%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM468+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 : Sun Sep 27 08:12:50 AM UTC 2026
% Result : Theorem 59.28s 8.57s
% Output : CNFRefutation 59.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 15
% Syntax : Number of formulae : 155 ( 42 unt; 0 def)
% Number of atoms : 402 ( 172 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 453 ( 206 ~; 201 |; 26 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 108 ( 0 sgn 21 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSortsC,axiom,
aNaturalNumber0(sz00) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ) ).
fof(mSortsB,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ) ).
fof(mAddComm,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ) ).
fof(m_AddZero,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ) ).
fof(mMulComm,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ) ).
fof(mMulAsso,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ) ).
fof(m_MulUnit,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ) ).
fof(m_MulZero,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ) ).
fof(mAMDistr,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ) ).
fof(mAddCanc,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
| sdtpldt0(X0,X1) = sdtpldt0(X0,X2) )
=> X1 = X2 ) ) ).
fof(mMulCanc,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 != sz00
=> ! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtasdt0(X1,X0) = sdtasdt0(X2,X0)
| sdtasdt0(X0,X1) = sdtasdt0(X0,X2) )
=> X1 = X2 ) ) ) ) ).
fof(m__1240,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ) ).
fof(m__1240_04,hypothesis,
( doDivides0(xl,xn)
& ? [X0] :
( xn = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) )
& doDivides0(xl,xm)
& ? [X0] :
( xm = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) ) ) ).
fof(m__,conjecture,
( xl != sz00
=> ( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( ( xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xn,xl)) )
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( xl != sz00
=> ( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( ( xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xn,xl)) )
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ) ),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c0,plain,
aNaturalNumber0(sz00),
inference(clausification,[status(esa)],[mSortsC]) ).
cnf(c1,plain,
aNaturalNumber0(sz10),
inference(clausification,[status(esa)],[mSortsC_01]) ).
cnf(c3,plain,
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mSortsB]) ).
cnf(c5,plain,
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mAddComm]) ).
cnf(c8,plain,
( X0 = sdtpldt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_AddZero]) ).
cnf(c9,plain,
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mMulComm]) ).
cnf(c10,plain,
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mMulAsso]) ).
cnf(c11,plain,
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_MulUnit]) ).
cnf(c12,plain,
( X0 = sdtasdt0(sz10,X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_MulUnit]) ).
cnf(c13,plain,
( sdtasdt0(X0,sz00) = sz00
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_MulZero]) ).
cnf(c14,plain,
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[m_MulZero]) ).
cnf(c15,plain,
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mAMDistr]) ).
cnf(c16,plain,
( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(clausification,[status(esa)],[mAMDistr]) ).
cnf(c18,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| X0 = X2
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X1) != sdtpldt0(X2,X1) ),
inference(clausification,[status(esa)],[mAddCanc]) ).
cnf(c19,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| X0 = sz00 ),
inference(clausification,[status(esa)],[mMulCanc]) ).
cnf(c54,plain,
aNaturalNumber0(xl),
inference(clausification,[status(esa)],[m__1240]) ).
cnf(c55,plain,
aNaturalNumber0(xm),
inference(clausification,[status(esa)],[m__1240]) ).
cnf(c56,plain,
aNaturalNumber0(xn),
inference(clausification,[status(esa)],[m__1240]) ).
cnf(c57,plain,
aNaturalNumber0(sK69),
inference(clausification,[status(esa)],[m__1240_04]) ).
cnf(c58,plain,
xm = sdtasdt0(xl,sK69),
inference(clausification,[status(esa)],[m__1240_04]) ).
cnf(c60,plain,
aNaturalNumber0(sK70),
inference(clausification,[status(esa)],[m__1240_04]) ).
cnf(c61,plain,
xn = sdtasdt0(xl,sK70),
inference(clausification,[status(esa)],[m__1240_04]) ).
cnf(c63,plain,
xl != sz00,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c64,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c65,plain,
xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c66,plain,
aNaturalNumber0(sdtsldt0(xn,xl)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c67,plain,
xn = sdtasdt0(xl,sdtsldt0(xn,xl)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c68,plain,
sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK70)
| sdtasdt0(xl,sdtpldt0(X0,sK70)) = sdtpldt0(sdtasdt0(xl,X0),xn) ),
inference(superposition,[status(thm)],[c61,c15]) ).
