%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET795+4 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:08:30 PM UTC 2026
% Result : Theorem 113.85s 69.82s
% Output : CNFRefutation 114.25s
% 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)
<=> ( member(X1,X3)
& upper_bound(X1,X6,X3)
& ! [X8] :
( ( member(X8,X4)
& upper_bound(X8,X6,X3) )
=> apply(X6,X1,X8) ) ) ),
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 = X1
| X3 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',unordered_pair) ).
fof(thIV7,conjecture,
! [X6,X4,X1,X2] :
( ( order(X6,X4)
& member(X1,X4)
& member(X2,X4)
& apply(X6,X1,X2) )
=> 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] :
( member(X3,X4)
=> apply(X6,X3,X3) )
& ! [X3,X5] :
( ( member(X3,X4)
& member(X5,X4) )
=> ( ( apply(X6,X3,X5)
& apply(X6,X5,X3) )
=> X3 = X5 ) )
& ! [X3,X5,X7] :
( ( member(X3,X4)
& member(X5,X4)
& member(X7,X4) )
=> ( ( apply(X6,X3,X5)
& apply(X6,X5,X7) )
=> apply(X6,X3,X7) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',order) ).
fof(c_0_5,plain,
! [X134,X135,X136,X137,X138,X139,X140] :
( ( ~ upper_bound(X136,X134,X135)
| ~ member(X137,X135)
| apply(X134,X137,X136) )
& ( member(esk6_3(X138,X139,X140),X139)
| upper_bound(X140,X138,X139) )
& ( ~ apply(X138,esk6_3(X138,X139,X140),X140)
| upper_bound(X140,X138,X139) ) ),
inference(distribute,[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,
! [X182,X183,X184,X185,X186,X187,X188,X189,X190] :
( ( member(X182,X183)
| ~ least_upper_bound(X182,X183,X184,X185) )
& ( upper_bound(X182,X184,X183)
| ~ least_upper_bound(X182,X183,X184,X185) )
& ( ~ member(X186,X185)
| ~ upper_bound(X186,X184,X183)
| apply(X184,X182,X186)
| ~ least_upper_bound(X182,X183,X184,X185) )
& ( member(esk12_4(X187,X188,X189,X190),X190)
| ~ member(X187,X188)
| ~ upper_bound(X187,X189,X188)
| least_upper_bound(X187,X188,X189,X190) )
& ( upper_bound(esk12_4(X187,X188,X189,X190),X189,X188)
| ~ member(X187,X188)
| ~ upper_bound(X187,X189,X188)
| least_upper_bound(X187,X188,X189,X190) )
& ( ~ apply(X189,X187,esk12_4(X187,X188,X189,X190))
| ~ member(X187,X188)
| ~ upper_bound(X187,X189,X188)
| least_upper_bound(X187,X188,X189,X190) ) ),
inference(distribute,[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,
! [X109,X110,X111] :
( ( ~ member(X109,unordered_pair(X110,X111))
| X109 = X110
| X109 = X111 )
& ( X109 != X110
| member(X109,unordered_pair(X110,X111)) )
& ( X109 != X111
| member(X109,unordered_pair(X110,X111)) ) ),
inference(distribute,[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] :
( member(X3,X4)
=> apply(X6,X3,X3) )
& ! [X3,X5] :
( ( member(X3,X4)
& member(X5,X4) )
=> ( ( apply(X6,X3,X5)
& apply(X6,X5,X3) )
=> X3 = X5 ) )
& ! [X3,X5,X7] :
( ( member(X3,X4)
& member(X5,X4)
& member(X7,X4) )
=> ( ( apply(X6,X3,X5)
& apply(X6,X5,X7) )
=> apply(X6,X3,X7) ) ) ) ),
introduced(definition) ).
fof(c_0_9,negated_conjecture,
~ ! [X6,X4,X1,X2] :
( ( order(X6,X4)
& member(X1,X4)
& member(X2,X4)
& apply(X6,X1,X2) )
=> least_upper_bound(X2,unordered_pair(X1,X2),X6,X4) ),
inference(assume_negation,[status(cth)],[thIV7]) ).
