%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM508+1 : 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 8.33s 1.64s
% Output : CNFRefutation 8.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 23 unt; 0 def)
% Number of atoms : 168 ( 16 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 196 ( 86 ~; 89 |; 14 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 47 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
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(f29,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> iLess0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f40,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X2,sdtasdt0(X0,X1))
& isPrime0(X2) )
=> ( iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(X2,X1)
| doDivides0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1799) ).
fof(f48,axiom,
( isPrime0(xr)
& doDivides0(xr,xk)
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(f49,axiom,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtlseqdt0(xr,xk) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2362) ).
fof(f51,axiom,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2478) ).
fof(f52,conjecture,
( doDivides0(xr,xm)
| doDivides0(xr,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f53,negated_conjecture,
~ ( doDivides0(xr,xm)
| doDivides0(xr,xn) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| doDivides0(X2,X1)
| doDivides0(X2,X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| doDivides0(X2,X1)
| doDivides0(X2,X0) ),
inference(flattening,[],[f56]) ).
fof(f59,plain,
( ~ doDivides0(xr,xm)
& ~ doDivides0(xr,xn) ),
inference(ennf_transformation,[],[f53]) ).
fof(f77,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f78,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f80,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f82,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(flattening,[],[f81]) ).
fof(f135,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f136,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f137,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f138,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| doDivides0(X2,X1)
| doDivides0(X2,X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f152,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f154,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f155,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f49]) ).
fof(f159,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(cnf_transformation,[],[f51]) ).
fof(f160,plain,
sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xr),
inference(cnf_transformation,[],[f51]) ).
fof(f161,plain,
~ doDivides0(xr,xm),
inference(cnf_transformation,[],[f59]) ).
fof(f162,plain,
~ doDivides0(xr,xn),
inference(cnf_transformation,[],[f59]) ).
fof(f181,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f182,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f80]) ).
fof(f183,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_49,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f137]) ).
tcf(c_50,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f136]) ).
tcf(c_51,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f135]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(X2,X1)
| doDivides0(X2,X0)
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_66,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f154]) ).
tcf(c_68,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f152]) ).
tcf(c_70,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f155]) ).
tcf(c_73,plain,
sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xr),
inference(cnf_transformation,[],[f160]) ).
tcf(c_74,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(cnf_transformation,[],[f159]) ).
tcf(c_75,negated_conjecture,
~ doDivides0(xr,xn),
inference(cnf_transformation,[],[f162]) ).
tcf(c_76,negated_conjecture,
~ doDivides0(xr,xm),
inference(cnf_transformation,[],[f161]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( iLess0(X0,X1)
| ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_4968,plain,
! [X0: $i] :
( ( sdtpldt0(X0,xn) = sdtpldt0(xn,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_49,c_95]) ).
tcf(c_5131,plain,
! [X0: $i] :
( doDivides0(xr,xn)
| doDivides0(xr,X0)
| ~ isPrime0(xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xr,sdtasdt0(xn,X0))
| ~ iLess0(sdtpldt0(sdtpldt0(xn,X0),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_5222,plain,
sdtpldt0(xn,xm) = sdtpldt0(xm,xn),
inference(superposition,[status(thm)],[c_50,c_4968]) ).
tcf(c_5264,plain,
( aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_5222,c_96]) ).
tcf(c_5265,plain,
aNaturalNumber0(sdtpldt0(xn,xm)),
inference(forward_subsumption_resolution,[status(thm)],[c_5264,c_50,c_49]) ).
tcf(c_5653,plain,
( iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr) )
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(superposition,[status(thm)],[c_74,c_97]) ).
tcf(c_5753,plain,
( iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5653,c_73]) ).
tcf(c_6411,plain,
( doDivides0(xr,xm)
| doDivides0(xr,xn)
| ~ isPrime0(xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(instantiation,[status(thm)],[c_5131]) ).
tcf(c_6543,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_17083,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_17084,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_17083,c_6543,c_6411,c_5753,c_5265,c_70,c_75,c_76,c_49,c_50,c_51,c_66,c_68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM508+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 04:21:13 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 8.33/1.64 % SZS status Started for theBenchmark.p
% 8.33/1.64 % SZS status Theorem for theBenchmark.p
% 8.33/1.64
% 8.33/1.64 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.33/1.64
% 8.33/1.64 % ------ iProver source info
% 8.33/1.64
% 8.33/1.64 % git: date: 2026-07-19 20:42:38 +0200
% 8.33/1.64 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.33/1.64 % git: non_committed_changes: false
% 8.33/1.64
% 8.33/1.64 % ------ Parsing...
% 8.33/1.64 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.33/1.64
% 8.33/1.64 % ------ Preprocessing... sup_sim: 0 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 %
% 8.33/1.64
% 8.33/1.64 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.33/1.64
% 8.33/1.64 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.33/1.64 % ------ Proving...
% 8.33/1.64 % ------ Problem Properties
% 8.33/1.64
% 8.33/1.64 %
% 8.33/1.64 % clauses 85
% 8.33/1.64 % conjectures 2
% 8.33/1.64 % EPR 34
% 8.33/1.64 % Horn 60
% 8.33/1.64 % unary 30
% 8.33/1.64 % binary 7
% 8.33/1.64 % lits 272
% 8.33/1.64 % lits eq 76
% 8.33/1.64 % fd_pure 0
% 8.33/1.64 % fd_pseudo 0
% 8.33/1.64 % fd_cond 15
% 8.33/1.64 % fd_pseudo_cond 11
% 8.33/1.64 % AC symbols 0
% 8.33/1.64
% 8.33/1.64 % ------ Schedule dynamic 5 is on
% 8.33/1.64
% 8.33/1.64 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.33/1.64
% 8.33/1.64
% 8.33/1.64 % ------
% 8.33/1.64 % Current options:
% 8.33/1.64 % ------
% 8.33/1.64
% 8.33/1.64
% 8.33/1.64 %
% 8.33/1.64
% 8.33/1.64 % ------ Proving...
% 8.33/1.64 %
% 8.33/1.64
% 8.33/1.64 % SZS status Theorem for theBenchmark.p
% 8.33/1.64
% 8.33/1.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.33/1.64
% 8.33/1.64
%------------------------------------------------------------------------------