%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG092+2 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/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 05:05:18 PM UTC 2026
% Result : Theorem 2.07s 2.02s
% Output : CNFRefutation 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 6 unt; 0 def)
% Number of atoms : 594 ( 114 equ)
% Maximal formula atoms : 477 ( 28 avg)
% Number of connectives : 984 ( 411 ~; 415 |; 142 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 100 ( 10 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 69 ( 2 sgn 29 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ! [X1,X2,X3] :
( ( ( ? [X4,X5] :
( aElementOf0(X4,xI)
& aElementOf0(X5,xJ)
& sdtpldt0(X4,X5) = X1 )
| aElementOf0(X1,sdtpldt1(xI,xJ)) )
& ( ? [X4,X5] :
( aElementOf0(X4,xI)
& aElementOf0(X5,xJ)
& sdtpldt0(X4,X5) = X2 )
| aElementOf0(X2,sdtpldt1(xI,xJ)) )
& aElement0(X3) )
=> ? [X4,X5] :
( aElementOf0(X4,xI)
& aElementOf0(X5,xJ)
& X1 = sdtpldt0(X4,X5)
& ? [X6,X7] :
( aElementOf0(X6,xI)
& aElementOf0(X7,xJ)
& X2 = sdtpldt0(X6,X7)
& aElementOf0(sdtpldt0(X4,X6),xI)
& aElementOf0(sdtpldt0(X5,X7),xJ)
& aElementOf0(sdtasdt0(X3,X4),xI)
& aElementOf0(sdtasdt0(X3,X5),xJ)
& sdtpldt0(X1,X2) = sdtpldt0(sdtpldt0(X4,X6),sdtpldt0(X5,X7))
& ? [X8,X9] :
( aElementOf0(X8,xI)
& aElementOf0(X9,xJ)
& sdtpldt0(X8,X9) = sdtpldt0(X1,X2) )
& aElementOf0(sdtpldt0(X1,X2),sdtpldt1(xI,xJ))
& ? [X8,X9] :
( aElementOf0(X8,xI)
& aElementOf0(X9,xJ)
& sdtpldt0(X8,X9) = sdtasdt0(X3,X1) )
& aElementOf0(sdtasdt0(X3,X1),sdtpldt1(xI,xJ)) ) ) )
=> ( ( aSet0(sdtpldt1(xI,xJ))
& ! [X1] :
( aElementOf0(X1,sdtpldt1(xI,xJ))
<=> ? [X2,X3] :
( aElementOf0(X2,xI)
& aElementOf0(X3,xJ)
& sdtpldt0(X2,X3) = X1 ) ) )
=> ( ! [X1] :
( aElementOf0(X1,sdtpldt1(xI,xJ))
=> ( ! [X2] :
( aElementOf0(X2,sdtpldt1(xI,xJ))
=> aElementOf0(sdtpldt0(X1,X2),sdtpldt1(xI,xJ)) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),sdtpldt1(xI,xJ)) ) ) )
| aIdeal0(sdtpldt1(xI,xJ)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(c_0_2,negated_conjecture,
~ ( ! [X1,X2,X3] :
( ( ( ? [X4,X5] :
( aElementOf0(X4,xI)
& aElementOf0(X5,xJ)
& sdtpldt0(X4,X5) = X1 )
| aElementOf0(X1,sdtpldt1(xI,xJ)) )
& ( ? [X4,X5] :
( aElementOf0(X4,xI)
& aElementOf0(X5,xJ)
& sdtpldt0(X4,X5) = X2 )
| aElementOf0(X2,sdtpldt1(xI,xJ)) )
& aElement0(X3) )
=> ? [X4,X5] :
( aElementOf0(X4,xI)
& aElementOf0(X5,xJ)
& X1 = sdtpldt0(X4,X5)
& ? [X6,X7] :
( aElementOf0(X6,xI)
& aElementOf0(X7,xJ)
& X2 = sdtpldt0(X6,X7)
& aElementOf0(sdtpldt0(X4,X6),xI)
& aElementOf0(sdtpldt0(X5,X7),xJ)
& aElementOf0(sdtasdt0(X3,X4),xI)
& aElementOf0(sdtasdt0(X3,X5),xJ)
& sdtpldt0(X1,X2) = sdtpldt0(sdtpldt0(X4,X6),sdtpldt0(X5,X7))
& ? [X8,X9] :
( aElementOf0(X8,xI)
& aElementOf0(X9,xJ)
& sdtpldt0(X8,X9) = sdtpldt0(X1,X2) )
& aElementOf0(sdtpldt0(X1,X2),sdtpldt1(xI,xJ))
& ? [X8,X9] :
( aElementOf0(X8,xI)
& aElementOf0(X9,xJ)
& sdtpldt0(X8,X9) = sdtasdt0(X3,X1) )
& aElementOf0(sdtasdt0(X3,X1),sdtpldt1(xI,xJ)) ) ) )
=> ( ( aSet0(sdtpldt1(xI,xJ))
& ! [X1] :
( aElementOf0(X1,sdtpldt1(xI,xJ))
<=> ? [X2,X3] :
( aElementOf0(X2,xI)
& aElementOf0(X3,xJ)
& sdtpldt0(X2,X3) = X1 ) ) )
=> ( ! [X1] :
( aElementOf0(X1,sdtpldt1(xI,xJ))
=> ( ! [X2] :
( aElementOf0(X2,sdtpldt1(xI,xJ))
=> aElementOf0(sdtpldt0(X1,X2),sdtpldt1(xI,xJ)) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),sdtpldt1(xI,xJ)) ) ) )
| aIdeal0(sdtpldt1(xI,xJ)) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_3,plain,
! [X109,X110] :
( ~ aSet0(X109)
| ~ aElementOf0(X110,X109)
| aElement0(X110) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(c_0_4,negated_conjecture,
! [X151,X152,X153,X154,X155,X156,X157,X166,X169,X170,X171] :
( ( aElementOf0(esk12_3(X151,X152,X153),xI)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(esk13_3(X151,X152,X153),xJ)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( X151 = sdtpldt0(esk12_3(X151,X152,X153),esk13_3(X151,X152,X153))