cnf(c_0_10,plain,
( apply(X2,X4,X1)
| ~ upper_bound(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
( upper_bound(esk12_4(X1,X2,X3,X4),X3,X2)
| least_upper_bound(X1,X2,X3,X4)
| ~ member(X1,X2)
| ~ upper_bound(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( member(esk6_3(X1,X2,X3),X2)
| upper_bound(X3,X1,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,
( order(esk14_0,esk15_0)
& member(esk16_0,esk15_0)
& member(esk17_0,esk15_0)
& apply(esk14_0,esk16_0,esk17_0)
& ~ least_upper_bound(esk17_0,unordered_pair(esk16_0,esk17_0),esk14_0,esk15_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_16,plain,
( least_upper_bound(X2,X3,X1,X4)
| ~ apply(X1,X2,esk12_4(X2,X3,X1,X4))
| ~ member(X2,X3)
| ~ upper_bound(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,plain,
( least_upper_bound(X1,X2,X3,X4)
| apply(X3,X5,esk12_4(X1,X2,X3,X4))
| ~ upper_bound(X1,X3,X2)
| ~ member(X5,X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_18,plain,
( member(X1,unordered_pair(X3,X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,plain,
( upper_bound(X3,X1,X2)
| ~ apply(X1,esk6_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_20,plain,
( esk6_3(X1,unordered_pair(X2,X3),X4) = X3
| esk6_3(X1,unordered_pair(X2,X3),X4) = X2
| upper_bound(X4,X1,unordered_pair(X2,X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_21,plain,
! [X124,X125] :
( ( ~ order(X124,X125)
| epred1_2(X124,X125) )
& ( ~ epred1_2(X124,X125)
| order(X124,X125) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])]) ).
cnf(c_0_22,negated_conjecture,
~ least_upper_bound(esk17_0,unordered_pair(esk16_0,esk17_0),esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( least_upper_bound(X1,X2,X3,X4)
| ~ upper_bound(X1,X3,X2)
| ~ member(X1,X2) ),
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,
( esk6_3(X1,unordered_pair(X2,X3),X4) = X3
| upper_bound(X4,X1,unordered_pair(X2,X3))
| ~ apply(X1,X2,X4) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_26,plain,
! [X206,X207,X208,X209,X210,X211,X212,X213,X214,X215] :
( ( ~ member(X208,X206)
| apply(X207,X208,X208)
| ~ epred1_2(X207,X206) )
& ( ~ member(X209,X206)
| ~ member(X210,X206)
| ~ apply(X207,X209,X210)
| ~ apply(X207,X210,X209)
| X209 = X210
| ~ epred1_2(X207,X206) )
& ( ~ member(X211,X206)
| ~ member(X212,X206)
| ~ member(X213,X206)
| ~ apply(X207,X211,X212)
| ~ apply(X207,X212,X213)
| apply(X207,X211,X213)
| ~ epred1_2(X207,X206) )
& ( member(esk21_2(X214,X215),X214)
| member(esk19_2(X214,X215),X214)
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( member(esk22_2(X214,X215),X214)
| member(esk19_2(X214,X215),X214)
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( member(esk23_2(X214,X215),X214)
| member(esk19_2(X214,X215),X214)
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( apply(X215,esk21_2(X214,X215),esk22_2(X214,X215))
| member(esk19_2(X214,X215),X214)
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( apply(X215,esk22_2(X214,X215),esk23_2(X214,X215))
| member(esk19_2(X214,X215),X214)
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( ~ apply(X215,esk21_2(X214,X215),esk23_2(X214,X215))
| member(esk19_2(X214,X215),X214)
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( member(esk21_2(X214,X215),X214)
| member(esk20_2(X214,X215),X214)
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( member(esk22_2(X214,X215),X214)
| member(esk20_2(X214,X215),X214)
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( member(esk23_2(X214,X215),X214)
| member(esk20_2(X214,X215),X214)
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( apply(X215,esk21_2(X214,X215),esk22_2(X214,X215))
| member(esk20_2(X214,X215),X214)
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( apply(X215,esk22_2(X214,X215),esk23_2(X214,X215))
| member(esk20_2(X214,X215),X214)
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( ~ apply(X215,esk21_2(X214,X215),esk23_2(X214,X215))
| member(esk20_2(X214,X215),X214)
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( member(esk21_2(X214,X215),X214)
| apply(X215,esk19_2(X214,X215),esk20_2(X214,X215))
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( member(esk22_2(X214,X215),X214)
