%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET840-2 : TPTP v9.3.1. Released v3.2.0.
% 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 02:15:33 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.46s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 41 ( 9 unt; 8 nHn; 27 RR)
% Number of literals : 84 ( 12 equ; 37 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 5 ( 1 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 : 111 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_OinsertE_0,axiom,
( ~ c_in(X1,c_insert(X2,X3,X4),X4)
| X1 = X2
| c_in(X1,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
cnf(cls_Set_OUnionI_0,axiom,
( ~ c_in(X2,X4,tc_set(X3))
| ~ c_in(X1,X2,X3)
| c_in(X1,c_Union(X4,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).
cnf(cls_Set_OsubsetI_1,axiom,
( ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
cnf(cls_Set_OinsertCI_0,axiom,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_insert(X4,X2,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).
cnf(cls_Set_OinsertCI_1,axiom,
c_in(X1,c_insert(X1,X2,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
cnf(cls_conjecture_1,negated_conjecture,
( ~ c_in(X1,v_S,tc_set(t_b))
| c_lessequals(c_Union(v_S,t_b),X1,tc_set(t_b)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_lessequals(v_S,c_insert(X1,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(c_0_9,plain,
( ~ c_in(X1,c_insert(X2,X3,X4),X4)
| X1 = X2
| c_in(X1,X3,X4) ),
inference(fof_simplification,[status(thm)],[cls_Set_OinsertE_0]) ).
cnf(c_0_10,plain,
( ~ c_in(X2,X4,tc_set(X3))
| ~ c_in(X1,X2,X3)
| c_in(X1,c_Union(X4,X3),X3) ),
inference(fof_simplification,[status(thm)],[cls_Set_OUnionI_0]) ).
cnf(c_0_11,plain,
( ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
inference(fof_simplification,[status(thm)],[cls_Set_OsubsetI_1]) ).
cnf(c_0_12,plain,
( ~ c_in(X1,c_insert(X2,X3,X4),X4)
| X1 = X2
| c_in(X1,X3,X4) ),
c_0_9 ).
cnf(c_0_13,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_14,plain,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_insert(X4,X2,X3),X3) ),
inference(fof_simplification,[status(thm)],[cls_Set_OinsertCI_0]) ).
cnf(c_0_15,plain,
( ~ c_in(X2,X4,tc_set(X3))
| ~ c_in(X1,X2,X3)
| c_in(X1,c_Union(X4,X3),X3) ),
c_0_10 ).
cnf(c_0_16,axiom,
c_in(X1,c_insert(X1,X2,X3),X3),
cls_Set_OinsertCI_1 ).
cnf(c_0_17,plain,
( ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
c_0_11 ).
cnf(c_0_18,plain,
( c_lessequals(c_insert(X1,X2,X3),X4,tc_set(X3))
| c_in(c_Main_OsubsetI__1(c_insert(X1,X2,X3),X4,X3),X2,X3)
| c_Main_OsubsetI__1(c_insert(X1,X2,X3),X4,X3) = X1 ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
( ~ c_in(X1,X2,X3)
| c_in(X1,c_insert(X4,X2,X3),X3) ),
c_0_14 ).
cnf(c_0_20,plain,
( ~ c_in(X1,X2,X4)
| c_in(X1,c_Union(c_insert(X2,X3,tc_set(X4)),X4),X4) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,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_22,plain,
( c_lessequals(c_insert(X1,X2,X3),X2,tc_set(X3))
| c_Main_OsubsetI__1(c_insert(X1,X2,X3),X2,X3) = X1 ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( ~ c_in(c_Main_OsubsetI__1(X1,c_insert(X2,X3,X4),X4),X3,X4)
| c_lessequals(X1,c_insert(X2,X3,X4),tc_set(X4)) ),
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( ~ c_in(X1,v_S,tc_set(t_b))
| c_lessequals(c_Union(v_S,t_b),X1,tc_set(t_b)) ),
inference(fof_simplification,[status(thm)],[cls_conjecture_1]) ).
