%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SET795+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 : n015.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 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 9 unt; 0 def)
% Number of atoms : 404 ( 27 equ)
% Maximal formula atoms : 256 ( 10 avg)
% Number of connectives : 478 ( 112 ~; 247 |; 99 &)
% ( 6 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 77 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-4 aty)
% Number of variables : 122 ( 3 sgn 69 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(upper_bound,axiom,
! [X6,X4,X8] :
( upper_bound(X8,X6,X4)
<=> ! [X3] :
( member(X3,X4)
=> apply(X6,X3,X8) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',upper_bound) ).
fof(least_upper_bound,axiom,
! [X1,X3,X6,X4] :
( least_upper_bound(X1,X3,X6,X4)
<=> ( ! [X8] :
( ( upper_bound(X8,X6,X3)
& member(X8,X4) )
=> apply(X6,X1,X8) )
& upper_bound(X1,X6,X3)
& member(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',least_upper_bound) ).
fof(unordered_pair,axiom,
! [X3,X1,X2] :
( member(X3,unordered_pair(X1,X2))
<=> ( X3 = X2
| X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',unordered_pair) ).
fof(thIV7,conjecture,
! [X6,X4,X1,X2] :
( ( apply(X6,X1,X2)
& member(X2,X4)
& member(X1,X4)
& order(X6,X4) )
=> least_upper_bound(X2,unordered_pair(X1,X2),X6,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV7) ).
fof(order,axiom,
! [X6,X4] :
( order(X6,X4)
<=> ( ! [X3,X5,X7] :
( ( member(X7,X4)
& member(X5,X4)
& member(X3,X4) )
=> ( ( apply(X6,X5,X7)
& apply(X6,X3,X5) )
=> apply(X6,X3,X7) ) )
& ! [X3,X5] :
( ( member(X5,X4)
& member(X3,X4) )
=> ( ( apply(X6,X5,X3)
& apply(X6,X3,X5) )
=> X3 = X5 ) )
& ! [X3] :
( member(X3,X4)
=> apply(X6,X3,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',order) ).
fof(c_0_5,plain,
! [X28,X29,X30,X31,X32,X33,X34] :
( ( upper_bound(X34,X32,X33)
| ~ apply(X32,esk6_3(X32,X33,X34),X34) )
& ( upper_bound(X34,X32,X33)
| member(esk6_3(X32,X33,X34),X33) )
& ( apply(X28,X31,X30)
| ~ member(X31,X29)
| ~ upper_bound(X30,X28,X29) ) ),
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)],[upper_bound])])])])])])]) ).
fof(c_0_6,plain,
! [X13,X14,X15,X16,X17,X18,X19,X20,X21] :
( ( least_upper_bound(X18,X19,X20,X21)
| ~ upper_bound(X18,X20,X19)
| ~ member(X18,X19)
| ~ apply(X20,X18,esk5_4(X18,X19,X20,X21)) )
& ( least_upper_bound(X18,X19,X20,X21)
| ~ upper_bound(X18,X20,X19)
| ~ member(X18,X19)
| upper_bound(esk5_4(X18,X19,X20,X21),X20,X19) )
& ( least_upper_bound(X18,X19,X20,X21)
| ~ upper_bound(X18,X20,X19)
| ~ member(X18,X19)
| member(esk5_4(X18,X19,X20,X21),X21) )
& ( ~ least_upper_bound(X13,X14,X15,X16)
| apply(X15,X13,X17)
| ~ upper_bound(X17,X15,X14)
| ~ member(X17,X16) )
& ( ~ least_upper_bound(X13,X14,X15,X16)
| upper_bound(X13,X15,X14) )
& ( ~ least_upper_bound(X13,X14,X15,X16)
| member(X13,X14) ) ),
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_upper_bound])])])])])])]) ).
fof(c_0_7,plain,
! [X23,X24,X25] :
( ( member(X23,unordered_pair(X24,X25))
| X23 != X25 )
& ( member(X23,unordered_pair(X24,X25))
| X23 != X24 )
& ( X23 = X25
| X23 = X24
| ~ member(X23,unordered_pair(X24,X25)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair])])])]) ).
