%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM427+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 : 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 02:24:13 PM UTC 2026
% Result : Theorem 3.42s 1.26s
% Output : CNFRefutation 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 74 ( 27 unt; 2 def)
% Number of atoms : 249 ( 82 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 287 ( 119 ~; 122 |; 34 &)
% ( 5 <=>; 7 =>; 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 78 !; 5 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(f4,axiom,
! [X0] :
( aInteger0(X0)
=> aInteger0(smndt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
fof(f6,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> aInteger0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
fof(f15,axiom,
! [X0] :
( aInteger0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(f17,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> ( sdtasdt0(X0,X1) = sz00
=> ( X1 = sz00
| X0 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroDiv) ).
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(f21,axiom,
( xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__704) ).
fof(f23,axiom,
( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__747) ).
fof(f24,axiom,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__767) ).
fof(f25,conjecture,
sdteqdtlpzmzozddtrp0(xb,xa,xq),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f26,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f28,plain,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(flattening,[],[f26]) ).
fof(f29,plain,
! [X0] :
( ~ aInteger0(X0)
| aInteger0(smndt0(X0)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f32,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f33,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f32]) ).
fof(f47,plain,
! [X0] :
( ~ aInteger0(X0)
| ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f49,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(ennf_transformation,[],[f17]) ).
fof(f50,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0] :
( ~ aInteger0(X0)
| ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f52,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(f53,plain,
! [X0,X1,X2] :
( sz00 = X2
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
inference(flattening,[],[f52]) ).
fof(f56,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,[],[f51]) ).
fof(f57,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,[],[f56]) ).
fof(f58,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,[],[f57]) ).
fof(f59,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))],[f58]) ).
fof(f60,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,[],[f53]) ).
fof(f61,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f63,plain,
! [X0] :
( ~ aInteger0(X0)
| aInteger0(smndt0(X0)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f65,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f78,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f82,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| sz00 != sdtasdt0(X0,X1)
| sz00 = X1
| sz00 = X0 ),
inference(cnf_transformation,[],[f50]) ).
fof(f87,plain,
! [X2,X0,X1] :
( ~ aInteger0(X0)
| sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2)
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f89,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,[],[f60]) ).
fof(f91,plain,
sz00 != xq,
inference(cnf_transformation,[],[f21]) ).
fof(f92,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f21]) ).
fof(f93,plain,
aInteger0(xb),
inference(cnf_transformation,[],[f21]) ).
fof(f94,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f21]) ).
fof(f97,plain,
aInteger0(xn),
inference(cnf_transformation,[],[f23]) ).
fof(f98,plain,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(cnf_transformation,[],[f24]) ).
fof(f99,plain,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(cnf_transformation,[],[f28]) ).
fof(f100,plain,
! [X2,X1] :
( ~ aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X2)
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,sdtasdt0(X1,X2)) ),
inference(equality_resolution,[],[f87]) ).
tcf(c_49,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f61]) ).
tcf(c_51,plain,
! [X0: $i] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_67,plain,
! [X0: $i] :
( ( sdtasdt0(sz00,X0) = sz00 )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ( X0 = sz00 )
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( sdtasdt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f82]) ).
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,[],[f100]) ).
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,[],[f89]) ).
tcf(c_79,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f94]) ).
tcf(c_80,plain,
aInteger0(xb),
inference(cnf_transformation,[],[f93]) ).
tcf(c_81,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f92]) ).
tcf(c_82,plain,
sz00 != xq,
inference(cnf_transformation,[],[f91]) ).
tcf(c_84,plain,
aInteger0(xn),
inference(cnf_transformation,[],[f97]) ).
tcf(c_86,plain,
sdtpldt0(xb,smndt0(xa)) = sdtasdt0(xq,smndt0(xn)),
inference(cnf_transformation,[],[f98]) ).
tcf(c_87,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(cnf_transformation,[],[f99]) ).
tcf(c_90,plain,
( ( sdtasdt0(sz00,sz00) = sz00 )
| ~ aInteger0(sz00) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_104,plain,
( ( sz00 = sz00 )
| ~ aInteger0(sz00)
| ( sdtasdt0(sz00,sz00) != sz00 ) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_110,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_513,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sz00 )
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(X2)))
| ( X2 != xa )
| ( X1 != xb )
| ( X0 != xq ) ),
inference(resolution_lifted,[status(thm)],[c_76,c_87]) ).
