%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET804+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 : 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 02:15:25 PM UTC 2026
% Result : Theorem 0.17s 5.53s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 9 unt; 0 def)
% Number of atoms : 85 ( 12 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 97 ( 37 ~; 30 |; 20 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 55 ( 2 sgn 34 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIV16,conjecture,
! [X1,X2] :
( order(X1,X2)
=> ! [X8,X9] :
( ( X8 != X9
& min(X9,X1,X2)
& min(X8,X1,X2) )
=> ~ ? [X6] : least(X6,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV16) ).
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_3,negated_conjecture,
~ ! [X1,X2] :
( order(X1,X2)
=> ! [X8,X9] :
( ( X8 != X9
& min(X9,X1,X2)
& min(X8,X1,X2) )
=> ~ ? [X6] : least(X6,X1,X2) ) ),
inference(assume_negation,[status(cth)],[thIV16]) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( order(X1,X2)
=> ! [X8,X9] :
( ( X8 != X9
& min(X9,X1,X2)
& min(X8,X1,X2) )
=> ~ ? [X6] : least(X6,X1,X2) ) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
fof(c_0_5,plain,
! [X23,X24,X25,X26,X27,X28,X29] :
( ( min(X29,X27,X28)
| ~ member(X29,X28)
| X29 != esk7_3(X27,X28,X29) )
& ( min(X29,X27,X28)
| ~ member(X29,X28)
| apply(X27,esk7_3(X27,X28,X29),X29) )
& ( min(X29,X27,X28)
| ~ member(X29,X28)
| member(esk7_3(X27,X28,X29),X28) )
& ( ~ min(X25,X23,X24)
| X25 = X26
| ~ apply(X23,X26,X25)
| ~ member(X26,X24) )
& ( ~ min(X25,X23,X24)
| member(X25,X24) ) ),
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])])])])])])]) ).
fof(c_0_6,negated_conjecture,
( least(esk5_0,esk1_0,esk2_0)
& esk3_0 != esk4_0
& min(esk4_0,esk1_0,esk2_0)
& min(esk3_0,esk1_0,esk2_0)
& order(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_7,plain,
! [X15,X16,X17,X18,X19,X20,X21] :
( ( least(X21,X19,X20)
| ~ member(X21,X20)
| ~ apply(X19,X21,esk6_3(X19,X20,X21)) )
& ( least(X21,X19,X20)
| ~ member(X21,X20)
| member(esk6_3(X19,X20,X21),X20) )
& ( ~ least(X17,X15,X16)
| apply(X15,X17,X18)
| ~ member(X18,X16) )
& ( ~ least(X17,X15,X16)
| member(X17,X16) ) ),
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_8,plain,
( ~ min(X4,X3,X2)
| ~ apply(X3,X1,X4)
| ~ member(X1,X2)
| X4 = X1 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
min(esk4_0,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( ~ least(X4,X3,X2)
| ~ member(X1,X2)
| apply(X3,X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
least(esk5_0,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( ~ least(X1,X3,X2)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( ~ min(X1,X3,X2)
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,negated_conjecture,
( ~ member(X1,esk2_0)
| ~ apply(esk1_0,X1,esk4_0)
| X1 = esk4_0 ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( ~ member(X1,esk2_0)
| apply(esk1_0,esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,negated_conjecture,
member(esk5_0,esk2_0),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_17,negated_conjecture,
member(esk4_0,esk2_0),
inference(spm,[status(thm)],[c_0_13,c_0_9]) ).
cnf(c_0_18,negated_conjecture,
min(esk3_0,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
esk5_0 = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]) ).
cnf(c_0_20,negated_conjecture,
( ~ member(X1,esk2_0)
| ~ apply(esk1_0,X1,esk3_0)
| X1 = esk3_0 ),
inference(spm,[status(thm)],[c_0_8,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
( ~ member(X1,esk2_0)
| apply(esk1_0,esk4_0,X1) ),
inference(rw,[status(thm)],[c_0_15,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
member(esk3_0,esk2_0),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
esk3_0 != esk4_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,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_20,c_0_21]),c_0_17]),c_0_22])]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET804+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/5.42 % Computer : n003.cluster.edu
% 0.14/5.42 % Model : x86_64 x86_64
% 0.14/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.42 % Memory : 8046.5625MB
% 0.14/5.42 % OS : Linux 6.8.0-71-generic
% 0.14/5.42 % CPULimit : 300
% 0.14/5.42 % WCLimit : 300
% 0.14/5.42 % DateTime : Mon Sep 21 05:40:36 UTC 2026
% 0.14/5.42 % CPUTime :
% 0.14/5.42 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/5.47 Running first-order theorem proving
% 0.14/5.47 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
% 0.17/5.53 % Version: 3.5.1
% 0.17/5.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/5.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/5.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/5.53 % Starting new_bool_3 with 300s (1) cores
% 0.17/5.53 % Starting new_bool_1 with 300s (1) cores
% 0.17/5.53 % Starting sh5l with 300s (1) cores
% 0.17/5.53 % new_bool_3 with pid 3518902 completed with status 0
% 0.17/5.53 % Result found by new_bool_3
% 0.17/5.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/5.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/5.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/5.53 % Starting new_bool_3 with 300s (1) cores
% 0.17/5.53 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/5.53 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/5.53 % Search class: FGUSF-FFLS32-SFFFFFNN
% 0.17/5.53 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/5.53 % Starting SubtermCWHack with 31s (1) cores
% 0.17/5.53 % SubtermCWHack with pid 3518909 completed with status 0
% 0.17/5.53 % Result found by SubtermCWHack
% 0.17/5.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.17/5.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/5.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.17/5.53 % Starting new_bool_3 with 300s (1) cores
% 0.17/5.53 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.17/5.53 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.17/5.53 % Search class: FGUSF-FFLS32-SFFFFFNN
% 0.17/5.53 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.17/5.53 % Starting SubtermCWHack with 31s (1) cores
% 0.17/5.53 % Preprocessing time : 0.002 s
% 0.17/5.53
% 0.17/5.53 % Proof found!
