%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM504+3 : 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 : n009.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 02:25:22 PM UTC 2026
% Result : Theorem 3.02s 1.09s
% Output : CNFRefutation 3.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 54 ( 24 unt; 0 def)
% Number of atoms : 197 ( 66 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 213 ( 70 ~; 56 |; 81 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 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; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 12 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 38 !; 14 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(f45,axiom,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& aNaturalNumber0(xk) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(f48,axiom,
( isPrime0(xr)
& ! [X0] :
( ( ( doDivides0(X0,xr)
| ? [X1] :
( xr = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xr
| X0 = sz10 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(f49,axiom,
( doDivides0(xr,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& ? [X0] :
( sdtpldt0(xr,X0) = xk
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2362) ).
fof(f51,axiom,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& ? [X0] :
( sdtpldt0(sdtasdt0(xp,xm),X0) = sdtasdt0(xp,xk)
& aNaturalNumber0(X0) )
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& ? [X0] :
( sdtpldt0(sdtasdt0(xn,xm),X0) = sdtasdt0(xp,xm)
& aNaturalNumber0(X0) )
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2414) ).
fof(f59,plain,
( isPrime0(xr)
& ! [X1] :
( ( ( doDivides0(X1,xr)
| ? [X2] :
( sdtasdt0(X1,X2) = xr
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( xr = X1
| sz10 = X1 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ),
inference(rectify,[],[f48]) ).
fof(f60,plain,
( doDivides0(xr,sdtasdt0(xn,xm))
& ? [X1] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X1)
& aNaturalNumber0(X1) )
& ? [X0] :
( sdtpldt0(xr,X0) = xk
& aNaturalNumber0(X0) ) ),
inference(rectify,[],[f49]) ).
fof(f61,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& ? [X1] :
( sdtasdt0(xp,xk) = sdtpldt0(sdtasdt0(xp,xm),X1)
& aNaturalNumber0(X1) )
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& ? [X0] :
( sdtpldt0(sdtasdt0(xn,xm),X0) = sdtasdt0(xp,xm)
& aNaturalNumber0(X0) )
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
inference(rectify,[],[f51]) ).
fof(f63,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f64,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f66,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f65]) ).
fof(f93,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f94,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f93]) ).
fof(f134,plain,
( isPrime0(xr)
& ! [X1] :
( ( ~ doDivides0(X1,xr)
& ! [X2] :
( sdtasdt0(X1,X2) != xr
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| xr = X1
| sz10 = X1 )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ),
inference(ennf_transformation,[],[f59]) ).
fof(f135,plain,
( isPrime0(xr)
& ! [X1] :
( ( ~ doDivides0(X1,xr)
& ! [X2] :
( sdtasdt0(X1,X2) != xr
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| xr = X1
| sz10 = X1 )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ),
inference(flattening,[],[f134]) ).
fof(f164,plain,
( isPrime0(xr)
& ! [X1] :
( ( ~ doDivides0(X1,xr)
& ! [X2] :
( sdtasdt0(X1,X2) != xr
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| xr = X1
| sz10 = X1 )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& xk = sdtasdt0(xr,sK13)
& aNaturalNumber0(sK13)
& aNaturalNumber0(xr) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X0,sK13)],[f135]) ).
fof(f165,plain,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xr,sK15)
& aNaturalNumber0(sK15)
& xk = sdtpldt0(xr,sK14)
& aNaturalNumber0(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X0,sK14),skolemize(X1,sK15)],[f60]) ).
fof(f167,plain,
( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
& sdtasdt0(xp,xk) = sdtpldt0(sdtasdt0(xp,xm),sK18)
& aNaturalNumber0(sK18)
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),sK17)
& aNaturalNumber0(sK17)
& sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18]),skolemize(X0,sK17),skolemize(X1,sK18)],[f61]) ).
fof(f171,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f172,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f199,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f94]) ).
fof(f276,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f45]) ).
fof(f290,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f164]) ).
fof(f292,plain,
sdtasdt0(xn,xm) = sdtasdt0(xr,sK15),
inference(cnf_transformation,[],[f165]) ).
fof(f293,plain,
aNaturalNumber0(sK15),
inference(cnf_transformation,[],[f165]) ).
fof(f299,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
inference(cnf_transformation,[],[f167]) ).
fof(f302,plain,
sdtasdt0(xp,xk) != sdtasdt0(xp,xm),
inference(cnf_transformation,[],[f167]) ).
fof(f303,plain,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(cnf_transformation,[],[f167]) ).
fof(f304,plain,
sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),sK17),
inference(cnf_transformation,[],[f167]) ).
fof(f305,plain,
aNaturalNumber0(sK17),
inference(cnf_transformation,[],[f167]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f172]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_156,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f276]) ).
