%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SCT171_1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 02:08:02 PM UTC 2026
% Result : Theorem 0.31s 0.48s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 3 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 20 ( 19 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 26 ( 26 usr; 13 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
fun_fu383145951l_bool: $tType ).
tff(decl_sort2,type,
fun_fu193278215t_bool: $tType ).
tff(decl_sort3,type,
fun_fu1760369922t_bool: $tType ).
tff(decl_sort4,type,
fun_bo292969573t_bool: $tType ).
tff(decl_sort5,type,
fun_Ar1871347069i_bool: $tType ).
tff(decl_sort6,type,
fun_Ar2100459655t_bool: $tType ).
tff(decl_sort7,type,
fun_nat_fun_nat_bool: $tType ).
tff(decl_sort8,type,
fun_Ar2035712896di_nat: $tType ).
tff(decl_sort9,type,
fun_Ar156616864t_bool: $tType ).
tff(decl_sort10,type,
fun_Ar2047178847t_bool: $tType ).
tff(decl_sort11,type,
fun_Ar2079322857t_bool: $tType ).
tff(decl_sort12,type,
fun_Ar1757019876t_bool: $tType ).
tff(decl_sort13,type,
arrow_1621810872le_alt: $tType ).
tff(decl_sort14,type,
nat: $tType ).
tff(decl_sort15,type,
fun_Pr1639951081t_bool: $tType ).
tff(decl_sort16,type,
fun_Ar2040671475t_bool: $tType ).
tff(decl_sort17,type,
bool: $tType ).
tff(decl_sort18,type,
produc624534567le_alt: $tType ).
tff(decl_sort19,type,
fun_fu50365883t_bool: $tType ).
tff(decl_26,type,
arrow_2009189698_above: fun_fu193278215t_bool ).
tff(decl_28,type,
arrow_1126550734_mkbot: fun_fu1760369922t_bool ).
tff(decl_29,type,
arrow_1275257820_mktop: fun_fu1760369922t_bool ).
tff(decl_31,type,
cOMBB_124649523e_indi: ( fun_Ar1871347069i_bool * fun_bo292969573t_bool ) > fun_Ar2100459655t_bool ).
tff(decl_32,type,
cOMBB_1514803447e_indi: ( fun_Ar2035712896di_nat * fun_nat_fun_nat_bool ) > fun_Ar156616864t_bool ).
tff(decl_33,type,
cOMBB_715840641e_indi: ( fun_Ar2047178847t_bool * fun_fu193278215t_bool ) > fun_Ar2079322857t_bool ).
tff(decl_34,type,
cOMBB_1932856316e_indi: ( fun_Ar2047178847t_bool * fun_fu1760369922t_bool ) > fun_Ar1757019876t_bool ).
tff(decl_35,type,
cOMBC_1994570734t_bool: ( arrow_1621810872le_alt * fun_Ar2079322857t_bool ) > fun_Ar1757019876t_bool ).
tff(decl_36,type,
cOMBC_377836265t_bool: ( arrow_1621810872le_alt * fun_Ar1757019876t_bool ) > fun_Ar2047178847t_bool ).
tff(decl_37,type,
cOMBC_998415407t_bool: ( nat * fun_Ar156616864t_bool ) > fun_Ar1871347069i_bool ).
tff(decl_62,type,
cOMBS_1833320732t_bool: ( fun_Ar2047178847t_bool * fun_Ar2100459655t_bool ) > fun_Ar2040671475t_bool ).
tff(decl_63,type,
cOMBS_1688227464t_bool: ( fun_Ar2047178847t_bool * fun_Ar2040671475t_bool ) > fun_Ar2047178847t_bool ).
tff(decl_84,type,
if_fun95824985t_bool: fun_bo292969573t_bool ).
tff(decl_86,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(decl_99,type,
produc170576535le_alt: ( arrow_1621810872le_alt * arrow_1621810872le_alt ) > produc624534567le_alt ).
tff(decl_107,type,
fequal_nat: fun_nat_fun_nat_bool ).
tff(decl_149,type,
hAPP_f718157575t_bool: ( fun_Ar2047178847t_bool * fun_fu50365883t_bool ) > fun_Pr1639951081t_bool ).