% 0.17/5.53 % SZS status Theorem
% 0.17/5.53 % SZS output start CNFRefutation
% See solution above
% 0.17/5.53 % Parsed axioms : 11
% 0.17/5.53 % Removed by relevancy pruning/SinE : 7
% 0.17/5.53 % Initial clauses : 79
% 0.17/5.53 % Removed in clause preprocessing : 0
% 0.17/5.53 % Initial clauses in saturation : 79
% 0.17/5.53 % Processed clauses : 28
% 0.17/5.53 % ...of these trivial : 0
% 0.17/5.53 % ...subsumed : 1
% 0.17/5.53 % ...remaining for further processing : 27
% 0.17/5.53 % Other redundant clauses eliminated : 0
% 0.17/5.53 % Clauses deleted for lack of memory : 0
% 0.17/5.53 % Backward-subsumed : 0
% 0.17/5.53 % Backward-rewritten : 3
% 0.17/5.53 % Generated clauses : 13
% 0.17/5.53 % ...of the previous two non-redundant : 12
% 0.17/5.53 % ...aggressively subsumed : 0
% 0.17/5.53 % Contextual simplify-reflections : 0
% 0.17/5.53 % Paramodulations : 13
% 0.17/5.53 % Factorizations : 0
% 0.17/5.53 % NegExts : 0
% 0.17/5.53 % Equation resolutions : 0
% 0.17/5.53 % Disequality decompositions : 0
% 0.17/5.53 % Total rewrite steps : 9
% 0.17/5.53 % ...of those cached : 5
% 0.17/5.53 % Propositional unsat checks : 0
% 0.17/5.53 % Propositional check models : 0
% 0.17/5.53 % Propositional check unsatisfiable : 0
% 0.17/5.53 % Propositional clauses : 0
% 0.17/5.53 % Propositional clauses after purity: 0
% 0.17/5.53 % Propositional unsat core size : 0
% 0.17/5.53 % Propositional preprocessing time : 0.000
% 0.17/5.53 % Propositional encoding time : 0.000
% 0.17/5.53 % Propositional solver time : 0.000
% 0.17/5.53 % Success case prop preproc time : 0.000
% 0.17/5.53 % Success case prop encoding time : 0.000
% 0.17/5.53 % Success case prop solver time : 0.000
% 0.17/5.53 % Current number of processed clauses : 24
% 0.17/5.53 % Positive orientable unit clauses : 8
% 0.17/5.53 % Positive unorientable unit clauses: 0
% 0.17/5.53 % Negative unit clauses : 1
% 0.17/5.53 % Non-unit-clauses : 15
% 0.17/5.53 % Current number of unprocessed clauses: 63
% 0.17/5.53 % ...number of literals in the above : 255
% 0.17/5.53 % Current number of archived formulas : 0
% 0.17/5.53 % Current number of archived clauses : 3
% 0.17/5.53 % Clause-clause subsumption calls (NU) : 82
% 0.17/5.53 % Rec. Clause-clause subsumption calls : 64
% 0.17/5.53 % Non-unit clause-clause subsumptions : 1
% 0.17/5.53 % Unit Clause-clause subsumption calls : 20
% 0.17/5.53 % Rewrite failures with RHS unbound : 0
% 0.17/5.53 % BW rewrite match attempts : 1
% 0.17/5.53 % BW rewrite match successes : 1
% 0.17/5.53 % Condensation attempts : 0
% 0.17/5.53 % Condensation successes : 0
% 0.17/5.53 % Termbank termtop insertions : 4006
% 0.17/5.53 % Search garbage collected termcells : 959
% 0.17/5.53
% 0.17/5.53 % -------------------------------------------------
% 0.17/5.53 % User time : 0.004 s
% 0.17/5.53 % System time : 0.004 s
% 0.17/5.53 % Total time : 0.008 s
% 0.17/5.53 % Maximum resident set size: 3860 pages
% 0.17/5.53
% 0.17/5.53 % -------------------------------------------------
% 0.17/5.53 % User time : 0.008 s
% 0.17/5.53 % System time : 0.006 s
% 0.17/5.53 % Total time : 0.014 s
% 0.17/5.53 % Maximum resident set size: 4864 pages
% 0.17/5.53 % E exiting
%------------------------------------------------------------------------------