%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET794+4 : 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 : n014.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 02:15:24 PM UTC 2026
% Result : Theorem 0.13s 0.51s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 7 unt; 0 def)
% Number of atoms : 111 ( 7 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 126 ( 42 ~; 55 |; 21 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 62 ( 1 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIV6,conjecture,
! [X1,X2,X6] :
( ( min(X6,X1,X2)
& total_order(X1,X2) )
=> least(X6,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV6) ).
fof(total_order,axiom,
! [X1,X2] :
( total_order(X1,X2)
<=> ( ! [X3,X4] :
( ( member(X4,X2)
& member(X3,X2) )
=> ( apply(X1,X4,X3)
| apply(X1,X3,X4) ) )
& order(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',total_order) ).
fof(min,axiom,
! [X1,X2,X6] :
( min(X6,X1,X2)
<=> ( ! [X3] :
( ( apply(X1,X3,X6)
& member(X3,X2) )
=> X6 = X3 )
& member(X6,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',min) ).
fof(least,axiom,
! [X1,X2,X6] :
( least(X6,X1,X2)
<=> ( ! [X3] :
( member(X3,X2)
=> apply(X1,X6,X3) )
& member(X6,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',least) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X6] :
( ( min(X6,X1,X2)
& total_order(X1,X2) )
=> least(X6,X1,X2) ),
inference(assume_negation,[status(cth)],[thIV6]) ).
fof(c_0_5,plain,
! [X10,X11,X12,X13,X14,X15] :
( ( total_order(X14,X15)
| ~ order(X14,X15)
| ~ apply(X14,esk2_2(X14,X15),esk1_2(X14,X15)) )
& ( total_order(X14,X15)
| ~ order(X14,X15)
| ~ apply(X14,esk1_2(X14,X15),esk2_2(X14,X15)) )
& ( total_order(X14,X15)
| ~ order(X14,X15)
| member(esk2_2(X14,X15),X15) )
& ( total_order(X14,X15)
| ~ order(X14,X15)
| member(esk1_2(X14,X15),X15) )
& ( ~ total_order(X10,X11)
| apply(X10,X13,X12)
| apply(X10,X12,X13)
| ~ member(X13,X11)
| ~ member(X12,X11) )
& ( ~ total_order(X10,X11)
| order(X10,X11) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[total_order])])])])])])]) ).
fof(c_0_6,negated_conjecture,
( ~ least(esk13_0,esk11_0,esk12_0)
& min(esk13_0,esk11_0,esk12_0)
& total_order(esk11_0,esk12_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_7,plain,
! [X58,X59,X60,X61,X62,X63,X64] :
( ( min(X64,X62,X63)
| ~ member(X64,X63)
| X64 != esk8_3(X62,X63,X64) )
& ( min(X64,X62,X63)
| ~ member(X64,X63)
| apply(X62,esk8_3(X62,X63,X64),X64) )
& ( min(X64,X62,X63)
| ~ member(X64,X63)
| member(esk8_3(X62,X63,X64),X63) )
& ( ~ min(X60,X58,X59)
| X60 = X61
| ~ apply(X58,X61,X60)
| ~ member(X61,X59) )
& ( ~ min(X60,X58,X59)
| member(X60,X59) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[min])])])])])])]) ).
cnf(c_0_8,plain,
( ~ total_order(X4,X2)
| ~ member(X3,X2)
| ~ member(X1,X2)
| apply(X4,X3,X1)
| apply(X4,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
total_order(esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ min(X1,X3,X2)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
min(esk13_0,esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_12,plain,
! [X42,X43,X44,X45,X46,X47,X48] :
( ( least(X48,X46,X47)
| ~ member(X48,X47)
| ~ apply(X46,X48,esk6_3(X46,X47,X48)) )
& ( least(X48,X46,X47)
| ~ member(X48,X47)
| member(esk6_3(X46,X47,X48),X47) )
& ( ~ least(X44,X42,X43)
| apply(X42,X44,X45)
| ~ member(X45,X43) )
& ( ~ least(X44,X42,X43)
| member(X44,X43) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[least])])])])])])]) ).
cnf(c_0_13,negated_conjecture,
( ~ member(X1,esk12_0)
| ~ member(X2,esk12_0)
| apply(esk11_0,X2,X1)
| apply(esk11_0,X1,X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,negated_conjecture,
member(esk13_0,esk12_0),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( ~ member(X3,X2)
| least(X3,X1,X2)
| member(esk6_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( ~ min(X4,X3,X2)
| ~ apply(X3,X1,X4)
| ~ member(X1,X2)
| X4 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,negated_conjecture,
( ~ member(X1,esk12_0)
| apply(esk11_0,X1,esk13_0)
| apply(esk11_0,esk13_0,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( member(esk6_3(X1,esk12_0,esk13_0),esk12_0)
| least(esk13_0,X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( ~ member(X1,esk12_0)
| ~ apply(esk11_0,X1,esk13_0)
| X1 = esk13_0 ),
inference(spm,[status(thm)],[c_0_16,c_0_11]) ).
cnf(c_0_20,negated_conjecture,
( apply(esk11_0,esk13_0,esk6_3(X1,esk12_0,esk13_0))
| apply(esk11_0,esk6_3(X1,esk12_0,esk13_0),esk13_0)
| least(esk13_0,X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
( ~ member(X2,X3)
| ~ apply(X1,X2,esk6_3(X1,X3,X2))
| least(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,negated_conjecture,
( apply(esk11_0,esk13_0,esk6_3(X1,esk12_0,esk13_0))
| least(esk13_0,X1,esk12_0)
| esk6_3(X1,esk12_0,esk13_0) = esk13_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_18]) ).