cnf(d1,plain,
( ~ aNaturalNumber0(sK70)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xl,sdtpldt0(X0,sK70)) = sdtpldt0(sdtasdt0(xl,X0),xn) ),
inference(resolution,[status(thm)],[c54,d0]) ).
cnf(d2,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(xl,sdtpldt0(X0,sK70)) = sdtpldt0(sdtasdt0(xl,X0),xn) ),
inference(resolution,[status(thm)],[c60,d1]) ).
cnf(d3,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| X0 = sdtpldt0(X0,sz00) ),
inference(superposition,[status(thm)],[c5,c8]) ).
cnf(d4,plain,
( ~ aNaturalNumber0(X0)
| X0 = sdtpldt0(X0,sz00) ),
inference(resolution,[status(thm)],[c0,d3]) ).
cnf(d5,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| X0 = X1
| X0 != sdtpldt0(X1,sz00) ),
inference(superposition,[status(thm)],[d4,c18]) ).
cnf(d6,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 != sdtpldt0(X1,sz00)
| X0 = X1 ),
inference(resolution,[status(thm)],[c0,d5]) ).
cnf(d7,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sz10,X0) = X0 ),
inference(superposition,[status(thm)],[c9,c11]) ).
cnf(d8,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sz10,X0) = X0 ),
inference(resolution,[status(thm)],[c1,d7]) ).
cnf(d9,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtpldt0(sz10,X1),X0) = sdtpldt0(X0,sdtasdt0(X1,X0)) ),
inference(superposition,[status(thm)],[d8,c16]) ).
cnf(d10,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sdtpldt0(sz10,X0),X1) = sdtpldt0(X1,sdtasdt0(X0,X1)) ),
inference(resolution,[status(thm)],[c1,d9]) ).
cnf(d11,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(superposition,[status(thm)],[c9,c14]) ).
cnf(d12,plain,
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(resolution,[status(thm)],[c0,d11]) ).
cnf(d13,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(X0)
| sdtasdt0(xn,X0) = sdtasdt0(xl,sdtasdt0(sdtsldt0(xn,xl),X0)) ),
inference(superposition,[status(thm)],[c67,c10]) ).
cnf(d14,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xn,X0) = sdtasdt0(xl,sdtasdt0(sdtsldt0(xn,xl),X0)) ),
inference(resolution,[status(thm)],[c66,d13]) ).
cnf(d15,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(xn,X0) = sdtasdt0(xl,sdtasdt0(sdtsldt0(xn,xl),X0)) ),
inference(resolution,[status(thm)],[c54,d14]) ).
cnf(d16,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(sz00)
| sdtasdt0(xn,sz00) = sdtasdt0(xl,sz00) ),
inference(superposition,[status(thm)],[d12,d15]) ).
cnf(d17,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xl))
| sdtasdt0(xn,sz00) = sdtasdt0(xl,sz00) ),
inference(resolution,[status(thm)],[c0,d16]) ).
cnf(d18,plain,
sdtasdt0(xn,sz00) = sdtasdt0(xl,sz00),
inference(resolution,[status(thm)],[c66,d17]) ).
cnf(d19,plain,
( ~ aNaturalNumber0(xn)
| sz00 = sdtasdt0(xl,sz00) ),
inference(superposition,[status(thm)],[d18,d12]) ).
cnf(d20,plain,
sz00 = sdtasdt0(xl,sz00),
inference(resolution,[status(thm)],[c56,d19]) ).
cnf(d21,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sz00,X0) = sdtasdt0(xl,sdtasdt0(sz00,X0)) ),
inference(superposition,[status(thm)],[d20,c10]) ).
cnf(d22,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sz00,X0) = sdtasdt0(xl,sdtasdt0(sz00,X0)) ),
inference(resolution,[status(thm)],[c0,d21]) ).
