%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET822-2 : 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 : n009.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 02:18:36 PM UTC 2026
% Result : Unsatisfiable 0.25s 0.53s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 21 ( 10 unt; 4 nHn; 18 RR)
% Number of literals : 36 ( 6 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 43 ( 9 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/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
cnf(cls_conjecture_1,negated_conjecture,
( ~ c_in(v_f(X1),X2,tc_IntDef_Oint)
| c_in(v_x(X1,X2),X2,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
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_conjecture_2,negated_conjecture,
( ~ v_P(v_x(X1,X2))
| ~ c_in(v_f(X1),X2,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_Set_OinsertCI_1,axiom,
c_in(X1,c_insert(X1,X2,X3),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
cnf(cls_conjecture_0,negated_conjecture,
v_P(v_f(v_b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(c_0_6,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_7,negated_conjecture,
( ~ c_in(v_f(X1),X2,tc_IntDef_Oint)
| c_in(v_x(X1,X2),X2,tc_IntDef_Oint) ),
inference(fof_simplification,[status(thm)],[cls_conjecture_1]) ).
cnf(c_0_8,plain,
~ c_in(X1,c_emptyset,X2),
inference(fof_simplification,[status(thm)],[cls_Set_OemptyE_0]) ).
cnf(c_0_9,plain,
( ~ c_in(X1,c_insert(X2,X3,X4),X4)
| X1 = X2
| c_in(X1,X3,X4) ),
c_0_6 ).
cnf(c_0_10,negated_conjecture,
( ~ c_in(v_f(X1),X2,tc_IntDef_Oint)
| c_in(v_x(X1,X2),X2,tc_IntDef_Oint) ),
c_0_7 ).
cnf(c_0_11,plain,
~ c_in(X1,c_emptyset,X2),
c_0_8 ).
cnf(c_0_12,negated_conjecture,
( ~ c_in(v_f(X1),c_insert(X2,X3,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(v_x(X1,c_insert(X2,X3,tc_IntDef_Oint)),X3,tc_IntDef_Oint)
| v_x(X1,c_insert(X2,X3,tc_IntDef_Oint)) = X2 ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( ~ v_P(v_x(X1,X2))
| ~ c_in(v_f(X1),X2,tc_IntDef_Oint) ),
inference(fof_simplification,[status(thm)],[cls_conjecture_2]) ).
cnf(c_0_14,negated_conjecture,
( ~ c_in(v_f(X1),c_insert(X2,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint)
| v_x(X1,c_insert(X2,c_emptyset,tc_IntDef_Oint)) = X2 ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,axiom,
c_in(X1,c_insert(X1,X2,X3),X3),
cls_Set_OinsertCI_1 ).
cnf(c_0_16,negated_conjecture,
( ~ v_P(v_x(X1,X2))
| ~ c_in(v_f(X1),X2,tc_IntDef_Oint) ),
c_0_13 ).
cnf(c_0_17,negated_conjecture,
v_x(X1,c_insert(v_f(X1),c_emptyset,tc_IntDef_Oint)) = v_f(X1),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
v_P(v_f(v_b)),
cls_conjecture_0 ).
cnf(c_0_19,negated_conjecture,
~ v_P(v_f(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_15])]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_18,c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET822-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n009.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 05:39:58 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.50 Running first-order theorem proving
% 0.25/0.50 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
% 0.25/0.53 % Version: 3.5.1
% 0.25/0.53 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.25/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.53 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.25/0.53 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.53 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.53 % Starting sh5l with 300s (1) cores
% 0.25/0.53 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 960191 completed with status 0
% 0.25/0.53 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.25/0.53 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.25/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.53 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.25/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.53 % No SInE strategy applied
% 0.25/0.53 % Search class: FGHSF-FFSF32-SFFFFFNN
% 0.25/0.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.53 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.53 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.25/0.53 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.25/0.53 % Starting new_bool_3 with 136s (1) cores
% 0.25/0.53 % Starting new_bool_1 with 136s (1) cores
% 0.25/0.53 % SubtermCWHack with pid 960196 completed with status 0
% 0.25/0.53 % Result found by SubtermCWHack
% 0.25/0.53 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.25/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.53 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.25/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.53 % No SInE strategy applied
% 0.25/0.53 % Search class: FGHSF-FFSF32-SFFFFFNN
% 0.25/0.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.53 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.53 % Preprocessing time : 0.001 s
% 0.25/0.53
% 0.25/0.53 % Proof found!
