%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM466+2 : 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 : n015.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 02:24:34 PM UTC 2026
% Result : Theorem 7.01s 1.77s
% Output : CNFRefutation 7.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 55 ( 23 unt; 0 def)
% Number of atoms : 160 ( 51 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 162 ( 57 ~; 47 |; 52 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 49 !; 15 ?; 16 :)
% 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(f10,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(f32,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1218) ).
fof(f33,conjecture,
( ( doDivides0(xm,xn)
& ? [X0] :
( xn = sdtasdt0(xm,X0)
& aNaturalNumber0(X0) )
& doDivides0(xl,xm)
& ? [X0] :
( xm = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) ) )
=> ( doDivides0(xl,xn)
| ? [X0] :
( xn = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f34,negated_conjecture,
~ ( ( doDivides0(xm,xn)
& ? [X0] :
( xn = sdtasdt0(xm,X0)
& aNaturalNumber0(X0) )
& doDivides0(xl,xm)
& ? [X0] :
( xm = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) ) )
=> ( doDivides0(xl,xn)
| ? [X0] :
( xn = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f37,plain,
~ ( ( doDivides0(xm,xn)
& ? [X1] :
( xn = sdtasdt0(xm,X1)
& aNaturalNumber0(X1) )
& doDivides0(xl,xm)
& ? [X0] :
( xm = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) ) )
=> ( doDivides0(xl,xn)
| ? [X2] :
( xn = sdtasdt0(xl,X2)
& aNaturalNumber0(X2) ) ) ),
inference(rectify,[],[f34]) ).
fof(f41,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f42,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f41]) ).
fof(f48,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f49,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(ennf_transformation,[],[f10]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(flattening,[],[f50]) ).
fof(f87,plain,
( doDivides0(xm,xn)
& ? [X1] :
( xn = sdtasdt0(xm,X1)
& aNaturalNumber0(X1) )
& doDivides0(xl,xm)
& ? [X0] :
( xm = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) )
& ~ doDivides0(xl,xn)
& ! [X2] :
( xn != sdtasdt0(xl,X2)
| ~ aNaturalNumber0(X2) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f88,plain,
( doDivides0(xm,xn)
& ? [X1] :
( xn = sdtasdt0(xm,X1)
& aNaturalNumber0(X1) )
& doDivides0(xl,xm)
& ? [X0] :
( xm = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) )
& ~ doDivides0(xl,xn)
& ! [X2] :
( xn != sdtasdt0(xl,X2)
| ~ aNaturalNumber0(X2) ) ),
inference(flattening,[],[f87]) ).
fof(f99,plain,
( doDivides0(xm,xn)
& ? [X2] :
( xn = sdtasdt0(xm,X2)
& aNaturalNumber0(X2) )
& doDivides0(xl,xm)
& ? [X1] :
( xm = sdtasdt0(xl,X1)
& aNaturalNumber0(X1) )
& ~ doDivides0(xl,xn)
& ! [X0] :
( xn != sdtasdt0(xl,X0)
| ~ aNaturalNumber0(X0) ) ),
inference(rectify,[],[f88]) ).
fof(f100,plain,
( doDivides0(xm,xn)
& xn = sdtasdt0(xm,sK3)
& aNaturalNumber0(sK3)
& doDivides0(xl,xm)
& xm = sdtasdt0(xl,sK2)
& aNaturalNumber0(sK2)
& ~ doDivides0(xl,xn)
& ! [X0] :
( xn != sdtasdt0(xl,X0)
| ~ aNaturalNumber0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X1,sK2),skolemize(X2,sK3)],[f99]) ).
fof(f105,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f42]) ).
fof(f110,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f154,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f32]) ).
fof(f155,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f32]) ).
fof(f157,plain,
xn = sdtasdt0(xm,sK3),
inference(cnf_transformation,[],[f100]) ).
fof(f158,plain,
aNaturalNumber0(sK3),
inference(cnf_transformation,[],[f100]) ).
fof(f160,plain,
xm = sdtasdt0(xl,sK2),
inference(cnf_transformation,[],[f100]) ).
fof(f161,plain,
aNaturalNumber0(sK2),
inference(cnf_transformation,[],[f100]) ).
fof(f163,plain,
! [X0] :
( xn != sdtasdt0(xl,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_100,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f155]) ).
tcf(c_101,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f154]) ).
tcf(c_103,negated_conjecture,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ( sdtasdt0(xl,X0) != xn ) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_105,negated_conjecture,
aNaturalNumber0(sK2),
inference(cnf_transformation,[],[f161]) ).
tcf(c_106,negated_conjecture,
sdtasdt0(xl,sK2) = xm,
inference(cnf_transformation,[],[f160]) ).
tcf(c_108,negated_conjecture,
aNaturalNumber0(sK3),
inference(cnf_transformation,[],[f158]) ).
tcf(c_109,negated_conjecture,
sdtasdt0(xm,sK3) = xn,
inference(cnf_transformation,[],[f157]) ).
tcf(c_156,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sK3) = sdtasdt0(sK3,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_108,c_58]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(xl,X0),X1) = sdtasdt0(xl,sdtasdt0(X0,X1)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_100,c_59]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(sK3,X0),X1) = sdtasdt0(sK3,sdtasdt0(X0,X1)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_108,c_59]) ).
