%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV749-1 : TPTP v9.3.1. Released v4.1.0.
% 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 02:59:52 PM UTC 2026
% Result : Unsatisfiable 9.16s 1.80s
% Output : CNFRefutation 9.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 38 ( 25 unt; 6 nHn; 20 RR)
% Number of literals : 58 ( 31 equ; 26 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 110 ( 47 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_keymode_Oinduct_0,axiom,
( ~ hBOOL(hAPP(X1,c_Public_Okeymode_OSignature))
| ~ hBOOL(hAPP(X1,c_Public_Okeymode_OEncryption))
| hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_keymode_Oinduct_0) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
cnf(cls_insert__commute_0,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
cnf(cls_insert__code_0,axiom,
( ~ hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| X3 = X2
| hBOOL(hAPP(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
cnf(cls_self__append__conv2_0,axiom,
( X1 != c_List_Oappend(X2,X1,X3)
| X2 = c_List_Olist_ONil(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
cnf(cls_list_Osimps_I2_J_0,axiom,
c_List_Olist_ONil(X1) != c_List_Olist_OCons(X2,X3,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
cnf(cls_Cons__eq__append__conv_5,axiom,
c_List_Olist_OCons(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X1,X2,X4),X3,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
cnf(cls_bot1E_0,axiom,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
cnf(cls_not__Cons__self_0,axiom,
X1 != c_List_Olist_OCons(X2,X1,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
cnf(cls_eq__Nil__appendI_0,axiom,
X1 = c_List_Oappend(c_List_Olist_ONil(X2),X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
cnf(c_0_10,plain,
( ~ hBOOL(hAPP(X1,c_Public_Okeymode_OSignature))
| ~ hBOOL(hAPP(X1,c_Public_Okeymode_OEncryption))
| hBOOL(hAPP(X1,X2)) ),
inference(fof_simplification,[status(thm)],[cls_keymode_Oinduct_0]) ).
cnf(c_0_11,plain,
( ~ hBOOL(hAPP(X1,c_Public_Okeymode_OSignature))
| ~ hBOOL(hAPP(X1,c_Public_Okeymode_OEncryption))
| hBOOL(hAPP(X1,X2)) ),
c_0_10 ).
cnf(c_0_12,axiom,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X1)),
cls_insert__code_1 ).
cnf(c_0_13,axiom,
c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4) = c_Set_Oinsert(X2,c_Set_Oinsert(X1,X3,X4),X4),
cls_insert__commute_0 ).
cnf(c_0_14,plain,
( ~ hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| X3 = X2
| hBOOL(hAPP(X1,X2)) ),
inference(fof_simplification,[status(thm)],[cls_insert__code_0]) ).
cnf(c_0_15,plain,
( ~ hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,X1,X2),c_Public_Okeymode_OEncryption))
| hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,c_Set_Oinsert(X2,X3,X4),X4),X2)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( X1 != c_List_Oappend(X2,X1,X3)
| X2 = c_List_Olist_ONil(X3) ),
inference(fof_simplification,[status(thm)],[cls_self__append__conv2_0]) ).
cnf(c_0_18,plain,
c_List_Olist_ONil(X1) != c_List_Olist_OCons(X2,X3,X1),
inference(fof_simplification,[status(thm)],[cls_list_Osimps_I2_J_0]) ).
cnf(c_0_19,plain,
( ~ hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| X3 = X2
| hBOOL(hAPP(X1,X2)) ),
c_0_14 ).
cnf(c_0_20,plain,
hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OEncryption,c_Set_Oinsert(c_Public_Okeymode_OSignature,X1,X2),X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_13]) ).
cnf(c_0_21,plain,
( X1 != c_List_Oappend(X2,X1,X3)
| X2 = c_List_Olist_ONil(X3) ),
c_0_17 ).
cnf(c_0_22,axiom,
c_List_Olist_OCons(X1,c_List_Oappend(X2,X3,X4),X4) = c_List_Oappend(c_List_Olist_OCons(X1,X2,X4),X3,X4),
cls_Cons__eq__append__conv_5 ).
