%------------------------------------------------------------------------------
% File : E---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 : n017.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 02:15:28 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.43s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 21 ( 11 unt; 4 nHn; 16 RR)
% Number of literals : 34 ( 5 equ; 16 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 : 42 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
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_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_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_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_conjecture_0,negated_conjecture,
v_P(v_f(v_b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(c_0_6,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_7,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_8,negated_conjecture,
( ~ c_in(v_f(X1),X2,tc_IntDef_Oint)
| c_in(v_x(X1,X2),X2,tc_IntDef_Oint) ),
c_0_6 ).
cnf(c_0_9,axiom,
c_in(X1,c_insert(X1,X2,X3),X3),
cls_Set_OinsertCI_1 ).
cnf(c_0_10,plain,
~ c_in(X1,c_emptyset,X2),
inference(fof_simplification,[status(thm)],[cls_Set_OemptyE_0]) ).
cnf(c_0_11,plain,
( ~ c_in(X1,c_insert(X2,X3,X4),X4)
| X1 = X2
| c_in(X1,X3,X4) ),
c_0_7 ).
cnf(c_0_12,negated_conjecture,
c_in(v_x(X1,c_insert(v_f(X1),X2,tc_IntDef_Oint)),c_insert(v_f(X1),X2,tc_IntDef_Oint),tc_IntDef_Oint),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
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,plain,
~ c_in(X1,c_emptyset,X2),
c_0_10 ).
cnf(c_0_15,negated_conjecture,
( c_in(v_x(X1,c_insert(v_f(X1),X2,tc_IntDef_Oint)),X2,tc_IntDef_Oint)
| v_x(X1,c_insert(v_f(X1),X2,tc_IntDef_Oint)) = v_f(X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
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_9])]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_18,c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET822-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:35:11 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.43 % Version: 3.5.1
% 0.09/0.43 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.09/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.09/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.09/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.09/0.43 % Starting sh5l with 300s (1) cores
% 0.09/0.43 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1540168 completed with status 0
% 0.09/0.43 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.09/0.43 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.09/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.09/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.43 % No SInE strategy applied
% 0.09/0.43 % Search class: FGHSF-FFSF32-SFFFFFNN
% 0.09/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.09/0.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.09/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.09/0.43 % Starting new_bool_1 with 136s (1) cores
% 0.09/0.43 % G-E--_208_C18_F1_SE_CS_SP_PS_S4d with pid 1540175 completed with status 0
% 0.09/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S4d
% 0.09/0.43 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.09/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.09/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.09/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.09/0.43 % No SInE strategy applied
% 0.09/0.43 % Search class: FGHSF-FFSF32-SFFFFFNN
% 0.09/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.09/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.09/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.09/0.43 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.09/0.43 % Preprocessing time : 0.001 s
% 0.09/0.43 % Presaturation interreduction done
% 0.09/0.43
% 0.09/0.43 % Proof found!
% 0.09/0.43 % SZS status Unsatisfiable
% 0.09/0.43 % SZS output start CNFRefutation
% See solution above
% 0.09/0.43 % Parsed axioms : 6
% 0.09/0.43 % Removed by relevancy pruning/SinE : 0
% 0.09/0.43 % Initial clauses : 6
% 0.09/0.43 % Removed in clause preprocessing : 0
% 0.09/0.43 % Initial clauses in saturation : 6
% 0.09/0.43 % Processed clauses : 16
% 0.09/0.43 % ...of these trivial : 0
% 0.09/0.43 % ...subsumed : 0
% 0.09/0.43 % ...remaining for further processing : 16
% 0.09/0.43 % Other redundant clauses eliminated : 0
% 0.09/0.43 % Clauses deleted for lack of memory : 0
% 0.09/0.43 % Backward-subsumed : 0
% 0.09/0.43 % Backward-rewritten : 0
% 0.09/0.43 % Generated clauses : 7
% 0.09/0.43 % ...of the previous two non-redundant : 5
% 0.09/0.43 % ...aggressively subsumed : 0
% 0.09/0.43 % Contextual simplify-reflections : 0
% 0.09/0.43 % Paramodulations : 6
% 0.09/0.43 % Factorizations : 0
% 0.09/0.43 % NegExts : 0
% 0.09/0.43 % Equation resolutions : 0
% 0.09/0.43 % Disequality decompositions : 0
% 0.09/0.43 % Total rewrite steps : 2
% 0.09/0.43 % ...of those cached : 1
% 0.09/0.43 % Propositional unsat checks : 0
% 0.09/0.43 % Propositional check models : 0
% 0.09/0.43 % Propositional check unsatisfiable : 0
% 0.09/0.43 % Propositional clauses : 0
% 0.09/0.43 % Propositional clauses after purity: 0
% 0.09/0.43 % Propositional unsat core size : 0
% 0.09/0.43 % Propositional preprocessing time : 0.000
% 0.09/0.43 % Propositional encoding time : 0.000
% 0.09/0.43 % Propositional solver time : 0.000
% 0.09/0.43 % Success case prop preproc time : 0.000
% 0.09/0.43 % Success case prop encoding time : 0.000
% 0.09/0.43 % Success case prop solver time : 0.000
% 0.09/0.43 % Current number of processed clauses : 9
% 0.09/0.43 % Positive orientable unit clauses : 3
% 0.09/0.43 % Positive unorientable unit clauses: 0
% 0.09/0.43 % Negative unit clauses : 2
% 0.09/0.43 % Non-unit-clauses : 4
% 0.09/0.43 % Current number of unprocessed clauses: 1
% 0.09/0.43 % ...number of literals in the above : 3
% 0.09/0.43 % Current number of archived formulas : 0
% 0.09/0.43 % Current number of archived clauses : 7
% 0.09/0.43 % Clause-clause subsumption calls (NU) : 0
% 0.09/0.43 % Rec. Clause-clause subsumption calls : 0
% 0.09/0.43 % Non-unit clause-clause subsumptions : 0
% 0.09/0.43 % Unit Clause-clause subsumption calls : 2
% 0.09/0.43 % Rewrite failures with RHS unbound : 0
% 0.09/0.43 % BW rewrite match attempts : 0
% 0.09/0.43 % BW rewrite match successes : 0
% 0.09/0.43 % Condensation attempts : 0
% 0.09/0.43 % Condensation successes : 0
% 0.09/0.43 % Termbank termtop insertions : 322
% 0.09/0.43 % Search garbage collected termcells : 11
% 0.09/0.43
% 0.09/0.43 % -------------------------------------------------
% 0.09/0.43 % User time : 0.002 s
% 0.09/0.43 % System time : 0.003 s
% 0.09/0.43 % Total time : 0.005 s
% 0.09/0.43 % Maximum resident set size: 3604 pages
% 0.09/0.43
% 0.09/0.43 % -------------------------------------------------
% 0.09/0.43 % User time : 0.006 s
% 0.09/0.43 % System time : 0.015 s
% 0.09/0.43 % Total time : 0.021 s
% 0.09/0.43 % Maximum resident set size: 4864 pages
% 0.09/0.43 % E exiting
%------------------------------------------------------------------------------