%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM489+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 : n009.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 1.24s 1.29s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 20 unt; 1 def)
% Number of atoms : 84 ( 32 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 85 ( 38 ~; 32 |; 10 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 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 : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 22 !; 0 ?; 2 :)
% Comments :
%------------------------------------------------------------------------------
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(f45,conjecture,
xn = sdtpldt0(xp,xr),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f46,negated_conjecture,
xn != sdtpldt0(xp,xr),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f49,plain,
xn != sdtpldt0(xp,xr),
inference(flattening,[],[f46]) ).
fof(f77,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(f78,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f77]) ).
fof(f119,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,[],[f78]) ).
fof(f120,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,[],[f119]) ).
fof(f158,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtmndt0(X1,X0) != X2
| sdtpldt0(X0,X2) = X1 ),
inference(cnf_transformation,[],[f120]) ).
fof(f199,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f201,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f205,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f206,plain,
xr = sdtmndt0(xn,xp),
inference(cnf_transformation,[],[f43]) ).
fof(f209,plain,
xn != sdtpldt0(xp,xr),
inference(cnf_transformation,[],[f49]) ).
fof(f213,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 ),
inference(equality_resolution,[],[f158]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_116,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f201]) ).
tcf(c_118,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f199]) ).
tcf(c_122,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f205]) ).
tcf(c_123,plain,
sdtmndt0(xn,xp) = xr,
inference(cnf_transformation,[],[f206]) ).
tcf(c_126,negated_conjecture,
sdtpldt0(xp,xr) != xn,
inference(cnf_transformation,[],[f209]) ).
tcf(c_3355,definition,
iPr_def_10 = sdtpldt0(xp,xr),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3356,negated_conjecture,
iPr_def_10 != xn,
inference(demodulation,[status(thm)],[c_126,c_3355]) ).
tcf(c_5919,plain,
( ( sdtpldt0(xp,sdtmndt0(xn,xp)) = xn )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_122,c_78]) ).
tcf(c_5959,plain,
( ( xn = iPr_def_10 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(light_normalisation,[status(thm)],[c_5919,c_123,c_3355]) ).
tcf(c_5960,plain,
xn = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_5959,c_118,c_116]) ).
tcf(c_6012,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_3356,c_5960]) ).
tcf(c_6013,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_6012]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM489+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 : n009.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 04:14:58 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 1.24/1.29 % SZS status Started for theBenchmark.p
% 1.24/1.29 % SZS status Theorem for theBenchmark.p
% 1.24/1.29
% 1.24/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.24/1.29
% 1.24/1.29 % ------ iProver source info
% 1.24/1.29
% 1.24/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.24/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.24/1.29 % git: non_committed_changes: false
% 1.24/1.29
% 1.24/1.29 % ------ Parsing...
% 1.24/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.24/1.29
% 1.24/1.29 % ------ 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 %
% 1.24/1.29
% 1.24/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.24/1.29
% 1.24/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.24/1.29 % ------ Proving...
% 1.24/1.29 % ------ Problem Properties
% 1.24/1.29
% 1.24/1.29 %
% 1.24/1.29 % clauses 74
% 1.24/1.29 % conjectures 1
% 1.24/1.29 % EPR 22
% 1.24/1.29 % Horn 49
% 1.24/1.29 % unary 16
% 1.24/1.29 % binary 7
% 1.24/1.29 % lits 269
% 1.24/1.29 % lits eq 75
% 1.24/1.29 % fd_pure 0
% 1.24/1.29 % fd_pseudo 0
% 1.24/1.29 % fd_cond 15
% 1.24/1.29 % fd_pseudo_cond 11
% 1.24/1.29 % AC symbols 0
% 1.24/1.29
% 1.24/1.29 % ------ Schedule dynamic 5 is on
% 1.24/1.29
% 1.24/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.24/1.29
% 1.24/1.29
% 1.24/1.29 % ------
% 1.24/1.29 % Current options:
% 1.24/1.29 % ------
% 1.24/1.29
% 1.24/1.29
% 1.24/1.29 %
% 1.24/1.29
% 1.24/1.29 % ------ Proving...
% 1.24/1.29 %
% 1.24/1.29
% 1.24/1.29 % SZS status Theorem for theBenchmark.p
% 1.24/1.29
% 1.24/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.24/1.29
% 1.24/1.29
%------------------------------------------------------------------------------