cnf(c_0_23,negated_conjecture,
~ least(esk13_0,esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,negated_conjecture,
esk6_3(esk11_0,esk12_0,esk13_0) = esk13_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_14])]),c_0_23]) ).
cnf(c_0_25,negated_conjecture,
apply(esk11_0,esk13_0,esk13_0),
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_24]),c_0_25]),c_0_14])]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET794+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:38:34 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 0.13/0.51 % Version: 3.5.1
% 0.13/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.51 % Starting sh5l with 300s (1) cores
% 0.13/0.51 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3246327 completed with status 0
% 0.13/0.51 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.51 % No SInE strategy applied
% 0.13/0.51 % Search class: FGUSF-FFLF32-SFFFFFNN
% 0.13/0.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.51 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.13/0.51 % Starting new_bool_3 with 136s (1) cores
% 0.13/0.51 % Starting new_bool_1 with 136s (1) cores
% 0.13/0.51 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3246335 completed with status 0
% 0.13/0.51 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.13/0.51 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.13/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.13/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.13/0.51 % No SInE strategy applied
% 0.13/0.51 % Search class: FGUSF-FFLF32-SFFFFFNN
% 0.13/0.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.13/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.13/0.51 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.13/0.51 % Preprocessing time : 0.002 s
% 0.13/0.51 % Presaturation interreduction done
% 0.13/0.51
% 0.13/0.51 % Proof found!
% 0.13/0.51 % SZS status Theorem
% 0.13/0.51 % SZS output start CNFRefutation
% See solution above
% 0.13/0.51 % Parsed axioms : 11
% 0.13/0.51 % Removed by relevancy pruning/SinE : 0
% 0.13/0.51 % Initial clauses : 110
% 0.13/0.51 % Removed in clause preprocessing : 0
% 0.13/0.51 % Initial clauses in saturation : 110
% 0.13/0.51 % Processed clauses : 202
% 0.13/0.51 % ...of these trivial : 0
% 0.13/0.51 % ...subsumed : 0
% 0.13/0.51 % ...remaining for further processing : 202
% 0.13/0.51 % Other redundant clauses eliminated : 0
% 0.13/0.51 % Clauses deleted for lack of memory : 0
% 0.13/0.51 % Backward-subsumed : 0
% 0.13/0.51 % Backward-rewritten : 0
% 0.13/0.51 % Generated clauses : 179
% 0.13/0.51 % ...of the previous two non-redundant : 165
% 0.13/0.51 % ...aggressively subsumed : 0
% 0.13/0.51 % Contextual simplify-reflections : 2
% 0.13/0.51 % Paramodulations : 179
% 0.13/0.51 % Factorizations : 0
% 0.13/0.51 % NegExts : 0
% 0.13/0.51 % Equation resolutions : 0
% 0.13/0.51 % Disequality decompositions : 0
% 0.13/0.51 % Total rewrite steps : 6
% 0.13/0.51 % ...of those cached : 2
% 0.13/0.51 % Propositional unsat checks : 0
% 0.13/0.51 % Propositional check models : 0
% 0.13/0.51 % Propositional check unsatisfiable : 0
% 0.13/0.51 % Propositional clauses : 0
% 0.13/0.51 % Propositional clauses after purity: 0
% 0.13/0.51 % Propositional unsat core size : 0
% 0.13/0.51 % Propositional preprocessing time : 0.000
% 0.13/0.51 % Propositional encoding time : 0.000
% 0.13/0.51 % Propositional solver time : 0.000
% 0.13/0.51 % Success case prop preproc time : 0.000
% 0.13/0.51 % Success case prop encoding time : 0.000
% 0.13/0.51 % Success case prop solver time : 0.000
% 0.13/0.51 % Current number of processed clauses : 92
% 0.13/0.51 % Positive orientable unit clauses : 6
% 0.13/0.51 % Positive unorientable unit clauses: 0
% 0.13/0.51 % Negative unit clauses : 1
% 0.13/0.51 % Non-unit-clauses : 85
% 0.13/0.51 % Current number of unprocessed clauses: 183
% 0.13/0.51 % ...number of literals in the above : 753
% 0.13/0.51 % Current number of archived formulas : 0
% 0.13/0.51 % Current number of archived clauses : 110
% 0.13/0.51 % Clause-clause subsumption calls (NU) : 5586
% 0.13/0.51 % Rec. Clause-clause subsumption calls : 2760
% 0.13/0.51 % Non-unit clause-clause subsumptions : 2
% 0.13/0.51 % Unit Clause-clause subsumption calls : 71
% 0.13/0.51 % Rewrite failures with RHS unbound : 0
% 0.13/0.51 % BW rewrite match attempts : 1
% 0.13/0.51 % BW rewrite match successes : 0
% 0.13/0.51 % Condensation attempts : 0
% 0.13/0.51 % Condensation successes : 0
% 0.13/0.51 % Termbank termtop insertions : 11898
% 0.13/0.51 % Search garbage collected termcells : 1655
% 0.13/0.51
% 0.13/0.51 % -------------------------------------------------
% 0.13/0.51 % User time : 0.027 s
% 0.13/0.51 % System time : 0.004 s
% 0.13/0.51 % Total time : 0.031 s
% 0.13/0.51 % Maximum resident set size: 3908 pages
% 0.13/0.51
% 0.13/0.51 % -------------------------------------------------
% 0.13/0.51 % User time : 0.063 s
% 0.13/0.51 % System time : 0.023 s
% 0.13/0.51 % Total time : 0.086 s
% 0.13/0.51 % Maximum resident set size: 4608 pages
% 0.13/0.51 % E exiting
%------------------------------------------------------------------------------