tcf(c_514,plain,
( ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(xb)
| ~ aInteger0(xa)
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) ),
inference(unflattening,[status(thm)],[c_513]) ).
tcf(c_515,plain,
( ( xq = sz00 )
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) ),
inference(global_subsumption_just,[status(thm)],[c_514,c_81,c_80,c_79,c_514]) ).
tcf(c_725,definition,
iPr_def_10 = smndt0(xa),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_726,definition,
iPr_def_11 = sdtpldt0(xb,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_729,plain,
( ( xq = sz00 )
| ~ aDivisorOf0(xq,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_515,c_725,c_726]) ).
tcf(c_732,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1286,plain,
! [X0: $i] :
( ( sz00 = xq )
| ( xq != X0 )
| ( sz00 != X0 ) ),
inference(instantiation,[status(thm)],[c_732]) ).
tcf(c_1287,plain,
( ( sz00 = xq )
| ( xq != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_1286]) ).
tcf(c_1297,plain,
sdtasdt0(xq,smndt0(xn)) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_86,c_725,c_726]) ).
tcf(c_1902,plain,
( aDivisorOf0(xq,iPr_def_11)
| ( sz00 = xq )
| ~ aInteger0(xq)
| ~ aInteger0(smndt0(xn)) ),
inference(superposition,[status(thm)],[c_1297,c_110]) ).
tcf(c_1990,plain,
( aDivisorOf0(xq,iPr_def_11)
| ~ aInteger0(smndt0(xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1902,c_82,c_81]) ).
tcf(c_2789,plain,
~ aInteger0(smndt0(xn)),
inference(global_subsumption_just,[status(thm)],[c_1990,c_49,c_82,c_90,c_104,c_729,c_1287,c_1990]) ).
tcf(c_2791,plain,
~ aInteger0(xn),
inference(superposition,[status(thm)],[c_51,c_2789]) ).
tcf(c_2792,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2791,c_84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM427+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 % Computer : n020.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Thu Sep 24 03:56:35 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.45 Running first-order theorem proving
% 0.13/0.45 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
% 0.13/0.46
% 0.13/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.46
% 0.13/0.46 % Detected problem language: tptp
% 0.13/0.47 % Proving...
% 3.42/1.26 % SZS status Started for theBenchmark.p
% 3.42/1.26 % SZS status Theorem for theBenchmark.p
% 3.42/1.26
% 3.42/1.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.42/1.26
% 3.42/1.26 % ------ iProver source info
% 3.42/1.26
% 3.42/1.26 % git: date: 2026-07-19 20:42:38 +0200
% 3.42/1.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.42/1.26 % git: non_committed_changes: false
% 3.42/1.26
% 3.42/1.26 % ------ Parsing...
% 3.42/1.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.42/1.26
% 3.42/1.26 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e %
% 3.42/1.26
% 3.42/1.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.42/1.26
% 3.42/1.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.42/1.26 % ------ Proving...
% 3.42/1.26 % ------ Problem Properties
% 3.42/1.26
% 3.42/1.26 %
% 3.42/1.26 % clauses 41
% 3.42/1.26 % conjectures 0
% 3.42/1.26 % EPR 12
% 3.42/1.26 % Horn 37
% 3.42/1.26 % unary 11
% 3.42/1.26 % binary 16
% 3.42/1.26 % lits 93
% 3.42/1.26 % lits eq 33
% 3.42/1.26 % fd_pure 0
% 3.42/1.26 % fd_pseudo 0
% 3.42/1.26 % fd_cond 3
% 3.42/1.26 % fd_pseudo_cond 0
% 3.42/1.26 % AC symbols 0
% 3.42/1.26
% 3.42/1.26 % ------ Schedule dynamic 5 is on
% 3.42/1.26
% 3.42/1.26 % ------ no conjectures: strip conj schedule
% 3.42/1.26
% 3.42/1.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.42/1.26
% 3.42/1.26
% 3.42/1.26 % ------
% 3.42/1.26 % Current options:
% 3.42/1.26 % ------
% 3.42/1.26
% 3.42/1.26
% 3.42/1.26 %
% 3.42/1.26
% 3.42/1.26 % ------ Proving...
% 3.42/1.26 %
% 3.42/1.26
% 3.42/1.26 % SZS status Theorem for theBenchmark.p
% 3.42/1.26
% 3.42/1.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.42/1.26
% 3.42/1.26
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