%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM482+3 : 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 : n020.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 02:25:11 PM UTC 2026
% Result : Theorem 3.35s 1.27s
% Output : CNFRefutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 11 unt; 1 def)
% Number of atoms : 206 ( 84 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 255 ( 82 ~; 75 |; 88 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 38 !; 22 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f38,axiom,
aNaturalNumber0(xk),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1716) ).
fof(f41,conjecture,
( ( isPrime0(xk)
& ! [X0] :
( ( ( doDivides0(X0,xk)
| ? [X1] :
( xk = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xk
| X0 = sz10 ) ) )
=> ? [X0] :
( ( isPrime0(X0)
| ( ! [X1] :
( ( doDivides0(X1,X0)
& ? [X2] :
( X0 = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
=> ( X1 = X0
| X1 = sz10 ) )
& X0 != sz10
& X0 != sz00 ) )
& ( doDivides0(X0,xk)
| ? [X1] :
( xk = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f42,negated_conjecture,
~ ( ( isPrime0(xk)
& ! [X0] :
( ( ( doDivides0(X0,xk)
| ? [X1] :
( xk = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xk
| X0 = sz10 ) ) )
=> ? [X0] :
( ( isPrime0(X0)
| ( ! [X1] :
( ( doDivides0(X1,X0)
& ? [X2] :
( X0 = sdtasdt0(X1,X2)
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1) )
=> ( X1 = X0
| X1 = sz10 ) )
& X0 != sz10
& X0 != sz00 ) )
& ( doDivides0(X0,xk)
| ? [X1] :
( xk = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f46,plain,
~ ( ( isPrime0(xk)
& ! [X0] :
( ( ( doDivides0(X0,xk)
| ? [X1] :
( xk = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xk
| X0 = sz10 ) ) )
=> ? [X2] :
( ( isPrime0(X2)
| ( ! [X4] :
( ( doDivides0(X4,X2)
& ? [X5] :
( sdtasdt0(X4,X5) = X2
& aNaturalNumber0(X5) )
& aNaturalNumber0(X4) )
=> ( X2 = X4
| sz10 = X4 ) )
& sz10 != X2
& sz00 != X2 ) )
& ( doDivides0(X2,xk)
| ? [X3] :
( xk = sdtasdt0(X2,X3)
& aNaturalNumber0(X3) ) )
& aNaturalNumber0(X2) ) ),
inference(rectify,[],[f42]) ).
fof(f60,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f111,plain,
( isPrime0(xk)
& ! [X0] :
( ( ~ doDivides0(X0,xk)
& ! [X1] :
( sdtasdt0(X0,X1) != xk
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0)
| X0 = xk
| X0 = sz10 )
& ! [X2] :
( ( ~ isPrime0(X2)
& ( ? [X4] :
( doDivides0(X4,X2)
& ? [X5] :
( sdtasdt0(X4,X5) = X2
& aNaturalNumber0(X5) )
& aNaturalNumber0(X4)
& X2 != X4
& sz10 != X4 )
| sz10 = X2
| sz00 = X2 ) )
| ( ~ doDivides0(X2,xk)
& ! [X3] :
( xk != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3) ) )
| ~ aNaturalNumber0(X2) ) ),
inference(ennf_transformation,[],[f46]) ).
fof(f112,plain,
( isPrime0(xk)
& ! [X0] :
( ( ~ doDivides0(X0,xk)
& ! [X1] :
( sdtasdt0(X0,X1) != xk
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0)
| X0 = xk
| X0 = sz10 )
& ! [X2] :
( ( ~ isPrime0(X2)
& ( ? [X4] :
( doDivides0(X4,X2)
& ? [X5] :
( sdtasdt0(X4,X5) = X2
& aNaturalNumber0(X5) )
& aNaturalNumber0(X4)
& X2 != X4
& sz10 != X4 )
| sz10 = X2
| sz00 = X2 ) )
| ( ~ doDivides0(X2,xk)
& ! [X3] :
( xk != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3) ) )
| ~ aNaturalNumber0(X2) ) ),
inference(flattening,[],[f111]) ).
fof(f137,plain,
( isPrime0(xk)
& ! [X2] :
( ( ~ doDivides0(X2,xk)
& ! [X3] :
( xk != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3) ) )
| ~ aNaturalNumber0(X2)
| xk = X2
| sz10 = X2 )
& ! [X0] :
( sP1(X0)
| ( ~ doDivides0(X0,xk)
& ! [X1] :
( sdtasdt0(X0,X1) != xk
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0) ) ),
inference(rectify,[],[f116]) ).
fof(f140,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f150,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f60]) ).
fof(f203,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f38]) ).
fof(f223,plain,
isPrime0(xk),
inference(cnf_transformation,[],[f137]) ).
fof(f227,plain,
! [X0,X1] :
( sP1(X0)
| sdtasdt0(X0,X1) != xk
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_50,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f140]) ).
tcf(c_60,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz10) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_113,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f203]) ).
tcf(c_133,negated_conjecture,
! [X0: $i,X1: $i] :
( sP1(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != xk ) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_137,negated_conjecture,
isPrime0(xk),
inference(cnf_transformation,[],[f223]) ).