cnf(c_0_25,plain,
( ~ c_in(c_Main_OsubsetI__1(X1,c_Union(c_insert(X2,X3,tc_set(X4)),X4),X4),X2,X4)
| c_lessequals(X1,c_Union(c_insert(X2,X3,tc_set(X4)),X4),tc_set(X4)) ),
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_26,plain,
( ~ c_lessequals(X2,X1,tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3))
| X2 = X1 ),
c_0_21 ).
cnf(c_0_27,plain,
( ~ c_in(X1,X2,X3)
| c_lessequals(c_insert(X1,X2,X3),X2,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_28,plain,
c_lessequals(X1,c_insert(X2,X1,X3),tc_set(X3)),
inference(spm,[status(thm)],[c_0_23,c_0_13]) ).
cnf(c_0_29,negated_conjecture,
( ~ c_in(X1,v_S,tc_set(t_b))
| c_lessequals(c_Union(v_S,t_b),X1,tc_set(t_b)) ),
c_0_24 ).
cnf(c_0_30,plain,
c_lessequals(X1,c_Union(c_insert(X1,X2,tc_set(X3)),X3),tc_set(X3)),
inference(spm,[status(thm)],[c_0_25,c_0_13]) ).
cnf(c_0_31,plain,
( ~ c_in(X1,X2,X3)
| c_insert(X1,X2,X3) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_32,negated_conjecture,
( ~ c_lessequals(X1,c_Union(v_S,t_b),tc_set(t_b))
| ~ c_in(X1,v_S,tc_set(t_b))
| X1 = c_Union(v_S,t_b) ),
inference(spm,[status(thm)],[c_0_26,c_0_29]) ).
cnf(c_0_33,plain,
( ~ c_in(X1,X2,tc_set(X3))
| c_lessequals(X1,c_Union(X2,X3),tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
( ~ c_in(X1,v_S,tc_set(t_b))
| X1 = c_Union(v_S,t_b) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_35,negated_conjecture,
( c_lessequals(v_S,X1,tc_set(tc_set(t_b)))
| c_Main_OsubsetI__1(v_S,X1,tc_set(t_b)) = c_Union(v_S,t_b) ),
inference(spm,[status(thm)],[c_0_34,c_0_13]) ).
cnf(c_0_36,negated_conjecture,
~ c_lessequals(v_S,c_insert(X1,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
inference(fof_simplification,[status(thm)],[cls_conjecture_0]) ).
cnf(c_0_37,negated_conjecture,
( ~ c_in(c_Union(v_S,t_b),X1,tc_set(t_b))
| c_lessequals(v_S,X1,tc_set(tc_set(t_b))) ),
inference(spm,[status(thm)],[c_0_17,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
~ c_lessequals(v_S,c_insert(X1,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
c_0_36 ).
cnf(c_0_39,negated_conjecture,
c_lessequals(v_S,c_insert(c_Union(v_S,t_b),X1,tc_set(t_b)),tc_set(tc_set(t_b))),
inference(spm,[status(thm)],[c_0_37,c_0_16]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_38,c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET840-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 % Computer : n018.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Mon Sep 21 05:42:59 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 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
% 0.20/0.46 % Version: 3.5.1
% 0.20/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.20/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.20/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.20/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.46 % Starting sh5l with 300s (1) cores
% 0.20/0.46 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1086340 completed with status 0
% 0.20/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.20/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.20/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.20/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.46 % No SInE strategy applied
% 0.20/0.46 % Search class: FGUSF-FFSF32-SFFFFFNN
% 0.20/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.20/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.20/0.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.20/0.46 % Starting new_bool_3 with 136s (1) cores
% 0.20/0.46 % Starting new_bool_1 with 136s (1) cores
% 0.20/0.46 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1086346 completed with status 0
% 0.20/0.46 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.20/0.46 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.20/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.20/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.46 % No SInE strategy applied
% 0.20/0.46 % Search class: FGUSF-FFSF32-SFFFFFNN
% 0.20/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.20/0.46 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.20/0.46 % Preprocessing time : 0.001 s
% 0.20/0.46 % Presaturation interreduction done
% 0.20/0.46
% 0.20/0.46 % Proof found!
