%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET843-2 : 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 : n019.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 02:15:33 PM UTC 2026
% Result : Unsatisfiable 0.15s 5.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 42 ( 12 unt; 4 nHn; 37 RR)
% Number of literals : 88 ( 28 equ; 47 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 79 ( 4 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_Zorn_OAbrial__axiom1_0,axiom,
c_lessequals(X1,c_Zorn_Osucc(X2,X1,X3),tc_set(tc_set(X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
cnf(cls_Set_OUnion__upper_0,axiom,
( ~ c_in(X1,X2,tc_set(X3))
| c_lessequals(X1,c_Union(X2,X3),tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__upper_0) ).
cnf(cls_Zorn_Oeq__succ__upper_0,axiom,
( X1 != c_Zorn_Osucc(X2,X1,X3)
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Oeq__succ__upper_0) ).
cnf(cls_Zorn_OTFin_OsuccI_0,axiom,
( ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_in(c_Zorn_Osucc(X2,X1,X3),c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin_OsuccI_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_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_conjecture_2,negated_conjecture,
( v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
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(cls_conjecture_1,negated_conjecture,
( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(c_0_10,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_11,plain,
( ~ c_lessequals(X2,X1,tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3))
| X2 = X1 ),
c_0_10 ).
cnf(c_0_12,axiom,
c_lessequals(X1,c_Zorn_Osucc(X2,X1,X3),tc_set(tc_set(X3))),
cls_Zorn_OAbrial__axiom1_0 ).
cnf(c_0_13,plain,
( ~ c_in(X1,X2,tc_set(X3))
| c_lessequals(X1,c_Union(X2,X3),tc_set(X3)) ),
inference(fof_simplification,[status(thm)],[cls_Set_OUnion__upper_0]) ).
cnf(c_0_14,plain,
( X1 != c_Zorn_Osucc(X2,X1,X3)
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3))) ),
inference(fof_simplification,[status(thm)],[cls_Zorn_Oeq__succ__upper_0]) ).
cnf(c_0_15,plain,
( ~ c_lessequals(c_Zorn_Osucc(X1,X2,X3),X2,tc_set(tc_set(X3)))
| c_Zorn_Osucc(X1,X2,X3) = X2 ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( ~ c_in(X1,X2,tc_set(X3))
| c_lessequals(X1,c_Union(X2,X3),tc_set(X3)) ),
c_0_13 ).
cnf(c_0_17,plain,
( ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_in(c_Zorn_Osucc(X2,X1,X3),c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))) ),
inference(fof_simplification,[status(thm)],[cls_Zorn_OTFin_OsuccI_0]) ).
cnf(c_0_18,plain,
( X1 != c_Zorn_Osucc(X2,X1,X3)
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3))) ),
c_0_14 ).
cnf(c_0_19,negated_conjecture,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
cls_conjecture_0 ).
cnf(c_0_20,plain,
( ~ c_in(c_Zorn_Osucc(X1,c_Union(X2,tc_set(X3)),X3),X2,tc_set(tc_set(X3)))
| c_Zorn_Osucc(X1,c_Union(X2,tc_set(X3)),X3) = c_Union(X2,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_in(c_Zorn_Osucc(X2,X1,X3),c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))) ),
c_0_17 ).
cnf(c_0_22,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_23,negated_conjecture,
( v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
cls_conjecture_2 ).
cnf(c_0_24,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
| c_lessequals(v_m,X1,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( ~ c_in(c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| 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(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,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_22 ).
cnf(c_0_27,axiom,
c_lessequals(X1,X1,tc_set(X2)),
cls_Set_Osubset__refl_0 ).
cnf(c_0_28,negated_conjecture,
( ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X1,v_m,tc_set(tc_set(t_a)))
| c_Zorn_Osucc(v_S,v_m,t_a) = v_m ),
inference(spm,[status(thm)],[c_0_16,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
( ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,X1,t_a),t_a) != c_Zorn_Osucc(v_S,X1,t_a)
| c_lessequals(v_m,c_Zorn_Osucc(v_S,X1,t_a),tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_30,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_25,c_0_26]),c_0_27])]) ).
cnf(c_0_31,negated_conjecture,
( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
inference(fof_simplification,[status(thm)],[cls_conjecture_1]) ).
cnf(c_0_32,negated_conjecture,
( ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_m,tc_set(tc_set(t_a)))
| c_Zorn_Osucc(v_S,v_m,t_a) = v_m ),
inference(spm,[status(thm)],[c_0_28,c_0_21]) ).
cnf(c_0_33,negated_conjecture,
( ~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(v_m,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_30])]) ).
cnf(c_0_34,negated_conjecture,
( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
c_0_31 ).
cnf(c_0_35,negated_conjecture,
c_Zorn_Osucc(v_S,v_m,t_a) = v_m,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_32]),c_0_19])]) ).
cnf(c_0_36,negated_conjecture,
c_lessequals(v_m,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_26]),c_0_27])]) ).
cnf(c_0_37,negated_conjecture,
c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) != v_m,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).
cnf(c_0_38,plain,
( ~ c_in(X3,c_Zorn_OTFin(X4,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(X1,c_Zorn_OTFin(X4,X2),tc_set(tc_set(tc_set(X2))))
| c_Zorn_Osucc(X4,X3,X2) != X3
| c_lessequals(c_Union(X1,tc_set(X2)),X3,tc_set(tc_set(X2))) ),
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_39,negated_conjecture,
~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_36]),c_0_37]) ).