% 0.25/0.53 % SZS status Unsatisfiable
% 0.25/0.53 % SZS output start CNFRefutation
% See solution above
% 0.25/0.53 % Parsed axioms : 6
% 0.25/0.53 % Removed by relevancy pruning/SinE : 0
% 0.25/0.53 % Initial clauses : 6
% 0.25/0.53 % Removed in clause preprocessing : 0
% 0.25/0.53 % Initial clauses in saturation : 6
% 0.25/0.53 % Processed clauses : 12
% 0.25/0.53 % ...of these trivial : 0
% 0.25/0.53 % ...subsumed : 1
% 0.25/0.53 % ...remaining for further processing : 11
% 0.25/0.53 % Other redundant clauses eliminated : 0
% 0.25/0.53 % Clauses deleted for lack of memory : 0
% 0.25/0.53 % Backward-subsumed : 0
% 0.25/0.53 % Backward-rewritten : 0
% 0.25/0.53 % Generated clauses : 10
% 0.25/0.53 % ...of the previous two non-redundant : 8
% 0.25/0.53 % ...aggressively subsumed : 0
% 0.25/0.53 % Contextual simplify-reflections : 0
% 0.25/0.53 % Paramodulations : 9
% 0.25/0.53 % Factorizations : 0
% 0.25/0.53 % NegExts : 0
% 0.25/0.53 % Equation resolutions : 0
% 0.25/0.53 % Disequality decompositions : 0
% 0.25/0.53 % Total rewrite steps : 3
% 0.25/0.53 % ...of those cached : 2
% 0.25/0.53 % Propositional unsat checks : 0
% 0.25/0.53 % Propositional check models : 0
% 0.25/0.53 % Propositional check unsatisfiable : 0
% 0.25/0.53 % Propositional clauses : 0
% 0.25/0.53 % Propositional clauses after purity: 0
% 0.25/0.53 % Propositional unsat core size : 0
% 0.25/0.53 % Propositional preprocessing time : 0.000
% 0.25/0.53 % Propositional encoding time : 0.000
% 0.25/0.53 % Propositional solver time : 0.000
% 0.25/0.53 % Success case prop preproc time : 0.000
% 0.25/0.53 % Success case prop encoding time : 0.000
% 0.25/0.53 % Success case prop solver time : 0.000
% 0.25/0.53 % Current number of processed clauses : 10
% 0.25/0.53 % Positive orientable unit clauses : 2
% 0.25/0.53 % Positive unorientable unit clauses: 0
% 0.25/0.53 % Negative unit clauses : 2
% 0.25/0.53 % Non-unit-clauses : 6
% 0.25/0.53 % Current number of unprocessed clauses: 2
% 0.25/0.53 % ...number of literals in the above : 8
% 0.25/0.53 % Current number of archived formulas : 0
% 0.25/0.53 % Current number of archived clauses : 1
% 0.25/0.53 % Clause-clause subsumption calls (NU) : 12
% 0.25/0.53 % Rec. Clause-clause subsumption calls : 10
% 0.25/0.53 % Non-unit clause-clause subsumptions : 0
% 0.25/0.53 % Unit Clause-clause subsumption calls : 1
% 0.25/0.53 % Rewrite failures with RHS unbound : 0
% 0.25/0.53 % BW rewrite match attempts : 0
% 0.25/0.53 % BW rewrite match successes : 0
% 0.25/0.53 % Condensation attempts : 0
% 0.25/0.53 % Condensation successes : 0
% 0.25/0.53 % Termbank termtop insertions : 386
% 0.25/0.53 % Search garbage collected termcells : 11
% 0.25/0.53
% 0.25/0.53 % -------------------------------------------------
% 0.25/0.53 % User time : 0.004 s
% 0.25/0.53 % System time : 0.002 s
% 0.25/0.53 % Total time : 0.006 s
% 0.25/0.53 % Maximum resident set size: 3620 pages
% 0.25/0.53
% 0.25/0.53 % -------------------------------------------------
% 0.25/0.53 % User time : 0.010 s
% 0.25/0.53 % System time : 0.009 s
% 0.25/0.53 % Total time : 0.019 s
% 0.25/0.53 % Maximum resident set size: 4608 pages
% 0.25/0.53 % E exiting
%------------------------------------------------------------------------------