%------------------------------------------------------------------------------
% File : E-SAT---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 : n007.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 02:18:32 PM UTC 2026
% Result : Theorem 0.14s 0.47s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 7 unt; 0 def)
% Number of atoms : 111 ( 7 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 129 ( 44 ~; 56 |; 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 : 63 ( 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,
! [X27,X28,X29,X30,X31,X32] :
( ( total_order(X31,X32)
| ~ order(X31,X32)
| ~ apply(X31,esk7_2(X31,X32),esk6_2(X31,X32)) )
& ( total_order(X31,X32)
| ~ order(X31,X32)
| ~ apply(X31,esk6_2(X31,X32),esk7_2(X31,X32)) )
& ( total_order(X31,X32)
| ~ order(X31,X32)
| member(esk7_2(X31,X32),X32) )
& ( total_order(X31,X32)
| ~ order(X31,X32)
| member(esk6_2(X31,X32),X32) )
& ( ~ total_order(X27,X28)
| apply(X27,X30,X29)
| apply(X27,X29,X30)
| ~ member(X30,X28)
| ~ member(X29,X28) )
& ( ~ total_order(X27,X28)
| order(X27,X28) ) ),
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(esk3_0,esk1_0,esk2_0)
& min(esk3_0,esk1_0,esk2_0)
& total_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,
! [X19,X20,X21,X22,X23,X24,X25] :
( ( min(X25,X23,X24)
| ~ member(X25,X24)
| X25 != esk5_3(X23,X24,X25) )
& ( min(X25,X23,X24)
| ~ member(X25,X24)
| apply(X23,esk5_3(X23,X24,X25),X25) )
& ( min(X25,X23,X24)
| ~ member(X25,X24)
| member(esk5_3(X23,X24,X25),X24) )
& ( ~ min(X21,X19,X20)
| X21 = X22
| ~ apply(X19,X22,X21)
| ~ member(X22,X20) )
& ( ~ min(X21,X19,X20)
| member(X21,X20) ) ),
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(esk1_0,esk2_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(esk3_0,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
( ~ member(X2,esk2_0)
| ~ member(X1,esk2_0)
| apply(esk1_0,X2,X1)
| apply(esk1_0,X1,X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,negated_conjecture,
member(esk3_0,esk2_0),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
fof(c_0_14,plain,
! [X11,X12,X13,X14,X15,X16,X17] :
( ( least(X17,X15,X16)
| ~ member(X17,X16)
| ~ apply(X15,X17,esk4_3(X15,X16,X17)) )
& ( least(X17,X15,X16)
| ~ member(X17,X16)
| member(esk4_3(X15,X16,X17),X16) )
& ( ~ least(X13,X11,X12)
| apply(X11,X13,X14)
| ~ member(X14,X12) )
& ( ~ least(X13,X11,X12)
| member(X13,X12) ) ),
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_15,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_16,negated_conjecture,
( ~ member(X1,esk2_0)
| apply(esk1_0,esk3_0,X1)
| apply(esk1_0,X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( ~ member(X3,X2)
| least(X3,X1,X2)
| member(esk4_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( ~ member(X1,esk2_0)
| ~ apply(esk1_0,X1,esk3_0)
| X1 = esk3_0 ),
inference(spm,[status(thm)],[c_0_15,c_0_11]) ).
cnf(c_0_19,negated_conjecture,
( ~ member(X1,esk2_0)
| apply(esk1_0,esk4_3(X2,esk2_0,X1),esk3_0)
| apply(esk1_0,esk3_0,esk4_3(X2,esk2_0,X1))
| least(X1,X2,esk2_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
( ~ member(X2,X3)
| ~ apply(X1,X2,esk4_3(X1,X3,X2))
| least(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,negated_conjecture,
( ~ member(X2,esk2_0)
| apply(esk1_0,esk3_0,esk4_3(X1,esk2_0,X2))
| least(X2,X1,esk2_0)
| esk4_3(X1,esk2_0,X2) = esk3_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_17]) ).
cnf(c_0_22,negated_conjecture,
~ least(esk3_0,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_23,negated_conjecture,
esk4_3(esk1_0,esk2_0,esk3_0) = esk3_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_13])]),c_0_22]) ).
cnf(c_0_24,negated_conjecture,
apply(esk1_0,esk3_0,esk3_0),
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_25,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_23]),c_0_24]),c_0_13])]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET794+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.37 % Computer : n007.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8046.5625MB
% 0.14/0.37 % OS : Linux 6.8.0-71-generic
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Mon Sep 21 05:36:35 UTC 2026
% 0.14/0.38 % CPUTime :
% 0.14/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 0.14/0.47 % Version: 3.5.1
% 0.14/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.47 % Starting sh5l with 300s (1) cores
% 0.14/0.47 % new_bool_1 with pid 283027 completed with status 0
% 0.14/0.47 % Result found by new_bool_1
% 0.14/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.47 % Search class: FGUSF-FFLF32-SFFFFFNN
% 0.14/0.47 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.47 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.47 % SubtermCWHack with pid 283035 completed with status 0
% 0.14/0.47 % Result found by SubtermCWHack
% 0.14/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.47 % Search class: FGUSF-FFLF32-SFFFFFNN
% 0.14/0.47 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.47 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.47 % Preprocessing time : 0.002 s
% 0.14/0.47
% 0.14/0.47 % Proof found!