cnf(d23,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sz00,X0) = sdtasdt0(xl,sdtasdt0(sz00,X0)) ),
inference(resolution,[status(thm)],[c54,d22]) ).
cnf(d24,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sz00,X0) = sdtasdt0(xl,sdtasdt0(X0,sz00)) ),
inference(superposition,[status(thm)],[c9,d23]) ).
cnf(d25,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sz00,X0) = sdtasdt0(xl,sdtasdt0(X0,sz00)) ),
inference(resolution,[status(thm)],[c0,d24]) ).
cnf(d26,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sK69)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xm,X0) = sdtasdt0(xl,sdtasdt0(sK69,X0)) ),
inference(superposition,[status(thm)],[c58,c10]) ).
cnf(d27,plain,
( ~ aNaturalNumber0(sK69)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xm,X0) = sdtasdt0(xl,sdtasdt0(sK69,X0)) ),
inference(resolution,[status(thm)],[c54,d26]) ).
cnf(d28,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(xm,X0) = sdtasdt0(xl,sdtasdt0(sK69,X0)) ),
inference(resolution,[status(thm)],[c57,d27]) ).
cnf(d29,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sK69)
| sdtasdt0(sz00,sK69) = sdtasdt0(xm,sz00) ),
inference(superposition,[status(thm)],[d28,d25]) ).
cnf(d30,plain,
( ~ aNaturalNumber0(sK69)
| sdtasdt0(sz00,sK69) = sdtasdt0(xm,sz00) ),
inference(resolution,[status(thm)],[c0,d29]) ).
cnf(d31,plain,
sdtasdt0(sz00,sK69) = sdtasdt0(xm,sz00),
inference(resolution,[status(thm)],[c57,d30]) ).
cnf(d32,plain,
( ~ aNaturalNumber0(xm)
| sdtasdt0(sz00,sK69) = sz00 ),
inference(superposition,[status(thm)],[d31,c13]) ).
cnf(d33,plain,
sdtasdt0(sz00,sK69) = sz00,
inference(resolution,[status(thm)],[c55,d32]) ).
cnf(d34,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sK69)
| sdtasdt0(sdtpldt0(sz10,sz00),sK69) = sdtpldt0(sK69,sz00) ),
inference(superposition,[status(thm)],[d33,d10]) ).
cnf(d35,plain,
( ~ aNaturalNumber0(sK69)
| sdtasdt0(sdtpldt0(sz10,sz00),sK69) = sdtpldt0(sK69,sz00) ),
inference(resolution,[status(thm)],[c0,d34]) ).
cnf(d36,plain,
sdtasdt0(sdtpldt0(sz10,sz00),sK69) = sdtpldt0(sK69,sz00),
inference(resolution,[status(thm)],[c57,d35]) ).
cnf(d37,plain,
( ~ aNaturalNumber0(sz10)
| sdtasdt0(sz10,sK69) = sdtpldt0(sK69,sz00) ),
inference(superposition,[status(thm)],[d4,d36]) ).
cnf(d38,plain,
sdtasdt0(sz10,sK69) = sdtpldt0(sK69,sz00),
inference(resolution,[status(thm)],[c1,d37]) ).
cnf(d39,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK69)
| X0 = sK69
| X0 != sdtasdt0(sz10,sK69) ),
inference(superposition,[status(thm)],[d38,d6]) ).
cnf(d40,plain,
( ~ aNaturalNumber0(X0)
| X0 = sK69
| X0 != sdtasdt0(sz10,sK69) ),
inference(resolution,[status(thm)],[c57,d39]) ).
cnf(d41,plain,
( ~ aNaturalNumber0(sdtasdt0(sz10,sK69))
| sdtasdt0(sz10,sK69) = sK69 ),
inference(equality_resolution,[status(thm)],[d40]) ).
cnf(d42,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0)
| X0 = sdtasdt0(X0,sz10) ),
inference(superposition,[status(thm)],[c9,c12]) ).
cnf(d43,plain,
( ~ aNaturalNumber0(X0)
| X0 = sdtasdt0(X0,sz10) ),
inference(resolution,[status(thm)],[c1,d42]) ).