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(esk14_3(X151,X152,X153),xI)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(esk15_3(X151,X152,X153),xJ)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( X152 = sdtpldt0(esk14_3(X151,X152,X153),esk15_3(X151,X152,X153))
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(sdtpldt0(esk12_3(X151,X152,X153),esk14_3(X151,X152,X153)),xI)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(sdtpldt0(esk13_3(X151,X152,X153),esk15_3(X151,X152,X153)),xJ)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(sdtasdt0(X153,esk12_3(X151,X152,X153)),xI)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(sdtasdt0(X153,esk13_3(X151,X152,X153)),xJ)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( sdtpldt0(X151,X152) = sdtpldt0(sdtpldt0(esk12_3(X151,X152,X153),esk14_3(X151,X152,X153)),sdtpldt0(esk13_3(X151,X152,X153),esk15_3(X151,X152,X153)))
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(esk16_3(X151,X152,X153),xI)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(esk17_3(X151,X152,X153),xJ)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( sdtpldt0(esk16_3(X151,X152,X153),esk17_3(X151,X152,X153)) = sdtpldt0(X151,X152)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(sdtpldt0(X151,X152),sdtpldt1(xI,xJ))
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(esk18_3(X151,X152,X153),xI)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(esk19_3(X151,X152,X153),xJ)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( sdtpldt0(esk18_3(X151,X152,X153),esk19_3(X151,X152,X153)) = sdtasdt0(X153,X151)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(sdtasdt0(X153,X151),sdtpldt1(xI,xJ))
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(esk12_3(X151,X152,X153),xI)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(esk13_3(X151,X152,X153),xJ)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( X151 = sdtpldt0(esk12_3(X151,X152,X153),esk13_3(X151,X152,X153))
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(esk14_3(X151,X152,X153),xI)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(esk15_3(X151,X152,X153),xJ)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( X152 = sdtpldt0(esk14_3(X151,X152,X153),esk15_3(X151,X152,X153))
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(sdtpldt0(esk12_3(X151,X152,X153),esk14_3(X151,X152,X153)),xI)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(sdtpldt0(esk13_3(X151,X152,X153),esk15_3(X151,X152,X153)),xJ)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(sdtasdt0(X153,esk12_3(X151,X152,X153)),xI)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(sdtasdt0(X153,esk13_3(X151,X152,X153)),xJ)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( sdtpldt0(X151,X152) = sdtpldt0(sdtpldt0(esk12_3(X151,X152,X153),esk14_3(X151,X152,X153)),sdtpldt0(esk13_3(X151,X152,X153),esk15_3(X151,X152,X153)))
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(esk16_3(X151,X152,X153),xI)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(esk17_3(X151,X152,X153),xJ)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( sdtpldt0(esk16_3(X151,X152,X153),esk17_3(X151,X152,X153)) = sdtpldt0(X151,X152)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(sdtpldt0(X151,X152),sdtpldt1(xI,xJ))
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(esk18_3(X151,X152,X153),xI)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(esk19_3(X151,X152,X153),xJ)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( sdtpldt0(esk18_3(X151,X152,X153),esk19_3(X151,X152,X153)) = sdtasdt0(X153,X151)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(sdtasdt0(X153,X151),sdtpldt1(xI,xJ))
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X154,xI)
| ~ aElementOf0(X155,xJ)
| sdtpldt0(X154,X155) != X151
| ~ aElement0(X153) )
