%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET820-2 : 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 : n020.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 0.16s 0.60s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 22 ( 12 unt; 4 nHn; 17 RR)
% Number of literals : 35 ( 5 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 44 ( 17 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_1,negated_conjecture,
( ~ c_in(X1,X2,tc_IntDef_Oint)
| c_in(v_x(X2),X2,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
cnf(cls_conjecture_2,negated_conjecture,
( ~ v_P(v_x(X2))
| ~ c_in(X1,X2,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_Set_OemptyE_0,axiom,
~ c_in(X1,c_emptyset,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
cnf(cls_conjecture_0,negated_conjecture,
v_P(v_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(c_0_6,negated_conjecture,
( ~ c_in(X1,X2,tc_IntDef_Oint)
| c_in(v_x(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(X1,X2,tc_IntDef_Oint)
| c_in(v_x(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,negated_conjecture,
( ~ v_P(v_x(X2))
| ~ c_in(X1,X2,tc_IntDef_Oint) ),
inference(fof_simplification,[status(thm)],[cls_conjecture_2]) ).
cnf(c_0_11,plain,
~ c_in(X1,c_emptyset,X2),
inference(fof_simplification,[status(thm)],[cls_Set_OemptyE_0]) ).
cnf(c_0_12,plain,
( ~ c_in(X1,c_insert(X2,X3,X4),X4)
| X1 = X2
| c_in(X1,X3,X4) ),
c_0_7 ).
cnf(c_0_13,negated_conjecture,
c_in(v_x(c_insert(X1,X2,tc_IntDef_Oint)),c_insert(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( ~ v_P(v_x(X2))
| ~ c_in(X1,X2,tc_IntDef_Oint) ),
c_0_10 ).
cnf(c_0_15,plain,
~ c_in(X1,c_emptyset,X2),
c_0_11 ).
cnf(c_0_16,negated_conjecture,
( c_in(v_x(c_insert(X1,X2,tc_IntDef_Oint)),X2,tc_IntDef_Oint)
| v_x(c_insert(X1,X2,tc_IntDef_Oint)) = X1 ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
~ v_P(v_x(c_insert(X1,X2,tc_IntDef_Oint))),
inference(spm,[status(thm)],[c_0_14,c_0_9]) ).
cnf(c_0_18,negated_conjecture,
v_x(c_insert(X1,c_emptyset,tc_IntDef_Oint)) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
v_P(v_a),
cls_conjecture_0 ).
cnf(c_0_20,negated_conjecture,
~ v_P(X1),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_19,c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET820-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.53 % Computer : n020.cluster.edu
% 0.12/0.53 % Model : x86_64 x86_64
% 0.12/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.53 % Memory : 8046.5625MB
% 0.12/0.53 % OS : Linux 6.8.0-71-generic
% 0.12/0.53 % CPULimit : 300
% 0.12/0.53 % WCLimit : 300
% 0.12/0.53 % DateTime : Mon Sep 21 05:40:33 UTC 2026
% 0.12/0.54 % CPUTime :
% 0.12/0.54 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.58 Running first-order theorem proving
% 0.16/0.58 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
% 0.16/0.60 % Version: 3.5.1
% 0.16/0.60 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.16/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.60 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.16/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.60 % Starting sh5l with 300s (1) cores
% 0.16/0.60 % sh5l with pid 2116091 completed with status 0
% 0.16/0.60 % Result found by sh5l
% 0.16/0.60 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.16/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.60 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.16/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.60 % Starting sh5l with 300s (1) cores
% 0.16/0.60 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.16/0.60 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.16/0.60 % Search class: FGHSF-FFSF32-SFFFFFNN
% 0.16/0.60 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.60 % Starting SubtermCWHack with 31s (1) cores
% 0.16/0.60 % SubtermCWHack with pid 2116098 completed with status 0
% 0.16/0.60 % Result found by SubtermCWHack
% 0.16/0.60 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.16/0.60 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.60 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.16/0.60 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.60 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.60 % Starting sh5l with 300s (1) cores
% 0.16/0.60 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.16/0.60 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.16/0.60 % Search class: FGHSF-FFSF32-SFFFFFNN
% 0.16/0.60 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.60 % Starting SubtermCWHack with 31s (1) cores
% 0.16/0.60 % Preprocessing time : 0.001 s
% 0.16/0.60
% 0.16/0.60 % Proof found!
