%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV409+1 : TPTP v9.3.1. Released v3.3.0.
% 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 02:54:40 PM UTC 2026
% Result : Theorem 0.11s 0.50s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 5 unt; 0 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 115 ( 46 ~; 45 |; 17 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 71 ( 0 sgn 37 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(stricly_smaller_definition,axiom,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( ~ less_than(X2,X1)
& less_than(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).
fof(l45_co,conjecture,
! [X1,X2,X3] :
( ( strictly_less_than(X2,X3)
& contains_slb(X1,X2) )
=> ( ? [X4] :
( less_than(X3,X4)
& pair_in_list(update_slb(X1,X3),X2,X4) )
| pair_in_list(update_slb(X1,X3),X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_co) ).
fof(l45_l48,lemma,
! [X1,X2,X3,X4] :
( ( strictly_less_than(X3,X4)
& strictly_less_than(X2,X4)
& pair_in_list(X1,X2,X3) )
=> pair_in_list(update_slb(X1,X4),X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_l48) ).
fof(l45_li4647,lemma,
! [X1,X2] :
( contains_slb(X1,X2)
=> ? [X3] : pair_in_list(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_li4647) ).
fof(totality,axiom,
! [X1,X2] :
( less_than(X2,X1)
| less_than(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',totality) ).
fof(l45_l49,lemma,
! [X1,X2,X3,X4] :
( ( less_than(X4,X3)
& strictly_less_than(X2,X4)
& pair_in_list(X1,X2,X3) )
=> ? [X5] :
( less_than(X4,X5)
& pair_in_list(update_slb(X1,X4),X2,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_l49) ).
fof(c_0_6,plain,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( ~ less_than(X2,X1)
& less_than(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[stricly_smaller_definition]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3] :
( ( strictly_less_than(X2,X3)
& contains_slb(X1,X2) )
=> ( ? [X4] :
( less_than(X3,X4)
& pair_in_list(update_slb(X1,X3),X2,X4) )
| pair_in_list(update_slb(X1,X3),X2,X3) ) ),
inference(assume_negation,[status(cth)],[l45_co]) ).
fof(c_0_8,lemma,
! [X56,X57,X58,X59] :
( pair_in_list(update_slb(X56,X59),X57,X59)
| ~ strictly_less_than(X58,X59)
| ~ strictly_less_than(X57,X59)
| ~ pair_in_list(X56,X57,X58) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l45_l48])])]) ).
fof(c_0_9,lemma,
! [X53,X54] :
( pair_in_list(X53,X54,esk1_2(X53,X54))
| ~ contains_slb(X53,X54) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l45_li4647])])])]) ).
fof(c_0_10,plain,
! [X12,X13] :
( ( strictly_less_than(X12,X13)
| less_than(X13,X12)
| ~ less_than(X12,X13) )
& ( ~ strictly_less_than(X12,X13)
| ~ less_than(X13,X12) )
& ( ~ strictly_less_than(X12,X13)
| less_than(X12,X13) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_11,plain,
! [X9,X10] :
( less_than(X10,X9)
| less_than(X9,X10) ),
inference(variable_rename,[status(thm)],[totality]) ).
fof(c_0_12,negated_conjecture,
! [X68] :
( ( ~ less_than(esk5_0,X68)
| ~ pair_in_list(update_slb(esk3_0,esk5_0),esk4_0,X68) )
& ~ pair_in_list(update_slb(esk3_0,esk5_0),esk4_0,esk5_0)
& strictly_less_than(esk4_0,esk5_0)
& contains_slb(esk3_0,esk4_0) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
fof(c_0_13,lemma,
! [X60,X61,X62,X63] :
( ( ~ less_than(X63,X62)
| ~ strictly_less_than(X61,X63)
| ~ pair_in_list(X60,X61,X62)
| less_than(X63,esk2_4(X60,X61,X62,X63)) )
& ( ~ less_than(X63,X62)
| ~ strictly_less_than(X61,X63)
| ~ pair_in_list(X60,X61,X62)
| pair_in_list(update_slb(X60,X63),X61,esk2_4(X60,X61,X62,X63)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l45_l49])])])])]) ).
