%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWW209+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 03:11:44 PM UTC 2026
% Result : Theorem 1.68s 1.13s
% Output : CNFRefutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 8 unt; 0 def)
% Number of atoms : 26 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 9 ~; 4 |; 1 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 34 ( 3 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
! [X4,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X5)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X4),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_o__apply,axiom,
! [X11,X1,X2,X10,X8,X9] : hAPP(hAPP(c_Fun_Ocomp(X9,X8,X10,X2),X1),X11) = hAPP(X2,hAPP(X1,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__apply) ).
fof(fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096,axiom,
! [X4,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X5)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,X4),hAPP(v_f____,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096) ).
fof(fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096,axiom,
! [X4,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X5)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,X4),hAPP(v_ga____,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096) ).
fof(c_0_4,negated_conjecture,
~ ! [X4,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X5)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X4),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X5)) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_5,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),esk1_0),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),esk2_0))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk1_0,esk2_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_6,plain,
! [X252,X253,X254,X255,X256,X257] : hAPP(hAPP(c_Fun_Ocomp(X257,X256,X255,X254),X253),X252) = hAPP(X254,hAPP(X253,X252)),
inference(variable_rename,[status(thm)],[fact_o__apply]) ).
cnf(c_0_7,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),esk1_0),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X294,X295] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,X294),hAPP(v_f____,X295))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X294,X295) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096])])]) ).
cnf(c_0_10,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,hAPP(v_ga____,esk1_0)),hAPP(v_f____,hAPP(v_ga____,esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
cnf(c_0_11,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,X1),hAPP(v_f____,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X243,X244] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,X243),hAPP(v_ga____,X244))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X243,X244) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096])])]) ).
cnf(c_0_13,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,esk1_0),hAPP(v_ga____,esk2_0)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,X1),hAPP(v_ga____,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,negated_conjecture,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW209+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.68 % Computer : n003.cluster.edu
% 0.21/0.68 % Model : x86_64 x86_64
% 0.21/0.68 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.68 % Memory : 8046.5625MB
% 0.21/0.68 % OS : Linux 6.8.0-71-generic
% 0.21/0.68 % CPULimit : 300
% 0.21/0.68 % WCLimit : 300
% 0.21/0.68 % DateTime : Mon Sep 21 09:42:47 UTC 2026
% 0.21/0.68 % CPUTime :
% 0.21/0.68 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.74 Running first-order theorem proving
% 0.25/0.74 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
% 1.68/1.13 % Version: 3.5.1
% 1.68/1.13 % Preprocessing class: FMLMSMSMSSSNFFN.
% 1.68/1.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.68/1.13 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.68/1.13 % Starting new_bool_3 with 300s (1) cores
% 1.68/1.13 % Starting new_bool_1 with 300s (1) cores
% 1.68/1.13 % Starting sh5l with 300s (1) cores
% 1.68/1.13 % new_bool_1 with pid 3983018 completed with status 0
% 1.68/1.13 % Result found by new_bool_1
% 1.68/1.13 % Preprocessing class: FMLMSMSMSSSNFFN.
% 1.68/1.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.68/1.13 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.68/1.13 % Starting new_bool_3 with 300s (1) cores
% 1.68/1.13 % Starting new_bool_1 with 300s (1) cores
% 1.68/1.13 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.68/1.13 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.68/1.13 % Search class: FGHSM-FSLS31-DFFFFFNN
% 1.68/1.13 % partial match(1): FGHSM-FSLM31-DFFFFFNN
% 1.68/1.13 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.68/1.13 % Starting SubtermCWHack with 28s (1) cores
% 1.68/1.13 % SubtermCWHack with pid 3983020 completed with status 0
% 1.68/1.13 % Result found by SubtermCWHack
% 1.68/1.13 % Preprocessing class: FMLMSMSMSSSNFFN.
% 1.68/1.13 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.68/1.13 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.68/1.13 % Starting new_bool_3 with 300s (1) cores
% 1.68/1.13 % Starting new_bool_1 with 300s (1) cores
% 1.68/1.13 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.68/1.13 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.68/1.13 % Search class: FGHSM-FSLS31-DFFFFFNN
% 1.68/1.13 % partial match(1): FGHSM-FSLM31-DFFFFFNN
% 1.68/1.13 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.68/1.13 % Starting SubtermCWHack with 28s (1) cores
% 1.68/1.13 % Preprocessing time : 0.008 s
% 1.68/1.13
% 1.68/1.13 % Proof found!