tcf(c_162,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f290]) ).
tcf(c_173,plain,
aNaturalNumber0(sK15),
inference(cnf_transformation,[],[f293]) ).
tcf(c_174,plain,
sdtasdt0(xn,xm) = sdtasdt0(xr,sK15),
inference(cnf_transformation,[],[f292]) ).
tcf(c_180,plain,
aNaturalNumber0(sK17),
inference(cnf_transformation,[],[f305]) ).
tcf(c_181,plain,
sdtpldt0(sdtasdt0(xn,xm),sK17) = sdtasdt0(xp,xm),
inference(cnf_transformation,[],[f304]) ).
tcf(c_182,plain,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(cnf_transformation,[],[f303]) ).
tcf(c_183,plain,
sdtasdt0(xp,xm) != sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f302]) ).
tcf(c_186,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
inference(cnf_transformation,[],[f299]) ).
tcf(c_1092,plain,
sdtasdt0(xp,xk) = sdtasdt0(xr,sK15),
inference(demodulation,[status(thm)],[c_174,c_156]) ).
tcf(c_1093,plain,
sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm)),
inference(demodulation,[status(thm)],[c_182,c_156]) ).
tcf(c_1126,plain,
sdtpldt0(sdtasdt0(xp,xk),sK17) = sdtasdt0(xp,xm),
inference(light_normalisation,[status(thm)],[c_181,c_156]) ).
tcf(c_11067,plain,
( aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sK15)
| ~ aNaturalNumber0(xr) ),
inference(superposition,[status(thm)],[c_1092,c_53]) ).
tcf(c_11074,plain,
aNaturalNumber0(sdtasdt0(xp,xk)),
inference(forward_subsumption_resolution,[status(thm)],[c_11067,c_173,c_162]) ).
tcf(c_11126,plain,
( aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sK17)
| ~ aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(superposition,[status(thm)],[c_1126,c_52]) ).
tcf(c_11127,plain,
aNaturalNumber0(sdtasdt0(xp,xm)),
inference(forward_subsumption_resolution,[status(thm)],[c_11126,c_180,c_11074]) ).
tcf(c_11496,plain,
( ( sdtasdt0(xp,xm) = sdtasdt0(xp,xk) )
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_11497,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11496,c_11127,c_11074,c_1093,c_183,c_186]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM504+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 04:19:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 0.14/0.44
% 0.14/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.44
% 0.14/0.44 % Detected problem language: tptp
% 0.14/0.45 % Proving...
% 3.02/1.09 % SZS status Started for theBenchmark.p
% 3.02/1.09 % SZS status Theorem for theBenchmark.p
% 3.02/1.09
% 3.02/1.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.02/1.09
% 3.02/1.09 % ------ iProver source info
% 3.02/1.09
% 3.02/1.09 % git: date: 2026-07-19 20:42:38 +0200
% 3.02/1.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.02/1.09 % git: non_committed_changes: false
% 3.02/1.09
% 3.02/1.09 % ------ Parsing...
% 3.02/1.09 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.02/1.09
% 3.02/1.09 % ------ Preprocessing... sup_sim: 8 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.02/1.09
% 3.02/1.09 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.02/1.09
% 3.02/1.09 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.02/1.09 % ------ Proving...
% 3.02/1.09 % ------ Problem Properties
% 3.02/1.09
% 3.02/1.09 %
% 3.02/1.09 % clauses 130
% 3.02/1.09 % conjectures 0
% 3.02/1.09 % EPR 48
% 3.02/1.09 % Horn 90
% 3.02/1.09 % unary 51
% 3.02/1.09 % binary 13
% 3.02/1.09 % lits 401
% 3.02/1.09 % lits eq 124
% 3.02/1.09 % fd_pure 0
% 3.02/1.09 % fd_pseudo 0
% 3.02/1.09 % fd_cond 24
% 3.02/1.09 % fd_pseudo_cond 11
% 3.02/1.09 % AC symbols 0
% 3.02/1.09
% 3.02/1.09 % ------ Schedule dynamic 5 is on
% 3.02/1.09
% 3.02/1.09 % ------ no conjectures: strip conj schedule
% 3.02/1.09
% 3.02/1.09 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.02/1.09
% 3.02/1.09
% 3.02/1.09 % ------
% 3.02/1.09 % Current options:
% 3.02/1.09 % ------
% 3.02/1.09
% 3.02/1.09
% 3.02/1.09 %
% 3.02/1.09
% 3.02/1.09 % ------ Proving...
% 3.02/1.09 %
% 3.02/1.09
% 3.02/1.09 % SZS status Theorem for theBenchmark.p
% 3.02/1.09
% 3.02/1.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.02/1.09
% 3.02/1.09
%------------------------------------------------------------------------------