%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM459+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n003.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 : Fri Sep 25 02:24:32 PM UTC 2026
% Result : Theorem 9.85s 2.25s
% Output : CNFRefutation 9.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 115 ( 51 unt; 2 def)
% Number of atoms : 336 ( 136 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 307 ( 125 ~; 117 |; 51 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 104 ( 0 sgn 94 !; 10 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f3,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f6,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
| sdtpldt0(X0,X1) = sdtpldt0(X0,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
fof(f16,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtpldt0(X0,X1) = sz00
=> ( X1 = sz00
& X0 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroAdd) ).
fof(f17,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(X0,X1) = sz00
=> ( X1 = sz00
| X0 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroMul) ).
fof(f21,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__745) ).
fof(f22,conjecture,
( ( sdtlseqdt0(xn,xm)
& ? [X0] :
( sdtpldt0(xn,X0) = xm
& aNaturalNumber0(X0) )
& sdtlseqdt0(xm,xn)
& ? [X0] :
( sdtpldt0(xm,X0) = xn
& aNaturalNumber0(X0) ) )
=> xm = xn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f23,negated_conjecture,
~ ( ( sdtlseqdt0(xn,xm)
& ? [X0] :
( sdtpldt0(xn,X0) = xm
& aNaturalNumber0(X0) )
& sdtlseqdt0(xm,xn)
& ? [X0] :
( sdtpldt0(xm,X0) = xn
& aNaturalNumber0(X0) ) )
=> xm = xn ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f25,plain,
~ ( ( sdtlseqdt0(xn,xm)
& ? [X1] :
( xm = sdtpldt0(xn,X1)
& aNaturalNumber0(X1) )
& sdtlseqdt0(xm,xn)
& ? [X0] :
( sdtpldt0(xm,X0) = xn
& aNaturalNumber0(X0) ) )
=> xm = xn ),
inference(rectify,[],[f23]) ).
fof(f26,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f27,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f26]) ).
fof(f30,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f31,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f35,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f36,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(flattening,[],[f35]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| X1 = X2 ),
inference(ennf_transformation,[],[f14]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| X1 = X2 ),
inference(flattening,[],[f43]) ).
fof(f47,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f48,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(ennf_transformation,[],[f17]) ).
fof(f50,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(flattening,[],[f49]) ).
fof(f56,plain,
( sdtlseqdt0(xn,xm)
& ? [X1] :
( xm = sdtpldt0(xn,X1)
& aNaturalNumber0(X1) )
& sdtlseqdt0(xm,xn)
& ? [X0] :
( sdtpldt0(xm,X0) = xn
& aNaturalNumber0(X0) )
& xm != xn ),
inference(ennf_transformation,[],[f25]) ).
fof(f57,plain,
( sdtlseqdt0(xn,xm)
& ? [X1] :
( xm = sdtpldt0(xn,X1)
& aNaturalNumber0(X1) )
& sdtlseqdt0(xm,xn)
& ? [X0] :
( sdtpldt0(xm,X0) = xn
& aNaturalNumber0(X0) )
& xm != xn ),
inference(flattening,[],[f56]) ).
fof(f63,plain,
( sdtlseqdt0(xn,xm)
& xm = sdtpldt0(xn,sK2)
& aNaturalNumber0(sK2)
& sdtlseqdt0(xm,xn)
& xn = sdtpldt0(xm,sK1)
& aNaturalNumber0(sK1)
& xm != xn ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f57]) ).
fof(f64,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f65,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f3]) ).
fof(f66,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f67,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f69,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f71,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f34]) ).
fof(f72,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f34]) ).
fof(f73,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f81,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f44]) ).
fof(f85,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f48]) ).
fof(f87,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| sz00 = X1
| sz00 = X0 ),
inference(cnf_transformation,[],[f50]) ).
fof(f95,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f21]) ).
fof(f96,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f21]) ).
fof(f98,plain,
xm = sdtpldt0(xn,sK2),
inference(cnf_transformation,[],[f63]) ).
fof(f99,plain,
aNaturalNumber0(sK2),
inference(cnf_transformation,[],[f63]) ).
fof(f101,plain,
xn = sdtpldt0(xm,sK1),
inference(cnf_transformation,[],[f63]) ).
fof(f102,plain,
aNaturalNumber0(sK1),
inference(cnf_transformation,[],[f63]) ).
fof(f103,plain,
xm != xn,
inference(cnf_transformation,[],[f63]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f64]) ).
tcf(c_50,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f66]) ).
tcf(c_51,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f65]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_56,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_57,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sdtpldt0(X2,X1) ) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_80,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f96]) ).
tcf(c_81,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f95]) ).
tcf(c_82,negated_conjecture,
xm != xn,
inference(cnf_transformation,[],[f103]) ).
tcf(c_83,negated_conjecture,
aNaturalNumber0(sK1),
inference(cnf_transformation,[],[f102]) ).
tcf(c_84,negated_conjecture,
sdtpldt0(xm,sK1) = xn,
inference(cnf_transformation,[],[f101]) ).