% 0.20/0.46 % SZS status Unsatisfiable
% 0.20/0.46 % SZS output start CNFRefutation
% See solution above
% 0.20/0.47 % Parsed axioms : 9
% 0.20/0.47 % Removed by relevancy pruning/SinE : 0
% 0.20/0.47 % Initial clauses : 9
% 0.20/0.47 % Removed in clause preprocessing : 0
% 0.20/0.47 % Initial clauses in saturation : 9
% 0.20/0.47 % Processed clauses : 69
% 0.20/0.47 % ...of these trivial : 0
% 0.20/0.47 % ...subsumed : 16
% 0.20/0.47 % ...remaining for further processing : 53
% 0.20/0.47 % Other redundant clauses eliminated : 0
% 0.20/0.47 % Clauses deleted for lack of memory : 0
% 0.20/0.47 % Backward-subsumed : 3
% 0.20/0.47 % Backward-rewritten : 1
% 0.20/0.47 % Generated clauses : 171
% 0.20/0.47 % ...of the previous two non-redundant : 148
% 0.20/0.47 % ...aggressively subsumed : 0
% 0.20/0.47 % Contextual simplify-reflections : 0
% 0.20/0.47 % Paramodulations : 171
% 0.20/0.47 % Factorizations : 0
% 0.20/0.47 % NegExts : 0
% 0.20/0.47 % Equation resolutions : 0
% 0.20/0.47 % Disequality decompositions : 0
% 0.20/0.47 % Total rewrite steps : 16
% 0.20/0.47 % ...of those cached : 6
% 0.20/0.47 % Propositional unsat checks : 0
% 0.20/0.47 % Propositional check models : 0
% 0.20/0.47 % Propositional check unsatisfiable : 0
% 0.20/0.47 % Propositional clauses : 0
% 0.20/0.47 % Propositional clauses after purity: 0
% 0.20/0.47 % Propositional unsat core size : 0
% 0.20/0.47 % Propositional preprocessing time : 0.000
% 0.20/0.47 % Propositional encoding time : 0.000
% 0.20/0.47 % Propositional solver time : 0.000
% 0.20/0.47 % Success case prop preproc time : 0.000
% 0.20/0.47 % Success case prop encoding time : 0.000
% 0.20/0.47 % Success case prop solver time : 0.000
% 0.20/0.47 % Current number of processed clauses : 40
% 0.20/0.47 % Positive orientable unit clauses : 7
% 0.20/0.47 % Positive unorientable unit clauses: 0
% 0.20/0.47 % Negative unit clauses : 1
% 0.20/0.47 % Non-unit-clauses : 32
% 0.20/0.47 % Current number of unprocessed clauses: 96
% 0.20/0.47 % ...number of literals in the above : 254
% 0.20/0.47 % Current number of archived formulas : 0
% 0.20/0.47 % Current number of archived clauses : 13
% 0.20/0.47 % Clause-clause subsumption calls (NU) : 165
% 0.20/0.47 % Rec. Clause-clause subsumption calls : 160
% 0.20/0.47 % Non-unit clause-clause subsumptions : 19
% 0.20/0.47 % Unit Clause-clause subsumption calls : 10
% 0.20/0.47 % Rewrite failures with RHS unbound : 0
% 0.20/0.47 % BW rewrite match attempts : 11
% 0.20/0.47 % BW rewrite match successes : 1
% 0.20/0.47 % Condensation attempts : 0
% 0.20/0.47 % Condensation successes : 0
% 0.20/0.47 % Termbank termtop insertions : 3169
% 0.20/0.47 % Search garbage collected termcells : 23
% 0.20/0.47
% 0.20/0.47 % -------------------------------------------------
% 0.20/0.47 % User time : 0.004 s
% 0.20/0.47 % System time : 0.004 s
% 0.20/0.47 % Total time : 0.008 s
% 0.20/0.47 % Maximum resident set size: 3636 pages
% 0.20/0.47
% 0.20/0.47 % -------------------------------------------------
% 0.20/0.47 % User time : 0.016 s
% 0.20/0.47 % System time : 0.016 s
% 0.20/0.47 % Total time : 0.032 s
% 0.20/0.47 % Maximum resident set size: 4608 pages
% 0.20/0.47 % E exiting
%------------------------------------------------------------------------------