%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG047+2 : 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 : n005.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 02:38:18 PM UTC 2026
% Result : Theorem 1.89s 6.38s
% Output : CNFRefutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 50 ( 29 unt; 6 def)
% Number of atoms : 162 ( 67 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 114 ( 38 ~; 29 |; 32 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 28 !; 0 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( szszuzczcdt0(X0) = szszuzczcdt0(X1)
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccEqu) ).
fof(f30,axiom,
! [X0] :
( aVector0(X0)
=> aNaturalNumber0(aDimensionOf0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
fof(f34,axiom,
( aDimensionOf0(xt) != sz00
& aDimensionOf0(xs) = aDimensionOf0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1329_01) ).
fof(f35,conjecture,
( ( ! [X0] :
( aNaturalNumber0(X0)
=> sdtlbdtrb0(sziznziztdt0(xs),X0) = sdtlbdtrb0(xs,X0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs)) )
=> ( ( ! [X0] :
( aNaturalNumber0(X0)
=> sdtlbdtrb0(sziznziztdt0(xt),X0) = sdtlbdtrb0(xt,X0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& aVector0(sziznziztdt0(xt)) )
=> aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f36,negated_conjecture,
~ ( ( ! [X0] :
( aNaturalNumber0(X0)
=> sdtlbdtrb0(sziznziztdt0(xs),X0) = sdtlbdtrb0(xs,X0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs)) )
=> ( ( ! [X0] :
( aNaturalNumber0(X0)
=> sdtlbdtrb0(sziznziztdt0(xt),X0) = sdtlbdtrb0(xt,X0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& aVector0(sziznziztdt0(xt)) )
=> aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f42,plain,
~ ( ( ! [X0] :
( aNaturalNumber0(X0)
=> sdtlbdtrb0(sziznziztdt0(xs),X0) = sdtlbdtrb0(xs,X0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs)) )
=> ( ( ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(sziznziztdt0(xt),X1) = sdtlbdtrb0(xt,X1) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& aVector0(sziznziztdt0(xt)) )
=> aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) ) ),
inference(rectify,[],[f36]) ).
fof(f47,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f5]) ).
fof(f48,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| X0 = X1 ),
inference(flattening,[],[f47]) ).
fof(f81,plain,
! [X0] :
( ~ aVector0(X0)
| aNaturalNumber0(aDimensionOf0(X0)) ),
inference(ennf_transformation,[],[f30]) ).
fof(f86,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtlbdtrb0(sziznziztdt0(xs),X0) = sdtlbdtrb0(xs,X0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs))
& ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtlbdtrb0(sziznziztdt0(xt),X1) = sdtlbdtrb0(xt,X1) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& aVector0(sziznziztdt0(xt))
& aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)) ),
inference(ennf_transformation,[],[f42]) ).
fof(f87,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtlbdtrb0(sziznziztdt0(xs),X0) = sdtlbdtrb0(xs,X0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs))
& ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtlbdtrb0(sziznziztdt0(xt),X1) = sdtlbdtrb0(xt,X1) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& aVector0(sziznziztdt0(xt))
& aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)) ),
inference(flattening,[],[f86]) ).
fof(f93,plain,
( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtlbdtrb0(sziznziztdt0(xs),X1) = sdtlbdtrb0(xs,X1) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& aVector0(sziznziztdt0(xs))
& ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtlbdtrb0(sziznziztdt0(xt),X0) = sdtlbdtrb0(xt,X0) )
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& aVector0(sziznziztdt0(xt))
& aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)) ),
inference(rectify,[],[f87]) ).
fof(f99,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f48]) ).
fof(f132,plain,
! [X0] :
( ~ aVector0(X0)
| aNaturalNumber0(aDimensionOf0(X0)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f142,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(cnf_transformation,[],[f34]) ).
fof(f144,plain,
aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))),
inference(cnf_transformation,[],[f93]) ).
fof(f145,plain,
aVector0(sziznziztdt0(xs)),
inference(cnf_transformation,[],[f93]) ).
fof(f147,plain,
aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))),
inference(cnf_transformation,[],[f93]) ).
fof(f148,plain,
aVector0(sziznziztdt0(xt)),
inference(cnf_transformation,[],[f93]) ).
fof(f149,plain,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(cnf_transformation,[],[f93]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( szszuzczcdt0(X0) != szszuzczcdt0(X1) ) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_87,plain,
! [X0: $i] :
( aNaturalNumber0(aDimensionOf0(X0))
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_96,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(cnf_transformation,[],[f142]) ).
tcf(c_98,negated_conjecture,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(cnf_transformation,[],[f149]) ).
tcf(c_99,negated_conjecture,
aVector0(sziznziztdt0(xt)),
inference(cnf_transformation,[],[f148]) ).
tcf(c_100,negated_conjecture,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt),
inference(cnf_transformation,[],[f147]) ).
tcf(c_102,negated_conjecture,
aVector0(sziznziztdt0(xs)),
inference(cnf_transformation,[],[f145]) ).
tcf(c_103,negated_conjecture,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs),
inference(cnf_transformation,[],[f144]) ).
tcf(c_496,plain,
szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xt),
inference(light_normalisation,[status(thm)],[c_103,c_96]) ).