cnf(c_0_40,plain,
( ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_Zorn_Osucc(X1,X3,X2) != X3
| c_lessequals(c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),X3,tc_set(tc_set(X2))) ),
inference(spm,[status(thm)],[c_0_38,c_0_27]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_35]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET843-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.38 % Computer : n019.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Mon Sep 21 05:41:11 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 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
% 0.15/5.44 % Version: 3.5.1
% 0.15/5.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.44 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.44 % Starting sh5l with 300s (1) cores
% 0.15/5.44 % new_bool_3 with pid 1797736 completed with status 0
% 0.15/5.44 % Result found by new_bool_3
% 0.15/5.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/5.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/5.44 % Search class: FGHSS-FFSF32-MFFFFFNN
% 0.15/5.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/5.44 % Starting SubtermCWHack with 31s (1) cores
% 0.15/5.44 % SubtermCWHack with pid 1797741 completed with status 0
% 0.15/5.44 % Result found by SubtermCWHack
% 0.15/5.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/5.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/5.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/5.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/5.44 % Search class: FGHSS-FFSF32-MFFFFFNN
% 0.15/5.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/5.44 % Starting SubtermCWHack with 31s (1) cores
% 0.15/5.44 % Preprocessing time : 0.001 s
% 0.15/5.44
% 0.15/5.44 % Proof found!
% 0.15/5.44 % SZS status Unsatisfiable
% 0.15/5.44 % SZS output start CNFRefutation
% See solution above
% 0.15/5.44 % Parsed axioms : 10
% 0.15/5.44 % Removed by relevancy pruning/SinE : 0
% 0.15/5.44 % Initial clauses : 10
% 0.15/5.44 % Removed in clause preprocessing : 0
% 0.15/5.44 % Initial clauses in saturation : 10
% 0.15/5.44 % Processed clauses : 34
% 0.15/5.44 % ...of these trivial : 0
% 0.15/5.44 % ...subsumed : 2
% 0.15/5.44 % ...remaining for further processing : 32
% 0.15/5.44 % Other redundant clauses eliminated : 0
% 0.15/5.44 % Clauses deleted for lack of memory : 0
% 0.15/5.44 % Backward-subsumed : 0
% 0.15/5.44 % Backward-rewritten : 7
% 0.15/5.44 % Generated clauses : 47
% 0.15/5.44 % ...of the previous two non-redundant : 37
% 0.15/5.44 % ...aggressively subsumed : 0
% 0.15/5.44 % Contextual simplify-reflections : 0
% 0.15/5.44 % Paramodulations : 47
% 0.15/5.44 % Factorizations : 0
% 0.15/5.44 % NegExts : 0
% 0.15/5.44 % Equation resolutions : 0
% 0.15/5.44 % Disequality decompositions : 0
% 0.15/5.44 % Total rewrite steps : 24
% 0.15/5.44 % ...of those cached : 15
% 0.15/5.44 % Propositional unsat checks : 0
% 0.15/5.44 % Propositional check models : 0
% 0.15/5.44 % Propositional check unsatisfiable : 0
% 0.15/5.44 % Propositional clauses : 0
% 0.15/5.44 % Propositional clauses after purity: 0
% 0.15/5.44 % Propositional unsat core size : 0
% 0.15/5.44 % Propositional preprocessing time : 0.000
% 0.15/5.44 % Propositional encoding time : 0.000
% 0.15/5.44 % Propositional solver time : 0.000
% 0.15/5.44 % Success case prop preproc time : 0.000
% 0.15/5.44 % Success case prop encoding time : 0.000
% 0.15/5.44 % Success case prop solver time : 0.000
% 0.15/5.44 % Current number of processed clauses : 25
% 0.15/5.44 % Positive orientable unit clauses : 6
% 0.15/5.44 % Positive unorientable unit clauses: 0
% 0.15/5.44 % Negative unit clauses : 2
% 0.15/5.44 % Non-unit-clauses : 17
% 0.15/5.44 % Current number of unprocessed clauses: 5
% 0.15/5.44 % ...number of literals in the above : 23
% 0.15/5.44 % Current number of archived formulas : 0
% 0.15/5.44 % Current number of archived clauses : 7
% 0.15/5.44 % Clause-clause subsumption calls (NU) : 92
% 0.15/5.44 % Rec. Clause-clause subsumption calls : 69
% 0.15/5.44 % Non-unit clause-clause subsumptions : 2
% 0.15/5.44 % Unit Clause-clause subsumption calls : 0
% 0.15/5.44 % Rewrite failures with RHS unbound : 0
% 0.15/5.44 % BW rewrite match attempts : 3
% 0.15/5.44 % BW rewrite match successes : 3
% 0.15/5.44 % Condensation attempts : 0
% 0.15/5.44 % Condensation successes : 0
% 0.15/5.44 % Termbank termtop insertions : 1732
% 0.15/5.44 % Search garbage collected termcells : 25
% 0.15/5.44
% 0.15/5.44 % -------------------------------------------------
% 0.15/5.44 % User time : 0.002 s
% 0.15/5.44 % System time : 0.004 s
% 0.15/5.44 % Total time : 0.006 s
% 0.15/5.44 % Maximum resident set size: 3640 pages
% 0.15/5.44
% 0.15/5.44 % -------------------------------------------------
% 0.15/5.44 % User time : 0.005 s
% 0.15/5.44 % System time : 0.007 s
% 0.15/5.44 % Total time : 0.012 s
% 0.15/5.44 % Maximum resident set size: 4608 pages
% 0.15/5.44 % E exiting
%------------------------------------------------------------------------------