%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET847-2 : TPTP v9.3.1. Released v3.2.0.
% 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 02:15:34 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 39 ( 14 unt; 5 nHn; 28 RR)
% Number of literals : 70 ( 16 equ; 39 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 86 ( 17 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_Osubset__antisym_0,axiom,
( ~ c_lessequals(X2,X1,tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3))
| X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_in(X1,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_Set_Oempty__subsetI_0,axiom,
c_lessequals(c_emptyset,X1,tc_set(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
cnf(cls_Set_OsubsetI_0,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
cnf(cls_Zorn_Osucc__not__equals_0,axiom,
( c_Zorn_Osucc(X2,X1,X3) != X1
| ~ c_in(X1,c_minus(c_Zorn_Ochain(X2,X3),c_Zorn_Omaxchain(X2,X3),tc_set(tc_set(tc_set(X3)))),tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Osucc__not__equals_0) ).
cnf(cls_Set_ODiffI_0,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_minus(X2,X4,tc_set(X3)),X3)
| c_in(X1,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).
cnf(cls_Set_OemptyE_0,axiom,
~ c_in(X1,c_emptyset,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
cnf(cls_Zorn_OTFin__chain__lemma4_0,axiom,
( ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_in(X1,c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__chain__lemma4_0) ).
cnf(cls_Zorn_OTFin__UnionI_0,axiom,
( ~ c_lessequals(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(tc_set(X3))))
| c_in(c_Union(X1,tc_set(X3)),c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__UnionI_0) ).
cnf(cls_Zorn_Oequal__succ__Union_1,axiom,
( ~ c_in(c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)) = c_Zorn_Osucc(X1,c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Oequal__succ__Union_1) ).
cnf(cls_Set_Osubset__refl_0,axiom,
c_lessequals(X1,X1,tc_set(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
cnf(c_0_11,plain,
( ~ c_lessequals(X2,X1,tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3))
| X2 = X1 ),
inference(fof_simplification,[status(thm)],[cls_Set_Osubset__antisym_0]) ).
cnf(c_0_12,negated_conjecture,
~ c_in(X1,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_13,plain,
( ~ c_lessequals(X2,X1,tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3))
| X2 = X1 ),
c_0_11 ).
cnf(c_0_14,axiom,
c_lessequals(c_emptyset,X1,tc_set(X2)),
cls_Set_Oempty__subsetI_0 ).
cnf(c_0_15,negated_conjecture,
~ c_in(X1,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
c_0_12 ).
cnf(c_0_16,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3) ),
cls_Set_OsubsetI_0 ).
cnf(c_0_17,plain,
( c_Zorn_Osucc(X2,X1,X3) != X1
| ~ c_in(X1,c_minus(c_Zorn_Ochain(X2,X3),c_Zorn_Omaxchain(X2,X3),tc_set(tc_set(tc_set(X3)))),tc_set(tc_set(X3))) ),
inference(fof_simplification,[status(thm)],[cls_Zorn_Osucc__not__equals_0]) ).
cnf(c_0_18,plain,
( ~ c_lessequals(X1,c_emptyset,tc_set(X2))
| X1 = c_emptyset ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
c_lessequals(c_Zorn_Omaxchain(v_S,t_a),X1,tc_set(tc_set(tc_set(t_a)))),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( c_Zorn_Osucc(X2,X1,X3) != X1
| ~ c_in(X1,c_minus(c_Zorn_Ochain(X2,X3),c_Zorn_Omaxchain(X2,X3),tc_set(tc_set(tc_set(X3)))),tc_set(tc_set(X3))) ),
c_0_17 ).
cnf(c_0_21,negated_conjecture,
c_Zorn_Omaxchain(v_S,t_a) = c_emptyset,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_minus(X2,X4,tc_set(X3)),X3)
| c_in(X1,X4,X3) ),
inference(fof_simplification,[status(thm)],[cls_Set_ODiffI_0]) ).
cnf(c_0_23,plain,
~ c_in(X1,c_emptyset,X2),
inference(fof_simplification,[status(thm)],[cls_Set_OemptyE_0]) ).