cnf(c_0_14,lemma,
( ~ strictly_less_than(X3,X4)
| ~ strictly_less_than(X2,X4)
| ~ pair_in_list(X1,X2,X3)
| pair_in_list(update_slb(X1,X4),X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,lemma,
( ~ contains_slb(X1,X2)
| pair_in_list(X1,X2,esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( ~ less_than(X1,X2)
| strictly_less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( less_than(X2,X1)
| less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( ~ less_than(esk5_0,X1)
| ~ pair_in_list(update_slb(esk3_0,esk5_0),esk4_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,lemma,
( ~ less_than(X2,X4)
| ~ strictly_less_than(X3,X2)
| ~ pair_in_list(X1,X3,X4)
| pair_in_list(update_slb(X1,X2),X3,esk2_4(X1,X3,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
strictly_less_than(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,lemma,
( ~ strictly_less_than(X3,X2)
| ~ strictly_less_than(esk1_2(X1,X3),X2)
| ~ contains_slb(X1,X3)
| pair_in_list(update_slb(X1,X2),X3,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
( less_than(X2,X1)
| strictly_less_than(X1,X2) ),
inference(csr,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( ~ less_than(esk5_0,X1)
| ~ less_than(esk5_0,esk2_4(esk3_0,esk4_0,X1,esk5_0))
| ~ pair_in_list(esk3_0,esk4_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_24,lemma,
( ~ less_than(X1,X4)
| ~ strictly_less_than(X3,X1)
| ~ pair_in_list(X2,X3,X4)
| less_than(X1,esk2_4(X2,X3,X4,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_25,lemma,
( ~ strictly_less_than(X3,X2)
| ~ contains_slb(X1,X3)
| less_than(X2,esk1_2(X1,X3))
| pair_in_list(update_slb(X1,X2),X3,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
contains_slb(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,lemma,
( ~ less_than(esk5_0,X1)
| ~ pair_in_list(esk3_0,esk4_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_20])]) ).
cnf(c_0_28,negated_conjecture,
( ~ strictly_less_than(esk4_0,X1)
| less_than(X1,esk1_2(esk3_0,esk4_0))
| pair_in_list(update_slb(esk3_0,X1),esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
~ pair_in_list(update_slb(esk3_0,esk5_0),esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_30,lemma,
~ less_than(esk5_0,esk1_2(esk3_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_15]),c_0_26])]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_20]),c_0_29]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV409+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 08:45:12 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.44 Running first-order theorem proving
% 0.11/0.44 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
% 0.11/0.50 % Version: 3.5.1
% 0.11/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.50 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.50 % Starting sh5l with 300s (1) cores
% 0.11/0.50 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1355775 completed with status 0
% 0.11/0.50 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.11/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.50 % No SInE strategy applied
% 0.11/0.50 % Search class: FGHSM-FFMF32-MFFFFFNN
% 0.11/0.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.11/0.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S033I with 136s (1) cores
% 0.11/0.50 % Starting new_bool_3 with 136s (1) cores
% 0.11/0.50 % Starting new_bool_1 with 136s (1) cores
% 0.11/0.50 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1355781 completed with status 0
% 0.11/0.50 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.11/0.50 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.50 % No SInE strategy applied
% 0.11/0.50 % Search class: FGHSM-FFMF32-MFFFFFNN
% 0.11/0.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.50 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.11/0.50 % Preprocessing time : 0.002 s
% 0.11/0.50 % Presaturation interreduction done
% 0.11/0.50
% 0.11/0.50 % Proof found!