fof(c_0_8,plain,
! [X4,X6] :
( epred1_2(X6,X4)
<=> ( ! [X3,X5,X7] :
( ( member(X7,X4)
& member(X5,X4)
& member(X3,X4) )
=> ( ( apply(X6,X5,X7)
& apply(X6,X3,X5) )
=> apply(X6,X3,X7) ) )
& ! [X3,X5] :
( ( member(X5,X4)
& member(X3,X4) )
=> ( ( apply(X6,X5,X3)
& apply(X6,X3,X5) )
=> X3 = X5 ) )
& ! [X3] :
( member(X3,X4)
=> apply(X6,X3,X3) ) ) ),
introduced(definition) ).
fof(c_0_9,negated_conjecture,
~ ! [X6,X4,X1,X2] :
( ( apply(X6,X1,X2)
& member(X2,X4)
& member(X1,X4)
& order(X6,X4) )
=> least_upper_bound(X2,unordered_pair(X1,X2),X6,X4) ),
inference(assume_negation,[status(cth)],[thIV7]) ).
cnf(c_0_10,plain,
( ~ member(X4,X3)
| ~ upper_bound(X1,X2,X3)
| apply(X2,X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
( ~ upper_bound(X1,X3,X2)
| ~ member(X1,X2)
| least_upper_bound(X1,X2,X3,X4)
| upper_bound(esk5_4(X1,X2,X3,X4),X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( ~ member(X1,unordered_pair(X2,X3))
| X1 = X3
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( upper_bound(X3,X1,X2)
| member(esk6_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_14,axiom,
! [X6,X4] :
( order(X6,X4)
<=> epred1_2(X6,X4) ),
inference(apply_def,[status(thm)],[order,c_0_8]) ).
fof(c_0_15,negated_conjecture,
( ~ least_upper_bound(esk4_0,unordered_pair(esk3_0,esk4_0),esk1_0,esk2_0)
& apply(esk1_0,esk3_0,esk4_0)
& member(esk4_0,esk2_0)
& member(esk3_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_9])])])]) ).
cnf(c_0_16,plain,
( ~ upper_bound(X2,X1,X3)
| ~ member(X2,X3)
| ~ apply(X1,X2,esk5_4(X2,X3,X1,X4))
| least_upper_bound(X2,X3,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,plain,
( ~ member(X1,X2)
| ~ member(X5,X2)
| ~ upper_bound(X1,X3,X2)
| apply(X3,X5,esk5_4(X1,X2,X3,X4))
| least_upper_bound(X1,X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_18,plain,
( X1 != X2
| member(X1,unordered_pair(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,plain,
( ~ apply(X1,esk6_3(X1,X2,X3),X3)
| upper_bound(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_20,plain,
( upper_bound(X4,X1,unordered_pair(X2,X3))
| esk6_3(X1,unordered_pair(X2,X3),X4) = X2
| esk6_3(X1,unordered_pair(X2,X3),X4) = X3 ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_21,plain,
! [X26,X27] :
( ( order(X26,X27)
| ~ epred1_2(X26,X27) )
& ( epred1_2(X26,X27)
| ~ order(X26,X27) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
cnf(c_0_22,negated_conjecture,
~ least_upper_bound(esk4_0,unordered_pair(esk3_0,esk4_0),esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( ~ member(X1,X2)
| ~ upper_bound(X1,X3,X2)
| least_upper_bound(X1,X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
member(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( ~ apply(X1,X2,X4)
| upper_bound(X4,X1,unordered_pair(X2,X3))
| esk6_3(X1,unordered_pair(X2,X3),X4) = X3 ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_26,plain,
! [X36,X37,X38,X39,X40,X41,X42,X43,X44,X45] :
( ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| esk8_2(X44,X45) != esk9_2(X44,X45)
| ~ apply(X45,esk10_2(X44,X45),esk12_2(X44,X45)) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| esk8_2(X44,X45) != esk9_2(X44,X45)
| apply(X45,esk11_2(X44,X45),esk12_2(X44,X45)) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| esk8_2(X44,X45) != esk9_2(X44,X45)
| apply(X45,esk10_2(X44,X45),esk11_2(X44,X45)) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| esk8_2(X44,X45) != esk9_2(X44,X45)
| member(esk12_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| esk8_2(X44,X45) != esk9_2(X44,X45)
| member(esk11_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| esk8_2(X44,X45) != esk9_2(X44,X45)
| member(esk10_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| apply(X45,esk9_2(X44,X45),esk8_2(X44,X45))
| ~ apply(X45,esk10_2(X44,X45),esk12_2(X44,X45)) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| apply(X45,esk9_2(X44,X45),esk8_2(X44,X45))
| apply(X45,esk11_2(X44,X45),esk12_2(X44,X45)) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| apply(X45,esk9_2(X44,X45),esk8_2(X44,X45))
| apply(X45,esk10_2(X44,X45),esk11_2(X44,X45)) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| apply(X45,esk9_2(X44,X45),esk8_2(X44,X45))
| member(esk12_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| apply(X45,esk9_2(X44,X45),esk8_2(X44,X45))