cnf(c_0_24,negated_conjecture,
( ~ c_in(X1,c_minus(c_Zorn_Ochain(v_S,t_a),c_emptyset,tc_set(tc_set(tc_set(t_a)))),tc_set(tc_set(t_a)))
| c_Zorn_Osucc(v_S,X1,t_a) != X1 ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_minus(X2,X4,tc_set(X3)),X3)
| c_in(X1,X4,X3) ),
c_0_22 ).
cnf(c_0_26,plain,
~ c_in(X1,c_emptyset,X2),
c_0_23 ).
cnf(c_0_27,plain,
( ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_in(X1,c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3))) ),
inference(fof_simplification,[status(thm)],[cls_Zorn_OTFin__chain__lemma4_0]) ).
cnf(c_0_28,negated_conjecture,
( ~ c_in(X1,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_Zorn_Osucc(v_S,X1,t_a) != X1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_29,plain,
( ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_in(X1,c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3))) ),
c_0_27 ).
cnf(c_0_30,plain,
( ~ c_lessequals(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(tc_set(X3))))
| c_in(c_Union(X1,tc_set(X3)),c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))) ),
inference(fof_simplification,[status(thm)],[cls_Zorn_OTFin__UnionI_0]) ).
cnf(c_0_31,plain,
( ~ c_in(c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)) = c_Zorn_Osucc(X1,c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),X2) ),
inference(fof_simplification,[status(thm)],[cls_Zorn_Oequal__succ__Union_1]) ).
cnf(c_0_32,negated_conjecture,
( ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_Zorn_Osucc(v_S,X1,t_a) != X1 ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
( ~ c_lessequals(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(tc_set(X3))))
| c_in(c_Union(X1,tc_set(X3)),c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))) ),
c_0_30 ).
cnf(c_0_34,plain,
( ~ c_in(c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)) = c_Zorn_Osucc(X1,c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),X2) ),
c_0_31 ).
cnf(c_0_35,axiom,
c_lessequals(X1,X1,tc_set(X2)),
cls_Set_Osubset__refl_0 ).
cnf(c_0_36,negated_conjecture,
( ~ c_lessequals(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a))))
| c_Zorn_Osucc(v_S,c_Union(X1,tc_set(t_a)),t_a) != c_Union(X1,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
c_Zorn_Osucc(X1,c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),X2) = c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_33]),c_0_35])]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET847-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.34 % Computer : n018.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Mon Sep 21 05:43:58 UTC 2026
% 0.10/0.34 % CPUTime :
% 0.10/0.34 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.39 Running first-order theorem proving
% 0.15/0.39 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
% 0.15/0.41 % Version: 3.5.1
% 0.15/0.41 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.41 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.41 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.41 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.41 % Starting sh5l with 300s (1) cores
% 0.15/0.41 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1089513 completed with status 0
% 0.15/0.41 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.15/0.41 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.41 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.41 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.41 % No SInE strategy applied
% 0.15/0.41 % Search class: FGHSS-FFSF32-MFFFFFNN
% 0.15/0.41 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.41 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.41 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.15/0.41 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.15/0.41 % Starting new_bool_3 with 136s (1) cores
% 0.15/0.41 % Starting new_bool_1 with 136s (1) cores
% 0.15/0.41 % SubtermCWHack with pid 1089517 completed with status 0
% 0.15/0.41 % Result found by SubtermCWHack
% 0.15/0.41 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.41 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.41 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.41 % No SInE strategy applied
% 0.15/0.41 % Search class: FGHSS-FFSF32-MFFFFFNN
% 0.15/0.41 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.41 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.41 % Preprocessing time : 0.001 s
% 0.15/0.41
% 0.15/0.41 % Proof found!