tff(decl_187,type,
hAPP_f1944886577l_bool: ( fun_Pr1639951081t_bool * fun_fu383145951l_bool ) > bool ).
tff(decl_201,type,
hBOOL: bool > $o ).
tff(decl_221,type,
member1484933012le_alt: produc624534567le_alt > fun_fu383145951l_bool ).
tff(decl_222,type,
f: fun_fu50365883t_bool ).
tff(decl_225,type,
p: fun_Ar2047178847t_bool ).
tff(decl_228,type,
c: arrow_1621810872le_alt ).
tff(decl_229,type,
d: arrow_1621810872le_alt ).
tff(decl_230,type,
e: arrow_1621810872le_alt ).
tff(decl_231,type,
h: fun_Ar2035712896di_nat ).
tff(decl_232,type,
n: nat ).
tff(conj_0,conjecture,
hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(fact_14_PW,axiom,
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e)))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_PW) ).
tff(fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).
tff(c_0_3,negated_conjecture,
~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p))),
inference(assume_negation,[status(cth)],[conj_0]) ).
tff(c_0_4,negated_conjecture,
~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p))),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
tff(c_0_5,plain,
( ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p)))
| ~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e)))))) )
& ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e))))))
| ~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p))) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_14_PW])]) ).
tff(c_0_6,negated_conjecture,
~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p))),
inference(fof_nnf,[status(thm)],[c_0_4]) ).
tcf(c_0_7,plain,
( ~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e))))))
| hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
tcf(c_0_8,plain,
hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(ord_less_nat,h),n)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1275257820_mktop,p),e)),cOMBS_1688227464t_bool(cOMBS_1833320732t_bool(cOMBB_124649523e_indi(if_fun95824985t_bool,cOMBC_998415407t_bool(cOMBB_1514803447e_indi(fequal_nat,h),n)),cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_2009189698_above,p),c),e)),cOMBC_377836265t_bool(cOMBB_1932856316e_indi(arrow_1126550734_mkbot,p),e)))))),
inference(split_conjunct,[status(thm)],[fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto]) ).
tcf(c_0_9,negated_conjecture,
~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(c,d)),hAPP_f718157575t_bool(f,p))),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8])]),c_0_9]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT171_1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 04:37:23 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 0.31/0.48 % Version: 3.5.1
% 0.31/0.48 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.31/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/0.48 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.31/0.48 % Starting new_bool_3 with 600s (2) cores
% 0.31/0.48 % Starting new_bool_1 with 300s (1) cores
% 0.31/0.48 % Starting sh5l with 300s (1) cores
% 0.31/0.48 % new_bool_3 with pid 4144418 completed with status 0
% 0.31/0.48 % Result found by new_bool_3
% 0.31/0.48 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.31/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/0.48 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.31/0.48 % Starting new_bool_3 with 600s (2) cores
% 0.31/0.48 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.31/0.48 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.31/0.48 % Search class: FGHSS-FSLM32-DFFFFFNN
% 0.31/0.48 % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 0.31/0.48 % Starting SubtermCWHack with 61s (1) cores
% 0.31/0.48 % Starting SAT001_MinMin_p005000_rr_RG with 361s (1) cores
% 0.31/0.48 % SAT001_MinMin_p005000_rr_RG with pid 4144425 completed with status 0
% 0.31/0.48 % Result found by SAT001_MinMin_p005000_rr_RG
% 0.31/0.48 % Preprocessing class: FSLMSMSMSSSNFFN.
% 0.31/0.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/0.48 % Starting G-E--_207_C18_F1_AE_CS_SP_PI_PS_S2S with 1200s (4) cores
% 0.31/0.48 % Starting new_bool_3 with 600s (2) cores
% 0.31/0.48 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.31/0.48 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.31/0.48 % Search class: FGHSS-FSLM32-DFFFFFNN
% 0.31/0.48 % Scheduled 5 strats onto 2 cores with 600 seconds (600 total)
% 0.31/0.48 % Starting SubtermCWHack with 61s (1) cores
% 0.31/0.48 % Starting SAT001_MinMin_p005000_rr_RG with 361s (1) cores
% 0.31/0.48 % Preprocessing time : 0.005 s
% 0.31/0.48 % Presaturation interreduction done
% 0.31/0.48
% 0.31/0.48 % Proof found!