cnf(d44,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtpldt0(X0,X1),sz10) = sdtpldt0(X0,sdtasdt0(X1,sz10)) ),
inference(superposition,[status(thm)],[d43,c16]) ).
cnf(d45,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtpldt0(X0,X1),sz10) = sdtpldt0(X0,sdtasdt0(X1,sz10)) ),
inference(resolution,[status(thm)],[c1,d44]) ).
cnf(d46,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sz00,X1) = sdtasdt0(sz00,sdtasdt0(X0,X1)) ),
inference(superposition,[status(thm)],[c14,c10]) ).
cnf(d47,plain,
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sz00,X0) = sdtasdt0(sz00,sdtasdt0(X1,X0)) ),
inference(resolution,[status(thm)],[c0,d46]) ).
cnf(d48,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(sz10)
| sdtasdt0(xn,sz10) = sdtasdt0(xl,sdtsldt0(xn,xl)) ),
inference(superposition,[status(thm)],[d43,d15]) ).
cnf(d49,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(sz10)
| sdtasdt0(xn,sz10) = xn ),
inference(demodulation,[status(thm)],[d48,c67]) ).
cnf(d50,plain,
( ~ aNaturalNumber0(sz10)
| sdtasdt0(xn,sz10) = xn ),
inference(resolution,[status(thm)],[c66,d49]) ).
cnf(d51,plain,
sdtasdt0(xn,sz10) = xn,
inference(resolution,[status(thm)],[c1,d50]) ).
cnf(d52,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn)
| sdtasdt0(sz00,sz10) = sdtasdt0(sz00,xn) ),
inference(superposition,[status(thm)],[d51,d47]) ).
cnf(d53,plain,
( ~ aNaturalNumber0(xn)
| sdtasdt0(sz00,sz10) = sdtasdt0(sz00,xn) ),
inference(resolution,[status(thm)],[c1,d52]) ).
cnf(d54,plain,
sdtasdt0(sz00,sz10) = sdtasdt0(sz00,xn),
inference(resolution,[status(thm)],[c56,d53]) ).
cnf(d55,plain,
( ~ aNaturalNumber0(xn)
| sz00 = sdtasdt0(sz00,sz10) ),
inference(superposition,[status(thm)],[d54,c14]) ).
cnf(d56,plain,
sz00 = sdtasdt0(sz00,sz10),
inference(resolution,[status(thm)],[c56,d55]) ).
cnf(d57,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00)
| sdtasdt0(sdtpldt0(X0,sz00),sz10) = sdtpldt0(X0,sz00) ),
inference(superposition,[status(thm)],[d56,d45]) ).
cnf(d58,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(sdtpldt0(X0,sz00),sz10) = sdtpldt0(X0,sz00) ),
inference(resolution,[status(thm)],[c0,d57]) ).
cnf(d59,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = sdtpldt0(X0,sz00) ),
inference(superposition,[status(thm)],[d4,d58]) ).
cnf(d60,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00)
| aNaturalNumber0(sdtasdt0(X0,sz10)) ),
inference(superposition,[status(thm)],[d59,c3]) ).
cnf(d61,plain,
( aNaturalNumber0(sdtasdt0(X0,sz10))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[c0,d60]) ).
cnf(d62,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(X0,sz10),sz10) = sdtpldt0(X0,sz00) ),
inference(superposition,[status(thm)],[d59,d58]) ).
cnf(d63,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,sz10))
| aNaturalNumber0(sdtpldt0(X0,sz00)) ),
inference(superposition,[status(thm)],[d62,d61]) ).
cnf(d64,plain,
( ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,sz00))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[d63,d61]) ).
cnf(d65,plain,
( ~ aNaturalNumber0(sK69)
| aNaturalNumber0(sdtasdt0(sz10,sK69)) ),
inference(superposition,[status(thm)],[d38,d64]) ).
cnf(d66,plain,
aNaturalNumber0(sdtasdt0(sz10,sK69)),
inference(resolution,[status(thm)],[c57,d65]) ).
cnf(d67,plain,
sdtasdt0(sz10,sK69) = sK69,
inference(resolution,[status(thm)],[d66,d41]) ).
