%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM492+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n004.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 02:25:17 PM UTC 2026
% Result : Theorem 10.39s 7.30s
% Output : CNFRefutation 10.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 64 ( 28 unt; 0 def)
% Number of atoms : 188 ( 38 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 227 ( 103 ~; 99 |; 16 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 69 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f19,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(f34,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,sdtpldt0(X1,X2))
& doDivides0(X0,X1) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivMin) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f42,axiom,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
fof(f43,axiom,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
fof(f46,axiom,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1951) ).
fof(f48,axiom,
( doDivides0(xp,sdtasdt0(xp,xm))
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2001) ).
fof(f49,conjecture,
doDivides0(xp,sdtasdt0(xr,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f50,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xr,xm)),
inference(negated_conjecture,[status(cth)],[f49]) ).
fof(f53,plain,
~ doDivides0(xp,sdtasdt0(xr,xm)),
inference(flattening,[],[f50]) ).
fof(f56,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f57,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f56]) ).
fof(f63,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f64,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(flattening,[],[f63]) ).
fof(f81,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f82,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f81]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(flattening,[],[f108]) ).
fof(f123,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( ( sdtmndt0(X1,X0) != X2
| ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
& ( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtmndt0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f82]) ).
fof(f124,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( ( sdtmndt0(X1,X0) != X2
| ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
& ( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtmndt0(X1,X0) ) ) ),
inference(flattening,[],[f123]) ).
fof(f139,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f144,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f163,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtmndt0(X1,X0) != X2
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f124]) ).
fof(f190,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(cnf_transformation,[],[f109]) ).
fof(f203,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f204,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f205,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f209,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f210,plain,
xr = sdtmndt0(xn,xp),
inference(cnf_transformation,[],[f43]) ).
fof(f214,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(cnf_transformation,[],[f46]) ).
fof(f216,plain,
doDivides0(xp,sdtasdt0(xp,xm)),
inference(cnf_transformation,[],[f48]) ).
fof(f217,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f48]) ).
fof(f218,plain,
~ doDivides0(xp,sdtasdt0(xr,xm)),
inference(cnf_transformation,[],[f53]) ).
fof(f221,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| aNaturalNumber0(sdtmndt0(X1,X0)) ),
inference(equality_resolution,[],[f163]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X0,sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_116,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f205]) ).
tcf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f204]) ).
tcf(c_118,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f203]) ).
tcf(c_122,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f209]) ).
tcf(c_123,plain,
sdtmndt0(xn,xp) = xr,
inference(cnf_transformation,[],[f210]) ).
tcf(c_127,plain,
sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) = sdtasdt0(xn,xm),
inference(cnf_transformation,[],[f214]) ).
tcf(c_129,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f217]) ).
tcf(c_130,plain,
doDivides0(xp,sdtasdt0(xp,xm)),
inference(cnf_transformation,[],[f216]) ).
tcf(c_131,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xr,xm)),
inference(cnf_transformation,[],[f218]) ).
tcf(c_2368,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_2377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3608,plain,
! [X0: $i] :
( doDivides0(xp,sdtasdt0(xr,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,X0)
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ doDivides0(xp,sdtpldt0(X0,sdtasdt0(xr,xm))) ),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_3616,plain,
! [X0: $i] :
( doDivides0(xp,sdtasdt0(xr,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,X0))
| ~ doDivides0(xp,sdtasdt0(xp,X0))
| ~ doDivides0(xp,sdtpldt0(sdtasdt0(xp,X0),sdtasdt0(xr,xm))) ),
inference(instantiation,[status(thm)],[c_3608]) ).
tcf(c_3620,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(xp,X0)
| ~ doDivides0(X2,X1)
| ( xp != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_2377]) ).
tcf(c_3640,plain,
( aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_3666,plain,
xp = xp,
inference(instantiation,[status(thm)],[c_2368]) ).
tcf(c_3752,plain,
! [X0: $i] :
( doDivides0(xp,X0)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ( xp != xp )
| ( X0 != sdtasdt0(xn,xm) ) ),
inference(instantiation,[status(thm)],[c_3620]) ).
tcf(c_3921,plain,
( doDivides0(xp,sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)))
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ( xp != xp )
| ( sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) != sdtasdt0(xn,xm) ) ),
inference(instantiation,[status(thm)],[c_3752]) ).
tcf(c_6190,plain,
( aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn) ),
inference(superposition,[status(thm)],[c_123,c_77]) ).
tcf(c_7243,plain,
( doDivides0(xp,sdtasdt0(xr,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ doDivides0(xp,sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm))) ),
inference(instantiation,[status(thm)],[c_3616]) ).
tcf(c_8775,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xm) = sdtasdt0(xm,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_117,c_58]) ).
tcf(c_8952,plain,
sdtasdt0(xm,xp) = sdtasdt0(xp,xm),
inference(superposition,[status(thm)],[c_118,c_8775]) ).
tcf(c_10535,plain,
( aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_8952,c_53]) ).
tcf(c_10537,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_10535,c_7243,c_6190,c_3921,c_3666,c_3640,c_127,c_131,c_129,c_130,c_122,c_116,c_117,c_118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM492+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.37 % Computer : n004.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Thu Sep 24 04:15:28 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.43
% 0.15/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.43
% 0.15/5.43 % Detected problem language: tptp
% 0.15/5.44 % Proving...
% 10.39/7.30 % SZS status Started for theBenchmark.p
% 10.39/7.30 % SZS status Theorem for theBenchmark.p
% 10.39/7.30
% 10.39/7.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.39/7.30
% 10.39/7.30 % ------ iProver source info
% 10.39/7.30
% 10.39/7.30 % git: date: 2026-07-19 20:42:38 +0200
% 10.39/7.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.39/7.30 % git: non_committed_changes: false
% 10.39/7.30
% 10.39/7.30 % ------ Parsing...
% 10.39/7.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.39/7.30
% 10.39/7.30 % ------ 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 %
% 10.39/7.30
% 10.39/7.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.39/7.30
% 10.39/7.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.39/7.30 % ------ Proving...
% 10.39/7.30 % ------ Problem Properties
% 10.39/7.30
% 10.39/7.30 %
% 10.39/7.30 % clauses 77
% 10.39/7.30 % conjectures 1
% 10.39/7.30 % EPR 21
% 10.39/7.30 % Horn 52
% 10.39/7.30 % unary 19
% 10.39/7.30 % binary 7
% 10.39/7.30 % lits 272
% 10.39/7.30 % lits eq 76
% 10.39/7.30 % fd_pure 0
% 10.39/7.30 % fd_pseudo 0
% 10.39/7.30 % fd_cond 15
% 10.39/7.30 % fd_pseudo_cond 11
% 10.39/7.30 % AC symbols 0
% 10.39/7.30
% 10.39/7.30 % ------ Input Options Time Limit: Unbounded
% 10.39/7.30
% 10.39/7.30
% 10.39/7.30 % ------
% 10.39/7.30 % Current options:
% 10.39/7.30 % ------
% 10.39/7.30
% 10.39/7.30
% 10.39/7.30 %
% 10.39/7.30
% 10.39/7.30 % ------ Proving...
% 10.39/7.30 %
% 10.39/7.30
% 10.39/7.30 % SZS status Theorem for theBenchmark.p
% 10.39/7.30
% 10.39/7.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.39/7.30
% 10.39/7.30
%------------------------------------------------------------------------------