tcf(c_4809,negated_conjecture,
isPrime0(xk),
inference(demodulation,[status(thm)],[c_137]) ).
tcf(c_4813,negated_conjecture,
! [X0: $i,X1: $i] :
( sP1(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != xk ) ),
inference(demodulation,[status(thm)],[c_133]) ).
tcf(c_6371,plain,
sdtasdt0(xk,sz10) = xk,
inference(superposition,[status(thm)],[c_113,c_60]) ).
tcf(c_6444,plain,
( sP1(xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sz10) ),
inference(superposition,[status(thm)],[c_6371,c_4813]) ).
fof(f115,definition,
! [X2] :
( ~ sP1(X2)
| ( ~ isPrime0(X2)
& ( ? [X4] :
( doDivides0(X4,X2)
& ? [X5] :
( sdtasdt0(X4,X5) = X2
& aNaturalNumber0(X5) )
& aNaturalNumber0(X4)
& X2 != X4
& sz10 != X4 )
| sz10 = X2
| sz00 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f116,plain,
( isPrime0(xk)
& ! [X0] :
( ( ~ doDivides0(X0,xk)
& ! [X1] :
( sdtasdt0(X0,X1) != xk
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0)
| X0 = xk
| X0 = sz10 )
& ! [X2] :
( sP1(X2)
| ( ~ doDivides0(X2,xk)
& ! [X3] :
( xk != sdtasdt0(X2,X3)
| ~ aNaturalNumber0(X3) ) )
| ~ aNaturalNumber0(X2) ) ),
inference(definition_folding,[],[f112,f115]) ).
fof(f134,plain,
! [X2] :
( ~ sP1(X2)
| ( ~ isPrime0(X2)
& ( ? [X4] :
( doDivides0(X4,X2)
& ? [X5] :
( sdtasdt0(X4,X5) = X2
& aNaturalNumber0(X5) )
& aNaturalNumber0(X4)
& X2 != X4
& sz10 != X4 )
| sz10 = X2
| sz00 = X2 ) ) ),
inference(nnf_transformation,[],[f115]) ).
fof(f135,plain,
! [X0] :
( ~ sP1(X0)
| ( ~ isPrime0(X0)
& ( ? [X1] :
( doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1)
& X0 != X1
& sz10 != X1 )
| sz10 = X0
| sz00 = X0 ) ) ),
inference(rectify,[],[f134]) ).
fof(f136,plain,
! [X0] :
( ~ sP1(X0)
| ( ~ isPrime0(X0)
& ( ( doDivides0(sK7(X0),X0)
& sdtasdt0(sK7(X0),sK8(X0)) = X0
& aNaturalNumber0(sK8(X0))
& aNaturalNumber0(sK7(X0))
& sK7(X0) != X0
& sz10 != sK7(X0) )
| sz10 = X0
| sz00 = X0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X1,sK7(X0)),skolemize(X2,sK8(X0))],[f135]) ).
fof(f216,plain,
! [X0] :
( ~ sP1(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_132,plain,
! [X0: $i] :
( ~ sP1(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f216]) ).
tcf(c_6350,plain,
~ sP1(xk),
inference(superposition,[status(thm)],[c_4809,c_132]) ).
tcf(c_6445,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6444,c_6350,c_113,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM482+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 04:13:33 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 3.35/1.27 % SZS status Started for theBenchmark.p
% 3.35/1.27 % SZS status Theorem for theBenchmark.p
% 3.35/1.27
% 3.35/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.35/1.27
% 3.35/1.27 % ------ iProver source info
% 3.35/1.27
% 3.35/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.35/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.35/1.27 % git: non_committed_changes: false
% 3.35/1.27
% 3.35/1.27 % ------ Parsing...
% 3.35/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.35/1.27
% 3.35/1.27 % ------ 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 %
% 3.35/1.27
% 3.35/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.35/1.27
% 3.35/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.35/1.27 % ------ Proving...
% 3.35/1.27 % ------ Problem Properties
% 3.35/1.27
% 3.35/1.27 %
% 3.35/1.27 % clauses 84
% 3.35/1.27 % conjectures 5
% 3.35/1.27 % EPR 22
% 3.35/1.27 % Horn 45
% 3.35/1.27 % unary 9
% 3.35/1.27 % binary 8
% 3.35/1.27 % lits 334
% 3.35/1.27 % lits eq 111
% 3.35/1.27 % fd_pure 0
% 3.35/1.27 % fd_pseudo 0
% 3.35/1.27 % fd_cond 26
% 3.35/1.27 % fd_pseudo_cond 12
% 3.35/1.27 % AC symbols 0
% 3.35/1.27
% 3.35/1.27 % ------ Schedule dynamic 5 is on
% 3.35/1.27
% 3.35/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.35/1.27
% 3.35/1.27
% 3.35/1.27 % ------
% 3.35/1.27 % Current options:
% 3.35/1.27 % ------
% 3.35/1.27
% 3.35/1.27
% 3.35/1.27 %
% 3.35/1.27
% 3.35/1.27 % ------ Proving...
% 3.35/1.27 %
% 3.35/1.27
% 3.35/1.27 % SZS status Theorem for theBenchmark.p
% 3.35/1.27
% 3.35/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.35/1.28
% 3.35/1.28
%------------------------------------------------------------------------------