%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM423+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 : n018.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 02:24:12 PM UTC 2026
% Result : Theorem 1.00s 16.36s
% Output : CNFRefutation 1.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 21 unt; 2 def)
% Number of atoms : 214 ( 71 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 253 ( 105 ~; 105 |; 33 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 7 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 69 !; 5 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(f6,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> aInteger0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
fof(f10,axiom,
! [X0] :
( aInteger0(X0)
=> ( sz00 = sdtpldt0(smndt0(X0),X0)
& sdtpldt0(X0,smndt0(X0)) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
fof(f15,axiom,
! [X0] :
( aInteger0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(f18,axiom,
! [X0] :
( aInteger0(X0)
=> ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).
fof(f19,axiom,
! [X0,X1,X2] :
( ( X2 != sz00
& aInteger0(X2)
& aInteger0(X1)
& aInteger0(X0) )
=> ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquMod) ).
fof(f20,axiom,
( xq != sz00
& aInteger0(xq)
& aInteger0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__671) ).
fof(f21,conjecture,
sdteqdtlpzmzozddtrp0(xa,xa,xq),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f22,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f24,plain,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(flattening,[],[f22]) ).
fof(f28,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f29,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f28]) ).
fof(f35,plain,
! [X0] :
( ~ aInteger0(X0)
| ( sz00 = sdtpldt0(smndt0(X0),X0)
& sdtpldt0(X0,smndt0(X0)) = sz00 ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f43,plain,
! [X0] :
( ~ aInteger0(X0)
| ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f47,plain,
! [X0] :
( ~ aInteger0(X0)
| ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f48,plain,
! [X0,X1,X2] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f49,plain,
! [X0,X1,X2] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0] :
( ~ aInteger0(X0)
| ! [X1] :
( ( ~ aDivisorOf0(X1,X0)
| ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) ) )
& ( ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f51,plain,
! [X0] :
( ~ aInteger0(X0)
| ! [X1] :
( ( ~ aDivisorOf0(X1,X0)
| ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) ) )
& ( ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ) ) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ~ aInteger0(X0)
| ! [X1] :
( ( ~ aDivisorOf0(X1,X0)
| ( ? [X3] :
( sdtasdt0(X1,X3) = X0
& aInteger0(X3) )
& X1 != sz00
& aInteger0(X1) ) )
& ( ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ) ) ),
inference(rectify,[],[f51]) ).
fof(f53,plain,
! [X0] :
( ~ aInteger0(X0)
| ! [X1] :
( ( ~ aDivisorOf0(X1,X0)
| ( sdtasdt0(X1,sK0(X0,X1)) = X0
& aInteger0(sK0(X0,X1))
& X1 != sz00
& aInteger0(X1) ) )
& ( ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( ( ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
& ( ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f55,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f59,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f65,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = sdtpldt0(X0,smndt0(X0)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f73,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f43]) ).
fof(f81,plain,
! [X2,X0,X1] :
( ~ aInteger0(X0)
| sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2)
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f83,plain,
! [X2,X0,X1] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f84,plain,
sz00 != xq,
inference(cnf_transformation,[],[f20]) ).
fof(f85,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f20]) ).
fof(f86,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f20]) ).
fof(f87,plain,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(cnf_transformation,[],[f24]) ).
fof(f88,plain,
! [X2,X1] :
( ~ aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X2)
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,sdtasdt0(X1,X2)) ),
inference(equality_resolution,[],[f81]) ).
tcf(c_49,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f55]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_58,plain,
! [X0: $i] :
( ( sdtpldt0(X0,smndt0(X0)) = sz00 )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_66,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz00) = sz00 )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( aDivisorOf0(X0,sdtasdt0(X0,X1))
| ( X0 = sz00 )
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aInteger0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdteqdtlpzmzozddtrp0(X1,X2,X0)
| ( X0 = sz00 )
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(X2))) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_78,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f86]) ).
tcf(c_79,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f85]) ).
tcf(c_80,plain,
sz00 != xq,
inference(cnf_transformation,[],[f84]) ).
tcf(c_81,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(cnf_transformation,[],[f87]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( aDivisorOf0(X0,sdtasdt0(X0,X1))
| ( X0 = sz00 )
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_71,c_53,c_71]) ).
tcf(c_456,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sz00 )
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(X2)))
| ( X2 != xa )
| ( X1 != xa )
| ( X0 != xq ) ),
inference(resolution_lifted,[status(thm)],[c_76,c_81]) ).
tcf(c_457,plain,
( ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) ),
inference(unflattening,[status(thm)],[c_456]) ).
tcf(c_458,plain,
( ( xq = sz00 )
| ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) ),
inference(global_subsumption_just,[status(thm)],[c_457,c_79,c_78,c_457]) ).
tcf(c_508,plain,
! [X0: $i,X1: $i] :
( ( sz00 = xq )
| ( X0 = sz00 )
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( X0 != xq )
| ( sdtpldt0(xa,smndt0(xa)) != sdtasdt0(X0,X1) ) ),
inference(resolution_lifted,[status(thm)],[c_104,c_458]) ).
