%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM490+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 : 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 02:25:16 PM UTC 2026
% Result : Theorem 34.02s 6.35s
% Output : CNFRefutation 34.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 70 ( 32 unt; 4 def)
% Number of atoms : 226 ( 50 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 236 ( 104 ~; 99 |; 22 &)
% ( 6 <=>; 5 =>; 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 : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 76 !; 5 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
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/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f42,axiom,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
fof(f43,axiom,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
fof(f46,axiom,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1951) ).
fof(f47,conjecture,
sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f48,negated_conjecture,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f51,plain,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(flattening,[],[f48]) ).
fof(f52,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f53,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f55,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f54]) ).
fof(f77,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f78,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f77]) ).
fof(f79,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(f80,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f79]) ).
fof(f118,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f78]) ).
fof(f119,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(rectify,[],[f118]) ).
fof(f120,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ( sdtpldt0(X0,sK0(X0,X1)) = X1
& aNaturalNumber0(sK0(X0,X1)) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f119]) ).
fof(f121,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,[],[f80]) ).
fof(f122,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,[],[f121]) ).
fof(f136,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f137,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f159,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
fof(f161,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtmndt0(X1,X0) != X2
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f122]) ).
fof(f162,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtmndt0(X1,X0) = X2 ),
inference(cnf_transformation,[],[f122]) ).
fof(f201,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f202,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f203,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f207,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f208,plain,
xr = sdtmndt0(xn,xp),
inference(cnf_transformation,[],[f43]) ).
fof(f212,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(cnf_transformation,[],[f46]) ).
fof(f213,plain,
sdtasdt0(xr,xm) != sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(cnf_transformation,[],[f51]) ).
fof(f214,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f159]) ).
fof(f215,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| sdtmndt0(sdtpldt0(X0,X2),X0) = X2 ),
inference(equality_resolution,[],[f162]) ).
fof(f216,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| aNaturalNumber0(sdtmndt0(X1,X0)) ),
inference(equality_resolution,[],[f161]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( ( sdtmndt0(sdtpldt0(X0,X1),X0) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f216]) ).
tcf(c_116,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f203]) ).
tcf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f202]) ).
tcf(c_118,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f201]) ).
tcf(c_122,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f207]) ).
tcf(c_123,plain,
sdtmndt0(xn,xp) = xr,
inference(cnf_transformation,[],[f208]) ).
tcf(c_127,plain,
sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) = sdtasdt0(xn,xm),
inference(cnf_transformation,[],[f212]) ).
tcf(c_128,negated_conjecture,
sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) != sdtasdt0(xr,xm),
inference(cnf_transformation,[],[f213]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i] :
( ( sdtmndt0(sdtpldt0(X0,X1),X0) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_76,c_52,c_76,c_179]) ).
tcf(c_3365,definition,
iPr_def_10 = sdtasdt0(xn,xm),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3366,definition,
iPr_def_11 = sdtasdt0(xp,xm),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_3367,definition,
iPr_def_12 = sdtmndt0(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_3368,definition,
iPr_def_13 = sdtasdt0(xr,xm),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_3369,negated_conjecture,
iPr_def_12 != iPr_def_13,
inference(demodulation,[status(thm)],[c_128,c_3368,c_3366,c_3365,c_3367]) ).
tcf(c_4728,plain,
( aNaturalNumber0(iPr_def_11)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_3366,c_53]) ).
tcf(c_4729,plain,
( aNaturalNumber0(iPr_def_13)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_3368,c_53]) ).
tcf(c_4744,plain,
( aNaturalNumber0(iPr_def_13)
| ~ aNaturalNumber0(xr) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4729,c_117]) ).
tcf(c_4747,plain,
aNaturalNumber0(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_4728,c_118,c_117]) ).
tcf(c_4853,plain,
sdtpldt0(iPr_def_11,iPr_def_13) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_127,c_3365,c_3366,c_3368]) ).
tcf(c_5050,plain,
( aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,xn) ),
inference(superposition,[status(thm)],[c_123,c_77]) ).
tcf(c_5063,plain,
aNaturalNumber0(xr),
inference(forward_subsumption_resolution,[status(thm)],[c_5050,c_118,c_116,c_122]) ).
tcf(c_5098,plain,
aNaturalNumber0(iPr_def_13),
inference(backward_subsumption_resolution,[status(thm)],[c_4744,c_5063]) ).
tcf(c_5353,plain,
! [X0: $i] :
( ( sdtmndt0(sdtpldt0(iPr_def_11,X0),iPr_def_11) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_4747,c_182]) ).
tcf(c_95467,plain,
sdtmndt0(sdtpldt0(iPr_def_11,iPr_def_13),iPr_def_11) = iPr_def_13,
inference(superposition,[status(thm)],[c_5098,c_5353]) ).
tcf(c_95532,plain,
iPr_def_12 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_95467,c_3367,c_4853]) ).
tcf(c_95533,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_95532,c_3369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM490+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n015.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 04:18:11 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 0.13/0.42
% 0.13/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.42
% 0.13/0.42 % Detected problem language: tptp
% 0.13/0.43 % Proving...
% 34.02/6.35 % SZS status Started for theBenchmark.p
% 34.02/6.35 % SZS status Theorem for theBenchmark.p
% 34.02/6.35
% 34.02/6.35 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 34.02/6.35
% 34.02/6.35 % ------ iProver source info
% 34.02/6.35
% 34.02/6.35 % git: date: 2026-07-19 20:42:38 +0200
% 34.02/6.35 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 34.02/6.35 % git: non_committed_changes: false
% 34.02/6.35
% 34.02/6.35 % ------ Parsing...
% 34.02/6.35 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 34.02/6.35
% 34.02/6.35 % ------ 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 %
% 34.02/6.35
% 34.02/6.35 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 34.02/6.35
% 34.02/6.35 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 34.02/6.35 % ------ Proving...
% 34.02/6.35 % ------ Problem Properties
% 34.02/6.35
% 34.02/6.35 %
% 34.02/6.35 % clauses 79
% 34.02/6.35 % conjectures 1
% 34.02/6.35 % EPR 22
% 34.02/6.35 % Horn 54
% 34.02/6.35 % unary 21
% 34.02/6.35 % binary 7
% 34.02/6.35 % lits 274
% 34.02/6.35 % lits eq 80
% 34.02/6.35 % fd_pure 0
% 34.02/6.35 % fd_pseudo 0
% 34.02/6.35 % fd_cond 15
% 34.02/6.35 % fd_pseudo_cond 11
% 34.02/6.35 % AC symbols 0
% 34.02/6.35
% 34.02/6.35 % ------ Schedule dynamic 5 is on
% 34.02/6.35
% 34.02/6.35 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 34.02/6.35
% 34.02/6.35
% 34.02/6.35 % ------
% 34.02/6.35 % Current options:
% 34.02/6.35 % ------
% 34.02/6.35
% 34.02/6.35
% 34.02/6.35 %
% 34.02/6.35
% 34.02/6.35 % ------ Proving...
% 34.02/6.35 %
% 34.02/6.35
% 34.02/6.35 % SZS status Theorem for theBenchmark.p
% 34.02/6.35
% 34.02/6.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 34.02/6.36
% 34.02/6.36
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