% 0.11/0.50 % SZS status Theorem
% 0.11/0.50 % SZS output start CNFRefutation
% See solution above
% 0.11/0.50 % Parsed axioms : 22
% 0.11/0.50 % Removed by relevancy pruning/SinE : 0
% 0.11/0.50 % Initial clauses : 33
% 0.11/0.50 % Removed in clause preprocessing : 0
% 0.11/0.50 % Initial clauses in saturation : 33
% 0.11/0.50 % Processed clauses : 120
% 0.11/0.50 % ...of these trivial : 0
% 0.11/0.50 % ...subsumed : 25
% 0.11/0.50 % ...remaining for further processing : 95
% 0.11/0.50 % Other redundant clauses eliminated : 3
% 0.11/0.50 % Clauses deleted for lack of memory : 0
% 0.11/0.50 % Backward-subsumed : 1
% 0.11/0.50 % Backward-rewritten : 0
% 0.11/0.50 % Generated clauses : 201
% 0.11/0.50 % ...of the previous two non-redundant : 146
% 0.11/0.50 % ...aggressively subsumed : 0
% 0.11/0.50 % Contextual simplify-reflections : 1
% 0.11/0.50 % Paramodulations : 187
% 0.11/0.50 % Factorizations : 12
% 0.11/0.50 % NegExts : 0
% 0.11/0.50 % Equation resolutions : 3
% 0.11/0.50 % Disequality decompositions : 0
% 0.11/0.50 % Total rewrite steps : 56
% 0.11/0.50 % ...of those cached : 37
% 0.11/0.50 % Propositional unsat checks : 0
% 0.11/0.50 % Propositional check models : 0
% 0.11/0.50 % Propositional check unsatisfiable : 0
% 0.11/0.50 % Propositional clauses : 0
% 0.11/0.50 % Propositional clauses after purity: 0
% 0.11/0.50 % Propositional unsat core size : 0
% 0.11/0.50 % Propositional preprocessing time : 0.000
% 0.11/0.50 % Propositional encoding time : 0.000
% 0.11/0.50 % Propositional solver time : 0.000
% 0.11/0.50 % Success case prop preproc time : 0.000
% 0.11/0.50 % Success case prop encoding time : 0.000
% 0.11/0.50 % Success case prop solver time : 0.000
% 0.11/0.50 % Current number of processed clauses : 59
% 0.11/0.50 % Positive orientable unit clauses : 11
% 0.11/0.50 % Positive unorientable unit clauses: 0
% 0.11/0.50 % Negative unit clauses : 6
% 0.11/0.50 % Non-unit-clauses : 42
% 0.11/0.50 % Current number of unprocessed clauses: 91
% 0.11/0.50 % ...number of literals in the above : 364
% 0.11/0.50 % Current number of archived formulas : 0
% 0.11/0.50 % Current number of archived clauses : 34
% 0.11/0.50 % Clause-clause subsumption calls (NU) : 574
% 0.11/0.50 % Rec. Clause-clause subsumption calls : 460
% 0.11/0.50 % Non-unit clause-clause subsumptions : 25
% 0.11/0.50 % Unit Clause-clause subsumption calls : 9
% 0.11/0.50 % Rewrite failures with RHS unbound : 0
% 0.11/0.50 % BW rewrite match attempts : 9
% 0.11/0.50 % BW rewrite match successes : 0
% 0.11/0.50 % Condensation attempts : 0
% 0.11/0.50 % Condensation successes : 0
% 0.11/0.50 % Termbank termtop insertions : 4710
% 0.11/0.50 % Search garbage collected termcells : 386
% 0.11/0.50
% 0.11/0.50 % -------------------------------------------------
% 0.11/0.50 % User time : 0.017 s
% 0.11/0.50 % System time : 0.005 s
% 0.11/0.50 % Total time : 0.022 s
% 0.11/0.50 % Maximum resident set size: 3656 pages
% 0.11/0.50
% 0.11/0.50 % -------------------------------------------------
% 0.11/0.50 % User time : 0.088 s
% 0.11/0.50 % System time : 0.020 s
% 0.11/0.50 % Total time : 0.108 s
% 0.11/0.50 % Maximum resident set size: 4608 pages
% 0.11/0.50 % E exiting
%------------------------------------------------------------------------------