tcf(c_86,negated_conjecture,
aNaturalNumber0(sK2),
inference(cnf_transformation,[],[f99]) ).
tcf(c_87,negated_conjecture,
sdtpldt0(xn,sK2) = xm,
inference(cnf_transformation,[],[f98]) ).
tcf(c_724,definition,
iPr_def_10 = sdtpldt0(xn,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_725,definition,
iPr_def_11 = sdtpldt0(xm,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_727,negated_conjecture,
iPr_def_10 = xm,
inference(demodulation,[status(thm)],[c_87,c_724]) ).
tcf(c_728,negated_conjecture,
aNaturalNumber0(sK2),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_730,negated_conjecture,
iPr_def_11 = xn,
inference(demodulation,[status(thm)],[c_84,c_725]) ).
tcf(c_731,negated_conjecture,
aNaturalNumber0(sK1),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_732,negated_conjecture,
xm != xn,
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_1278,plain,
iPr_def_10 != iPr_def_11,
inference(light_normalisation,[status(thm)],[c_732,c_727,c_730]) ).
tcf(c_1279,plain,
sdtpldt0(iPr_def_11,sK2) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_724,c_730]) ).
tcf(c_1280,plain,
aNaturalNumber0(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_80,c_727]) ).
tcf(c_1281,plain,
aNaturalNumber0(iPr_def_11),
inference(light_normalisation,[status(thm)],[c_81,c_730]) ).
tcf(c_1284,plain,
sdtpldt0(iPr_def_10,sK1) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_725,c_727]) ).
tcf(c_1293,plain,
sdtpldt0(iPr_def_10,sz00) = iPr_def_10,
inference(superposition,[status(thm)],[c_1280,c_56]) ).
tcf(c_1304,plain,
sdtpldt0(sz00,iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_1281,c_57]) ).
tcf(c_1506,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sK1) = sdtpldt0(sK1,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_731,c_54]) ).
tcf(c_1507,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sK2) = sdtpldt0(sK2,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_728,c_54]) ).
tcf(c_1541,plain,
sdtpldt0(sz10,sK1) = sdtpldt0(sK1,sz10),
inference(superposition,[status(thm)],[c_50,c_1506]) ).
tcf(c_1545,plain,
sdtpldt0(sK1,sK2) = sdtpldt0(sK2,sK1),
inference(superposition,[status(thm)],[c_728,c_1506]) ).
tcf(c_1546,plain,
sdtpldt0(sK1,iPr_def_10) = sdtpldt0(iPr_def_10,sK1),
inference(superposition,[status(thm)],[c_1280,c_1506]) ).
tcf(c_1548,plain,
sdtpldt0(sK1,iPr_def_10) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_1546,c_1284]) ).
tcf(c_1566,plain,
( aNaturalNumber0(sdtpldt0(sK1,sK2))
| ~ aNaturalNumber0(sK2)
| ~ aNaturalNumber0(sK1) ),
inference(superposition,[status(thm)],[c_1545,c_52]) ).
tcf(c_1567,plain,
aNaturalNumber0(sdtpldt0(sK1,sK2)),
inference(forward_subsumption_resolution,[status(thm)],[c_1566,c_728,c_731]) ).
tcf(c_1610,plain,
sdtpldt0(sK2,iPr_def_11) = sdtpldt0(iPr_def_11,sK2),
inference(superposition,[status(thm)],[c_1281,c_1507]) ).
tcf(c_1612,plain,
sdtpldt0(sK2,iPr_def_11) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_1610,c_1279]) ).
tcf(c_1623,plain,
( aNaturalNumber0(sdtpldt0(sz10,sK1))
| ~ aNaturalNumber0(sK1)
| ~ aNaturalNumber0(sz10) ),
inference(superposition,[status(thm)],[c_1541,c_52]) ).
tcf(c_1624,plain,
aNaturalNumber0(sdtpldt0(sz10,sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_1623,c_731,c_50]) ).
tcf(c_1643,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sK1) = sdtasdt0(sK1,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_731,c_58]) ).
tcf(c_2034,plain,
sdtasdt0(sdtpldt0(sz10,sK1),sK1) = sdtasdt0(sK1,sdtpldt0(sz10,sK1)),
inference(superposition,[status(thm)],[c_1624,c_1643]) ).
tcf(c_2302,plain,
( ( sz00 = sz10 )
| ~ aNaturalNumber0(sK1)
| ~ aNaturalNumber0(sz10)
| ( sdtpldt0(sz10,sK1) != sz00 ) ),
inference(superposition,[status(thm)],[c_1541,c_71]) ).
tcf(c_2303,plain,
( ( sz00 = sK1 )
| ~ aNaturalNumber0(sK2)
| ~ aNaturalNumber0(sK1)
| ( sdtpldt0(sK1,sK2) != sz00 ) ),
inference(superposition,[status(thm)],[c_1545,c_71]) ).
tcf(c_2314,plain,
( ( sz00 = sK1 )
| ( sdtpldt0(sK1,sK2) != sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2303,c_728,c_731]) ).