| member(esk11_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| apply(X45,esk9_2(X44,X45),esk8_2(X44,X45))
| member(esk10_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| apply(X45,esk8_2(X44,X45),esk9_2(X44,X45))
| ~ apply(X45,esk10_2(X44,X45),esk12_2(X44,X45)) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| apply(X45,esk8_2(X44,X45),esk9_2(X44,X45))
| apply(X45,esk11_2(X44,X45),esk12_2(X44,X45)) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| apply(X45,esk8_2(X44,X45),esk9_2(X44,X45))
| apply(X45,esk10_2(X44,X45),esk11_2(X44,X45)) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| apply(X45,esk8_2(X44,X45),esk9_2(X44,X45))
| member(esk12_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| apply(X45,esk8_2(X44,X45),esk9_2(X44,X45))
| member(esk11_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| apply(X45,esk8_2(X44,X45),esk9_2(X44,X45))
| member(esk10_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| member(esk9_2(X44,X45),X44)
| ~ apply(X45,esk10_2(X44,X45),esk12_2(X44,X45)) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| member(esk9_2(X44,X45),X44)
| apply(X45,esk11_2(X44,X45),esk12_2(X44,X45)) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| member(esk9_2(X44,X45),X44)
| apply(X45,esk10_2(X44,X45),esk11_2(X44,X45)) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| member(esk9_2(X44,X45),X44)
| member(esk12_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| member(esk9_2(X44,X45),X44)
| member(esk11_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| member(esk9_2(X44,X45),X44)
| member(esk10_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| member(esk8_2(X44,X45),X44)
| ~ apply(X45,esk10_2(X44,X45),esk12_2(X44,X45)) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| member(esk8_2(X44,X45),X44)
| apply(X45,esk11_2(X44,X45),esk12_2(X44,X45)) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| member(esk8_2(X44,X45),X44)
| apply(X45,esk10_2(X44,X45),esk11_2(X44,X45)) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| member(esk8_2(X44,X45),X44)
| member(esk12_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| member(esk8_2(X44,X45),X44)
| member(esk11_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| ~ apply(X45,esk7_2(X44,X45),esk7_2(X44,X45))
| member(esk8_2(X44,X45),X44)
| member(esk10_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| esk8_2(X44,X45) != esk9_2(X44,X45)
| ~ apply(X45,esk10_2(X44,X45),esk12_2(X44,X45)) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| esk8_2(X44,X45) != esk9_2(X44,X45)
| apply(X45,esk11_2(X44,X45),esk12_2(X44,X45)) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| esk8_2(X44,X45) != esk9_2(X44,X45)
| apply(X45,esk10_2(X44,X45),esk11_2(X44,X45)) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| esk8_2(X44,X45) != esk9_2(X44,X45)
| member(esk12_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| esk8_2(X44,X45) != esk9_2(X44,X45)
| member(esk11_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| esk8_2(X44,X45) != esk9_2(X44,X45)
| member(esk10_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| apply(X45,esk9_2(X44,X45),esk8_2(X44,X45))
| ~ apply(X45,esk10_2(X44,X45),esk12_2(X44,X45)) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| apply(X45,esk9_2(X44,X45),esk8_2(X44,X45))
| apply(X45,esk11_2(X44,X45),esk12_2(X44,X45)) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| apply(X45,esk9_2(X44,X45),esk8_2(X44,X45))
| apply(X45,esk10_2(X44,X45),esk11_2(X44,X45)) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| apply(X45,esk9_2(X44,X45),esk8_2(X44,X45))
| member(esk12_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| apply(X45,esk9_2(X44,X45),esk8_2(X44,X45))
| member(esk11_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| apply(X45,esk9_2(X44,X45),esk8_2(X44,X45))
| member(esk10_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| apply(X45,esk8_2(X44,X45),esk9_2(X44,X45))
| ~ apply(X45,esk10_2(X44,X45),esk12_2(X44,X45)) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| apply(X45,esk8_2(X44,X45),esk9_2(X44,X45))
| apply(X45,esk11_2(X44,X45),esk12_2(X44,X45)) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| apply(X45,esk8_2(X44,X45),esk9_2(X44,X45))