cnf(d68,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sK69)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xl,sdtpldt0(sK69,X0)) = sdtpldt0(xm,sdtasdt0(xl,X0)) ),
inference(superposition,[status(thm)],[c58,c15]) ).
cnf(d69,plain,
( ~ aNaturalNumber0(sK69)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xl,sdtpldt0(sK69,X0)) = sdtpldt0(xm,sdtasdt0(xl,X0)) ),
inference(resolution,[status(thm)],[c54,d68]) ).
cnf(d70,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(xl,sdtpldt0(sK69,X0)) = sdtpldt0(xm,sdtasdt0(xl,X0)) ),
inference(resolution,[status(thm)],[c57,d69]) ).
cnf(d71,plain,
( ~ aNaturalNumber0(sz00)
| sdtasdt0(xl,sdtpldt0(sK69,sz00)) = sdtpldt0(xm,sz00) ),
inference(superposition,[status(thm)],[d20,d70]) ).
cnf(d72,plain,
sdtasdt0(xl,sdtpldt0(sK69,sz00)) = sdtpldt0(xm,sz00),
inference(resolution,[status(thm)],[c0,d71]) ).
cnf(d73,plain,
( ~ aNaturalNumber0(sK69)
| sdtasdt0(xl,sK69) = sdtpldt0(xm,sz00) ),
inference(superposition,[status(thm)],[d4,d72]) ).
cnf(d74,plain,
( ~ aNaturalNumber0(sK69)
| xm = sdtpldt0(xm,sz00) ),
inference(demodulation,[status(thm)],[d73,c58]) ).
cnf(d75,plain,
xm = sdtpldt0(xm,sz00),
inference(resolution,[status(thm)],[c57,d74]) ).
cnf(d76,plain,
sdtasdt0(xl,sdtpldt0(sK69,sz00)) = xm,
inference(demodulation,[status(thm)],[d72,d75]) ).
cnf(d77,plain,
( ~ aNaturalNumber0(sK69)
| sdtasdt0(xl,sdtasdt0(sK69,sz10)) = xm ),
inference(superposition,[status(thm)],[d59,d76]) ).
cnf(d78,plain,
sdtasdt0(xl,sdtasdt0(sK69,sz10)) = xm,
inference(resolution,[status(thm)],[c57,d77]) ).
cnf(d79,plain,
( ~ aNaturalNumber0(sK69)
| ~ aNaturalNumber0(sz10)
| sdtasdt0(xl,sdtasdt0(sz10,sK69)) = xm ),
inference(superposition,[status(thm)],[c9,d78]) ).
cnf(d80,plain,
( ~ aNaturalNumber0(sK69)
| sdtasdt0(xl,sdtasdt0(sz10,sK69)) = xm ),
inference(resolution,[status(thm)],[c1,d79]) ).
cnf(d81,plain,
sdtasdt0(xl,sdtasdt0(sz10,sK69)) = xm,
inference(resolution,[status(thm)],[c57,d80]) ).
cnf(d82,plain,
sdtasdt0(xl,sK69) = xm,
inference(demodulation,[status(thm)],[d81,d67]) ).
cnf(d83,plain,
( ~ aNaturalNumber0(sK69)
| sdtasdt0(xl,sdtpldt0(sK69,sK70)) = sdtpldt0(xm,xn) ),
inference(superposition,[status(thm)],[d82,d2]) ).
cnf(d84,plain,
sdtasdt0(xl,sdtpldt0(sK69,sK70)) = sdtpldt0(xm,xn),
inference(resolution,[status(thm)],[c57,d83]) ).
cnf(d85,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| xl = sz00
| sdtsldt0(xm,xl) = X0
| xm != sdtasdt0(xl,X0) ),
inference(superposition,[status(thm)],[c65,c19]) ).
cnf(d86,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(X0)
| xm != sdtasdt0(xl,X0)
| sdtsldt0(xm,xl) = X0 ),
inference(resolution,[status(thm)],[c63,d85]) ).
cnf(d87,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| xm != sdtasdt0(xl,X0)
| sdtsldt0(xm,xl) = X0 ),
inference(resolution,[status(thm)],[c64,d86]) ).