& ( aElementOf0(esk12_3(X151,X152,X153),xI)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(esk13_3(X151,X152,X153),xJ)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( X151 = sdtpldt0(esk12_3(X151,X152,X153),esk13_3(X151,X152,X153))
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(esk14_3(X151,X152,X153),xI)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(esk15_3(X151,X152,X153),xJ)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( X152 = sdtpldt0(esk14_3(X151,X152,X153),esk15_3(X151,X152,X153))
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(sdtpldt0(esk12_3(X151,X152,X153),esk14_3(X151,X152,X153)),xI)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(sdtpldt0(esk13_3(X151,X152,X153),esk15_3(X151,X152,X153)),xJ)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(sdtasdt0(X153,esk12_3(X151,X152,X153)),xI)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(sdtasdt0(X153,esk13_3(X151,X152,X153)),xJ)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( sdtpldt0(X151,X152) = sdtpldt0(sdtpldt0(esk12_3(X151,X152,X153),esk14_3(X151,X152,X153)),sdtpldt0(esk13_3(X151,X152,X153),esk15_3(X151,X152,X153)))
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(esk16_3(X151,X152,X153),xI)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(esk17_3(X151,X152,X153),xJ)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( sdtpldt0(esk16_3(X151,X152,X153),esk17_3(X151,X152,X153)) = sdtpldt0(X151,X152)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(sdtpldt0(X151,X152),sdtpldt1(xI,xJ))
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(esk18_3(X151,X152,X153),xI)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(esk19_3(X151,X152,X153),xJ)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( sdtpldt0(esk18_3(X151,X152,X153),esk19_3(X151,X152,X153)) = sdtasdt0(X153,X151)
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(sdtasdt0(X153,X151),sdtpldt1(xI,xJ))
| ~ aElementOf0(X156,xI)
| ~ aElementOf0(X157,xJ)
| sdtpldt0(X156,X157) != X152
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(esk12_3(X151,X152,X153),xI)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(esk13_3(X151,X152,X153),xJ)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( X151 = sdtpldt0(esk12_3(X151,X152,X153),esk13_3(X151,X152,X153))
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(esk14_3(X151,X152,X153),xI)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(esk15_3(X151,X152,X153),xJ)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( X152 = sdtpldt0(esk14_3(X151,X152,X153),esk15_3(X151,X152,X153))
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(sdtpldt0(esk12_3(X151,X152,X153),esk14_3(X151,X152,X153)),xI)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(sdtpldt0(esk13_3(X151,X152,X153),esk15_3(X151,X152,X153)),xJ)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(sdtasdt0(X153,esk12_3(X151,X152,X153)),xI)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(sdtasdt0(X153,esk13_3(X151,X152,X153)),xJ)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( sdtpldt0(X151,X152) = sdtpldt0(sdtpldt0(esk12_3(X151,X152,X153),esk14_3(X151,X152,X153)),sdtpldt0(esk13_3(X151,X152,X153),esk15_3(X151,X152,X153)))
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(esk16_3(X151,X152,X153),xI)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(esk17_3(X151,X152,X153),xJ)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( sdtpldt0(esk16_3(X151,X152,X153),esk17_3(X151,X152,X153)) = sdtpldt0(X151,X152)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(sdtpldt0(X151,X152),sdtpldt1(xI,xJ))
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(esk18_3(X151,X152,X153),xI)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(esk19_3(X151,X152,X153),xJ)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( sdtpldt0(esk18_3(X151,X152,X153),esk19_3(X151,X152,X153)) = sdtasdt0(X153,X151)
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& ( aElementOf0(sdtasdt0(X153,X151),sdtpldt1(xI,xJ))