cnf(c_0_23,plain,
c_List_Olist_ONil(X1) != c_List_Olist_OCons(X2,X3,X1),
c_0_18 ).
cnf(c_0_24,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
inference(fof_simplification,[status(thm)],[cls_bot1E_0]) ).
cnf(c_0_25,plain,
( hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,X2,X3),X1))
| X1 = c_Public_Okeymode_OEncryption ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
c_List_Olist_OCons(X1,c_List_Oappend(X2,X3,X4),X4) != X3,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_27,plain,
X1 != c_List_Olist_OCons(X2,X1,X3),
inference(fof_simplification,[status(thm)],[cls_not__Cons__self_0]) ).
cnf(c_0_28,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
c_0_24 ).
cnf(c_0_29,plain,
( hBOOL(hAPP(X2,X1))
| X1 = c_Public_Okeymode_OSignature
| X1 = c_Public_Okeymode_OEncryption ),
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_30,plain,
c_List_Olist_OCons(X1,c_List_Olist_OCons(X2,c_List_Oappend(X3,X4,X5),X5),X5) != X4,
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_31,axiom,
X1 = c_List_Oappend(c_List_Olist_ONil(X2),X1,X2),
cls_eq__Nil__appendI_0 ).
cnf(c_0_32,plain,
X1 != c_List_Olist_OCons(X2,X1,X3),
c_0_27 ).
cnf(c_0_33,plain,
( X1 = c_Public_Okeymode_OEncryption
| X1 = c_Public_Okeymode_OSignature ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
c_List_Olist_OCons(X1,c_List_Olist_OCons(X2,X3,X4),X4) != X3,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
c_List_Olist_OCons(X1,c_Public_Okeymode_OSignature,X2) = c_Public_Okeymode_OEncryption,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33])]) ).
cnf(c_0_36,plain,
c_List_Olist_OCons(X1,c_Public_Okeymode_OEncryption,X2) != c_Public_Okeymode_OSignature,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_37,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_33]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV749-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 % Computer : n019.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 09:23:34 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.51 Running first-order theorem proving
% 0.26/0.51 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
% 9.16/1.80 % Version: 3.5.1
% 9.16/1.80 % Preprocessing class: FSLSSMSMSSSNFFN.
% 9.16/1.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.16/1.80 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 9.16/1.80 % Starting new_bool_3 with 300s (1) cores
% 9.16/1.80 % Starting new_bool_1 with 300s (1) cores
% 9.16/1.80 % Starting sh5l with 300s (1) cores
% 9.16/1.80 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2232453 completed with status 0
% 9.16/1.80 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 9.16/1.80 % Preprocessing class: FSLSSMSMSSSNFFN.
% 9.16/1.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.16/1.80 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 9.16/1.80 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 9.16/1.80 % No SInE strategy applied
% 9.16/1.80 % Search class: FGHSM-FSLM31-DFFFFFNN
% 9.16/1.80 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 9.16/1.80 % Starting SubtermCWHack with 136s (1) cores
% 9.16/1.80 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 9.16/1.80 % Starting C07_19_nc_SAT001_MinMin_p005000_rr with 354s (1) cores
% 9.16/1.80 % Starting U----_206c_10_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 9.16/1.80 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 9.16/1.80 % SubtermCWHack with pid 2232460 completed with status 0
% 9.16/1.80 % Result found by SubtermCWHack
% 9.16/1.80 % Preprocessing class: FSLSSMSMSSSNFFN.
% 9.16/1.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.16/1.80 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 9.16/1.80 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 9.16/1.80 % No SInE strategy applied
% 9.16/1.80 % Search class: FGHSM-FSLM31-DFFFFFNN
% 9.16/1.80 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 9.16/1.80 % Starting SubtermCWHack with 136s (1) cores
% 9.16/1.80 % Preprocessing time : 0.013 s
% 9.16/1.80
% 9.16/1.80 % Proof found!