tcf(c_2317,plain,
sdtpldt0(sz10,sK1) != sz00,
inference(forward_subsumption_resolution,[status(thm)],[c_2302,c_51,c_731,c_50]) ).
tcf(c_2594,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(sdtpldt0(sK1,X0),X1) = sdtpldt0(sK1,sdtpldt0(X0,X1)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_731,c_55]) ).
tcf(c_7460,plain,
! [X0: $i] :
( ( sdtpldt0(sdtpldt0(sK1,sK2),X0) = sdtpldt0(sK1,sdtpldt0(sK2,X0)) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_728,c_2594]) ).
tcf(c_8159,plain,
sdtpldt0(sdtpldt0(sK1,sK2),iPr_def_11) = sdtpldt0(sK1,sdtpldt0(sK2,iPr_def_11)),
inference(superposition,[status(thm)],[c_1281,c_7460]) ).
tcf(c_8175,plain,
sdtpldt0(sdtpldt0(sK1,sK2),iPr_def_11) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_8159,c_1548,c_1612]) ).
tcf(c_8965,plain,
! [X0: $i] :
( ( sdtpldt0(sK1,sK2) = X0 )
| ~ aNaturalNumber0(iPr_def_11)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(sK1,sK2))
| ( sdtpldt0(X0,iPr_def_11) != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_8175,c_67]) ).
tcf(c_8972,plain,
! [X0: $i] :
( ( sdtpldt0(sK1,sK2) = X0 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,iPr_def_11) != iPr_def_11 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8965,c_1281,c_1567]) ).
tcf(c_8981,plain,
( ( sdtpldt0(sK1,sK2) = sz00 )
| ~ aNaturalNumber0(sz00)
| ( sdtpldt0(sz00,iPr_def_11) != iPr_def_11 ) ),
inference(instantiation,[status(thm)],[c_8972]) ).
tcf(c_10450,plain,
( ( sz00 = sK1 )
| ( sdtpldt0(sz10,sK1) = sz00 )
| ~ aNaturalNumber0(sK1)
| ~ aNaturalNumber0(sdtpldt0(sz10,sK1))
| ( sdtasdt0(sK1,sdtpldt0(sz10,sK1)) != sz00 ) ),
inference(superposition,[status(thm)],[c_2034,c_72]) ).
tcf(c_10455,plain,
( ( sz00 = sK1 )
| ( sdtasdt0(sK1,sdtpldt0(sz10,sK1)) != sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10450,c_2317,c_731,c_1624]) ).
tcf(c_10875,plain,
sz00 = sK1,
inference(global_subsumption_just,[status(thm)],[c_10455,c_49,c_1304,c_2314,c_8981]) ).
tcf(c_11028,plain,
sdtpldt0(iPr_def_10,sz00) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1284,c_10875]) ).
tcf(c_11042,plain,
iPr_def_10 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_11028,c_1293]) ).
tcf(c_11043,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11042,c_1278]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM459+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 04:06:35 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 9.85/2.25 % SZS status Started for theBenchmark.p
% 9.85/2.25 % SZS status Theorem for theBenchmark.p
% 9.85/2.25
% 9.85/2.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 9.85/2.25
% 9.85/2.25 % ------ iProver source info
% 9.85/2.25
% 9.85/2.25 % git: date: 2026-07-19 20:42:38 +0200
% 9.85/2.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 9.85/2.25 % git: non_committed_changes: false
% 9.85/2.25
% 9.85/2.25 % ------ Parsing...
% 9.85/2.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 9.85/2.25
% 9.85/2.25 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 9.85/2.25
% 9.85/2.25 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 9.85/2.25
% 9.85/2.25 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 9.85/2.25 % ------ Proving...
% 9.85/2.25 % ------ Problem Properties
% 9.85/2.25
% 9.85/2.25 %
% 9.85/2.25 % clauses 42
% 9.85/2.25 % conjectures 7
% 9.85/2.25 % EPR 13
% 9.85/2.25 % Horn 39
% 9.85/2.25 % unary 14
% 9.85/2.25 % binary 7
% 9.85/2.25 % lits 113
% 9.85/2.25 % lits eq 38
% 9.85/2.25 % fd_pure 0
% 9.85/2.25 % fd_pseudo 0
% 9.85/2.25 % fd_cond 3
% 9.85/2.25 % fd_pseudo_cond 4
% 9.85/2.25 % AC symbols 0
% 9.85/2.25
% 9.85/2.25 % ------ Schedule dynamic 5 is on
% 9.85/2.25
% 9.85/2.25 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 9.85/2.25
% 9.85/2.25
% 9.85/2.25 % ------
% 9.85/2.25 % Current options:
% 9.85/2.25 % ------
% 9.85/2.25
% 9.85/2.25
% 9.85/2.25 %
% 9.85/2.25
% 9.85/2.25 % ------ Proving...
% 9.85/2.25 %
% 9.85/2.25
% 9.85/2.25 % SZS status Theorem for theBenchmark.p
% 9.85/2.25
% 9.85/2.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.85/2.26
% 9.85/2.26
%------------------------------------------------------------------------------