| ~ aElementOf0(X152,sdtpldt1(xI,xJ))
| ~ aElementOf0(X151,sdtpldt1(xI,xJ))
| ~ aElement0(X153) )
& aSet0(sdtpldt1(xI,xJ))
& ( aElementOf0(esk20_1(X166),xI)
| ~ aElementOf0(X166,sdtpldt1(xI,xJ)) )
& ( aElementOf0(esk21_1(X166),xJ)
| ~ aElementOf0(X166,sdtpldt1(xI,xJ)) )
& ( sdtpldt0(esk20_1(X166),esk21_1(X166)) = X166
| ~ aElementOf0(X166,sdtpldt1(xI,xJ)) )
& ( ~ aElementOf0(X170,xI)
| ~ aElementOf0(X171,xJ)
| sdtpldt0(X170,X171) != X169
| aElementOf0(X169,sdtpldt1(xI,xJ)) )
& aElementOf0(esk22_0,sdtpldt1(xI,xJ))
& ( aElement0(esk24_0)
| aElementOf0(esk23_0,sdtpldt1(xI,xJ)) )
& ( ~ aElementOf0(sdtasdt0(esk24_0,esk22_0),sdtpldt1(xI,xJ))
| aElementOf0(esk23_0,sdtpldt1(xI,xJ)) )
& ( aElement0(esk24_0)
| ~ aElementOf0(sdtpldt0(esk22_0,esk23_0),sdtpldt1(xI,xJ)) )
& ( ~ aElementOf0(sdtasdt0(esk24_0,esk22_0),sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtpldt0(esk22_0,esk23_0),sdtpldt1(xI,xJ)) )
& ~ aIdeal0(sdtpldt1(xI,xJ)) ),
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_2])])])])])]) ).
cnf(c_0_5,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,negated_conjecture,
( aElement0(esk24_0)
| aElementOf0(esk23_0,sdtpldt1(xI,xJ)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
aSet0(sdtpldt1(xI,xJ)),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
( aElementOf0(sdtpldt0(X1,X2),sdtpldt1(xI,xJ))
| ~ aElementOf0(X2,sdtpldt1(xI,xJ))
| ~ aElementOf0(X1,sdtpldt1(xI,xJ))
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,negated_conjecture,
( aElement0(esk24_0)
| aElement0(esk23_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_7])]) ).
cnf(c_0_10,negated_conjecture,
( aElementOf0(sdtasdt0(X1,X2),sdtpldt1(xI,xJ))
| ~ aElementOf0(X3,sdtpldt1(xI,xJ))
| ~ aElementOf0(X2,sdtpldt1(xI,xJ))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_11,negated_conjecture,
aElementOf0(esk22_0,sdtpldt1(xI,xJ)),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_12,negated_conjecture,
( aElement0(esk24_0)
| ~ aElementOf0(sdtpldt0(esk22_0,esk23_0),sdtpldt1(xI,xJ)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,negated_conjecture,
( aElementOf0(sdtpldt0(X1,X2),sdtpldt1(xI,xJ))
| ~ aElementOf0(X2,sdtpldt1(xI,xJ))
| ~ aElementOf0(X1,sdtpldt1(xI,xJ)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_8]) ).
cnf(c_0_14,negated_conjecture,
( ~ aElementOf0(sdtasdt0(esk24_0,esk22_0),sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtpldt0(esk22_0,esk23_0),sdtpldt1(xI,xJ)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_15,negated_conjecture,
( aElementOf0(sdtasdt0(X1,X2),sdtpldt1(xI,xJ))
| ~ aElementOf0(X2,sdtpldt1(xI,xJ))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,negated_conjecture,
aElement0(esk24_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_11])]),c_0_6]) ).
cnf(c_0_17,negated_conjecture,
( aElementOf0(esk23_0,sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtasdt0(esk24_0,esk22_0),sdtpldt1(xI,xJ)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_18,negated_conjecture,
~ aElementOf0(sdtpldt0(esk22_0,esk23_0),sdtpldt1(xI,xJ)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_11]),c_0_16])]) ).
cnf(c_0_19,negated_conjecture,
aElementOf0(esk23_0,sdtpldt1(xI,xJ)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_15]),c_0_11]),c_0_16])]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_13]),c_0_19]),c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG092+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/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 01:49:46 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.07/2.02 % Version : CSE_E---1.7
% 2.07/2.02 % Problem : theBenchmark.p
% 2.07/2.02 % SZS status Theorem for theBenchmark.p
% 2.07/2.02 % SZS output start CNFRefutation
% See solution above
% 2.20/2.02 % Total time : 1.372s
%------------------------------------------------------------------------------