| apply(X215,esk19_2(X214,X215),esk20_2(X214,X215))
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( member(esk23_2(X214,X215),X214)
| apply(X215,esk19_2(X214,X215),esk20_2(X214,X215))
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( apply(X215,esk21_2(X214,X215),esk22_2(X214,X215))
| apply(X215,esk19_2(X214,X215),esk20_2(X214,X215))
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( apply(X215,esk22_2(X214,X215),esk23_2(X214,X215))
| apply(X215,esk19_2(X214,X215),esk20_2(X214,X215))
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( ~ apply(X215,esk21_2(X214,X215),esk23_2(X214,X215))
| apply(X215,esk19_2(X214,X215),esk20_2(X214,X215))
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( member(esk21_2(X214,X215),X214)
| apply(X215,esk20_2(X214,X215),esk19_2(X214,X215))
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( member(esk22_2(X214,X215),X214)
| apply(X215,esk20_2(X214,X215),esk19_2(X214,X215))
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( member(esk23_2(X214,X215),X214)
| apply(X215,esk20_2(X214,X215),esk19_2(X214,X215))
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( apply(X215,esk21_2(X214,X215),esk22_2(X214,X215))
| apply(X215,esk20_2(X214,X215),esk19_2(X214,X215))
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( apply(X215,esk22_2(X214,X215),esk23_2(X214,X215))
| apply(X215,esk20_2(X214,X215),esk19_2(X214,X215))
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( ~ apply(X215,esk21_2(X214,X215),esk23_2(X214,X215))
| apply(X215,esk20_2(X214,X215),esk19_2(X214,X215))
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( member(esk21_2(X214,X215),X214)
| esk19_2(X214,X215) != esk20_2(X214,X215)
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( member(esk22_2(X214,X215),X214)
| esk19_2(X214,X215) != esk20_2(X214,X215)
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( member(esk23_2(X214,X215),X214)
| esk19_2(X214,X215) != esk20_2(X214,X215)
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( apply(X215,esk21_2(X214,X215),esk22_2(X214,X215))
| esk19_2(X214,X215) != esk20_2(X214,X215)
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( apply(X215,esk22_2(X214,X215),esk23_2(X214,X215))
| esk19_2(X214,X215) != esk20_2(X214,X215)
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( ~ apply(X215,esk21_2(X214,X215),esk23_2(X214,X215))
| esk19_2(X214,X215) != esk20_2(X214,X215)
| member(esk18_2(X214,X215),X214)
| epred1_2(X215,X214) )
& ( member(esk21_2(X214,X215),X214)
| member(esk19_2(X214,X215),X214)
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( member(esk22_2(X214,X215),X214)
| member(esk19_2(X214,X215),X214)
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( member(esk23_2(X214,X215),X214)
| member(esk19_2(X214,X215),X214)
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( apply(X215,esk21_2(X214,X215),esk22_2(X214,X215))
| member(esk19_2(X214,X215),X214)
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( apply(X215,esk22_2(X214,X215),esk23_2(X214,X215))
| member(esk19_2(X214,X215),X214)
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( ~ apply(X215,esk21_2(X214,X215),esk23_2(X214,X215))
| member(esk19_2(X214,X215),X214)
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( member(esk21_2(X214,X215),X214)
| member(esk20_2(X214,X215),X214)
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( member(esk22_2(X214,X215),X214)
| member(esk20_2(X214,X215),X214)
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( member(esk23_2(X214,X215),X214)
| member(esk20_2(X214,X215),X214)
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( apply(X215,esk21_2(X214,X215),esk22_2(X214,X215))
| member(esk20_2(X214,X215),X214)
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( apply(X215,esk22_2(X214,X215),esk23_2(X214,X215))
| member(esk20_2(X214,X215),X214)
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( ~ apply(X215,esk21_2(X214,X215),esk23_2(X214,X215))
| member(esk20_2(X214,X215),X214)
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( member(esk21_2(X214,X215),X214)
| apply(X215,esk19_2(X214,X215),esk20_2(X214,X215))
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( member(esk22_2(X214,X215),X214)