tcf(c_810,definition,
iPr_def_13 = sziznziztdt0(xs),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_811,definition,
iPr_def_14 = aDimensionOf0(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_812,definition,
iPr_def_15 = szszuzczcdt0(iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_813,definition,
iPr_def_16 = aDimensionOf0(xt),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_815,definition,
iPr_def_18 = aDimensionOf0(iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_816,definition,
iPr_def_19 = szszuzczcdt0(iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_817,plain,
iPr_def_15 = iPr_def_16,
inference(demodulation,[status(thm)],[c_496,c_813,c_810,c_811,c_812]) ).
tcf(c_819,negated_conjecture,
aVector0(iPr_def_13),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_821,negated_conjecture,
iPr_def_19 = iPr_def_16,
inference(demodulation,[status(thm)],[c_100,c_815,c_816]) ).
tcf(c_822,negated_conjecture,
aVector0(iPr_def_17),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_823,negated_conjecture,
iPr_def_14 != iPr_def_18,
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_1692,plain,
iPr_def_15 = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_821,c_817]) ).
tcf(c_1708,plain,
szszuzczcdt0(iPr_def_18) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_816,c_1692]) ).
tcf(c_1745,plain,
( aNaturalNumber0(iPr_def_14)
| ~ aVector0(iPr_def_13) ),
inference(superposition,[status(thm)],[c_811,c_87]) ).
tcf(c_1746,plain,
( aNaturalNumber0(iPr_def_18)
| ~ aVector0(iPr_def_17) ),
inference(superposition,[status(thm)],[c_815,c_87]) ).
tcf(c_1749,plain,
aNaturalNumber0(iPr_def_18),
inference(forward_subsumption_resolution,[status(thm)],[c_1746,c_822]) ).
tcf(c_1750,plain,
aNaturalNumber0(iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_1745,c_819]) ).
tcf(c_3086,plain,
! [X0: $i] :
( ( X0 = iPr_def_18 )
| ~ aNaturalNumber0(iPr_def_18)
| ~ aNaturalNumber0(X0)
| ( szszuzczcdt0(X0) != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1708,c_54]) ).
tcf(c_3093,plain,
! [X0: $i] :
( ( X0 = iPr_def_18 )
| ~ aNaturalNumber0(X0)
| ( szszuzczcdt0(X0) != iPr_def_15 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3086,c_1749]) ).
tcf(c_3235,plain,
( ( iPr_def_14 = iPr_def_18 )
| ~ aNaturalNumber0(iPr_def_14) ),
inference(superposition,[status(thm)],[c_812,c_3093]) ).
tcf(c_3242,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3235,c_823,c_1750]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG047+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.43 % Computer : n005.cluster.edu
% 0.16/5.43 % Model : x86_64 x86_64
% 0.16/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.43 % Memory : 8046.5625MB
% 0.16/5.43 % OS : Linux 6.8.0-71-generic
% 0.16/5.43 % CPULimit : 300
% 0.16/5.43 % WCLimit : 300
% 0.16/5.43 % DateTime : Thu Sep 24 07:57:23 UTC 2026
% 0.16/5.43 % CPUTime :
% 0.16/5.43 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.49 Running first-order theorem proving
% 0.16/5.49 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
% 0.19/5.50
% 0.19/5.50 % ======== iProver multi-core TPTP/SMT =========
% 0.19/5.50
% 0.19/5.50 % Detected problem language: tptp
% 0.19/5.52 % Proving...
% 1.89/6.38 % SZS status Started for theBenchmark.p
% 1.89/6.38 % SZS status Theorem for theBenchmark.p
% 1.89/6.38
% 1.89/6.38 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.89/6.38
% 1.89/6.38 % ------ iProver source info
% 1.89/6.38
% 1.89/6.38 % git: date: 2026-07-19 20:42:38 +0200
% 1.89/6.38 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.89/6.38 % git: non_committed_changes: false
% 1.89/6.38
% 1.89/6.38 % ------ Parsing...
% 1.89/6.38 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.89/6.38
% 1.89/6.38 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.89/6.38
% 1.89/6.38 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.89/6.38
% 1.89/6.38 % ------ Preprocessing... sf_s rm: 4 0s sf_e sf_s rm: 0 0s sf_e
% 1.89/6.38 % ------ Proving...
% 1.89/6.38 % ------ Problem Properties
% 1.89/6.38
% 1.89/6.38 %
% 1.89/6.38 % clauses 66
% 1.89/6.38 % conjectures 6
% 1.89/6.38 % EPR 16
% 1.89/6.38 % Horn 56
% 1.89/6.38 % unary 19
% 1.89/6.38 % binary 18
% 1.89/6.38 % lits 180
% 1.89/6.38 % lits eq 53
% 1.89/6.38 % fd_pure 0
% 1.89/6.38 % fd_pseudo 0
% 1.89/6.38 % fd_cond 1
% 1.89/6.38 % fd_pseudo_cond 5
% 1.89/6.38 % AC symbols 0
% 1.89/6.38
% 1.89/6.38 % ------ Schedule dynamic 5 is on
% 1.89/6.38
% 1.89/6.38 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.89/6.38
% 1.89/6.38
% 1.89/6.38 % ------
% 1.89/6.38 % Current options:
% 1.89/6.38 % ------
% 1.89/6.38
% 1.89/6.38
% 1.89/6.38 %
% 1.89/6.38
% 1.89/6.38 % ------ Proving...
% 1.89/6.38 %
% 1.89/6.38
% 1.89/6.38 % SZS status Theorem for theBenchmark.p
% 1.89/6.38
% 1.89/6.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.89/6.38
% 1.89/6.38
%------------------------------------------------------------------------------