tcf(c_509,plain,
! [X0: $i] :
( ( xq = sz00 )
| ( sz00 = xq )
| ~ aInteger0(xq)
| ~ aInteger0(X0)
| ( sdtpldt0(xa,smndt0(xa)) != sdtasdt0(xq,X0) ) ),
inference(unflattening,[status(thm)],[c_508]) ).
tcf(c_511,plain,
! [X0: $i] :
( ( xq = sz00 )
| ~ aInteger0(X0)
| ( sdtpldt0(xa,smndt0(xa)) != sdtasdt0(xq,X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_509,c_79,c_80,c_509]) ).
tcf(c_814,definition,
iPr_def_10 = smndt0(xa),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_815,definition,
iPr_def_11 = sdtpldt0(xa,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_816,plain,
! [X0: $i] :
( ( xq = sz00 )
| ~ aInteger0(X0)
| ( iPr_def_11 != sdtasdt0(xq,X0) ) ),
inference(demodulation,[status(thm)],[c_511,c_814,c_815]) ).
tcf(c_1265,plain,
sdtasdt0(xq,sz00) = sz00,
inference(superposition,[status(thm)],[c_79,c_66]) ).
tcf(c_1408,plain,
( ( sz00 = xq )
| ~ aInteger0(sz00)
| ( sz00 != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_1265,c_816]) ).
tcf(c_1409,plain,
sz00 != iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_1408,c_80,c_49]) ).
tcf(c_1420,plain,
sdtpldt0(xa,smndt0(xa)) = sz00,
inference(superposition,[status(thm)],[c_78,c_58]) ).
tcf(c_1424,plain,
sz00 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_1420,c_814,c_815]) ).
tcf(c_1425,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1424,c_1409]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM423+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/15.41 % Computer : n018.cluster.edu
% 0.11/15.41 % Model : x86_64 x86_64
% 0.11/15.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.41 % Memory : 8046.5625MB
% 0.11/15.41 % OS : Linux 6.8.0-71-generic
% 0.11/15.41 % CPULimit : 300
% 0.11/15.41 % WCLimit : 300
% 0.11/15.41 % DateTime : Thu Sep 24 03:56:04 UTC 2026
% 0.11/15.41 % CPUTime :
% 0.11/15.41 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/15.47 Running first-order theorem proving
% 0.11/15.47 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
% 0.11/15.48
% 0.11/15.48 % ======== iProver multi-core TPTP/SMT =========
% 0.11/15.48
% 0.11/15.48 % Detected problem language: tptp
% 0.16/15.50 % Proving...
% 1.00/16.36 % SZS status Started for theBenchmark.p
% 1.00/16.36 % SZS status Theorem for theBenchmark.p
% 1.00/16.36
% 1.00/16.36 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.00/16.36
% 1.00/16.36 % ------ iProver source info
% 1.00/16.36
% 1.00/16.36 % git: date: 2026-07-19 20:42:38 +0200
% 1.00/16.36 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.00/16.36 % git: non_committed_changes: false
% 1.00/16.36
% 1.00/16.36 % ------ Parsing...
% 1.00/16.36 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.00/16.36
% 1.00/16.36 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 1.00/16.36
% 1.00/16.36 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.00/16.36
% 1.00/16.36 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.00/16.36 % ------ Proving...
% 1.00/16.36 % ------ Problem Properties
% 1.00/16.36
% 1.00/16.36 %
% 1.00/16.36 % clauses 30
% 1.00/16.36 % conjectures 0
% 1.00/16.36 % EPR 5
% 1.00/16.36 % Horn 27
% 1.00/16.36 % unary 7
% 1.00/16.36 % binary 11
% 1.00/16.36 % lits 73
% 1.00/16.36 % lits eq 27
% 1.00/16.36 % fd_pure 0
% 1.00/16.36 % fd_pseudo 0
% 1.00/16.36 % fd_cond 3
% 1.00/16.36 % fd_pseudo_cond 0
% 1.00/16.36 % AC symbols 0
% 1.00/16.36
% 1.00/16.36 % ------ Schedule dynamic 5 is on
% 1.00/16.36
% 1.00/16.36 % ------ no conjectures: strip conj schedule
% 1.00/16.36
% 1.00/16.36 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.00/16.36
% 1.00/16.36
% 1.00/16.36 % ------
% 1.00/16.36 % Current options:
% 1.00/16.36 % ------
% 1.00/16.36
% 1.00/16.36
% 1.00/16.36 %
% 1.00/16.36
% 1.00/16.36 % ------ Proving...
% 1.00/16.36 %
% 1.00/16.36
% 1.00/16.36 % SZS status Theorem for theBenchmark.p
% 1.00/16.36
% 1.00/16.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.00/16.36
% 1.00/16.36
%------------------------------------------------------------------------------