| apply(X45,esk10_2(X44,X45),esk11_2(X44,X45)) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| apply(X45,esk8_2(X44,X45),esk9_2(X44,X45))
| member(esk12_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| apply(X45,esk8_2(X44,X45),esk9_2(X44,X45))
| member(esk11_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| apply(X45,esk8_2(X44,X45),esk9_2(X44,X45))
| member(esk10_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| member(esk9_2(X44,X45),X44)
| ~ apply(X45,esk10_2(X44,X45),esk12_2(X44,X45)) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| member(esk9_2(X44,X45),X44)
| apply(X45,esk11_2(X44,X45),esk12_2(X44,X45)) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| member(esk9_2(X44,X45),X44)
| apply(X45,esk10_2(X44,X45),esk11_2(X44,X45)) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| member(esk9_2(X44,X45),X44)
| member(esk12_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| member(esk9_2(X44,X45),X44)
| member(esk11_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| member(esk9_2(X44,X45),X44)
| member(esk10_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| member(esk8_2(X44,X45),X44)
| ~ apply(X45,esk10_2(X44,X45),esk12_2(X44,X45)) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| member(esk8_2(X44,X45),X44)
| apply(X45,esk11_2(X44,X45),esk12_2(X44,X45)) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| member(esk8_2(X44,X45),X44)
| apply(X45,esk10_2(X44,X45),esk11_2(X44,X45)) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| member(esk8_2(X44,X45),X44)
| member(esk12_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| member(esk8_2(X44,X45),X44)
| member(esk11_2(X44,X45),X44) )
& ( epred1_2(X45,X44)
| member(esk7_2(X44,X45),X44)
| member(esk8_2(X44,X45),X44)
| member(esk10_2(X44,X45),X44) )
& ( ~ epred1_2(X37,X36)
| apply(X37,X41,X43)
| ~ apply(X37,X42,X43)
| ~ apply(X37,X41,X42)
| ~ member(X43,X36)
| ~ member(X42,X36)
| ~ member(X41,X36) )
& ( ~ epred1_2(X37,X36)
| X39 = X40
| ~ apply(X37,X40,X39)
| ~ apply(X37,X39,X40)
| ~ member(X40,X36)
| ~ member(X39,X36) )
& ( ~ epred1_2(X37,X36)
| apply(X37,X38,X38)
| ~ member(X38,X36) ) ),
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)],[c_0_8])])])])])])]) ).
cnf(c_0_27,plain,
( ~ order(X1,X2)
| epred1_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,negated_conjecture,
order(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_29,negated_conjecture,
~ upper_bound(esk4_0,esk1_0,unordered_pair(esk3_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_30,plain,
( ~ apply(X2,X3,X1)
| ~ apply(X2,X4,X1)
| upper_bound(X1,X2,unordered_pair(X3,X4)) ),
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_31,negated_conjecture,
apply(esk1_0,esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_32,plain,
( ~ epred1_2(X3,X2)
| ~ member(X1,X2)
| apply(X3,X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
epred1_2(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,negated_conjecture,
~ apply(esk1_0,esk4_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_35,negated_conjecture,
( ~ member(X1,esk2_0)
| apply(esk1_0,X1,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
member(esk4_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET795+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.35 % Computer : n015.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 05:41:50 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.39 Running first-order theorem proving
% 0.15/0.39 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
% 0.15/0.44 % Version: 3.5.1
% 0.15/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.44 % Starting sh5l with 300s (1) cores
% 0.15/0.44 % new_bool_3 with pid 672199 completed with status 0
% 0.15/0.44 % Result found by new_bool_3
% 0.15/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.44 % Search class: FGUSF-FFLS32-SFFFFFNN
% 0.15/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.44 % SubtermCWHack with pid 672204 completed with status 0
% 0.15/0.44 % Result found by SubtermCWHack
% 0.15/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/0.44 % Search class: FGUSF-FFLS32-SFFFFFNN
% 0.15/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.15/0.44 % Preprocessing time : 0.002 s
% 0.15/0.44
% 0.15/0.44 % Proof found!