tcf(c_200,plain,
sdtasdt0(xl,sK3) = sdtasdt0(sK3,xl),
inference(superposition,[status(thm)],[c_100,c_156]) ).
tcf(c_201,plain,
sdtasdt0(xm,sK3) = sdtasdt0(sK3,xm),
inference(superposition,[status(thm)],[c_101,c_156]) ).
tcf(c_203,plain,
sdtasdt0(sK2,sK3) = sdtasdt0(sK3,sK2),
inference(superposition,[status(thm)],[c_105,c_156]) ).
tcf(c_324,plain,
! [X0: $i] :
( ( sdtasdt0(sdtasdt0(sK3,xl),X0) = sdtasdt0(sK3,sdtasdt0(xl,X0)) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_100,c_186]) ).
tcf(c_422,plain,
! [X0: $i] :
( ( sdtasdt0(sdtasdt0(xl,sK3),X0) = sdtasdt0(xl,sdtasdt0(sK3,X0)) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_108,c_182]) ).
tcf(c_482,plain,
( aNaturalNumber0(sdtasdt0(sK2,sK3))
| ~ aNaturalNumber0(sK3)
| ~ aNaturalNumber0(sK2) ),
inference(superposition,[status(thm)],[c_203,c_53]) ).
tcf(c_499,plain,
sdtasdt0(sK3,xm) = xn,
inference(light_normalisation,[status(thm)],[c_201,c_109]) ).
tcf(c_871,plain,
! [X0: $i] :
( ( sdtasdt0(sdtasdt0(xl,sK3),X0) = sdtasdt0(sK3,sdtasdt0(xl,X0)) )
| ~ aNaturalNumber0(X0) ),
inference(light_normalisation,[status(thm)],[c_324,c_200]) ).
tcf(c_880,plain,
sdtasdt0(sdtasdt0(xl,sK3),sK2) = sdtasdt0(sK3,sdtasdt0(xl,sK2)),
inference(superposition,[status(thm)],[c_105,c_871]) ).
tcf(c_1266,plain,
sdtasdt0(sdtasdt0(xl,sK3),sK2) = sdtasdt0(xl,sdtasdt0(sK3,sK2)),
inference(superposition,[status(thm)],[c_105,c_422]) ).
tcf(c_1537,plain,
aNaturalNumber0(sdtasdt0(sK2,sK3)),
inference(global_subsumption_just,[status(thm)],[c_482,c_108,c_105,c_482]) ).
tcf(c_4698,plain,
sdtasdt0(sdtasdt0(xl,sK3),sK2) = xn,
inference(light_normalisation,[status(thm)],[c_880,c_106,c_499]) ).
tcf(c_6671,plain,
sdtasdt0(xl,sdtasdt0(sK2,sK3)) = xn,
inference(light_normalisation,[status(thm)],[c_1266,c_203,c_4698]) ).
tcf(c_6674,plain,
~ aNaturalNumber0(sdtasdt0(sK2,sK3)),
inference(superposition,[status(thm)],[c_6671,c_103]) ).
tcf(c_6675,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_1537,c_6674]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM466+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/0.44 % Computer : n015.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Thu Sep 24 04:10:42 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.23/0.50 Running first-order theorem proving
% 0.23/0.50 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
% 0.23/0.51
% 0.23/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.51
% 0.23/0.51 % Detected problem language: tptp
% 0.23/0.52 % Proving...
% 7.01/1.77 % SZS status Started for theBenchmark.p
% 7.01/1.77 % SZS status Theorem for theBenchmark.p
% 7.01/1.77
% 7.01/1.77 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.01/1.77
% 7.01/1.77 % ------ iProver source info
% 7.01/1.77
% 7.01/1.77 % git: date: 2026-07-19 20:42:38 +0200
% 7.01/1.77 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.01/1.77 % git: non_committed_changes: false
% 7.01/1.77
% 7.01/1.77 % ------ Parsing...
% 7.01/1.77 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.01/1.77 % ------ Proving...
% 7.01/1.77 % ------ Problem Properties
% 7.01/1.77
% 7.01/1.77 %
% 7.01/1.77 % clauses 62
% 7.01/1.77 % conjectures 8
% 7.01/1.77 % EPR 17
% 7.01/1.77 % Horn 47
% 7.01/1.77 % unary 13
% 7.01/1.77 % binary 9
% 7.01/1.77 % lits 222
% 7.01/1.77 % lits eq 62
% 7.01/1.77 % fd_pure 0
% 7.01/1.77 % fd_pseudo 0
% 7.01/1.77 % fd_cond 6
% 7.01/1.77 % fd_pseudo_cond 13
% 7.01/1.77 % AC symbols 0
% 7.01/1.77
% 7.01/1.77 % ------ Input Options Time Limit: Unbounded
% 7.01/1.77
% 7.01/1.77
% 7.01/1.77 % ------
% 7.01/1.77 % Current options:
% 7.01/1.77 % ------
% 7.01/1.77
% 7.01/1.77
% 7.01/1.77 %
% 7.01/1.77
% 7.01/1.77 % ------ Proving...
% 7.01/1.77 %
% 7.01/1.77
% 7.01/1.77 % SZS status Theorem for theBenchmark.p
% 7.01/1.77
% 7.01/1.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.01/1.77
% 7.01/1.77
%------------------------------------------------------------------------------