% 0.15/0.41 % SZS status Unsatisfiable
% 0.15/0.41 % SZS output start CNFRefutation
% See solution above
% 0.15/0.41 % Parsed axioms : 11
% 0.15/0.41 % Removed by relevancy pruning/SinE : 0
% 0.15/0.41 % Initial clauses : 11
% 0.15/0.41 % Removed in clause preprocessing : 0
% 0.15/0.41 % Initial clauses in saturation : 11
% 0.15/0.41 % Processed clauses : 23
% 0.15/0.41 % ...of these trivial : 0
% 0.15/0.41 % ...subsumed : 2
% 0.15/0.41 % ...remaining for further processing : 21
% 0.15/0.41 % Other redundant clauses eliminated : 0
% 0.15/0.41 % Clauses deleted for lack of memory : 0
% 0.15/0.41 % Backward-subsumed : 0
% 0.15/0.41 % Backward-rewritten : 3
% 0.15/0.41 % Generated clauses : 18
% 0.15/0.41 % ...of the previous two non-redundant : 17
% 0.15/0.41 % ...aggressively subsumed : 0
% 0.15/0.41 % Contextual simplify-reflections : 0
% 0.15/0.41 % Paramodulations : 18
% 0.15/0.41 % Factorizations : 0
% 0.15/0.41 % NegExts : 0
% 0.15/0.41 % Equation resolutions : 0
% 0.15/0.41 % Disequality decompositions : 0
% 0.15/0.41 % Total rewrite steps : 7
% 0.15/0.41 % ...of those cached : 1
% 0.15/0.41 % Propositional unsat checks : 0
% 0.15/0.41 % Propositional check models : 0
% 0.15/0.41 % Propositional check unsatisfiable : 0
% 0.15/0.41 % Propositional clauses : 0
% 0.15/0.41 % Propositional clauses after purity: 0
% 0.15/0.41 % Propositional unsat core size : 0
% 0.15/0.41 % Propositional preprocessing time : 0.000
% 0.15/0.41 % Propositional encoding time : 0.000
% 0.15/0.41 % Propositional solver time : 0.000
% 0.15/0.41 % Success case prop preproc time : 0.000
% 0.15/0.41 % Success case prop encoding time : 0.000
% 0.15/0.41 % Success case prop solver time : 0.000
% 0.15/0.41 % Current number of processed clauses : 18
% 0.15/0.41 % Positive orientable unit clauses : 4
% 0.15/0.41 % Positive unorientable unit clauses: 0
% 0.15/0.41 % Negative unit clauses : 1
% 0.15/0.41 % Non-unit-clauses : 13
% 0.15/0.41 % Current number of unprocessed clauses: 4
% 0.15/0.41 % ...number of literals in the above : 8
% 0.15/0.41 % Current number of archived formulas : 0
% 0.15/0.41 % Current number of archived clauses : 3
% 0.15/0.41 % Clause-clause subsumption calls (NU) : 3
% 0.15/0.41 % Rec. Clause-clause subsumption calls : 3
% 0.15/0.41 % Non-unit clause-clause subsumptions : 1
% 0.15/0.41 % Unit Clause-clause subsumption calls : 0
% 0.15/0.41 % Rewrite failures with RHS unbound : 0
% 0.15/0.41 % BW rewrite match attempts : 3
% 0.15/0.41 % BW rewrite match successes : 2
% 0.15/0.41 % Condensation attempts : 0
% 0.15/0.41 % Condensation successes : 0
% 0.15/0.41 % Termbank termtop insertions : 921
% 0.15/0.41 % Search garbage collected termcells : 26
% 0.15/0.41
% 0.15/0.41 % -------------------------------------------------
% 0.15/0.41 % User time : 0.006 s
% 0.15/0.41 % System time : 0.002 s
% 0.15/0.41 % Total time : 0.007 s
% 0.15/0.41 % Maximum resident set size: 3640 pages
% 0.15/0.41
% 0.15/0.41 % -------------------------------------------------
% 0.15/0.41 % User time : 0.018 s
% 0.15/0.41 % System time : 0.013 s
% 0.15/0.41 % Total time : 0.031 s
% 0.15/0.41 % Maximum resident set size: 4864 pages
% 0.15/0.41 % E exiting
%------------------------------------------------------------------------------