.57/0.62 % Propositional preprocessing time : 0.000
% 0.57/0.62 % Propositional encoding time : 0.000
% 0.57/0.62 % Propositional solver time : 0.000
% 0.57/0.62 % Success case prop preproc time : 0.000
% 0.57/0.62 % Success case prop encoding time : 0.000
% 0.57/0.62 % Success case prop solver time : 0.000
% 0.57/0.62 % Current number of processed clauses : 498
% 0.57/0.62 % Positive orientable unit clauses : 257
% 0.57/0.62 % Positive unorientable unit clauses: 0
% 0.57/0.62 % Negative unit clauses : 3
% 0.57/0.62 % Non-unit-clauses : 238
% 0.57/0.62 % Current number of unprocessed clauses: 2305
% 0.57/0.62 % ...number of literals in the above : 5260
% 0.57/0.62 % Current number of archived formulas : 0
% 0.57/0.62 % Current number of archived clauses : 8
% 0.57/0.62 % Clause-clause subsumption calls (NU) : 4023
% 0.57/0.62 % Rec. Clause-clause subsumption calls : 3715
% 0.57/0.62 % Non-unit clause-clause subsumptions : 256
% 0.57/0.62 % Unit Clause-clause subsumption calls : 847
% 0.57/0.62 % Rewrite failures with RHS unbound : 0
% 0.57/0.62 % BW rewrite match attempts : 835
% 0.57/0.62 % BW rewrite match successes : 3
% 0.57/0.62 % Condensation attempts : 0
% 0.57/0.62 % Condensation successes : 0
% 0.57/0.62 % Termbank termtop insertions : 52863
% 0.57/0.62 % Search garbage collected termcells : 55
% 0.57/0.62
% 0.57/0.62 % -------------------------------------------------
% 0.57/0.62 % User time : 0.092 s
% 0.57/0.62 % System time : 0.011 s
% 0.57/0.62 % Total time : 0.102 s
% 0.57/0.62 % Maximum resident set size: 3648 pages
% 0.57/0.62
% 0.57/0.62 % -------------------------------------------------
% 0.57/0.62 % User time : 0.095 s
% 0.57/0.62 % System time : 0.017 s
% 0.57/0.62 % Total time : 0.111 s
% 0.57/0.62 % Maximum resident set size: 4864 pages
% 0.57/0.62 % E exiting
%------------------------------------------------------------------------------