% 9.16/1.80 % SZS status Unsatisfiable
% 9.16/1.80 % SZS output start CNFRefutation
% See solution above
% 9.16/1.80 % Parsed axioms : 692
% 9.16/1.80 % Removed by relevancy pruning/SinE : 0
% 9.16/1.80 % Initial clauses : 692
% 9.16/1.80 % Removed in clause preprocessing : 4
% 9.16/1.80 % Initial clauses in saturation : 688
% 9.16/1.80 % Processed clauses : 5336
% 9.16/1.80 % ...of these trivial : 1427
% 9.16/1.80 % ...subsumed : 1752
% 9.16/1.80 % ...remaining for further processing : 2157
% 9.16/1.80 % Other redundant clauses eliminated : 96
% 9.16/1.80 % Clauses deleted for lack of memory : 0
% 9.16/1.80 % Backward-subsumed : 39
% 9.16/1.80 % Backward-rewritten : 273
% 9.16/1.80 % Generated clauses : 53048
% 9.16/1.80 % ...of the previous two non-redundant : 36434
% 9.16/1.80 % ...aggressively subsumed : 0
% 9.16/1.80 % Contextual simplify-reflections : 0
% 9.16/1.80 % Paramodulations : 52907
% 9.16/1.80 % Factorizations : 11
% 9.16/1.80 % NegExts : 0
% 9.16/1.80 % Equation resolutions : 130
% 9.16/1.80 % Disequality decompositions : 0
% 9.16/1.80 % Total rewrite steps : 38260
% 9.16/1.80 % ...of those cached : 32537
% 9.16/1.80 % Propositional unsat checks : 0
% 9.16/1.80 % Propositional check models : 0
% 9.16/1.80 % Propositional check unsatisfiable : 0
% 9.16/1.80 % Propositional clauses : 0
% 9.16/1.80 % Propositional clauses after purity: 0
% 9.16/1.80 % Propositional unsat core size : 0
% 9.16/1.80 % Propositional preprocessing time : 0.000
% 9.16/1.80 % Propositional encoding time : 0.000
% 9.16/1.80 % Propositional solver time : 0.000
% 9.16/1.80 % Success case prop preproc time : 0.000
% 9.16/1.80 % Success case prop encoding time : 0.000
% 9.16/1.80 % Success case prop solver time : 0.000
% 9.16/1.80 % Current number of processed clauses : 1845
% 9.16/1.80 % Positive orientable unit clauses : 1021
% 9.16/1.80 % Positive unorientable unit clauses: 9
% 9.16/1.80 % Negative unit clauses : 101
% 9.16/1.80 % Non-unit-clauses : 714
% 9.16/1.80 % Current number of unprocessed clauses: 31374
% 9.16/1.80 % ...number of literals in the above : 57965
% 9.16/1.80 % Current number of archived formulas : 0
% 9.16/1.80 % Current number of archived clauses : 314
% 9.16/1.80 % Clause-clause subsumption calls (NU) : 137267
% 9.16/1.80 % Rec. Clause-clause subsumption calls : 101877
% 9.16/1.80 % Non-unit clause-clause subsumptions : 1570
% 9.16/1.80 % Unit Clause-clause subsumption calls : 9749
% 9.16/1.80 % Rewrite failures with RHS unbound : 3
% 9.16/1.80 % BW rewrite match attempts : 22255
% 9.16/1.80 % BW rewrite match successes : 294
% 9.16/1.80 % Condensation attempts : 0
% 9.16/1.80 % Condensation successes : 0
% 9.16/1.80 % Termbank termtop insertions : 753499
% 9.16/1.80 % Search garbage collected termcells : 1221
% 9.16/1.80
% 9.16/1.80 % -------------------------------------------------
% 9.16/1.80 % User time : 1.135 s
% 9.16/1.80 % System time : 0.058 s
% 9.16/1.80 % Total time : 1.193 s
% 9.16/1.80 % Maximum resident set size: 4964 pages
% 9.16/1.80
% 9.16/1.80 % -------------------------------------------------
% 9.16/1.80 % User time : 5.516 s
% 9.16/1.80 % System time : 0.273 s
% 9.16/1.80 % Total time : 5.789 s
% 9.16/1.80 % Maximum resident set size: 5376 pages
% 9.16/1.80 % E exiting
%------------------------------------------------------------------------------