% 0.31/0.48 % SZS status Theorem
% 0.31/0.48 % SZS output start CNFRefutation
% See solution above
% 0.31/0.48 % Parsed axioms : 558
% 0.31/0.48 % Removed by relevancy pruning/SinE : 474
% 0.31/0.48 % Initial clauses : 175
% 0.31/0.48 % Removed in clause preprocessing : 35
% 0.31/0.48 % Initial clauses in saturation : 140
% 0.31/0.48 % Processed clauses : 145
% 0.31/0.48 % ...of these trivial : 1
% 0.31/0.48 % ...subsumed : 49
% 0.31/0.48 % ...remaining for further processing : 94
% 0.31/0.48 % Other redundant clauses eliminated : 21
% 0.31/0.48 % Clauses deleted for lack of memory : 0
% 0.31/0.48 % Backward-subsumed : 0
% 0.31/0.48 % Backward-rewritten : 0
% 0.31/0.48 % Generated clauses : 19
% 0.31/0.48 % ...of the previous two non-redundant : 19
% 0.31/0.48 % ...aggressively subsumed : 0
% 0.31/0.48 % Contextual simplify-reflections : 0
% 0.31/0.48 % Paramodulations : 0
% 0.31/0.48 % Factorizations : 0
% 0.31/0.48 % NegExts : 0
% 0.31/0.48 % Equation resolutions : 21
% 0.31/0.48 % Disequality decompositions : 0
% 0.31/0.48 % Total rewrite steps : 2
% 0.31/0.48 % ...of those cached : 0
% 0.31/0.48 % Propositional unsat checks : 0
% 0.31/0.48 % Propositional check models : 0
% 0.31/0.48 % Propositional check unsatisfiable : 0
% 0.31/0.48 % Propositional clauses : 0
% 0.31/0.48 % Propositional clauses after purity: 0
% 0.31/0.48 % Propositional unsat core size : 0
% 0.31/0.48 % Propositional preprocessing time : 0.000
% 0.31/0.48 % Propositional encoding time : 0.000
% 0.31/0.48 % Propositional solver time : 0.000
% 0.31/0.48 % Success case prop preproc time : 0.000
% 0.31/0.48 % Success case prop encoding time : 0.000
% 0.31/0.48 % Success case prop solver time : 0.000
% 0.31/0.48 % Current number of processed clauses : 75
% 0.31/0.48 % Positive orientable unit clauses : 7
% 0.31/0.48 % Positive unorientable unit clauses: 0
% 0.31/0.48 % Negative unit clauses : 7
% 0.31/0.48 % Non-unit-clauses : 61
% 0.31/0.48 % Current number of unprocessed clauses: 14
% 0.31/0.48 % ...number of literals in the above : 105
% 0.31/0.48 % Current number of archived formulas : 0
% 0.31/0.48 % Current number of archived clauses : 0
% 0.31/0.48 % Clause-clause subsumption calls (NU) : 1792
% 0.31/0.48 % Rec. Clause-clause subsumption calls : 708
% 0.31/0.48 % Non-unit clause-clause subsumptions : 30
% 0.31/0.48 % Unit Clause-clause subsumption calls : 2
% 0.31/0.48 % Rewrite failures with RHS unbound : 0
% 0.31/0.48 % BW rewrite match attempts : 12
% 0.31/0.48 % BW rewrite match successes : 0
% 0.31/0.48 % Condensation attempts : 0
% 0.31/0.48 % Condensation successes : 0
% 0.31/0.48 % Termbank termtop insertions : 22379
% 0.31/0.48 % Search garbage collected termcells : 4524
% 0.31/0.48
% 0.31/0.48 % -------------------------------------------------
% 0.31/0.48 % User time : 0.016 s
% 0.31/0.48 % System time : 0.006 s
% 0.31/0.48 % Total time : 0.022 s
% 0.31/0.48 % Maximum resident set size: 5244 pages
% 0.31/0.48
% 0.31/0.48 % -------------------------------------------------
% 0.31/0.48 % User time : 0.042 s
% 0.31/0.48 % System time : 0.015 s
% 0.31/0.48 % Total time : 0.057 s
% 0.31/0.48 % Maximum resident set size: 5376 pages
% 0.31/0.48 % E exiting
%------------------------------------------------------------------------------