| apply(X215,esk19_2(X214,X215),esk20_2(X214,X215))
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( member(esk23_2(X214,X215),X214)
| apply(X215,esk19_2(X214,X215),esk20_2(X214,X215))
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( apply(X215,esk21_2(X214,X215),esk22_2(X214,X215))
| apply(X215,esk19_2(X214,X215),esk20_2(X214,X215))
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( apply(X215,esk22_2(X214,X215),esk23_2(X214,X215))
| apply(X215,esk19_2(X214,X215),esk20_2(X214,X215))
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( ~ apply(X215,esk21_2(X214,X215),esk23_2(X214,X215))
| apply(X215,esk19_2(X214,X215),esk20_2(X214,X215))
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( member(esk21_2(X214,X215),X214)
| apply(X215,esk20_2(X214,X215),esk19_2(X214,X215))
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( member(esk22_2(X214,X215),X214)
| apply(X215,esk20_2(X214,X215),esk19_2(X214,X215))
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( member(esk23_2(X214,X215),X214)
| apply(X215,esk20_2(X214,X215),esk19_2(X214,X215))
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( apply(X215,esk21_2(X214,X215),esk22_2(X214,X215))
| apply(X215,esk20_2(X214,X215),esk19_2(X214,X215))
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( apply(X215,esk22_2(X214,X215),esk23_2(X214,X215))
| apply(X215,esk20_2(X214,X215),esk19_2(X214,X215))
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( ~ apply(X215,esk21_2(X214,X215),esk23_2(X214,X215))
| apply(X215,esk20_2(X214,X215),esk19_2(X214,X215))
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( member(esk21_2(X214,X215),X214)
| esk19_2(X214,X215) != esk20_2(X214,X215)
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( member(esk22_2(X214,X215),X214)
| esk19_2(X214,X215) != esk20_2(X214,X215)
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( member(esk23_2(X214,X215),X214)
| esk19_2(X214,X215) != esk20_2(X214,X215)
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( apply(X215,esk21_2(X214,X215),esk22_2(X214,X215))
| esk19_2(X214,X215) != esk20_2(X214,X215)
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( apply(X215,esk22_2(X214,X215),esk23_2(X214,X215))
| esk19_2(X214,X215) != esk20_2(X214,X215)
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) )
& ( ~ apply(X215,esk21_2(X214,X215),esk23_2(X214,X215))
| esk19_2(X214,X215) != esk20_2(X214,X215)
| ~ apply(X215,esk18_2(X214,X215),esk18_2(X214,X215))
| epred1_2(X215,X214) ) ),
inference(distribute,[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,
( epred1_2(X1,X2)
| ~ order(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,negated_conjecture,
order(esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_29,negated_conjecture,
~ upper_bound(esk17_0,esk14_0,unordered_pair(esk16_0,esk17_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,
( upper_bound(X1,X2,unordered_pair(X3,X4))
| ~ apply(X2,X4,X1)
| ~ apply(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_31,negated_conjecture,
apply(esk14_0,esk16_0,esk17_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_32,plain,
( apply(X3,X1,X1)
| ~ member(X1,X2)
| ~ epred1_2(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
epred1_2(esk14_0,esk15_0),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,negated_conjecture,
~ apply(esk14_0,esk17_0,esk17_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,plain,
( apply(esk14_0,X1,X1)
| ~ member(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
member(esk17_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_37,plain,
$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
% 0.00/0.12 % Problem : SET795+4 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n005.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:35:15 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 113.85/69.82 % Version : CSE_E---1.7
% 113.85/69.82 % Problem : theBenchmark.p
% 113.85/69.82 % SZS status Theorem for theBenchmark.p
% 113.85/69.82 % SZS output start CNFRefutation
% See solution above
% 114.25/70.28 % Total time : 51.727s
%------------------------------------------------------------------------------