% 0.14/0.47 % SZS status Theorem
% 0.14/0.47 % SZS output start CNFRefutation
% See solution above
% 0.14/0.47 % Parsed axioms : 11
% 0.14/0.47 % Removed by relevancy pruning/SinE : 6
% 0.14/0.47 % Initial clauses : 83
% 0.14/0.47 % Removed in clause preprocessing : 0
% 0.14/0.47 % Initial clauses in saturation : 83
% 0.14/0.47 % Processed clauses : 118
% 0.14/0.47 % ...of these trivial : 0
% 0.14/0.47 % ...subsumed : 4
% 0.14/0.47 % ...remaining for further processing : 114
% 0.14/0.47 % Other redundant clauses eliminated : 0
% 0.14/0.47 % Clauses deleted for lack of memory : 0
% 0.14/0.47 % Backward-subsumed : 0
% 0.14/0.47 % Backward-rewritten : 0
% 0.14/0.47 % Generated clauses : 258
% 0.14/0.47 % ...of the previous two non-redundant : 187
% 0.14/0.47 % ...aggressively subsumed : 0
% 0.14/0.47 % Contextual simplify-reflections : 5
% 0.14/0.47 % Paramodulations : 258
% 0.14/0.47 % Factorizations : 0
% 0.14/0.47 % NegExts : 0
% 0.14/0.47 % Equation resolutions : 0
% 0.14/0.47 % Disequality decompositions : 0
% 0.14/0.47 % Total rewrite steps : 61
% 0.14/0.47 % ...of those cached : 57
% 0.14/0.47 % Propositional unsat checks : 0
% 0.14/0.47 % Propositional check models : 0
% 0.14/0.47 % Propositional check unsatisfiable : 0
% 0.14/0.47 % Propositional clauses : 0
% 0.14/0.47 % Propositional clauses after purity: 0
% 0.14/0.47 % Propositional unsat core size : 0
% 0.14/0.47 % Propositional preprocessing time : 0.000
% 0.14/0.47 % Propositional encoding time : 0.000
% 0.14/0.47 % Propositional solver time : 0.000
% 0.14/0.47 % Success case prop preproc time : 0.000
% 0.14/0.47 % Success case prop encoding time : 0.000
% 0.14/0.47 % Success case prop solver time : 0.000
% 0.14/0.47 % Current number of processed clauses : 114
% 0.14/0.47 % Positive orientable unit clauses : 6
% 0.14/0.47 % Positive unorientable unit clauses: 0
% 0.14/0.47 % Negative unit clauses : 1
% 0.14/0.47 % Non-unit-clauses : 107
% 0.14/0.47 % Current number of unprocessed clauses: 152
% 0.14/0.47 % ...number of literals in the above : 1128
% 0.14/0.47 % Current number of archived formulas : 0
% 0.14/0.47 % Current number of archived clauses : 0
% 0.14/0.47 % Clause-clause subsumption calls (NU) : 2661
% 0.14/0.47 % Rec. Clause-clause subsumption calls : 1034
% 0.14/0.47 % Non-unit clause-clause subsumptions : 9
% 0.14/0.47 % Unit Clause-clause subsumption calls : 120
% 0.14/0.47 % Rewrite failures with RHS unbound : 0
% 0.14/0.47 % BW rewrite match attempts : 1
% 0.14/0.47 % BW rewrite match successes : 0
% 0.14/0.47 % Condensation attempts : 0
% 0.14/0.47 % Condensation successes : 0
% 0.14/0.47 % Termbank termtop insertions : 12029
% 0.14/0.47 % Search garbage collected termcells : 1039
% 0.14/0.47
% 0.14/0.47 % -------------------------------------------------
% 0.14/0.47 % User time : 0.019 s
% 0.14/0.47 % System time : 0.003 s
% 0.14/0.47 % Total time : 0.021 s
% 0.14/0.47 % Maximum resident set size: 3396 pages
% 0.14/0.47
% 0.14/0.47 % -------------------------------------------------
% 0.14/0.47 % User time : 0.020 s
% 0.14/0.47 % System time : 0.008 s
% 0.14/0.47 % Total time : 0.028 s
% 0.14/0.47 % Maximum resident set size: 4864 pages
% 0.14/0.47 % E exiting
%------------------------------------------------------------------------------