% 0.15/0.44 % SZS status Theorem
% 0.15/0.44 % SZS output start CNFRefutation
% See solution above
% 0.15/0.44 % Parsed axioms : 22
% 0.15/0.44 % Removed by relevancy pruning/SinE : 17
% 0.15/0.44 % Initial clauses : 82
% 0.15/0.44 % Removed in clause preprocessing : 0
% 0.15/0.44 % Initial clauses in saturation : 82
% 0.15/0.44 % Processed clauses : 86
% 0.15/0.44 % ...of these trivial : 0
% 0.15/0.44 % ...subsumed : 4
% 0.15/0.44 % ...remaining for further processing : 82
% 0.15/0.44 % Other redundant clauses eliminated : 4
% 0.15/0.44 % Clauses deleted for lack of memory : 0
% 0.15/0.44 % Backward-subsumed : 5
% 0.15/0.44 % Backward-rewritten : 0
% 0.15/0.44 % Generated clauses : 125
% 0.15/0.44 % ...of the previous two non-redundant : 107
% 0.15/0.44 % ...aggressively subsumed : 0
% 0.15/0.44 % Contextual simplify-reflections : 0
% 0.15/0.44 % Paramodulations : 119
% 0.15/0.44 % Factorizations : 2
% 0.15/0.44 % NegExts : 0
% 0.15/0.44 % Equation resolutions : 4
% 0.15/0.44 % Disequality decompositions : 0
% 0.15/0.44 % Total rewrite steps : 10
% 0.15/0.44 % ...of those cached : 3
% 0.15/0.44 % Propositional unsat checks : 0
% 0.15/0.44 % Propositional check models : 0
% 0.15/0.44 % Propositional check unsatisfiable : 0
% 0.15/0.44 % Propositional clauses : 0
% 0.15/0.44 % Propositional clauses after purity: 0
% 0.15/0.44 % Propositional unsat core size : 0
% 0.15/0.44 % Propositional preprocessing time : 0.000
% 0.15/0.44 % Propositional encoding time : 0.000
% 0.15/0.44 % Propositional solver time : 0.000
% 0.15/0.44 % Success case prop preproc time : 0.000
% 0.15/0.44 % Success case prop encoding time : 0.000
% 0.15/0.44 % Success case prop solver time : 0.000
% 0.15/0.44 % Current number of processed clauses : 75
% 0.15/0.44 % Positive orientable unit clauses : 7
% 0.15/0.44 % Positive unorientable unit clauses: 0
% 0.15/0.44 % Negative unit clauses : 3
% 0.15/0.44 % Non-unit-clauses : 65
% 0.15/0.44 % Current number of unprocessed clauses: 103
% 0.15/0.44 % ...number of literals in the above : 550
% 0.15/0.44 % Current number of archived formulas : 0
% 0.15/0.44 % Current number of archived clauses : 5
% 0.15/0.44 % Clause-clause subsumption calls (NU) : 857
% 0.15/0.44 % Rec. Clause-clause subsumption calls : 339
% 0.15/0.44 % Non-unit clause-clause subsumptions : 9
% 0.15/0.44 % Unit Clause-clause subsumption calls : 1
% 0.15/0.44 % Rewrite failures with RHS unbound : 0
% 0.15/0.44 % BW rewrite match attempts : 1
% 0.15/0.44 % BW rewrite match successes : 0
% 0.15/0.44 % Condensation attempts : 0
% 0.15/0.44 % Condensation successes : 0
% 0.15/0.44 % Termbank termtop insertions : 6979
% 0.15/0.44 % Search garbage collected termcells : 1067
% 0.15/0.44
% 0.15/0.44 % -------------------------------------------------
% 0.15/0.44 % User time : 0.014 s
% 0.15/0.44 % System time : 0.003 s
% 0.15/0.44 % Total time : 0.017 s
% 0.15/0.44 % Maximum resident set size: 3672 pages
% 0.15/0.44
% 0.15/0.44 % -------------------------------------------------
% 0.15/0.44 % User time : 0.016 s
% 0.15/0.44 % System time : 0.009 s
% 0.15/0.44 % Total time : 0.024 s
% 0.15/0.44 % Maximum resident set size: 4864 pages
% 0.15/0.44 % E exiting
%------------------------------------------------------------------------------