% 0.16/0.60 % SZS status Unsatisfiable
% 0.16/0.60 % SZS output start CNFRefutation
% See solution above
% 0.16/0.60 % Parsed axioms : 6
% 0.16/0.60 % Removed by relevancy pruning/SinE : 0
% 0.16/0.60 % Initial clauses : 6
% 0.16/0.60 % Removed in clause preprocessing : 0
% 0.16/0.60 % Initial clauses in saturation : 6
% 0.16/0.60 % Processed clauses : 13
% 0.16/0.60 % ...of these trivial : 0
% 0.16/0.60 % ...subsumed : 1
% 0.16/0.60 % ...remaining for further processing : 12
% 0.16/0.60 % Other redundant clauses eliminated : 0
% 0.16/0.60 % Clauses deleted for lack of memory : 0
% 0.16/0.60 % Backward-subsumed : 2
% 0.16/0.60 % Backward-rewritten : 0
% 0.16/0.60 % Generated clauses : 16
% 0.16/0.60 % ...of the previous two non-redundant : 13
% 0.16/0.60 % ...aggressively subsumed : 0
% 0.16/0.60 % Contextual simplify-reflections : 0
% 0.16/0.60 % Paramodulations : 15
% 0.16/0.60 % Factorizations : 0
% 0.16/0.60 % NegExts : 0
% 0.16/0.60 % Equation resolutions : 0
% 0.16/0.60 % Disequality decompositions : 0
% 0.16/0.60 % Total rewrite steps : 2
% 0.16/0.60 % ...of those cached : 0
% 0.16/0.60 % Propositional unsat checks : 0
% 0.16/0.60 % Propositional check models : 0
% 0.16/0.60 % Propositional check unsatisfiable : 0
% 0.16/0.60 % Propositional clauses : 0
% 0.16/0.60 % Propositional clauses after purity: 0
% 0.16/0.60 % Propositional unsat core size : 0
% 0.16/0.60 % Propositional preprocessing time : 0.000
% 0.16/0.60 % Propositional encoding time : 0.000
% 0.16/0.60 % Propositional solver time : 0.000
% 0.16/0.60 % Success case prop preproc time : 0.000
% 0.16/0.60 % Success case prop encoding time : 0.000
% 0.16/0.60 % Success case prop solver time : 0.000
% 0.16/0.60 % Current number of processed clauses : 9
% 0.16/0.60 % Positive orientable unit clauses : 3
% 0.16/0.60 % Positive unorientable unit clauses: 0
% 0.16/0.60 % Negative unit clauses : 2
% 0.16/0.60 % Non-unit-clauses : 4
% 0.16/0.60 % Current number of unprocessed clauses: 6
% 0.16/0.60 % ...number of literals in the above : 16
% 0.16/0.60 % Current number of archived formulas : 0
% 0.16/0.60 % Current number of archived clauses : 3
% 0.16/0.60 % Clause-clause subsumption calls (NU) : 3
% 0.16/0.60 % Rec. Clause-clause subsumption calls : 2
% 0.16/0.60 % Non-unit clause-clause subsumptions : 0
% 0.16/0.60 % Unit Clause-clause subsumption calls : 4
% 0.16/0.60 % Rewrite failures with RHS unbound : 0
% 0.16/0.60 % BW rewrite match attempts : 0
% 0.16/0.60 % BW rewrite match successes : 0
% 0.16/0.60 % Condensation attempts : 0
% 0.16/0.60 % Condensation successes : 0
% 0.16/0.60 % Termbank termtop insertions : 363
% 0.16/0.60 % Search garbage collected termcells : 11
% 0.16/0.60
% 0.16/0.60 % -------------------------------------------------
% 0.16/0.60 % User time : 0.001 s
% 0.16/0.60 % System time : 0.004 s
% 0.16/0.60 % Total time : 0.005 s
% 0.16/0.60 % Maximum resident set size: 3592 pages
% 0.16/0.60
% 0.16/0.60 % -------------------------------------------------
% 0.16/0.60 % User time : 0.002 s
% 0.16/0.60 % System time : 0.009 s
% 0.16/0.60 % Total time : 0.011 s
% 0.16/0.60 % Maximum resident set size: 4608 pages
% 0.16/0.60 % E exiting
%------------------------------------------------------------------------------