% 1.68/1.13 % SZS status Theorem
% 1.68/1.13 % SZS output start CNFRefutation
% See solution above
% 1.68/1.13 % Parsed axioms : 1161
% 1.68/1.13 % Removed by relevancy pruning/SinE : 951
% 1.68/1.13 % Initial clauses : 304
% 1.68/1.13 % Removed in clause preprocessing : 15
% 1.68/1.13 % Initial clauses in saturation : 289
% 1.68/1.13 % Processed clauses : 2333
% 1.68/1.13 % ...of these trivial : 193
% 1.68/1.13 % ...subsumed : 1474
% 1.68/1.13 % ...remaining for further processing : 666
% 1.68/1.13 % Other redundant clauses eliminated : 128
% 1.68/1.13 % Clauses deleted for lack of memory : 0
% 1.68/1.13 % Backward-subsumed : 3
% 1.68/1.13 % Backward-rewritten : 31
% 1.68/1.13 % Generated clauses : 10445
% 1.68/1.13 % ...of the previous two non-redundant : 9151
% 1.68/1.13 % ...aggressively subsumed : 0
% 1.68/1.13 % Contextual simplify-reflections : 1
% 1.68/1.13 % Paramodulations : 10301
% 1.68/1.13 % Factorizations : 10
% 1.68/1.13 % NegExts : 0
% 1.68/1.13 % Equation resolutions : 140
% 1.68/1.13 % Disequality decompositions : 0
% 1.68/1.13 % Total rewrite steps : 2979
% 1.68/1.13 % ...of those cached : 2357
% 1.68/1.13 % Propositional unsat checks : 0
% 1.68/1.13 % Propositional check models : 0
% 1.68/1.13 % Propositional check unsatisfiable : 0
% 1.68/1.13 % Propositional clauses : 0
% 1.68/1.13 % Propositional clauses after purity: 0
% 1.68/1.13 % Propositional unsat core size : 0
% 1.68/1.13 % Propositional preprocessing time : 0.000
% 1.68/1.13 % Propositional encoding time : 0.000
% 1.68/1.13 % Propositional solver time : 0.000
% 1.68/1.13 % Success case prop preproc time : 0.000
% 1.68/1.13 % Success case prop encoding time : 0.000
% 1.68/1.13 % Success case prop solver time : 0.000
% 1.68/1.13 % Current number of processed clauses : 596
% 1.68/1.13 % Positive orientable unit clauses : 149
% 1.68/1.13 % Positive unorientable unit clauses: 7
% 1.68/1.13 % Negative unit clauses : 232
% 1.68/1.13 % Non-unit-clauses : 208
% 1.68/1.13 % Current number of unprocessed clauses: 7097
% 1.68/1.13 % ...number of literals in the above : 13796
% 1.68/1.13 % Current number of archived formulas : 0
% 1.68/1.13 % Current number of archived clauses : 34
% 1.68/1.13 % Clause-clause subsumption calls (NU) : 7934
% 1.68/1.13 % Rec. Clause-clause subsumption calls : 6332
% 1.68/1.13 % Non-unit clause-clause subsumptions : 202
% 1.68/1.13 % Unit Clause-clause subsumption calls : 3080
% 1.68/1.13 % Rewrite failures with RHS unbound : 0
% 1.68/1.13 % BW rewrite match attempts : 9728
% 1.68/1.13 % BW rewrite match successes : 37
% 1.68/1.13 % Condensation attempts : 0
% 1.68/1.13 % Condensation successes : 0
% 1.68/1.13 % Termbank termtop insertions : 161403
% 1.68/1.13 % Search garbage collected termcells : 9964
% 1.68/1.13
% 1.68/1.13 % -------------------------------------------------
% 1.68/1.13 % User time : 0.268 s
% 1.68/1.13 % System time : 0.024 s
% 1.68/1.13 % Total time : 0.292 s
% 1.68/1.13 % Maximum resident set size: 5520 pages
% 1.68/1.13
% 1.68/1.13 % -------------------------------------------------
% 1.68/1.13 % User time : 0.332 s
% 1.68/1.13 % System time : 0.033 s
% 1.68/1.13 % Total time : 0.365 s
% 1.68/1.13 % Maximum resident set size: 5888 pages
% 1.68/1.13 % E exiting
%------------------------------------------------------------------------------