cnf(d88,plain,
( ~ aNaturalNumber0(X0)
| xm != sdtasdt0(xl,X0)
| sdtsldt0(xm,xl) = X0 ),
inference(resolution,[status(thm)],[c54,d87]) ).
cnf(d89,plain,
( ~ aNaturalNumber0(sK69)
| sdtsldt0(xm,xl) = sK69
| xm != xm ),
inference(superposition,[status(thm)],[d82,d88]) ).
cnf(d90,plain,
( xm != xm
| sdtsldt0(xm,xl) = sK69 ),
inference(resolution,[status(thm)],[c57,d89]) ).
cnf(d91,plain,
( ~ aNaturalNumber0(sK69)
| sdtasdt0(xl,sK69) = xm ),
inference(superposition,[status(thm)],[d4,d76]) ).
cnf(d92,plain,
( ~ aNaturalNumber0(sK69)
| xm = xm ),
inference(demodulation,[status(thm)],[d91,c58]) ).
cnf(d93,plain,
xm = xm,
inference(resolution,[status(thm)],[c57,d92]) ).
cnf(d94,plain,
sdtsldt0(xm,xl) = sK69,
inference(resolution,[status(thm)],[d93,d90]) ).
cnf(d95,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(xn,xl))
| xl = sz00
| sdtsldt0(xn,xl) = X0
| xn != sdtasdt0(xl,X0) ),
inference(superposition,[status(thm)],[c67,c19]) ).
cnf(d96,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(X0)
| xn != sdtasdt0(xl,X0)
| sdtsldt0(xn,xl) = X0 ),
inference(resolution,[status(thm)],[c63,d95]) ).
cnf(d97,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| xn != sdtasdt0(xl,X0)
| sdtsldt0(xn,xl) = X0 ),
inference(resolution,[status(thm)],[c66,d96]) ).
cnf(d98,plain,
( ~ aNaturalNumber0(X0)
| xn != sdtasdt0(xl,X0)
| sdtsldt0(xn,xl) = X0 ),
inference(resolution,[status(thm)],[c54,d97]) ).
cnf(d99,plain,
( ~ aNaturalNumber0(sK70)
| sdtsldt0(xn,xl) = sK70
| xn != xn ),
inference(superposition,[status(thm)],[c61,d98]) ).
cnf(d100,plain,
( xn != xn
| sdtsldt0(xn,xl) = sK70 ),
inference(resolution,[status(thm)],[c60,d99]) ).
cnf(d101,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(sz10)
| sdtasdt0(xn,sz10) = sdtasdt0(xl,sdtsldt0(xn,xl)) ),
inference(superposition,[status(thm)],[c11,d15]) ).
cnf(d102,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(sz10)
| xn = sdtasdt0(xl,sdtsldt0(xn,xl)) ),
inference(demodulation,[status(thm)],[d101,d51]) ).
cnf(d103,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(sz10)
| xn = xn ),
inference(demodulation,[status(thm)],[d102,c67]) ).
cnf(d104,plain,
( ~ aNaturalNumber0(sz10)
| xn = xn ),
inference(resolution,[status(thm)],[c66,d103]) ).
cnf(d105,plain,
xn = xn,
inference(resolution,[status(thm)],[c1,d104]) ).
cnf(d106,plain,
sdtsldt0(xn,xl) = sK70,
inference(resolution,[status(thm)],[d105,d100]) ).
cnf(d107,plain,
sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sK70)),
inference(demodulation,[status(thm)],[c68,d106]) ).
cnf(d108,plain,
sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sK69,sK70)),
inference(demodulation,[status(thm)],[d107,d94]) ).
cnf(d109,plain,
sdtpldt0(xm,xn) != sdtpldt0(xm,xn),
inference(demodulation,[status(thm)],[d108,d84]) ).
cnf(d110,plain,
$false,
inference(equality_resolution,[status(thm)],[d109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM468+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 02:52:18 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 59.28/8.57 % SZS status Theorem for theBenchmark.p
% 59.28/8.57 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------